suppose that a random sample of 25 measurements is selected from a population with mean 70 and standard deviation 10. what is the mean and standard deviation of the sampling distribution of the sample mean?

The equation of transformation in g(x ) is 3x³ - 6x + 8

what is transformation?

A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations. The pre-image is the shape of the object as it was originally, and the transformed shape of the object is termed the image.

solution:

1. f(x) = x³ - 2x + 3.

Then g(x) = 3f(x) + 1

substitute f(x) in g(x)

g( x ) = 3 (x³ - 2x + 3) + 1

        = 3x³ - 6x + 9 + 1

g( x ) =  3x³ - 6x + 8

2. The graph of the function f(x) = x³ - 2x + 3 is obtained by just moving the graph of g( x ) =  3x³ - 6x + 8  by 2 units up.

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Answer:

X=437 over 100

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

x = 0 is a vertical line. It's the y-axis.

y = 3 is a horizontal line.

x = 0 and y = 3 are perpendicular lines because they intersect

Answer:

Step-by-step explanation:

Yes, you can figure it out by drawing it out. Unfortunately, you can't compare slopes in this case as vertical lines are undefined.

Answer:

30%

Step-by-step explanation:

4 pounds of almonds is $22 --> 1 pound of almonds is $5.50

Cashew price per pound = 160/100 * $5.50. = $8.80

22 + 8.80x = 6.50(4+x)

22 + 8.80x = 26 + 6.50x

2.30x = 4

x = 1.739130435 approx 1.74 lbs of cashews

percent of the mixture, by weight, for cashews =

1.739130435 / (4 + 1.739130435) = 0.303030303 approx 30%

Answer:

down below

Step-by-step explanation:

Assuming you meant multiplying:

61.295

Hope this helps! :)

There is a difference between orthogonal and orthogonal subspaces. According to this, two planes cannot be orthogonal in R3.

Considering, in the case of the orthogonal planes, each plane should have a basis of orthogonal vectors, and also, one of the pairs in each of the vector,  is shared between the two planes and the other vector that is present, should form a orthogonal pair to each other.

Taking the case of orthogonal subspaces,  the main requirement is that each vector of each of the pairs should be orthogonal to each vector of each of the other pair. Also, the dimension of the ambient pair should be not less than 4 (2+2).

When we talk about two planes in R3, planes are orthogonal if and only if, their normal vectors are orthogonal. If this condition is not present, then planes are not orthogonal in R3.

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The pairs of triangles that are similar are △jkl ~ △abc and their corresponding angles are congruent.

The fact that, When two triangles are comparable, their corresponding sides have a proportional ratio and their corresponding angles have a congruent relationship.

In this issue

△jkl ~ △abc

Because the proportion between its corresponding sides

Verify

CA/LJ=BC/KL

replace the specified values

14/7=20/10

2=2 >>>>> is correct

so

The proportion between the corresponding sides is linear.

therefore △jkl ~ △abc are similar.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

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Answer: b & e

Step-by-step explanation: cuz

Answer:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30

Factors of 45: 1, 3, 5, 9, 15, and 45

Step-by-step explanation:

The projected percentage for 2060 is nearly double from 52 million in 2018 to 95 million by 2060.

Given in 1970, about 10 percent of the u.s. population was age 65 and older.

Demographic Shifts

The number of Americans ages 65 and older is projected to nearly double from 52 million in 2018 to 95 million by 2060, and the 65-and-older age group's share of the total population will rise from 16 percent to 23 percent. The older population is becoming more racially and ethnically diverse.

Hence the answer is the projected percentage for 2060 is nearly double from 52 million in 2018 to 95 million by 2060.

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Answer:

The answer is -17/15

(Decimal: -4.733333)

Answer:

its C.

Step-by-step explanation:

If a researcher is using a one sample t statistic to test a null hypothesis about a population, he needs average, standard deviation and sample size to calculate the one sample t statistics.

What is t- Statistic test ?

Comparing the means of two groups is done statistically using a t test. It is frequently used in hypothesis testing to ascertain whether a method or treatment truly has an impact on the population of interest or whether two groups are distinct from one another.

Since the researcher wants to use one sample t statistic to test a null hypothesis about a population, the formula for t statistic will be followed which can be computed by using some figures which are the average, standard deviation and sample size to calculate the one sample t statistic.

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Answer:

5.8x3.8

Step-by-step explanation:

x times (x+2) = 22

The measure of the unknown angles in the kite are as follows;

A kite has two pairs of adjacent equal sides.

In other words, a kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

One pair of opposite angles is equal. Diagonals are perpendicular to each other.

A kite has four interior angles and the sum of these interior angles is 360°

Therefore, the measures of the

x = 66 degrees.

Let's find y.

y = 360 - 70 - 66 - 66

y = 158 degrees.

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The probability that someone who tests positive has the genetic disease is  0.142

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Let E be the people test positive

Let F be the people who has disease

P(F)= 1/10000 = 0.0001

P(E/F)= 99.5% = 0.995

P(E/F bar ) = 0.06 % = 0.0006

Baye's theorem:

P(F/E) =  [ P(E/F) * P(F) ] /  [ P(E/F) * P(F) + P(E/F bar ) * P( F bar ) ]

conditional probability :

P(B/A) = P ( A [tex]\cap[/tex] B ) / P(A)

Complement rule is given  by:

P (F bar ) = 1 - P(F) = 1 - 0.0001 = 0.9999

The probability that someone who tests positive has the genetic disease :

P(F/E) =  [ P(E/F) * P(F) ] /  [ P(E/F) * P(F) + P(E/F bar ) * P( F bar ) ]

         = ( 0.995 * 0.0001 ) / ( 0.995 * 0.0001 + 0.0006 *0.9999)

          =  0.142

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Answer: 9

Step-by-step explanation: The number of sides that a regular polygon has can be determined by the measure of one of its exterior angles. A regular polygon is a polygon with sides of equal length and angles of equal measure.

The measure of one exterior angle of a regular polygon is equal to 360° divided by the number of sides of the polygon. Therefore, if one exterior angle of a regular polygon measures 40°, we can use the following equation to find the number of sides of the polygon:

exterior angle measure = 360° / number of sides

40° = 360° / number of sides

number of sides = 360° / 40°

number of sides = 9

Therefore, a regular polygon with one exterior angle measuring 40° has 9 sides.

Answer: -3 is a rational number

Step-by-step explanation:

-3 is a rational number because it can be written as a fraction -3/1 and have the same value of -3. Therefore -3 is a rational number and Hannah is correct.

Answer: August 12th

Step-by-step explanation: 4 and 6 have common multiples of 2, so you need to multiply 6 by 2 and 4 by 3. Both get you 12, so the earliest they have tennis practice is the 12th of August (12 days after July 31st).

Answer:

August 12

Step-by-step explanation:

To solve this question, we need to find the Least Common Multiple (LCM) of 4 and 6.

Since we know that Nick and Mark both had practice on July 31st, we can simply add {LCM of 4 and 6} days to that date to get when they will next both have practice.

To find the LCM of 4 and 6, find the prime factorization of both:

[tex]4 = 2 \times 2[/tex]          [tex]6 = 2 \times 3[/tex]

Now, take the largest quantity of each distinct prime number and multiply them together:

The largest number of 2's is 2. The largest number of 3's is 1. So, we multiply

[tex](2 \times 2) \times (1 \times 3)[/tex]

[tex]= 4 \times 3[/tex]

[tex]= 12[/tex]

Therefore, the LCM of 4 and 6 is 12.

This means that Nick and Mark will have practice on the same day in 12 days.

The last step to solve this problem is to add 12 days to July 31.

[tex]\textrm{July } 31 + 12 \textrm{ days} = \textrm{August } 12[/tex]

Nick and Mark will next have practice on the same day on August 12.

