The sum of three numbers is 30. The third number is twice the second, and is also 2 less than 3 times the first. What are the three numbers?

Answer:

191.0

Step-by-step explanation:

Answer:

[tex]\displaystyle \sin(2\theta)=\frac{2\sqrt{418}}{49}\approx0.8345[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \cos(\theta)=\frac{\sqrt{11}}{7}[/tex]

Where θ is in QI.

And we want to determine sin(2θ).

First, note that since θ is in QI, all trig ratios will be positive.

Next, recall that cosine is the ratio of the adjacent side to the hypotenuse. Therefore, the adjacent side a = √(11) and the hypotenuse c = 7.

Then by the Pythagorean Theorem, the opposite side to θ is:

[tex]b=\sqrt{(7)^2-(\sqrt{11})^2}=\sqrt{49-11}=\sqrt{38}[/tex]

So, with respect to θ, the adjacent side is √(11), the opposite side is √(38), and the hypotenuse is 7.

We can rewrite as expression as:

[tex]\sin(2\theta)=2\sin(\theta)\cos(\theta)[/tex]

Using the above information, substitute. Remember that all ratios will be positive:

[tex]\displaystyle =2\Big(\frac{\sqrt{38}}{7}\Big)\Big(\frac{\sqrt{11}}{7}\Big)[/tex]

Simplify. Therefore:

[tex]\displaystyle \sin(2\theta)=\frac{2\sqrt{418}}{49}\approx0.8345[/tex]

Answer:

(6,0) and (0,-8)

Step-by-step explanation:

Substitute a zero for each variable

So 4(0) - 3y = 24 to find the y-int so -3y = 24, y = -8, so y-int is (0,-8)

to find x-int y = 0 so 4x - 3(0) =24   so 4x = 24, so x = 6 so x-int is (6,0)

Answer:

Radius= 5.4

Step-by-step explanation:

Formula for Sphere- V= 4/3(pi)• r^3

r=(3 V/4 pi) = (3•660/4•pi)= 5.40114 (5.4)

Answer:

x = 1

y = 9

Step-by-step explanation:

The diagonals of the parallelogram bisect each other. Therefore:

✔️2x + 13 = 15

2x + 13 - 13 = 15 - 13

2x = 2

2x/2 = 2/2

x = 1

✔️5y - 36 = y

5y - 36 - 5y = y - 5y

-36 = -4y

-36/-4 = -4y/-4

9 = y

y = 9

Answer:

c

Step-by-step explanation:

Answer:

a) .389

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

Counting from the top:

fist option

fourth option

fifth option.

Step-by-step explanation:

Any set that has a multiplicative outcome, such that the total number of outcomes is 24.

Remember that if we have a combination of two events, one with N outcomes and the other with M outcomes, the total number of outcomes is:

M*N

This is the main thing we need to see.

Let's analyze each option:

1) flip a coin (2 outcomes)

  flip a coin again (2 outcomes)

  roll a 6 sided dice ( 6 outcomes)

total number of outcomes:

2*2*6 = 24

2) Selecting a number from 1 to 16 (16 outcomes) and rolling a dice of 8 sides (8 outcomes).

The total number of outcomes is:

8*16 = 128

We wanted only 24.

3) Selecting a number from the set {1, 3, 5, 7, 9} (5 outcomes)

   flip a coin (2 outcomes)

   flip the coin again (2 outcomes)

total number of outcomes:

2*2*5 = 20

We wanted 24, we can discard this.

4) Spin the thing (3 outcomes)

   roll an 8-sided dice (8 outcomes)

Total number of outcomes:

8*3 = 24

This is a correct option.

5) Select a card from A to D (4 outcomes)

Roll the thing (6 outcomes)

total number of outcomes:

6*4 = 24

This is a correct option.

6) Select a card from A to N {14 options}

   Roll the thing once (10 outcomes)

Total number of outcomes:

14*10 = 140

We wanted 24, so we can discard this option.

Then the correct options are:

first one, fourth one, and fifth one.

