A sphere is inscribed in a cube with a surface area of 216 square centimeters. What is the volume of the sphere? Round your answer to the nearest whole number.

Answer:

Hope this helps!!

The percentage of the total hours did Andrea work is,

⇒ 27.1%

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Total number of hours to work is,

⇒ 5.8 + 8.1 + 7.3 + 8.7 hours

⇒ 29.9 hours

Here, Andre work 8.1 hours.

Hence, The percentage of the total hours did Andrea work is,

⇒ 8.1 / 29.9 × 100

⇒ 27.1%

Thus, The percentage of the total hours did Andrea work is,

⇒ 27.1%

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The 100%-Norm.Dist(value,mean,sd,true) percent of the population has an iq over 115

According to the statement

we have to find that the what percent of the population has an iq over 115.

And from given information,

the mean iq score is 100 and the standard deviation is 15.

And

Normal distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

And by use of this formula, we find the percentage of the population has an iq over 115.

Then the result will comes as 100%.

hence, 100%-Norm.Dist(value,mean,sd,true)

So, The 100%-Norm.Dist(value,mean,sd,true) percent of the population has an iq over 115.

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The response variable is the birth weight and the predictor variable is the mother's age.

The reason for this is that the goal is to understand how mother's age affects birth weight, rather than how birth weight affects mother's age. The predictor variable (mother's age) is the variable that is being used to explain or predict the response variable (birth weight).

In other words, we want to determine whether there is a relationship between mother's age and birth weight, and if so, what that relationship looks like. Therefore, mother's age is the independent variable or predictor, and birth weight is the dependent variable or response.

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All types of chi-square-based measure of association can accommodate both discrete and continuous data, and ordinal as well as nominal data.

According to statement

we have explain that the which type of the chi-square-based measure of association can accommodate both discrete and continuous data, and ordinal as well as nominal data.

So,For this purpose, we know that the

A chi-squared test is a statistical hypothesis test that is valid to perform when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test.

it is used in the every type of the data measurement.

And all types of the chi-squared test compare all type of the data set. which are the applicable for the.

So, All types of chi-square-based measure of association can accommodate both discrete and continuous data, and ordinal as well as nominal data.

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Answer:

AC = 15

Step-by-step explanation:

Point B is on line segment AC .

Given

AB=3x

BC=4x+8,

AC=5x+10

determine the numerical length of AC

                 3x                                4x+8

A-----------------------------B----------------------------------C

|<----------------------------5x+10 --------------------------->|

AB + BC = AC

3x + 4X + 8 = 5X + 10

combine like terms:

3x + 4x - 5x = 10 - 8

simplify:

2x = 2

x = 2 / 2

x = 1

solve for AC

AC = 5x + 10

AC = 5(1) + 10

AC = 15

The numerical length of AC is 15 units.

It is required to find the numerical length of AC.

Length is defined as the measurement or extent of something from end to end.  The greater of two or the greatest of three dimensions of an object. It can be measured in different units like centimeters, inches, meters, etc.

Given:

AB=3x

BC=4x+8,

AC=5x+10

If B is on AC,

we can say:

AB + BC = AC

3X + 4X + 8 = 5X + 10

Combine like terms we get,

3x + 4x - 5x = 10 - 8

then simplify and get

2X = 2

X = 1.

Put the value of x in AC we get,

AC = 5X + 10

AC = 5*1+10

AC = 15

Therefore, the numerical length of AC is 15 units.

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The probability of rolling two dice and getting a sum of 7 is 1/6.

The probability is the ratio of the number of favorable outcomes to the total outcomes in that sample space. Probability of an event P(E) = (Number of favorable outcomes) ÷ (Sample space).

Sample space for rolling a pair of dice we have:

=> S {(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)}

n(S) = 36

Let A = sum of numbers is 7 = { (1, 6)(2, 5)(3, 4) (4, 3) (5, 2) (6, 1)}

n(A) = 6

P (Sum of numbers is 7) = n(A) / n(S)

= 6/36 = 1/6

Therefore, the probability of rolling two dice and getting a sum of 7 is 1/6.

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Hey there! I'm happy to help!

NUMBER 1

This is a trick to solve any proportion.

Multiply the diagonal numbers.

5(16)=80

Divide by the number that isn't the one you want to find.

90/8=10

And you are left with the number you haven't touched. We haven't touched x, so x=10.

NUMBER 2

Cross multiply.

45(-50)=-2250

Divide.

-2250/3=-750

So x=-750.

QUESTION 3

4(27)=108

108/12=9

So x+3=9, subtract 3 from both sides x=6.

