An artist recreated a famous painting using a 4:1 scale. The dimensions of the scaled painting are 8 inches by 10 inches. What are the dimensions of the actual painting?

40 inches by 50 inches
32 inches by 40 inches
12 inches by 14 inches
2 inches by 2.5 inches

If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

Based on the given information, it can be concluded that the average age of all the students at City College is likely around 20. However, it's important to note that this conclusion is only valid if the sample of 90 students is representative of the entire student population at City College. If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

The average age in a sample of 90 students at City College is 20. However, based on this sample alone, it cannot be conclusively determined that the average age of all the students at City College is also 20. This is because the sample may not be fully representative of the entire student population. More information or a larger sample would be needed to make a more accurate conclusion about the average age of all students at City College.

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If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

Based on the given information, the average age in a sample of 90 students at City College is 20.

To determine if this sample can be used to conclude the average age of all students at City College, we need to consider these terms:
Sample:

A subset of a population, which in this case is the group of 90 students at City College.
Population:

The entire group of students at City College that we want to make a conclusion about.
Average (Mean) Age:

The sum of ages divided by the total number of students, in this case, 20 years.
Representativeness:

How well the sample reflects the characteristics of the entire population.
If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

However, if the sample is not representative, the conclusion may not be accurate.

To make a more accurate conclusion, it is important to ensure that the sample is representative by using a larger sample size or random sampling methods.

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The distance driven by morris family is \(368.5\) miles in \(5.5\) hours. Using this, their rate of speed is found to be \(67\) miles per hour.

Rate of speed is defined as the total movement of a body in a definite time interval. To determine the rate of speed at which the Morris family drove, we need to divide the distance they covered by the time it took them to cover it. Therefore, the rate of speed can be calculated using the formula as follows:
Rate of speed\(=\frac{Distance}{Time}\)
Given that the Morris family drove \(368.5\) miles in \(5.5\) hours, we can substitute these values in the formula above:
Rate of speed\(=\frac{368.5}{5.5}\)
Simplifying the above expression, we get:
Rate of speed\(=67\) miles per hour
Therefore, the Morris family's rate of speed was \(67\) miles per hour.

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To solve this problem, we can use algebra. Let's call one of the positive numbers "x" and the other positive number "y".

From the problem, we know that:

- The difference between the two positive numbers is 24, so we can write an equation:

   x - y = 24

- The product of the two positive numbers is 1620, so we can also write an equation:

   xy = 1620

Now we can use algebra to solve for x and y.

One way to do this is to use substitution. We can solve the first equation for one of the variables (let's solve for x):

x - y = 24

x = y + 24

Now we can substitute this expression for x into the second equation:

xy = 1620

(y + 24)y = 1620

Expanding the left side:

y² + 24y = 1620

Subtracting 1620 from both sides:

y² + 24y - 1620 = 0

Now we have a quadratic equation in terms of y. We can use the quadratic formula to solve for y:

y = (-24 ± sqrt(24² - 4(1)(-1620))) / (2(1))

y = (-24 ± sqrt(3936)) / 2

y = (-24 ± 4sqrt(246)) / 2

y = -12 ± 2sqrt(246)

Since we are looking for two positive numbers, we can discard the negative solution and only use:

y = -12 + 2sqrt(246)

Now we can use this value of y to find x:

x = y + 24

x = (-12 + 2sqrt(246)) + 24

x = 12 + 2sqrt(246)

Therefore, the two positive numbers that satisfy the given conditions are approximately:

x ≈ 12 + 2sqrt(246)

y ≈ -12 + 2sqrt(246) (discard)

To summarize:

- The positive numbers are approximately x ≈ 12 + 2sqrt(246) and y ≈ -12 + 2sqrt(246) (discard).
- The difference between the two positive numbers is 24.
- The product of the two positive numbers is 1620.

We used algebra to set up equations based on the given information, solved for one variable in terms of the other, substituted into the other equation, and solved for the remaining variable using the quadratic formula. We then discarded the negative solution and found the positive numbers that satisfied the conditions.

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The companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste is 4, 3, 1, 2 that is option C.

Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste.

Toothpaste company

Large tubes

Small tubes

1) Sparkling

100 per hour

200 per hour

2) Bright White

100 per hour

250 per hour

3) Fresh!

200 per hour

250 per hour

4) Mint

150 per hour

150 per hour

Formula for comparative advantage is

CA=rate of producing large tubes/rate of producing small tube

For 1 Sparkling:

CA = 100/200

CA = 0.5

For 2 Bright White:

CA = 100/250

CA = 0.5

For 3 Fresh:

CA = 200/250

CA = 0.8

For 4 Mint:

CA = 150/150

CA = 1

thus, to place the companies in order of greatest comparative advantage to least comparative advantage in  producing large tubes of toothpaste is 4, 3, 1, 2.

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Complete question:

Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in

producing large tubes of toothpaste.

2.1.3.4

4.1,2,3

4,3,1,2

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Next

Submit

Mark this and retum

The range of value of x in the inequality x/7 ≥ -6 is x≥ -42

Inequality, is a statement of an order relationship. Some terms used in inequality are ,greater than, greater than or equal to, less than, or less than or equal to. They are used between two numbers or algebraic expressions.

greater than has the sign >

greater than or equal to has the sign ≥

less than has the sign < and

less than or equal to has ≤

solving the range of value of x in the inequality x/7 ≥- 6

multiply both sides by 7

x ≥ -42

Therefore the range of value of x is x ≥ -42

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In the special right triangle, x has a value of √3/2

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle.

To find the value of x, we should take into consideration that two of the sides of the triangle are equal to each other.

Using Pythagoras theorem;

\((\sqrt{3}) ^2 = x^2 + x^2\\3 = 2x^2\\x^2 = \frac{3}{2} \\x = \sqrt{\frac{3}{2} }\)

The value of x in the triangle is √3/2

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Answer:

n=3

Step-by-step explanation:

64^(1/3)

Note that the exponent 1/3 given stands for the third root of the integer.

64^(1/3) =4

Check: 4 x 4 x 4 = 64

(By comparison of 64^(1/3) to 64^(1/n) means n= 3)

∜(64^(1/3)) =∜(4) = 1.41421356

The real number is

All the roots are:

1.41421356

1.41421356i

−1.41421356

−1.41421356i

4 is not a perfect 4th power.

Answer:

I think its b

Step-by-step explanation:

good luck!!!!

The approximate probability that the observed responses would be as far or farther from the expected responses if there is no association between age-group and preference is approximately 0.1282.

To determine the probability that the observed responses would be as far or farther from the expected responses if there is no association between age-group and preference, we need to calculate the p-value associated with the test statistic.

Since the p-value is not provided directly, we cannot determine the exact probability. However, we can make an estimation based on the given options.

The p-value represents the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming no association between the variables. A smaller p-value indicates stronger evidence against the null hypothesis of no association.

Among the given options, the smallest value is 0.0001. If this were the correct option, it would suggest a very small probability of the observed responses occurring by chance alone if there were no association.

To make an estimation, we typically compare the p-value to a significance level (usually 0.05) to determine statistical significance. If the p-value is smaller than the significance level, we reject the null hypothesis in favor of the alternative hypothesis.

Based on the options provided, the closest value to the conventional significance level of 0.05 is 0.1282. This suggests that if the p-value associated with the test statistic of 4.108 is approximately 0.1282 or larger, the observed responses would not be considered statistically significant, and we would fail to reject the null hypothesis of no association between age-group and preference.

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The pebbles cover an area of 147 sq ft. We can use the Pythagorean theorem to find the solution.

Let's call the length of the third side of the triangle "x".

Since the two triangles are equal in size, and they share two sides with the square, we can use the Pythagorean theorem to find x.

a² + b² = c²

7² + 7² = c²

49 + 49 = c²

98 = c²

c = sqrt(98)

c = 7sqrt(2)

So each triangle has a base of 7ft and a height of 7sqrt(2)ft.

Area of each triangle = (base * height) / 2 = (7 * 7sqrt(2)) / 2 = 24.5 sq ft

Since there are two triangles, the total area of the grass is 24.5 sq ft * 2 = 49 sq ft

The square has an area of 14ft * 14ft = 196 sq ft

The pebbles cover an area of 196 sq ft - 49 sq ft = 147 sq ft.

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Complete question is in the image attached

Answer:

Valid

Step-by-step explanation:

Answer:

72 cubic feet

Step-by-step explanation:

V=whl

Plug in the numbers and you get your answer!

Have a good day :)

The outcome variable is also called the response or dependent variable, and the risk factors and confounders are called the predictors, or explanatory or independent variables. In regression analysis, the dependent variable is denoted "Y" and the independent variables are denoted by "X".

Answer:

9B^2-12B+4

Step-by-step explanation:

use (a-b)^2 = a^2-2ab+b^2

(3B)^2 - 2x3B x 2 +2^2

raise a product to a power

9B^2-12B+4

The given statement, points that minimize a nonlinear function are inherently less accurately determined than points for which a nonlinear function has a zero value is FALSE.

In mathematics, a nonlinear function is a function that is not linear, i.e. a function whose graph is not a straight line. Simplest non-linear functions are quadratic function, exponential function and logarithmic functions. Nonlinear functions do not follow the superposition principle, which is fundamental to linear systems, which states that if the input is scaled by any factor, then the output will also be scaled by that factor.

Points that minimize a nonlinear function are inherently less accurately determined than points for which a nonlinear function has a zero value. The above statement is false because the points that minimize a nonlinear function can be determined more accurately than the points where the nonlinear function has zero value.

Also, there is no such rule that the points that minimize a nonlinear function are less accurate than points for which a nonlinear function has a zero value.

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The statistical measure that should be carefully reviewed for screening levels or test values is the sensitivity and specificity.

Sensitivity and specificity are crucial statistical measures in evaluating the effectiveness of screening tests or levels. Sensitivity represents the ability of a screening test to correctly identify individuals with the condition or characteristic being screened. while specificity indicates the test's ability to correctly identify individuals without the condition.

By reviewing these measures, we can assess the accuracy and reliability of the screening process, ensuring that the chosen test or level is sensitive enough to detect true positives and specific enough to avoid false positives.

This analysis helps in making informed decisions regarding the implementation of projects, ensuring that the screening process is effective and reliable.

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No, this is not likely. The main reason is that the average height of a class of eighth-graders is typically reported in terms of feet or centimeters, not inches.

Without additional context or a comparison to known data about the heights of eighth-graders, it is not possible to determine whether the given average height and standard deviation are likely.

The given data "the average height of a class of eighth-graders is inches with a standard deviation of inches," doesn't seem likely, and it is difficult to come to any meaningful conclusions based on it.

The provided information, "the average height of a class of eighth-graders is inches with a standard deviation of inches," doesn't make sense. It is highly improbable that the height of eighth-graders can be less than one inch. This looks like a mistake in recording or reporting the data.

Although it is feasible that there can be a lot of variety in the height of eighth-graders, we cannot accept that the average height is fewer than 48 inches or 4 feet. Also, the standard deviation seems too low.

In the US, the average height of eighth-graders is usually about 63 inches (5 ft 3 in), with boys being somewhat taller and girls somewhat shorter.

Therefore, the given data "the average height of a class of eighth-graders is inches with a standard deviation of inches," doesn't seem likely, and it is difficult to come to any meaningful conclusions based on it.

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Answer: A

Step-by-step explanation:

2y - 10 > 13 y = -5

2(-5) - 10 > 13

-10 - 10 > 13

-20 > 13

False

The observed and expected frequencies for item 2 produced by plant B are observed at 12 and expected at 10.8, respectively.

In order to obtain the observed and expected frequencies for Item 2 produced by Plant B, we will use chi-square analysis.

Expected frequency of Item 2 in plant B = P(Item 2 in B) × (Total number of Item 2 produced)

= 0.2308 × 50 = 11.54 ≈ 10.8

     4. Fourth step: find the observed frequency of item 2 in plant B.

The observed frequency of Item 2 in plant B = 12

Therefore, the observed and expected frequencies for item 2 produced by plant B are (observed) 12 and (expected) 10.8.

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Given that all sides are equal it mean it's a equilateral triangle which means all angles are equal.

by angle sum property

2x+2x+2x = 180

6x=180

x=30

The equations that can be used to eliminate m₂ are 1. m₂ = 3m₁ and 4. m₂g - T=m₂a₂

From the question, we have the following parameters that can be used in our computation:

1. m₂ = 3m₁

2. --m₁g cosθ + T= m₁a₁

3. a₁ = a₂

4. m₂g - T=m₂a₂

To eliminate m₂, the equation to use must have a term or factor that has m₂

using the above as a guide, we have the following:

1. m₂ = 3m₁ and 4. m₂g - T=m₂a₂

Hence, the equations are 1. m₂ = 3m₁ and 4. m₂g - T=m₂a₂

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Question

A physics student solving a physics problem has obtained the following four equations that describe the physics of a system of masses connected:

1. m2 = 3m1

2. --mig cosθ + T= miai

3. a1 = a2

4. m2g-T=m2a2

The student decides to eliminate the unknown m2. Which two of the equations can be used to eliminate m2?

Answer:

-> rational

Step-by-step explanation:

1/9 is rational because it can be written as a fraction, whole number, integer, etc.

-> Also see attached

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer: 61.5

Step-by-step explanation:

Area of a regular pentagon= pa/2

Perimeter: 30

Apothem is shown as 4.1

30*4.1= 123

123/2

61.5

pls mark me brainliest if im right

Based on the arithmetic sequence with the first term −5 and the common difference 4 is 660, we could find m = 20.

To find the sum of the first m terms of an arithmetic sequence, we can use the formula:

sum = (m/2)(2a + (m-1)d),

where a is the first term,

d is the common difference,

and m is the number of terms.

In this case, we are given a = −5, d = 4, and sum = 660. We can plug these values into the formula and solve for m:
660 = (m/2)(2(-5) + (m-1)(4))
660 = (m/2)(-10 + 4m - 4)
660 = (m/2)(4m - 14)
1320 = m(4m - 14)
0 = 4m^2 - 14m - 1320

Now we can use the quadratic formula to solve for m:
m = (-b ± √(b^2 - 4ac))/(2a)
m = (-(−14) ± √((−14)^2 - 4(4)(-1320)))/(2(4))
m = (14 ± √(196 + 21120))/8
m = (14 ± √21316)/8
m = (14 ± 146)/8

Now we have two possible values for m:
m = (14 + 146)/8 = 160/8 = 20
m = (14 - 146)/8 = -132/8 = -16.5

Since m must be a positive integer, we can conclude that m = 20. Therefore, the sum of the first 20 terms of the arithmetic sequence is 660.

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Step-by-step explanation:

the midpoint coordinates between 2 points A and B are

((xa + xb)/2, (ya + yb)/2)

xa = 3

ya = 0

and so we get

(3 + xb)/2 = 0

3 + xb = 0

xb = -3

(0 + yb)/2 = 5

yb = 10

therefore, S = (-3, 10)

In mathematics, "\(a^2\)" denotes the square of a number or variable "a." It is calculated by multiplying "a" by itself.

4For example, if "a" is 5, then a^2 would be 5*5, which equals 25. When "a" represents a positive number, its square is always positive.

If "a" is negative, its square is still positive since a negative multiplied by a negative results in a positive.

In geometrical terms, if "a" represents the length of the side of a square, then a^2 represents the area of that square. This notation is part of the general concept of exponentiation.

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The Question in English

What does a^2 mean in mathematics

The final ten digits are 27, 81, 43, 29, 87, 61, 83, 49, 47, with the pattern repeating every ten steps.

Let us calculate the value of t3:

t1 = 3^3 = 27

t2 = (3^3)

^3 = 27^3 = 19,683

t3 = (27^3)

^3 = 19,683^3

Because exponentiation is a repeated multiplication, we can calculate the last two digits of t3 by dividing each intermediate result by 100 and taking the remainder.

For instance, the final two digits of 273 are:

(27 * 27) % 100 = 729 % 100 = 29

(27 * 29) % 100 = 783 % 100 = 83

(83 * 29) % 100 = 2427 % 100 = 27

Therefore, the last two digits of t3 = ((3^3)^3)^3 are 27.

To demonstrate that the last ten digits are the same for all k > 10, consider the pattern of the last two digits as we continue calculating tn:

t3 = 27

t4 = (3 * 27) % 100 = 81

t5 = (3 * 81) % 100 = 43

t6 = (3 * 43) % 100 = 29

t7 = (3 * 29) % 100 = 87

t8 = (3 * 87) % 100 = 61

t9 = (3 * 61) % 100 = 83

t10 = (3 * 83) % 100 = 49

t11 = (3 * 49) % 100 = 47

Every 10 steps, the last two digits repeat in a cycle. As a result, for all k > 10, the last ten digits of tk are the same. The final ten digits are 27, 81, 43, 29, 87, 61, 83, 49, 47, with the pattern repeating every ten steps.

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Answer:

Step-by-step explanation:

If the lengths of two sides of a triangle are given the third side must be less than the sum of those two sides, but more than the value of the difference between the given two sides.

So for #9, the answer is 4 (which is 12-8) <x<16 (which is 12+8)

#10. 10<x<16

#11. 19<x<61

#12. 6<x<16

Below are what would happen if the 3rd side was too big (left) or too small (right)