A sphere has a diameter of 12 ft. What is the volume of the sphere? Give the exact value in terms of
[tex]\pi[/tex]
​

Answer:

22

Step-by-step explanation:

In the series 14 + 6 + (–2) + (–10) + . . . + (–154)

The gap between entities is 8.

Therefore number of entities between -10 and -154 = (154 - 10)/8 =18

Total number of terms in the series = 18 + 4 = 22

There are 22 terms in the given arithmetic series.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

In the given arithmetic series 14 + 6 + (–2) + (–10) + . . . + (–154)

The common difference between entities is 8.

Therefore, the number of entities between -10 and -154

= (154 - 10)/8

=18

The Total number of terms in the series = 18 + 4 = 22

Hence, there are 22 terms in the given arithmetic series.

Learn more about arithmetic sequence here:

https://brainly.com/question/3702506

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Answer:

Step-by-step explanation:

Money markets accounts offer a annual percentage yield which is higher compared to other types of savings accounts

These accounts also require a higher minimum deposits to get a higher rate

These accounts may also be insured and secured by the Federal Deposit Insurance Corp in banks and the National Credit Union Administration in credit unions.

They are also relatively easy to access.

Answer:

A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutes

Step-by-step explanation:

x% confidence interval is between a ± b.

a is the sample mean.

b is the margin of error.

Interpretation: We are x% sure that the population mean is between a-b and a+b.

In this question:

96% confidence interval for the mean time that students will require to complete a particular examination. Between 62.4 - 12.6 = 49.8 minutes and 62.4 + 12.6 = 75 minutes.

The correct interpretation is that we are 96% sure that the population mean is in this interval.

So the correct answer is:

A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutes

Answer:

The confidence interval for the true mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The confidence interval for this case i given by:

[tex] 62.4 -12.6 \leq \mu \leq 62.4+12.6[/tex]

[tex] 49.8 \leq \mu \leq 75.0[/tex]

For this case we can conclude that the true mean for the time that students will require to complete a particular examination is between 49.8 and 75.0 minutes. And the best option for this case by:

A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutes

Step-by-step explanation:

The confidence interval for the true mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The confidence interval for this case i given by:

[tex] 62.4 -12.6 \leq \mu \leq 62.4+12.6[/tex]

[tex] 49.8 \leq \mu \leq 75.0[/tex]

For this case we can conclude that the true mean for the time that students will require to complete a particular examination is between 49.8 and 75.0 minutes. And the best option for this case by:

A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutes

Answer:

The correct option is C

Step-by-step explanation:

The average variation is spread out more than the middle 50% of the data.

Answer:

4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.

Step-by-step explanation:

Given:

[tex] (x^2 + y^2)y' = y^2[/tex]

Solving the differential equation, we have:

[tex] \frac{dy}{dx} = \frac{y^2}{x^2 + y^2}[/tex]

Thus, except at (0,0), for all real values of x and y, the function[tex] \frac{y^2}{x^2 + y^2}[/tex] is defined.

The (0,0) values of x&y causes the denominator to be 0, so the function is not defined at this (0,0) condition.

Therefore,

[tex] \frac{d}{dy} \frac{y^2}{x^2 + y^2} = \frac{x^2 + y^2 (2y) - y^2 (2y)}{(x^2 + y^2)^2} [/tex]

[tex] = \frac{2x^2y + 2y^3 - 2y^3}{(x^2 + y^2)^2} [/tex]

[tex] = \frac{2x^2y}{(x^2 + y^2)^2} [/tex].

Apart from the point of origin (0,0), this is continuous.

This means a unique solution exists in the region consisting of all points in the xy-plane except the origin.

Answer:

Given:

Mean, u = 135

Sample size, n = 42

Sample mean, x' = 126

Standard deviation = 16

Significance level = 0.05

1) The null and alternative hypotheses:

H0 : u = 135 (the revenue per day is $135)

H1 : u < 135 (the revenue per day is less than $135)

2) In this case, we have a left tailed test.

Let's use the formula:

[tex] = \frac{x' - u}{s/ \sqrt{n}} = \frac{126 - 135}{16 / \sqrt{42}} = -3.645 [/tex]

t = - 3.645

Critical value: at a significance level of 0.05, left tailed test,

tcritical = -1.683

We reject null hypothesis, H0, since t calculated, -3.645 is less than tcritical, -1.683.

3) Given, a = 0.05, df = 41, left tailed test,

t-value = 2.02

For the corresponding confidence interval, we have:

[tex] CI = (x' - \frac{t * \sigma}{\sqrt{n}}, x' + \frac{t * \sigma}{\sqrt{n}}) [/tex]

[tex] CI = (126 - \frac{2.02 * 16}{\sqrt{42}}, 126 + \frac{2.02 * 16}{\sqrt{42}}) [/tex]

CI = (121.014, 130.986)

4) Conclusion:

We reject the estimated potential revenue advised by the consultant, H0, as it is too high, because the t-calculated falls in rejection region(i.e, less than critical value), also the upper limit of the confidence interval is less than $135.

A parallelogram

P=2(a+b)

The answer is 64

P=2(a+b)=2·(24+8)=64

Answer:

1. a

2. d

3. b

4.a

5 d

6. b

7. b

8.a

9. d

10. a

Answer:

we need picture

Step-by-step explanation:

Answer:

G 0.04 Times D

Step-by-step explanation:

Answer:

[tex] \frac{337}{4} [/tex]

Step-by-step explanation:

[tex]84 \frac{1}{4} = \frac{84 \times 4 + 1}{4} = \frac{336 + 1}{4} = \frac{337}{4} [/tex]

Answer:

[tex]1\dfrac{3}{5}[/tex]

Step-by-step explanation:

Because these two triangles are similar:

[tex]\dfrac{4}{5}=\dfrac{x}{2}\\x=\dfrac{8}{5}=1\dfrac{3}{5}[/tex]

Hope this helps!

Answer:

36 ÷ 3 = j

Step-by-step explanation:

The quotient of 36 and 3 is '36 ÷ 3'.

'Is j' would be '= j'.

Put it together, and you get:

36 ÷ 3 = j

'j = 12'

[tex]\frac{36}{3} = j\\\\\text {Divide the two numbers: }36/3 = 12\\\boxed {12=j}[/tex]

Brainiest Appreciated

Answer:

(C) Sample: the 120 students surveyed. Population: the 1200 students at the high school. Parameter of interest: the average number of hours a student at this high school sleeps per night.

Step-by-step explanation:

The correct answer is (C). The sample is a subset of the population, and the parameter is a characteristic of the population of interest.

Answer:their is something wrong in the question

Step-by-step explanation:

Answer:

13 ounces

Step-by-step explanation:

291/21.5=13.5348837209

Answer:

π∫52(ey3)2dy

The work I did to solve this equation:

Step 1

ln(3x)=2

3x=2e

x=2e3

Step 2

ln(3x)=5

3x=5e

x=5e3

Step 3

y=ln(3x)⟺ey=3x⟺ey3=x

Step 4

π∫52(ey3)2dy

Answer:

The coordinates of point B are (-2, 2)

Step-by-step explanation:

We have two points: A and C.

The coordinates for A are (2, -8) and the coordinates for C are (-4, 7).

We have to find the coordinates of the point B, that satisfies the condition that the distance AB is 2 times the distance BC.

We also know that B is a point of the line AC.

We can calculate the line AC as a linear function y=mx+b.

The slope m is:

[tex]m=\dfrac{y_c-y_a}{x_c-x_a}=\dfrac{7-(-8)}{-4-2}=\dfrac{15}{-6}=-2.5[/tex]

Then, the y-intercept b can be calculated using the coordinates of one of the points, in this case point A:

[tex]y=-2.5x+b\\\\b=y_a+2.5x_a=-8+2.5*2=-8+5=-3[/tex]

Then, we know that B is a point of the linear function y=-2.5x-3, within the range x ∈ (-4; 2).

To have a ratio AB to BC of 2 to 1, we can divide the length of the line AC in 3 parts, and the point B will be located in the  end of the segment nearer to point C.

In the picture attached, you can see the division of the segment AC in three parts and the location of point B=(x, y).

Applying the Thales theorem, we can divide the segment in the y-axis in three and calculate y, and the same for the x-axis.

Then, the coordinate y for the point B is:

[tex]y=y_c-(y_c-y_a)/3\\\\y=7-[7-(-8)]/3=7-15/3=7-5=2\\\\\\x=x_c-(x_c-x_a)/3\\\\x=-4-(-4-2)/3=-4-(-6)/3=-4+2=-2[/tex]

Then, the point B has coordinates (-2, 2).

We can verify the distances as:

[tex]AB=\sqrt{(2-(-2))^2+((-8)-2)^2}=\sqrt{16+100}=\sqrt{116}\\\\\\BC=\sqrt{((-2)-(-4))^2+(2-7)^2}=\sqrt{4+25}=\sqrt{29}\\\\\\\dfrac{AB}{BC}=\dfrac{\sqrt{116}}{\sqrt{29}}=\sqrt{\dfrac{116}{29}}=\sqrt{4}=2[/tex]

Answer: (-2,2)

Step-by-step explanation:

Answer:

B im not to sur tho tell me if you got it

Answer:

1054.00

Step-by-step explanation:

Answer:

5 ≥ p

Step-by-step explanation:

Add 5 to both sides:

0 ≥ p - 5

+5      + 5

________

5 ≥ p

Answer:

p <= 5

Step-by-step explanation:

Let's solve your inequality step-by-step.

0≥p−5

Step 1: Flip the equation.

p−5≤0

Step 2: Add 5 to both sides.

p−5+5≤0+5

p≤5

Answer:

p≤5

Answer:

3x (x² + x + 1)

You could write any trinomial like this

Answer:

443

Step-by-step explanation:

Answer:426.196

Step-by-step explanation:

Answer:

3x+100

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

We are told that the length of a side of the square is x.

Now, perimeter of square = 4 × side length

Perimeter of square = 4x

Also,we are told that the triangle is equilateral and a side is (x + 1).

Thus, perimeter of triangle = 3(x + 1)

Since we are told that the perimeter of the square is equal to that of the equilateral triangle. Thus;

4x = 3(x + 1)

4x = 3x + 3

Subtract 3x from both sides to get;

4x - 3x = 3

x = 3

Answer:

pretty sure it's C

Step-by-step explanation:

Answer:

[tex]g(\frac{1}{2}) = 0.5[/tex]

The input is [tex]x = \frac{1}{2}[/tex] and the output is [tex]g(x) = g(\frac{1}{2}) = 0.5[/tex]

Step-by-step explanation:

Suppose we have a function g(x) = a. The input is the value of x and the output is the value of g.

In this question:

[tex]g(x) = 2x^{2}[/tex]

We want g(1/2) = g(0.5). So

[tex]g(0.5) = 2*(0.5)^{2} = 2*0.25 = 0.5[/tex]

[tex]g(\frac{1}{2}) = 0.5[/tex]

The input is [tex]x = \frac{1}{2}[/tex] and the output is [tex]g(x) = g(\frac{1}{2}) = 0.5[/tex]

Answer:

Yes

Step-by-step explanation:

Given the system of equations

[tex]\begin{aligned} &y=2x +1 \\\\ &x-y=-3 \end{aligned}[/tex]

We want to determine if (2,5) is a solution of the system.

We can do this by substitution of the given point into the equations and see if it holds.

Given (x,y)=(2,5), x=2, y=5

In the first equation

y=2x+1

5=2(2)+1

5=5

Therefore, the point (2,5) satisfies the first equation.

In the second equation

[tex]x-y=2-5=-3[/tex]

Since our result (-3) is equal to the Right Hand Side, the point also satisfies the second equation.

Therefore, (2,5) is a solution of the system.

Answer:  3.5 pounds

Step-by-step explanation:

17+12.5=29.5

33-29.5=3.5

Answer:

Step-by-step explanation:

H0: μ1____ μ2For Q17(circle one: equal to, less than or equal to, greater than or equal to, not equal to )

H1 : μ1____ μ2For Q18(circle one: equal to, less than, greater than, not equal to )

Formula for calculating the the test:

t = [ (x₁ - x₂) - d ] / sqrt[(s₁²/n₁) + (s₂²/n₂)]

where x₁ = 37.6, x₂ = 39.3, d = 0 assuming equality = 37.6 - 39.3 = -1.7

s₁² = 4.92 = 24.01, s₂² = 2.72 = 7.29, n₁ = 50, n₂ = 58.

thus, t = [ (-1.7) - (0)] / √(24.01/50) + (7.29/58)

    t = (-1.7) / (0.4802 + 0.1257)

   t = -1.7 / 0.6059

   t = -2.8057. = -2.81

P value:

Lets find the degree of freedom:

DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }

DF = (24.01/50 + 7.29/58)² / {[(24.01 / 50)² / 50-1)] + (7.29/58)² / 58-1)]}

DF = (0.4802 + 0.1257)² /{[ (0.4802)²/49] + (0.1257)²/57)]}

DF = (0.6059)²/ (0.00471 + 0.00028)

DF = 0.3671 / 0.00499 = 75.37

Thus, P value = 0.9968 using a t distribution calculator.

Decision/Conclusion: Since the P value 0.9968 is greater than α (.05), Fail to Reject H0, There is not sufficient evidence to warrant the rejection of the claim.

Answer:

A.

Explaintion:

n=13. 13+2 = 15

I hope this helps ( :

Answer: B

Step-by-step explanation:

because 4 is the number of (n) plus the 2

The formula to find the area of a triangle is :

1/2 base*height

For instance:

base=4 cm

height=5cm

area of traingle=1/2*b*h

=1/2*4*5

=10cm^2

Hope it helps...

Good luck on your assignment