Quick, please! Stephanie is making a gingerbread house similar to her real-life house. She is using a scale of 1 cm equals 5 feet. If Stephanie's house is 30 feet wide, how wide will the gingerbread house be?

A right circular cylinder with the largest volume that can fit inside a sphere with a radius of 12 has a radius of √7238/πh units.

The right circular cylinder is a cylinder with circular bases that are parallel to one another.

Three dimensions make up its form.

The two bases of the cylinder are joined at their centers by the cylinder's axis.

Sphere:

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same distance from a single point.

The radius of the right circular cylinder will be:

The formula for the volume of a sphere: V = 4/3πr²

Now, substitute r = 12 as shown:

V = 4/3πr²

V = 4/3π12²

V = 4/3π144

V = 7238.22947

Rounding off: 7238 units³

Nw, the formula for the volume of a right circular cylinder:

V = πr²h

Substitute V = 7238 and calculate for r as follows:

V = πr²h

7238 = πr²h

r² = 7238/πh

r = √7238/πh

Therefore, a right circular cylinder with the largest volume that can fit inside a sphere with a radius of 12 has a radius of √7238/πh units.

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I believe the answer you seek would be that the area of the shaded region would be [tex]64.43 cm^2[/tex].

Hope this helps!

When testing the differences between means, the research hypothesis suggests that population means are not equal.  (Option B)

Hypothesis refers to a concept or explanation for a trend that is based on known facts but has not yet been proved. A research hypothesis, also known as scientific hypothesis, is a statement about the expected result of a study. It is the proposed answer to the research question and generally includes an explanation (e.g., x affect y because …). It introduces a research question and proposes an expected result. It illustrates the relationship between two variables - an independent and dependent variable. Hence, when testing the difference between means, the hypothesis that suggests that population means are not equal is a research hypothesis.

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Answer:

B. 21

Step-by-step explanation:

Composite numbers have more than two factors.

Answer: 21

Step-by-step explanation:

Answer:

20 cm²

Step-by-step explanation:

It is a right triangle.

So, using Pythagorean theorem: OS² = OR² - RS²

OR = r (radius) + 8

OS = r

RS = 16

=> r² = (r+8)² - 16²

r² = r² + 16r + 64 - 256

r² = r² + 16r - 192

16r = 192

r = 192 / 16 = 12cm²

a) 12 cm²

b) 12 + 8 = 20 cm²

V=Vw-ce^-kt is the velocity V as a function of time t when wind is blowing 20 knots and after 1 half hour the boat moves at 10 knots

Acceleration is a vector quantity that is defined as the rate at which an object's velocity varies. When an object's velocity changes, it is said to be accelerating.

On occasion, sports broadcasters will suggest that a person is accelerating if they are traveling quickly. But speed has nothing to do with acceleration. Even while traveling very quickly, a person may not be accelerating. Changing the speed at which an item is travelling is what acceleration is all about. A substance is not accelerating if its velocity is not changing. The information on the right depicts an object that is speeding as it moves northward. Throughout time, the velocity is shifting. Every second, the velocity is changing by a fixed amount of 10 m/s.

How to solve?

Based on the information from the exercise, we have the equation:

dt/dv=k(Vw−V)

where V is velocity of the boat in knots/hour, tt is time in hours, Vw is velocity of wind.

This equation can be written:

dv/dt = k(Vw -V)

dv/Vw-V =kdt

Now, the variables are separated, tt appears only on the right side, and v only on the left. Integrate the left side in relation to v, and the right side in relation to t:

dv/Vw-V =kdt

∫dv/Vw-V =∫kdt

let Vw -V = u

-dv=du

dv= -du

∫-du/u =k∫dt

-ln|u| =kt +C

-ln|Vw-V| = kt + C

V=Vw-ce^-kt

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Juliet was charged $18 for driving 120 miles.

Given,

The rent of car per day = $80

The charge for per miles driven = $0.15

Juliet was charged a total of $98 for the rental and mileage.

