a high school coach claims that the average pulse rate of those trying out for sports is 62.4 beats per minute (bpm). the ap statistics instructor suspects this is a made-up number and runs a hypothesis test on a simple random sample (srs) of 32 students trying out for sports, calculating a mean of 65.0 bpm with a standard deviation of 10.3 bpm. what is the p-value?

Solution set for both inequalities is x ≤ 3 and x ≥ 3, which can be written as x = 3.

The two inequalities are: x + 5 < 8 and x + 5 > 8. The first inequality states that the sum of x and 5 is less than 8, while the second inequality states that the sum of x and 5 is greater than 8.

To solve the first inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x < 3. This means that any value of x that is less than 3 will satisfy the inequality.

To solve the second inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x > 3. This means that any value of x that is greater than 3 will satisfy the inequality.

The solutions of the two inequalities differ in terms of the values of x that satisfy each inequality. The first inequality has a solution set that consists of all values of x less than 3, while the second inequality has a solution set that consists of all values of x greater than 3. Therefore, the solutions of the two inequalities do not overlap.

The second set of inequalities are x + 5 ≤ 8 and x + 5 ≥ 8. The first inequality states that the sum of x and 5 is less than or equal to 8, while the second inequality states that the sum of x and 5 is greater than or equal to 8.

To solve the first inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x ≤ 3. This means that any value of x that is less than or equal to 3 will satisfy the inequality.

To solve the second inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x ≥ 3. This means that any value of x that is greater than or equal to 3 will satisfy the inequality.

The solutions of the two inequalities in this case do overlap. The common solution is x = 3, which satisfies both inequalities since it is both less than or equal to 8 and greater than or equal to 8. Therefore, the solution set for both inequalities is x ≤ 3 and x ≥ 3, which can be written as x = 3.

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A correlation coefficient is consistently a number between 1 and - 1 .

The correlation coefficient is a factual measure that demonstrates the strength and heading of the straight connection between two factors. It goes from - 1 to 1, where - 1 addresses a completely bad correlation (i.e., as one variable expands, different declines), 0 addresses no correlation, and 1 addresses an entirely sure correlation (i.e., as one variable builds, the other likewise increments).

The indication of the correlation coefficient demonstrates the heading of the relationship, while the extent of the coefficient shows the strength of the relationship. A correlation coefficient of 0 shows no straight connection between the factors, while values nearer to - 1 or 1 demonstrate a more grounded direct relationship.

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Answer:

b) 0.57

c) 0.74

Step-by-step explanation:

part a:

frequency graph is attached with this answer (in png format).

part b:

let A be the event an entry is picked at random and the entry is a poem that has not been shortlisted.

P(A) = [tex]\dfrac{\text{number of poems not shortlisted}}{\text{total number of entries}}[/tex]

P(A) = [tex]\dfrac{570}{1000}[/tex] (see the frequency graph)

P(A) = 0.57

part c:

let B be the event a story is picked at random and the story has not been shortlisted.

P(B) = [tex]\dfrac{\text{number of stories not shortlisted}}{\text{total number of stories}}[/tex]

P(B) = [tex]\dfrac{185}{250}[/tex] (see the frequency graph)

P(B) = 0.74

Hopefully this answer helped you!!

The three students who are correct in their approach to solving the problem are Nico, Aditi, Sandra.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols to solve equations and solve problems. It involves using letters, symbols, and numbers to represent variables and unknowns in mathematical expressions, equations, and functions.

In algebra, variables represent quantities that can vary, such as the height of a building, the speed of a car, or the price of a product. Algebraic expressions and equations involve combining these variables, symbols, and numbers using operations such as addition, subtraction, multiplication, and division.

Algebra includes various topics such as linear algebra, quadratic equations, polynomials, matrices, and functions. It also includes the use of graphs and charts to represent mathematical relationships and solve problems.

The three students who are correct in their approach to solving the problem are:

Nico: Two-fifths (5 + x) = 8. (Five-halves)

Aditi: Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8

Sandra: Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8

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Answer:

125pi units cubed

Step-by-step explanation:

Answer:

The equation for the relationship is [tex]y=\frac{7}{2} \times x[/tex].

Step-by-step explanation:

Given that point [tex](x,y)=(6,21)[/tex] is part of a direct relationship. That is:

[tex]y \ \infty \ x[/tex]

[tex]y=k\times x[/tex] (1)

Where [tex]k[/tex] is the proportionality constant.

If we know that [tex]x=6[/tex] and [tex]y=21[/tex], then the proportionality constant is:

[tex]k=\dfrac{y}{x}[/tex]

[tex]k=\dfrac{21}{6}[/tex]

[tex]k=\dfrac{7}{2}[/tex]

Lastly, the equation for the relationship is [tex]y=\frac{7}{2} \times x[/tex].

The measure of the angle obtained from the specified measure of the arc CD and the diameter of the circle CF are;

An arc of a circle is a part or portion of the circumference of the circle.

1. The angle at C, obtained from the measure of the arc CD is; (360 - (120 + 120))/2 = 60 (Angle at the center of a triangle theorem)

Therefore; m∠CAF = 90° - 60°/2 = 60°

m∠CAF = 90° - 60°/2 = 60°

2. m∠AFB = m∠FCB = 30°

3. m∠CEF = m∠CAF = 60°

4. m∠CFB = m∠CAF = 60° (Corresponding angles theorem)

5. m∠DCF = m∠BCF = 30° (Sum of angles at a point and angles formed by the diameter of a circle)

6. m∠BCD = m∠BCF + m∠DCF

Therefore; m∠BCD = 30° + 30° = 60°

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The volume of the fish tank is 2000 cubic centimeters, which is calculated by multiplying the length, width, and depth of the tank (25 x 10 x 8 = 2000).

The volume of a fish tank is an important piece of information to know when setting up a fish tank. To calculate the volume of a fish tank, you must multiply the length, width, and depth of the tank. In this example, the fish tank has a length of 25 centimeters, a width of 10 centimeters, and a depth of 8 centimeters. To calculate the volume of the fish tank, we would multiply these three measurements, 25 x 10 x 8 = 2000. This means that the fish tank has a volume of 2000 cubic centimeters. Knowing the volume of the fish tank is important for selecting the right type and size of filter, heater, and other equipment for the tank, as well as for selecting the right number and size of fish for the tank. Furthermore, it is necessary to know the volume of the tank when adding water and testing water parameters, such as pH and nitrate levels, as these readings are related to the size of the tank. Knowing the volume of a fish tank is essential for successful fish keeping.

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The measure of the angle that Zane is using the protractor is a 113 degrees.

Degree is the unit of measure of an angle and is measured by using the geometric tool - a protractor. A degree is denoted by the symbol '°'. A circle completely rotates at a 360° and a degree is a part of that 360° rotation as it is divided into 360 equal parts.

Therefore, The measure of the angle that Zane is using the protractor is a 113 degrees.

Answer:

24.3ft

Step-by-step explanation:

36.2ft - 15ft = 21.2ft

Cade height = 6.2 - 2.5 = 3.7

21.2 + 3.7 = 24.9ft

24.9ft - 15.6ft = 24.3ft

The number in which the digit 3 has a value that is 10 times as great as the value of the digit 3 in 143,728 is 392,097.

The unit digit of a number refers to the rightmost digit of that number when it is written in a positional numeral system. In the decimal system, which is the most common positional numeral system used today, the unit digit is the digit in the ones place.

Let's consider the options one by one:

A. 137,982: This number does not have any digit equal to 3.

B. 142,398: This number does not have a digit 3 with a value as 30,000.

C. 292,389: This number has a digit 3 in the hundred thousands place, which has a value of 3 x 100,000 = 300,000. This is more than 10 times the value of the digit 3 in 143,728, so this option does not satisfy the condition.

D. 392,097: This number has a digit 3 in the ten thousands place, which has a value of 3 x 10,000 = 30,000. This satisfies the condition, so the answer is (D) 392,097.

Therefore, the number in which the digit 3 has a value that is 10 times as great as the value of the digit 3 in 143,728 is 392,097.

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Analytics will count three goal conversions if a user completes the newsletter sign-up three times in three separate sessions.

When a goal is set up in analytics, it is assigned a unique ID. When a user completes the desired action that triggers the goal, the ID is recorded in the user's session data. Each time the user completes the action, a new session is created, and a new goal completion is recorded with a unique ID.

Therefore, if the user completes the newsletter sign-up three times in three separate sessions, analytics will count three goal conversions, each with a unique ID.

It's worth noting that while this behavior is typical for most analytics platforms, it's possible to configure goals in different ways, so the behavior may vary depending on the specific implementation. Therefore, it's important to consult the analytics documentation or work with a knowledgeable analyst to confirm the expected behavior.

Therefore, the correct answer is three goal conversions will be counted in analytics.

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Yes, because[tex]np0 > 10[/tex]and [tex]n(1-p0) > 10[/tex].

Thus, the sampling distribution of p-hat is approximately normal, given the conditions of [tex]np0 > 10 and n(1-p0) > 10.[/tex]

This is because the sampling distribution of p-hat follows the Central Limit Theorem, which states that when sample sizes are greater than 30,

the sampling distribution of the sample proportion will be approximately normal. The Central Limit Theorem is used in this example because the number of BYU students from Texas (n) is greater than 30, so the sample proportion (p-hat) is normally distributed.

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The three orderer pairs in the form (x,y) that could be produced by the function y=12x+3x​ are (0,0), (1,15) and (-2,-30).

what is orderer pair?

