The function, after the transformations is y'' = 1/4(x +84)
How to determine the function, after the transformations?The function equation is given as:
y = |x|
1) Reflect the function about the y-axis.
This is represented as
(x, y) = (-x, y)
So, we have:
y' = |-x|
This gives
y' = |x|
2) Compress the function vertically by a factor of 1/4.This is represented as
(x, y) = (x, 1/4y)
So, we have:
y'' = 1/4y'
This gives
y'' = 1/4|x|
3) Shift the function left 84 units.This is represented as
(x, y) = (x + 84, y)
So, we have:
y'' = 1/4(x +84)
Hence, the function, after the transformations is y'' = 1/4(x +84)
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Where’s 1 7/10 on a number line?
The location of 17/10 on the number line is given below .
A number line provides a "picture" of what a number is. Visually see where your number is and other numbers nearby. Large numbers are always on the right and small numbers are always on the left.Small marks along the line represent the next highest or next lowest number. In most cases, the small marks are one count apart. There is no problem. The arrows at the ends of the number line mean infinite left and right movement, just like numbers move infinitely.
The fraction 17/10 is equals 1.7 .
Also note that minus 17/10 is the same distance from 0, but to the left of 0 instead of to the right.
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In a sample of 1100 U.S. adults, 203 think that most celebrities are good role models. U.S. adults are selected from this sample without replacement. Complete parts (a) through (c). (a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is nothing. (Round to three decimal places as needed.) (b) Find the probability that neither adult thinks most celebrities are good role models. The probability that neither adult thinks most celebrities are good role models is nothing. (Round to three decimal places as needed.) (c) Find the probability that at least one of the two adults thinks most celebrities are good role models. The probability that at least one of the two adults thinks most celebrities are good role models is nothing. (Round to three decimal places as needed.)
Using the hypergeometric distribution, the probabilities are given as follows:
a) 0.034 = 3.4%.
b) 0.665 = 66.5%.
c) 0.3352 = 33.5%.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.For this problem, the parameters are given as follows:
N = 1100, k = 203, n = 2.
In item a, the probability is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,1100,2,203) = \frac{C_{203,2}C_{897,0}}{C_{1100,2}} = 0.034[/tex]
For item b, the probability is P(X = 0), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,1100,2,203) = \frac{C_{203,0}C_{897,2}}{C_{1100,2}} = 0.665[/tex]
For item c, the probability is:
P(X >= 0) = 1 - P(X = 0) = 1 - 0.665 = 0.335.
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Which whole number property is represented?
5 × (10 + 7) = (5 × 10) + (5 ×7)
Associative Property of Multiplication
Identity Property of Multiplication
Distributive Property of Multiplication
Commutative Property of Multiplication
5 × (10 + 7) = (5 × 10) + (5 ×7) whole number property is represented by
distributive property of multiplication.
As given in the question,
Given number : 5 × (10 + 7) = (5 × 10) + (5 ×7)
Here whole number 5 is first multiplied to addend 10 and then whole number 5 is multiplied to addend 7.
Then, their products are added.
This is represented by property of Distributive Property of Multiplication.
Therefore,5 × (10 + 7) = (5 × 10) + (5 ×7) whole number property is represented by distributive property of multiplication.
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Answer:
Distributive Property of Multiplication
Step-by-step explanation:
The Distributive Property of Multiplication states that multiplying a number by a group of numbers added together is the same as multiplying each number separately:
[tex]\large\text{$a(b + c) = ab + ac$}[/tex]
Therefore, applying the Distributive Property of Multiplication to the given expression:
⇒ 5 × (10 + 7) = 5(10) + 5(7)
--------------------------------------------------------------------------------------------
Here are the definitions of the other properties for information purposes:
Associative Property of Multiplication
The grouping of numbers by parentheses in a different way does not affect their product.
[tex]\large\text{$(a \times b) \times c = a \times (b \times c) = (a \times c) \times b$}[/tex]
Identity Property of Multiplication
This property is also known as the identity property of one.
Multiplying any number by 1 does not change the number, i.e. the number keeps its identity.
[tex]\large\text{$a \times 1 = a = 1 \times a$}[/tex]
Commutative Property of Multiplication
Changing the order or position of two numbers does not change the end result.
[tex]\large\text{$a \times b = b \times a$}[/tex]
Divisibility rules for 2, 5, and 10
Answer the questions below. Be sure to mark all answers that apply.
(a) Which numbers are divisible by 2?
(b) Which numbers are divisible by 5?
(c) Which numbers are divisible by 10?
