Claim: The standard deviation of pulse rates of adult males is less than 12bpm. For a random sample of 141 adult males, the pulse rates have a standard deviation of 10.5bpm. Find the value of the test statistic.

Answer:

x=2

Step-by-step explanation:

28−(3x+4)=2(x+6)+x

We need to use the distributive property for the right side.

28−3x−4=(2)(x)+(2)(6)+x)

28−3x−4=2x+2+x

−3x+24=3x+12

From here we need to subtract 3x from both side.

−3x+24−3x=3x+12−3x

6x+24=12

Transfer +24 on the right side.

6x=12−24

6x=−12

Finally, divide both sides by −6

6x/-6 = -12/-6

x=2

Answer:

need more information

The function with an amplitude of 3 and a phase shift of π/2 is h(x) = 3 cos (2x - π/2) + 3.

The amplitude of a function is the distance between the maximum and minimum values of the function, divided by 2. The phase shift of a function is the horizontal shift of the function from the standard position,

(y = cos(x) or y = sin(x)).
To find the function with an amplitude of 3 and a phase shift of π/2, we need to look for a function that has a coefficient of 3 on the cosine term and a horizontal shift of π/2.
Looking at the given options, we can eliminate option a) because it has a coefficient of -3 on the cosine term, which means that its amplitude is 3 but it is inverted.

Option b) has a coefficient of 3 on the cosine term but it has a phase shift of -π/2, which means it is shifted to the left instead of to the right. Option d) has a phase shift of π/2, but it has a coefficient of -2 on the cosine term, which means its amplitude is 2 and not 3.
A*cos(B( x - C)) + D

Where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

f(x) = -3 cos(2x - π) + 4

Amplitude: |-3| = 3

Phase shift: π (not π/2) b) g(x) = 3cos(2x + π) -1

Amplitude: |3| = 3

Phase shift: -π (not π/2) c) h(x) = 3 cos (2x - π/2) + 3

Amplitude: |3| = 3

Phase shift: π/2 d) j(x) = -2cos(2x + π/2) + 3200

Amplitude: |-2| = 2 (not 3)

Phase shift: -π/2
Therefore, the only option left is c) h(x) = 3 cos (2x - π/2) + 3. This function has a coefficient of 3 on the cosine term and a horizontal shift of π/2, which means it has an amplitude of 3 and a phase shift of π/2.
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Answer:

Brandon is 7 years old

Step-by-step explanation:

(27 - 6) / 3 = 7

27 = Sam's age

6 = years greater compared to/than means subtraction

3 =  times greater compared to/than means divion.

27 - 6 is in parentheses because it must be done first.

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The Pigeonhole Principle states that if you have more objects than the number of distinct categories they can be assigned to, then at least one category must have more than one object. In the case of picking socks from a drawer, if there are m pairs of socks (2m socks total), picking m + 1 socks ensures that at least two socks will make up a matching pair.

The Pigeonhole Principle can be applied to the scenario of picking socks from a drawer. Suppose there are m pairs of socks in the drawer, which means there are a total of 2m socks. Now, let's consider the act of picking m + 1 socks at random.

When you pick the first sock, there are m + 1 possibilities for a matching pair. As you pick the subsequent socks, each sock can either match a previously picked sock or be a new one. However, once you have picked m socks, all the pairs of socks have been exhausted, and the next sock you pick is guaranteed to match one of the previously chosen socks.

Since you have picked m + 1 socks and all the pairs have been accounted for after m socks, there must be at least one matching pair among the m + 1 socks you have selected. This is a direct consequence of the Pigeonhole Principle, as there are more socks (m + 1) than distinct pairs of socks (m).

Therefore, by applying the Pigeonhole Principle, we can conclude that if you pick m + 1 socks at random from a drawer containing m pairs of socks, at least two socks will make up a matching pair.

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Answer:

Correct options:

(x – 8)² + (y – 9)² = 3

(x – 8)² + (y – 9)² = 14

Step-by-step explanation:

If the circle has a center at (8,9), the equation for this circle is:

\((x-8)^2 + (y - 9)^2 = r^2\)

All concentric circles have the same center, so their equations need to have the same left side of the equation above.

-> x2 + y2 = 25

This circle has a center at (0,0), so it's not concentric to our circle.

-> (x – 8)² + (y – 9)² = 3

This circle has a center at (8,9), so it's concentric to our circle.

-> (x – 8)² + (y – 9)² = 14

This circle has a center at (8,9), so it's concentric to our circle.

-> (x – 8)² + (y + 9)² = 3

This circle has a center at (8,-9), so it's not concentric to our circle.

-> (x + 8)² + (y + 9)² = 25

This circle has a center at (-8,-9), so it's not concentric to our circle.

-> (x + 9)² + (y + 8)² = 3

This circle has a center at (-8,-9), so it's not concentric to our circle.

Correct options:

(x – 8)² + (y – 9)² = 3

(x – 8)² + (y – 9)² = 14

Answer:

B. (x – 8)² + (y – 9)² = 3

C.(x – 8)² + (y – 9)² = 14

Step-by-step explanation:

edg 2020

Answer:

------------------------

We have a repeating decimal 4.6(1).

Let's express it as a GP:

Fund the sum of infinite GP, with the first term of a = 0.01 and common ratio of r = 0.1:

Add 4.6 to the sum:

Hence the fraction is 4 11/18.

Answer: 8

Step-by-step explanation:

CF looks like the radius of the circle.

ED looks like the diameter.

.: ED = 2 x CF = 2 x 4 = 8

.: ED = 8

Answer:

The length of ED, or the diameter, is 8

Step-by-step explanation:

As the other person explained, CF is the radius, as the radius is from the centermost point to the edge.  I also see that ED is the diameter, as the diameter is from edge to edge, going through the centermost point.  Therefore, since the diameter is double the radius, we can solve this with the following equation:

2 * r = d, where r is radius and d is diameter.

2 * 4 = d

8 = d

Answer:

240

Step-by-step explanation:

First start with the inner most bracket

20 - 6 = 14

Then solve the next bracket

14 + 1 = 15

Then the next

15 x 8 = 120

Then divide by a half (times by 2)

120 / 0.5 = 240

The columns of a matrix are dependent if there exists a vector combination that results in a vector of zeroes.

This can be tested using a vector V of coefficients, such that:

\(MV = 0\)

If this is true, then the columns of M are dependent. To illustrate this with an example, consider a 3x3 matrix:

\(M = [[a, b, c], [d, e, f], [g, h, i]]\)

To find the vector combination V that results in a vector of zeroes, we can use Gaussian elimination to reduce the matrix to row echelon form:

\(M = [[1, 0, -c/a], [0, 1, -f/e], [0, 0, 0]]\)

From this, we can deduce the vector combination V:

\(V = [1, -(c/a)*(f/e), 1]\)

Therefore, the columns of M are dependent.

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Answer:

3.14*15^2=706.5

706.5/2=353.25

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The area of the semi-circle with a diameter of 60 cm is approximately 1413 square centimeters.

A semicircle is formed by simply dividing a circle into exactly two halves.

Hence, the area of a semi-circle is half the area of a circle.

Area of semi-circle = 1/2 × πr²

Given the parameters:

Diameter d = 60 cm

Radius r = diameter/2 = 60/2 = 30 cm

Area =?

To determine the area of the semi-circle, plug the value of the radius into the above formula and simplify:

Area of semi-circle = 1/2 × πr²

Area of semi-circle = 1/2 × 3.14 × 30²

Area of semi-circle = 1/2 × 3.14 × 900

Area of semi-circle = 3.14 × 450

Area of semi-circle = 1413 cm²

The area is approximately 1413 square centimeters.

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We would use the confidence interval formula for a proportion when you have summary information as a percentage or survey sample data.

The correct answer is an option (d)

We know that the confidence interval formula for a proportion is:

\(\hat{p} \pm z' \sqrt{\frac{\hat{p}(1-\hat{p})}{n} }\)

where \(\hat{p}\) is the standard error,

the value of z' is determined by the confidence level C

Also, C percent of the standard normal distribution is between -z' and z'

The sample proportion is calculated by counting the number of successes in our sample and then dividing by the total number of individuals in the sample.

