In the table below, replace a with a value that will make the relation a function: 1 3 5 b(n) 9 8 9 11 a

There is no statistical evidence of a prolonged lifetime of the stents.

Given data,

n (sample size) = 100

X (sample mean) = 9.3

s (sample standard deviation) = 3.8

Next, we need to define the null hypothesis and alternative hypothesis

Null hypothesis

[tex]H_{o}[/tex] : u (mu) = 8.7

Alternative hyptohesis

[tex]H_{o}[/tex] : u (mu) > 8.7

Next, we need to do hypothesis testing to get the claim about a population mean is tested under the null and the alternative hypotheses by using t-test and p-value.

t-test is a sampling test statistic and used when the population standard deviation is unknown.

the t-test can be calculated as follows:

= [tex]\frac{X-u}{s/\sqrt{n} }[/tex]

= [tex]\frac{9.3-8.7}{3.8/\sqrt{100} }[/tex]

= 1.578

Next, we need to calculate the p-value using Microsoft excel function. The p-value helps decide whether to reject the null hypothesis.

Enter the function below in excel to calculate p-value:

=TDIST(1.578,40-1,1)

= 0.061322.

The p-values is greater than the common threshold ( p<0.05), which means We can conclude that there is no statistical evidence of a prolonged lifetime of the stents.

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The excise tax on 1 gallon of gasoline = 18.2 cents

You will buy 18.5 gallons

We need to find the excise tax you should pay

At first let us change the cent to dollar

1 cent = 1/100 dollars

18.2 cents = 18.2 * 1/100 = 0.182 dollars

Now you will buy 18.5 gallons

You will pay = 18.5 * 0.182 = 3.367 Dollars

The state excise tax = $3.367

Round the number to the nearest cent, then it will be $3.37

Answer:

$2.90

Step-by-step explanation:

87 cents / 3 packs = 29 cents per pack

$0.29 × 10 = $2.90

Solve for y

Subtract 4x both sides

Divide by 3 into both sides

Answer:

The equation of the line is that passes through (1,4) and (3, -6) is

y = -5x + 9

First, write the equation in slope-intercept form:

y = mx + b

(the m is the slope, and b is the y-intercept)

Now, Lets find the slope(m) of the line by using the formula:

y2-y1/x2-x1

(-6 - 4)/ (3 - 1) = -10/2 = -5

Next, find the y-intercept (b) by using the slope-intercept form equation and substituting -5 in for m and one of the ordered pairs in for x and y:

4 = (-5)(1) + b

b = 9

-OR-

-6 = (-5)(3) + b

b = -6 + 15 = 9

b = 9

Now, we can write the full equation of the line:

y = -5x + 9 is the answer

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the given expression is,

16x = 156.8

x = 156.8/16

x = 9.8

thus, the answer is 9.8

Answer:

x = 9.8

Step-by-step explanation:

16x=156.8

x = 156.8/16

x = 9.8

Answer

Option 1 is correct.

The graph could easily be the graph of a linear function.

Explanation

The points (2, 5) and (8, 5) can be seen to lie on the same line of y = 5

So, we can conclude that the graph could be a simple linear function, or a curve that passes this point twice.

So, option A is the only correct option here.

Hope this Helps!!!

From the given information, we know that the expression that models the population of amoebas with respect to time is:

Where x is the number of hours. by replacing 9 for x, we can find the population after 9 hours, like this:

Then, the population of amoebas after 9 hours is 5832.

The equation of the line that passes through the point (-4, -5) and is parallel to y = 1/2x -4 is y = 1/2x - 3

From the question, we are to determine the equation of the line that passes through the given point and is parallel to the given equation.

The given point is (-4, -5)

The given equation is y = 1/2x - 4

NOTE: If two lines are parallel, then their slopes are equal

Now, we will determine the slope of the given line '

y = 1/2x - 4

Compare to the general form of an equation of a straight line

y = mx + b

Where m is the slope

and b is the y-intercept

Therefore, m = 1/2

That is, the slope of the line is 1/2

Now, we will determine the equation of the line that has a slope of 1/2 and that passes through the point (-4, -5)

Using the point-slope form of the equation of a straight line

y - y₁ = m(x - x₁)

Then,

y - (-5) = 1/2(x - (-4))

y + 5 = 1/2(x + 4)

y + 5 = 1/2x + 2

y = 1/2x + 2 - 5

y = 1/2x -3

Hence, the equation of the line is y = 1/2x - 3

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We will have that Sarah's function is the correct one, since each hour she will get $9, then when we multiply will give us the amount of money she makes in the number of hours.

H = 9h

Answer:

24:14

Step-by-step explanation:

Age and you can also use weight too

you can easily group people by their age and weight but not by eye color

example

age people

5 - 10 14

10 - 15 5

the table above shows that we have 14 people within the range of 5 to 10 years

and likewise the weight of the people can serve the same purpose

Answer: 8.953333333.

Step-by-step explanation: All I know is that a negative divided (or times) a negative is always a positive.

The result of each part is

Part 1

3.8% of 25 is 0.95

Part 2

0.2% of 50 is 0.1

Part 3

180.5% of 99 is 178.695

Part 1

The given expression is

3.8% of 25

Here we have to find the 3.8 percentage of 25

Then the mathematical expression will be

25 × 3.8% = 25 × 3.8/100

= 25 × 0.038

= 0.95

Part 2

The given expression is

0.2% of 50

The mathematical expression will be

50 × 0.2% = 50 × 0.2/100

= 50 × 0.002

= 0.1

Part 3

The expression is

180.5% of 99

The mathematical expression will be

99 × 180.5% = 99 × 180.5/100

= 99 × 1.805

= 178.695

Hence, the result of each part is

Part 1

3.8% of 25 is 0.95

Part 2

0.2% of 50 is 0.1

Part 3

180.5% of 99 is 178.695

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Given the function:

To graph the given function, first, we will graph the parent function [ cot x]

the function [cot x] has a period of π and has an x-intercept at x = π/2

then we will make a shift to the left side by (π/6)

the graph of the function will be as shown in the following picture:

As shown, the red dot graph is the function [cot x]

and the blue graph is the given function f(x)

According to the diagram, we can conclude:

If ED is the midsegment of triangle ABC, then that means that the points E and D are the midpoints of segments AC and AB since the midsegment is found by joining the midpoints of a triangle. Since E and D are midpoints then:

Also, by the midsegments theorem we have:

Also, since segments ED and BC are parallel, that means that:

On solving the equation [tex]v=u+at[/tex] for t the result will be [tex]t=\frac{v-u}{a}[/tex].

How to solve any mathematical equation?

1. Open all brackets by applying the distibutive property.

2. Add the same number on the both sides.

3. Subtract the same number on the both sides.

4. Multiply with the same number on the both sides.

5. Divide with the same number on the both sides.

Consider the equqtion.

[tex]v=u+at[/tex]

Subtact [tex]u[/tex] from both the sides.

[tex]v-u=u+at-u\\v-u=at[/tex]

Now, divide both the sides by [tex]a[/tex].

[tex](v-u)/a=at/a\\(v-u)/a=t\\t=(v-u)/a[/tex]

Hence, on solving the equation [tex]v=u+at[/tex] for t the result will be [tex]t=\frac{v-u}{a}[/tex].

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Solution

We have

square will cancel out the square root

Option A

Given

A = (3.5, 2.2)

B = (1.5, -4.8)

Procedure

A midpoint is a point on a line segment that divides the segment into two equal segments.