The measure of missing angles is 48° and 36°.

The angle sum property of a triangle states that the sum of the three internal angles of a triangle equals 180 degrees. Three line segments combine to form a triangle, a closed shape having interior and exterior angles. When the values of the other two angles are known, one may utilize the angle sum property to determine the measure of an unknown interior angle.

Given Measure of one angle= 96, one angle= 2x, other angle= x + 12.

Using the angle sum property, we get

96 + 2x + x + 12 = 180

108 + 3x = 180

3x = 180 - 108

3x = 72

x = 72/3

x = 24

So, one angle = 2(24

= 48

The other angle is

x + 12 = 24 +12

= 36

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The complete question is:

One measure of an angle in a triangle is 96°. The other two angle measures are represented by 2x and x + 12. Determine the other two degree measures for the missing angles."

The process of reasoning from a premise or premises to a conclusion based on those premises is known as deductive reasoning.

According to the question,

We have to find the name of the process of reasoning from a premise or premises to a conclusion based on those premises.

We know that there are two types of reasoning. One is inductive reasoning and the second one is deductive reasoning.

In deductive reasoning, we make a final statement which is often called conclusion from various statements which are given. For example, if we say 25th November is my birth date and today is my birth date then the conclusion is today is 25th November.

Hence, the process of reasoning from a premise or premises to a conclusion based on those premises is known as deductive reasoning.

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Answer:

If you divide 76 by 6, you would get 12.6666667.

76 divided by 6 is equal to 12 and 2/3, or simply 12.67 when expressed as a decimal.

To divide 76 by 6, we perform the division operation to find the quotient.

When dividing, we start with the largest multiple of 6 that is less than or equal to 76, which is 72. We divide 72 by 6, which equals 12.

Next, we subtract the product of 6 and 12 from 76 to find the remainder:

76 - (6 x 12) = 76 - 72 = 4

Since there is still a remainder of 4, we can express the result as a mixed number: 12 and 4/6.

To simplify the mixed number, we can reduce the fraction. The greatest common divisor of 4 and 6 is 2, so we can divide both the numerator and denominator by 2:

4/2 ÷ 6/2 = 2/3

Therefore, 76 divided by 6 is equal to 12 and 2/3, or simply 12.67 when expressed as a decimal.

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The the diameter of the shaft is  to be in order to transmit 60 hp at 150 rpm 1.88 inch.

We must first obtain the formula for calculating horsepower.

The phrase to use is as follows:

hp = k  × v  × d³ ......eq(1)

Where:

Since k is a constant, it will always have the same value when the shaft is transferring 60 horsepower at 150 rpm.

Therefore, using the first set of information, we can determine the value of k and subsequently the diameter.

When we solve for k in (1), we get:

k = hp / (v × d³)

Put the values;

k = 45 / (100  × 3³)

k = 0.02

Put the value of k and solve for diameter.

d = ∛hp / (k   × v)

d = ∛60 / (150 × 0.06)

d = 1.88 inch

Thus, the the diameter of the shaft is  to be in order to transmit 60 hp at 150 rpm 1.88 inch.

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By using normal distribution of probability, it can be calculated that

13.59 %of men are between 64 and 66.5 inches tall

What is normal distribution of probability?

Normal distribution of probability is a continuous type probability distribution whose probability density function is given by

f(x) = [tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}}[/tex] where z = [tex]\frac{x - \mu}{\sigma}[/tex]

[tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

Here, normal distribution of probability is used

Mean = 69 inches

Standard deviation = 2.5 inches

P(64 < X < 66.5) = P(X <66.5) - P(X < 64)

For X < 64

z = [tex]\frac{64 - 69}{2.5}[/tex] = -2

P(X < 64) = P(z < -2) = 0.0228

For X < 66.5

z = [tex]\frac{66.5 - 69}{2.5}[/tex] = -1

P(X < 66.5) = P(z < -1) = 0.1587

P(64 < X < 66.5) = 0.1587 - 0.0228 = 0.1359

13.59 % men are between  64 and 66.5 inches tall

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As the probabilities of random variables are negative so we can expect to lose roughly 50 cents on each $1.00 ticket we purchase.

