A simple random sample of 36 men from a normally distributed population results in a standard deviation of 64 beats per minute. The normal range of pulse rates of adults is typically given an 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the cam that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below a. Identify the null and attemative hypotheses. Choose the correct answer below OA H₂ 2 10 beats per minute He<10 beats per minute OB. He 10 beats per minute H: 10 beats per minute OC. He 10 beats per minute OD H10 beats per minute He 10 beats per minute H₁ #10 beats per minute b. Compute the test statistic. (Round to three decimal places as needed) c. Find the P-value P-value- (Round to four decimal places as needed.) d. State the conclusion. evidence to warrant rejection of the claim that the standard deviation of men's puise alas H. because the P-value is is equal to 10 beats per minute. the level of significance.

Using p-hat formula and probability,

we get

a) Sampling distribution of p-hat = 0.02029286

b)The probability that in a random sample of 500 adults more than 30% do not own a credit card is

=0.3121

c) The probability that in a random sample of 500 adults between 25% and 30% do not own a credit card is 0.6635

We have given that

29% of adults do not own a credit card according to creditcard.com.

a) Sample size (n) = 500 of adults have own credit card

sample proportion, for the adults do not own a credit= 29% = 0.29

Normal distribution exits here with p

= 1-0.29=0.71 and

Standard error (p-hat) =sqrt(p(1-p)/n)

=sqrt(0.71× 0.29/500)

p-hat = 0.02029286

b) Now, more than 30% do not have own credit card.

P(p-hat>0.3) = P((phat- p)/sqrt(p×(1-p)/n) >(0.3-0.29)/sqrt(0.29× (1-0.29)/500))

=P(Z>0.49) =0.3121 (from standard normal table)

c) Sample size (n) = 500 and p-hat lies between 25% to 30% .

P(0.25<phat<0.3)

= P((0.25-0.29)/sqrt(0.29*(1-0.29)/500) <Z< (0.3-0.29)/sqrt(0.29*(1-0.29)/500))

=P(-1.97<Z<0.49)

=0.6635 (from standard normal table)

Hence, we calculated all the required probabilities.

a) p-hat = 0.02029286

b) P(p-hat>0.3) =0.3121

c) P(0.25<phat<0.3) =0.6635

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Complete question:

According to creditcard.com, 29% of adults do not own a credit card.

a. Suppose a random sample of 500 adults is asked, "Do you own a credit card?" Describe the sampling distribution of p-hat, the proportion of adults who own a credit card.

b. What is the probability that in a random sample of 500 adults more than 30% do not own a credit card?

c. What is the probability that in a random sample of 500 adults between 25% and 30% do not own a credit card?

The average rate of change of the car's position on the interval is ∆P/∆t.

To find the average rate of change of the car's position on the interval, follow these steps:

Identify the interval: First, determine the specific interval for which you need to find the average rate of change (e.g.,

between times t1 and t2).

Calculate the change in position:

Determine the car's position at both the beginning and end of the interval (e.g., positions P1 and P2).

Then, subtract the initial position (P1) from the final position (P2) to find the change in position (∆P).

Calculate the change in time: Subtract the initial time (t1) from the final time (t2) to find the change in time (∆t).

Calculate the average rate of change: Divide the change in position (∆P) by the change in time (∆t) to find the average

rate of change.

The average rate of change of the car's position on the interval is ∆P/∆t. Include units in your answer (e.g., meters per

second or miles per hour) to indicate the car's rate of change in position.

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Answer:

10 months

Step-by-step explanation:

30x = 22x + 80

8x = 80

x = 10

Answer:

answer SHOULD be 3 sandwiches

Step-by-step explanation:

33-6=27÷9=3

Answer:

9x + 6 = 33; 3

Step-by-step explanation:

9x + 6 represents the number of sandwiches and gallon of milk Tito purchased. 33 represents the total cost of the sandwiches and milk. Using this equation, we can solve to find x (the number of sandwiches purchased). Therefore, x = 3.

Answer:

Part A: The appropriate design for the study includes;

Treatment used; Chamomile oil treatment

Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves

Treatment assignment; Treatment should be assigned to patients with pinched nerves

Variables that should be measured; Reduction or relief of pain as reported by the patients

Part B; The study should be administered equally to both male and female as the symptoms can be experienced by both male and female

Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.

Step-by-step explanation:

Answer:

f(x) = 0.5x.

Step-by-step explanation:

The line passes through (0,0) and the slope = 3-0/6-0 = 0.5.

The required equation of the line will be y = 1/6 x + 27 and it will be perpendicular to 18x+3y=81.

The line which makes the angle of 90 degree with each other is perpendicular line to each other.

  One property of the line is m1 × m2 = -1

Given line,

18x+3y=81

Equation of the general line

  y = mx + c

Coverting the given line in the general form

         18x+3y=81

          3y = -18x + 81

Dividing both sides by 3

   we get,

               y = -6x + 27

Hence the slope is -6.

We know that in case of perpendicular lines

           m1 × m2 = -1

As the slope is -6

So,  -6 × m2 = -1

Then, the second line slope will be 1 / 6.

So the required equation of the line will be

       y = 1/6 x + 27.

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Answer:

Square root of 77.44 = height and length of gray squares = 8.8 cm

Since there are 3 squares that make up the height of that object 8.8 cm * 3 =

26.4 cm (the height of  3 gray squares

Square root of 4.84 = 2.2 cm

So the total height = 26.4 + 2.2 = 28.6 cm

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the line y = - x

a point (x, y ) → (- y, - x ), thus

T(- 1, 3 ) → T'(- 3, 1 )

U(- 1, 10 ) → U'(- 10, 1 )

V(- 2, 4 ) → V'(- 4, 2 )

Answer:

Six times a number

Step-by-step explanation:

X can be referred to as a number and the expression is multiplying it by six so you can say six times a number.

Answer:

The product of 6 and a number, or also C

Step-by-step explanation:

✨ E d g e n u i t y✨

The result of a multiplication operation is called a product. The multiplication of whole numbers may be thought of as a repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier.

Answer:

Let x be the first unknown angle, and y be the second unknown angle.

We know that the sum of the three angles in a triangle is 180 degrees, so:

85 + 9kx + 10kx = 180

where k is a constant representing the ratio of the other two angles.

Simplifying the equation, we get:

19kx = 95

Dividing both sides by 19k, we get:

x = 5/k

Since the ratio of the other two angles is 9:10, we know that:

y = 9kx = 9k(5/k) = 45

So the measures of the two unknown angles are:

x = 5/k and y = 45

We cannot find the exact measures of x and y without more information, but we know that x and y are in a ratio of 9:10 and their sum is 180 - 85 = 95 degrees. We can set up the following equation to solve for k:

5/k + 45/k = 95

50/k = 95

k = 50/95

Using this value of k, we can find the measures of x and y:

x = 5/k = 5/(50/95) = 9.5

y = 9kx = 9(50/95)(9.5) = 47.37

Therefore, the measures of the two unknown angles are x = 9.5 degrees and y = 47.37 degrees (rounded to two decimal places).

Step-by-step explanation:

Answer:

Step-by-step explanation:

      Atsu  :  Sabu

         3     :     7

         x     :    x + 20

x is equal to the number of cedis

cross multiply the ratio above

3(x+20) = 7x

3x + (20×3) = 7x

3x + 60 = 7x

3x - 3x + 60 = 7x - 3x                  (put - 3x on both sides of the equation)

60 = 4x

60/4 = 4x/4                                (divide both sides by 4)

15 = x

Answer:

the fourth

Step-by-step explanation:

The bit string with all zeros represents the empty subset of the finite universal set.

In a general sense, a universal set refers to a collection or set that contains all the possible elements under consideration. A bit string is a sequence of binary digits, typically representing information in computing and digital systems. When all the digits in a bit string are zeros, it indicates the absence or lack of any element or information.

Thus, the bit string with all zeros represents the empty subset of the universal set. The empty subset, also known as the null set or the set with no elements, is a subset that contains no elements at all. It is a fundamental concept in set theory and is often denoted by the symbol Ø or {}.

In the context of the universal set, the empty subset is a valid subset since every set, including the universal set, contains the empty subset as one of its subsets. Therefore, the bit string with all zeros represents the empty subset of the finite universal set.

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Answer:

162L= 0.1620000m³

Mia works at a skateboard shop and she gets 25 dollars per month

y -intercept = $200

Since at y -intercept x = 0

So coordinate is : (0,200)

x -intercept = 8 months

Since, at x intercept y = 0

So, coordinate is (8, 0)

The general equation of line is express as :

Substitute the coordinates : (8,0) (0,200)

Equation : y = 200 - 25x

Substitute the coordinates on the graph :

So, the graph of the equation y = 200 - 25x is

When \(\sin A = -\frac{4}{5}\) and \(A\) is in Quadrant III, we find \(\tan (2A) = \frac{72}{5}\) using the double-angle formula for tangent.

To find \(\tan (2A)\), we can use the double-angle formula for tangent:

\[\tan (2A) = \frac{2\tan A}{1 - \tan^2 A}\]

First, we need to find \(\tan A\) using the given information. Since \(\sin A = -\frac{4}{5}\) and \(A\) is in Quadrant III, we can use the Pythagorean identity to find \(\cos A\):

\(\cos A = -\sqrt{1 - \sin^2 A} = -\sqrt{1 - \left(-\frac{4}{5}\right)^2} = -\frac{3}{5}\)

Now, we can calculate \(\tan A\) using \(\tan A = \frac{\sin A}{\cos A}\):

\(\tan A = \frac{-\frac{4}{5}}{-\frac{3}{5}} = \frac{4}{3}\)

Finally, substituting \(\tan A\) into the double-angle formula, we find:

\(\tan (2A) = \frac{2\times\frac{4}{3}}{1 - \left(\frac{4}{3}\right)^2} = \frac{8}{3 - \frac{16}{9}} = \frac{8}{\frac{5}{9}} = \frac{72}{5}\)

Therefore, \(\tan (2A) = \frac{72}{5}\) when \(\sin A = -\frac{4}{5}\) and \(A\) is in Quadrant III.

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100 same-day tickets were sold for the cost using equation.

To solve this problem, we can use a system of two equations with two variables. Let x be the number of advance tickets sold and y be the number of same-day tickets sold. Then we have:

x + y = 600   (equation 1: total number of tickets sold)
50x + 30y = 28000   (equation 2: total amount paid for tickets)

We can solve for x and y by using elimination or substitution. Here's one way to do it using substitution:
From equation 1, we have y = 600 - x. Substitute this into equation 2:

50x + 30(600 - x) = 28000

Simplify and solve for x:
50x + 18000 - 30x = 28000
20x = 10000
x = 500

So 500 advance tickets were sold. To find the number of same-day tickets, we can substitute x = 500 into equation 1:

500 + y = 600
y = 100

So 100 same-day tickets were sold.

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Answer:

15:8

6:x

15×0.4=6

so, 8÷0.4=x=3.2 units

Answer:

$64

Step-by-step explanation:

Answer:

The length of the island is 699 feet.

Step-by-step explanation:

Let the distance from the foot of the cliff to the near side be represented by x, and the distance from the foot of the cliff to the far side be represented by y.

Applying the trigonometric function to calculate the value of x;

Tan θ = \(\frac{opposite}{adjacent}\)

Tan \(16^{o}\) = \(\frac{320}{x}\)

0.2867 = \(\frac{320}{x}\)

x = \(\frac{320}{0.2867}\)

  = 1116.1493

x = 1116.15 feet

The distance from the foot of the cliff to the near side of the island is 1116.15 feet.

To determine the value of y;

Tan θ = \(\frac{opposite}{adjacent}\)

Tan \(10^{o}\) = \(\frac{320}{y}\)

0.1763 = \(\frac{320}{y}\)

y = \(\frac{320}{0.1763}\)

  = 1815.0879

y = 1815.09 feet

The distance from the foot of the cliff to the far side of the island is 1815.09 feet.