Therefore, we can conclude that the confidence interval formula for a proportion is used when you have summary information as a percentage or survey sample data.

The correct answer is an option (d)

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The complete question is:

when would you use the confidence interval formula for a proportion? (choose one or more) group of answer choices

a) to determine if the groups are significantly different

b) you do not know the standard deviation

c) your sample size is under 30

d) you have summary information as a percentage or survey sample data

The probability that represents the likelihood of a single event occurring by itself is called marginal probability.

Marginal probability refers to the probability of an individual event happening independently without considering any other events. It focuses on a single variable or outcome without considering the relationship or dependencies with other variables.

To calculate marginal probability, you divide the number of times the specific event occurs by the total number of observations. For example, if you have a bag of marbles with different colors and you want to find the marginal probability of drawing a red marble, you would count the number of red marbles and divide it by the total number of marbles in the bag.

Marginal probability is often used when working with categorical variables or when studying the probability of a single event without considering any other variables or conditions. It provides a fundamental understanding of the likelihood of an event occurring in isolation, independent of any other factors.

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Answer:

2 to the power of 6

Step-by-step explanation:

2 x 2 x 2 x 2 x 2 x 2

Answer:

x >5

Step-by-step explanation:

4(x - 3) - 2(x - 1) >0

Distribute

4x -12 -2x +2 > 0

Combine like terms

2x -10 >0

Add 10 to each side

2x-10+10 > 10

2x>10

Divide each side by 2

2x/2 > 10/2

x >5

The answer is: [C]: " {x | x > 5} " .

__________________________________________

Explanation:

__________________________________________

Given: " 4(x − 3) − 2(x − 1) > 0 " ;

__________________________________________

Note the "distributive property of multiplication" :

__________________________________________

a(b+c) = ab + ac ;

a(b−c) = ab − ac ;

___________________________________________

So, given:

_________________________________________________

→ 4(x − 3) − 2(x − 1) > 0 ;

_________________________________________________

Let us simplify; and rewrite:

_________________________________________________

Start with:

______________________________________________________

→ -2 (x − 1) = (-2*x) − (-2 *1) = -2x − (-2) = -2x + 2 ;

______________________________________________________

Now, continue with:

→ 4(x − 3) = (4*x) − (4*3) = 4x − 12 ;

______________________________________________________

So, given the original problem:

______________________________________________________

→ 4(x − 3) − 2(x − 1) > 0 ;

______________________________________________________

Rewrite;

Replacing: "4(x − 3)" ; with: "4x − 12" ;

and replacing "− 2(x − 1)" ; with: " -2x + 2" ;

______________________________________________________

as follows: → " 4x − 12 − 2x + 2 " > 0 ;

______________________________________________________

On the "left-hand side", combine the "like terms", and simplify ;

______________________________________________________

+4x −2x = +2x ; −12 +2 = -10 ; and rewrite:

______________________________________________________

→ 2x − 10 > 0 ; Add "10" to EACH SIDE of the inequality;

______________________________________________________

→ 2x − 10 + 10 > 0 + 10 ;

______________________________________________________

to get: → 2x > 10 ;

______________________________________________________

→ Now, divide EACH SIDE of the inequality by "2";

to isolate "x" on one side of the inequality; & to "solve"/"simply" for "x" ;

_______________________________________________________

→ 2x / 2 > 10 / 2 ;

_______________________________________________________

→ x > 5 ; which is:

_______________________________________________________

→ Answer choice: [C]: " {x | x > 5} " .

_______________________________________________________

The required missing values are $2.5 when the cup of milk is 1, $8.75 when the cup of milk is 3.5, and $6.25 when the cup of milk is 2.5.