21 pieces of ribbon

Step-by-step explanation:

6.3/0.3= 21

Step-by-step explanation:

cosθ = 15/17 and sinθ = -8/17

So, tanθ = sinθ / cosθ = -8/15 and cscθ = 1 / sinθ = -17/8

Answer:

7 inches

Step-by-step explanation:

Now the area of a rectangle equals to length by width or in this scenario, height by base.

Therefore, we take a look at what we already have.

We got 5 inches for height and 35 squared inches as the area.

h= 5 inches a=35squared inches b=?

*Therefore, 5 x b =35

Through substitution this becomes:

*35/5= b

*Therefore b=7 inches

Answer:

The minimum weight resistance possible for a 240-pound man is 19.2 pounds.

Step-by-step explanation:

Since the U Gym provides weight resistance through adjustments of incline, and the minimum weight resistance is 8% of the weight of the person using the U Gym, to find the minimum weight resistance possible for a 240-pound man the following calculation:

240 x 8/100 = X

1,920 / 100 = X

19.2 = X

Thus, the minimum weight resistance possible for a 240-pound man is 19.2 pounds.

Step-by-step explanation:

hmmmmmmmmm

Bots are not welcome here!

Answer:

See explanation

Step-by-step explanation:

Recall that

Amount = Principal + Interest

The formula is;

A = P(1 + r)^n

Where;

P= principal, n = time and r = rate

Hence;

P + I =  P(1 + r)^n

P + 193.03 = P(1.021)^2

P + 193.03 = 1.04P

P - 1.04P = -  193.03

-0.04 P =  -  193.03

P = 193.03/0.04

P = $ 4825.75

B) When A = $6000, n=?

From;

A=   P(1 + r)^n

6000 = 4825.75 (1.021)^n

6000/4825.75 = (1.021)^n

1.24 =  (1.021)^n

Taking logarithm of both sides;

log 1.24 = n log 1.021

n = log 1.24/log 1.021

n = 0.0934/0.009

n = 10 years

Answer:

1. 85 in squared

Work: b=17 h=10

17*1/2=8.5

8.5*10=85

2. 142.5 mm squared

Work:b=15 h=19

15*1/2=7.5

7.5*19=142.5

3. 110.5 mm squared

Work:b=17 h=13

17*1/2=8.5

8.5*13=110.5

4. 9km squared

Work:b=2 h=9

2*1/2=1

1*9=9

5. 924 mm squared

Work:b=77 h=24

77*1/2=33.5

33.5*24=924

6. 104.5 m squared

Work: b=19 h=11

19*1/2=9.5

9.5*11=104.5

Step-by-step explanation:

Answer:

1. 10x17=170

170/2=85in

2. 19x15=285

285/2=142.5mm

3. 13x17=221

221/2=110.5mm

4. 9x2=18

18/2= 9km

5. 24x77=1,848

1,848/2=924mm

6. 11x19=209

209/2=104.5m

Step-by-step explanation:

y = mx + b. where m is the slope and b is the y intercept

y = 3/4x - 2

Answer:

The two triangles are related by A - S - A test of similarity , so the triangles are congruent.

Answer: Method B is an experiment because it randomly assigns volunteers a sunscreen, while method A is an observational study.

Step-by-step explanation:

Based on the information given, we can infer that method A is an observational study. An observational study simply refers to the study whereby the researchers just observe the impact of a rise factor without them trying to change the people or things exposed to it. This can be seen as the survey adults visited the beach on the busy weekend asking each adult the brand of sunscreen that they use and then assess their arms for sun exposure.

Method B is an experiment. An experiment refers to a test that's carried out in order to evaluate a particular hypothesis or theory. Method B is an experiment because it randomly assigns volunteers a sunscreen.

Therefore, the correct option is D.

The probability that a restaurant customer approves of the food given that they already approved of the service is 0.8, or 80%.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Let's use Bayes' theorem to solve this problem.

