The rectangular solid with the maximum volume would be a cube.
The surface area of a cube = 6A,
where A = the area of any one side
hence, the area of one side = 150/6 = 25 sq in.
The length of one face,
L = 25^0.5 = 5 in.
The volume, V of a cube = L^3.
Surface area
Surface area is the amount of space covering the outside of a three-dimensional shape.
volume
Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. It means the amount of three-dimensional space a closed figure can occupy is measured by its volume.
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Talia travelled part of the journey by train and the rest by bus. The total fare was sh 4000.On return,the fare of the bus was hiked by a half of what he paid and the total fare of the return journey hiked to sh 4800.Find the train fare.
Answer: Let "t" be the fare of the train.
The fare of the bus is "b".
We know that t + b = 4000 (the total fare of the journey)
On the return trip, the fare of the bus was hiked by half of what was paid, so b*1.5 = b + (b/2) = new fare of the bus.
The total fare of the return journey is 4800, so t + (b + (b/2)) = 4800
Now we have two equations:
t + b = 4000
t + b + (b/2) = 4800
We can substitute the first equation into the second equation:
t + b + (b/2) = 4800
t + (4000 - t) + (b/2) = 4800
t + (b/2) = 800
t = 800 - (b/2)
Now we have an equation that only involves one variable "t" (the fare of the train)
We can substitute the first equation back in:
t + b = 4000
800 - (b/2) + b = 4000
800 = (3/2)b
b = 1200
So the fare of the bus is 1200 and the fare of the train is 800
Step-by-step explanation:
What is the quotient of 154,504 divided by 28 with long division?
The value of the equation A = 154,504 / 28 = 5518
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Let the dividend be p = 154,504
Let the divisor be q = 28
Substituting the values in the equation , we get
A = p / q
A = 5,518
5518
28 | 154504
1 4 0
1 4 5
1 4 0
5 0
2 8
2 2 4
2 2 4
0
So , the remainder of the equation is 0 and the quotient is 5518
Hence , the equation is A = 5518
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The function y = - x7 + 24x models the profit y in dollars earned by a tour guide when x people sign up for a tour.
a. How many people need to sign up for a tour in order for the profit to be at least $108?
b. How many people need to sign up for a tour in order for the profit to be more than $144?
c. Is it possible for the tour guide to lose money (make a negative profit) on a tour? Explain
Given the above function:
a) Note that the number of people that need to sign up for a tour in order for the profit to be at least $108 is:
b) The number of people that need to sign up for a tour in order for the profit to be more than $144 is:
c) Yes, it is possible to make a negative profit on the tour in which case they would have made a loss.
What is the calculation justifying the above?a) To find out the number of people that need to sign up for the profit to be at least $108 where the function y = - x7 + 24x, models profit in y,
we must equate the function to $108 and solve for x.
Thus:
- x7 + 24x = 108
resolve like terms
17x = 108
x = 108/17
x = 6.35294117647
x [tex]\approx[/tex] 6. 4
Plug x back into the formula, and we have:
-(6.4) * 7 + 24 (6.4) = 108.8 this shows that our calculation is correct. Since you can have 6.4 persons, the best number to aim for is 7.
b) The number of people that need to sign up for the project to turn a profit of $144 is:
- x7 + 24x = 144
resolve like terms
17x = 144
x = 144/17
x = 8.4705882353
Let's impute back 8.5 into the equation:
-(8.5)7 + 24(8.5)
= 144.5.
This shows that our calculation is correct. However since you cannot have 8.5 persons, the number to budget for would be 9 persons.
c) for the tour guide to lose money, the amount made, that is revenue, would have to be less than the amount invested.
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Which equation accurately represents this statement? Select three options. Negative 3 less than 4.9 times a number, x, is the same as 12.8. Negative 3 minus 4.9 x = 12.8 4.9 x minus (negative 3) = 12.8 3 + 4.9 x = 12.8 (4.9 minus 3) x = 12.8 12.8 = 4.9 x + 3
The equation that accurately represents the statement "negative 3 less than 4.9 times a number, x, is the same as 12.8" is:
4.9 x - 3 = 12.8
How to interpret Algebraic Equations?This equation can be gotten by replacing "negative 3 less than 4.9 times a number, x" with "4.9 x - 3" and "is the same as" with "=". The correct form of the equation is gotten by using the correct order of operations:
negative 3 less than 4.9 x
= 4.9 x - 3
= 12.8
The other equations listed do not accurately represent the statement. For example, the equation "Negative 3 minus 4.9 x = 12.8" would be incorrect because it does not use the correct order of operations. The correct order of operations would be to subtract 4.9 x from negative 3, which would give us 4.9 x - 3 = 12.8.
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WILL GIVE BRAINLIEST IF ANSWERED IN TIME MUST GIVE EXPLANATION TOO BTW
in which case does the transformation of triangle QRS result in an image triangle DEF where angle Q is congruent to angle D, angle R is congruent to angle E, and angle S is congruent to angle S and QR/DE = QS/DR = RS/EF ≠ 1
Answer:
Step-by-step explanation:
The transformation of triangle QRS that results in an image triangle DEF where angle Q is congruent to angle D, angle R is congruent to angle E, and angle S is congruent to angle F, and QR/DE = QS/DF = RS/EF ≠ 1 is a similarity transformation.
A similarity transformation is a type of transformation that preserves the angles between the corresponding sides of the original and the image figures. It means that the corresponding angles of the two figures are congruent, and the ratios of the corresponding sides are equal. In the case of a triangle, it preserves the angles and the ratios of the sides.
So, if a transformation of triangle QRS results in an image triangle DEF where angle Q is congruent to angle D, angle R is congruent to angle E, and angle S is congruent to angle F, and QR/DE = QS/DF = RS/EF ≠ 1, it is a similarity transformation.
The transformation is similarity transformation.
What is Similarity Transformation?Similarity transformations are transformations where there occurs a dilation with one or more transformations like rotation, reflection or translation.
This is called so because the triangles so formed will be similar triangles.
We need two triangles QRS and DEF to be similar triangles.
Similar triangles are those triangles which has the same shape but different size and the length of sides are proportional.
This is the required transformation here.
Similar triangles can be formed by transforming a triangle first with dilation.
Then you can do any of the other rigid transformations.
The triangles will be similar.
Hence the transformation here is similarity transformation.
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Leo wrote s of his 20-page paper last week. He finished writing the paper this week. How many pages did Leo write this week?
20-s is the number of pages written by Leo this week.
What is Expression?An expression is combination of variables, numbers and operators.
Given that Leo wrote s of his 20-page paper last week.
In last week she wrote s pages.
Leo completed his writing the paper this week.
20-s
Twenty minus s is the expression which gives the pages Leo write this week
Hence, 20-s is the number of pages written by Leo this week.
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Question content area top
Part 1
A 150-pound person uses 6.7 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 250 calories?
The number of miles that a person walks at this speed to use at least 250 calories will be 2.49 miles.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
A 150-pound person uses 6.7 calories per minute when walking at a speed of 4 mph. If the number of calories burnt is 250. Then the number of minutes the person is given as,
T = 250 / 6.7
T = 37.313 minutes
T = 0.62 hours
Then the distance is given as,
D = 4 x 0.62
D = 2.49 miles
The number of miles that a person walks at this speed to use at least 250 calories will be 2.49 miles.
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A horse's body temperature T is considered to be normal if it is within at least 0. 9o F of 99. 9o F. Write the normal range of body temperature of a horse as an inequality
If horse's body temperature T is considered to be normal if it is within at least 0.9 °F of 99.9 °F , then normal range of body temperature of a horse as an inequality 99 ≤ T ≤ 100.8 .
If the temperature of the horse denoted by "T" , is within at least 0.9 °F of 99.9 °F , then it is considered as Normal ;
To express this as an inequality, we can use the following:
⇒ 99.9 - 0.9 ≤ T ≤ 99.9 + 0.9 ;
Simplifying further , this inequality can also be written as:
⇒ 99 ≤ T ≤ 100.8
Therefore , the normal range of body temperature of a horse is 99 ≤ T ≤ 100.8 .
The given question is incomplete , the complete question is
A horse's body temperature T is considered to be normal if it is within at least 0.9 °F of 99.9 °F. Write the normal range of body temperature of a horse as an inequality .
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an insurance company conducted an opinion poll for a new health policy. in a sample of 200 participants, 117 of them supported this policy. does this provide strong evidence that more than a half of americans are supporting the new health policy? find the -value of the test (round off to third decimal place).
Sample proportion of 0.585, p-value of 0.0491, not strong evidence of more than 50% support.
What is null hypothesis ?
The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.
The null hypothesis is that the proportion of Americans supporting the new health policy is less than or equal to 0.5 (p <= 0.5). The alternative hypothesis is that the proportion of Americans supporting the new health policy is greater than 0.5 (p > 0.5).
The test statistic for a one-sample proportion test is:
z = (p^ - p) / sqrt((p * (1-p)) / n)
where p^ is the sample proportion (117/200 = 0.585), p is the hypothesized proportion of Americans supporting the new health policy (0.5), and n is the sample size (200).
Sample proportion of 0.585, p-value of 0.0491, not strong evidence of more than 50% support.
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Select the equivalent expression. \left(3^2\cdot 5\right)^{3}=?(3 2 ⋅5) 3 =?
The simplified exponential expression for this problem is given as follows:
(3² x 5)³ = 3^6 x 5³.
How to simplify the expression?The exponential expression for this problem is defined as follows:
(3² x 5)³.
As we have a product applied to the exponent, the exponent can be applied to each factor of the exponent, as follows:
(3²)³ x 5³.
Applying the power of power rule, we have that:
(3²)³ = 3^(2 x 3) = 3^6.
Hence the simplified exponential expression for this problem is given as follows:
(3² x 5)³ = 3^6 x 5³.
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Grade 5 mathematics
8➗0.4=
Hi There! Your Answer would be 20. Why you might ask? allow me to tell you the reason!
you first make a "House" Around the Dividend, the biggest number goes outside of the box, then you just do basic division until you get a zero!
We would be left with 20.
If this helped you make me brainliest
Keep Learning; Keep Asking!
help me pleaseeeeeeeeeeeeeeeeeeeee
Select ALL factors of 44. (Be sure to select ALL correct factors for full credit).
Question 3 options:
3
22
44
1
16
88
4
8
11
2
Answer:
There are only 6 factors of the number 44 which are 1, 2, 4, 11, 22 and 44.
From this list, the factors of 44 are:
1) 22
2) 44
3) 1
4) 4
5) 11
6) 2
Answer:
1,2,4,11,22,44
Step-by-step explanation:
Let's work our way up.
You can start with 1, cause every number has a factor of 1. Then you can find that 44, cause every number is divisible by itself. and 1 × 44 = 44. Since 44 ends with a 4, it has to be divisible by 2. So to find the number that multiplies with 2 to get 44, divide 44 by 2 which equals 22. So 2×22=44. 44 is not divisible by 3. But it is divisible by 4. 4×11=44. No other number is a factor of 44. Therefore; 1,2,4,11,22,44
Hope that helps. Let me know if you have any further questions!
kallie and jeie et up lemonade tand in their front yard thi morning. They old both regular (for 1.50) and trawberry (for $2). They old 12 more trawberry lemonade than regular. If they made a total of $45, how many of each did they ell?
Kallie and Jeie sold 4 regular lemonade for $1.50 amount each, and 16 strawberry lemonade for $2 each, and made a total of $45.
Regular Lemonade: 9
Strawberry Lemonade: 21
Regular Lemonade:
Price of Regular Lemonade = 1.50
Total earnings from Regular Lemonade = 9 x 1.50 = 13.50
Strawberry Lemonade:
Price of Strawberry Lemonade = 2
Total earnings from Strawberry Lemonade = 45 - 13.50 = 31.50
Number of Strawberry Lemonade sold = 31.50 / 2 = 15.75
Number of Regular Lemonade sold = 15.75 - 12 = 3.75
Rounded to nearest whole number,
Number of Regular Lemonade sold = 4
Number of Strawberry Lemonade sold = 16
Kallie and Jeie sold 4 regular lemonade for $1.50 amount each, and 16 strawberry lemonade for $2 each, and made a total of $45.
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if the sum of the measures of the angles of a polygon is three times the sum of the measures of its exterior angles, how many sides does the polygon have?
Answer:
Step-by-step explanation:Seriously you probably going to need a ruler because you don't like you can't just remember measurement inside your head you have to really like a ruler so actually go get a ruler and then take a picture of it doing with the ruler and then you might like get it.
What must you do to keep the equation x + 5 = 12 balanced?
Answer:
see below
Step-by-step explanation:
make x = 7
Answer:
Subtract 5 from both sides
x = 7
Step-by-step explanation:
x + 5 = 12 Subtract 5 from both sides
x + 5 - 5 = 12 - 5
x = 7
How to find proportional parts in triangles and parallel lines?
The proportional parts in triangles and parallel lines can be found by similarity and ratios.
The ratio of any related side lengths is always the same when two triangles are similar. The scale factor can be used to identify the triangle's proportionate components. The longer side of one triangle is twice as long as the comparable side in the other. In contrast, the alternate interior angles are identical when two parallel lines are cut by a transverse line. Additionally, the matching angle pairs are all equal. Trigonometry can be used to determine the length of the opposite side of a pair of parallel lines if we know the length of one side and the matching angle.
One can use similarity ratios to determine the proportional components of triangles and parallel lines. Comparable geometries have equivalent sides that are in proportion. To get the missing side length, one can arrange ratios of corresponding sides and utilise cross-multiplication. Further, similar triangles can also be employed. When two triangles are comparable, their corresponding sides and angles are proportionate and equal.
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Problem ID:
Which number line shows all the values of x that make the inequality - 3x + 1 < 7 true?
A
-5
4
0
-3
5
-2
N + NE
4
- البیا بیا بیا
-3
-4
-2
B
-5
С
-5
D-
-5
A A A
in un
4
-4
-نما
2
-2
-3
4.
2
-1
N
N
0
3
5
Select one:
ОА
OB
Ос
OD
The number line which shows all the values of x that make the provided inequality -3x+1<7 true is shown in number line D.
Now, According to the question:
The number line is the way of representation of number and digits in a arranged form to understand the data batter.
The inequality is :
- 3x + 1 < 7
Subtract 1 both side of the equation and solve it further,
-3x + 1 - 1 < 7 - 1
-3x < 6
Divide with number 3,on both sides
-x < 6/3
-x < 2
Change the sign of the inequality by filliping the inequality sign,
x > -2
Here, the inequality is greater than the number negative 2. The value of x is greater than, thus, the arrow will point towards left and there will be open circle. This is shown in the option D.
Thus, the number line which shows all the values of x that make the provided inequality -3x+1<7 true is shown in number line D.
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Consider the scatter plot.
Select an answer from the drop-down menu to correctly complete the statement.
The scatter plot shows a
Choose...
association.
Scatter plot of 10 points. Generally, the points form an upside down U shape.
The scatter plot shows data points that do not follow a trend, thus it shows a: nonlinear association.
How to find a Non-linear Association?A nonlinear association is a relationship between two variables, whereby a change in one does not correspond to a change in another.
Thus, on a scatter plot showing a nonlinear association, the data points do not follow a trend line and are scattered, therefore, predictions cannot be made using the scatter plot.
Thus, the scatter plot that is given shows: nonlinear association.
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chantel has a goal to complete a triathlon. the race consists of a 0.93-mile swim, a 24.8-mile bike ride, and a 6.2-mile run. in training, chantel can swim at an average pace of 2.1mph. she rides her bike at an average of 18.2mph and runs at 5.1mph. estimate how long it will take her to complete the triathlon.
It will take Chantel approximately 2.028 hours or 122.68 minutes to complete the triathlon.
What is average ?
An average, also known as a mean, is a measure of central tendency that represents the typical value of a set of data. To calculate the average of a set of numbers, you add them up and then divide by the number of items in the set.
Time = Distance / Speed
For the swimming segment, the distance is 0.93 miles and the speed is 2.1 mph. So the time it will take Chantel to swim the 0.93 miles is:
Time = 0.93 / 2.1 = 0.445 hours or 26.7 minutes
For the biking segment, the distance is 24.8 miles and the speed is 18.2 mph. So the time it will take Chantel to bike the 24.8 miles is:
Time = 24.8 / 18.2 = 1.367 hours or 81.02 minutes
For the running segment, the distance is 6.2 miles and the speed is 5.1 mph. So the time it will take Chantel to run the 6.2 miles is:
Time = 6.2 / 5.1 = 1.216 hours or 72.96 minutes
To get the total time, you have to add the time for each segment:
Total time = 0.445 + 1.367 + 1.216 = 2.028 hours or 122.68 minutes
So , It will take Chantel approximately 2.028 hours or 122.68 minutes to complete the triathlon.
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Invest $10000 in a stock with 5% compounded monthly. How much will you have in 10 years?
If you invested $10000 in a stock with 5% compounded monthly you will have $16470 in 10 years.
What is Compound interest?Compound interest is simply interest that is earned over prior interest. You receive interest on the initial principal as well as the interest that builds up over time when you open a savings account that pays compound interest.
When you deposit funds into a savings account or other type of account, you will earn interest on the amount you deposited. For instance, after a year, if you deposited $1,000 in an account with 1% annual interest, you would have received $10 in interest.
Compound interest formula is
[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Here,
P = $10000
r = 5%
n = 12
t = 10
A = to find
Lets solve,
[tex]$\text A = 10000(1 + \frac{0.05}{12})^{12\times 10}[/tex]
A = 16470
Thus, If you invested $10000 in a stock with 5% compounded monthly you will have $16470 in 10 years.
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Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). Show your work for full credit. No work - no credit.
Find the coordinates of P so that P partitions the segment AB in the ratio 3 to 1 if A(7, -4) and B(-5, 4). Show your work for credit. No work - no credit.
Answer:
To find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8), we can use the formula:
P = (1 - t)A + tB
where t is a scalar value that represents the position of P on the segment AB, and A and B are the coordinates of the two endpoints of the segment.
In this case, we know that the part-to-whole ratio is 1:5, so t = 1/6.
So we substitute the values for A, B and t into the formula:
P = (1 - 1/6)A + (1/6)B
P = (5/6)A + (1/6)B
P = (-95/6, 35/6) + (1/6, 8/6)
P = (-15/2, 5/2) + (1/6, 4/3)
P = (-15/2 + 1/6, 5/2 + 4/3)
P = (-30/3, 23/6)
The coordinates of P are (-10,3.83)
For the second problem,
To find the coordinates of P so that P partitions the segment AB in the ratio 3 to 1 if A(7, -4) and B(-5, 4), we can use the same formula as above:
P = (1 - t)A + tB
In this case, we know that the part-to-whole ratio is 3:1, so t = 3/4.
So we substitute the values for A, B and t into the formula:
P = (1 - 3/4)A + (3/4)B
P = (1/4)A + (3/4)B
P = (7/4, -4/4) + (-53/4, 43/4)
P = (7/4 + -15/4, -4/4 + 3)
P = (-8/4, -1/4)
The coordinates of P are (-2,-0.25)
So in the first problem point P is (-10,3.83) and in the second problem point P is (-2,-0.25)
what is the likelihood that two people born on different days of the year have a golden birthday within the same calender year
The probability that two random people being born on the same day is thus 1/365 or about 0.3%
We apply our probability model above to the task at hand.
First, we suppose Person 1. This person is born on a certain date of the year.
Since this is a random person, we can fix this person's birthday to a specific date (a number between 1 and 365) without loss of generality for the problem.
Let's say this person is born on 10. (i.e. January 10th)
Now, we take Person 2. In order to achieve the event that Person 2 is born on the same date as Person 1,
we need them to be born on 10. In other words, we seek the probability of Person 2 being born on 10.
Based on our model, we have that this probability is 1/365.
The probability that two random people being born on the same day is thus 1/365 or about 0.3%
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A student simplifies the expression correctly. 3x+10/2+4(x+3/2). Which could be the student's result?
The correct result for the expression 3x + 10/2 + 4(x + 3/2) is solved to be
x = -1 4/7How to to simplify the expressionThe math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as
the full meaning include
P - parenthesis
E - exponents
M - multiplication
D - division
A - addition
S - subtraction
applying the sequence the problem is solved as follows
= 3x + 10/2 + 4(x + 3/2)
parenthesis
= 3x + 10/2 + 4x + 6
division
= 3x + 5 + 4x + 6
addition
= 3x + 4x + 6 + 5
= 7x + 11
solving for x
7x = -11
x = -11/7
x = -1 4/7
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You invited 24 people to your house for a party. You want to spend a $70 gift card completely on the items shown. You also want to have exactly two servings of food for each person.
Pizza Chicken wings
$6.00 $7.00
4 servings 5 servings
Write a system of linear equations to model this situation where x represents the pizza and y represents the bags of wings.
How many pizzas should you buy? How many bags of chicken wings should you buy?
You have one additional guest that you forget to invite. Now, how many of each items should you buy so everyone still gets exactly two servings? Show or explain your work.
The amount of each item, pizza and chicken wings that should be bought are 7 and 4 respectively. For an additional member the additional number of pizzas is 0 and chicken wings are 10.
What is an equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
A: X is the quantity of pizzas, while Y is the quantity of bags of chicken wings.
1 pizza cost x, thus 6 cost = 6 x
1 bag of chicken wings costs y dollars, thus 7 cost = 7 y.
Given: Total cost = 6x + 7y = 70
Total servings are now equal to (24)(2) for a total of 48.
One pizza includes four portions, thus 1 x 4 = 4
Servings in a bag of chicken wings are 5y.
Servings total: 4x + 5y = 48
The set of linear equations is hence 1.
6x + 7y = 70 .....(I)
4x + 5y = 48 ......(II)
Having solved (I) and (II), we obtain x = 7 and y = 4.
B:
One more guest brings the total to 25.
Total portions are therefore 4x + 5y = 2.25 = 50.
The total cost of 6x + 7y stays at 70.
The set of linear equations is hence 1.
6x + 7y = 70 .....(I)
4x + 5y = 50 ......(II)
We obtain x = 0 and y = 10 by solving for (I) and (II).
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what is the example for the Y-intercept, slope, two points, and the ordered pair
The example for the y-intercept, slope, two points, and the ordered pair
are given below.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction
Let a line in the slope-intercept form,
y = x + 1.
And the line passes through the two ordered pairs (3, 4) and (5, 6).
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
m = 1
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
y - 4 = x -3
y = x+1
Substitute x = 0,
then y = 1
the y-intercept is 1.
Therefore, all the required values are given above.
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Solve for x using logarithms.
[tex]3^{2-3x} = 4^{2x+1}[/tex]
Answer:
[tex]\large\boxed{\sf 0.133 }[/tex]
Step-by-step explanation:
The given equation to us is ,
[tex]\longrightarrow 3^{2-3x}= 4^{2x+1} \\[/tex]
Take log to base 10 on both sides,
[tex]\longrightarrow \log_{10} 3^{2-3x}= \log_{10} 4^{2x+1} \\[/tex]
Now recall that, [tex] \log a^m = m\ log \ a [/tex]
[tex]\longrightarrow (2-3x) \log_{10} 3 = (2x+1)(\log_{10} 4)\\[/tex]
We can write it as ,
[tex]\longrightarrow (2-3x) \log_{10}3=(2x+1)\log_{10}2^2 \\[/tex]
Again using the property mentioned above,
[tex]\longrightarrow (2-3x)\log_{10}3 = 2(2x+1)\log_{10} 2 \\[/tex]
[tex]\longrightarrow (2-3x)\log_{10}3 = (4x+2)\log_{10} 2 \\[/tex]
Now we know that ,
log 3 = 0.477log 2 = 0.301On substituting the values, we have ,
[tex]\longrightarrow (2-3x)0.477 = (4x+2)0.301 \\[/tex]
simplify by opening the brackets,
[tex]\longrightarrow 0.954 - 1.431x = 1.204x + 0.602 \\[/tex]
[tex]\longrightarrow 1.204x + 1.431x = 0.954 - 0.602 \\[/tex]
[tex]\longrightarrow 2.635x = 0.352 \\[/tex]
[tex]\longrightarrow x =\dfrac{0.352}{2.635} \\[/tex]
[tex]\longrightarrow \underline{\underline{ x = 0.133 }} \\[/tex]
and we are done!
In the figure, Angle RQS Is-congruent-to Angle QLK.
3 lines are shown. Lines S P and K N are parallel. Line R M intersects line S P at point Q, and intersects line K N at point L. Angle R Q S is x degrees. Angle K L M is (x minus 36) degrees.
What is the value of x?
36
72
108
144
Where in the figure, ∠RQS Is-congruent to ∠QLK. 3 lines are shown. Lines SP and KN are parallel. Line R M intersects line SP at point Q, and intersects line KN at point L. ∠RQS is x degrees. ∠ KLM is (x minus 36) degrees. Note that the value of x will be 108°.
What is the rationale for the above response?With regard to the problem description and the image attached, we know that
m∠RQS≅m∠QLK ⇒ by corresponding angles
m∠KLM + m∠QLK=180° ⇒ by supplementary angles (consecutive interior angles)
Since
m∠RQS=x° ⇒ given in the problem
Therefore,
m∠QLX = x°
m∠KLM=(x-36)° ⇒ given problem
executing a substitution we have:
(x - 36)° + x° = 180°
2x = 180 + 36
2x = 216
x = 216/2
x = 108°
Thus, it is correct to state that the value of x in the diagram is 108°
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What is the constant of proportionality in this proportional relationship?
The constant of proportionality of the proportional relationship, given the values of x and y is D. 5 / 12
How to find the constant of proportionality?The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship.
The Constant of proportionality can therefore be found by picking a random point on the graph which is ( 2, 5 / 6 )
The constant of proportionality is:
= 5 / 6 ÷ 2
= 5 / 6 x 1 / 2
= 5 / 12
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A manufacturer of bolts has a quality-control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. The quality-control engineer knows that the bolts coming off the assembly line have mean length of 10 cm with a standard deviation of 0. 05 cm. For what lengths will a bolt be destroyed?
The bolts that are destroyed due to being more than 2 standard deviations from the mean will have a length of 10 cm ± 0.15 cm.
This means that any bolts that are shorter than 9.85 cm or longer than 10.15 cm will be destroyed. Any bolts that fall within this range will pass the quality-control check and will not be destroyed.
The manufacturer should also have a policy in place to ensure that bolts that are found to be too short or too long are discarded and not put into circulation. This will help maintain the quality of the bolts that are produced.
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