The rules of the "numbers" game are simple: a player selects a three-digit number between 000 and 999. Anyone who picks the winning number receives a payout equal to 600 times their original wager. The winning number is decided by a publicly disclosed source. The majority of bets were for $1 or less, and frequently.

A permutation is an arrangement (or ordering) of a collection of items. (We can also arrange only some of the objects in the set.) The arrangement of the objects in a permutation depends on their order.

The random variable-0.499/1000

The random variable "winning" are $1 and $600.

and their probabilities are 999/1000 and 1/1000, respectively.

The expected "winnings" are calculated as follows:

=(999/1000)(-1)+(1/1000)(500)

=-0.499/1000

=-0.499 cents

so we can expect to lose roughly 50 cents on each $1.00 ticket we purchase.

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(a) The value of p(x) is 0.15 when x = 3.

(b) The mean of the discrete random variable is 0.1

What is meaning of discrete random variable?

A discrete random variable has a countable number of different possible values, such as 0,1,2,3,4, etc. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values.

Given table is

X        0         1          2        3

P(x)  0.72     0.11    0.02  

The sum of the probability of an event is 1.

Therefore

P(0) + P(1) + P(2) + P(3) = 1

Putting the value of P(0), P(1), P(2)

0.72 + 0.11 + 0.02 + P(3) = 1

0.85 + P(3) = 1

P(3) = 1- 0.85

P(3) = 0 .15

The mean of the discreate random variable is Σ xp(x) / Σ x

=[(0 × P(0)) + (1 × P(1)) + (2 × P(2)) + (3 × P(3))]/(0 + 1 + 2 + 3)

= (0 + 0.11 + 0.04 + 0.45) / 6

= 0 .1

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Answer:

Solve for Y

by simplifying both sides of the equation, then isolating the variable.

Hope this helped

Step-by-step explanation:

The answer would be: y=-18x+2

The correct answer is $6

To solve this question, we need to multiply the numbers given.

Given:

[tex]10,5,3,2[/tex]

Therefore, the equation goes like this:

[tex]5*2\\3*2[/tex]

Therefore, the correct answer is $6

Hypothesis:

H0: The mean startup time for both computers is equal.

H1: The mean startup time for both computers is not equal.

A hypothesis is a potential explanation for a phenomenon.A hypothesis must be testable in order to be considered scientific according to the scientific method. Scientists typically base their scientific hypotheses on prior observations that cannot be adequately explained by the body of knowledge. Despite the fact that the terms "hypothesis" and "theory" are frequently used interchangeably, they are not the same thing. A working hypothesis is a theory that has been tentatively accepted and is put forth for further study after starting with an educated guess or idea.

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If the area of the pentagon is 36, then the area of the pentagon FGHIJ is 64.

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".

Given that the length of the side of the smaller pentagon is 12, while the length of the side of the larger pentagon is 16.

Since the two of the given figures are similar figures, therefore, we can write,

(Area of smaller pentagon)/(Area of larger pentagon) = (Ratio of the sides)²

(Area of pentagon ABCDE)/(Area of pentagon FGHIJ) = (AE / FJ)²

(36)/(Area of pentagon FGHIJ) = (12/16)²

Area of pentagon FGHIJ = 36 × (16/12)²

Area of pentagon FGHIJ = 36 × (256/144)

Area of pentagon FGHIJ = 64

Hence, the area of the pentagon FGHIJ is 64.

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Answer: Water at sea level boils at a temperature of 212 degrees Fahrenheit. For every increase in altitude of 1000 feet, the boiling point drops by 1.8 degrees. Write a linear function that gives the boiling point of water as a function of the altitude. What is the boiling point of water at 15,000 feet?

Draw a chart with the column heading as follows

Step-by-step explanation: