Find the SURFACE AREA of this composite solid.

Answer:

Step-by-step explanation:

Answer:

S = ⅙ π (65^³/₂ − 5^³/₂)

Step-by-step explanation:

z = x² + y², 1 < z < 4

Surface area is:

S = ∫∫√(1 + (fₓ)² + (fᵧ)²) dA

where fₓ and fᵧ are the partial derivatives of f(x,y) with respect to x and y, respectively.

fₓ = 2x, fᵧ = 2y

S = ∫∫√(1 + (2x)² + (2y)²) dA

S = ∫∫√(1 + 4x² + 4y²) dA

For ease, convert to polar coordinates.

S = ∫∫√(1 + 4r²) dA

S = ∫∫√(1 + 4r²) r dr dθ

At z = 1, r = 1.  At z = 4, r = 4.

So 1 < r < 4, and 0 < θ < 2π.  These are the limits of the integral.

S = ∫₀²ᵖⁱ∫₁⁴√(1 + 4r²) r dr dθ

To integrate, use u-substitution.

u = 1 + 4r²

du = 8r dr

⅛ du = r dr

When r = 1, u = 5.  When r = 4, u = 65.

S = ∫₀²ᵖⁱ∫₅⁶⁵√u (⅛ du) dθ

S = ∫₀²ᵖⁱ (⅛ ∫₅⁶⁵√u du) dθ

S = ∫₀²ᵖⁱ (¹/₁₂ u^³/₂ |₅⁶⁵) dθ

S = ∫₀²ᵖⁱ (¹/₁₂ (65^³/₂ − 5^³/₂)) dθ

S = (¹/₁₂ (65^³/₂ − 5^³/₂)) θ |₀²ᵖⁱ

S = (¹/₁₂ (65^³/₂ − 5^³/₂)) (2π)

S = ⅙ π (65^³/₂ − 5^³/₂)

Answer:

The margin of error is 370.8.

The 90​% confidence interval for the population mean is between $167.2 and $908.8

The correct interpretation is that we are 90% sure that the true mean price for all cellphones in within the interval end-points, so option B.

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 6 - 1 = 5

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0150

The margin of error is:

M = T*s = 2.0150*184 = 370.8.

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 538 - 370.8 = $167.2

The upper end of the interval is the sample mean added to M. So it is 538 + 370.8 = $908.8

The 90​% confidence interval for the population mean is between $167.2 and $908.8

The correct interpretation is that we are 90% sure that the true mean price for all cellphones in within the interval end-points, so option B.

Answer:

3¹²

Step-by-step explanation:

Move 3⁻² to the numerator using the negative exponent rule

1/b-n = bⁿ

(3⁵)² ⋅ 3²

Multiply the exponents

3¹⁰ · 3²

Multiply by adding the exponents

3¹⁰⋅ 3²

3¹²

Answer:

For someone who is a head coach - their expected income for the remainder of their professional coaching career will be

Expected income = 1×$41,389 + 2×$62,993 + 10×$104,485

Expected income = $1,212,225

Step-by-step explanation:

Professional basketball coaches may coach at one of three levels:

On average, the annual salary is given by

Using our P matrix, we have solved to find the fundamental matrix (we have called it the (I-Q) inverse matrix):

                      Assistant      Associate     Head

Assistant              6                     4              2

Associate             2                     6              6        

Head                    1                      2              10

For someone who is a head coach - what is their expected income for the remainder of their professional coaching career?

As per the given P matrix, for someone who is a head coach will be:

Assistant = 1 time

Associate = 2 times

Head = 10 times

Therefore, the expected income will be,

Expected income = 1×$41,389 + 2×$62,993 + 10×$104,485

Expected income = $1,212,225

Answer:

£2.70 fig rolls and £5.72 crisps

Step-by-step explanation:

£1.08+0.54+£1.08= £2.70 fig rolls

£1.43+£1.43+£1.43-£1.43= £2.86 x 2= £5.72 for 6 packets of crisps

£2.70+ £5.72= £8.42

Answer:

d: please note I am not sure about this but look at my reasoning and maybe you can find your own answer that you are sure about.

D: i am sure about this.

Step-by-step explanation:

From what I looked up, i believe what you are talking about is deductive reasoning, which is based off of facts. It can't be a or b because that wasn't defined in the statement. Squares and rectangles are not the same thing since you can have a square that is a rectangle, but a rectangle that is not a square, so D is correct.

corresponding angles i believe since they are matching

I know that the 2 lines are parallel because 5 and 6 are alternate interior angles since they are on opposite sides.

4 and 6 are not vertical or right angles, so it must be d, also they follow what a corresponding angle is, which is them being matching.

Answer:

13. B

14. D

Step-by-step explanation:

13. Law of Detachment says that if two statements are true then we can derive a third true statement. So, for example, say the first statement is that you are a human. Say the second statement is that you breathe. You can write this as: if you are a human, you breathe. In this case, if you have a square, then you have a rectangle. You have a quadrilateral.

14. 4 and 6 are corresponding angles, since you can tell that there are two parallel lines from angle 5 = angle 6. You can also use angle addition theorem.

Answer:

Step-by-step explanation:

2 3x6

the 3 is an exponet so supost to be smaller

the answer-  2^3 x^6

i think its right

Answer:

y=-5/2x-1

Step-by-step explanation:

first find the gradient whereas since the two lines are parallel they hav the same gradient. y=mx+c whereas m is the gradient. 5x+2y=12

2y=-5x+12

y=-5/2x+12(so the gradient is -5/2x..... gradient=-5/2

y-4=-5/2

x+2

y-4=-5/2(x+2)

y-4=-5/2x-5

y=-5/2x-5+4

y=-5/2x-1

The equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4) is y = -5/2 x - 1.

Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.

Given that the equation of the line is,

5x + 2y = 12

2y = -5x + 12

y = -5/2 x + 6

This is in the slope intercept form, where the slope = -5/2.

Slopes of two parallel lines are equal.

So any line parallel to the given line will be of the form y = -5/2 x + c

Given line passes through (-2, 4).

Substituting (-2, 4) in y = -5/2 x + c, we get,

(-5/2) (-2) + c = 4

c = -1

So the equation is, y = -5/2 x - 1

Hence the required equation is y = -5/2 x - 1.

Learn more about Slope Intercept form here :

https://brainly.com/question/21298390

#SPJ7

Answer:

A.

Step-by-step explanation:

In the attached file

Answer:

a. Standard deviation: 4.082

Standard error: 2.041

b. The 95% confidence interval for the actual temperature is (298.5, 311.5).

Upper bound: 311.5

Lower bound: 298.5

c. Test statistic t=2.45

P-value = 0.092

d. There is no enough evidence to claim that the dial of the oven is not properly calibrated. The actual temperature does not significantly differ from 300 °F.

e. If we use a significance level of 10% (a less rigorous test, in which the null hypothesis is rejected with with less requirements), the conclusion changes and now there is enough evidence to claim that the dial is not properly calibrated.

This happens because now the P-value (0.092) is smaller than the significance level (0.10), given statististical evidence for the claim.

Step-by-step explanation:

The mean and standard deviation of the sample are:

[tex]M=\dfrac{1}{4}\sum_{i=1}^{4}(305+310+300+305)\\\\\\ M=\dfrac{1220}{4}=305[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{3}\cdot [(305-(305))^2+(310-(305))^2+(300-(305))^2+(305-(305))^2]}\\\\\\ s=\sqrt{\dfrac{1}{3}\cdot [(0)+(25)+(25)+(0)]}\\\\\\ s=\sqrt{\dfrac{50}{3}}=\sqrt{16.667}\\\\\\s=4.082[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=305.

The sample size is N=4.

When σ is not known, s divided by the square root of N is used as an estimate of σM (standard error):

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{4.082}{\sqrt{4}}=\dfrac{4.082}{2}=2.041[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=4-1=3[/tex]

The t-value for a 95% confidence interval and 3 degrees of freedom is t=3.18.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=3.18 \cdot 2.041=6.5[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 305-6.5=298.5\\\\UL=M+t \cdot s_M = 305+6.5=311.5[/tex]

The 95% confidence interval for the actual temperature is (298.5, 311.5).

This is a hypothesis test for the population mean.

The claim is that the actual temperature of the oven when the dial is at 300 °F does not significantly differ from 300 °F.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=300\\\\H_a:\mu\neq 300[/tex]

The significance level is 0.05.

The sample has a size n=4.

The sample mean is M=305.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.028.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.082}{\sqrt{4}}=2.041[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{305-300}{2.041}=\dfrac{5}{2.041}=2.45[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=4-1=3[/tex]

This test is a two-tailed test, with 3 degrees of freedom and t=2.45, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>2.45)=0.092[/tex]

As the P-value (0.092) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the actual temperature of the oven when the dial is at 300 °F does not significantly differ from 300 °F.

If the significance level is 10%, the P-value (0.092) is smaller than the significance level (0.1) and the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the actual temperature of the oven when the dial is at 300 °C does not significantly differ from 300 °C.

Answer:

[tex]x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]

Step-by-step explanation:

[tex]x^2-4x-7=0\\\mathrm{Solve\:with\:the\:quadratic\:formula}\\Quadratic\:Equation\:Formula\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=1,\:b=-4,\:c=-7:\quad x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}\\x=\frac{-\left(-4\right)+\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2+\sqrt{11}[/tex]

[tex]x=\frac{-\left(-4\right)-\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2-\sqrt{11}\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]

Answer:

22,203 ft^2

Step-by-step explanation:

The area of a triangle with angle ∅ and two sides a and b is;

Area A = 1/2 × absin∅ ......1

The park is in the shape of a triangle, with two sides and an angle given;

Given;

a = 190 ft

b = 235 ft

∅ = 84°

Substituting the values into equation 1;

Area of the park;

A = 1/2 × 190 × 235 × sin84°

A = 22,202.70131409 ft^2

A = 22,203 ft^2 (to the nearest whole number)

Area of the park is 22,203 ft^2

Answer:

9/25

Step-by-step explanation:

Don't worry, I just took this test and got it correct. Best of luck to you all!

Answer:

Step-by-step explanation:

For the null hypothesis,

H0 : p = 0.63

For the alternative hypothesis,

Ha : p < 0.63

This is a left tailed test

Considering the population proportion, probability of success, p = 0.63

q = probability of failure = 1 - p

q = 1 - 0.63 = 0.37

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 478

n = number of samples = 800

P = 478/800 = 0.6

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76

From the normal distribution table, the area below the test z score in the left tail 0.039

Thus

p = 0.039

Answer:

-3.66

Step-by-step explanation:

Answer: 600 of the 500ml energy drinks be sold be sold at $45

Step-by-step explanation:

The linear relationship between the price (p) of 500ml soft drink and the number sold (x) is expressed as

x = ap + b

At N$20 she sells 1500 of the 500ml soft drinks. This means that the first equation would be

1500 = 20a + b - - - - - - - - -1

the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. This means that the new quantity sold is 1500 - 200 = 1300

The price at which they were sold is

20 + (50/100 × 20) = $30

The second equation would be

1300 = 30a + b - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

200 = - 10a

a = 200/- 10 = - 20

Substituting a = - 20 into equation 2, it becomes

1300 = 10 × - 20 + b

1300 = - 200 + b

b = 1300 + 200 = 1500

The linear relationship becomes

x = - 20p + 1500

If x = 600, then

600 = - 20p + 1500

- 20p = 600 - 1500 = - 900

p = - 900/ - 20

p = $45

Answer:

Board Games: 30%

Karaoke: 50%

Bowling: 20%

Step-by-step explanation:

Board Games: [tex]\frac{3}{3+5+2} =\frac{3}{10} =\frac{30}{100}[/tex] or 30%

Karaoke: [tex]\frac{5}{3+5+2} =\frac{5}{10} =\frac{50}{100}[/tex] or 50%

Bowling: [tex]\frac{2}{3+5+2} =\frac{2}{10} =\frac{20}{100}[/tex] or 20%

Answer:

Board Games: 30%

Karaoke: 50%

Bowling: 20%

Step-by-step explanation:

3 + 5 + 2 = 10 so there are 10 family members.

3 out of 10 equals 30%

5 out of 10 equals 50%

2 out of 10 equals 20%

Please mark Brainliest if correct

Hope this helps!

Answer:

Top prism = 262 in.² Bottom prism = 478 in.²

Step-by-step explanation:

top prism:

front + back: 5 x 3 = 15

sides: 19 x 4 x 2 = 152

bottom: 19 x 5 = 95

15 + 152 + 95 = 262

bottom prism:

front + back: 5 x 6 x 2 = 60

sides: 19 x 6 x 2 = 228

top + bottom: 19 x 5 x 2 = 190

60 + 228 + 190 = 478

Answer:

30

Step-by-step explanation:

It is an equalateral triangle

Answer:

C. F(x) = 4x² + 1

Step-by-step explanation:

→The function F(x) shifted 1 unit upwards, meaning there needs to be a 1 being added to the function.

→In addition, the function F(x) has grown narrower, compared to the function G(x). This is from the absolute value of a number being greater than 1, which is being multiplied.

This means the correct answer should be "C. F(x) = 4x² + 1."

Answer:

g-7

Step-by-step explanation:

Multiply the numbers

g-(1*7)

g-7

Answer:

5

Step-by-step explanation:

We know that g is an invertible function and so it must also be a one-to-one function.

This means that each input is paired with exactly one output and that each output is paired with exactly one input.

We know that g(a)=7g and g(5)=7. If the output of 7 is to be paired with exactly one input, then a must be equal to 5.

Answer:

65

Step-by-step explanation:

C^2= A^2 + B^2

C^2 = (60)^2 + (25)^2

C^2 = 4225

Take the square root of C

C = 65

Answer:

65

Step-by-step explanation:

Use the Pythagorean Theorem to find the length of the hypotenuse.

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

I'm assuming that '60' and '25' are measures of the legs, since the question asks to find the hypotenuse.

[tex]60^2+25^2=c^2\\\rightarrow 60^2=3600\\\rightarrow 25^2 = 625\\3600+625=c^2\\4225=c^2\\\sqrt{4225}=\sqrt{c^2}\\\boxed{65=c}[/tex]

The hypotenuse should measure 65 units.

Answer:

The value of x^3 + 1/x^3 is 47/x + 1/x^3 - 1/x^5

Step-by-step explanation:

x^4 + 1/x^4 = 47

x^4 = 47 - 1/x^4

x^3 + 1/x^3 = 1/x(x^4 + 1/x^2)

x^4 = 47 - 1/x^4

x^3 + 1/x^3 = 1/x(47 - 1/x^4 + 1/x^2) = 47/x - 1/x^5 + 1/x^3 = 47/x + 1/x^3 - 1/x^5

Answer:

11 y 23

Step-by-step explanation:

Nombrando los números como [tex]x[/tex] y [tex]y[/tex],

Planteamos las siguientes ecuaciones:

[tex]xy=253[/tex] (el producto de los numeros es 253)

[tex]x=2y+1[/tex] (uno de los enteros debe ser uno más que el doble del otro).

Sustituimos la segunda ecuación en la primera:

[tex](2y+1)(y)=253[/tex]

resolvemos para encontrar y:

[tex]2y^2+y=253\\2y^2+y-253=0[/tex]

usando la formula general para resolver la ecuación cuadrática:

[tex]y=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

donde

[tex]a=2,b=1,c=-253[/tex]

Sustituyendo los valores:

[tex]y=\frac{-1+-\sqrt{1-4(2)(-253)} }{2(2)} \\\\y=\frac{-1+-\sqrt{2025} }{4}\\ \\y=\frac{-1+-45}{4} \\[/tex]

usando el signo mas obtenemos que y es:

[tex]y=\frac{-1+45}{4} \\y=\frac{44}{4}\\ y=11[/tex]

(no usamos el signo menos, debido a que obtendriamos fracciones y buscamos numeros enteros)

con este valor de y, podemos encontrar x usando:

[tex]x=2y+1[/tex]

sustituimos [tex]y=11[/tex]

[tex]x=2(11)+1\\x=22+1\\x=23[/tex]

y comprobamos que el producto sea 253:

[tex]xy=253[/tex]

[tex](23)(11)=253[/tex]

Answer:

1.46666 miles / minutes

88 miles per hour

Step-by-step explanation:

The speed is distance over time

44 miles / 30 minutes

1.46666 miles / minutes

or if we want in miles per hour

44 miles / .5 hours

88 miles per hour

Answer:

1.467 mile/minute

Step-by-step explanation:

you should divide the distance on the time i.e. 44/30

Answer:

The height of the ball is at it's maximum 1.5 units of time after launch.

Step-by-step explanation:

Suppose we have a quadratic function in the following format:

[tex]h(t) = at^{2} + bt + c[/tex]

If t is negative, the maximu value of h(t) will happen at the point

[tex]t_{MAX} = -\frac{b}{2a}[/tex]

In this question:

[tex]h(t) = -25t^{2} + 75t + 24[/tex]

So

[tex]a = -25, b = 75, c = 24[/tex]

Then

[tex]t_{MAX} = -\frac{b}{2a} = -\frac{75}{2*(-25)} = 1.5[/tex]

The height of the ball is at it's maximum 1.5 units of time after launch.

Answer: Answer choices 1, 3, 4

Step-by-step explanation:

As long as it ends in .0, .2, .4, .6, or .8 it's fine. Therefore the first and last 2 work, since 0.2 can end in either of those 5 values.

Hope that helped,

-sirswagger21

Answer:

B. F(x) = 3(x - 2)² - 2

Step-by-step explanation:

→The function F(x) narrowed, meaning the absolute value being multiplied to the function is greater than 1.

→The function F(x) flipped over the x-axis, this means that the number being multiplied has to be a negative.

→The function F(x) shifted to the left 2 units, this means there needs to be a 2 being added.

→The function F(x) shifted downwards 2 units, meaning there needs to be a 2 being subtracted from the whole function.

This gives us the correct answer of "B. F(x) = 3(x - 2)² - 2."

Answer: The complete question is "A circle has a radius of \blue{3}3start color #6495ed, 3, end color #6495ed. An arc in this circle has a central angle of 20^\circ20 ∘ 20, degrees. What is the length of the arc?"

The length of the arc is 1.06667 units.

Step-by-step explanation:

According to the question the radius of the circle [tex]R=3 \, units[/tex] and central angle of arc is [tex]\Theta =20^{o}[/tex]

As we know that the length of the arc is given as: [tex]L=R\Theta[/tex]

Where R is radius of the circle, L is the length of the arc and  [tex]\Theta[/tex] is central angle in radian.

Now, [tex]\Theta =20^{o}\times \frac{\Pi }{180}=\frac{\Pi }{9} \, rad[/tex]

Therefore, length of the arc is

[tex]L=3\times \frac{\Pi }{9}=\frac{\Pi }{3} =\frac{3.14}{3}=1.0466667 \, units[/tex]