4.3.3 Refer to Exercise 4.3.1. Suppose we select a simple random sample of five adults. Use Equation 4.3.2 to find the probability that, in the sample, the number of people who have been told that they have hypertension will be: (a) Zero (b) More than one (c) Between one and three, inclusive (d) Two or fewer (e) Fiv

The correct statement regarding the linear function passing through the coordinates (2, 1), (3,3), (5,7), (6,9) is given as follows:

A. The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

A linear function represents a proportional relationship if it has an intercept of zero.

For the points in this problem, when x increases by one, y increases by two, hence the slope is given as follows:

m = 2/1 = 2.

Hence:

y = 2x + b.

When x = 2, y = 1, hence the intercept b is given as follows:

1 = 2 + b

b = -1.

As the intercept is different of zero, this is not a proportional relationship, and option A is correct.

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Answer:

10.74666666666667 per quart

Step-by-step explanation3 divided 36.24

Answer:

Step-by-step explanation:

[tex]\sf 37-\cfrac{48}{8}[/tex]

Divide numbers ( 48/8 = 6)

Subtract numbers:-

31 is your answer!

___________________

Hope this helps!

Have a great day!

Answer:

Step-by-step explanation:

You want to find a sequence of transformations that will map ∆PZY to ∆RST as shown in the figure.

First of all, we notice the triangles are not the same size. We can find the required dilation factor by finding the ratio of corresponding side lengths.

The first two letters in the triangle designators in the similarity statement are PZ and RS. Since RS is the target size, the dilation factor needs to be ...

  k = RS/PZ

Counting grid squares in the figure, we see this ratio is ...

  k = 2/4 = 1/2

Dilation by a factor of 1/2 will make triangle PZY the same size as ∆RST.

Using the origin as the center of the dilation, all of the points of ∆PZY move to a position that is half their original distance from the origin. The dilated triangle is purple triangle P'Z'Y' in the attached figure.

When we name the vertices of ∆PZY or ∆P'Z'Y', we are naming them in counterclockwise order. The vertices of ∆RST are being named in clockwise order. This reversal of the sequence of vertices is caused by a reflection over a line.

The line of reflection will be halfway between a vertex and its reflected image. For example, reflecting ∆P'Z'Y' across the y-axis give ∆P"Z"Y", as shown in the attached figure. This reflection requires an additional transformation to map P"Z"Y" to RST.

We want to map P' to R, Z' to S, and Y' to T. As it happens the line halfway between these pairs of points is the line y=-x, the dashed line shown in the attachment.

Reflection across the line y = -x will map ∆P'Z'Y' to ∆RST.

This transformation, together with the dilation above, will map the ∆PZY to ∆RST as required.

__

If we use the reflection over the y-axis described above, we are faced with mapping ∆P"Z"Y" to ∆RST. We notice that segment P"Z" points "east" (in the +x direction). We want to map this segment to RS, which points "north" (in the +y direction). That can be accomplished by rotating ∆P"Z"Y" 90° counterclockwise about the origin.

So, another sequence of transformation that will make the required mapping is ...

The order of reflection and rotation is important. The dilation can occur anywhere in the sequence.

Perhaps you realize that we could reflect the figure across the x-axis instead of the y-axis. In that case, the rotation needs to be 90° CW to complete the mapping. That is, yet another sequence could be ...

If you decide you want to do the rotation before the reflection, then the direction of rotation is reversed.

__

Additional comment

Figuring the answer to these mapping problems requires a certain amount of spatial sense. It can help to cut a figure from paper or cardboard and label the vertices. Then you can translate it, rotate it, flip it over, to see what works to get it to the right position. If you have a little trouble with the rotation, you can stick a pin through the center of rotation so your figure keeps its appropriate distance and orientation relative to that center.

Tracing paper and/or transparencies can be helpful for these exercises.

Answer: the bottom two graphs show continuous data

Step-by-step explanation:

Answer:

+ 8

Step-by-step explanation:

This is an arithmetic progression (AP) as there is a common difference between successive terms.

For example, looking at the first two terms,

Difference = 2nd term - 1st term

                  = -11 -(-19)

                  = -11 + 19

                  = +8

To check,

Looking at the second and third terms,

Difference = 3rd term - 2nd term

                  = -3 -(-11)

                  = -3 + 11

                  = +8

Hence, there is a common difference of +8 between consecutive terms, making it an AP.

Answer:

The three statements that are always true regarding this diagram are:

m∠3 + m∠4 + m∠5 = 180°

m∠2 + m∠3 + m∠5 = 180°

m∠2 + m∠3 = m∠6

Here's why:

The sum of the measures of the interior angles of a triangle is always 180°. Therefore, m∠2 + m∠3 + m∠5 = 180°.

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠4 = m∠2 + m∠5, and m∠3 + m∠4 + m∠5 = 180°.

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠6 = m∠2 + m∠3.

The other two statements are not always true. For example, if m∠5 = 100° and m∠3 = 80°, then m∠5 + m∠3 = 180°, but m∠4 ≠ 0°. Similarly, if m∠5 = 100° and m∠6 = 80°, then m∠5 + m∠6 ≠ 180°.

Step-by-step explanation:

Answer:

Q = 3.667

Step-by-step explanation:

The equation to represent the cost of renting the car, given the cost per week and the cost per mile, is y = 42 + 0.25x.

The total cost of renting the car at any given point, would be:

= Cost to rent per week + ( Cost per mile x Number of miles driven)

If we assume the number of miles driven is denoted by x, then the equation becomes :
= 42 + 0. 25 x

If we further take y to be the total cost, the equation then becomes :

y = 42 + 0. 25 x

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The value of π can be written with upper and lower limits as -

3.12 ± 0.062.

Significant figures of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something.

Given is that Helen draws a random circle, she then measures the circumference and diameter. She gets a circumference {C} of 405mm correct to 2 significant figures She gets a diameter {D} of 130mm correct to 2 significant figures.

We can write -

Circumference {C} = (405 ± 2) mm

Diameter {D} = (130 ± 2) mm

The value of π can be calculated as -

π = {C}/{D}

π = (405 ± 2)/(130 ± 2)

Now, divide the numbers without errors first -

405/130

3.12

Now, we will calculate the relative errors in each number -

2/405 = 0.004

2/130 = 0.016

Adding the relative errors -

0.004 + 0.016

0.02

Absolute error = 0.02 x 3.12 = 0.062

The value of π can be written with upper and lower limits as -

3.12 ± 0.062

Therefore, the value of π can be written with upper and lower limits as -

3.12 ± 0.062.

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Answer:

Step-by-step explanation:

if 2021 is 35% decrease of the original number then 2020 is 100% ,and 2021 = 65%.

so, we do the rule of three:

x = (94900 * 100)/ 65

x = 146000

and that is the population in 2020.

Answer:

Hey there! Based on the information provided, it seems that the population of the town decreased by 35% between 2020 and 2021. We can use this information to calculate that in 2021, the population of the town was 65% of its population in 2020. If the population of the town in 2021 was 94,900, then we can use this information to calculate that the population of the town in 2020 was 146,155. Does that make sense?

Answer: 5%

Step-by-step explanation:

Answer:

answer is 10

Step-by-step explanation:

Answer: x = 2.

LN = MP = 2.

Solution in the photo, below.

Answer:

  1400

Step-by-step explanation:

You want to know the number of customers in April if the number in May was 10% lower. That number was 140 fewer.

The problem statement is telling us ...

  April - (10% × April) = April - 140

  10% × April = 140 . . . . . . . . subtract April, multiply by -1

  April = 140/10% = 1400 . . . . divide by 10%

The number of customer visits in April was 1400.

__

Additional comment

The 1400 customers in April fell by 140 to 1260 in may. That's 10% fewer than in April.

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Answer: ( see image )

Step-by-step explanation:

Answer:

Step-by-step explanation:

So, the factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300. [Note: If we divide 300 by 21, we get the quotient and remainder as 14 and 6, respectively. So, 21 is not a factor of 300.

Step-by-step explanation:

the tax rate gives us a ratio of tax amount to value.

this ratio (in our case 1.25/100) is constant for any value.

therefore, when we know how many $1.25 units are in $2000, we know that there are exactly as many $100 units in the value.

in other words, we multiply

1.25/100 × f/f

so that the numerator reaches the total of $2000 of taxes. and then the enumerator gives us the total value.

f = 2000 / 1.25 = 1600

so, we get

1.25/100 × 1600/1600 = 2000 / 160000

so, the value of the condominium is

value = $160,000

Answer:

Basically, LON would be 8z + 112 + 6z - 17

So, our equation will look like this

8z + 112 + 6z - 17 = -1z + 65

Subtract the 6z from the 8z

2z + 112 - 17 = -1z + 65

112 - 17 = 95

2z + 95 = -1z + 65

add the 1z

3z + 95 = 65

subtract the 95

-30

3z = -30

The answer is -10 :)

Step-by-step explanation:

Answer:

LON=75

Step-by-step explanation:

LON= LOM=NOM

-1z+65=8z+112-6z-17

-1z+65=2z+95

3z=-30

z=-10

LON= -1z+65

       = -1(-10)+65

       = 10+65

LON= 75

well, we know that 37.5% have finished it, that leaves unaccounted for 100% - 37.5% = 62.5%.

now, of those 62.5% fellows only 40% have finished only half of it, how many are those?

well, what's 62.5% of 32?   what's 40% of that much?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{62.5\% of 32}}{\left( \cfrac{62.5}{100} \right)32}\implies 20 ~\hfill \stackrel{\textit{40\% of 20}}{\left( \cfrac{40}{100} \right)20}\implies \text{\LARGE 8}[/tex]

The solution is Option A.

The shortest distance is given by the two hypotenuses of the triangles and the distance is X = 7.8 cm

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the shortest distance be represented as X

Let the first triangle be the first face of the rectangular box ΔABC

The length of the triangle AB = 3 cm

The height of the triangle BC = 2 cm

Now ,

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

The measure of AC = √ ( 3² + 2² )

The measure of AC = √13 cm

And , the second triangle is the second face of the rectangular box ΔDEF

The length of the triangle DE = 4 cm

The height of the triangle EF = 2 cm

The measure of DF = √ ( 4² + 2² )

The measure of DF = √18 cm

Now , the shortest distance X = The measure of AC  + measure of DF

Substituting the values in the equation , we get

The shortest distance X = √13 cm + √18 cm

The shortest distance X = 3.60 + 4.24

The shortest distance X = 7.8 cm

Therefore , the value of A is 7.8 cm

Hence , the shortest distance for the ant is 7.8 cm

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Therefore , the solution of the given problem of expression comes out to be  22[tex]z^{8}[/tex].

A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Here,

Given : -20[tex]z^{8}[/tex]+ (-2[tex]z^{8}[/tex])

=> -22[tex]z^{8}[/tex]

So ,

In order to find the solution we add them

Thus ,

simplification of given expression is:

=> - 22[tex]z^{8}[/tex]

Therefore , the solution of the given problem of expression comes out to be  22[tex]z^{8}[/tex].

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Answer:

8RST. That is, N has thousands digit 8, hundreds digit R, tens digits S, and ones

(units) digit T, which means that N = 8000 + 100R + 10S + T. Suppose that the

following conditions are all true:

• The two-digit integer 8R is divisible by 3.

• The three-digit integer 8RS is divisible by 4.

The four-digit integer 8RST is divisible by 5.

The digits of N are not necessarily all different.

The number of possible values for the integer N is

(A) 8

(B) 16

(C) 12

(D) 10

87

(E) 14

Since 8R is divisible by 3, R must be a multiple of 3. The possible values for R are 3, 6, and 9.

Since 8RS is divisible by 4, S must be a multiple of 2. The possible values for S are 0, 2, 4, 6, and 8.

Since 8RST is divisible by 5, T must be 0 or 5.

The possible values for N are therefore:

8000 + 300 + 00 + 0 = 8300

8000 + 600 + 00 + 0 = 8600

8000 + 900 + 00 + 0 = 8900

8000 + 300 + 20 + 0 = 8320

8000 + 600 + 20 + 0 = 8620

8000 + 900 + 20 + 0 = 8920

8000 + 300 + 40 + 0 = 8340

8000 + 600 + 40 + 0 = 8640

8000 + 900 + 40 + 0 = 8940

8000 + 300 + 60 + 0 = 8360

8000 + 600 + 60 + 0 = 8660

8000 + 900 + 60 + 0 = 8960

8000 + 300 + 80 + 0 = 8380

8000 + 600 + 80 + 0 = 8680

8000 + 900 + 80 + 0 = 8980

8000 + 300 + 00 + 5 = 8305

8000 + 600 + 00 + 5 = 8605

8000 + 900 + 00 + 5 = 8905

8000 + 300 + 20 + 5 = 8325

8000 + 600 + 20 + 5 = 8625

8000 + 900 + 20 + 5 = 8925

8000 + 300 + 40 + 5 = 8345

8000 + 600 + 40 + 5 = 8645

8000 + 900 + 40 + 5 = 8945

8000 + 300 + 60 + 5 = 8365

8000 + 600 + 60 + 5 = 8665

8000 + 900 + 60 + 5 = 8965

8000 + 300 + 80 + 5 = 8385

8000 + 600 + 80 + 5 = 8685

8000 + 900 + 80 + 5 = 8985

There are a total of 30 possible values for N. The answer is therefore (E) 14.

Step-by-step explanation:

Answer:

0.27 is the answer

I wish you luck in your assignments.

Answer:

Step-by-step explanation:

0.27

Step-by-step explanation:

please refer to the 3 pages of sketch for details

it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both using principle of inclusion-exclusion we can say 38 students are enrolled in either algebra or physics.

To find how many students are enrolled in either algebra or physics, you can use the principle of inclusion-exclusion, which states that the total number of elements in two sets can be found by adding the number of elements in each set and then subtracting the number of elements that are in both sets.

So, the number of students enrolled in either algebra or physics is:

29 (students enrolled in algebra) + 14 (students enrolled in physics) - 5 (students enrolled in both) = 38

So, 38 students are enrolled in either algebra or physics.

It is important to notice that in the table you provided is a two-way frequency table also known as a contingency table, it shows the relationship between two variables, in this case, Algebra and Physics and the frequencies of each combination.

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Answer: a) The control in the experiment, 0 kHz, or no sound, serves as a baseline against which to compare the other treatments. By using the control with no sound, researchers can determine whether the deer's response to the sound-emitting devices is due to the sound itself or some other factor. Without the control, it would be unclear what caused any differences in the deer's responses to the different sound treatments.

(b)(i) One advantage to keeping the loudness at a constant 60 decibels for all treatments is that it allows researchers to directly compare the deer's responses to the different sound pitches without the added variable of loudness.

(b)(ii) One disadvantage to keeping the loudness at a constant 60 decibels for all treatments is that loudness may also play a role in deer's response. So, it would be unclear if the different in deer's responses are due to sound frequency only or also caused by sound loudness

(c) Based on the results shown in the bar chart, it can be seen that the deer's response to the sound-emitting devices varies depending on the pitch of the sound. At lower pitches, around 0.28 kHz, the deer's response is more likely to be negative or neutral, indicating that they move away from or don't move towards the highway. At higher pitches, around 15 kHz, the deer's response is more likely to be positive, indicating that they move towards the highway. It suggests that the frequency of sound has an impact on the deer's response. So, based on this data, we cannot recommend using a sound-emitting device to keep deer from running across highways without further research on the optimal frequency and loudness that should be used to make sure that it is effective and safe for the deer.

Step-by-step explanation:

The sound-emitting device may have both advantages and disadvantages depending on the pitch. More research is necessary to find the optimal frequency and volume for the device to be effective and safe.

Based on the results of the experiment, it would not be advisable to use a sound-emitting device to prevent deer from running across highways without further research. The experiment showed that the deer's response varied depending on the pitch of the sound. Although the device showed some advantages, such as moving deer away from the highway at lower pitches, it also presented potential disadvantages. At higher pitches, the deer had a tendency to move towards the highway, which could increase the risk of accidents. More research would be needed to determine the optimal frequency and volume to use for the device to be both effective and safe for the deer.

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the quadratic equation have been solved and the required graph is attached below.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The equation:

[tex]\frac{x^{2}-7x+12 }{x^{2} -1}[/tex]

Its a quadratic equation in both numerator and denominator, by dividing the x² will be get a graph as given in the attached file.

Hence, the quadratic equation will be solved and the required graph is attached below.

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The key features of the graph of the given equation -8x + 20y = 240 include the following:

D. As x → -∞, y → ∞.

E. The y-intercept is (0, 12).

H. The x-intercept is (-30, 0).

Making y the subject of formula in order to determine the slope, we have:

20y = 8x + 240

Dividing both sides of the equation, we have:

y = 8x/20 + 240/20

y = 8x/20 + 12

Therefore, the slope is equal to 8/20.

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

When x = 0, the y-intercept is given by;

20y = 8(0) + 240

y = 240/20

y = 12.

Therefore, the y-intercept is equal to (0, 12).

When y = 0, the x-intercept is given by;

-8x + 20(0) = 240

x = -240/8

x = -30

Answer:y=(x+3)2−17

Step-by-step explanation: 3,11 5,15