= P(approves of food | approves of service)

By Bayes' theorem, we can express this probability in terms of the probabilities of approving of the service and the food separately:

P(approves of food | approves of service) = P(approves of service and food) / P(approves of service)

We know that the overall customer approval rating for the service is 75%, so:

P(approves of service) = 0.75

We also know that the customer approval rating for both the service and the food is 60%, so:

P(approves of service and food) = 0.60

Substituting these values into the formula, we get:

P(approves of food | approves of service) = 0.60 / 0.75

P(approves of food | approves of service) = 0.8

Therefore, the probability that a restaurant customer approves of the food given that they already approved of the service is 0.8, or 80%.

Learn more about probability here:

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Answer:

63 kilometers per hour for train A and 83 kilometers for train B

Step-by-step explanation:

Same beginning

but train B 20 kilometers per hour faster

15 minutes from 20 kilometers per hours are 5 kilometers

So, train B is 45 kilometers travel more far than train B.

= 360 kilometers - 45 kilometers

= 315 kilometers ÷ 5 hours

= 63 kilometers per hours

Hope it's right><

Answer:

She forgot to make the 4 a -4

3x-2x-4=7

Step-by-step explanation:

Answer:

6.3

Step-by-step explanation:

√((8-2)^2 + (4-6)^2)

√ (36 + 4)

√40

6.3

Answer:

The median of the numbers is 3.66 less than the mean

Step-by-step explanation:

To find the median, find the middle of the numbers

0.6, 0.7, 0.85, 1.5, 5.4

To find the mean, add all the numbers and divide by the number of numbers

0.6 + 0.7 + 0.85 + 15 + 5.4 = 22.55

22.55/5 = 4.51

To find how less, subtract the median from the mean

4.51 - 0.85 = 3.66

Answer:

Step-by-step explanation:

A vertical reflection is given by the equation y=−f(x) and results in the curve being "reflected" across the x-axis. A horizontal reflection is given by the equation y=f (−x) and results in the curve being "reflected" across the y-axis. You can see that the reflections are presented in the terms of a function.

As for translations, the function would just increase or decrease based on the translations.  

In translation the graph of function moves certain distance and in reflection the graph of function reflected along the axis of reflection.

"It is a transformation in which the graph of function is moved from one location to another location without changing its size, shape or orientation."

"It is a transformation in which the graph of function is reflected along the line of reflection."

"It defines a relation between input and output values"

Consider a function f(x).

Translations in function f(x):

1) When function f(x) is transformed to f(x) + k, it means function f(x) is translated vertically up by 'k' units.

2) When function f(x) is transformed to f(x) - k, it means function f(x) is translated vertically down by 'k' units.

3) When function f(x) is transformed to f(x + k), it means function f(x) is translated horizontally left by 'k' units.

4) When function f(x) is transformed to f(x - k), it means function f(x) is translated horizontally right by 'k' units.

Now consider reflections in function f(x):

1) When function f(x) is transformed to -f(x) , it means function f(x) is reflected over X-axis.

2) When function f(x) is transformed to f(-x) , it means function f(x) is reflected over Y-axis.

Therefore, in translation the graph of function moves certain distance and in reflection the graph of function reflected along the axis of reflection.

Learn more about the function transformation here:

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Answer:

5 pizzas

Step-by-step explanation:

So first you subtract 18 so that you know that there is at least one cake.

84 - 18 = 66

When you get 66 dollars remaining, you divide it by 12 to see how many you can afford.

66/12 = 5.5

So because you can’t say you have an additonal amount of money, you would actually round down to 5.

So Matt can buy a total of 5 pizzas and 1 cake.

Answer:

5

Step-by-step explanation:

To find the number of pizzas Matt can buy while still being able to afford a cake set up an inequality. The inequality should look like [tex]84\geq 12x+18[/tex]  where x is the number of pizzas Matt bought. Then, solve the inequality by first subtracting 18 from both sides, [tex]66\geq 12x[/tex]. Next, divide both sides by 12, [tex]5.5\geq x[/tex]. This means that Matt can buy 5 pizzas. At first, it might seem like you should round up; however, if you rounded up at all then Matt could not afford the cake, so you must round down.

Answer:

37

Step-by-step explanation:

Here the 2 angles are the same. So

74 = 2x

74/2 = x

x = 37

Answer ;

( refer the attachment for the division )

hence , x = 53

hope my answer helps you !!