Z = X/Y is normally distributed because the ratio of two independent normal variables is itself normally distributed and the same has been proved below:
To prove this, we can use the Central Limit Theorem. This theorem states that if X and Y are independently and identically distributed random variables, then the ratio of the two, Z = X/Y, will be normally distributed regardless of the distribution of X and Y. This is due to the fact that the ratio of two independent normal variables is itself normally distributed.
For example, let X and Y be two independent normal variables. Then their ratio Z = X/Y will follow a normal distribution. This means that the probability density function (pdf) of Z is given by:
f_Z(z) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{z^2}{2\sigma^2}}
where \sigma^2 = \frac{\sigma_x^2}{\sigma_y^2} is the variance of Z.
Therefore, we can conclude that Z = X/Y is normally distributed when X and Y are independent normal distributions.
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18. John's car was purchased for $32,451. He put a down payment of $3,500 and financed the rest with a 5.5% annual interest rate compounded monthly.
a.) How much with his payments be if he takes the loan out for 6 years?
b.) The dealership has a special of a 4.75% rate for 4 years. How much more will John have to pay each month?
c) How much will John end up saving by going with the special?
d.) John decides to go with the special financing John's car depreciates at a continuous rate of 6% annually. How much will his car be worth when he finishes paying off his loan?
e.) At the end of the 4-year loan, how much did John actually lose?
a) Monthly payment = $489.77
b) John will paying $163.69 less per month
c) John will end up saving $3,943.28
d) John's car will be worth approximately $23,142.58
e) John actually lost $8,182.86 at the end of the 4-year loan.
What is the interest rate?The interest rate is the percentage of the amount of money borrowed, lent or invested that is charged or earned as a fee or return over a certain period of time. It is usually expressed as an annual percentage rate (APR) and can be fixed or variable depending on the type of loan or investment.
a) To calculate John's monthly payments, we need to use the formula for the present value of an annuity, which is:
PMT = P*(r/12)/(1-(1+r/12)^(-n*12))
Where PMT is the monthly payment, P is the principal amount (the amount financed after the down payment), r is the monthly interest rate, and n is the number of years.
So, we have:
P = 32,451 - 3,500 = 28,951
r = 0.055/12
n = 6
PMT = 28,951*(0.055/12)/(1-(1+0.055/12)^(-6*12)) = $489.77
Therefore, John's monthly payments would be $489.77.
b) Using the same formula, we can calculate John's monthly payments with the special financing:
P = 28,951
r = 0.0475/12
n = 4
PMT = 28,951*(0.0475/12)/(1-(1+0.0475/12)^(-4*12)) = $653.46
So, John's monthly payments with the special financing would be $653.46.
Difference in monthly payments between the above options is:
$653.46 - $489.77 = $163.69
Therefore, John would have to pay $163.69 more per month with the special financing.
c) To calculate how much John will save by going with the special financing, we need to calculate the total cost of each option.
For the original financing, the total cost can be found by multiplying the monthly payment by the number of payments:
Total cost = $489.77 * (6 * 12) = $35,268.72
For the special financing, the total cost is:
Total cost = $653.46 * (4 * 12) = $31,325.44
Therefore, John will save:
$35,268.72 - $31,325.44 = $3,943.28
So, John will end up saving $3,943.28 by going with the special financing.
d) To calculate the value of John's car when he finishes paying off his loan, we need to use the formula for continuous compounding:
A = P*e^(rt)
Where A is the final amount, P is the initial amount (the purchase price of the car), e is the mathematical constant e (approximately 2.71828), r is the annual interest rate, and t is the time in years.
The car depreciates at a continuous rate of 6%, which means that the value of the car decreases by 6% every year. So, the effective annual rate of depreciation is:
r = e^(-0.06) - 1 = -0.0589
Note that we use a negative value for r, since the value of the car is decreasing.
John will finish paying off his loan in 4 years. So, the time t is 4 years.