Have a wonderful day! :D

The cοrrect οptiοn is Optiοn D. The p-value is less than α, and the null hypοthesis is nοt rejected. There is nο cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

Frοm the given data,

A cοmpany that ships glass fοr a manufacturer claimed that its shipping bοxes are cοnstructed sο that nο mοre than 8 percent οf the bοxes arrive with brοken glass.

The glass manufacturer believes that the actual percentage is greater than 8 percent.

The manufacturer tested the hypοtheses

H0: p = 0.08 and Ha: p > 0.08

The test yielded a p-value οf 0.1

Since the significance level (alpha) is 0.1 and the calculated p-value is 0.1,

we cοmpare the p-value tο alpha.

If the p-value is less than οr equal tο alpha, we reject the null hypοthesis H0: p = 0.08 in favοr οf the alternative hypοthesis Ha: p > 0.08.

If the p-value is greater than the alpha, we fail tο reject the null hypοthesis.

In this case, the calculated p-value οf 0.1 is greater than the significance level οf 0.1.

Therefοre, we fail tο reject the null hypοthesis and cοnclude that there is nοt enοugh evidence tο suppοrt the claim that the actual prοpοrtiοn οf bοxes with brοken glass is greater than 8%.

It is pοssible that the cοmpany's claim οf nο mοre than 8% brοken bοxes is accurate.

Therefοre,

The cοrrect οptiοn is Optiοn D.

The p-value is less than α, and the null hypοthesis is nοt rejected. There is nο cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

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Cοmplete questiοn:

A cοmpany that ships glass fοr a glass manufacturer claimed that its shipping bοxes are cοnstructed sο that nο mοre than 8 percent οf the bοxes arrive with brοken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a randοm sample οf bοxes and recοrded the prοpοrtiοn οf bοxes that arrived with brοken glass. The manufacturer tested the hypοtheses H0:p=0.08 versus Ha:p>0.08 at the significance level οf α=0.01.

The test yielded a p-value οf 0.001. Assuming all cοnditiοns fοr inference were met, which οf the fοllοwing is the cοrrect cοnclusiοn?

The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

The p-value is greater than α, and the null hypοthesis is rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08

The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

75% of the beads are green in color.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Chase ordered a set of beads

He received 4,000 beads in all.

3,000 of the beads were green.

We need to find the  percentage of the beads were green of 4000.

x/100×4000=3000

40x=3000

Divide both sides by 40

x=75%

Hence, 75% of the beads are green in color.

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The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

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The given sequence 9, 3, 1, 1/3 can be classified as a geometric sequence.

To find the rule for the n'th term, we need to determine the common ratio (r) between consecutive terms.

To find the common ratio, we divide each term by its previous term:

3/9 = 1/3, 1/3 = 1/3

We can see that the common ratio (r) is 1/3.

The rule for the n'th term of a geometric sequence is given by:

a(n) = a(1) * r^(n-1)

In this case, the first term (a(1)) is 9, and the common ratio (r) is 1/3.

Therefore, the rule for the n'th term is:

a(n) = 9 * (1/3)^(n-1)

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The inverse matrix of the given matrix exist and is: \left[\begin{array}{ccc} -\frac13 & -\frac13 & \frac23 \\ -\frac13 & -\frac29 & -\frac{14}{27} \\ -\frac13 & \frac23 & -\frac13 \end{array}\right]

The matrix is:

\left[\begin{array}{ccc}2&0&-1\\-1&-1&1\\3&2&0\end{array}\right]

To check whether the matrix has an inverse, we need to determine its determinant. We do this as follows:  

\left[\begin{array}{ccc}2&0&-1\\-1&-1&1\\3&2&0\end{array}\right]  = 2\left[\begin{array}{ccc}-1&1\\2&0\end{array}\right] - 0\\left[\begin{array}{ccc} -1 & 1 \\ 3 & 0\end{array}\right] - 1\\left[\begin{array}{ccc} -1 & -1 \\ 3 & 2 \end{array}\right]= -4 - 0 - 5 = -9

Since the determinant of the matrix is not zero, it has an inverse. The inverse matrix is obtained as follows:

\left[\begin{array}{ccc} 2 & 0 & -1 \\ -1 & -1 & 1 \\ 3 & 2 & 0\end{array}\right] \left[\begin{array}{ccc}  x_{11} & x_{12} & x_{13} \\ x_{21} & x_{22} & x_{23} \\ x_{31} & x_{32} & x_{33} \end{array}\right]  =  \left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]

Solving for the entries of the inverse matrix, we obtain:

\left[\begin{array}{ccc} x_{11} & x_{12} & x_{13} \\ x_{21} & x_{22} & x_{23} \\ x_{31} & x_{32} & x_{33} \end{array}\right] = \left[\begin{array}{ccc} -\frac13 & -\frac13 & \frac23 \\ -\frac13 & -\frac29 & -\frac{14}{27} \\ -\frac13 & \frac23 & -\frac13 \end{array}\right]

Thus, the inverse matrix of the given matrix is: \left[\begin{array}{ccc} -\frac13 & -\frac13 & \frac23 \\ -\frac13 & -\frac29 & -\frac{14}{27} \\ -\frac13 & \frac23 & -\frac13 \end{array}\right]

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Using scientific notation the product 19,898 × 0.002 = 99.49

Scientific notation is the expression of a number in the form a × 10ⁿ where 1 ≤ a < 10 and n is an integer

So, find the closest to the product 19,898 × 0.002, we write each number in scientific notation and then multiply.

So, 19898 = 1.9898 × 10⁴

0.002 = 2 × 10⁻³

Using the rule of multiplication, we have

a × 10ⁿ × b × 10ˣ = a × b × 10ⁿ⁺ˣ

So, we have that

19,898 × 0.002 = 1.9898 × 10⁴ × 2 × 10⁻³

= 1.9898 × 2 × 10⁴⁺⁽⁻³⁾

= 9.949  × 10⁴⁻³

= 9.949 × 10

= 99.49

So, 19,898 × 0.002 = 99.49

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In this problem, we are given a second-order linear differential equation with a sinusoidal forcing term. We are asked to find the particular integral, which represents the response of the system to the forcing term. Specifically, we need to determine the particular solution that satisfies the given equation.

To find the particular integral, we assume a particular solution in the form of yp = A sin(8t) + B cos(8t), where A and B are constants to be determined. This form of the particular solution matches the form of the forcing term, which is 4.5 sin(8t).

We substitute this assumed particular solution into the given differential equation and simplify the equation by taking the derivatives. Plugging the derivatives into the equation, we can solve for the constants A and B.

After solving for A and B, we substitute their values back into the assumed particular solution, giving us the final expression for the particular integral, yp.

The particular integral represents the response of the system to the sinusoidal forcing term, and by adding it to the complementary solution (the solution to the homogeneous equation), we obtain the complete solution to the differential equation.

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Answer:

U' (5, 1 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

U (5, - 1 ) → U' (5, - (- 1) ) → U' (5, 1 )

Answer:

the answer is one.

Step-by-step explanation:

1, is: 1.66666666667

2, is: 0.6

3. is: 0.06666666666

4. is: 0.6

Answer:

1.5

Step-by-step explanation:

The value of the angle θ₁, located in Quadrant IV with sin(θ₁) = -13/85, is such that cosθ₁ = 84/85.

In the given scenario, the angle θ₁ is located in Quadrant IV and sin(θ₁) is given as -13/85. We can use the trigonometric identity to determine the value of cosθ₁.

Using the Pythagorean identity sin²θ + cos²θ = 1, we can substitute sin(θ₁) = -13/85:

(-13/85)² + cos²θ₁ = 1

Simplifying:

169/7225 + cos²θ₁ = 1

cos²θ₁ = 1 - 169/7225

cos²θ₁ = (7225 - 169)/7225

cos²θ₁ = 7056/7225

Taking the square root of both sides, we get:

cosθ₁ = √(7056/7225)

Since the angle θ₁ is located in Quadrant IV where cosθ₁ is positive, the value of cosθ₁ is:

cosθ₁ = √(7056/7225)

Simplifying the square root:

cosθ₁ = 84/85

Therefore, the value of the angle cosθ₁ is 84/85.

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The complete question is:

The angle θ₁ is located in Quadrant IV and  sin(θ₁) = -13/85. What is the value of the angle cosθ₁?

Answer:

-6

Step-by-step explanation:

Answer:

3 is a whole number but 2x is 2 multiplied by a variable

The expected number of flips until getting the first heads is equal to the reciprocal of the probability of getting heads on a single flip, which is 1/p.

The number of independent flips x until the first heads follows a geometric distribution. In general, the probability of getting the first heads on the kth flip is given by \((1-p)^(^k^-^1^)\)p. Thus, the expected value or mean of the geometric distribution is E(x) = 1/p.

This means that on average, we need to flip the coin 1/p times until we get the first heads. For example, if the probability of getting heads is 0.5, then on average we need to flip the coin 2 times until we get the first heads. If the probability of getting heads is 0.1, then on average we need to flip the coin 10 times until we get the first heads.

The geometric distribution is a fundamental concept in probability theory and has many applications in fields such as finance, engineering, and computer science.

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The spread of the women's scores is therefore somewhat larger than the spread of the men's scores based on the range.

The MAD indicates that the men's score spread is marginally less than the women's score spread.

The difference between a dataset's largest and lowest values is known as the range.

The range for the men's scores is: 75 - 65 = 10.

The range for the women's scores is 80 - 69 = 11.

The spread of the women's scores is therefore somewhat larger than the spread of the men's scores based on the range.

The average distance between each data point and the dataset's mean is measured by the mean absolute deviation (MAD).

Find the mean first before calculating the MAD for the men's scores:

(65 + 68 + 70 + 72 + 73 + 75) / 6 = 70.5

The MAD indicates that the men's score spread is marginally less than the women's score spread.

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The equation that represents a line that is perpendicular to the line represented by 2x - y = 7 is y = -1/2x + 6

The equation of a line in slope-intercept form is expressed as;

y = mx + b

where;

m is the slope

b is the y-intercept

For two lines to be perpendicular, the product of their slope must be -1

Given the equation 2x - y =7​

Rewrite

y = 2x - 7

The slope of the line is 2, the slope of the line perpendicular must be -1/2. Hence from the given option, the equation that represents a line that is perpendicular to the line represented by 2x - y = 7 is y = -1/2x + 6

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Answer:

see below

Step-by-step explanation:

1. a = 18, 2. n = -19, 3. x = -17, 4. v = -6, 5. a = 9, 6. x = -2, 7. k = -4,  8. m = -19

9. n = 3, 10.  a = -7, 11. n = -5, 12. n = -6, 13. x = -1/3, 14. m = 2/3 15. m = -9.8

16. n = 7.9, 17. x = 0, 18. b = 2, 19. v = -8, 20. b = -4, 21. n = 3, 22. p = 3.3

The area D is bounded by the lines x = 0, y = 3 – 37, and y = 3x – 3. To calculate the iterated double integral for ∫∫xdA over D, the value of the iterated double integral ∫∫xdA over the area D is 0.

To set up the iterated double integral for ∫∫xdA over D, we first need to determine the limits of integration for x and y. Looking at the given lines, x = 0 indicates that x varies from 0 to some upper limit. The line y = 3 – 37 represents a horizontal line, indicating that y has a constant value of 3 – 37, which simplifies to -34. The line y = 3x – 3 represents a slanted line with a slope of 3, indicating that y varies linearly with x.

To find the limits of integration for x, we need to determine the x-values where the slanted line and the vertical line intersect. Setting 3x – 3 equal to 0, we find x = 1. Substituting this value back into the slanted line equation, we get y = 3(1) – 3 = 0. Therefore, x varies from 0 to 1.

For y, since it has a constant value of -34, the limits of integration for y are -34 to -34.

Setting up the iterated double integral, we have ∫∫xdA = ∫[0 to 1]∫[-34 to -34] x dy dx. Integrating with respect to y first, we have ∫[0 to 1] x(-34 - (-34)) dx, which simplifies to ∫[0 to 1] 0 dx. Finally, integrating with respect to x, we get 0. Therefore, the value of the iterated double integral ∫∫xdA over the area D is 0.

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Answer:

-40

Step-by-step explanation:

f(10)=-4(10)

f(10)=-40

The total amount of money paid for the tickets in the first two hours is given as follows:

$13,475.

The total amount of money paid for the tickets in the first two hours is obtained applying the proportions in the context of the problem.

The amount of people that purchased tickets in each hour is given as follows:

Then the total number of people is given as follows:

350 + 420 = 770 people.

Each ticket costs $17.50, hence the amount earned is given as follows:

770 x 17.50 = $13,475.

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An airship propelled by some mechanical device travels five miles in ten minutes in the direction of the wind, but requires one hour to go back again to the starting point against the same wind. How long would it have taken to go the whole ten miles in a calm day without any wind? Hint: You don't have to use equations to solve this problem.

we have that

5 miles -------> 10 minutes (direction of the wind)

5 miles ------> 1 hour (against the same wind)

therefore

10 miles ------> ? (without any wind)

so

Let

x -----> speed of the wind

y -----> speed of the airship

direction of the wind

speed=d/t ------> 5/10=0.5 miles per min

against the same wind

speed=5/60=1/12 miles per min

so

x+y=0.5 ------> x=0.5-y -----> equation 1

y-x=1/12 -----> equation 2

solve the system

substitute equation 1 in equation 2

y-(0.5-y)=1/12

2y=(1/12)+1/2

2y=7/12

y=7/24=0.2917 miles per min

Find the value of x

x=(1/2)-7/24

x=5/24=0.2083 miles per min

therefore

10 miles without any wind

speed=d/t ------> t=d/speed

t=10/(7/24)

The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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