Data were collected on the distance a baseball will travel when hit by a baseball bat at a certain speed. The speed, s, is measured in miles per hour, and distance, y, is
measured in yards. The line of fit is given by ý = 3.98 +53.59s.
If the ball travels for a duration of 5 seconds, what is the predicted distance of the ball?
O 267.95 feet
O271.93 feet
O 283.87 feet
O287.85 feet

Answer:

87

Step-by-step explanation:

the whole sequence would be 15, 24, 33, 42, 51, 60, 69, 78, 87

Answer:

Step-by-step explanation:

Given,

The ratio of boys to girls in Fiona's class is 1:3

The total student in the class is 24

To find,

how many students are girls

Solution,

It is clear that the total number of boys and girls is 24

i.e., boys + girls=24 ------ (equation 1)

Let the ratio be in the terms of x

Consider boys ratio as x

And the girl's ratio as 3x

Now as per the equation 1,

x + 3x= 24

4x= 24

x= 6

Hence, Boys (x)= 6

And Girls (3x)= 3× (6)= 18

You can verify it by adding 6+18= 24

Answer is 6

9 - 6 = 3

The difference of a number and 9 means to subtract said number from 9.

The side length of the triangle Elizabeth drew cannot form a right triangle.

A right triangle is a triangle that has one of its angle as 90 degrees.

The sides of a right triangles are hypotenuse side, adjacent side and the opposite side. This is base on the angle position.

Right triangle obeys Pythagoras's theorem.

a² + b² = c²

where

Therefore, let's test if the labelled side of the triangle Elizabeth drew is a right triangle.  We will use Pythagoras theorem to confirm it

5² + 8² = 14²

25 + 64 = 196

Therefore,

89 ≠ 196

Therefore, the side length cannot form a right triangle

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We have to find the equation of the line that passes through the points (-1,5) and (0,1). We will write the equation in the slope-intercept form, which is given by:

Where m represents the slope of the function, and b the y-intercept. We will find the slope, and then the y-intercept.

1. Finding the slope

For finding the slope we will use the formula:

where (x₁,y₁) and (x₂,y₂) are two points that passes through the line. In this case, the points (-1,5) and (0,1).

Replacing, we obtain:

Thus, the slope is -4.

2. Finding the y-intercept

For doing this step, we want to know the value of the function when x equals zero. But, as we have that the line passes through (0,1), this means that this value will be 1. This is, the y-intercept is 1.

3. Putting all together

Now, we just have to put the values obtained in the slope-intercept form:

And this means that the equation of the line that passes through (-1,5) and (0,1) is y=-4x+1.

The formula that most accurately captures the dilatation that Triangle ABC underwent to produce A'B'C will be:

(x, y) → (1/2x, 1/2y)

Detailed explanation?

A triangle's vertices are given.

A(-2, -4) (-2, -4)

B(2, -4) (2, -4)

C(-8, -4) (-8, -4)

The vertices of an image triangle should be after the dilatation

A' (-1, -2) (-1, -2)

B '(1, -2) (1, -2)

C' (-4, -2) (-4, -2)

If we look attentively, we can see that the vertices of the image triangle, A'B'C', make up half of the original triangle ABC.

For example, (x, y) (1/2x, 1/2y)

verification

A(-2, -4) → A'(-2/2, -4/2) = A'(-1, -2) (-1, -2)

B(2, -4) → B'(2/2, -4/2) = B'(1, -2) (1, -2)

C(-8, -4) → C'(-8/2, -4/2) = C'(-4, -2) (-4, -2)

As a result, it is confirmed, and we come to the conclusion that the rule that best captures the dilatation that Triangle ABC underwent to form A'B'C' will be:

(x, y) → (1/2x, 1/2y)

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Using the arithmetic progression, If a theatre has 30 rows of seats there are 22 seats in the first row,26 in the second row, 30 in the third row, then the total number of people that the theatre hold is 2400

The total number of rows = 30

Number of seats in the first row = 22

Number of seats in the second row = 26

Number of seats in the third row = 30

Common difference= Second term - first term

= 26-22

= 4

The given sequence is in arithmetic progression

Sum of n terms = [tex]\frac{n}{2}[2a+(n-1)d][/tex]

Substitute the values in the equation

= [tex]\frac{30}{2}[2(22)+(30-1)4][/tex]

= 15[44+29×4]

= 15[44+116]

= 15×160

= 2400

Hence, using the arithmetic progression, if a theatre has 30 rows of seats  and there are 22 seats in the first row,26 in the second row, 30 in the third row, then the total number of people that the theatre hold is 2400

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The given expression is :

To simplify the expression for x :

Add 5 on both side :

Divide the expression by 4 on both side :

Thus : x ≥ 3

The graph is :

Since x is greater than or equal to 3

So, it is closed on 3

Answer :

The graph has a closed circle on 3 and is shaded to the right of the origin

4/15 = 3.75

10/13 = 1.3    

you have to divide it from its higher number or you'll get something like this: 0.7692307692307692 but if it helps it = 0.00205128205

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The function exists a Power function. The power of function is 3 and the constant variation is - 1/3

Any function where y = x n, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions. A few other power functions are y = x³, y = 1/x, and y = x squared.

A parameter function used in statistical testing that represents the likelihood of rejecting the null hypothesis for a given value of the parameter, assuming that value is true.

Therefore, the power of function is 3 and the constant variation is - 1/3.

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Answer:

P(B) = 0,35

Step-by-step explanation:

P(B) = P(A and B) divided by P(A)

If four friends have $525 that they want to share equally and they divide the money so that each friend gets a $100 bill, then next step will be divide the remaining money so that each friend gets a $31.25

Total money the have = $525

they divide the money so that each friend gets a $100 bill

The amount of money they split equally = 4×100

= $400

Remaining money = 525-400

= $125

Split the remaining money into 4 = 125/4

= $31.25

Hence, If four friends have $525 that they want to share equally and they divide the money so that each friend gets a $100 bill, then next step will be divide the remaining money equally so that each friend gets a $31.25

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The slope of the graph that models the amount Sarah owed after a given number of x months, represents the monthly payment Sarah makes to repay the loan

Monthly payment on a loan is the payment made each month within the period specified in the loan, to repay the loan and the interest on the loan.

The given parameters of the graph are;

Information on the graph = The amount owed for a number of x months

Taking the y–axis (Vertical axis) of the graph as specifying the amount owed given in Dollars, and the x–axis as the number of months of payment, we have;

[tex] \displaystyle{Slope = \frac{\Delta y}{\Delta x}} [/tex]

Where;

∆y = Change in the amount Sarah owes

∆x = Change in the time

Which gives;

[tex] \displaystyle{Slope = \frac{Change\: in\: the\: amount \:owed}{Change\: in\: time }}[/tex]

Whereby the graph is a straight line graph, we have;

The slope = Constant

Therefore, the change in the amount owed over a given time frame such a month, is constant

Which gives;

The slope represents the amount by which the Sarah's student loan changes each month, which is equivalent to and therefore;

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Answer: 25 ft

Step-by-step explanation:

Let the shortest side be s. Then, the other two sides are 2s and s+21.

[tex]s+2s+s+21=121\\\\4s+21=121\\\\4s=100\\\\s=25[/tex]

Answer:

B. Diagonals that are congruent

The perimeter is the sum of all the sides of a geometric figure, so

To resolve this inequality you can first subtract 8 from both sides

Then you divide by 4 on both sides of the inequality

Therefore, for the perimeter of the rectangle to be less than 120, its shortest side must measure less than 28.

Given:

Let's solve using law of indices below:

Using the same method, we have:

ANSWER:

Resting body temperatures are normally distributed with an average of 98.25 degrees

Fahrenheit and a standard deviation of 0.73 degrees Fahrenheit. A nurse examines 40 patients in one hour. What is the probability the average temperature of the 40 patients is between 98.0 degrees Fahrenheit and 98.50 degrees Fahrenheit? (Round to the hundredths)



A)0.97

B)0.11542313

C)0.99

D)Sample size is not larger than 40 so we cannot compute probability

step 1

Find the z-scores

For x=98.0 degrees

z=(98-98.25)/0.73 --------> z=-0.3425

For x=98.50

z=(98.50-98.25)/0.73 ------> z=0.3425

using a Z-score Calculator

we have that

P=0.26803

step 2

we have that

Airthemetic Sequence : arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

It express as :

In the given question the 88 term is ( 25)

Substitute the value in the expression of n terms

In the given Airthmetic sequence the constant difference, d = 4

Now for the position of term 8

for n= 5 terms is 8

Now for the term of position 8:

So, the term with position 8 is 20

Now for the position of term 36 :

Thus, for n = 10, an = 36

Now, for the term of position 19

Thus at n = 19 the term i 64

Answer:

0.0475

Step-by-step explanation:

Population of Planet Eenie is  1.4 × [tex]10^{3}[/tex] times greater than the population of Planet Meenie.

Two planets named Eenie and Meenie.

Population of  Planet Eenie = 72,980,001

Population of  Planet Meenie =  54,908

We need to find how many times greater is the population of Planet

Eenie than the population of Planet Meenie. So, we need to follow the steps written below:

( Population of  Planet Eenie / Population of  Planet Meenie )

= ( 72,980,001 / 54,908 )

= 1329.1323

= 1.33 × [tex]10^{3}[/tex]

This calculated value is near option 2 i.e., 1.4 × [tex]10^{3}[/tex]. So,  1.4 × [tex]10^{3}[/tex] is the correct option.

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The savings plan balance (future value) after 3 years with a 7% APR and monthly payments of $100 is $3,993.01.

The future value is the present value or cash flows compounded at an interest rate for a period.

The future value can be computed using an online finance calculator.

N (# of periods) = 36 months

I/Y (Interest per year) = 7%

PV (Present Value) = $0

PMT (Periodic Payment) = $100

Results:

FV = $3,993.01

Sum of all periodic payments = $3,600 ($100 x 36)

Total Interest = $393.01

Thus, at the end of 3 years, the saving plan balance grew to a future value of $3,993.01.

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By using a trigonometric identity, we will see that the value of sin(x/2) is:sin(x/2) =  ±√39/√56 = ± 0.834

Here we need to use the identity: (sin(x/2))^2 = (1 - cos(x))/2

So, we know that:

cos(x) = -11/28

Then:

(1 - cos(x)) = 1 + 11/28 = 28/28 + 11/28 = 39/28

Replacing the identity that we get:

(sin(x/2))^2 = (1 - cos(x))/2 ]= (39/28)/2 = (39/56)

Now we can apply the square root in both sides, so we will get:

sin(x/2) = ±√(39/56)=  ±√39/√56 = ± 0.834

So, the value of sin(x/2) can be either 0.834 or -0.834.

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Option b. The number of girls is neither significantly low nor significantly high.

How is the subjective judgement given?

Total number of births selected= 600

Half of the total number = 300

Number of girls = 309

What is subjective judgement ?

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Conclusions that can be made about the line in the table include:

The slope of a line is found by the formula:

= Change in y / Change in x

Two points from the table:

(-6, -7) (2, -3)

Slope is:
= (-3 - (-7)) / 2 - (-6))

= 4 / 8

= 1/2

The y-intercept is:

y = Slope (x) + y-intercept

-3 = 2(1/2) + y-intercept

y-intercept  = -3 - 1

y-intercept  = -4

Points on the line as shown on the table:

(-2, -5) and (8,0)

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The given expression xy = yx represents the cumulative property of multiplication.

If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics. Numerous binary operations share this essential characteristic, and numerous mathematical arguments rely on it.

The given expression is xy = yx.

The expression xy = yx is representing the cumulative property of multiplication. According to this property, the value of the expression will remain the same after the order is changed.

Let x = 5 and y = 10. Now verify the cumulative property of multiplication.

xy = yx

5 x 10 = 10 x 5

50 = 50

Therefore, the given expression xy = yx represents the cumulative property of multiplication.

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Answer:

para hacer la repuesta xd

The perimeter of the hexagon ABCDEF is 36.01.

Given,

The hexagon ABCDEF

We have given the points:

A(-6, 2), B(1, 5), C(6, 5), D(6, -1), E(1, -3), F(-6, -3)

We have to find the perimeter of hexagon.

Perimeter of hexagon = AB + BC + CD + DE + EF + FA

Now,

Distance formula is as [tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

So,

A(-6, 2), B(1, 5) : x₁ = 1, x₂ = -6, y₁ = 2, y₂ = 5

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(1-(-6))^{2} +(5-2)^{2} }[/tex]

=[tex]\sqrt{7^{2} +3^{2} }[/tex]

= [tex]\sqrt{49+9}[/tex]

= √58

= 7.62

B(1, 5), C(6, 5) : x₁ = 1, x₂ = 6, y₁ = 5, y₂ = 5

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(6-1)^{2}+(5-5)^{2} }[/tex]

= √5²

= 5

C(6, 5), D(6, -1) : x₁ = 6, x₂ = 6, y₁ = 5, y₂ = -1

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(6-6)^{2}+(-1-5)^{2} }[/tex]

= √-6²

= 6

D(6, -1), E(1, -3) : x₁ = 6, x₂ = 1, y₁ = -1, y₂ = -3

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(1-6)^{2}+(-3-(- 1))^{2} }[/tex]

= [tex]\sqrt{(-5)^{2} +(-3+1)^{2} }[/tex]

= [tex]\sqrt{25 + 4}[/tex]

= √29

= 5.39

E(1, -3), F(-6, -3)  : x₁ = 1, x₂ = -6, y₁ = -3, y₂ = -3

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(-6-1)^{2}+(-3-(-3))^{2} }[/tex]

= √-7²

= 7

F(-6, -3), A(-6, 2)  : x₁ = -6, x₂ = -6, y₁ = -3, y₂ = 2

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(-6-(-6))^{2} +(-3-(2))^{2} }[/tex]

= √-5²

= 5

So, we have

AB = 7.62

BC = 5

CD = 6

DE = 5.39

EF = 7

FA = 5

Now,

Perimeter of hexagon = AB + BC + CD + DE + EF + FA

Perimeter of hexagon= 7.62 + 5 + 6 + 5.39 + 7 + 5

Perimeter of hexagon = 36.01

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1)

Let:

N = Total people every week = 207

r = People which needs a ramp = 1:9 = 1/9

So:

Answer: 23 people

2)

Therefore:

3)

The percentage of the people that don't need the ramp will be given by:

Answer: Approximately 89%

4)

5)