Similar Triangles

Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms.

a. 4/15 = 5/12 = 4/15
b. 4/5 = 12/15 = 4/5
c. 4/12 = 5/15 = 1/3
d. 5/4 = 15/12 = 5/4

Please select the best answer from the choices provided

Answer: B

Step-by-step explanation: An Isosceles triangle has two equal sides. A equallateral triangle has all the sides equal

Answer:

X 30

Step-by-step explanation:

I did the math and all you had to do was times all the nymbers!

Answer:

a) 0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

b) 0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes

c) 0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 8.9 minutes and a standard deviation of 2.9 minutes.

This means that [tex]\mu = 8.9, \sigma = 2.9[/tex]

Sample of 37:

This means that [tex]n = 37, s = \frac{2.9}{\sqrt{37}}[/tex]

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?

320/37 = 8.64865

Sample mean below 8.64865, which is the p-value of Z when X = 8.64865. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{8.64865 - 8.9}{\frac{2.9}{\sqrt{37}}}[/tex]

[tex]Z = -0.53[/tex]

[tex]Z = -0.53[/tex] has a p-value of 0.2981

0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?

275/37 = 7.4324

Sample mean above 7.4324, which is 1 subtracted by the p-value of Z when X = 7.4324. So

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

[tex]Z = \frac{7.4324 - 8.9}{\frac{2.9}{\sqrt{37}}}[/tex]

[tex]Z = -3.08[/tex]

[tex]Z = -3.08[/tex] has a p-value of 0.001

1 - 0.001 = 0.999

0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.

(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?

Sample mean between 7.4324 minutes and 8.64865 minutes, which is the p-value of Z when X = 8.64865 subtracted by the p-value of Z when X = 7.4324. So

0.2981 - 0.0010 = 0.2971

0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

Answer:

339.4cm³

Step-by-step explanation:

V

=

π

r

2

h

3

22/7×6²×9/3= 339.42

Answer:

60

Step-by-step explanation:

5 * 12 = 60

Answer:

a) This is the p-value of Z when X = A subtracted by the p-value of Z when X = B.

b) P-value of Z when X = 76 subtracted by the p-value of X = 68.

c) Because the underlying distribution(pulse rates of females) is normal.

Step-by-step explanation:

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex].

standard deviation of beats per minute.

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between A beats per minute and B beats per minute.

This is the p-value of Z when X = A subtracted by the p-value of Z when X = B.

b. If 4 adult females are selected, find the probability that they have pulse rates with a mean between 68 beats per minute and 76 beats per minute.

Sample of 4 means that we have [tex]n = 4, s = \frac{\sigma}{\sqrt{4}} = 0.5\sigma[/tex]

The formula for the z-score is:

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

[tex]Z = \frac{X - \mu}{0.5\sigma}[/tex]

[tex]Z = 2\frac{X - \mu}{\sigma}[/tex]

This probability is the p-value of Z when X = 76 subtracted by the p-value of X = 68.

c. Why can the normal distribution be used in heartbeat even the sample side does not exceed 30?

Because the underlying distribution(pulse rates of females) is normal.

Answer:

Step-by-step explanation:

1 m =0.001 km

15m=15*0.001

=0.015 km

Answer:

Complementary Angles - 3rd one (at the bottom)

Supplementary Angles - 2nd one (at the top-right)

Vertical Angles - 1st one (at the top-left)

Feel free to mark it as brainliest :D

Answer:

60 cm³

Step-by-step explanation:

Applying,

Volume (V) = Area of the base(A)×Height(h)

V = Ah................ Equation 1

From the diagram,

A =  Area of Trapezium

A = 1/2(a+b)c............. Equation 2

Substitute equation 2 into equation 1

V = [1/2(a+b)c]h........... Equation 3

Given: a = 3 cm, b = 7 cm, c = 3 cm, h = 4 cm

Substitute these values into equation 3

V = [3(3+7)/2]4

V = (3×10/2)4

V = (3×5)4

V = 15×4

V = 60 cm³

Answer:

4*(7-2)2÷10

=4*5*1/5

=20/5

=4

Step-by-step explanation:

Answer:

0.1357 = 13.57% of bolts will have a diameter greater than 1.211 inches

Step-by-step explanation:

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 1.20 inches and a standard deviation of 0.01 inches.

This means that [tex]\mu = 1.20, \sigma = 0.01[/tex]

What proportion of bolts will have a diameter greater than 1.211 inches?

This is 1 subtracted by the p-value of Z when X = 1.211. So

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

[tex]Z = \frac{1.211 - 1.20}{0.01}[/tex]

[tex]Z = 1.1[/tex]

[tex]Z = 1.1[/tex] has a p-value of 0.8643.

1 - 0.8643 = 0.1357

0.1357 = 13.57% of bolts will have a diameter greater than 1.211 inches

Answer:

The arm routine lasts 10 minutes, and the abs routine lasts 15 minutes.

Step-by-step explanation:

Since Oscar is trying to incorporate more exercise into his busy schedule, and he has several short exercise routines he can complete at home, and last week, he worked out for a total of 35 minutes by doing 2 arm routines and 1 abdominal routine while That this week, he has completed 4 arm routines and 1 abdominal routine and spent a total of 55 minutes exercising, to determine how long does each routine last the following calculation must be performed:

2ARM + 1ABS = 35

4ARM + 1ABS = 55

4ARM + 1ABS - 2ARM - 1ABS = 55 - 35

2ARM = 20

ARM = 20/2

ARM = 10

2 x 10 + ABS = 35

ABS = 15

Therefore, the arm routine lasts 10 minutes, and the abs routine lasts 15 minutes.

x^2 + 21^2 = 29^2

x^2 + 441 = 841

x^2 = 841 - 441

x^2 = 400

x = √400

x = 20

Answer:

C) 86

Step-by-step explanation:

To find the mean you first add all of the numbers together. So you would add 75+90+84+95=344. Then you would divide the sum by the amount if numbers there are. So it would be 344÷4 =86

Hope this helped :)

Answer:

x = 75, 90 , 84, 95

[tex]Mean = \frac{ \sum x}{n}= \frac{75+90+84+95}{4} = 86[/tex]

Answer:

A. 8.737

Step-by-step explanation:

I calculated it logically

Answer:22

Step-by-step explanation:

The complete sentence is

The price with coupon B is $10 less than the price with coupon A.

It depends on the original price of the S41 shoes.

Coupon A offers a 15% discount on S41 shoes, while Coupon B provides a $10 rebate on S41 shoes.

Let's assume the original price of the S41 shoes is P dollars.

Using Coupon A, the discounted price would be 85% of the original price = (0.85 * P) dollars.

Using Coupon B, the price after the $10 rebate =  (P - $10) dollars.

Now, compare (0.85 * P) with (P - $10).

simplify the expression (0.85 * P) < (P - $10) as

0.85P < P - $10

0.85P - P < - $10

-0.15P < - $10

P > (- $10) / (-0.15)  

P > $66.67

Therefore, if the original price of the S41 shoes is greater than $66.67, Coupon A (15% off) will give a lower price. If the original price is lower than $66.67, Coupon B ($10 rebate) will give a lower price.

Learn more about Inequality here:

https://brainly.com/question/20383699

#SPJ4

Answer:

[tex]I = \frac{1}{6}\cdot \sin^{2} 3x + C[/tex]

Where [tex]C[/tex] is the integration constant.

Step-by-step explanation:

We use integration by substitution to obtain the integral, where:

[tex]u = \sin 3x[/tex], [tex]du = 3\cdot \cos 3x\,dx[/tex]

[tex]I = \int {\sin 3x\cdot \cos 3x} \, dx[/tex]

[tex]I = \frac{1}{3} \int {u} \, du[/tex]

[tex]I = \frac{1}{6}\cdot u^{2} + C[/tex]

[tex]I = \frac{1}{6}\cdot \sin^{2} 3x + C[/tex]

Where [tex]C[/tex] is the integration constant.

Answer:

(D)

Step-by-step explanation:

The slope of the given line is (2/3) which means that a line perpendicular to it must have a slope of (-3/2).

Answer:

Step-by-step explanation:

area of circle=π*r^2

=3.14*2.5^2

=3.14*6.25

=19.625

=19.63

Answer:

9ft

Step-by-step explanation:

Use the pythagorean theorem.

15^2 = 12^2 + x^2

solve for x

x^2 = 81

x = 9

Answer:

C

Step-by-step explanation:

The answer is c because the point where they meet is -6 so it has to be all real number greater than.

==========================================================

Explanation:

a = 8, b = 13, and c = 15 are the sides of the triangle

s = (a+b+c)/2 = (8+13+15)/2 = 18 is the semi-perimeter, aka half the perimeter.

Those values are then plugged into Heron's Formula below

[tex]A = \sqrt{s*(s-a)*(s-b)*(s-c)}\\\\A = \sqrt{18*(18-8)*(18-13)*(18-15)}\\\\A = \sqrt{18*(10)*(5)*(3)}\\\\A = \sqrt{2700}\\\\A = \sqrt{900*3}\\\\A = \sqrt{900}*\sqrt{3}\\\\A = 30\sqrt{3}\\\\A \approx 51.9615\\\\A \approx 52\\\\[/tex]

The triangular plaque has an area of approximately 52 square inches.

Answer:

1/5

Step-by-step explanation:

Answer:

as given 20%,

so 20% into fraction

20

100

=>1

5 is the answer

Answer:

the x coordinate is negative and y coordinate is positive

Step-by-step explanation:

Answer:

oh god I wanna feel dead oh god i wanna feel dead

Answer:

20 lawyers

Step-by-step explanation:

48 ÷ 12 = 4

which means every year 4 lawyers are hired

5 × 4 = 20

so this means the law firm has hired 20 lawyers in the last 5 years

9514 1404 393

Answer:

  32%

Step-by-step explanation:

The man invested a total of ...

  3600 +150 = 3750

in the house. He sold it for a profit of ...

  4950 -3750 = 1200

The percentage profit on his investment is ...

  (1200/3750) × 100% = 32%

Answer:

A = 254.34 in² and circumference = 56.52 inch

Step-by-step explanation:

The attached figure shows a pizza having diameter of 18 inches

Radius of the pizza = 9 inches

The area of the pizza is given by :

[tex]A=\pi r^2\\\\=3.14\times 9^2\\\\=254.34\ in^2[/tex]

The circumference of the pizza is given by :

[tex]A=2\pi r\\\\=2\times 3.14\times 9\\\\=56.52\ inch[/tex]

Hence, this is the required solution.

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A graphing calculator is useful for this.

The region of interest is below the parabola and above the line.

Answer:

Step-by-step explanation:

x+2x+27=90

3x=90-27

3x=63

x=63/3

x=21

Answer:

x = 21

Step-by-step explanation:

Since ∠ PQR = 90° , then the sum of the 3 angles = 90° , that is

x + 2x + 27 = 90

3x + 27 = 90 ( subtract 27 from both sides )

3x = 63 ( divide both sides by 3 )

x = 21