The given function is:

y = 12x + 3x

Simplifying, we get:

y = 15x

To find ordered pairs in the form (x,y) that could be produced by this function, we can choose different values of x and substitute them into the equation to find the corresponding value of y. Here are three examples:

1. When x = 0:

y = 15x = 15(0) = 0

Therefore, the ordered pair is (0,0).

2. When x = 1:

y = 15x = 15(1) = 15

Therefore, the ordered pair is (1,15).

3. When x = -2:

y = 15x = 15(-2) = -30

Therefore, the ordered pair is (-2,-30).

In general, we can choose any value of x and find the corresponding value of y using the given function to obtain an ordered pair in the form (x,y).

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{\sqrt{21}}\\ a=\stackrel{adjacent}{YZ}\\ o=\stackrel{opposite}{3} \end{cases} \\\\\\ (\sqrt{21})^2= (YZ)^2 + (3)^2\implies 21=YZ^2+9 \\\\\\ 12=YZ^2 \implies \sqrt{12}=YZ \\\\[-0.35em] ~\dotfill[/tex]

[tex]\tan(Y )=\cfrac{\stackrel{opposite}{3}}{\underset{adjacent}{\sqrt{12}}}\implies \tan(Y )=\cfrac{3}{\sqrt{12}}\cdot \cfrac{\sqrt{12}}{\sqrt{12}}\implies \tan(Y )=\cfrac{3\sqrt{12}}{12} \\\\\\ \tan(Y )=\cfrac{3\sqrt{2^2\cdot 3}}{12}\implies \tan(Y )=\cfrac{6\sqrt{3}}{12}\implies \tan(Y )=\cfrac{\sqrt{3}}{2}[/tex]

Answer:

First box is seven; second box is 16; third box is 14

Step-by-step explanation:

Since a square has all equal sides, we know that s+s+s+s or 4s=Perimeter.

SInce we are finding the area of a square, the equation would be s^2. 7 squared is 49, 16 squared is 256, and 14 squared is 196.

Answer:There are two cases to consider: a hand that consists of all red cards and a hand that consists of all black cards.

Case 1: All red cards

There are 26 red cards in a standard deck of 52 cards. To form a 5-card hand consisting of all red cards, we need to choose 5 cards from the 26 red cards. The number of ways to do this is:

C(26, 5) = (26!)/(5!21!) = 65,780

Case 2: All black cards

Similar to the first case, there are 26 black cards in a standard deck of 52 cards. To form a 5-card hand consisting of all black cards, we need to choose 5 cards from the 26 black cards. The number of ways to do this is:

C(26, 5) = (26!)/(5!21!) = 65,780

Therefore, the total number of hands that include all red cards or all black cards is the sum of the two cases:

65,780 + 65,780 = 131,560

So there are 131,560 hands that consist of either all red cards or all black cards.

Step-by-step explanation:

Answer:

It depends, sometimes it continues with a pattern in the decimal places, sometimes it ends.

Step-by-step explanation:

The two numbers of books read that occur the least frequently are 7 and 15.

To determine which two numbers occur the least frequently, we need to count the number of tally marks for each number on the line plot. Based on the line plot, we can see that the number of tally marks for each number is as follows:

7: 1 tally mark

8: 2 tally marks

9: 3 tally marks

10: 4 tally marks

11: 2 tally marks

12: 4 tally marks

13: 3 tally marks

14: 2 tally marks

15: 1 tally mark

The two numbers that occur the least frequently are 7 and 15, as they each have only one tally mark.

Therefore, the answers to the question are: 7 in the first box and 15 in the second box.

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Students in ms seiko's made a line plot of the number of books they read over the summer.

books read

7 8 9 10 11 12 13 14 15

what two numbers of books read occur the least frequently enter your answers in the boxes in increasing order?

If a student had 50 minutes of homework on Monday and 30 minutes of homework on Tuesday, then there was a 40% decrease in homework time from Monday to Tuesday.

To calculate the percent decrease in homework time from Monday to Tuesday, we need to find the difference between the two values and then divide that difference by the original value (Monday’s homework time). The difference between 50 minutes and 30 minutes is 20 minutes. Dividing this difference by the original value (50 minutes) gives us:

(20 / 50) x 100% = 40%

Therefore, there was a 40% decrease in homework time from Monday to Tuesday.

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Answer:

Step-by-step explanation:

You want f(3) and g(-6) when f(x) = -4x² -3 and g(x) = 5x +2.

To find the value of the function for a particular value of the variable, put that value in place of the variable and do the arithmetic.

  f(3) = -4(3²) -3 = -4(9) -3 = -36 -3

  f(3) = -39

  g(-6) = 5(-6) +2 = -30 +2

  g(-6) = -28

__

Additional comment

Your calculator can help with the arithmetic.

Answer:

B

Step-by-step explanation:

The length of the side e for the triangle ∆DEF is equal to 553.1 inches to the nearest tenth tenth of an inch using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

We shall first evaluate for the angle m∠F and then solve for the e using the sine rule as follows:

m∠F = 180° - (27 + 101) {sum of interior angles of a triangle}

m∠F = 52°

e/sin27 = 960/sin52

e = (960 × sin27)/sin52 {cross multiplication}

e = 553.0773

Therefore, the length of the side e for the triangle ∆DEF is equal to 553.1 inches to the nearest tenth tenth of an inch using the sine rule.

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Assuming that the function A calculates the surface area of a mold, the appropriate domain for A would be a set of all possible molds, which can be represented by a set of positive real numbers.

It is important to note that the mold's geometry, size, and complexity will affect the calculation of its surface area. Therefore, the domain of the mold area function A should include all possible variations of mold shapes and sizes.

In practical applications, the domain of A may also be limited by the manufacturing capabilities or constraints, such as the maximum size or complexity of molds that can be produced. In such cases, the domain of A may need to be further restricted to reflect these limitations.

Overall, the appropriate domain for the mold area function A would depend on the specific context and application of the function.

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Answer:

B) P = 42; A = 84

Step-by-step explanation:

Perimeter:

You have two right triangles, so you need to find the third side length.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]5^{2}[/tex] + [tex]12^{2}[/tex] = [tex]c^{2}[/tex]

25 + 144 = [tex]c^{2}[/tex]

169 = [tex]c^{2}[/tex]

[tex]\sqrt{169}[/tex] = [tex]\sqrt{c^{2} }[/tex]

13 = c

The top right missing outside length is 13

We do the same thing to find the missing bottom outside.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]12^{2}[/tex] + [tex]9^{2}[/tex] = [tex]c^{2}[/tex]

144 + 81 = [tex]c^{2}[/tex]

225 = [tex]c^{2}[/tex]

[tex]\sqrt{225}[/tex] = [tex]\sqrt{c^{2} }[/tex]

15 = c

The perimeter of triangle xyz is 5 + 9 + 13 + 15 = 42 units

Area:

a = 1/2 bh

a= 1/2 (5 + 9) (12)

a = 1/2 (14)(12)

a = 84 [tex]units^{2}[/tex]

Helping in the name of Jesus.

Step-by-step explanation:

c = 2,8    and   d = 6,5

Use the distance formula  ( kind of a modified Pythagorean theorem)

s^2 = (x1-x2)^2  + (y1-y2)^2             ( s = distance)

s^2 = ( 2-6)^2 + ( 8-5)^2

s^2 = 25

s = 5 units

Answer:

Step-by-step explanation:

add c with b and then add a multiply 30 and divide by 12

Given equation is: 24+ 0.44x = 19+ 1. 69x is x = 4.

Equation:

In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. Solving an equation involving variables involves determining which values ​​of the variables make the equation true. The variables for which the equation must be solved are also called unknowns, and the values ​​of the unknowns that satisfy the equation are called solutions of the equation. There are two types of comparisons: identity comparisons and conditional comparisons. The identity is true for all values ​​of the variable. A conditional comparison is only true for certain values ​​of a variable.

According to the Question:

Given equation:

24+0. 44x = 19+ 1. 69x

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

   24 - 19 = 1.69x - 0.44x

⇒ 5 = 1.25x

⇒ x = 5/1.25

⇒ x = 4

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Answer:

  74π cm²

Step-by-step explanation:

You want to know the painted area of a cone 10 cm in diameter and 12 cm high that has an unpainted hole in the base that has a 4 cm radius.

The area of the curved surface of the cone is found using the given formula. To use that formula, we need to know the slant height of the cone. The slant height is the hypotenuse of a right triangle that is 12 cm high and has a base of 5 cm:

  l² = r² +h²

  l = √(5² +12²) = √(25 +144) = √169

  l = 13 . . . . cm

Then the lateral area is ...

  LA = πrl = π(5 cm)(13 cm) = 65π cm²

The painted area of the base is the difference between the areas of circles 5 cm in radius and 4 cm in radius:

  A = π(r₁² - r₂²) = π((5 cm)² -(4 cm)²) = π(25 -16) cm² = 9π cm²

The painted area is the sum of the areas of the curved surface and the donut base:

  A = 65π cm² +9π cm² = 74π cm²

__

Additional comment

The radius of the base is half the diameter. If you slice the cone through its vertex and perpendicular to its base, the cross section is an isosceles triangle with height 12 cm and base 10 cm. The altitude of that triangle divides it into two congruent right triangles that have base 5 cm and height 12 cm.

You may recognize this as the {5, 12, 13} right triangle, which tells you the slant height is 13 cm. If not, you can use the Pythagorean theorem to find the slant height, as above.