We have to find the total miles of driving;

Here,

Charge for miles driven = Total charge - Rent of car for a day

Charge for miles driven = 98 - 80

Charge for miles driven = $18

Now,

Total miles driven = Charge for miles driven / Charge for one mile

Total miles driven = 18/0.15

Total miles driven = 120

That is,

Juliet was charged $18 for 120 miles of driving.

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Answer:

n = 15

Step-by-step explanation:

the triangles are similar so the correspondent sides are proportional

2: 5 = 6 : n

n = 6 x 5 /2

n = 3 x 5

n = 15

The equation of the hyperbola is

[tex]144 {x}^{2} - 25 {y}^{2} - 50y - 3650 = 0[/tex]

What is a hyperbola?

In mathematics, a hyperbola is a conic section formed by the intersection of the double cone by a plane surface, but not necessarily at the centre. It is a type of smooth curve lying in a plane and has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

The standard form of writing an equation of the hyperbola is,

[tex]\frac{ {(x - h)}^{2} }{ {a}^{2} } - \frac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]

Where (h, k) is the centre; a is the distance from the centre to vertices; b is the distance from co-vertices to the centre.

Given,

Foci of the hyperbola are (13, -1); (-13, -1)

Co-vertices are (0,11); (0,-13)

As we know that the centre of the hyperbola is the midpoint of the foci, then it will be (h,k) = (0,-1)

Distance from centre to foci is, c = 13 [2c = 26; c = 26 / 2 = 13]

Distance from co vertices to foci is, b = 12 [ 2b = 24; c = 24 / 2 = 12]

let us assume a is the distance from the centre to the vertices.

we know that,

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

then,

[tex]a = \sqrt{ {c}^{2} - {b}^{2} } [/tex]

[tex]a = \sqrt{ {13}^{2} - {12}^{2} } [/tex]

[tex]a = \sqrt{169 - 144} [/tex]

[tex]a = \sqrt{25} [/tex]

[tex]a = 5[/tex]

Now, the equation of the hyperbola is,

[tex] \frac{ {(x - h)}^{2} }{ {a}^{2} } - \frac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]

[tex] \frac{ {(x - 0)}^{2} }{ {5}^{2} } - \frac{ {(y + 1})^{2} }{ {12}^{2} } = 1[/tex]

[tex] \frac{ {x}^{2} }{25} - \frac{ {y}^{2} + 2y + 1 }{144} = 1[/tex]

[tex] \frac{144 {x}^{2} - 25 {y}^{2} - 50y - 50 }{25 \times 144} = 1[/tex]

[tex]144 {x}^{2} - 25 {y}^{2} - 50y - 50 = 25 \times 144[/tex]

Hence the required equation is,

[tex]144 {x}^{2} - 25 {y}^{2} - 3650 = 0[/tex]

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The expected value of the mean, variance and standard deviation are-

For the given data in the question-

The formula for the mean;

μ = n×n /N

Put the values,

μ = 5×5/7

μ = 3.57

μ ≈ 4 (mean)

The formula for the variance is;

σ = nμ/N × (N - μ)(N - n)/N(N - 1)   ....eq 1

σ = 5×4/7 × (7 - 4)(7 - 5)/7(7 - 1)  

σ = 0.61 (variance)

For the calculation of the standard deviation-

δ = √σ   ...eq 2

δ = √0.61

δ = 0.78 (standard deviation).

Thus, the expected value of the mean, variance and standard deviation are  calculated.

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The correct statement to represent the comparison between defective parts produced by machines is option d. Machine A usually, but not always, produced fewer defective parts than machine B.

As given in the question,

Number of machines in a factory = 2

Statement compares the :

Number of defective parts produced by machines during first 4 hours

for 19 days.

Observations from the given scatterplot are:

a. Machine A always produced the same number of defective parts as machine B.

False. Variation in producing number of defective parts.

b. Machine A always produced fewer defective parts than machine B.

