The solution of the system of linear equations is :-
x = 6 hours .
y = 330 miles.
Now, According to the question:
Let x be the number of hours that have elapsed since Zac started traveling .
Let y be the number of miles traveled .
We know that,
Speed = Distance / Time.
so,
Speed of Zac = D / T = 123.75 / 2.25 = 55 miles / hour.
Speed of Lynn = D / T = 105 / 1.75 = 60 miles / hour.
then, Distance travelled by Zac in x hours = S * T
y = 55 × x
y = 55x miles
and, Distance travelled by Lynn in (x - 0.5) hours = S * T
y = 60 × (x - 0.5)
y = 60x - 30
Therefore, a system of linear equations that represents the distance each of them has traveled since Zac left on his trip are :-
y = 55x ----------- Eqn.(1)
y = 60x - 30 ------------- Eqn.(2)
Now, putting value of Eqn.(1) in Eqn.(2) , we get,
55x = 60x - 30
60x - 55x = 30
5x = 30
x = 6 hours.
Putting value of x in Eqn.(1),
y = 55 * 6
y = 330 miles.
Hence, the solution of the system of linear equations is :-
x = 6 hours .
y = 330 miles.
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A professional pool player claims that she sinks at least one ball in a pocket on 80% of her opening break shots. In a recent set of 20 games, she sunk at least one ball on her break shot in only 14 of the games. A simulation of 100 trials was conducted to see how unusual these most recent games are. A dotplot titled the professional pool player has number of games with at least one ball made on the break on the x-axis, and frequency on the y-axis. 10, 1; 12, 3; 13, 11; 14, 12; 15, 17; 16, 25; 17, 16; 18, 9; 19, 5; 20, 2. Based on the dotplot of the simulation results and the pool player’s last 20 games, which conclusion can be drawn?
There is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games and no convincing evidence that her average is less than 80%.
Based on the dot plot of the simulation results, it appears that the player's true probability of sinking at least one ball on her break is not 80%. In the simulation, there were only 12 trials out of 100 where the player sank at least one ball on her break 14 or fewer times in 20 games. This corresponds to a probability of 12/100, or 12%.
Since the player's actual performance in the last 20 games (14 out of 20) is less likely to occur than what was observed in the simulation, we can get the conclusion that the player has a lower than 80% chance of sinking at least one ball during her break.
Therefore, the correct conclusion is, "there is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games. This result is not unusual and there is no convincing evidence that her average is less than 80%."
The question is incomplete. The complete question is 'The player’s true probability of sinking at least one ball on her break is 27%. another 100 simulated trials would show a much different outcome; therefore, we cannot draw any conclusions. it is most likely that she would sink at least one ball during her break exactly 16 times. there is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games. this result is not unusual and there is no convincing evidence that her average is less than 80%.'
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Answer:
d
Step-by-step explanation:
edge 2020
Debra is seven years younger than her sister, Pam. The table represents the relationship. Which is the equation representing the relationship between their ages?
(x) (y)
9 2
11 4
13 6
15 8
1. y = x - 2
2. y = 7x
3. y = x + 7
4.y = x - 7
y = x + 2
Answer: y = x - 2
Step-by-step explanation:
The equation representing the relationship between the ages of Debra and Pam is y = x + 2. This is determined by analyzing the table provided, which shows the ages of Pam (x) and Debra (y) in years. From the table, we can see that for every 1 year increase in Pam's age, Debra's age also increases by 1 year. This is represented in the equation y = x + 2, where y (Debra's age) is equal to x (Pam's age) plus 2 years. This equation is supported by the data in the table, as all of the ordered pairs (x, y) in the table satisfy the equation y = x + 2.
a and b are parallel. Find the missing angles.
The missing angles are as calculated below. Fill them accordingly.
How to find the missing angles?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Check the attached image for labeling
a = 125° (vertically opposite angles are equal)
a + b = 180 (sum of angles on a line)
b = 180 - 125 = 55°
b + c = 90 (sum of angles in a triangle)
c = 90 - 55 = 35°
d = b (alternate angle)
d = 55°
e = 125° (alternate angle)
Fill in the missing angles accordingly
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Find the average rate of change of y=0.5x-3 over the interval -3(equal to or <)x(equal to or <)4
The value of average rate of change of y = 0.5x - 3 over the interval
- 3 ≤ x ≤ 4 is, 0.5.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The function is,
⇒ y = 0.5x - 3
Now, The average rate of change is,
⇒ y = 0.5x - 3
⇒ dy / dx = 0.5
Hence, The value of average rate of change of y = 0.5x - 3 over the interval - 3 ≤ x ≤ 4 is, 0.5.
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What do I put in the boxes?
The values in the result of the division operation, 7 ÷ 6 are as follows;
The quotient = 12
The remainder = 4
Please find attached the diagram with the correct values in the boxes created with MS Word
What is the quotient in a division operation?The quotient is the result following the complete division by the devisor. The remainder is the part of the dividend yet to be divided by the divisor.
The division operation is 76 ÷ 6
The quotient is the integer value obtained following the division operation of 76 by 6 which is 12 times. Therefore, the quotient is 12
The values in each box are therefore;
The value at the top left box, is 10
The value in the box below 2 and to the right of 60 is 12
The value outside to the top right of the rectangle is the remainder
The remainder is the difference between the dividend and the product of the quotient and the divisor as follows;
Remainder = 76 - 12 × 6 = 4
The remainder is 4
Please find attached a drawing of the figure, created with MS Word, showing the values that are to be placed in the boxes
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provide numerical measures of individuals. the measures can be added or​ subtracted, and provide meaningful results.
Quantitative variables provide numerical measures of individuals. The measurements yield useful results and can be added to or removed from.
A quantitative variable is one for which the data display amounts (e.g. height, weight, or age). A categorical variable is one where the data indicate categories. As was discussed in the chapter's section on variables, quantitative variables are those that are measured on a numeric scale.
Height, weight, reaction speed, subjective pain rating, temperature, and exam score are a few examples of quantitative variables.
A quantitative study works with numbers and data, whereas a qualitative study concentrates on words and meanings. Variables can be quantified, and hypotheses can be tested quantitatively. You can go more deeply into concepts and experiences by using qualitative research methods.
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suppose the die is tossed and we are told that the result is a number greater than 4 4 . based on this information, what is the probability that the result was a 6 6 ?
The probability that the result was a 6 is P(A)=1/3 the die is tossed and we are told that a result is a number greater than 4.
A standard 6-sided die numbered 1 to 6 has 2 sides that meet the criterion of greater than 4, which are 5 and 6. So out of 6, there are 2 ways.
A die has 6 faces with the numbers 1,2,3,4,5 and 6 on each of the six faces. Now consider an unbiased die and the probability of any of the faces appearing in a single roll is 1/6.
So,
P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6
The numbers that are greater than 4 are 5 and 6
So it can be P(5) or P(6)=
P(5)+P(6)=2/6=1/3.
If you had stated at least a 4, then there are three chances which are to be 4,5,6 that meet the criterion, and the chance would be 3/6=1/2.
Hence, by the classical definition of probability, the probability of getting a number more than 4 in a single throw of a die is 1/3.
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If the hypotenuse of a 30°-60°-90° triangle is 8 cm, what is the measure of the longer leg of the triangle?
The measure of the longer leg of the triangle is given as follows:
6.93 cm.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The longer leg is opposite to the angle of 60º, hence the sine relation is used to find the length, as follows:
sin(60º) = x/8
x = 8 x sine of 60 degrees
x = 6.93 cm.
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Jack and Diane are designing a trellis for some special plants they are planning to put in their backyard garden. Use the values provided on the sketch of the trellis to find the missing values for X, Y, and Z
The value of X is 40/3ft, Y is 27/4ft and Z is 469/27ft. The solution has been obtained by using the properties of triangle.
What is a triangle?
The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. The triangle's three angles add up to a total of 180 degrees.
We know that if a line is parallel to the third side of the triangle, then the ratio of the sides is equal.
So,
⇒10/6 = x/8
⇒80/6 = x
⇒40/3 = x
Similarly,
⇒y/10 = 9/(40/3)
⇒y/10 = 27/40
⇒y = 27/4
Similarly,
⇒y/(y+10) = 7/z
⇒(27/4)/((27/4)+10) = 7/z
⇒469/27 = z
Hence, the value of X is 40/3ft, Y is 27/4ft and Z is 469/27ft.
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If I bought a computer for $420. It had been reduced by 25%.
What was the original price of the computer before the reduction?
(If I could get an answer asap that would be great!)
Answer:
$560
Step-by-step explanation:
if 25% is the discount than the total of the item after the discount is .75x. So to find the original total we need the equation 420=.75x
first we need to isolate x so we divide both sides by .75, doing this will give us 560= x
to check our answer you need to multiply 560 by .75 (which I got by subtracting the discount, .25, from 1) which gives us our discounted total of $420
David wants to measure the height of a tree. He sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 37 ft from the tree, and
David is standing 9.3 ft from the mirror, as shown in the figure. His eyes are 6 ft above the ground. How tall is the tree? Round your answer to the nearest foot.
(The figure is not drawn to scale.)
6 ft
9.3 ft
37 ft
X
David's method to find the height of the tree is the use of the properties of similar triangles. The height of the tree is approximately 24 feet
Laws of ReflectionAccording to the laws of reflection, we have;
Angle of incidence of the light from the top of the tree = Angle of the reflected light ray David sees.
The possible values in the question are;
Distance of the mirror from the tree = 37 feet
Distance from where David is standing to the mirror = 9.3 ft.
Height of his eyes above the ground = 6 ft.
Required: Height of Tree
Therefore;
The triangle formed by David's height, the reflected ray from the mirror and his distance from the mirror is similar to the right triangle formed by the tree, which by the relationship of similar triangles, gives;
[tex]\frac{9.3}{37}[/tex] = [tex]\frac{6}{Height of the Tree}[/tex]
Height of the tree × 9.3 = 6 × 37
Height of the tree = [tex]\frac{6 X 37}{9.3}[/tex] = 23.87 ≅ 24 feet
Therefore, the tree is approximately 24 feet tall
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The smallest gecko on record is 0.8 inch long. Sarah's drawing has a scale factor of 1 inch to 0.1 inch. Which equation could be used to find g, the length of Sarah's drawing of the gecko?
The length of Sarah's drawing is given by the following equation:
0.1g = 0.8.
How to obtain the scale of the drawing?The scale of the drawing is obtained applying the proportions in the context of this problem.
The scale is defined as the division of the drawn length by the actual length.
Sarah's drawing has a scale factor of 1 inch to 0.1 inch, meaning that each inch she draws has an actual length of 0.1 inch.
The rule of three is defined as follows:
1 inch - 0.1 inches
g inches - 0.8 inches
Hence the equation is:
0.1g = 0.8.
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For the given region, calculate the shaded area. You can assume right angles.
The area of the shaded region is equal to 116 sq units.
It is given that we can assume the angles to be right angle. So from the fig we can see that it is a quadrilateral and length and breadth for the given figure are different. So the given fig is a rectangle.
The area of a rectangle = length × breadth
∴ The area of the bigger rectangle = 10×20=200 sq units
Similarly,
The area of the smaller rectangle = 14 × 6 = 84 sq units
Now,
The area of the shaded region = Bigger rectangle - Smaller rectangle
⇒ 200 - 84 = 116 sq units
Therefore, The area of the shaded region is equal to 116 sq units.
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1. Which method would be the simplest way to solve the system? y= 1/2x 2x+3y=28 A) graphing B) substitution C)elimination D) distributive 2.How many solutions does this system have?
Since the value of y can be known from equation 1, we can use the substitution method to solve the system of equations. By entering the value of y in equation 2, we can quickly get the value of x. So the option B is correct.
The system of equation are:
y = 1/2x...................(1)
2x + 3y = 28...................(2)
To solve the system of equation we use substitution method because the value of y is know from the equation 1. We can find easily the value of x by putting the value of y in equation 2.
Now putting the value of y in equation 2.
2x + 3(1/2x) = 28
2x + 3/2 x = 28
7/2 x = 28
Multiply by 2 on both side, we get
7x = 56
Divide by 7 on both side, we get
x = 8
Now putting the value of x in equation 1
y = 8/2 = 4
The solution of the system of equation is (8, 4).
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Given the function g(x)=-x²+5x+14, determine the average rate of change of the function over the interval 1 ≤ x ≤ 9
the average rate of change of the function over the interval 1 ≤ x ≤ 9 is 3.75.
What is the average rate of change?It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Given the function g(x)=-x²+5x+14, within the interval 1 ≤ x ≤ 9
At the lower interval x = 1
g(x) = -1 +5 + 14
g(x) = 18
At the lower interval x = 9
g(x) = -9²+5*9+14
g(x) = -22
The average change of the function will be expressed as:
Δy/Δx = (-22 - 8)/ (9-1)
Δy/Δx = -30/8
Δy/Δx = 3.75
therefore, the average rate of change of the function over the interval 1 ≤ x ≤ 9 is 3.75.
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solve for side h with the given side and angle
Answer: 33.93 in
Step-by-step explanation:
we can see it is a right angle there. h is oppsite line of the right triangle and 70in is Hypotenuse. So, we can use the formula sin29 = h/70. Then sin29*70=h. h=33.93 in.
Can you help me please thank you so much.
Answer: It is the last one on he far right.
Step-by-step explanation:
;)
Mr. Sato sells fish at a 60% markup. He pays $3.75 per pound for haddock one week. At what price per pound will he sell it?
Answer: $6
Step-by-step explanation:
60% of 3.75
3.75 * 0.60 = 2.25
2.25 + 3.75 = 6
Step-by-step explanation:
The answer is 2.25 because 60% of 3.75 is equal to 2.25
Find the measure of angle A in the figure below.
Answer: 40°
Step-by-step explanation:
Given 450 grams of bacteria that decreases at a rate of 1/2 per year, what would be an appropriate range after 3 years?
The approximate range will be 56.25 gm. after the end of 3 years.
As per the question,
We have, the value of the weight of the bacteria = 450 gm
As the rate of bacteria is decreasing with rate of 1/2
So, after 1 year the number of bacteria will be half as it was at the start of the year.
So, the number of bacteria after 1 year will be = 450 *(1/2)=225
As the rate of bacteria is again decreasing with the rate of 1/2
So, after 2 years the number of bacteria will be half as it was at the start of the year.
So, the number of bacteria after 2 years will be = 225 *(1/2)=112.5
As the rate of bacteria is decreasing with the rate of 1/2
So, after 3 year the number of bacteria will be half as it was at the start of the year.
So, the number of bacteria after 3 years will be = 112.5*(1/2)=56.25
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For the translation below, give the vertices of ABC
A' = (-1, 3)
B' = (-4, 0)
C' = (1, 6)
=======================================================
Reason:
The notation [tex]T_{ < -3, 5 > }[/tex] means "translate 3 units left, 5 units up".
Another way to write out this rule is [tex](\text{x},\text{y}) \to (\text{x}-3,\text{y}+5)[/tex]
-------------------
Let's apply that rule to the coordinates of point A.
[tex](\text{x},\text{y}) \to (\text{x}-3,\text{y}+5)\\\\(2,-2) \to (2-3,-2+5)\\\\(2,-2) \to (-1,3)\\\\[/tex]
Point A' is located at (-1, 3)
-------------------
Repeat for the coordinates of point B.
[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+5)\\\\(-1,-5)\to(-1-3,-5+5)\\\\(-1,-5)\to(-4,0)\\\\[/tex]
Point B' is located at (-4, 0)
-------------------
Lastly do the same for point C.
[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+5)\\\\(4,1)\to(4-3,1+5)\\\\(4,1)\to(1,6)\\\\[/tex]
Point C' is located at (1, 6)
(8.6 x 10^-3)(8 x 10^-1)
Answer:
(8,6×10^-3) (8×10^-1)
=(0,0086). ( 0.8)
The measures of the acute angles of a right triangle are (2x-3)^degree. What is the measure of the smallest angle in the triangle?
The required measure of the smallest angle in the triangle is 37°.
What is Right angled triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The sum of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
According to question:We know that one angle in right angled triangle is 90 degree and sum of other two angle is 90 degree.
So, acute angles are (2x -3) and (3x-7).