Answer: $1.33

This can be worked out as a simple algebra problem: 15x=20, x being 1 pizza dough. In order to find the value of one pizza dough (x) you need to isolate it. To do that, divide 15 from both sides and you'll be left with x=1.33

15x=20

/15   /15

x=1.33

Answer:

length = 12 miles

width = 6 miles

Step-by-step explanation:

        length = x miles

       width = (x - 6) miles

  Area of rectangle = 72 square miles

         length * width = 72

           x * (x - 6)        = 72

          x*x - 6*x          = 72

             x² - 6x - 72 = 0

Sum = -6

Product = -72

Factors = 6 , (-12)         { 6 + (-12) = -6 and 6*(-12) =-72 }

Rewrite the middle term using the factors.

x² + 6x - 12x - 72 = 0

x(x + 6) -12(x + 6) =0

(x + 6)(x - 12) = 0

    {x + 6 = 0 is rejected as length will not have negative value}

x - 12 = 0

     [tex]\sf \boxed{\bf x = 12 \ miles}[/tex]

length = 12 miles

Width = 12 - 6 = 6 miles

Answer:

X = 9
Landyn is 9 and his brother is 14

Step-by-step explanation:

X + Y = 23
Y = X + 5
X + X + 5 = 23
2x + 5 + 23

     - 5   - 5  

2x / 2 = 18 / 2

Simplified = 9 / 1
Y = 9 + 5
Y = 14

The rules of the transformations using the translation notation are;

11) [tex]T_{(2, \,-1)}[/tex]

12) [tex]T_{(-5, \,2)}[/tex]

13) [tex]T_{(-1, \,3)}[/tex]

14) [tex]T_{(0, \,-1)}[/tex]

15) [tex]T_{(3, \,4)}[/tex]

16) [tex]T_{(-3, \,1)}[/tex]

17)  [tex]T_{(1, \,0)}[/tex]

18) [tex]T_{(6, \,-5)}[/tex]

19) [tex]T_{(4, \,0)}[/tex]

20) [tex]T_{(2, \,4)}[/tex]

21) [tex]T_{(1, \,-5)}[/tex]

22) [tex]T_{(5, \,-1)}[/tex]

23) [tex]T_{(0, \,-1)}[/tex]

24) [tex]T_{(-2, \,-1)}[/tex]

25) [tex]T_{(-3, \,-2)}[/tex]

A translation transformation is a rigid transformation in which the location of the image obtained from the pre-image is different, but the dimensions are the same.

11) The transformation is similar to a rigid transformation

The change in coordinate is from (2, 2), to (4, 1), which is a translation 2 units to the right and -1 unit down

12) The shape is preserved and the length of the sides are also preserved, therefore, the transformation is a rigid transformation, with a change from (5, 3) to (0, 5), which is a translation 5 units to the left  and 2 units up.

13) The change in the coordinates from the pre-image to the image are from V(-3, 2) to V(-4, 5), which is a transformation of 1 unit to the left and 3 units up

14) The coordinates of a point on the pre-image is T(-5, 2), and the coordinates of the corresponding point on the image is T'(-5, 1), which is a translation of one unit downwards, [tex]T_{(0, \,-1)}[/tex]

15) A point on the pre-image is T(-3, -1), the corresponding point on the image is T'(0, 3), which indicates that the rule for the transformation is a translation of 3 units to the right and a vertical translation of 4 units upwards

16) The difference between the x and y values are;

Δx = 0 - 3 = -3

Δy = -3 - (-4) = 1

The transformation is therefore of the form [tex]T_{(-3, \,1)}[/tex], which is a translation of 3 units to the left and 1 unit upwards

17) The change in the x and y values are;

Δx = -2 - (-3) = 1

Δy = -3 - (-3) = 0

The rule of the transformation is therefore of the form [tex]T_{(1, \,0)}[/tex], which is a translation one unit to the right.

18) The change in the x and y values of the transformation are;

Δx = 1 - (-5) = 6

Δy = -4 - 1 = -5

The rule of the transformation is therefore, [tex]T_{(6, \,-5)}[/tex], which is a translation of 6 units to the right and 5 units down

19) The transformation of J(-5, 3), K(-3, 5), L(0, 1) to J'(-1, 3), K'(1, 5), L'($, 1) is a transformation of the form [tex]T_{(4, \,0)}[/tex] which is a horizontal translation 4 units to the right

20) H(-4, -3), I(-5, 0), J(-3, 0), K(-2, 1) to H'(-2, 1), 'I(-3, 4), J'(-1, 4), K'(0, 5) The transformation rule is [tex]T_{(2, \,4)}[/tex], which is a translation 2 units to the right and 3 units up

21) E(0, 1), F(-1, 5), G(0, 5), H(3, 2), to E'(1, -4), F'(0, 0), G'(1, 0), H'(4, -3), which is a transformation with the rule, [tex]T_{(1, \,-5)}[/tex], which is a translation one unit to the right and five units down

22) B(-4, -2), C(-3, 3), D(-2, 1) to B'(1, -3), C'(2, 2), D'(3, 0), which is a transformation of the form [tex]T_{(5, \,-1)}[/tex], which is a translation of 5 units to the right and 1 units down

23) I(2, 1), H(4, 4), G(5, 0) to  I'(2, 0), H'(4, 3), G'(5, -1), which is a transformation with the rule [tex]T_{(0, \,-1)}[/tex], which is a translation of one unit down

24) X(1, -4) W(3, 0), V(3, -4) to X(3, -5) W(5, -1), V(5, -5), which is a transformation with the rule, [tex]T_{(-2, \,-1)}[/tex], which is a translation of 2 units to the left and 1 units down

25) G(1, -1), F(2, 3), E(4, 2), D(4, -3) to G'(-2, -3), F'(-1, 1), E'(1, 0), D'(1, -5) which is a transformation with the rule, [tex]T_{(-3, \,-2)}[/tex], which is a translation of 3 units to the left and 2 units down

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Cost of 3 bus tickets is $ 192 and cost of 4 train tickets is $ 328.

Explain the use of multiplication?

The process of finding the sum of two or more numbers is known as multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. We can rapidly determine the total number of things by multiplying.

When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group.

It is given ,

Cost of each  bus ticket = $ 64

Cost of each train ticket = $ 82

Number of bus ticket = 3

Number of train ticket = 4

Total cost of bus ticket = 3 × 64 = $ 192

Total cost of train ticket = 4 × 82 =  $ 328

Hence , cost of 3 bus tickets is $ 192 and cost of 4 train tickets is $ 328.

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Solution

Total cards in a deck = 52

Total Queens = 4

Total King = 4

Total Ace = 4

P(Queen, King, or Ace). =

The answer is 3/13

Answer:

x = 3

y = -1

Step-by-step explanation:

x-y=4 [1]

2x+y=5 [2]

rearrange [1] and label it [3]

x = 4 + y [3]

substitute [3] into [2]

2(4 + y) + y = 5

8 + 3y = 5

3y = -3

y = -1

substitute y = -1 into [1]

x - (-1) = 4

x = 3

The volume of a sphere is (4/3)(Pi)(r^3)

If the ball has a diameter of 27 cm, the radius would be 27/2 = 13.5 cm

Unsing the formula:

V = (4/3)(3.1416)(13.5)^3 = (4/3)(3.1416)(2460.375) = 10306.0188

Answer: Volume is 10,306.0188 cm^3

Answer:

x = 10

Step-by-step explanation:

2(2x-14) = x+2

4x - 28 = x + 2

3x = 30

x = 10

The function describes the motorboat's distance from the shore

y = -4x+50

Given,

In the question:

A motorboat moves across a lake as a constant speed. when it begins, it is 50 km from the shore

After 9 minutes, it is 14 km from the shore.

So, The rate of change =

                 =   [tex]\frac{Final Distance - initial distance}{time} \\\\\frac{14-50}{9} = -4[/tex]

Negative sign shows that there is decrease in distance per minute

The rate of change of distance is 4 km / minutes

General equation : y = mx+ c

Where m is the slope and c is the constant

Substitute the values in the equation :

y= -4x +50

Where y is the final distance and x is the minutes

So, Option C is true

Hence, The function describes the motorboat's distance from the shore

y = -4x + 50.

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