If the smaller sphere has a surface area of 200.96 in2, what is the surface area of the larger sphere?
A.
602.88 in2
B.
803.84 in2
C.
301.44 in2
D.
5,425.92 in2

The area of the regular polygon is  [tex]49\sqrt3[/tex] square unit.

What is area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Here the given triangle ,

Apothem a = [tex]\frac{7\sqrt3}{3}[/tex]

Now side length s = [tex]2\sqrt3 a[/tex]

=> side length s = [tex]2\sqrt3\times \frac{7\sqrt3}{3} = \frac{14\times3}{3}[/tex] = 14

Now area of equilateral triangle A = [tex]\frac{\sqrt3 s^2}{4}[/tex] square unit.

=> A = [tex]\frac{\sqrt3\times14^2}{4}[/tex] = [tex]49\sqrt3[/tex] square unit.

Hence the area of the regular polygon is  [tex]49\sqrt3[/tex] square unit.

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The study design described is a cross-sectional study.

The study design in this scenario is a cross-sectional study. The study aims to examine the relationship between family status and school performance. The sample is selected by randomly choosing every 5th child from the list of children at the ABC elementary school. Data is collected from the school record for each child, and family status is operationalized by whether the child lives in a single-parent household, dual-parent household, or has a non-parent guardian in the household. The school performance is measured by administering a student math test and a student reading test to the child in April, with each test including 20 questions and each correct answer being worth five points.

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The 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center is (2.166, 2.634). So, the correct option is B).

To find the 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center, we can use the formula:

CI = X ± z*(σ/√n)

where X is the sample mean, σ is the sample standard deviation, n is the sample size, and z is the z-score associated with the desired confidence level (90% in this case).

The z-score for a 90% confidence level is 1.645.

Plugging in the values given in the problem, we get:

CI = 2.4 ± 1.645*(2.1/√220)

Solving this equation gives us a confidence interval of (2.166, 2.634) rounded to three decimal places.

Therefore, the correct answer is (2.166, 2.634) and option is B).

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Answer:

x = 55°

Step-by-step explanation:

Inscribed Angle Theorem says that the angle inside the circle is equal to 0.5 times the measurement of the arc it span. For example, the 70° spans 140° of the arc.

Create two equations to solve for x and r.

x = 0.5r

2r + 2(70) = 360

2r + 140 = 360

2r = 220

r = 110

x = 0.5 * 110

x = 55°

Absolute value equation for a straight horizontal line with marked points and x-axis intercepts. Therefore, the absolute value equation that has the given solution set is:y + 1 = | x + 3 | .

How to write an absolute value equation that has the following solution set?

To find the absolute value equation that corresponds to the given solution set, we need to determine the axis of symmetry of the V-shaped graph formed by the absolute value function. The axis of symmetry is the vertical line that passes through the vertex of the graph. Since the vertex of the graph is located at the midpoint of the two given points, which is at x = -3, the axis of symmetry is x = -3.

The equation of the absolute value function can be written as:

b + | x - a |  

= y

where a is the x-coordinate of the vertex and b is the y-coordinate of the point where the graph intersects the y-axis. In this case, the y-coordinate of the point where the graph intersects the y-axis is -1, so we have b = -1.

Substituting the value of a and b in the equation above, we get:

| x - (-3) | - 1 = y

Simplifying the equation, we get:

y + 1  = | x + 3 |

Therefore, the absolute value equation that has the given solution set is:

y + 1 = | x + 3 | .

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The value of x is 40 given that the two prisms are similar.

If the two prisms are comparable, then their corresponding sides will be proportionately the same.

x / 20 =  10 / 5

x/ 20 = 2

x = 2 * 20

x = 40

Therefore, the value of x is 40 given that the two prisms are similar.

A prism is a geometric shape that has two parallel and congruent bases that are connected by a set of rectangular or parallelogram faces. When light enters a prism, it is refracted, or bent, due to the different angles of the surfaces of the prism.

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the question lack some information.

See more detail of the question on the attached image.

Answer:

Step-by-step explanation:

Answer:

The interval estimate is:

41.5 - 2.45 ≤ true average time ≤ 41.5 + 2.45

or

38.05 ≤ true average time ≤ 44.95

Inequality notation:

[38.05, 44.95]

The interval estimate that will estimate the true average time that people spend brushing their teeth is [39.05, 43.95] seconds.

Given that the mean time spent brushing teeth from the sample is 41.5 seconds, and the margin of error is 2.45 seconds, we can construct a confidence interval estimate using the formula:

(sample mean) ± (margin of error)

Substituting the given values, we get:

41.5 ± 2.45

Simplifying, we get:

[39.05, 43.95]

Therefore, we can be 95% confident that the true average time that all people spend brushing their teeth falls within this interval.

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The probability that at least one of the next ten earthquakes to strike this region will exceed 5.0 on the Richter scale is approximately 0.867.

To solve this problem, we need to use the cumulative distribution function (CDF) of the exponential distribution.

Let X be the magnitude of earthquakes in this region, and [tex]X ~ exp(1/2.4).[/tex]

To find the probability that an earthquake striking this region will exceed 3.0 on the Richter scale, we need to calculate P(X > 3).

[tex]P(X > 3) = 1 - P(X ≤ 3)\\= 1 - F(3) (where F is the CDF of X)\\= 1 - (1 - e^(-3/2.4))\\= e^(-1.25)[/tex]

≈ 0.286

Therefore, the probability that an earthquake striking this region will exceed 3.0 on the Richter scale is approximately 0.286.

To find the probability that an earthquake striking this region will fall between 2.0 and 3.0 on the Richter scale, we need to calculate P(2 < X ≤ 3).

[tex]P(2 < X ≤ 3) = F(3) - F(2)= (1 - e^(-3/2.4)) - (1 - e^(-2/2.4))[/tex]

≈ 0.285

Therefore, the probability that an earthquake struck this region will fall between 2.0 and 3.0 on the Richter scale is approximately 0.285.

To find the probability that at least one of the next ten earthquakes to strike this region will exceed 5.0 on the Richter scale, we need to use the complement rule and the fact that the number of earthquakes is a Poisson distribution with mean 10/2.4 = 4.17. Let Y be the number of earthquakes that exceed 5.0 on the Richter scale.

[tex]P(Y ≥ 1) = 1 - P(Y = 0)\\= 1 - e^(-4.17) * (4.17^0 / 0!)[/tex]

≈ 0.867

Therefore, the probability that at least one of the next ten earthquakes to strike this region will exceed 5.0 on the Richter scale is approximately 0.867.

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Pythagoras theorem is the square of two sides gives the square of third side.

Given,

Height of flagpole= 25 ft

base= 5 ft

Let the broken part be x

The remaining part becomes 25-x

Apply Pythagoras theorem

[tex]5^{2}[/tex] + [tex]x^{2}[/tex] = [tex](25-x)^{2}[/tex]

25 + [tex]x^{2}[/tex] = [tex]25^{2}[/tex] + [tex]x^{2}[/tex] - 2*25*x

25 + [tex]x^{2}[/tex] = 625 + [tex]x^{2}[/tex] - 50x

([tex]x^{2}[/tex] cancels out on both side)

50x = 625- 25

50x = 600

x = 600/50

x = 12

Answer:

1) 70 meters

2) at 3 seconds

3) about 114 meters

[tex]h(3) = - 4.9 ({3}^{2} ) + 29.4(3)+ 70 = 114.1[/tex]

4) about 8 seconds

5)

[tex]h(t) = - 4.9 {t}^{2} + 40.5t + 70[/tex]

The equations that are quadratic functions are 6 x - 1 = 4 x + 7 x^2 and x^2 + 5 x - 7 = 0

The quadratic equation is an equation of the form:

ax^2 + bx + c = 0

where a, b, and c are constants, and x is the variable.

Out of the given equations, the following are quadratic equations:

6 x - 1 = 4 x + 7 x^2

x^2 + 5x - 7 = 0

The other equations are not quadratic equations:

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we can represent this as a trinomial with a perfect square:(y-10)²-100

PRECISE SQUARE TERMINAL: WHAT IS IT?

A quadratic expression that can be factored into a binomial squared is a perfect square trinomial. When it is factored, it follows a pattern where the first and last terms are monomial perfect squares and the middle term is the product of the first two. A given trinomial is not a perfect square trinomial if the pattern does not fit for it1.

For instance, the trinomial x2+6x+9 is a perfect square trinomial since it factors into (x+3)². The square of x is represented by the first term, x², and the square of 3 by the last term, 9. Its result 2(x)(3) is twice as long as the middle term 6x.

Y has a coefficient of -20. A fraction of -20 is -10.

-10 is squared to give 100.

As a result, we can add and take 100 to finish the square.

It is necessary to add and subtract the square of the y-half coefficient's in order to finish the square for y²–20y.

y²-20y+100-100

=(y-10)²-100

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Answer:

x = 4

Step-by-step explanation:

They can get 32 portions of 1/8 lb each from a 4-pound block of Parmesan cheese.

To determine how many portions can be made from a 4-pound block of Parmesan cheese at the market, follow these steps:
1. Identify the size of each portion: 1/8 lb
2. Identify the total weight of the cheese block: 4 lb
3. Divide the total weight by the portion size to find the number of portions:

4 lb ÷ 1/8 lb

To do this division, you can multiply 4 by the reciprocal of 1/8 (which is 8/1):
4 × 8/1 = 32.

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Answer:

B) Decay

Step-by-step explanation:

This is a decay function because if you look at the number being raised to the power of t it is (1-0.43) meaning that the factor is less than 1, and numbers less than 1 result in a decay function. Whereas function that have a rate of 1 of more will be growth.

There are 90 positive odd integers less than 1000 that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 by choosing any of the three odd digits as the last digit, and any of the remaining digits for the first and second positions.

To form a positive odd integer, the last digit must be an odd number, i.e., 1, 3, 5. For each of these three possible last digits, we can choose any of the remaining six digits for the first position, and any of the remaining five digits for the second position (since we cannot repeat digits in forming a positive integer).

Therefore, the total number of positive odd integers less than 1000 that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 is:

3 × 6 × 5 = 90

So there are 90 positive odd integers less than 1000 that can be formed from the given digits.

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The value of the expression m + (7.9) is 10.4. when m= 2.5 and n = 5

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

m + (7.9)

The expression m + (7.9) means that we need to add the value of m to 7.9.

Substituting m = 2.5, we get:

m + (7.9) = 2.5 + 7.9 = 10.4

Therefore, when m = 2.5, the value of the expression m + (7.9) is 10.4.

Note that the value of n is not used in this expression since it is not included in the expression to be evaluated.

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The answer of the given question based on circle  is ,  the width of the shaded region is 4 inches, and the answer is (a).

Radius is distance from center of  circle to any point on circle. It is a fixed length and is the same for all points on the circle. The radius is usually denoted by the letter "r".

The radius is an important parameter of a circle and is used in many geometric calculations, like finding the circumference, area, diameter, chord length, and arc length of a circle. The diameter of a circle is twice the radius, and the circumference of a circle is equal to 2π times the radius.

The area of shaded region is equal to area of the outer circle minus area of inner circle. We are given that the area of the shaded region is 56π in², and the radius of the inner circle is 5 in.

Let radius of outer circle be " r ". Then we have:

Area of the shaded region = Area of the outer circle - Area of the inner circle

56π = πr² - π(5²)

56π = π(r² - 25)

r² - 25 = 56

r² = 81

r = 9

So, the radius of the outer circle is 9 inches.

The width of the shaded region is the difference between the radius of the outer circle and the radius of the inner circle:

Width of shaded region = 9 in - 5 in = 4 in

Therefore, the width of the shaded region is 4 inches, and the answer is (a).

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Since, distribution is skewed right even after we remove the outlier (600) from the data set. The median is a good measure regardless of whether the outlier is included.

We have a data set represents the dollar amounts of donations collected at the entrance to a free museum during one hour. The data present in above figure. Now, first we determine the median. As we know, median of a data set is equals to the middle value of data set, so sometimes it is called middle value. It is the value which separates upper and lower halves of data sample or population etc. First we ordered the data values in ascending order. In case odd number of data values, median = middle value and in case of even number of terms, median = mean of two middle terms. Now, here data values in ascending order are 1,5,5,5,5,5,10,10,10,15,600. That is total data values = 11 ( odd) , so median

= 6th value = 5.

So, regardless of whether the outlier is included median is good measure in this situation.

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Answer:

No solutions

Step-by-step explanation:

- 3x - y = 10 ⇒ ( 1 )

3x + y = - 8 ⇒ ( 2 )

( 1 ) + ( 2 )

-3x - y + 3x + y = 10 - 8

Combine like terms.

0 ≠ 2

NO solutions

The probability that a woman with breast cancer will survive after her surgery is less than -1.33 is approximately 0.0918.

Therefore P(X < 6) = 0.0918 or 9.18%.

 To find the probability that a woman with breast cancer will survive after surgery, we need to use the normal distribution formula.

z = (x - μ) / σ

where z =z-score

x=survival time in years,

μ =mean survival time,

and σ= standard deviation of survival time.

Let X be the survival time, then [tex]X ~ N(8, 1.5^2).[/tex]

a) 10+ year survival probability:

I would like to find P(X > 10). Using the formula above, we get:

z = (10 - 8) / 1.5 = 1.33

A standard normal distribution table or calculator tells us that the probability that z is greater than 1.33 is approximately 0.0918.

Therefore P(X > 10) = 0.0918 or 9.18%. b) 5- to 7-year survival probabilities:

b) 5- to 7-year survival probabilities: I would like to find P(5 < X < 7).

Using the formula above, we get: z1 = (5 - 8) / 1.5 = -2

z2 = (7 - 8) / 1.5 = -0.67

From a standard normal distribution table or calculator, we know that the

probability that z is between -2 and -0.67 is approximately 0.1841.

Therefore P(5 < X < 7) = 0.1841 or 18.41%.

c) Probability of survival <6 years:

Find P(X < 6). Using the formula above, we get:

z = (6 - 8) / 1.5 = -1.33

A standard normal distribution table or calculator tells us that the probability that z is less than -1.33 is approximately 0.0918. Therefore P(X < 6) = 0.0918 or 9.18%.  

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The sample size required to provide a 95% confidence interval with a margin of error of 3, assuming a population standard deviation of 50, is approximately 106.

To calculate the sample size needed for a confidence interval, we use the formula:

n = (Z² × σ²) / E²

where:

n = sample size

Z = Z-value (corresponding to the desired confidence level)

σ = population standard deviation

E = margin of error

For a 95% confidence interval, the Z-value is 1.96. Plugging in the values, we get:

n = (1.96² × 50²) / 3²

n = 3841 / 9

n = 426.78

Since we need a whole number, we round up to the nearest integer, giving us a sample size of 107.

Therefore, the sample size required to provide a 95% confidence interval with a margin of error of 3, assuming a population standard deviation of 50, is approximately 106.

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Answer:

6x^(3/2)

Step-by-step explanation:

To simplify the expression (2√x) × (3³√x), we can first use the properties of exponents to rewrite the cube root as a fractional exponent:

3³√x = x^(1/3)^3 = x^(1)

Using this, we can rewrite the expression as:

(2√x) × (3³√x) = 2x^(1/2) × 3x^(1)

To multiply these two terms, we can add the exponents since the bases are the same:

2x^(1/2) × 3x^(1) = 6x^(1/2 + 1) = 6x^(3/2)

Therefore, the simplified expression is 6x^(3/2).

The truth of ΔABC and ΔDEF is that both triangles i.e. ΔABC and ΔDEF are similar because[tex]\frac{12-6}{4-2} = \frac{27-15}{9-5}[/tex],So the correct option is Option(D).

A three-sided polygon with three corners is termed as triangle.

This is the simplest polygon produced when three non-collinear points are connected by line segments.

Triangles can be classified according to the length of sides and size of the angles. There are several triangles that are as :

Scalene triangle: A triangle without equal sides.

isosceles triangle: A triangle with tow equal and same sides.

ΔABC and ΔDEF are similar because:-  

[tex]\frac{12-6}{4-2} = \frac{27-15}{9-5}[/tex]

[tex]\frac{6}{2} = \frac{12}{4}[/tex]

3 = 3

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The complete question is :-

Answer:

41cm

Step-by-step explanation:

If observed closely you can see that perimeter C is the merged factor of both perimeter A and B.

To get the perimeter of C, merge both perimeter A and B together

The height will be 10cm

The bottom will be 6cm seeing as the top of perimeter A is 6cm and there are the same length

The top will be 6+7 = 13cm because perimeter A and B have been merged meaning they will be added

The right side will be 5cm because 5cm is the side of perimeter B

The long bottom will be 7cm because it is the same as perimeter B and they have the same length meaning

10+6+13+5+7 =  41cm(The answer is not squared because we only added the sides not multiplied it)

The area of each part of the figure and the whole figure is Rectangle A = 15 square units
Triangle B = 6 square units
Rectangle C = 8 square units
Whole figure = 29 square units

To find the area of each part of the figure, we need to use the formula for the area of a rectangle and the area of a triangle.

Let's start with Rectangle A. We can see from the figure that its length is 5 units and its width is 3 units. To find its area, we use the formula A = l x w, where A represents the area, l represents the length, and w represents the width. So, for Rectangle A, we have:

A = 5 x 3 = 15 square units

Next, let's move on to Triangle B. We can see from the figure that the base of the triangle is 4 units and the height is 3 units. To find its area, we use the formula A = (1/2) x b x h, where A represents the area, b represents the base, and h represents the height. So, for Triangle B, we have:

A = (1/2) x 4 x 3 = 6 square units

Finally, let's find the area of Rectangle C. We can see from the figure that its length is 4 units and its width is 2 units. To find its area, we use the same formula as for Rectangle A:

A = 4 x 2 = 8 square units

Now that we have the area of each part, we can add them up to find the whole figure. So, we have:

Whole figure = Rectangle A + Triangle B + Rectangle C
Whole figure = 15 + 6 + 8
Whole figure = 29 square units

Therefore, The area of each part of the figure and the whole figure are as follows:
Rectangle A = 15 square units
Triangle B = 6 square units
Rectangle C = 8 square units
Whole figure = 29 square units

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The sampling technique used in this scenario is stratified random sampling.

This is because Kane grouped the population of licensed nurses in Florida into two distinct strata, namely urban and nonurban areas, based on a specific characteristic (geographical location). Then, he randomly selected 250 nurses from each stratum, resulting in a total sample size of 500 nurses.

The purpose of stratified random sampling is to ensure that the sample is representative of the population by including participants from each stratum in proportion to their representation in the population. This allows for more accurate and precise estimates of population parameters than simple random sampling, especially when there are significant differences between strata.

By stratifying the population and randomly selecting participants from each stratum, Kane can draw more reliable conclusions about the attitudes of licensed nurses toward evidence-based practice in urban and nonurban areas of Florida.

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In order to determine the chi-squared value and the predicted level of significance as represented by the test, we need to conduct a hypothesis test. We will use the chi-squared test for a population variance. The null hypothesis is that the population variance is equal to 20 minutes squared (the square of the standard deviation), and the alternative hypothesis is that the population variance is greater than 20 minutes squared.

Therefore, the chi-squared value is calculated as:χ2 = (n - 1) × s2 / σ20where n is the sample size, s is the sample standard deviation, and σ0 is the hypothesized population standard deviation. Substituting the values given in the question, we get:χ2 = (7 - 1) × 29² / 20²= 21.19.

The degrees of freedom for this test are df = n - 1 = 6.Using a chi-squared distribution table with 6 degrees of freedom, we can find the predicted level of significance. For a chi-squared value of 21.19 and 6 degrees of freedom, the level of significance is less than 0.005. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the population variance is greater than 20 minutes squared.

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