A. 3 B. 23√3 C. 33–√ D. 63–√

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:

- 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

Answer:

see explanation

Step-by-step explanation:

The restriction a ≠ 0 and b ≠ 0 is applied since division by zero would make

[tex]\frac{a}{b}[/tex] and its reciprocal [tex]\frac{b}{a}[/tex] undefined, thus meaningless

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.

Find the probability that a record player will last less than 2 years?

Answer:

the  probability that a record player will last less than 2 years is 0.1586

Step-by-step explanation:

Given that:

A mean which is normally distributed = 3

and a standard deviation = 1

The objective is to find that a record player will last less than 2 years

Let X be the random variable

i.e

[tex]P(X<2) = P( \dfrac{X - \mu}{\sigma}<\dfrac{X - \mu}{\sigma})[/tex]

[tex]P(X<2) = P( \dfrac{2 - \mu}{\sigma}<\dfrac{2 - 3}{1})[/tex]

[tex]P(X<2) = P( Z< \dfrac{-1}{1})[/tex]

[tex]P(X<2) = P( Z< -1)[/tex]

From the standard normal tables :

[tex]P(X<2) = 1- P( Z< 1)[/tex]

[tex]P(X<2) = 1- 0.8414[/tex]

P(X < 2) = 0.1586

Therefore; the  probability that a record player will last less than 2 years is 0.1586

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:

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

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

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:

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

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

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:

70

Step-by-step explanation:

Answer:

The answer is 1.514571894×10^21.

Step-by-step explanation:

Here, the divisors of 288 are,

1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288.

now, their product =1×2×3×4×6×8×9×12×16×18×24×32×36×48×72×96×144×288

=1.514571894×10^21.

is answer.

Hope it helps...

Answer:

Step-by-step explanation:

2 * 3 * 4 * 6 * 8 * 9 * 12 * 16* 18 * 24 * 32 * 36 * 48 * 96 * 144

Some teachers would include 288. I would not.

You can get the actual answer by using the calculator that came with your computer. An ordinary calculator will not work because the answer will come out in scientific notation.

657,366,253,849,018,368 is the answer.

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:

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:

HYPOTHESIS

Step-by-step explanation:

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: If a scatterplot is included in the assignment

The dots plotted on the graph might closely follow the graph of exponential decline. There is a large number of texts per day by 19-20-21 year-olds, but the number seems to decline exponentially as age increases. With a little work, it may be possible to plot the curve and write an equation to model the decline.

Step-by-step explanation:  Look at some graphs of exponential decay. Also consider harmonic and hyperbolic decay. The trend in the data is evident. The main challenge is to look at the data and create an equation that models it.

Answer:

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

Answer:

Devi's present age = 15 years

Devi's Mother's present age = 45 years

Step-by-step explanation:

Let the present age of Devi be x years.

Therefore, mother's present age = 3x

Five years ago:

Devi's age = (x - 5) years

Mother's age =( 3x - 5) years

According to the given condition:

Five years ago:

Devi's mother's age = 4 times Devi's age

3x - 5 = 4( x - 5)

3x - 5 = 4x - 20

20 - 5 = 4x - 3x

15 = x

x = 15 years

3x = 3* 15 = 45 years

Hence,

Devi's present age = 15 years

Devi's Mother's present age = 45 years

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:

The equation, when graphed together with the line y=-3x +6, which will form a system of equations with no solution is y=-3(x +6), meaning the second option on the picture.

Step-by-step explanation:

hope this helps!

Answer: 2 or B

Step-by-step explanation:

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:

[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

Now I’m no genius but I‘m pretty sure the answers are “c” and “d”

Ya’ll have a good day or night, whichever one!

The true statement for the Pentagon in the given graph is

The scale factor of the dilation is 1/2 with the center at the origin(0,0).  

Dilation implies resize of any object.

The scale factor of the dilation of the pentagon is 1/2.

        1. The line EA does not passes through the center of the dilation

            at origin(0,0), which can be clearly seen from the given graph.

       2. For two lines to be parallel it is not necessary for one of the

            lines to pass through the origin.

Hence the scale factor of the given pentagon is 1/2.

To learn more about the Dilation of polygons:

https://brainly.com/question/3020085?referrer=searchResults

#SPJ2

its b the answer is b

Answer:

the answer on the B

Step-by-step explanation:

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:

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:

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

[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°