a company making refrigerators strives for the internal temperature to have a mean of 37.5 degrees with a standard deviation of 0.6 degrees, based on samples of 100. a sample of 100 refrigerators have an average temperature of 37.37 degrees. are the refrigerators within the 90% confidence interval?

We are unable to reject the null hypothesis since the p-value is bigger than the level of significance of 0.10. The pressure of playing in the final round is 0.10 < P < 0.20.

The information shows the results from the first and fourth rounds. The level of relevance is

α = 0.10

The Null Hypothesis is

H(0) = μ(d)

This indicates that the population mean score for the first round and the fourth round are the same.

Alternative Hypothesis:

H(α): mμ(d) ≠ 0

This indicates that the population score from the first round and the fourth round are different.

The following is the testing procedure:

t = (d - μ(d))/(s(d)/√n)

This can solved using the excel is given as:

0.10 < P < 0.20

We are unable to reject the null hypothesis since the p-value is bigger than the level of significance of 0.10.

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Answer:

Step-by-step explanation:

area of field=1/2(a+b)h

a=12

b=20

h=?

h=pythagoras theorem

a²+b²=c²

a²+8²=17²

a²+64=289

a²=289-64

a²=221

a=√221

a=14.9

area of field=1/2(12+20)14.9

area=238.4m²

£19.75×3=£59.25

The investment compounded periodically will be worth $14,054.52, which is $596.10 more than the investment compounded annually.

To calculate the future value of the investment compounded periodically, we need to use the formula:

FV = P * (1 + (r / n))^(n * t)

where:

P = $6,000 (principal)

r = 6% (annual interest rate)

n = 12 (number of interest periods per year)

t = 17 (number of years)

Plugging in the values, we get:

FV = $6,000 * (1 + (0.06 / 12))^(12 * 17) = $6,000 * (1 + 0.005)^204

FV = $6,000 * (1.005)^204

FV = $14,054.52

So, the investment compounded periodically will be worth $14,054.52 after 17 years.

To calculate the future value of the investment compounded annually, we use the same formula but with n = 1 (one interest period per year):

FV = $6,000 * (1 + 0.06)^17

FV = $6,000 * (1.06)^17

FV = $13,458.42

So, the investment compounded annually will be worth $13,458.42 after 17 years.

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The measure of each angle is -

∠E = 63°

∠F = 43°

∠D = 74°

Scale factor tells us by how much one quantity is greater than the other. It is denoted by {K}. Mathematically -

K = a/b                        .... Eq { 1 }

Rewriting, we get -

a = Kb                             .... Eq { 2 }

If a side length [a] of any 2 - D figure is dilated by a scale factor of [k], then the length of new side will be [Ka].

Given are the two similar triangles as ΔABC and ΔDEF.

Since the triangles are similar, their corresponding angles are equal. We can write -

∠C = ∠F                                    {triangles are similar}

(5x + 8) = (6x + 1)

6x - 5x = 8 - 1

x = 7                                                   .... Eq { 1 }

∠A = ∠D                                                     {triangles are similar}

(8y + 2) = (11y - 25)

11y - 8y = 27

3y = 27

y = 9                                                                   .... Eq { 2 }

We can write -

∠D + ∠E + ∠F = 180°                                                        .... Eq { 3 }

(6x + 1) + (11y - 25) + ∠E = 180°

(6 x 7 + 1) + (11 x 9 - 25) + ∠E = 180°

43 + 74 + ∠E = 180°

∠E = 180 - 117

∠E = 63°

∠F = (6x + 1) = 43°

∠F = 43°

∠E = (11y - 25) = 74°

∠D = 74°

Therefore, the measure of each angle is -

∠E = 63°

∠F = 43°

∠D = 74°

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There are 363600 ways to arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people if the bride must be in the picture.

There are 2 possibilities for the position of the bride: either she is first in the row, or she is not first in the row.

If the bride is first in the row, then there are 5 people to choose from for the second person, 4 people to choose from for the third person, and so on, until there is only 1 person left to choose from for the last person in the row. Thus, there are 5! (5 factorial) ways to arrange the 5 people after the bride.

If the bride is not first in the row, then there are 9 people to choose from for the first person, 8 people to choose from for the second person, and so on, until there is only 1 person left to choose from for the last person in the row. Thus, there are 9! (9 factorial) ways to arrange the 9 people before the bride.

Therefore, the total number of ways to arrange the 6 people in a row is 5! + 9! = 720 + 362880 = 363600.

So, in total, there are 363600 ways to arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people if the bride must be in the picture.

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--The given question is incomplete; the complete question is

"In how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people if the bride must be in the picture."--

Answer:

$49.93

Step-by-step explanation:

The mean of the data set is   427.5

We know that the mean of the data set as computed is obtained from; 345+340+400+625/ 4=  427.5

To obtain the variance of the data.

We now have to take the difference of the values and square it.

345-427.5 = -82.5

340-427.5 =-87.5

400-427.5 = -27.5

625-427.5 =197.5

Thus;

Variance=σ2 =(-82.5)^2 + (-87.5)^2 + (-27.5)^2+ (197.5)^2 /4  

σ2=6806.25+7656.25+756.25+39006.25/4

σ2=13556.25

The variance is 13556.2

For  the Standard deviation (S.D) of the data;

σ = √13556.25

σ =116.43

The Standard deviation of the data is 116.4

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The required unit of the measure of the mean is given as in Dollars. Option A is correct.

What does math's median mean?

When a data set's median value is used, 50% of the data points in the collection have values that are lower or equal to the median and 50% of them have values that are higher or equal to the median.

                               When working with a small data collection, you must first count the number of data points (n) and organize them in ascending order.

Due to that,

With a mean of $21,800 and a standard deviation of $400, the price distribution for a specific car model is roughly typical. Four of the model's cars will be chosen at random as the sample.

                                  It must be established which unit of measurement is appropriate for the mean of the sample distribution of the car's pricing.

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A graph of the solution to this system of equations on a coordinate plane is shown in the image attached below.

This system of equations has: A. one solution.

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

7x - 6y = -12     ......equation 1.

x - y = -1     ......equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant III and it is given by the ordered pair (-6, -5).

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The rate of change of the distance among the car and the person at that instant is 110,98 m/s.

To find the average rate of change, we need to divide the change in y (output) by the change in x (input). And visually, all we are doing is calculating the slope of the secant line passing among two points. Finding the average rate of change is particularly useful for determining changes in measurable values like average speed or average velocity.

In this case, consider A as the point where a person is, the intersection (o) and the car from the north form a right triangle. So, based on Pythagoras Theorem:

L^2 = x^2 + y^2

where:

L is the distance between the person and the car.

x is constant since the person does not move.

Now, taking derivatives with respect to time, we will have:

2 * L * dL/dt = 2 * y * dy/dt (1)

where:

x = 15 mts

y = 888

dy/dt = 111 m/s

Now, substitute all the values into the formula:

L^2 = x^2 + y^2

L = √ (15)^2 + (888)^2

L = √ 225 + 788544

L = 888,13 m

So, when we apply to the (1) equation, it will be:

2 * L * dL/dt = 2 * 888 * 111

dL/dt = (888) * 111 / 888,13

dL/dt = 0,99 * 111

dL/dt = 110,98 m/s

Hence, the rate of change of the distance is 110,98 m/s.

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Answer:

3.5 gallons

Step-by-step explanation:

A gallon is 4 quarts

7*2= 14 quarts

14/4 = 3.5

The simplified form of ix^{73}ix is C. -i−i

The power rule of exponents states that when you raise a number to a power, and that number is being multiplied by another number raised to the same power, then you can multiply the numbers together and raise the result to the same power.

For example, if you are raising 8 to the third power, and 3 to the third power, then you can multiply the two together and raise the result to the third power (8x3=24; 24^3=13824).

Therefore, by using the power rule of exponents, ix^{73}ix can be simplified to i^48i, which is equal to (-i)(-i) or C. -i−i.

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An equation for Windy Kite's total cost, y, in terms of the number of kites purchased, x, is y = 2x + 20.

An equation for Kites-R-Fun's total cost, y, in terms of the number of kites purchased, x, is y = 4x + 8.

Based on the table, if the Alaskan customer wants to buy 4 kites, Kites-R-Fun charges the least.

If the Alaskan customer wants to buy 10 kites, Windy kites charges the least.

The solution to the system of equations is (6, 32)

In order to write a linear equation to describe this situation, we would a assign variable to the number of kites purchased and the total cost respectively, and then translate the word problem into a linear equation as follows:

Since Wendy charges $2 per kite and a flat rate of $20 for shipping, a linear equation that models the total cost is given by:

y = 2x + 20

When x = 4, the total cost for Windy kites is given by:

y = 2(4) + 20

y = $28.

When x = 7, the total cost for Windy kites is given by:

y = 2(7) + 20

y = $34.

When x = 10, the total cost for Windy kites is given by:

y = 2(10) + 20

y = $40.

For Kites-R-Fun, a linear equation that models the total cost is given by:

y = 4x + 8

When x = 4, the total cost for Kites-R-Fun is given by:

y = 4(4) + 8

y = $24.

When x = 7, the total cost for Kites-R-Fun is given by:

y = 4(7) + 8

y = $36.

When x = 10, the total cost for Kites-R-Fun is given by:

y = 4(10) + 8

y = $48.

Lastly, we would use an online graphing calculator to plot the system of linear equations as shown in the graph attached below.

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The number of years is given by the equation T = 10 years

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of years to qualify to receive Social Security benefits when Stacy retires be T

Now , the equation will be

The present age of Stacy = 46 years

The maximum number of credits each year = 4 credits

As to earn the social security benefits, she needs to earn 40 credits

So , the number of years = 40 credits / maximum number of credits each year

Substituting the values in the equation , we get

The number of years to qualify to receive Social Security benefits when Stacy retires T = 40/4

On simplifying the equation , we get

The number of years to qualify to receive Social Security benefits when Stacy retires T = 10 years

Hence , the number of years is 10 years

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The correct option Input-Output Tables for Function Rules is

f(x)= 2x +3.

Input (x):       3   6  9   12

Output(f(x)):  9  15 21  27

Give:

Observe the table:

Each pair of numbers in the table is related by the same function rule. That rule is: multiply each input number (x-value) by 2 then add 3 to find each output number (y-value) or f(x). You can use a rule like this to find other values for this function, too.

Now look at how to use a function rule to complete a table.

Input (x) Output (f(x))      Rule : f(x)=2x + 3

3               9                          2x3+3= 9

6                   15                          2x6+3=15

9               21                          2x9+3=21

12              27                          2x12+3=27

So here we can see by using f(x)=2x + 3, we can find the output.

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The sum of this infinite geometric series is -25/9.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

The given geometric series is -5+4-16/5+64/25-256/125

The general formula for finding the sum of an infinite geometric series is S= a/1-r, where s is the sum, a is the first term of the series, and r is the common ratio.

Here, a=-5 and r= -4/5

Now, S = -5/(1+4/5)

= -5/(9/5)

= -25/9

Therefore, the sum of the series is -25/9.

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The equation is 230-q=336 which is solved by combining like terms to result in q=-106.

What are like terms?

The term "like terms" in algebra refers to terms that have the same variable raised to the same power. Only the numerical coefficients can vary in terms that are similar to algebra. To make the algebraic formulae simpler, we can combine like terms.

The statement of an equation is given as -

336 is 230 decreased by q.

230 is decreased by q is equivalent to 230 subtracted by q and the number obtained by the above arithmetic operation of subtraction is equal to 336.

The mathematical equation is written as -

230-q=336

Simplify the equation by combining like terms -

-q=336-230

-q=106

q=-106

Therefore, on evaluating the equation the result is -106.

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Answer:

15/2

Step-by-step explanation:

If y is proportional to x, then the equation is

y = kx, where k is the constant of proportionality.

Here we have

f = 15/2 g, so the constant of proportionality is 15/2.

The function The output is one more than twice the input x" is f(x) = 2x + 1.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

The given statement is "The output is one more than twice the input x"

Therefore, If 'x' is the input then the output is 2x + 1.

So, The function can be written as f(x) = 2x + 1.

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Answer:

35 million

Step-by-step explanation:

The peak of sales in this problem is the vertex of the parabola that can be graphed from the given equation.

The vertex of a parabola is defined as:

[tex]\left(-\dfrac{b}{2a}, \dfrac{b^2 - 4ac}{4a} \right)[/tex]

when a, b, and c correspond to the unfactored quadratic form: [tex]ax^2 + bx + c[/tex].

So, we can use the given equation:

[tex]S = -4x^2 + 24x - 1[/tex]

to assign the following variables:

[tex]a = -4[/tex],   [tex]b = 24[/tex],   [tex]c=-1[/tex]

Using these variables, we can find the vertex of the parabola by plugging them into the above definition.

[tex]\left(-\dfrac{b}{2a}, \dfrac{b^2 - 4ac}{4a} \right)[/tex]

[tex]\left(-\dfrac{24}{2(-4)}, \dfrac{24^2 - 4(-4)(-1)}{4(-4)} \right)[/tex]

[tex]\left(\dfrac{24}{8}, \dfrac{576 - 16}{-16)} \right)[/tex]

[tex]\left(3, 35 \right)[/tex]

So, the peak sales for the game are 35 million.

The given statement in the form of inequality is given as -

c - 6 > 24.

An inequality is used to make unequal comparisons between two or more expressions. For example → ax + b > c

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the statement as -

"Six subtracted from c is greater than 24"

We can write the inequality as -

c - 6 > 24

Therefore, the given statement in the form of inequality is given as -

c - 6 > 24.

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{Question in english -

Six subtracted from c is greater than 24}

Mr. Kama and Mrs. Ronoh meet at 26.72 km away from point R.

The relative speed is the net speed of two different objects with respect to each other.

If two objects move in the same direction we take the difference between their speeds.

If two objects move in the opposite direction we take the sum of their speeds.

Given, Mr. Kama left town 'S' at 6:00 am and travels at an average speed of 24 km/hr towards 'R',

And Mrs. Ronoh left town R to town IS 10 minutes later and arrived at

7:00 am.

So, The speed of Mrs. Ronoh is 42 km/hr as the distance between RS is

42 km.

Therefore, The point at which they meet is,

= (42/(24 + 42))×42.

= 0.63×42 = 26.72 km from the point 'R' as Mrs. Ronoh is faster.

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Answer:x=4

Step-by-step explanation:

A set of outcomes from an experiment to which a probability is assigned is called "Event." Therefore, the option d is the correct answer. This term is related to probability.

Probability is a statistic that expresses the results of a specific experiment or activity. A simple experiment is to flip a coin twice. There are some terms related to probability, as below:

Examining a procedure or interviewing a chosen sample of people in order to collect data is known as a survey.

The population is the entire group of participants in research with its characteristics that will be a data source.

The sample space is the set of all possible outcomes. The sample space is indicated with letter S.

S = {H, T}.

Event is a set of outcomes from an experiment to which a probability is assigned. Any subset of the sample space (S) is called an event.

S = {H, T}.

The number of individuals or observations included in a study is referred to as the sample size. Usually, n is used to indicate this number.

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The probability of a defective rivet be to ensure that only 11% of all seams need reworking must be less than or equal to 11%.

Let's say the probability of a defective rivet is p. The probability of k defective rivets in n seams is given by the binomial distribution:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) is the number of combinations of n items taken k at a time.

We want to find the smallest value of p such that P(k) <= 0.11 for k = 0, 1, 2, ..., n. In other words, we want the smallest p such that the probability of having 0 to n defective rivets is less than or equal to 11%.

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Based on the scatterplots provided, the answer would be A. A power model is suitable because the scatterplot of log(weeks) against log(stock price) shows a curved relationship.

In the scatterplots of log(weeks) against log(stock price), we can see that the relationship between the two variables is not linear, but rather appears to be curved. This suggests that a power model may be more appropriate, since this type of model can capture non-linear relationships.

A linear model is not suitable in this case, as the relationship between weeks and stock price does not appear to be linear. While the scatterplot of weeks against log(stock price) shows a strong linear relationship, this plot is not as appropriate for estimating the stock price as the plot of log(weeks) against log(stock price).

An exponential model may also be appropriate for capturing non-linear relationships, but the plot of weeks against log(stock price) does not show a strong linear relationship, so it is less appropriate than the plot of log(weeks) against log(stock price).

Overall, based on the provided scatterplots, a power model is the most suitable for estimating the stock price.

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Based on the scatterplots, which type of model is most suitable for estimating the stock price?

A. A power model is suitable because the scatterplot of log(weeks) against log(stock price) shows a curved relationship.

B. A linear model is suitable because the scatterplot of weeks against log(stock price) shows a strong linear relationship.

C. An exponential model is suitable because the scatterplot of log(weeks) against log(stock price) shows a curved relationship.

D. An exponential model is suitable because the scatterplot of weeks against log(stock price) shows a strong linear relationship.

The resulting disjoint sets after the operation union({7, 4}) would be: {5, 7, 9, 1, 11, 4, 2, 3, 6, 8, 10}.

The union of two sets A and B is denoted by A ∪ B and is defined as the set of all elements that are either in A or in B or in both. Therefore, the resulting disjoint sets after the operation union({7, 4}) would be:

{5, 7, 9, 1, 11, 4, 2, 3, 6, 8, 10}.

To calculate the union, we can use the following formula:

A ∪ B = {x : x ∈ A or x ∈ B}

Therefore, the union of {7, 4} can be calculated as:

{7, 4} ∪ {7, 4} = {x : x ∈ {7, 4} or x ∈ {7, 4}}

= {7, 4}

Therefore, the resulting disjoint sets after the operation union({7, 4}) would be: {5, 7, 9, 1, 11, 4, 2, 3, 6, 8, 10}.

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Answer:

x = 11√2

Step-by-step explanation:

This is a special right triangle. It is marked with a small box in one angle. That is a right angle. So it is a right triangle. It is also marked on two sides with a single hash mark to show that those two sides are the same. This means that the two smaller angles are the same. This is a 45°-45°-90° triangle.

A 45°-45°-90° triangle has a special pattern for knowing the sides of the triangle. One leg is given that it is 11. So the other leg is also 11. Then you could use Pythagorean theorem to find x. But there is a short cut!

Because this is a 45°-45°-90° triangle the hypotenuse (the long side) is:

hypotenuse = leg√2

hypotenuse = 11√2

x = 11√2

This is a handy shortcut, it works for all 45°-45°-90° triangles.