Therefore, the value of John's car when he finishes paying off his loan is:
A = 32,451e^(-0.05894) = $23,142.58
So, John's car will be worth $23,142.58 when he finishes paying off his loan.
e) To calculate how much John actually lost at the end of the 4-year loan, we need to subtract the value of his car at the end of the loan from the total amount he paid:
Total amount paid = $653.46 * (4 * 12) = $31,325.44
Value of car at end of loan = $23,142.58
Amount lost = Total amount paid - Value of car at end of loan
= $31,325.44 - $23,142.58 = $8,182.86
Therefore, John actually lost $8,182.86 at the end of the 4-year loan.
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if they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are linearly independent, find the only scalars that will make the equation below true.Are the vectors 4 1 and 16 nearly independent? 45 Choose If they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are linearly independent, find the only scalars that will make the equation below true 171 01 45
The vectors 4 1 and 16 are linearly dependent because they can be expressed as multiples of each other. This means that there are scalars that are not all zero that will make the equation below true:
4a + 16b = 0
To find the scalars, we can set one of them to any non-zero value and solve for the other. For example, if we set a = 1, then we can solve for b:
4(1) + 16b = 0
16b = -4
b = -4/16
b = -1/4
So the scalars that will make the equation true are a = 1 and b = -1/4. These are not all zero, which confirms that the vectors are linearly dependent.
If the vectors were linearly independent, then the only scalars that would make the equation true would be all zero. In other words, a = 0 and b = 0 would be the only solution. However, since we found scalars that are not all zero that make the equation true, we know that the vectors are not linearly independent.
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Bobo and the Bouncing Ball Bobo was walking down the street one day, minding his own business, when a ball feil right in front of him and bounced straight up. It soared to tremendous height and came down again. Bobo caught the ball and climbed to the top of the 64 foot tall building to investigate _ On the roof, he saw a little girl peering over the edge. "What's wrong, little girl?" he asked, The girl answered without turning around, "I dropped my special magic ball; It always bounces exactly half its previous height and it'Il bounce forever if nobody catches it:" "Wowl" exclaimed Bobo. "Id give anything for a ball like thatl" "Il make a deal with you, sald the little girl, "If you answer two questions for me, I'Il give you the ball.Please help Bobo find the answers to these questions: (1) How high did the ball bounce on its 10t bounce? (2) How far had the ball traveled altogether by the time it reached its peak after its 10th bounce. 5 EINSTEIN POINT EXTENSION: If Bobo drops his magic ball from the top of the Empire State Building, how far will it have traveled when it hits the pavement for the 7h time? Explain your solution in detail.
1) The ball bounced 0.125 feet high on its 10th bounce.
2) The total distance traveled by the ball by the time it reached its peak after its 10th bounce is 255.75 feet.
3) If Bobo drops his magic ball from the top of the Empire State Building, the ball will have traveled 382 feet by the time it hits the pavement for the 7th time.
1) To find out how high the ball bounced on its 10th bounce, we can use the fact that the ball always bounces to half its previous height. We can start by finding the height of the first bounce, which we know is 64 feet since that's the height of the building. Then, we can keep dividing by 2 to find the height of each subsequent bounce. So, the height of the 2nd bounce is 32 feet, the height of the 3rd bounce is 16 feet, and so on. Continuing this pattern, we can find that the height of the 10th bounce is:
64 feet / 2^(10-1) = 64 feet / 512 = 0.125 feet
2) To find out how far the ball had traveled altogether by the time it reached its peak after its 10th bounce, we can use the fact that the distance traveled is equal to the sum of the distances of each bounce. The distance of each bounce is equal to twice the height of the bounce (since the ball travels up and then back down). So, the distance of the first bounce is 264 = 128 feet. The distance of the second bounce is 232 = 64 feet, and so on. Continuing this pattern, we can find that the distance of the 10th bounce is:
2×0.125 = 0.25 feet
So the total distance traveled by the ball by the time it reached its peak after its 10th bounce is:
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 + 0.5 + 0.25 = 255.75 feet
3) We know that the height of each bounce is half the height of the previous bounce, so we can use this to find the height of the 7th bounce. Starting with the height of the first bounce (which is the height of the Empire State Building), we can keep dividing by 2 to find the height of each subsequent bounce. So, the height of the 2nd bounce is 64/2 = 32 feet, the height of the 3rd bounce is 32/2 = 16 feet, and so on. Continuing this pattern, we can find that the height of the 7th bounce is:
64/2^(7-1) = 1 foot
Since the ball bounces up and down, it travels twice the height of each bounce. So, the distance traveled by the ball on each bounce is 2 feet. To find out how far the ball will have traveled by the time it hits the pavement for the 7th time, we can add up the distances traveled on the first 7 bounces:
2×(64 + 32 + 16 + 8 + 4 + 2 + 1) = 382 feet
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What is the arc measure of AE ⌢ A, E, start superscript, \frown, end superscript in degrees?
The arc measure of AE A, E, start superscript, frown, finish superscript in degrees cannot be determined without more information. To make this conclusion, additional information .
Such as the locations of points A and E and/or the degree measures of other angles in the same circle would be required. An arc is a piece of a circle's circumference, and its degree measure is equal to the degree measure of the central angle that subtends the arc. To compute the arc measure of AE A, E, start superscript, frown, end superscript in degrees, we would need to know the degree measure of the central angle that subtends this arc or the degree measure of the central angle that subtends this arc.
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Question at position 5 The sum of two numbers is 15. If the second number is twice the other, what is the working equation for this problem as well as the values of the two numbers?
The two numbers are 5 and 10 and the working equation for this problem is:x + 2x = 15
The sum of the two numbers is 15. If the second number is twice the other, then the working equation for this problem as well as the values of the two numbers according to the given question is the second number y is twice the first number x.
Therefore,y = 2x
Also, the sum of these two numbers is given as 15.
Therefore,x + y = 15
Substituting the value of y in terms of x, we get x + 2x = 15
Simplifying the above equation, we get:3x = 15x = 5
Substituting this value of x in the equation y = 2x, we get:y = 2(5)y = 10
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When Aaron runs the 400 m dash is finishing times are normally distributed with a mean of 80 seconds and a standard deviation of 2. 5 seconds using the elliptical rule determine the interval of times that represent the middle 99. 7% of his finishing times in the 400 m race
The interval of times that represent the middle 99.7% of Aaron's finishing times in the 400 m race is [72.5, 87.5].
Using the empirical rule or the elliptical rule, we know that in a normal distribution:
approximately 68% of data falls within one standard deviation of the meanapproximately 95% of data falls within two standard deviations of the meanapproximately 99.7% of data fall within three standard deviations of the meanIn this case, we want to find the interval of times that represents the middle 99.7% of Aaron's finishing times, which means we need to find the range of values that fall within three standard deviations of the mean.
So, using the formula for finding the interval of values within k standard deviations of the mean:
lower bound = mean - k * standard deviation
upper bound = mean + k * standard deviation
where k = 3 for this problem, we get:
lower bound = 80 - 3 * 2.5 = 72.5
upper bound = 80 + 3 * 2.5 = 87.5
Therefore, the interval of times that represents the middle 99.7% of Aaron's finishing times in the 400 m race is [72.5, 87.5].
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
Answer:
b d
Step-by-step explanation:
What is the greatest common factor of 53 and 11?
Answer:
1
Step-by-step explanation:
Both of those numbers are prime, so their GCF's are 1
log4 n=1/4 log4 81 + 1/2 log4 25
Solve and show work
(I cannot for the life of me figure this one out, so please help me !!)
Answer:
Step-by-step explanation:
We can start by using the logarithmic rule that states:
log a (mn) = log a (m) + log a (n)
And also the property:
log a (b^c) = c*log a (b)
With these rules, we can simplify the given expression as follows:
log4 n = 1/4 log4 81 + 1/2 log4 25
log4 n = log4 81^(1/4) + log4 25^(1/2) (using the above properties)
log4 n = log4 (3^4)^(1/4) + log4 (5^2)^(1/2) (81 = 3^4 and 25 = 5^2)
log4 n = log4 3 + log4 5 (using the rule log a (b^c) = c*log a (b))
log4 n = log4 (3*5) (using the rule log a (mn) = log a (m) + log a (n))
log4 n = log4 15
Therefore, the solution to the equation log4 n=1/4 log4 81 + 1/2 log4 25 is:
n = 15
The cost of cleaning up pollution in a stream is given by C=42000/(100-p), where C is the cost in dollars to clean p percent of the stream. (For instance, when p is 20, then the formula will calculate the cost to clean up 20 percent of the stream. )
a. Find the cost of cleaning up 40% of the stream.
b. What percent can be cleaned up for $1100
c. P must be greater than or equal to zero and p must be less than what number? Why?
The cost of cleaning up 40% of the stream is amount $7000, and 97.45% of the stream can be cleaned up for $1100. P must be greater than or equal to zero and p must be less than 100.
a. C = 42000/(100-p) => C = 42000/(100-40) = $7000
b. 1100 = 42000/(100-p) => p = (42000-1100)/42000 = 97.45%
c. P must be greater than or equal to zero and p must be less than 100. This is because the cost of cleaning up a stream cannot be negative and the stream cannot be cleaned up more than 100%.
The cost of cleaning up 40% of the stream is amount $7000, and 97.45% of the stream can be cleaned up for $1100. P must be greater than or equal to zero and p must be less than 100.
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The straightaway on each side measures 1,000 meters. The curves are semicircles with diameter 74 meters. What is the distance, in meters, around the entire track? Use the π button on your calculator and express your answer to the nearest hundredth
If the straightaway on each side measures 1,000 meters, the distance around the entire track is approximately 2,465.09 meters.
To find the distance around the entire track, we need to add the distance of the straightaways on both sides and the distance around the curves. The straightaways measure 1,000 meters on each side, so the total distance covered in straightaways is 2,000 meters.
The curves are semicircles with diameter 74 meters. The circumference of a circle is given by the formula 2πr, where r is the radius. Since the diameter of the semicircle is given as 74 meters, the radius will be half of it, i.e., 37 meters. Hence, the distance around each semicircle will be:
Circumference = 2πr = 2π(37) = 74π
Since there are two semicircles in the track, the total distance around the curves is 2(74π) = 148π meters.
Therefore, the total distance around the entire track is:
Total distance = Straightaways + Curves
= 2,000 + 148π
= 2,000 + 465.09 (approximating π as 3.14)
= 2,465.09 meters (rounded to the nearest hundredth)
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3. If 55% of a number is 11, find the number?
Answer:
20
Step-by-step explanation:
[tex]55% of a number = 11[/tex]% of a number = 11
[tex]\frac{55}{100} * x = 11[/tex]
solve for x
[tex]55x = 1100[/tex]
[tex]x = 20[/tex]
Hope this helps!
Answer:20
Step-by-step explanation:
55%---------11
100%------x
x=100*11/55=20
Which number makes the statement true?
0.42 < ?
A 0.4
B 0.45
C 0.415
D 0.4008
Answer:
b.0.45
Step-by-step explanation:
Answer: B 0.45
0.42 < 0.45
Step-by-step explanation:
Akio has succeeded as a public communications specialist. He likes to think
cooperative behavior. Akio likes to achieve objectives with coworkers using
of himself as a friendly person who places a high priority on friendships and
understanding and mutual respect. This reflects that Akio fits the
social style.
Akio is a public communication specialist with skill sets to influence and raise awareness for public.
What do you mean by public communication specialist?
Specialists in public-relations develop and uphold a positive public image for the people, groups, or organisations they represent. To influence how the public perceives their clients and to raise awareness of each client's efforts and objectives, they prepare press releases and create social media strategies.
Public relations, information output, and media requests are handled by communications specialists. They can also plan an organization's social media or advertising campaigns.
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please help me. I need help
Answer:5 3/8
Step-by-step explanation:
[tex]3\frac{1}{8} =\frac{25}{8}\\4\frac{7}{28} =4\frac{1}{4}=\frac{17}{4}\\1\frac{5}{6} =\frac{11}{6}=\frac{33}{18}\\\frac{\frac{25}{8}}{x-\frac{17}{4}}=\frac{17}{18}+\frac{33}{18}=\frac{50}{18}=\frac{25}{9}\\\frac{\frac{25}{8}}{x-\frac{17}{4}}=\frac{\frac{25}{9}}{1}\\\frac{25}{8}=\frac{25}{9}*(x-\frac{17}{4})\\(x-\frac{17}{4})=\frac{25}{8}:\frac{25}{9}=\frac{25}{8}*\frac{9}{25}=\frac{9}{8}\\x=\frac{9}{8}+\frac{17}{4}=\frac{9}{8}+\frac{34}{8}=\frac{43}{8}=5\frac{3}{8}[/tex]
Chocolate Co. mixes two kinds of chocolate bars in a gift bag that weighs 3 pounds and has a total cost of $15. The expensive candy bars are $6 a pound and the other cost $4.50. How many pounds of each are used to make the gift bag? x=expensive y=Other
Answer:
1 lb expensive chocolate
2 lbs other chocolate
Step-by-step explanation:
let x = number of pounds of the expensive candy bars
let y = number of pounds of the other candy bars
here is the first equation:
(the expensive lbs + other lbs comes to a total of 3 lbs altogether)
x + y = 3
here is the second equation:
($6 per pound + $4.5 per pound = $15)
6x + 4.5y = 15
we can do substitution, elimination, or graph.
let's do elimination with these two equations:
x + y = 3 AND 6x + 4.5y = 15
Let's eliminate the variable x to find variable y, and then use what we found for variable y to find variable x.
Multiply (x + y = 3) with 6
Which looks like this: 6(x+y = 3)
And the above becomes 6x + 6y = 18
the equation x + y = 3 becomes 6x + 6y = 18
the equation 6x + 4.5y = 15 stays the same
Subtract to eliminate x.
6x + 6y = 18
- 6x +4.5y = 15
-------------------------
0 + 1.5y = 3
1.5y = 3, divide both sides by 1.5 to get y
1.5y 3
----- = -----
1.5 1.5
y = 2
Therefore, there are 2 pounds of "other" chocolate in the gift bag. Let's use that to find the pounds of the "expensive" chocolate.
Take one of the original equations and plug in "2" for the variable y.
x + y = 3 OR 6x + 4.5y = 15
Lets use x + y = 3, which becomes x + 2 = 3. Solve that, and you will get:
x = 1
Therefore, there is 1 pound of "expensive" chocolate in the gift bag.
(after you are done solving, plug in the numbers you found to one of the equations...ps i checked already so those are correct.
e.g 1 + 2 = 3 )
:))
Mathew, your classmate, who is also an SK Chairman in your Barangay Matayog,
organized a KITE FLYING FESTIVAL. He informed your school principal to motivate
students to join the said KITE FLYING FESTIVAL.
1. Suppose you are one of the students in your barangay, how will you prepare the design of
the kite?
2 Make a design of the kite assigned to you.
3. Illustrate every part or portion of the kite including their measures.
4. Using the design of the kite made, determine all the mathematics concepts or principles
involved.
patulong poh.
By following the steps mentioned we can create unique kite design and enjoy flying it with your friends and family using mathematics concepts.
Steps:
Designing the kite:
Designing a kite can be a fun and creative process. First, you need to determine the shape and size of your kite. You can choose from different shapes such as diamond, triangle, hexagon, or even a custom design. Once you have determined the shape, you can start working on the materials. For instance, you may choose to use plastic, paper, or cloth. After that, you need to consider the frame of the kite. You may use bamboo sticks or other lightweight materials. Lastly, you can decorate your kite with colors, patterns, and designs.
Sample kite design:
For this sample design, we will use a diamond shape kite, measuring 50cm by 50cm. The materials used are plastic for the kite body and bamboo sticks for the frame. Here's how you can make the kite:Cut the plastic into a diamond shape, measuring 50cm by 50cm.Attach the bamboo sticks on the edges of the kite, using adhesive tape or glue.Add a tail to the kite, measuring 100cm long.Cut a small hole in the center of the kite, where you will attach the string.Parts of the kite:
Here are the different parts of the kite and their measures:Kite body: Diamond shape, measuring 50cm by 50cm.Frame: Bamboo sticks, measuring 55cm for the vertical sticks, and 60cm for the horizontal sticks.Tail: Made of lightweight materials, measuring 100cm long.String: Attached to the center of the kite, measuring 50 meters long.Mathematics concepts involved:
Designing a kite involves several mathematical concepts, such as:
Geometry: Determining the shape, size, and measurements of the kite requires an understanding of geometry concepts such as angles, triangles, and polygons.Measurement: Measuring the different parts of the kite, including the body, frame, tail, and string, requires an understanding of measurement units such as centimeters, meters, and feet.Proportions: Ensuring that the frame and tail are proportionate to the kite body requires an understanding of ratios and proportions.Physics: Flying a kite involves concepts such as lift, drag, and gravity, which are all related to the principles of physics.Learn more about mathematics here:
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Ruth is making Lemonade. For 1 cup of water she uses 3 lemins, for 2 cups 6 lemons, ect. If this pattern continues, how many lemons will she need for 10 cups of water?
Ruth will need 30 lemons to make lemonade with 10 cups of water.
Ruth is making Lemonade. For 1 cup of water she uses 3 lemins, for 2 cups 6 lemons, ect. The formula to calculate the number of lemons needed for a given cups of water is:
Lemons = 3 × Cups of Water
Therefore, the number of lemons needed for 10 cups of water is:
Lemons = 3 × 10
Lemons = 30
Hence, Ruth will need 30 lemons to make lemonade with 10 cups of water.
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A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special. Restaurant Number of Side Dishes Total Cost 2 $10.25 4 $13.25 5 $14.75 8 $19.25 Which of the following graphs shows the relationship given in the table? graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 25 hundredths through the point 3 comma 11 and 75 hundredths graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 75 hundredths through the point 3 comma 12 and 25 hundredths graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 3 comma 9 and 75 hundredths graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 5 tenths through the point 5 comma 13
A graph with the x-axis labelled number of side dishes and the y-axis equation labelled cost in dollars, as well as a line connecting the points 0, 7.25 and 3, 11.75.
What is equation?An equation is a mathematical statement that validates the equivalent of two expressions joined by the equal symbol '='. For instance, 2x - 5 = 13. 2x-5 and 13 are two examples of expressions. The character '=' connects the two expressions. An equation is a mathematical formula that has two algebras on each side of an assignment operator (=). It demonstrates the equivalency link between the left and middle formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
The table depicts the link between the quantity of side dishes and the overall cost of a restaurant's lunch special. We need to plot the data points on the graph and see which graph matches the pattern to identify which graph exhibits the relationship given in the table.
Number of Side Dishes Total Cost
2 $10.25
4 $13.25
5 $14.75
8 $19.25
The first choice has a shorter slope than the second, and the data points are perfectly aligned with the line. As a result, the first graph depicts the link described in the table. The solution is:
A graph with the x-axis labelled number of side dishes and the y-axis labelled cost in dollars, as well as a line connecting the points 0, 7.25 and 3, 11.75.
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5. Solve for x.
16
IE
25
20
X =
Answer:
The value of x in the given figure is 36
What is a line?
A line is a straight arrangement of points that extends in opposite directions. It has no beginning and no end in any way (infinite). It has only one dimension.
What are Parallel lines?
Parallel lines are two lines in the same plane that are equal distances apart and never intersect. They can be both horizontal and vertical in orientation.
According to the given information:
By the Triangle proportionality theorem, If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally separates these two sides.
Then we have
[tex]\frac{x-16}{16} =\frac{25}{20}[/tex]
On simplifying,
[tex]x-16=\frac{25}{20}*16[/tex]
x-16 = 20
x = 36
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Evaluate the expression below at x = 5.
Answer:
A
Step-by-step explanation:
[tex](2x-5)^{(x-1)}[/tex] ← substitute x = 5
[tex](2(5)-5)^{(5-1)}[/tex]
= [tex](10-5)^{4}[/tex]
= [tex]5^{4}[/tex]
= 625
A turtle and a snail are 300 feet apart when they start moving towards each other. The turtle is moving at a speed of 5 feet per minute, and the snail is moving at a speed of 1 foot per minute. How fast are the turtle and snail approaching each other
The turtle and snail are apprοaching each οther at a rate οf 6 feet per minute.
Let's use the cοncept οf relative speed tο sοlve this prοblem. The relative speed οf twο οbjects mοving tοwards each οther is the sum οf their individual speeds.
What is relative speed?Relative speed is the speed οf an οbject οr persοn in relatiοn tο anοther οbject οr persοn. It is the difference between the velοcities οf twο οbjects mοving relative tο each οther. The relative speed can be calculated by subtracting the velοcity οf οne οbject frοm the velοcity οf the οther οbject.
Let's call the rate at which the turtle and snail are apprοaching each οther "r".
Relative speed = turtle's speed + snail's speed
r = 5 + 1
r = 6 feet per minute
Sο the turtle and snail are apprοaching each οther at a rate οf 6 feet per minute.
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Answer:
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Step-by-step explanation:
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Eleven percent of students at a large high school are left- handed: A statistics teacher selects a random sample of 100 students and records X = the number of left-handed students in the sample. Calculate the mean and standard deviation of the sampling distribution of X. Interpret the standard deviation
The mean of the sampling distribution of X turns out as 11 and the standard deviation is identified as 3.13. By using concepts of standard deviation, the sample deviation can be calculated.
The mean and standard deviation of the sampling distribution of X can be calculated using the formulas for the mean and standard deviation of a binomial distribution. The mean is given by: [tex]μ = np[/tex]
Where n is the sample size and p is the proportion of left-handed students in the population. In this case, n = 100 and p = 0.11, so:
[tex]μ = (100)(0.11) = 11[/tex]
The standard deviation is given by:
[tex]σ = √(np(1-p))σ = √((100)(0.11)(1-0.11)) = √(9.79) = 3.13[/tex]
So the mean of the sampling distribution of X is 11 and the standard deviation is 3.13.
The standard deviation of the sampling distribution of X tells us how much variability we can expect in the number of left-handed students in a random sample of 100 students from the population.
In this case, the standard deviation of 3.13 tells us that there is a moderate amount of variability in the number of left-handed students in different samples of 100 students from the population.
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Using the graph as your guide, complete the following statement.
The discriminant of the function is
• A. positive
B. zero
C. negative
PLEASE HELP ASAP
Answer:
THE ANSWER IS B
Step-by-step explanation:
Answer:
B : Zero
Step-by-step explanation:
Beth bought 15 tickets to a movie, where adult tickets cost $6.00 and senior citizen tickets cost $4.00. She spent a total of $76. Which system of equations will determine the number of adult tickets, a, and the number of senior citizen tickets, s, Beth purchased?
Answer: a + s = 15
6.00a + 4.00s = 76
Oliver makes two mosaics using coloured tiles.
For the first mosaic he uses red, blue and
purple tiles in the ratio 12 : 3:2.
For the second mosaic he uses red and blue
tiles in the ratio 8 : 5.
Oliver uses the same number of blue tiles for
each mosaic.
What is the ratio of red tiles in the first mosaic
to red tiles in the second mosaic?
Give your answer in its simplest form.
Therefore, the ratio of red tiles in the first mosaic to red tiles in the second mosaic is 33:34 in its simplest form.
What is ratio?A ratio is a way of comparing two or more quantities that are of the same type. It is a mathematical expression that compares the size or amount of one quantity relative to another. Ratios are expressed as a pair of numbers separated by a colon (:) or as a fraction. For example, the ratio of apples to oranges in a basket might be 3:2 or 3/2, which means there are three apples for every two oranges in the basket. Ratios are used in many different areas of mathematics and in real-world applications such as cooking, finance, and engineering.
Here,
17x tiles used in the first mosaic, and 13x tiles used in the second mosaic.
If we want to use the same number of blue tiles in each mosaic, we need to make sure that the total number of tiles used in each mosaic is the same. This means we need to find a common multiple of 17 and 13 that we can use as the total number of tiles in each mosaic. The smallest such multiple is:
17 * 13 = 221
So, we'll assume that Oliver used 221 tiles in each mosaic (even though we don't know the actual number of tiles he used).
For the first mosaic, the ratio of red to blue to purple tiles is 12:3:2. This means that for every 17 tiles used, we have:
12/17 (red tiles), 3/17 (blue tiles), and 2/17 (purple tiles)
Multiplying each of these fractions by 221 (the total number of tiles), we get:
132 (red tiles), 33 (blue tiles), and 44 (purple tiles)
For the second mosaic, the ratio of red to blue tiles is 8:5. This means that for every 13 tiles used, we have:
8/13 (red tiles) and 5/13 (blue tiles)
Multiplying each of these fractions by 221 (the total number of tiles), we get:
136 (red tiles) and 85 (blue tiles)
So, the ratio of red tiles in the first mosaic to red tiles in the second mosaic is:
132/136 = 33/34
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Calculate the value o x if:
72:64=x:16
7 The time in minutes (7) taken to cook a joint of beef is given by T-35w +25,
where w is the weight of the joint in kg.
a) How long would it take to cook a 1.5 kg joint?
b) Make w the subject of the formula.
c) What weight of beef needs to be cooked for 207 minutes?
d) What weight of beef needs to be cooked for 3 hours and 48 minutes?
1:11
In conclusion for part A it would take T - 32.5 minutes to cook a 1.5 kg joint. For part B w is given by the formula w = (T - 25) / (-35). For part C 6.6 kg of beef needs to be cooked for 207 minutes. For part D 5.91 kg of beef needs to be cooked for 3 hours and 48 minutes.
How to solve?
a) To find how long it would take to cook a 1.5 kg joint, we can substitute w = 1.5 into the formula:
T - 35w + 25 = T - 35(1.5) + 25 = T - 32.5
So, it would take T - 32.5 minutes to cook a 1.5 kg joint.
b) To make w the subject of the formula, we need to isolate w on one side of the equation. We can start by subtracting 25 from both sides:
T - 35w = T - 25
Next, we can divide both sides by -35:
w = (T - 25) / (-35)
Therefore, w is given by the formula w = (T - 25) / (-35).
c) To find the weight of beef that needs to be cooked for 207 minutes, we can substitute T = 207 into the original formula:
T - 35w + 25 = 207
Simplifying this equation, we get:
-35w = -232
Dividing both sides by -35, we get:
w = 6.6 kg
Therefore, 6.6 kg of beef needs to be cooked for 207 minutes.
d) To find the weight of beef that needs to be cooked for 3 hours and 48 minutes (which is equivalent to 3 × 60 + 48 = 228 minutes), we can substitute T = 228 into the original formula:
T - 35w + 25 = 228
Simplifying this equation, we get:
-35w = -207
Dividing both sides by -35, we get:
w = 5.91 kg
Therefore, 5.91 kg of beef needs to be cooked for 3 hours and 48 minutes.
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Mila has a DRF of 1. 15 and a 6-month basic rate of $650. What is her annual premium?
Mila has a DRF of 1. 15 and a 6-month basic rate of $650. Her annual premium is $1,495.
Mila has a 6-month basic cost of $650 and a DRF of 1.15.
We have to determine her annual premium.
As we know that in a year have 12 months and 6 months basic cost is $650. So the time period is 2.
Annual premium is the total amount of money paid in one year for an insurance policy. It is usually paid in one lump sum or in installments throughout the year.
Since we know the cost of premium of 6 months. So
Mila annual premium = 650 x 2 x 1.15
Mila annual premium = $1,495
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At the start of an experiment, some chemicals had a mass of 73 g, rounded to 2 significant figures.
During the experiment, the mass of the chemicals decreased by 8. 2 g, rounded to 2 significant figures.
Calculate the lower and upper bounds of the mass of the chemicals at the end of the experiment
The lower bound of the mass at the end of the experiment is 65.25 g and the upper bound is 64.25 g.
To calculate the lower and upper bounds of the mass of the chemicals at the end of the experiment, we need to take into account the uncertainty in the initial mass and the change in mass.
The initial mass of the chemicals is given as 73 g, rounded to 2 significant figures. This means that the actual value of the initial mass could lie anywhere between 72.5 g and 73.4 g, since the last significant digit (the 3) is uncertain.
Similarly, the change in mass during the experiment is given as 8.2 g, rounded to 2 significant figures. This means that the actual value of the change in mass could lie anywhere between 8.15 g and 8.25 g.
To find the lower bound of the mass at the end of the experiment, we assume that the initial mass was at its upper bound (73.4 g) and the change in mass was at its lower bound (8.15 g):
Lower bound = 73.4 g - 8.15 g = 65.25 g
To find the upper bound of the mass at the end of the experiment, we assume that the initial mass was at its lower bound (72.5 g) and the change in mass was at its upper bound (8.25 g):
Upper bound = 72.5 g - 8.25 g = 64.25 g
Therefore, the lower bound of the mass at the end of the experiment is 65.25 g and the upper bound is 64.25 g.
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