145 891
O
O
O
890
X
None of these
O
Ś
Answer:
2 is divisible by 1 and all even numbers are divisible by 2 so that means 4 but 2 is not divisible by 8 and 9 is not divisible by 2 but 1 is.
5 is not divisible by 4. 5 is divisible by 5, 5 is not divisible by 8, 9 is not divisible by 5, 1 is not divisible by 5.
10 is divisible by 1, 4 is not, 5 is not, 8 is not, 9 is not divisible by 10 but 1 is.
Debra runs 4 miles in 30 minutes. At the same rate, how many miles would she run in 48 minutes?
========================================================
Work Shown:
(4 miles)/(30 minutes) = (x miles)/(48 minutes)
4/30 = x/48
4*48 = 30x
30x = 4*48
x = 4*48/30
x = 6.4
why do you get different answers for -5^2 and (-5)^2. And why is one positive (33) and one negative (-18) !!
Answers to both the given expressions are the same that is 25 and both answers are positive.
What are exponents?The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. 2 x 3 = 6 does not equal 23.Product of powers rule — When multiplying like bases, add powers together.When dividing like bases, apply the power quotient rule.Power of powers rule — When raising power by another exponent, multiply the powers together.So,
-5² = -5 × -5 = 25Similarly,
(-5)² = -5² = -5 × -5 = 25Hence, we can say that the answers to both the expressions are the same and both have positive answers.
As, when we take a square of any negative number, after the multiplication the results always come positive.Therefore, the answers to both the given expressions are the same that is 25 and both answers are positive.
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find the gradients of line a and b
Answer:
[tex]a = 4[/tex]
[tex]b = - 2[/tex]
Step-by-step explanation:
See the attached image above for explanation.
I hope it helpsIf f ( x ) = – 2 x + 3 then f ( 3 ) – f ( 4 ) =
For the function f ( x ) = – 2 x + 3, the value of f ( 3 ) – f ( 4 ) will be 2
What is a function?A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given,
f ( x ) = – 2 x + 3
f(3) = -2(3) + 3
= -6 + 3
f(3) = -3
f(4) = -2(4) + 3
= -8 + 3
= -5
f ( 3 ) – f ( 4 ) = -3 + 5
= 2
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An isolated agricultural country has two distinct regions: a lowland plain and an upland of rugged hills. On one unit of land on the PLAIN, a farmer can raise 10 bushels of grain or graze 10 sheep. On one unit of land in the HILLS, a farmer can raise 2 bushels of grain or graze 4 sheep.
Determine which region has the absolute advantage for sheep production. Explain your answer.
Because food grows more quickly in the hills when exposed to heat and rain rather than sunlight all day. Then for 1 sheep 1 bushel is required in the hills.
What are statistics?The practice or science of organizing and interpreting numerical data in big quantities, particularly for the objective of concluding proportions in a whole from those in an expected sample.
Given that a remote agricultural nation is divided into two distinct geographic areas: a lowland plain and an upland of rough hills. A farmer can grow 10 bushels of grain or pasture 10 sheep on one unit of land on the plain. A farmer in the hills can pasture 4 sheep or grow 2 bushels of grain on one unit of land.
As opposed to being exposed to sunlight all day, food develops more quickly in the hills when it is exposed to heat and rain.
For uphills = 10 sheeps = 10 bushels
For uphills = 1 sheeps = 1 bushels
For down plain = 4 sheeps = 2 bushels
For down plain = 1 sheeps = (1 / 2 ) bushels
Therefore, then for 1 sheep 1 bushel is required in the hills.
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3 0.24 divided by 0.4
Answer:
0.6
Step-by-step explanation:
0.24 divided by 0.4 equals to 0.6.
[tex]0.24 \div 0.4 = 0.6[/tex]
Answer:
0.6
Step-by-step explanation:
Two angles of a triangle have the same measure and the third one is 48 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
Answer: The LARGEST angle has a measure of
degrees.
The LARGEST interior angle of the triangle has a measure of 92 degrees.
What is the largest angle of the triangle?The sum of the interior angle of a triangle is 180 degrees.
Given the data in the question;
Let x represent the measure of the first two angles.
Since they have same measurements.
Measure of angle 1 = xMeasure of angle 2 = xMeasure of angle 3 = x + 48Since the sum of the interior angle of a triangle is 180 degrees.
m∠1 + m∠2 + m∠3 = 180°
x + x + x+48 = 180
3x + 48 = 180
3x = 180 - 48
3x = 132
x = 132/3
x = 44°
Measure of the largest angle will be;
Measure of angle 3 = x + 48 = 44 + 48 = 92°
Therefore the LARGEST interior angle of the triangle has a measure of 92 degrees.
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How many portions of 8 ¾ ounces each can be made from a boneless roast weighing 28 pounds? (Remember, 1 pound = 16 ounces.)
portions
The portions of 8 ¾ ounces that can be made from a boneless roast weighing 28 pounds is 51.2 portions.
How to calculate the value?1 pound = 16 ounces
Therefore, 28 pounds will be:
= 28 × 16
= 448. ounces
Therefore the number of portions will be:
= 448 / 8 3/4
= 448 / 8.75
= 51.2 portions
Therefore, the portions of 8 ¾ ounces that can be made from a boneless roast weighing 28 pounds is 51.2 portions.
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Question is in photo
Answer:
Initial temp is 20 degrees C
Function shows decay
Temp changes by 97% every minute
Step-by-step explanation:
The temperature as a function of time is:
C(t)=20(0.97)[tex]t^{2}[/tex]
when t = 0, C(0) = 20(0.97)0, or -20(1) = 20C
The temperature changes by 0.97, or 97% every minute.
> Read and try to solve the problem below.
Mei is building a raised bed in her garden to grow lettuce.
She wants the base of the bed to be a square with an area of
2 square meters. Find an approximate side length of the base
of the bed. Plot the value on the number line.
Side length of the base of the bed is √2.
What is square?A square is a plane shape with four equal sides and four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).
The bed's base will be square.
An area of 2 square meters.
So, the area A=a2 is 2=a2
So, the area of square is √2
Therefore, Side length of the base of the bed is √2
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For these data, which measures of central tendency take more than one value? Choose all that apply
Answer:
Step-by-step explanation:
The product of powers law of exponents states to keep the ______ then _______ the powers.
A. base. A. add
B. coefficient B. subtract
C. exponent C. multiply
10C5 use the formula for nCr to evaluate given expression.
Answer:
The value of ¹⁰C₅ using [tex]\;^nC_r[/tex] formula is 252.Step-by-step explanation:
Given that
¹⁰C₅To find
The value of ¹⁰C₅ using [tex]\;^nC_r[/tex] formula.So according the question
We know that,
Combination, also known as [tex]\;^nC_r[/tex], is the process of choosing r objects from a group of n objects so that the order of the objects is irrelevant. The following is the formula to find combinations of r objects from n objects:
[tex]\;^nC_r = \frac{n!}{r!(n-r)!}[/tex] and from question.n = 10r = 5Now, put the value of n and r in [tex]\;^nC_r[/tex] formula.
So, we get
[tex]\;^nC_r = \frac{n!}{r!(n-r)!}[/tex]
[tex]\;^{10}C_5 = \frac{10!}{5!(10-5)!}[/tex]
∵ n! = n×(n-1)×(n-2)×........................×3×2×1∴ 5! = 5×4×3×2×1∴ 10! = 10×9×8×7×6×5![tex]= \frac{10\times9\times8\times7\times6\times5!}{5! \;\;5!}[/tex]
[tex]= \frac{10\times9\times8\times7\times6}{5\times4\times3\times2\times1}[/tex]
[tex]= {\times9\times2\times7\times2}[/tex]
[tex]= {252}[/tex]
Answer:
The value of ¹⁰C₅ using [tex]\;^nC_r[/tex] formula is 252.To learn more about Combination please click on the link
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58000Thousands= millions
Using the mathematical operation of multiplication, the value, 58000Thousands = 58 million.
What are mathematical operations?Mathematical operations are the ways mathematical expressions and values can be manipulated.
The basic mathematical operations include addition, subtraction, division, and multiplication.
Data and Calculations:58000Thousands converted into millions
= 58,000,000 (58,000 x 1000)
= 58 million
Thus, using the mathematical operation of multiplication, the value, 58000Thousands = 58 million.
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Ashley runs 11 miles in 95 minutes. How many miles does she run per minute? miles per minute
Answer:
0.11578947368 mil/min
Step-by-step explanation:
11/95=0.11578947368
Answer:
8.6 miles
Step-by-step explanation:
95 mins divided by 11 miles= amount of minutes per mile
solve for m + 1/4 < -1 2/5
The solution for the equation m + ( ¼ ) < -1 ( 2/5 ) is m < -1 ( 13/20 )
Given,
The equation: m + ( ¼ ) < -1 ( 2/5 )
We have to solve this:
m + ( ¼ ) < -1 ( 2/5 )
Subtract (1/4) from both sides:
That is,
m + ( ¼ ) – ( ¼ ) < -1 ( 2/5 ) – ( ¼ )
Here, ( ¼ ) – ( ¼ ) becomes 0.