Then
(2x -3) + (3x-7) = 90
5x - 10 = 90
5x = 100
x = 20
Smallest angle = 2x - 3
= 2(20) - 3
= 40 - 3
= 37°
Thus, required Smallest angle is 37°
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45% as a fraction or a mixed number in simplest form
Answer:
[tex]\frac{9}{20}[/tex]
Step-by-step explanation:
45% = [tex]\frac{45}{100}[/tex]
[tex]\frac{45}{100}[/tex] ÷ [tex]\frac{5}{5}[/tex] = [tex]\frac{9}{20}[/tex]
Answer:45%=9/20 I hope this helps
Step-by-step explanation:
45%
By definition p%=p/100 which something like this
45/100
then you Cancel out the common factor 5
45/100 cancel these numbers out by 5
Then you will get your answer which is something like this
9/20
So 45%=9/20 as a fraction
Your mother is very fond of collecting rare philodendron (an ornamental and
indoor plant). If she has a garden which measures 100 m2 (10 m by 10 m)
and each philodendron will occupy an estimated area of 0. 6 by 0. 6 m of the
garden, what is the maximum number of philodendron plants that will occupy
the whole area?
help me please
The maximum number of philodendron plants that will occupy the whole area is 256.
The term area in math is defined as the region bounded by the shape of an object
Here we have given that your mother is very fond of collecting rare philodendron and here we have know that If she has a garden which measures 100 m² and each philodendron will occupy an estimated area of 0. 6 x 0. 6 m of the garden.
Here we have to 10 meters divided by 0.6 of a meter gives 16 philodendrons in one direction and the same number in the other direction.
Then the maximum number of plants is calculated as,
=> 16 x 16 = 256
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*PLEASE HELP SOON* Use the laws of exponents to simplify the expression so that the base, x, appears once, and the exponent is positive.
Using the laws of exponential used to simplify the expression, we have; 1/x^2.
What is an exponential expression?When a given expression has an exponent, this implies that the degree of one of its variable is more than 1. So that the laws of exponent which is also law of indices can be used to determine the required simplification of the expression if required.
From the given question, we have;
x^3/ x^5
So that from the law of indices,
x^3/ x^5 = x^3 x^-5
= x^(3 - 5)
= x^-2
From the inverse law of exponent,
x^-2 = 1/ x^2
Using the law of exponents, the simplified form of the expression is 1/ x^2.
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Radiotelescopes
reveal that space
is full of:
Answer: No real "space" exists. There is plenty of air all around us
Step-by-step explanation: I'm sorry If I am wrong tysm
-☈⊙⌘☿
Answer:
cosmic microwave background radiation
Step-by-step explanation:
Can someone please help me with this please?
Click on image for full view
Answer:
Obtuse and isosceles
Step-by-step explanation:
Cuz 2 sides and angles are equal and there is one obtuse angle
Answer:
obtuse and isoscelies
Step-by-step explanation:
120 is greater than 90 so obtuse
isoscelies means to sides of equal length and one of different length
2 sides are 3ft and one is 5ft
Using a 3-4-5 right triangle and a 5-12-13 right triangle, John sets up the
proportion 3:4=5:12. Show that the proportion is incorrect. Explain what John
might have been thinking when he wrote the proportion.
ents
The proportion taken by John 3:4 = 5:12 is correct.
The term called proportion in math is defined as the values of the proportion that are close to each other when written in ratio form using a colon.
Here we know that the a 3-4-5 right triangle and a 5-12-13 right triangle are set by John.
And the taken proportion is written as,
=> 3:4 = 5:12
Here we have to use the Pythagoras theorem to verify this one, then we get,
=> 3² + 4² = 5²
=> 9 + 16 = 25
=> 25 = 25
Now, we have to take the other values and verify that one also,
=> 5² + 12² = 13²
=> 25 + 144 = 169
=> 169 = 169
Therefore the proportion is correct.
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need help algebra 2. write in rational exponent form
The rational exponent form is 5^3/5x. Option D
What is the rational exponent form?We know that a rational function would be the function that does not have the radical sign in it. We can see that we have the expression that have been written for us here as; 5√125x^5.
When we open up the radical we would have;
125^1/5 * 5^5/5
But we know that;
125 = 5^3
We now have;
5^3/5 * x
This becomes;
5^3/5x
Thus we are going to end up in the rational exponent form of the expression as 5^3/5x.
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