If 45/60 is equivalent to 3/x, find the value of x

Answer:

m<W: 23

Step-by-step explanation:

8x - 9 + 30x - 4 + 13x - 11 = 180

51x - 24 = 180

51x = 204

x = 4

m<W:

8x - 9

8(4) - 9

32 - 9

23

Answer:

x-axis = [tex]\frac{9\pi }{2}[/tex]

y-axis = [tex]\frac{4\pi }{5} .3(^{\frac{5}{2} } )[/tex]

Line x =3 :  [tex]\frac{44\sqrt{3} }{5} \pi[/tex]

Line x = 6 : [tex]\frac{84\sqrt{3}\pi }{5}[/tex]

Step-by-step explanation:

Given lines : y = √x

                     y = 0

                     x = 3

To determine the volumes generated we will use the disk method for each of the lines,

attached below is the detailed solution for  line x =3 , same procedure will be repeated for each value of x and y to obtain the given results

The volume generated  ( x axis )

= [tex]\frac{9\pi }{2}[/tex]

volume generated ( y _axis )

=  [tex]\frac{4\pi }{5} .3(^{\frac{5}{2} } )[/tex]

Volume about  x = 3

=  [tex]\frac{44\sqrt{3}\pi }{5}[/tex]

Volume about  x = 6

= [tex]\frac{84\sqrt{3}\pi }{5}[/tex]

Answer:

The area of the rectangle is increasing at a rate of 168 square centimeters per second.

Step-by-step explanation:

Geometrically speaking, the area of a rectangle ([tex]A[/tex]), in square centimeters, is described by following expression:

[tex]A = w\cdot l[/tex] (1)

Where:

[tex]w[/tex] - Width, in centimeters.

[tex]h[/tex] - Height, in centimeters.

By Differential Calculus, we find an expression for the rate of change of the area of the rectangle ([tex]\dot A[/tex]), in square centimeters per second:

[tex]\dot A = \dot w\cdot l + w\cdot \dot l[/tex] (2)

Where:

[tex]\dot w[/tex] - Rate of change of the width of the rectangle, in centimeters per second.

[tex]\dot l[/tex] - Rate of change of the length of the rectangle, in centimeters per second.

If we know that [tex]w = 12\,cm[/tex], [tex]l = 15\,cm[/tex], [tex]\dot w = 4\,\frac{cm}{s}[/tex] and [tex]\dot l = 9\,\frac{cm}{s}[/tex], then the rate of change of the area of the rectangle is:

[tex]\dot A = \dot w\cdot l + w\cdot \dot l[/tex]

[tex]\dot A = 168\,\frac{cm^{2}}{s}[/tex]

The area of the rectangle is increasing at a rate of 168 square centimeters per second.

Answer:

∠ BDC = 30°

Step-by-step explanation:

The angle on the circle is half the measure of the central angle subtended by the arc BC

∠ BDC = [tex]\frac{1}{2}[/tex] × 60° = 30°

Answer:38.07

Step-by-step explanation:

If you don't have the apothem value, you will need more information to find the area accurately. The radius alone does not provide enough information to find the area of the regular pentagon.

To find the area of a regular pentagon with a given radius, we need to know the apothem (the distance from the center of the pentagon to the midpoint of one of its sides) in addition to the radius. However, you mentioned only the radius, and it is not sufficient to directly find the area.

If you have the apothem value, you can use the following formula to calculate the area of a regular pentagon:

Area = (5/4) * apothem * side length

To know more about area:

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#SPJ2

Answer:

the answer is c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

I will post 4,5 and 6 separately.

Answer:

17.25

Step-by-step explanation:

8556 / 32 / 15.5 = 17.25

Answer:

[tex] \frac{ |a + x| }{2} - \frac{ |a - x| }{2} \\ \\ = \frac{ | - 2 - 6| }{2} - \frac{ | - 2 + 6| }{2} \\ \\ = \frac{ | - 8| }{2} - \frac{ |4| }{2} \\ \\ = \frac{8}{2} - \frac{4}{2} \\ \\ = 4 - 2 = 2[/tex]

Answer:

The t-distribution is used, as we have the standard deviation of the sample.

The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.

Step-by-step explanation:

We have the standard deviation for the sample, which meas that the t-distribution should be used to solve this question.

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 = 81 - 1 = 80

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 80 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.99

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.99\frac{4}{\sqrt{81}} = 0.88[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 8 - 0.88 = 7.12 hours.

The upper end of the interval is the sample mean added to M. So it is 8 + 0.88 = 8.88 hours.

The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.

Answer:

Step-by-step explanation:

B.28.1

Answer:

It's BBBBBBBBBBBBBBBBB

Step-by-step explanation:

[tex] \sqrt{3} is \: between \: 1.73and1.74[/tex]

Answer:

557.8 square inches

each square is 5". the base is 4x4 squares- so 20 inches square. 20x20= 400sq inches.

the semicircle at the top is 20 inches in diameter, which makes the radius 10 inches.

pi× 10^2= 314.16.

duvide that by 2 to get a semicircle- 157.8

so, the total area is the 400+ 157.8, for a total area of 557.8 square inches

Answer:

8 weeks

Step-by-step explanation:

Given data

Matteo

Amount= $400

Spending per week= $10

Hence his balance after x weeks is given as

y=400-10x-------------1

Luca

Amount= $200

Spending per week= $15

Hence his balance after x weeks is given as

y=200+15x-------------2

Equate 1 and 2

400-10x=200+15x

collect like terms

400-200=15x+10x

200=25x

x= 200/25

x= 8 weeks

Hence it will take 8 weeks

Answer:

117π or 367.56634047

Step-by-step explanation:

Volume = π × r² × h          (r=radius and h=height)

Volume = π × 4² × 13

Volume = π × 9 × 13

Volume = π × 117

Volume = 117π

Answer:

area of one pie : πr² = π d²/4 = π× 2²/4 = π ≈ 3.14

Answer: 20% of 90 = 18

Answer:

90%

Step-by-step explanation:

i hope this helps:)

Answer:

Answer:

x=17

Step-by-step explanation:

4x+8+44+60=180

4x+112=180

4x=180-112

4x=68

x=68/4

x=17

Answer:

Step-by-step explanation:

arc between cars = 360°/25 = 14.4°

θ = 14.4° × π/180 ≅ 0.2512 radian

r = 150/2 = 75 ft

s = rθ = 75×0.2512 = 18.84 ft

area of circle = πr² = 75²π ≅ 17,662.5 ft²

area of sector = 17,662.5/25 = 706.5 ft²

Answer:

35

Step-by-step explanation:

Answer:

First time=7hours

First speed=990km/hour

First distance=first time×first speedD=(

S×T)

D=990km/hr×7hrs

D=6930km.

Second time=6&14min.

Second speed=920km/hr

Second distance=second speed×second time (D=s×t)

D=920km/hr×6&14min.

D=1500

Total distance=6930+1500

=8430

Answer:

No, the table is not linear.

Step-by-step explanation:

Between the x and y there has to be a constant rate. There is no constant rate.

The probability that the Yankees will lose when they score fewer than 5 runs is 0.821 (nearest to the thousandth).

For two events A and B:

The chain rule states that the probability that A and B both occur is given by:

[tex]P(A \cap B) = P(A)P(B|A) = P(B)P( A|B)[/tex]

Lets suppose here that:

Suppose A' and B' are their complementary events, then we have:

Then, by the given data, we have:

[tex]P(A) = 0.56\\P(B) = 0.61\\P(A' \cap B') = 0.32[/tex]

We've to find [tex]P(A' | B')[/tex]

Using chain rule, we have:

[tex]P(A'|B') = \dfrac{P(A' \cap B')}{P(B')}[/tex]

Since P(B') = 1-P(B) = 100.61 = 0.39, therefore, we get:

[tex]P(A'|B') = \dfrac{P(A' \cap B')}{P(B')} = \dfrac{0.32}{0.39} \\\\P(A'|B') \approx 0.821[/tex]

Thus, the probability that the Yankees will lose when they score fewer than 5 runs is 0.821

Learn more about probability here:

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Answer:

12.5

Step-by-step explanation:

u put the decimal at the end of 25 then u times it by 50 and there u get ur answer

hope this helps :D

Answer:

a) The standard score associated with a gestation period of 13.8 months is of [tex]Z = -1[/tex]

b) 34% of whale pregnancies will have a gestation period between 13.8 and 15 months.

c) Since when [tex]X = 21[/tex], [tex]Z = 5 \geq 2[/tex], it would be unusual for a whale to have a gestation period of 21 months.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If [tex]Z \geq 2[/tex] or [tex]Z \leq -2[/tex], the measure X is considered to be unusual.

According to a website, the mean gestation period for a whale is 15 months. Assume the distribution of gestation periods is Normal with a standard deviation of 1.2 months.

I corrected to 1.2 because it is what makes sense considering the questions.

This means that [tex]\mu = 15, \sigma = 1.2[/tex]

a. Find the standard score associated with a gestation period of 13.8 months

This is Z when X = 13.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{13.8 - 15}{1.2}[/tex]

[tex]Z = -1[/tex]

The standard score associated with a gestation period of 13.8 months is of [tex]Z = -1[/tex]

b. Using the Empirical Rule and your answer to part a, what percentage of whale pregnancies will have a gestation period between 13.8 and 15 months?

The standard score associated with a gestation period of 13.8 months is of [tex]Z = -1[/tex], which means that it is one standard deviation below the mean.

The normal distribution is symmetric, which means that of the approximately 68% of measures within one standard deviation of the mean, 68%/2 = 34% are within one standard deviation below the mean(in this case, 13.8) and the mean(in this case 15), and 34% are within the mean and one standard deviation above the mean.

So 34% of whale pregnancies will have a gestation period between 13.8 and 15 months.

c. Would it be unusual for a whale to have a gestation period of 21 months? Why or why not?

Let's find the z-score

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{21 - 15}{1.2}[/tex]

[tex]Z = 5[/tex]

Since when [tex]X = 21[/tex], [tex]Z = 5 \geq 2[/tex], it would be unusual for a whale to have a gestation period of 21 months.

Answer:

Here's what we know:

n + d = 20 (there are a total of 20 nickels and dimes)

.05n + .1d = 1.4 (total change equals $1.40)

There are a couple of ways to solve this. You can go the elimination method by multiplying the second equation by an amount to get rid of a variable, or we can go substitution by isolating a variable in the first equation. I'll go with elimination in this case:

-10(.05n + .1d = 1.4) this will cause the d-variable to equal 0:

n  +  d = 20

-.5n - d = -14

------------------

.5n = 6

n = 12

Now that we know n, we can solve for d:

12 + d = 20

d = 8

Check:

.05 * 12 + .1 + 8 = 1.4

.6 + .8 = 1.4

1.4 = 1.4

Step-by-step explanation: