The life of a Radio Shack record player is normally distributed with a mean of 3 years and a standard deviation of 1 years. Radio Shack guarantees its record players for 2 years.

Answer:

The 90% confidence interval

(74.71, 82.63)

Step-by-step explanation:

Confidence Interval Formula is given as:

Confidence Interval = μ ± z (σ/√n)

Where

μ = mean score

z = z score

N = number of the population

σ = standard deviation

The mean is calculated as = The average of their scores

N = 6 students

(71.6 + 81.0 + 88.9 + 80.4 + 78.1 + 72.0 )/ 6

Mean score = 472/6

= 78.666666667

≈ 78.67

We are given a confidence interval of 90% therefore the

z score = 1.645

Standard Deviation for the scores =

s=(x -σ)²/ n - 1 =(71.6 - 78.67)²+(81.0 - 78.67)²+(88.9 - 78.67)² + (80.4 - 78.67)²+ (78.1 - 78.67)²+( 72.0 - 78.67)2/ 6 - 1

= 5.886047531

= 5.89

The confidence interval is calculated as

= μ ± z (σ/√N)

= 78.67 ± 1.645(5.89/√6)

= 78.67 ± 3.9555380987

The 90% confidence interval

is :

78.67 + 3.9555380987 = 82.625538099

78.67 - 3.9555380987 = 74.714619013

Therefore, the confidence interval is approximately between

(74.71, 82.63)

Answer:

G(x) = (1 - x)/4

is the inverse function required.

Step-by-step explanation:

Given F(x) = -4x + 1

Let y = F(x)

Then y = -4x + 1

=> y - 1 = -4x

4x = 1 - y

x = (1 - y)/4

That is, the inverse is (1 - x)/4

Therefore, G(x) has to be (1 - x)/4

Answer:

70

Step-by-step explanation:

Answer:

the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%  is 0.0042

Step-by-step explanation:

Given that :

A film distribution manager calculates that 9% of the films released are flops

Let p be the probability for the movies that were released are flops;

[tex]\mu_p = P = 0.9[/tex]

If the manager is right, what is the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%

now; we know that our sample size = 442

the standard deviation of the variance  is [tex]\sigma_p= \sqrt{\dfrac{p(1-p)}{n}}[/tex]

[tex]\sigma_p= \sqrt{\dfrac{0.9(1-0.9)}{442}}[/tex]

[tex]\sigma_p= \sqrt{\dfrac{0.9(0.1)}{442}}[/tex]

[tex]\sigma_p= \sqrt{\dfrac{0.09}{442}}[/tex]

[tex]\sigma_p= \sqrt{2.0361991 \times 10^{-4}}[/tex]

[tex]\sigma _p = 0.014[/tex]

So; if the manager is right; the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% can be calculated as:

[tex]P(|p-P|>0.04)=1 -P(p-P|<0.04)[/tex]

[tex]P(|p-P|>0.04)=1 -P(-0.04 \leq p-P \leq 0.04)[/tex]

[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{\sigma_p} \leq \dfrac{ p-P}{\sigma_p} \leq \dfrac{0.04}{\sigma_p})[/tex]

[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{0.014} \leq Z\leq \dfrac{0.04}{0.014})[/tex]

[tex]P(|p-P|>0.04)=1 -P( -2.8571 \leq Z\leq 2.8571)[/tex]

[tex]P(|p-P|>0.04)=1 -[P(Z \leq 2.8571) -P (Z\leq -2.8571)[/tex]

[tex]P(|p-P|>0.04)=1 -(0.9979 -0.0021)[/tex]

[tex]P(|p-P|>0.04)=1 -0.9958[/tex]

[tex]\mathbf{P(|p-P|>0.04)=0.0042}[/tex]

∴

the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%  is 0.0042

Answer:

1.35 degrees per mg.

Step-by-step explanation:

The patient's temperature went from 105.85 to 99.1. That is a decrease of 6.75 degrees. You want to find the temperature decrease per milligram, which can be found by dividing the temperature by the number of mg of the drug.

6.75 / 5 = 675 / 500 = 1.35

So, the rate at which her temperature decreased per milligram is 1.35 degrees per mg.

Hope this helps!

Answer:

1/16.4616

Step-by-step explanation:

(1.9^2*2.4^-3) (1.9^3*2.4^-2)^-3

(1.9^2*2.4^-3) * 1 / (1.9^3*2.4^-2)^3

1.9^2*2.4^-3 / (1.9^3*2.4^-2)^3

1.9^2 * 1 / 2.4^3 ÷ (1.9^3* 1 / 2.4^2)3

1.9^2 / 2.4^3 × (2.4^2/1.9^3)^3

(1/2.4) (1/1.9)^3

(1/2.4) (1/6.859)

1/16.4616

Answer: C) Plane: 235 km/h, Wind: 24 km/h

Step-by-step explanation:

Given that :

Average Speed while flying with a tailwind = 259km/hr

Return trip = 211km/hr

Let the speed of airplane = a, and wind speed = w

Therefore ;

Average Speed while flying with a tailwind = 259km/hr

a + w = 259 - - - (1)

Return trip = 211km/hr

a - w = 211 - - - (2)

From (2)

a = 211 + w

Substitute the value of a into (1)

a + w = 259

211 + w + w = 259

211 + 2w = 259

2w = 259 - 211

2w = 48

w = 48/2

w = 24km = windspeed

Substituting w = 24 into (2)

a - 24 = 211

a = 211 + 24

a = 235km = speed of airplane

Answer:

He reached the top of the tree on the 31st day

Step-by-step explanation:

The total distance for the owl to climb is 93 units.

If the owl climbed 18 units up the tree every day without coming down, the owl would have taken 93/18 days to reach the top of the tree.

However, the owl descends by 15 units every night. This just reduces the overall distance covered at the end of each day's climb.

The net distance covered by the owl after each day is 18-15 units = 3 units of climb. This is the steady distance the owl gains up the three at the end of each day after the ascent and descent.

The time taken for the climb moving at this pace of 3 units per day will be

93 units / 3 units per day = 31 days

Answer:

6πx³ + 2πx²

Step-by-step explanation:

The formula for the volume of a cylinder is πr² · h.

1. Plugin the values into the formula

π2x² · (3x + 1)

2. Distribute 2πx² to (3x + 1)

6πx³ + 2πx²

Compute the integral with respect to x, then with respect to y:

[tex]\displaystyle16\int_0^\pi\int_0^1x^2\sin y\,\mathrm dx\,\mathrm dy=16\int_0^\pi\sin y\frac{x^3}3\bigg|_0^1\,\mathrm dy[/tex]

[tex]=\displaystyle\frac{16}3\int_0^\pi\sin y\,\mathrm dy[/tex]

[tex]=\displaystyle\frac{16}3(-\cos y)\bigg|_0^\pi=\boxed{\dfrac{32}3}[/tex]

Alternatively, in this case you can "factorize" the integral as

[tex]\displaystyle16\left(\int_0^\pi\sin y\,\mathrm dy\right)\left(\int_0^1x^2\,\mathrm dx\right)[/tex]

and get the same result.

Answer:

median

Step-by-step explanation:

(median is used to measure the middle)

you just line up all the numbers from least to greatest, then pick the middle number, IF there are NO numbers in the middle, you add the the 2 middle numbers up, then divided by 2

Answer:

Median, because there is 1 outlier that affects the center

Step-by-step explanation:

"The median is the middle number of the data set. It is exactly like it sounds. To figure out the median you put all the numbers in order (highest to lowest or lowest to highest) and then pick the middle number. If there is an odd number of data points, then you will have just one middle number."

Answer:

30.045

Step-by-step explanation:

the length of rectangle=140 which is also the diameter of circle

R=d/2=140/2=70 ( which is the width of rectangle)

perimeter of rectangle=2l+2w=140+280=420

perimeter of semicircle=πr+d=70π+140=359.911

the difference between two perimeter

(perimeter of rectangle- perimeter of semi circle) =

420-359.911=60.089

since only one shaded area :

60.089/2=30.0445 close to 30.045

Answer:

- 204

Step-by-step explanation:

2x = 60

x = 30

6 - 7(30) = -204

Answer:

-204

Step-by-step explanation:

Step 1- Solve for the value of x

2x = 60

Divide 60 by 2 so x is by its self

x = 30

Step 2- Plug in 30 for x in the second equation

6 - 7(30)

6 - 210

-204 is the answer

Your question has been heard loud and clear.

Answer is option d or the fourth option.

thank you

Answer:

[tex] g(x) =\sqrt{x-4}[/tex]

[tex] h(x) =2x-8[/tex]

And we want to find:

[tex] g o h(x)[/tex]

Replacing we got:

[tex] go h(x)= \sqrt{2x-8 -4}= \sqrt{2x-12}[/tex]

And the restriction for this case would be:

[tex] 2x-12 \geq 0[/tex]

[tex] 2x \geq 12[/tex]

[tex] x \geq 6[/tex]

Step-by-step explanation:

Assumign that we have the following two functions:

[tex] g(x) =\sqrt{x-4}[/tex]

[tex] h(x) =2x-8[/tex]

And we want to find:

[tex] g o h(x)[/tex]

Replacing we got:

[tex] go h(x)= \sqrt{2x-8 -4}= \sqrt{2x-12}[/tex]

And the restriction for this case would be:

[tex] 2x-12 \geq 0[/tex]

[tex] 2x \geq 12[/tex]

[tex] x \geq 6[/tex]

Answer:

104 are your answer and decimal intergers 31 mm are not don't this answer

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Inverse Trigonometry Function.

So here, we get as

SinX = 1/2

X = Sin^-1(1/2)

X= 30°

Answer:

second one

Step-by-step explanation:

The function g has this expression g(x) = ax²+c

To find when g reaches it's minimum we must derivate it

solve g'(x) = 0

replace x with 0 in g(x)

g(0) = a(0)²+c

g(0) = c

the maximum of f(x) is 1 so for g(x) to have a grather minimum c should be greather than 1

the second statement is true

its b the answer is b

Answer:

the answer on the B

Step-by-step explanation:

Answer:

n × 0.77

Step-by-step explanation:

Decreasing a number by 23% is the same as multiplying that number by 0.77, so n number of animals decreased by 23% is:

n × 0.77

Answer:

The tree was 40 inches tall when planted

The tree's growth rate is 10 inches per year

Ten years after planting, is 140 inches tall

Step-by-step explanation:

From the graph attached, the height of the tree is plotted on the y axis and the year is on the x axis. The line passes through (2, 60) and (5, 90). The equation of a line passing through two point is given as:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

Therefore the equation of the line passing through (2, 60) and (5, 90) is:

[tex]y-60=\frac{90-60}{5-2}(x-2) \\y-60=\frac{30}{3} (x-2)\\y-60=10(x-2)\\y-60=10x-20\\y=10x-20+60\\y=10x+40[/tex]

The equation of a line in standard form is y = mx + c where c is the intercept on y axis and m is the slope. Since y = 10x + 40, m = 10 and c = 40.

The y intercept is 40 inches, this means the height of the tree at 0 years was 40 inches tall when planted, therefore The tree was 40 inches tall when planted is correct.

The slope of the line is 10, this means the tree grow at a rate of 10 inches per year. Therefore The tree's growth rate is 10 inches per year is correct.

The tree was 2 years old when planted is not correct

The slope of a linear function is constant, therefore the growth rate is constant. As it ages, the trees growth rate slows  is not correct

The height of the tree at 10 years can be gotten by substituting x = 10 in y = 10x + 40. y = 10(10) + 40 = 100 + 40 = 140 inches. Therefore Ten years after planting, it is 140 inches tall. is correct

Answer:

[tex]b = 74\ cm[/tex]

Step-by-step explanation:

The volume of a prism is given by the following equation:

[tex]Volume = base\ area * height[/tex]

In our case, the base is a triangle, so the area is given by:

[tex]base\ area = base * height_{\Delta}/2[/tex]

The base of the triangle is 43 cm, the height of the triangle is b, the height of the prism is 24 and the volume of the prism is 38,184, so we have:

[tex]base\ area = 43 * b/2 = 21.5b[/tex]

[tex]38184 = 21.5b * 24[/tex]

[tex]b = 38184/(24*21.5)[/tex]

[tex]b = 74\ cm[/tex]

The question was not written properly above.

Complete Question :

Lea's car travels an average of 30 miles per gallon of gas. If she spent $20.70 on gas for 172.5 mile trip, what was the approximate cost of gas in dollars per gallon?

Answer:

$3.6

Step-by-step explanation:

From the above question, we have the following information:

For

30 miles = 1 gallon of gas

We are also told she travelled,

$20.70 on gas for 172.5 miles

Step 1

Find how many gallons of gas was issued in the 172.5 miles

30 miles = 1 gallon of gas

172.5 miles = y

Cross multiply

30 × y = 172.5 miles × 1

y = 172.5 miles/30

y = 5.75 gallons

Therefore, for 172.5 miles she used 5.75 gallons of gas

Step 2

For step 2 we find the approximate cost of gas in dollars per gallon

$20.70 = 172.5 miles = 5.75 gallons of gas

Hence,

5.75 gallons of gas = $20.70

1 gallon of gas = $X

Cross Multiply

5.75 gallons × $X = $20.70 × 1 gallon

$X = $20.70 × 1 gallon/ 5.75 gallons

$X = $3.6

X = $3.6

Therefore, the approximate cost of gas in dollars per gallon = $3.6

Explanation:

The outer term 2p is distributed among the three terms inside the parenthesis. We will multiply 2p by each term inside

2p times 4p^2 = 2*4*p*p^2 = 8p^3

2p times 5p = 2*5*p*p = 10p^2

2p times 7 = 2*7p = 14p

The results 8p^3, 10p^2 and 14p are added up to get the final answer shown above. We do not have any like terms to combine, so we leave it as is.

Answer:

Add the equations to eliminate x.  

Step-by-step explanation:

(1)  y = 10 + x

(2) y =   3 - x

An easy way to solve this problem is to add the two equations to eliminate x.

(3) 2y = 13

From here, you can calculate y and then x.

Answer: (1) 2p: 5q.

(2) 3:10.

(3) 5:6.

Step-by-step explanation:

To find : Ratio

(1) 4p²q : 10pq²

[tex]=\dfrac{4p^2q}{10pq^2}\\\\=\dfrac{2p^{2-1}}{5q^{2-1}}\\\\=\dfrac{2p}{5q}[/tex]

i.e. Simplified ratio of 4p²q : 10pq²  is 2p: 5q.

(2) 9 months : 2½ years

1 year = 12 months

[tex]2\dfrac{1}{2}\text{years}=\dfrac{5}{2}\text{years}\\\\=\dfrac{5}{2}\times12=30\text{ months}[/tex]

Now, 9 months : 2½ years = [tex]\dfrac{9\text{ months}}{30\text{ months}}=\dfrac{3}{10}[/tex]

Hence, Simplified ratio of 9 months : 2½ years is 3:10.

(3) 5 m : 600 cm

1 m = 100 cm

So, 5m = 500 cm

Now, 5 m : 600 cm = [tex]\dfrac{500\ cm}{600\ cm}=\dfrac{5}{6}[/tex]

Hence, Simplified ratio of  5 m : 600 cm  is 5:6.

Answer:

12.5% failed

Step-by-step explanation:

Convert the fraction 10 out of 80 into a decimal to become the percentage

Answer: 87.5% failed driving test is 12.5%

Step-by-step explanation:

Answer:

B) 5 + 3√5 units

Step-by-step explanation:

The length of ZX is 2√5 units. What is the perimeter of triangle XYZ?  

A) 5 +√3 + 2 √5 units  

B) 5 + 3√5 units  

C) 5 + √6 + 2√5 units  

D) 10 + 2√5 units

From the diagram attached, point X is at (-1, 4), Y(3, 1), Z(1, 0).

The distance between two point

[tex]O(x_1,y_1)\ and\ A(x_2,y_2)\ is\ given\ as:\\\\OA=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

The lengths of the sides of the triangle are:

[tex]|XY| = \sqrt{(3-(-1))^2+(1-4)^2}=\sqrt{25} =5\ unit\\ \\|XZ|= \sqrt{(1-(-1))^2+(0-4)^2}=\sqrt{20} =2\sqrt{5} \ unit\\\\|YZ|= \sqrt{(1-3)^2+(0-1)^2}=\sqrt{5} \ unit[/tex]

The perimeter of the triangle is the sum of all the sides, i.e.

Perimeter = |XY| + |YZ| + |XZ| = 5 + 2√5 + √5 = 5 + 3√5  

Answer:

B

Step-by-step explanation:

Answer:

we reject  H₀

Step-by-step explanation:  Se annex

The test is one tail-test (greater than)

Using   α = 0,05   (critical value )  from z- table we get

z(c) = 1,64

And Test hypothesis is:

H₀         Null hypothesis           μ   =  μ₀

Hₐ       Alternate hypothesis   μ   >  μ₀

Which we need to compare with z(s) = 2,19  (from problem statement)

The annex shows z(c), z(s), rejection and acceptance regions, and as we can see z(s) > z(c) and it is in the rejection region

So base on our drawing we will reject  H₀

Answer:

[tex]\Large \boxed{\sf\ \ (0,-9) \ \ }[/tex]

Step-by-step explanation:

Hello,

We know that when the parabola equation is

   [tex]y=a(x-h)^2+k[/tex]

the vertex is (h,k) and the focus is

   [tex](h,k+\dfrac{1}{4a})[/tex]

Here, the equation is

   [tex]y=-\dfrac{1}{12}x^2-6[/tex]

so

   [tex]a=-\dfrac{1}{12}\\\\h = 0\\\\k =-6[/tex]

So,

[tex]k+\dfrac{1}{4a}=-6-\dfrac{12}{4}=-6-3=-9[/tex]

Then, the focus is

[tex]\large \boxed{\sf\ \ (0,-9) \ \ }[/tex]

I attached the graph, included the focus so that you can see it :-)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you