Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below:

Population 1: 69, 68, 62, 68, 68, 62, 69

Population 2: 76, 68, 68, 72, 76, 70, 70, 70

Is there evidence, at an α=0.025
level of significance, to conclude that those who exercise regularly have lower resting heart rates? (Assume that the population variances are equal.) Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:
B. The rejection region for the standardized test statistic:
C. Your decision for the hypothesis test:

The volume of the triangular prism as shown in the attached image is 30 cm³.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the height of the prism.

The area of the triangular base can be found using the formula:

Area = (1/2) × base × height

In this case, the base is 5 cm and the height is 4 cm, so the area of the triangular base is:

Area = (1/2) × 5 cm × 4 cm = 10 cm²

The height of the prism is 3 cm.

Therefore, the volume of the triangular prism is:

Volume = Area of triangular base × height

= 10 cm² × 3 cm

= 30 cm³

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If x + 3y = 1, then x = 1 - 3y.

Then in the second equation, replace x with 1 - 3y :

-x + 2y = 4

- (1 - 3y) + 2y = 4

-1 + 3y + 2y = 4

-1 + 5y = 4

5y = 5

y = 1   →   x = -2

since x = 1 - 3•1 = 1 - 3 = -2.

Alternatively, you can instead solve for y in the first equation, so that if x + 3y = 1, you get

x + 3y = 1

3y = 1 - x

y = (1 - x)/3

Then replace y in the second equation:

-x + 2y = 4

-x + 2 ((1 - x)/3) = 4

-x + 2/3 (1 - x) = 4

Multiply both sides by 3 to get rid of the fraction:

-3x + 2 (1 - x) = 12

-3x + 2 - 2x = 12

-5x + 2 = 12

-5x = 10

x = -2   →   y = 1

since y = (1 - (-2))/3 = (1 + 2)/3 = 3/3 = 1.

A'(15) = 2 * 15 = 30.The meaning of A'(15) in this situation is that if the side length of the wafer changes by 1 mm, the area will change by 30 mm^2 when the side length is 15 mm.

The area A(x) of a square wafer is given by A(x) = x², where x is the side length of the wafer. The derivative of A(x) with respect to x, denoted A'(x), represents the rate of change of the area with respect to the side length. To find A'(15), we need to find the derivative of A(x) at x = 15.

A'(x) = 2x

Therefore, A'(15) = 2 * 15 = 30.

The meaning of A'(15) in this situation is that if the side length of the wafer changes by 1 mm, the area will change by 30 mm² when the side length is 15 mm. This means that for every 1 mm increase in the side length, the area of the wafer will increase by 30 mm², and for every 1 mm decrease in the side length, the area of the wafer will decrease by 30 mm².

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Answer:

-1/4

Step-by-step explanation:

you do change in y over change in x which is 4-5 over 6-2

when you do the calculations you get -1/4

Answer:

Statistical questions are asking for ABOUT how much not an exact amount or number.

Answer:

The expression is 7x-5

Answer: the present age of son is 15 years, and the present age of father is 45 years.

Step-by-step explanation:

Let the age of son be 'x' and that of his father be 'y'.

So according to the question, the 1st equation that can be formed will be:

y = 3(x) ->(1)

[as father's age is 3 times the age of son]

Now after 5 years:

Age of son = (x+5)

Age of father = (y+5)

So according to the question, the 2nd equation that can be formed will be:

(y+5) = 2.5×(x+5) ->(2)

[as father is now two and half times old as his son]

Substituting the value of equation (1) in (2), we get:

(3x+5) = 2.5×(x+5)

=> 3x + 5 = 2.5x + 12.5

=> 3x - 2.5x = 12.5 - 5

=> 0.5x = 7.5

=> x = 7.5/0.5 = 15

Thus, the present age of son is 15 years.

Note : we can calculate the age of father by putting the value of x in equation (1) or (2):

y = 3(x) = 3 × 15 = 45 (putting x in equation 1)

Thus, the present age of father is 45 years.

Answer:

\((x+2.3)^{2} +y^{2} =36/49\)

Step-by-step explanation:

To get the equation of a circle we plug your information into this equation:

\((x-h)^{2} +(y-k)^{2} =r^{2}\)

Your h is the x coordinate of the center, -2.3 and your k is the y coordinate of the center, 0. The r is your radius. So we plug these values in to get \((x+2.3)^{2} +y^{2} =(6/7)^{2}\) which then gives us the final answer of \((x+2.3)^{2} +y^{2} =36/49\).

Answer:

  one solution: (1, 4)

Step-by-step explanation:

You want the graphs and number of solutions to the system of equations ...

The graph is attached. The first equation has a y-intercept of +1 and a slope of 3. The second equation has a y-intercept of +2 and a slope of 2.

The different slopes mean there is exactly one solution. The graph shows that solution to be (x, y) = (1, 4).

__

Additional comment

The slope is the x-coefficient when the equations are written in this "slope-intercept" form. It is the "rise/run" for the line on the graph. A slope of 3, for example, means the line has a rise of 3 grid squares for a run of 1 square (to the right). Knowing the y-intercept and slope makes it easy to graph the line.

The sequence given by b(1) = 2, b(n) = 2 × b(n-1) - 1 (for n > 2) is neither arithmetic nor geometric.

To determine the first five terms of the sequence and whether it is arithmetic, geometric, or neither, let's calculate the values step by step.

Sequence 1: b(1) = 2, b(n) = 2 × b(n-1) - 1 (for n > 2)

Let's find the first five terms:

b(1) = 2 (given)

b(2) = 2 × b(1) - 1 = 2 × 2 - 1 = 4 - 1 = 3

b(3) = 2 × b(2) - 1 = 2 × 3 - 1 = 6 - 1 = 5

b(4) = 2 × b(3) - 1 = 2 × 5 - 1 = 10 - 1 = 9

b(5) = 2 × b(4) - 1 = 2 × 9 - 1 = 18 - 1 = 17

The first five terms of the sequence are: 2, 3, 5, 9, 17.

To determine whether this sequence is arithmetic, geometric, or neither, we can calculate the common difference (d) for arithmetic sequences and the common ratio (r) for geometric sequences.

Arithmetic sequences have a constant difference between consecutive terms, while geometric sequences have a constant ratio between consecutive terms.

Let's check the differences between consecutive terms:

d(1) = b(2) - b(1) = 3 - 2 = 1

d(2) = b(3) - b(2) = 5 - 3 = 2

d(3) = b(4) - b(3) = 9 - 5 = 4

d(4) = b(5) - b(4) = 17 - 9 = 8

The differences are not constant, so the sequence is not arithmetic.

Now, let's check the ratios between consecutive terms:

r(1) = b(2) / b(1) = 3 / 2 = 1.5

r(2) = b(3) / b(2) = 5 / 3 ≈ 1.6667

r(3) = b(4) / b(3) = 9 / 5 = 1.8

r(4) = b(5) / b(4) = 17 / 9 ≈ 1.8889

The ratios are also not constant, so the sequence is not geometric either.

Therefore, the sequence given by b(1) = 2, b(n) = 2 × b(n-1) - 1 (for n > 2) is neither arithmetic nor geometric.

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The height of the rectangular prism is 2x^3

The volume of a rectangular prism is given by the product of its length, width, and height.

We know that the volume is 48x^8, so we can write an equation:

48x^8 = (4x^2)(6x^3)(h)

We can simplify the left side:

48x^8 = 24x^5 * h

And divide both sides by 24x^5 to find the height:

h = 48x^8 / 24x^5 = 2x^3

So the height of the rectangular prism is 2x^3

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Answer:

3 cups

Step-by-step explanation:

The same amount of each is needed if I read that correctly.

Answer:

C) 3 5/12

Step-by-step explanation:

Answer:

B. 47 7/12

Step-by-step explanation:

=126 1/4 - 78 2/3

Change the two mix fraction to improper fractions.

= 505/4 - 236/3

= 1515-944/12

= 571/12

= 47 7/12

Answer:

Quick answer option C

Step-by-step explanation:

Answer:

Note: Numbers are blocked in groups of two digits for convenience only. In using this table you can read numbers of any number of digits in any way you want.

Step-by-step explanation:

09/14/2022 9 ‑ 10 ‑ 20 ‑ 22 ‑ 52 25 3 $206 Million Roll

09/12/2022 6 ‑ 14 ‑ 16 ‑ 34 ‑ 66 25 3 $193 Million Roll

09/10/2022 38 ‑ 42 ‑ 56 ‑ 68 ‑ 69 4 2 $186 Million Roll

Answer:

-7.

Step-by-step explanation:

g(x) = x^2 - 6x - 7

g(2) = 2^2 - 6(2) - 7

= 4 - 12 - 7

= -8 - 7

= -15

f(x) = x + 8

f(-15) = (-15) + 8

= 8 - 15

= -7

Hope this helps!

Answer:

\(x = \frac{2 \pm 3\sqrt3}{5}\)

Step-by-step explanation:

Hello!

Standard form of a Quadratic: \(ax^2 + bx + c = 0\)

Quadratic Formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Given our Equation: \(25x^2 - 20x -23 = 0\)

The solutions are \(x = \frac{2 + 3\sqrt3}{5}\) and \(x = \frac{2 - 3\sqrt3}{5}\).

Answer:

y=-1/2+3

Step-by-step explanation:

Look for b first. On the y axis, that is where the line intersects. That means that it'd be 3. For the slope, you read graphs to the right (like you'd read a book), so you go down first and over 2 because that's where the line intersects next. It would be negative since you have to go downwards. I hope this helps <3

With the added parentheses, the expression simplified to 212.5.

PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.

To simplify the expression 30·5·7-3+2 and ensure that the order of operations is clear, we can place parentheses around the first two terms:

That is, (30.5·7)-3+2

= 213.5-3+2

Then, we can simplify by performing the addition and subtraction:

212.5

Therefore, with the added parentheses, the expression simplified to 212.5.

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Answer:

Sara has $144 at the beginning of the month.

Step-by-step explanation:

At the beginning of the month, x = 0 because no days have passed since the beginning of the month. When x = 0, g(0) = -4.5(0) + 144 = 144, therefore, we know that Sara has $144 on her card at the beginning of the month.

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

terminating.

Step-by-step explanation:

9/16 converted to a decimal is .5625 which is terminating

Answer:

(-1, -3)

Step-by-step explanation:

Answer:

\(0.424 - 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.286\)

\(0.424 + 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.562\)

The 99% confidence interval would be given by (0.286;0.562)

Step-by-step explanation:

Information given:

\( X= 36\) represent the families owned at least one DVD player

\( n= 85\) represent the total number of families

\(\hat p=\frac{36}{85}= 0.424\) represent the estimated proportion of families owned at least one DVD player

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \(\alpha=1-0.99=0.01\) and \(\alpha/2 =0.05\). And the critical value would be given by:

\(z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58\)

The confidence interval for the mean is given by the following formula:  

\(\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}\)

If we replace the values obtained we got:

\(0.424 - 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.286\)

\(0.424 + 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.562\)

The 99% confidence interval would be given by (0.286;0.562)

Answer:

y=6x

Step-by-step explanation:

y-y1=m(x-x1)

y-0=6(x-0)

y=6(x)

y=6x

Answer:

14)  m∠WYZ = 23°

15)  m∠ACB = 87°

Step-by-step explanation:

If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

According to the SAS Similarity Theorem, triangle VWX and triangle YWV are similar triangles.

If two triangles are similar their corresponding angles are congruent.

Therefore, m∠WYZ is the same as m∠WVX.

Angles on a straight line sum to 180°:

\(\implies m \angle WYZ + m \angle VYZ = 180^{\circ}\)

\(\implies (3x-7)^{\circ} + (16x-3)^{\circ} = 180^{\circ}\)

\(\implies (3x-7) + (16x-3) = 180\)

\(\implies 3x-7+ 16x-3 = 180\)

\(\implies 19x-10= 180\)

\(\implies 19x= 190\)

\(\implies x=10\)

To find the measure of angle WYZ, substitute the found value of x into the expression for the angle:

\(\begin{aligned}\implies m \angle WYZ &=(3x-7)^{\circ}\\&=(3(10)-7)^{\circ}\\&=(30-7)^{\circ}\\&=23^{\circ}\end{aligned}\)

Therefore, the measure of angle WYZ is 23°.

According to the SAS Similarity Theorem, triangle ABC and triangle AED are similar triangles.

If two triangles are similar their corresponding angles are congruent.

Therefore, m∠ABC is equal to m∠AED:

\(\implies m \angle AED=m \angle ABC\)

\(\implies (11x-2)^{\circ}=(6x+13)^{\circ}\)

\(\implies 11x-2=6x+13\)

\(\implies 5x=15\)

\(\implies x = 3\)

To find the measure of angle ABC, substitute the found value of x into the expression for the angle:

\(\begin{aligned}\implies m \angle ABC&=(6x+13)^{\circ}\\&=(6(3)+13)^{\circ}\\&=(18+13)^{\circ}\\&=31^{\circ}\end{aligned}\)

Interior angles of a triangle sum to 180°:

\(\implies m \angle ACB + m \angle ABC + m \angle BAC = 180^{\circ}\)

\(\implies m \angle ACB + 31^{\circ}+ 62^{\circ} = 180^{\circ}\)

\(\implies m \angle ACB + 93^{\circ} = 180^{\circ}\)

\(\implies m \angle ACB =87^{\circ}\)

Therefore, the measure of angle ACB is 87°.

Answer:

Incorrect

Step-by-step explanation:

Well since there is only 18 cups of dog food he will only be able to feed his dog for 18 days since he feeds his dog 1 cup a day.

Answer:

Incorrect

Explanation:

Maxwell's dog eats one cup of food a day. The bag contains only eighteen cups, so it will feed the dog for eighteen days. There will not be enough food to last Maxwell for 27 days. So, the answer is incorrect.

Answer:

14 square units