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Answer:

Diameter = 33 feet

Step-by-step explanation:

Diameter = 2 x radius

Given that the volume = 18174 \(ft^{3}\), then;

Volume of sphere = \(\frac{4}{3}\)\(\pi\)\(r^{3}\)

where r is the radius of the sphere.

Thus,

18174 = \(\frac{4}{3}\) x \(\frac{22}{7}\) x \(r^{3}\)

         = \(\frac{88}{21}\) \(r^{3}\)

18174 x 21 = 88 \(r^{3}\)

381654 = 88 \(r^{3}\)

\(r^{3}\) = \(\frac{381654}{88}\)

   = 4336.9773

r = \(\sqrt[3]{4336.9773}\)

r = 16.3078

The diameter of the sphere = 2 x 16.3078

                                              = 32.6156

                                              = 33 feet

The number of subsets contained in Q if Q={x∣∣x is an even, positive integer and x < 27] is 13.

A subset implies a part of the mathematical concept that's referred to as the set. The set is the collection of the elements that are grouped in the curly braces.

In this case, since x is an even number and less than 27, this will be:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, and 26.

Therefore, the numbers are 13.

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The Length of the rod is 3/5 meters.

The civil engineer wants to find the length of a rod that stretches for 1 meter and can be given by the function x=2y^(3/2).

To find the length of the rod, we need to integrate the function x=2y^(3/2) with respect to y. Integrating both sides of the equation,

we have:'int dx = int 2y^(3/2) evaluating the left-hand side gives x = 2/5 y^(5/2) + C, where C is the constant of integration. To find the value of C,

we use the given information that the rod stretches for 1 meter. At y = 0, x = 0 since the rod has no length when it is not stretched. At y = 1, x = 1 since the rod stretches for 1 meter.

Therefore, we have:1 = 2/5 (1)^(5/2) + C1 = 2/5 + CC = 3/5 Substituting C = 3/5 back into the equation for x,

we have:x = 2/5 y^(5/2) + 3/5

The length of the rod is given by the value of x when y = 1. Substituting y = 1,

we have:x = 2/5 (1)^(5/2) + 3/5 = 3/5

The length of the rod is 3/5 meters.

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The area of carpet required to be bought for the living room is 127.75 square feet.

Thus the area of carpet required is 127.75 square feet.

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The distance traveled by airplane is 180 miles.

The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°

The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.

Then, the total distance traveled by airplane will be:

= 100 miles + 80 miles = 180 miles.

The speed can be defined as the distance traveled by the total time taken.

Speed = distance/time

Speed = 180 miles/ 1 hour

Speed = 180 miles/60 minutes

Speed = 3 miles per minute

The angle of direction from its origin will be:

tan (x) = 100 miles/80 miles

x = tan⁻¹ ( 100/80)

x = tan⁻¹ ( 10/8) =  tan⁻¹ ( 5/4)

x = 51.34°

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If a data set contains three points, and two of the residuals are -10 and 20, the third residual is 10 (option B).

A residual is the difference between the observed value and the estimated value of the quantity of interest.

The residual of a data points should normally sum up to zero (0). This means the following applies:

-10 + 20 + x = 0

x = 10

Therefore, if data set contains three points, and two of the residuals are -10 and 20, the third residual is 10.

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Answer:

40 girls

Step-by-step explanation:

To get the number of girl students, we first do 48 divided by 6 to get 8. Then we do 8 x 5 to get 40.  

To establish trust with Martina, the nurse should show respect, use non-verbal communication, incorporate play, involve the parent, and individualize the approach.

To establish a trusting relationship with Martina, the nurse can employ several approaches:

Respect and empathy: The nurse should approach Martina with genuine respect and empathy, recognizing her unique needs and individuality. This can be conveyed through a calm and patient demeanor.

Non-verbal communication: Since Martina may not be responsive to verbal cues, the nurse can utilize non-verbal communication to establish connection and trust. This can include maintaining eye contact, using gentle touch, and respecting Martina's personal space.

Play and familiar objects: Given Martina's engagement with the blue stuffed dog, the nurse can incorporate play into their interactions. Bringing familiar objects or toys that Martina finds comforting can help create a sense of familiarity and security.

Parental involvement: Involving Martina's mother in the care process can be beneficial. The nurse can communicate with the mother, seek her input, and involve her in the administration of medications. This helps build trust not only with Martina but also with her caregiver.

Individualized approach: Recognizing Martina's autistic disorder, the nurse should tailor their approach to her specific needs. Understanding her sensory sensitivities and preferences can help create a safe and comfortable environment.

By implementing these strategies, the nurse can foster trust and a positive therapeutic relationship with Martina, promoting her overall well-being and care.

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Complete Question:

What approach would help the nurse establish a trusting relationship with Martina, a 3-year-old with bronchitis and autistic disorder, who is intensely occupied with a blue stuffed dog and does not seem responsive to the nurse's presence in the room, while the mother is also present?

Spotify charges $0.98 for individual song and $10 for entire album

According to the question,

Spotify charges "x" dollars for individual songs and "y" for entire album

Also, Person A pays $14.9 to download 5 individual songs and 1 album

Which can be written as

=> 5x + y = 14.9 --------------(1)

Person B pays $22.95 to download 3 individual songs and 2 albums

=> 3x + 2y = 22.95 ---------(2)

Solving these two linear equations by elimination method

Multiplying equation (1) by 2

=> 10x + 2y = 29.8

Now, subtracting these equation

10x + 2y - 3x - 2y = 29.8 - 22.95

=> 7x = 6.85

=> x = 0.98

Replacing value of x in equation (1),

=> 5(0.98) + y = 14.9

=> 4.9 + y = 14.9

=> y = 10

Hence , Spotify charges $0.98 for individual song and $10 for entire album

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Hey girl! It's me again to explain this to you :)

Number 21.) If we start from our y-intercept -2 and move up 2 on our y-axis we get to point (0,0). If we move over 1 space to the right, we are on (1,0), which is the x-intercept.

Slope: 2/1 or just 2

Y-intercept: -2

You didn't ask for this but i'm gonna write it anyways. The equation for this line is y=2x-2

Number 22.) If we start from our y-intercept 2 and move down 2 on your y-axis we get to point (0,0). If we move over 1 space to the right, we are on (1,0), which is the x-intercept.

Slope: -2/1 or just -2

Y-intercept: 2

Again you didn't ask for this but the equation for this line is y=-2x+2

Hope this helped you understand and again make this brainliest and reply if you need more help or have any more questions :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

simplify

4x-12=28

4x=40

x=10

---------{NOTICE}----------

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The amount of the sale of the home is $2090181.82

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

Commission = 5.5% on the sale of a home

Also, we have

Commission  = 114960

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

5.5% on the sale of a home = 114960

So, we have

5.5% * sale of a home = 114960

Divide both sides by 5.5%

sale of a home = 114960/(5.5%)

Evaluate

sale of a home = 2090181.82

Hence, the sale of the home is $2090181.82

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Answer:

5000

Step-by-step explanation:

I took the test so that's how I know

There is evidence to suggest that the market share for the Honda Civic in the city is different from its national market share of 20% by using Hypothesis test. 95% confident that the proportion of compact cars sold in the city that are either a Honda Civic, Toyota Corolla, or Nissan Sentra is between 0.512 and 0.613.

Conduct a hypothesis test at the 5% level of significance to determine if the market share for the Honda Civic in the city is different from its national market share of 20%. First, we need to calculate the expected frequencies for each category based on the national market shares:

Honda Civic: 0.20 x 400 = 80

Toyota Corolla: 0.17 x 400 = 68

Nissan Sentra: 0.12 x 400 = 48

Hyundai Elantra: 0.10 x 400 = 40

Chevrolet Cruze: 0.10 x 400 = 40

Ford Focus: 0.08 x 400 = 32

Others: 0.23 x 400 = 92

Then, we can use the chi-squared goodness-of-fit test to determine if the observed frequencies in the sample are significantly different from the expected frequencies.

The test statistic is calculated as follows:

chi-squared = sum((observed - expected)^2 / expected)

Using the observed and expected frequencies from the sample, we get:

chi-squared = ((99-80)^2/80) + ((73-68)^2/68) + ((53-48)^2/48) + ((45-40)^2/40) + ((41-40)^2/40) + ((26-32)^2/32) + ((63-92)^2/92) = 14.68

The degrees of freedom for this test are df = k - 1 = 7 - 1 = 6, where k is the number of categories. Using a chi-squared distribution table with 6 degrees of freedom and a significance level of 0.05, the critical value is 12.59.

Since our calculated chi-squared value of 14.68 is greater than the critical value of 12.59, we reject the null hypothesis and conclude that there is evidence to suggest that the market share for the Honda Civic in the city is different from its national market share of 20%.

b) Construct a 95% confidence interval for the proportion of compact cars sold in the city that are either a Honda Civic, Toyota Corolla, or Nissan Sentra.