Then,
m + 0 < -1 ( 2/5 ) – ( ¼ )
m < -1 ( 18-5 / 20 )
m < -1 ( 13/20 )
That is, the solution for the equation m + ( ¼ ) < -1 ( 2/5 ) is m < -1 ( 13/20 )
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Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree.
Answer:
Approximately [tex]36^{\circ}[/tex], assuming that the tree is upright.
Step-by-step explanation:
Refer to the diagram attached. The upright tree and its shadow are in a right triangle. In this right triangle, the angle of elevation of the sun would be the angle adjacent to the shadow of this tree. At the same time, this angle would be opposite to the side representing the tree. Thus, the tangent of this angle could be represented as:
[tex]\begin{aligned}\tan(\text{angle of elevation}) &= \frac{\text{opposite}}{\text{adjacent}} \\ &= \frac{10\; \text{yard}}{14\; \text{yard}} \\ &= \frac{5}{7}\end{aligned}[/tex].
Take the arctangent of this value to find the measure of this angle:
[tex]\begin{aligned} (\text{angle of elevation}) &= \arctan(\tan(\text{angle of elevation})) \\ &= \arctan\left(\frac{5}{7}\right) \\ &\approx 0.620 \times \frac{360^{\circ}}{2\, \pi} \\ &\approx 36^{\circ}\end{aligned}[/tex].
Thus, the angle of elevation of the sun at this moment would be approximately [tex]36^{\circ}[/tex].
In ALMN, l= 97 cm, m = 52 cm and ZN=39°. Find ZL, to the nearest degree.
Answer: In ALMN, l= 97 cm,
m = 52 cm,
ZN=39°,
ZL= 66°
Step-by-step explanation:
Given data,
In ALMN, l= 97 cm, m = 52 cm and ZN=39°.
The law of cosines can be used to find the missing side.
n² = m² +n² -2ml·cos(L)
n² = [tex]52^{2}[/tex] + [tex]97^{2}[/tex] - 2(52)(97). cos (39°)
n² = 9409 + 2704 - 2(52)(97). cos (39°)
n² = 12113 - 2(52)(97). cos (39°)
n² = 12113 - 10088 cos (39°) (eq - 1)
So, that cos (39°) = 0.777
Substitute cos (39°) value in this equation 1
So,
We can write,
n² = 12113 - 10088* 0.777
n² = 12113 - 7838.3
n² = 4274.62
n = √4274.62
n = 65.38 ≅ 66
Therefore,
In ALMN, l= 97 cm,
m = 52 cm,
ZN=39°,
ZL= 66°
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Solve the inequality.
-12
The solution is:
Graph the solution.
Answer:
13
Step-by-step explanation:
salu grt it
Airlines limit the size of carry-on luggage, so that the sum of the length, width, and height of a piece of luggage cannot exceed 55 inches. A passenger has a box with a base which measures 15 inches by 20 inches. Which inequality represents the possible height (h) of the box, so that the airline will allow it to be carried on the plane?
The inequality that represents the possible height (h) of the box is h ≤ 20
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let h represent the height of the box. The base measures 15 inches by 20 inches and the height cannot exceed 55 inches. Hence:
height + length + width ≤ 55
h + 20 + 15 ≤ 55
h ≤ 20
The inequality that represents the possible height (h) of the box is h ≤ 20
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On Saturday, some adults and some children were in a theatre. AC
The ratio of the number of adults to the number of children was 4:3.
Each person had a seat in the Circle or had a seat in the Stalls.
of the children had seats in the Stalls.
114 children had seats in the Circle.
13
There are exactly 1100 seats in the theatre.
On this Saturday, were there people on more than 70% of the seats?
You must show how you get your answer.
If 114 kids were seated in the stall, just 21% of the seats were filled.
If 117 youngsters were seated in the circles, then yes, more than 60% of the seats were filled.
A third of the kids were seated in the stalls.
if there are 117 kids who can fit in the stalls.
Given that 3/4 of the children had chairs in the stall and x children, we have:
3/4*x = 3/4x.
There were 117 kids in the 3/4 portion.
= 3/4 of x = 117
= 3x/4 = 117
3x =117 x 4
3x = 468
x = 156 kids overall.
39 kids sat in the circle, compared to 117 in the stalls.
The number of adults to children was 5:2, which equals 5+2 to 7.
Use the ratio of children to represent as y and the total number of individuals to determine. So, here we are
2/7 of y = 156
2y/7 = 156
2y = 156x7
2y= 1092
y = 546
In all, 546 persons are present, and 546 of the 2600 seats are occupied by them. We now have:
546 / 2600 = 0.21 = 21%.
If there were 117 kids in the circle, there would be 117 x 4 = 468 kids (total number of children)
Consequently, considering the ratio: 2/7 of y = 468 = 2y = 468x7
2y = 3276
y= 1,638
There are therefore 1,638 individuals present in all, and 1,638 of the 2600 seats are occupied by them. We now have:
1638 / 2600 = 0.63 = 63%.
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The frequency table represents the job status of a number of high school students. A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for job with entries 12, 38, 50. The third column is labeled not looking for a job with entries 28, 72, 100. The fourth column is labeled total with entries 40, 110, 150. Which shows the conditional relative frequency table by column? A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for a job with entries 0.3, nearly equal to 0.33, 1.0. The third column is labeled not looking for job with entries 0.7, nearly equal to 0.65, 1.0. the fourth column is labeled total with entries nearly equal to 0.27, nearly equal to 0.73, 1.0. A 4-column table with 3 rows titled job status. The first column is blank with entries currently employed, not currently employed, total. The second column is labeled Looking for a job with entries 0.12, 0.38, 050. The third column is labeled not looking for a job with entries 0.28, 0.72, 1.00. The fourth column is labeled total with entries 0.4, 1.1, 1.5. A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for a job with entries 0.24, 0.76, 1.0. The third column is labeled not looking for a job with entries 0.28, 0.72, 1.0. The fourth column is labeled total with entries nearly equal to 0.27, nearly equal to 0.73, 1.0. A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for job with entries 0.08, nearly equal to 0.25, nearly equal to 0.33. The third column is labeled not looking for a job with entries nearly equal to 0.19, 0.48, nearly equal to 0.67.
The relative frequency table is given at the end of the question.
What is a relative frequency?A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.
For this problem, we have that out of 150 people, 40 and currently employed and 110 are not, hence the relative frequencies are given as follows:
Currently employed: 40/150 = 0.27.Not currently employed: 0.73.Of those 40 currently employed, 12 are looking for jobs and 28 are not, hence the relative frequencies are given as follows:
Looking for a job: 12/150 = 0.08.Not looking for a job: 28/150= 0.19.Of those 110 that are not currently employed, 38 are are looking for jobs and 72 are not, hence the relative frequencies are given as follows:
Looking for a job: 38/150 = 0.35.Not looking for a job: 72/150 = 0.48.Hence the frequency table is given at the end of the question.
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please help with math problem.
The cups of water needed to fill one container is 1 1/8. The expression is 1 1/8 cups
The container of water needed to fill one cup is 8/9. The division expression is 2/3 ÷ 3/4
How much cup and container is needed?A fraction is a non-integer that is made up of a numerator and a denominator that is separated by a line. An example of a fraction is 1/2. 1 is the numerator and 2 is the denominator.
In order to determine the cups of water that is needed to fill one container, divide the fraction of a cup that is needed to fill 2/3 of the container by 2/3.
Water needed to fill one container = 3/4 ÷ 2/3
3/4 x 3/2 = 9/8 = 1 1/8 cups
In order to determine the container that is needed to fill one cup, divide the fraction of a container that is needed to fill 2/3 of the container by 3/4.
Water needed to fill one cup = 2/3 ÷ 3/4
2/3 x 4/3 = 8/9
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Given f(x) = -5x – 3, find ƒ(-6).
hi
f(x) = -5x – 3,
then f(-6) = -5 (-6) -3
= -11 -3
= -14
To find a baseball pitcher's earned run average (ERA), you can use the formula El=9r, in which E
represents ERA, I represents the number of Innings pitched, and r represents the number of earned runs allowed.
Solve the equation for E. What is a pitcher's ERA if he allows 15 earned runs in 36 innings pitched?
If necessary, round your answer to the nearest hundredth.
The equation for E is E= _____?
If a pitcher allows 15 earned runs in 36 innings, then the ERA= ____?
The value of the ERA is the 3.75.
According to the statement
We have to find that the value of the ERA.
So, For this purpose, we know that the
ERA is the number which represents the average number of earned runs given up by the pitcher per nine innings.
From the given information:
First, we are given the formula E * i = 9 * r.
Second, we are asked to resolve for E. If i doesn't equal zero, then we are able to divide both side of this equation by i. (Note that i = the quantity of innings pitched, which isn't zero.) We then have the equation E = (9 * r) / i.
Third, we are given some numerical values for our variables, and asked to use this equation to unravel for E.
Substituting r = 15 (earned runs allowed) and that i = 36 (innings pitched) into the equation and that we have
E = (9 * 15) / 36 = 3.75 (rounded to the closest hundredth)
So, The value of the ERA is the 3.75.
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need someone to help me quick please
Answer:
the answer is no relation