False.

c. Machine A always produced more defective parts than machine B.

False.

d. Machine A usually, but not always, produced fewer defective parts than machine B.

True. Sometimes like when Machine A produce 7 defective parts machine B produce 5.

e. Machine A usually, but not always, produced more defective parts than machine B.

False.

Therefore, option d) Machine A usually, but not always, produced fewer defective parts than machine B is the correct answer.

The complete question is:

A factory has two machines, A and B, making the same part for refrigerators. The number of defective parts produced by each machine during the first hour of operation was recorded on 19 randomly selected days. The scatterplot below shows the number of defective parts produced by each machine on the selected days.

Which statement gives the best comparison between the number of defective parts produced by the machines during the first hour of operation on the 19 days?

a. Machine A always produced the same number of defective parts as machine B.

b. Machine A always produced fewer defective parts than machine B.

c. Machine A always produced more defective parts than machine B.

d. Machine A usually, but not always, produced fewer defective parts than machine B.

e. Machine A usually, but not always, produced more defective parts than machine B.

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The angle sweeped by chances during counterclockwise direction is 175.15° and in radian is 3.05, the distance of chance is from right and the above the centre of the circle is 0.27 km and 0.261km respectively.

Chance is running on a circular track that has a radius 0.9 km and he goes 2.75km into the counter clockwise direction from the 3-o'clock position.

The arc length of the circle is given by,

L = 2πR(A/360)

R is the radius,

L is the length of the arc,

A is the angle made in degrees.

Putting values,

2.75 =2π(0.9)(A/360)

A = 175.15°C.

Now, converting it into radians,

A in radian is 3.05.

Distance D of chance to the right of centre of the ski trail is,

D = R(1-0.7)

D = R(0.3)

D = 0.27 Km.

The distance D' of chance above the centre of the ski trail is,

D' = R(1-0.71)

D' = R(0.29)

D' = 0.261 Km.

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Answer:

Yes you are right

Step-by-step explanation:

It equals 5.45

Answer:

You can make up to "9" different 5-digit codes

The degrees of freedom for goodness-of-fit chi-square tests are calculated with the formula: df=bins(or categories)−1−number of parameters of the distribution and the degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) .

In the given question we have to calculate degrees of freedom for goodness-of-fit chi-square tests versus chi-square tests for independence and homogeneity.

When a categorical variable has more than two levels, a chi-square goodness-of-fit test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.

The degrees of freedom in this case are calculated with the formula:

df=bins(or categories)−1−number of parameters of the distribution.

The degrees of freedom for the chi-square are calculated using the following formula:

df = (r-1)(c-1)

where r is the number of rows and c is the number of columns.

The null hypothesis can be rejected if the observed chi-square test statistic is higher than the crucial value.

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Answer:

$400

Step-by-step explanation:

y= 320×(1+0.25)=400

Answer:

-1/3

Step-by-step explanation:

3-6/5-(-4) = -3/9

simplify -3/9

-1/3

Answer:

i. X represents the difference between the mean entry-level mechanical engineering salary and the mean entry-level electrical engineering salary.

ii. t distribution with df = 96

iii. t = -2.38

iv. p-value = 0.0190

v. Alpha = 0.05

i. The random variable X - Xe represents the difference in mean salaries between mechanical engineering (X) and electrical engineering (Xe).

ii. We used the t-distribution for the test due to unknown population standard deviations and relatively small sample sizes.

iii. The calculated test statistic is -2.1095.

iv. The degrees of freedom for the t-distribution are approximately 113242.

v. The p-value associated with the test statistic and degrees of freedom is approximately 0.0001.

i. The random variable X - Xe represents the difference in mean salaries between mechanical engineering (X) and electrical engineering (Xe).

ii. We will use the t-distribution for the test since the population standard deviations are unknown, and the sample sizes are relatively small (less than 30).

iii. The test statistic for this hypothesis test is calculated as:

[tex]t = (X - Xe) / \sqrt(s_m^2 / n_m) + (s_e^2 / n_e))}[/tex]

Where:

X = sample mean for mechanical engineering

Xe = sample mean for electrical engineering

Sm = standard deviation for mechanical engineering

Se= standard deviation for electrical engineering

nm = sample size for mechanical engineering

ne = sample size for electrical engineering

t = (46100 - 46900) / √(3450² / 46) + (4230² / 52))

= -800 / √(3450² / 46) + (4230² / 52))

= -800 / 379.4303

= -2.1095

iv.

Calculating the degrees of freedom:

df = (3450² / 46 + 4230² / 52)² / ((3450² / 46)² / (46 - 1) + (4230² / 52)² / (52 - 1))

= (119023.913 + 180714.2308)² / ((119023.913)² / 45 + (180714.2308)² / 51)

= 113242.1436

The degrees of freedom are approximately 113242.

Now, we need to find the p-value associated with the test statistic and degrees of freedom.

We can use a t-distribution table to look up the p-value.

Since the test is one-tailed and the test statistic is negative, we will look up the p-value in the left tail of the t-distribution with the given degrees of freedom.

Assuming the p-value is less than 0.0001, we can state that the p-value is approximately 0.0001.

v. To conduct a hypothesis test at the 5% level to determine if you agree that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.

So, the significance level (alpha) is given as 5%.

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If the P value in a statistical test of hypotheses is more than, we may claim that the data are statistically significant at level. Less than is the P-value. =0.05 .

An assumption is said to as a hypothesis when it is supported by evidence. Any investigation that turns the research questions into predictions must start here. Variables, the population, and the relationships between the variables are among its constituent parts. A hypothesis used to examine the link between two or more variables is known as a research hypothesis.

One dependent variable and one independent variable are shown to be related. For instance, eating more vegetables will help you lose weight more quickly. In this scenario, increasing your vegetable intake is an independent variable, while weight loss is the dependent variable.

It makes a claim that conflicts with the premise. There is no connection between the independent and dependent variables, which is a negative assertion. The emblem stands for.

Hence, If the P value in a statistical test of hypotheses is more than, we may claim that the data are statistically significant at level. Less than is the P-value. =0.05 .

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Answer:

(2x - 1) (4x + 3)

Step-by-step explanation:

The correct option D)c = –3, d = –2; for which the expression becomes real number.

For the given question,

The expression is-

= i(2 + 3i)(c + di)

Simplifying,

= i(2c + 2di + 3ci + 3d²)

= 2ci + 2di² + 3ci² + 3di³

= 2ci - 2d -3c - 3di

= (2c - 3di)i - 2d - 3c

Now, again for expression to produce a real number, the coefficient of must be zero.

Let's evaluate each choice.

A: 2c - 3d = 2x2 -3x3 = -5

B: 2x(-2) - 3x3 = -13

C: 2x3 - 3x(-2) = -12

D: 2x(-3) - 3x(-2) = 0

As option D only has the positive number, thus define the expression.

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The complete question is-

What values of c and d would make the following expression represent a real number? i(2 + 3i)(c + di)

choices: A)c = 2, d = 3 B)c = –2, d = 3 C)c = 3, d = –2 D)c = –3, d = –2

Answer: D) c = –3, d = –2

Step-by-step explanation:

Correct on Edge

6.908 is greater than 6.098 as the second digit from the left is greater.

We round off numbers to make them easier to remember and it also keeps its value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given, are two numbers 6.098 and 6.908.

Now, starting from left both the numbers have the same digit so we can't

differentiate.

The digit after the decimal place to the first number is 0 and on the second it is 9 so definitely, the second number is greater.

∴ 6.098 < 6.908.

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The correct option is (a). basic statistical tests the technique is likely to discover a value that is 10x larger than the next highest value in a dataset of 500,000 records is basic statistical tests.

Statistical assessments are utilized in speculation trying out. They may be used to: decide whether a predictor variable has a statistically substantial relationship with an outcome variable. estimate the distinction between or more groups.

Two main statistical techniques are used in data analysis: descriptive facts, which summarize records of the usage of indexes along with suggestions and median and every other is inferential facts, which draw conclusions from records of the usage of statistical assessments including pupil's t-take look at.

In fact, there are foremost kinds of assessments: parametric and non-parametric. each sort of assessment is used to make inferences about a populace based on a sample. The difference between the 2 styles of tests lies within the assumptions that they make about the records.

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She owe $167.25 of the credit card company at the end of 3 months.

To compute simple interest, duplicate the chief sum by the loan fee and the time. The recipe worked out is "simple interest = Principal x Interest Rate x Time." This condition is the easiest approach to ascertaining interest.

We ave,

interest = 10%, loaned amount = $250, monthly payment = $50

Then,

interest of first month = $250×1×0.1 = $25

She makes a payment of $50

Then $250 - $50 + $25 = $225

Second month:

interest = $225 ×0.1 = $22.5

Payment of $50

remain loan = $225 - $50 + 22.5 = $197.5

And third month

interest = $197.5×0.1 = $19.75

payment of $50 Then

Net payable loan = $197.5 - $50 + $19.75 = $167.25

Thus, remaining loan amount is $167.25.

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Simplified form of fourth root of 2401x¹²y¹⁶  is  7x³y⁴

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

Given,

⁴√2401 x¹² y¹⁶=⁴√7*7*7*7 (x³)⁴(y⁴)⁴

                       =⁴√(7)⁴ (x³)⁴(y⁴)⁴

                       =⁴√(7 x³y⁴)⁴

                       =  7 x³y⁴

Therefore, Simplified form  fourth root of 2401x¹²y¹⁶  is  7x³y⁴.

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The increase in the price of the bananas = 8%

We know that the formula for percent change:

percent change = [(new value - old value)/ old value ] * 100

Here, the price for bananas was 75 cents per pound over last month. today, we see that it's been marked up to 81 cents per pound.

old value = 75 cents per pound

new value = 81 cents per pound

So, the percent increase in the price of bananas would be,

percent increase in price = [(81 - 75)/ 75 ] * 100

percent change = (6/75) * 100

percent change = 8%

Therefore, the increase is 8%

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We are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.

The correct interpretation of a 99% confidence interval is that we are 99% confident that the true population mean falls in it.

The probability that it contains the true population mean is 99%.

Given  99% confidence interval : 4.1 < μ < 5.6

Then, the correct interpretation is we are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.

Hence the answer is We are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.

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Based on the graph showing the different gang-related activities reported in small and large communities, a gang-related activity which is least reported in a large community is: B. robbery.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors.

Additionally, a pie chart is generally considered as the best graph to be used in graphically representing percentages and relative proportions.

According to the graph, we can logically deduce the following percentages of people that reported the different gang-related activities in small and large communities;

In conclusion, robbery is the least reported gang-related activity in a large community with a percentage of 5 percent (5%).

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The square root √(7 · x - 4) = 2 has a solution for the variable x is 8 / 7.

In this problem, we find a square root whose solution for the variable x has to be found solely by algebra properties. First, write the radical equation:

√(7 · x - 4) = 2

Second, elevate to the square of the expression:

7 · x - 4 = 4

Third, clear the variable x by algebra properties:

7 · x = 8

x = 8 / 7

The solution to the square root is equal to 8 / 7.

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The Area of annulus - the region between the two circle is 50.26cm²

According to the question,

The length of chord of the large circle which is tangent to the small circle : AB = 8cm

Le the radius of large circle "R" and radius of smaller circle "r"

AB is a tangent to the smaller circle

AM = 8/2

=> AM = 4cm

In ΔOAM,

Using Pythagoras theorem ,

OA² = OM² + AM²

=> R² = r² + (4)²

=> R² - r² = 16

So, the area of annulus = π(R² - r²)

=> 16π (putting π = 3.14)

=> 50.26cm² is required area

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