We can use the formula for a confidence interval for a proportion:

CI = p ± zsqrt(p(1-p)/n)

where p is the proportion of interest, z is the critical value from the standard normal distribution (1.96 for a 95% confidence interval), and n is the sample size.

We want to find the proportion of compact cars sold in the city that are either a Honda Civic, Toyota Corolla, or Nissan Sentra. From the sample, the total number of sales for these three models is 99 + 73 + 53 = 225. The total sample size is 400.

So, the proportion we are interested in is:

p = 225/400 = 0.5625

Plugging in the values, we get:

CI = 0.5625 ± 1.96sqrt(0.5625(1-0.5625)/400) = 0.512 to 0.613

Therefore, we can be 95% confident that the proportion of compact cars sold in the city that are either a Honda Civic, Toyota Corolla, or Nissan Sentra is between 0.512 and 0.613.

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_____The given question is incommplete, the complete question is given below:

Based on 2017 sales, the six top-selling compact cars are the Honda Civic Toyota Corolla_ Nissan Sentra Hyundal Elantra_ Chevrolet Cruze; and Ford Focus (New York Daily News) . The 2017 market shares are Honda Civic 20 %, Toyota Corolla 17%, Nissan Sentra 12 %, Hyundar Elantra 10 %, Chevrolet Cruze 10%_ and Ford Focus 8% with other small car models comprising the remaining 23%. sample of 400 compact car sales in Chicago showed the following number of vehicles sold_ Excel File: datal2-27xlsx Honda Civic Toyota Corolla Nissan Sentra Hyundai Elantra Chevrolet Cruze Ford Focus Others Use goodness of fit test to determine whether the sample data indicate that the market shares for cars in Chicago are different than the market shares suggested by nationwide 2017 sales_ Using 0.05 level of significance what is the P-value? Use Table of Appendix The p-value Select your answer What is your conclusion? Conclude that the markets shares for the seven compact cars in Chicago Select your GMAAT the market shares reported_ What market share differences, if any; exist in Chicago? Round your answers to three decimal places Enter negative values as negative numbers_ Sample Hypothesized Market Share Compact Car Market Share Honda Civic Difference Toyota Corolla Nissan Sentra Hyundai Elantra Chevrolet Cruze 0.10 0.10 Ford Focus Others 0.23

Answer:

3/8

Step-by-step explanation:

Values we are given :

We know that :

Therefore,

Answer:

It is correct

Step-by-step explanation:

Given

\(Height = 42\ in\) ---- Missing information

\(Minimum\ Height = 48\ in\)

Represent the additional height (i.e. 6 inches) with h

Required

Is \(48 \le h + 42\) correct

The term at most mean less than or equal to \(\le\)

So, for him to grow at most 6 inches; it means that 48 inches must be less than or equal to the sum of his current height and additional height needed.

Mathematically:

\(48 \le 42 + 6\)

Substitute h for 6

\(48 \le 42 + h\)

Hence, the expression is correct.

Answer:

sample response

Step-by-step explanation:

No, the work is correct, but the interpretation is not. “6 is less than or equal to h” means that h is greater than or equal to 6. He must grow at least 6 inches, not at most 6 inches.

The length of the total distance the particle traveled is, 327π/8.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

A particle is moving on the perimeter of a circle with radius r=5 with angular speed of π/8 radians per second.

Now, First of all, let's calculate the the circumference. This is found by this equation:

⇒ P = 2πr

Here, r = 5

⇒ P = 2π × 5

⇒ P = 10π

And, The distance of completing 4 full rotations is,

⇒ D = 4P

⇒ D = 4 × 10π

⇒ D = 40π

Since, In one second the particle traveled π/8 radians.

Here, the particle traveled for 7 more seconds and stopped, this distance is,

⇒ 7 (π/8)

⇒ 7π/8

Thus, the length of the total distance the particle traveled is;

⇒ 40π + 7π/8

⇒ 327π/8

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Answer:90 shirts

Step-by-step explanation: do 1.5 x 1.6 = that answer and + 60 to that answer ok

Answer:

\(\sqrt{128x^8y^3} = 8 x^4 y \sqrt{2y}\)

Step-by-step explanation:

Given

\(\sqrt{128x^8y^3}\) --- the complete expression

Required

The equivalent expression

We have:

\(\sqrt{128x^8y^3}\)

Expand

\(\sqrt{128x^8y^3} = \sqrt{128* x^8 * y^3}\)

Further expand

\(\sqrt{128x^8y^3} = \sqrt{64 * 2* x^8 * y^2 * y}\)

Rewrite as:

\(\sqrt{128x^8y^3} = \sqrt{64 * x^8 * y^2* 2 * y}\)

Split

\(\sqrt{128x^8y^3} = \sqrt{64 * x^8 * y^2} * \sqrt{2 * y}\)

Express as:

\(\sqrt{128x^8y^3} = (64 * x^8 * y^2)^\frac{1}{2} * \sqrt{2y}\)

Remove bracket

\(\sqrt{128x^8y^3} = (64)^\frac{1}{2} * (x^8)^\frac{1}{2} * (y^2)^\frac{1}{2} * \sqrt{2y}\)

\(\sqrt{128x^8y^3} = 8 * x^\frac{8}{2} * y^\frac{2}{2} * \sqrt{2y}\)

\(\sqrt{128x^8y^3} = 8 * x^4 * y * \sqrt{2y}\)

\(\sqrt{128x^8y^3} = 8 x^4 y \sqrt{2y}\)

Answer:

c 435

Step-by-step explanation:

took the test

The percentage of our new facility's seating is full will be 76%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Initial value - Final value] / Initial value x 100

Our new training room can seat 150 employees.

If 6 tables consisting of 6 chairs are now taken.

Then the number of occupied seats by tables will be

⇒ 6 x 6

⇒ 36

Then the percentage of our new facility's seating is full will be

P = [(150 - 36) / 150]  x 100

P = (114/150) x 100

P = 0.76 x 100

P = 76%

The percentage of our new facility's seating is full will be 76%.

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The value of x is 6

A line segment can be defined as the partition formed by end points of a line.

From the information given, we have that line JL is the line with segments JK, KL and JL and K and the midpoint between J and L

This can be represented as;

JK + KL = JL

Where;

Substitute the values into the formula, we have;

5x -8 + 7x - 12 = 52

Now, collect like terms

12x = 52 + 20

Add like terms

12x = 72

Make 'x' the subject of formula

x = 72/12

x = 6

Thus, the value of x is 6

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Around 33.98 juniors, or 13.59% of the 250 juniors, had scores between 30 and 36.

(a) The mean is given as 27. The standard deviation is given as 3. Three standard deviations from the mean would be:

\(27 + (33) = 27 + 9 = 36\\\\27 - (33) = 27 - 9 = 18\)

So the mean is 27 and three standard deviations from the mean are 18 and 36.

b) the z-score corresponding to a raw score of 30, and then find the proportion of the distribution above that z-score. The z-score is calculated as:

\(z = (30 - 27) / 3 = 1\)

Using a standard normal distribution table or calculator, we can find that the proportion of scores above a z-score of 1 is approximately 0.1587 or 15.87%.

Therefore, approximately 15.87% of scores are greater than 30.

c)Since we know that the mean is 27 and the standard deviation is 3, we can find the z-scores corresponding to the raw scores of 30 and 36 as follows:

\(z_1 = (30 - 27) / 3 = 1\\\\z_2 = (36 - 27) / 3 = 3\)

Using a standard normal distribution table or calculator, we can find that the proportion of scores between these two z-scores is approximately 0.1359 or 13.59%.

Therefore, approximately 13.59% of the 250 juniors, or about 33.98 juniors, scored between 30 and 36.

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Answer:

A factor is a number that can be evenly divided into other whole number without having a remainder left over.

Answer:

The deck will cover 153.86 square feet of Nicole's yard

Step-by-step explanation:

We want to find the area of the deck as the area is "the total space taken up by a flat (2-D) surface".  Furthermore, the mention of square feet also indicates that we want to find area since the area is always in square units.

The formula for the area of a circle is given by:

A = πr^2, where

Thus, we can plug in 3.14 for π and 7 for r, allowing us to solve for A, the area of the circular deck in square feet:

A = 3.14(7)^2

A = 3.14(49)

A = 153.86

Thus, the deck will cover 153.86 square feet of Nicole's yard.

Answer:

The system of equations has one solution. The two equations are intersecting lines.

Step-by-step explanation:

if you want to use the substitution method, you would have to plug in y for 12x+2 in the second equation.

2(12x+2)=x+4

next, you have to distribute

24x+4=x+4

subtract 24x from each side

4=-23x+4

subtract 4 from each side

0=23x

divide each side by 23

x=0

now, plug in 0 to one equation.

y=12(0)+2

y=2

the lines intersect at one point, (0,2)

Answer:

0.5

Step-by-step explanation:

7 / 15.02 US dollars = 0.466045273

Round to the nearest tenth: 0.5