The table is given in the question as :

Tea (cups) $3.75

Milk (cups) $1.5  $1   $3.5   $2.5

Let the missing value cup of tea would be x when the cup of milk is 1,

The missing value cup of tea would be y when the cup of milk is 3.5,

And the missing value cup of tea would be z when the cup of milk is 2.5,

According to the given question, we can write the ratio as:

$3.75 Tea (cups) : $1.5 Milk (cups) = x Tea (cups) : $1 Milk (cups)

⇒ 3.75 / 1.5 = x / 1

⇒ x = 3.75 / 1.5

⇒ x = $2.5

$3.75 Tea (cups) : $1.5 Milk (cups) = y Tea (cups) : $3.5 Milk (cups)

⇒ 3.75 / 1.5 = y / 3.5

⇒ y = (3.75 / 1.5) × 3.5  

⇒ y = 2.5 × 3.5  

Apply the multiplication operation,

⇒ y = $8.75

$3.75 Tea (cups) : $1.5 Milk (cups) = z Tea (cups) : $2.5 Milk (cups)

⇒ 3.75 / 1.5 = y / 2.5

⇒ z = (3.75 / 1.5) × 2.5  

⇒ z = 2.5 × 2.5  

Apply the multiplication operation,

⇒ z = $6.25

Thus, the required missing values are $2.5 when the cup of milk is 1, $8.75 when the cup of milk is 3.5, and $6.25 when the cup of milk is 2.5.

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Answer:

3/4n=15

1/4n=15/3

4n=3/15

n=3/15×4

n=3/60

n=1/20

Step-by-step explanation:

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Answer:

n=20

Step-by-step explanation:

4 * 3/4n=15 * 4

3n=60

3n/3=60/3

n=20

The Practice Operations with radical expressions is simplified using the basic of the Algebra:

Algebraic expressions incorporating radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both). The root might be an nth root, a square root, or a cube root. Radical expressions can be made simpler by taking them down to their most basic form and, if feasible, getting rid of all of the radicals.

Radical expressions are simplified by taking them down to their most basic form and, if feasible, altogether deleting the radical. An algebraic expression's numerator and denominator are multiplied by the appropriate radical expression if the denominator contains a radical expression.

Practice Operations with radical expressions are:

1) \(\sqrt{540}\) = \(\sqrt{36 * 15 }\)

= 6√15

2) \(\sqrt[3]{432}\) = \(\sqrt[3]{216*2}\)

= \(6\sqrt[3]{2}\)

3) \(\sqrt[3]{128}\) = \(\sqrt[3]{64*2}\)

= \(4\sqrt[3]{2}\)

4) \(-\sqrt[4]{405}\) = \(-\sqrt[4]{81*5}\)

= \(-3\sqrt[4]{5}\)

5) \(\sqrt[3]{-5000}\) = \(-\sqrt[3]{1000*5}\)

= \(-10\sqrt[3]{5}\)

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Using the Bayes' theorem, we find the probability that the transferred ball was white given that the second ball drawn was white to be 52/89, or approximately 0.5843.

To solve this problem, we can use Bayes' theorem, which relates the conditional probability of an event A given an event B to the conditional probability of event B given event A:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this problem, we want to find the probability that the transferred ball was white (event A) given that the second ball drawn was white (event B). We can calculate this probability as follows:

P(A|B) = P(B|A) * P(A) / P(B)

P(B|A) is the probability of drawing a white ball from urn b given that the transferred ball was white and is now in urn b. Since there are now six white balls and three black balls in urn b, the probability of drawing a white ball is 6/9 = 2/3.

P(A) is the prior probability of the transferred ball being white, which is the number of white balls in urn a divided by the total number of balls in urn a, or 6/13.

P(B) is the prior probability of drawing a white ball from urn b, which can be calculated using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where P(B|not A) is the probability of drawing a white ball from urn b given that the transferred ball was black and P(not A) is the probability that the transferred ball was black, which is 7/13.

To calculate P(B|not A), we need to first calculate the probability of the transferred ball being black and then the probability of drawing a white ball from urn b given that the transferred ball was black.

The probability of the transferred ball being black is 7/13. Once the transferred ball is moved to urn b, there are now five white balls and four black balls in urn b, so the probability of drawing a white ball from urn b given that the transferred ball was black is 5/9.

Therefore, we can calculate P(B) as follows:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= (2/3) * (6/13) + (5/9) * (7/13)

= 89/117

Now we can plug in all the values into Bayes' theorem to find P(A|B):

P(A|B) = P(B|A) * P(A) / P(B)

= (2/3) * (6/13) / (89/117)

= 52/89

Therefore, the probability that the transferred ball was white given that the second ball drawn was white is 52/89, or approximately 0.5843.

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Answer:

no

Step-by-step explanation:

adding random numbers and variables to any equation changes the equation. No, the answer would not be equal.

The equation can be written in the form f(x) = a(1 + r)x or f(x) = abx where b = 1 + r. a is the initial or starting value of the function, r is the percent growth or decay rate, written as a decimal, b is the growth factor or growth multiplier.

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Answer:

The equation of the line through the given points is y = (1/2)x + 1.

Step-by-step explanation:

To find the equation of a line passing through two given points, we can calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Given the points (7, 2) and (-1, 0), we have:

m = (0 - 2) / (-1 - 7) = -2 / -8 = 1/4

Next, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) represents one of the given points. Let's choose the point (7, 2):

y - 2 = (1/4)(x - 7)

Expanding and rearranging the equation, we get:

y - 2 = (1/4)x - (7/4)

y = (1/4)x - (7/4) + 2

y = (1/4)x - (7/4) + (8/4)

y = (1/4)x + 1

Therefore, the equation of the line passing through the points (7, 2) and (-1, 0) is y = (1/4)x + 1.

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Answer:

13mm

Step-by-step explanation:

To calculate the mean length of the insects Mick found, we need to find the sum of all the lengths multiplied by their respective frequencies, and then divide it by the total frequency.

The length intervals and their frequencies are as follows:

0 < x ≤ 10 (frequency = 9)

10 < x ≤ 20 (frequency = 6)

20 < x < 30 (frequency = 5)

To calculate the mean length, we can follow these steps:

Multiply each length interval by its corresponding frequency:

Sum = (9 * (0 + 10)/2) + (6 * (10 + 20)/2) + (5 * (20 + 30)/2)

= (9 * 5) + (6 * 15) + (5 * 25)

= 45 + 90 + 125

= 260

Calculate the total frequency by adding up the frequencies:

Total frequency = 9 + 6 + 5

= 20

Divide the sum by the total frequency to find the mean length:

Mean length = Sum / Total frequency

= 260 / 20

= 13

Therefore, the estimate of the mean length of the insects Mick found is 13 mm.

Answer:

1008 calories

Step-by-step explanation:

one pound = 16 ounces

16 ÷ 8 = 2

504 × 2 =

1008

To estimate 179% of 41 by rounding and using the distributive property, the expression would be 1.79 × 41, which is approximately equal to 73.39.

To estimate 179% of 41 by rounding, we can use the following expression: (180% of 40).
First, let's break down the expression step by step.
1. Start with 41, the number we want to find 179% of.
2. Round 41 down to the nearest ten to get 40. This simplifies the calculation.
3. Take 180% of 40. To do this, we first convert 180% to a decimal by dividing it by 100. 180% becomes 1.8. Then, multiply 1.8 by 40 to get the result.
  Calculation: 1.8 * 40 = 72.
In summary, to estimate 179% of 41 by rounding, we use the expression (180% of 40). This is equivalent to multiplying 1.8 by 40, which gives us an answer of approximately 72.

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Answer:

180%(40)D

(100%)(40)+(80%)(40)B

72    B

Step-by-step explanation:

trus

Answer:

Answer:

angle 1 and angle 2 are supplementary angles

Step-by-step explanation:

When the base of the angles forms a straight line, the sum of the angles is 180°. That's the definition of supplementary angles.

Complementary angles form a right angle. The sum of complementary angles is 90°

A slightly silly way to remember Complementary angles: The two angles look at each other and compliment each other saying, "You look all right to me!"

"Yes, we are so right together!"

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