The length of the island = y - x

                                        = 1815.09 - 1116.15

                                        = 698.94

The length of the island is 699 feet.

a). The difference between the two population means is estimated at a location to be 2.7.

b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.

c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).

d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.

Using the equation \(x_1-x_2\), we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample

\(1(x_1=22.8)\) and deducting it from the mean of Sample \(2(x_2=20.1)\).

With the use of the equation \(df=n_1+n_2-2\), it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because \(n_1\) = 20 and \(n_2\) = 30.

We must apply the formula to determine the margin of error at 95% confidence \(ME=t*\sqrt[s]{n}\).

The sample standard deviation (s) is equal to the average of \(s_1\) and \(s_2\) (3.4), the t value with 95% confidence is 1.67, and n is equal to the

average of \(n_1\) and \(n_2\) (25). When these values are entered into the formula, we get \(ME=1.67*\sqrt[3.4]{25}=1.7\).

Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means \(CI=x_1-x_2+/-ME\).

The confidence interval's bottom limit in this instance is \(x_1-x_2-ME2.7-1.7=0.0\) and the upper limit is \(x_1+x_2+ME=2.7+1.7=5.4\).

As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

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The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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The correct option is a) $5161.24

To evaluate the expression P(1+rt) with the given values:

P = 1575

r = 0.055

t = 168/365

First, let's calculate rt:

rt = 0.055 * (168/365)

= 0.0252836 (rounded to 7 decimal places)

Now, substitute the values into the expression P(1+rt):

P(1+rt) = 1575 * (1 + 0.0252836)

= 1575 * 1.0252836

= 1615.85846 (rounded to 5 decimal places)

The result is approximately $1615.86.

Therefore, the correct option is a) $5161.24

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Step-by-step explanation:

x+35+25=180

x+60 =180

x = 120.

y+x =18

1. The total retail sales for grocery stores for 1990 through 2000 is approximately $2,700.17 billion.

2. The total distance traveled by the rubber ball after it hits the ground for the fifth time is approximately 7.744 meters.

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols to solve equations and study relationships between variables.

1. To approximate the total retail sales for grocery stores from 1990 to 2000 using the given formula, we need to find the sum of the values of a(1-rⁿ)/(1-r) from n=0 to n=10, where a = 208 and r = 1.05.

Using the formula, we get:

a(1-rⁿ)/(1-r) = 208(1-1.05¹¹)/(1-1.05)

Simplifying this expression, we get:

= 208(1-1.64872)/(-0.05)

= 208(0.64872)/0.05

= 2700.17

2. The total distance traveled by the rubber ball after it hits the ground for the fifth time is equal to the sum of the distances traveled during each bounce. The distance traveled during each bounce can be found using the formula d = 2h, where d is the distance traveled and h is the height of the bounce.

For the first bounce, the height is 2 meters. For each subsequent bounce, the height is 60% of the previous height. Therefore, the heights of the bounces form a geometric sequence with a = 2 and r = 0.6.

The distance traveled during each bounce is given by:

d = 2h = 2(2)(0.6ⁿ)

The total distance traveled after the fifth bounce is:

d total = d1 + d2 + d3 + d4 + d5

= 2(2) + 2(2)(0.6) + 2(2)(0.6)² + 2(2)(0.6)³ + 2(2)(0.6)⁴

= 7.744 meters

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Answer:

3

Step-by-step explanation:

4 x 3 = 12

4 ÷ 12 = 3

its like multiplication just changing the way you solve it

Answer:

.33

Step-by-step explanation:

The number which when increased by 12 is two times its opposite. is

N = -4

final equation N + 12 = -2N

Additive inverse is the opposite of a number in terms of addition, this is the number that gives zero when added to the original number.

To get a result equal to 0, add the original number and the additive inverse or by simply changing the sign of the integer. On the basis of negation of the original number.

The problem says

N + 12 = -2N

N + 2N = -12

3N = -12

N = -4

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