Find the lateral surface area of the triangular prism shown below.

Answer:

1843:6754.9709254546.,657675

Step-by-step explanation:

The measure of the angle of the triangle is calculated by the law of sines and m∠S = 59.7°

The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

Given data ,

Let the triangle be represented as ΔRST

Now , the measure of s = 620 cm

The measure of side r = 210 cm

And , the measure of angle m∠R = 17°

From the law of sines , we get

a / sin A = b / sin B

On simplifying , we get

sin ( 17 )° / 210 = sin ( S ) / 620

Multiply by 620 on both sides , we get

sin ( S ) = ( 620 / 210 ) x 0.2923717

On further simplification , we get

sin S = 0.86319265203

Taking inverse on both sides , we get

S = sin⁻¹ ( 0.86319265203 )

S = 59.68°

S = 59.7°

Therefore , the value of S is 59.7°

Hence , the measure of angle m∠S = 59.7°

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Step-by-step explanation:

Find the slope /rate of change using the following ordered pair:(8,40) and (6,30)

also

6300

8400

= B= 14056

Answer:

5

Step-by-step explanation:

Calculate the slope , rate of change m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (8, 40) and (x₂, y₂ ) = (6, 30)

m = [tex]\frac{30-40}{6-8}[/tex] = [tex]\frac{-10}{-2}[/tex] = 5

use symolab its super easy

Answer:

a=16n+27

Step-by-step explanation:

Answer:

Angle A = 56° check the attachment for detailed solution

Answer:

39.6 cm²

Step-by-step explanation:

The formula for the area of a trapezoid is given as:

Area of a Trapezoid = 1/2(a + b) h

Where, from the question:

a = 8.9 cm

b = 5.5 cm

h = 5.5cm

Hence,

1/2 (8.9cm + 5.5cm) × 5.5cm

= 1/2 × 14.4 cm × 5.5 cm

= 39.6 cm²

Area of the Trapezoid = 39.6 cm²

Answer:

Step-by-step explanation:

[tex]\sqrt{}[/tex]A ^ 2 + B ^2 = C ^2 for hypotenuse

20^2 + 5^2 = C

400+25 = 425

[tex]\sqrt{425}[/tex] = 20.61

20.61 is hypotenuse.

X = 180 - 20.61 = 159.39

Hope that helps

The probability that a student chosen randomly from the class has a sister, in a class of 25 students, is 2/5.

For two events A and B, we have:

Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.

This can be written symbolically as:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

For three events, A, B and C:

[tex]P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A\cap B) - P(A \cap C) - P(B \cap C) + P(A \cap B \cap C)[/tex]

In a class of 25 students, 16 have a brother and 10 have a sister. There are 6 students who have a brother and a sister.

Let A is event of a student having a brother and B is event of a student having a sister.

The probability of event A is,

[tex]P(A)=\dfrac{16}{25}[/tex]

The probability of event B is,

[tex]P(B)=\dfrac{10}{25}\\P(B)=\dfrac{2}{5}[/tex]

The probability of occurrence of both event A and B together,

[tex]P(A\cap B)=\dfrac{6}{25}[/tex]

Thus, the probability that a student chosen randomly from the class has a sister, in a class of 25 students, is 2/5.

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Answer:

24,831.28

Step-by-step explanation:

Brainliest pls

Answer:

t = 16.6

Step-by-step explanation:

In the formula:

[tex]a = p(1 + r )^{t} [/tex]

A is the final amount, in this case is 11500 people. P is the initial amount, in this case is 6500 people. r is the growth rate, which in this case is 0.035 - we have to express it s a decimal, not a percent. And finally t is the time, which is the variable we want to find.

Let's clear t first and replace all these values at the end. To clear t we have to leave only the factor which exponent is t on one side of the equation. To do this we have to divide both sides by P:

[tex] \frac{a}{p} = \frac{p}{p} (1 + r) ^{t} \\ \frac{a}{p} = (1 + r)^{t} [/tex]

Now we have to use the following rule for the exponents and logarithms:

[tex] {a}^{x} = b[/tex]

Apply logarithms on both sides:

[tex]log( {a}^{x}) = log(b)[/tex]

By the exponents rule of logarithms

[tex]x \: log(a) = log(b)[/tex]

For this problem we have:

[tex]log \frac{a}{p} = log(1 + r)^{t} \\ log \frac{a}{p} =t \: . \: log(1 + r)[/tex]

Now we have to divide both sides by log(1+r) to clear t:

[tex]log \frac{a}{p} = t \: . \: \frac{log(1 + r)}{log(1 + r)} \\ t = \frac{log \: \frac{a}{p} }{log(1 + r)} [/tex]

And finally we just have to replace the values into this equation we found: A = 11500, P = 6500 and r = 0.035:

[tex]t = log \: \frac{11500}{6500} \\ log(1 + 0.035) \\ log \: \frac{23}{13} \\ t = log \: 1.035 \\ t = 16.6[/tex]

Answer:

$156

Step-by-step explanation:

First you must find out the number of dollars Prasad receives per hour.

Since he earns $195 in 15 hours we can do 195/15 = 13 to find out the amount of dollars he earns per hour which is $13.

Next we must find out how much money he receives when he work for 12 hours so we simply do 13 (payment per hour) * 12 (amount of hours he works) which will give us $156!

This makes sense cuz 156 is a little bit less than 195 and ofc 12 is a little bit less than 15!

Prasad earn $156 next week if he is scheduled to work 12 hours

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Prasad worked 15 hours this week and earned $195

We have to find the amount earned by prasad for work 12 hours

Let us form an proportional equation.

Let x be the amount earned for 12 hours

15/195 = 12/x

Apply cross multiplication

15x=195(12)

15x=2340

Divide both sides by 15

x=2340/15

x=156

Hence, Prasad earn $156 next week if he is scheduled to work 12 hours

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Answer:The coordinates of point P are -8, -4.

Step-by-step explanation:

Answer:

The coordinate of P is -8, -4

Step-by-step explanation:

sorry i don't know. this answer.

Answer:

0 as an exponent would look something like 6^0 and anything to the power of 0 is always 1

Answer:

100 i think

Step-by-step explanation:

Answer:

Probability of Sarah NOT selecting a mystery book  = 0.67

Step-by-step explanation:

Probability helps to show how likely an event will occur;

The probability an event will not occur can be obtained by subtracting the probability that the event will occur from 1.

We can take this route to solve this problem

The probability of picking an option from a broad list of alternatives can be calculated using the formula:

Probability = number of expected outcomes/ total number of options

For our problem, there are only 6 mystery books on the shelf. Hence, the number of expected outcomes is = 6. Sarah cannot pick any more than 6 mystery books, and any mystery book she picks will be from that lot.

The total number of options refers to the total number of books available to pick from; whether mystery, science history, and adventure.

We can get this by adding 6 + 5 + 4 + 3 = 18

Probability of Sarah selecting a mystery book = 6/18

Probability of Sarah NOT selecting a mystery book = 1 - (6/18) = 0.67

Answer:

14√6.

Step-by-step explanation:

√54 = √9√6 = 3√6

√486 = √81 √6 = 9√6.

√24 = √4√6 = 2√6.

So √54 + √486 + √24

= 3√6 + 9√6 + 2√6

= 14√6.

Answer: 2880

Step-by-step explanation:

Answer:

4/7

Step-by-step explanation:

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Reflection over x = -1 performs the transformation ...

  (x, y) ⇒ (-2-x, y)

Answer:

point x

Step-by-step explanation:

it's like the positive side of the line, but in reverse. with negatives, the higher the number the lower it is and since 3.3 is bigger than 2 it would be closer to 4

Answer:

Step-by-step explanation:

What is 2 units up and 0 to the right from (-4,2).

Answer:

(-4,4)

Step-by-step explanation:

Answer:

a) A

b) A

c) B

c) B

Step-by-step explanation:

Answer:

4/11 (I think I'm not sure. I'm sorry if I'm wrong)

Step-by-step explanation:

Answer: I believe you are correct I got the same answer as you.

Answer:

wrong, it would be 1/2 and 5/8

Step-by-step explanation:

7/8ths is over 3/4ths. to check use decimal form which is done by dividing numerator by denominator.

Answer:

x = 2

Step-by-step explanation:

x2 + 6x - 13 = 3

first you add 13 to other side and get

x2 + 6x = 16

next you combine x's

8x = 16

then you divde the 8x by 16

and you get x = 2

Answer:

$8250

Step-by-step explanation:

In other words, a 15% discount for a item with original price of $55000 is equal to $8250 (Amount Saved). Note that to find the amount saved, just multiply it by the percentage and divide by 100.

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Answer:

Step-by-step explanation:

15% is equivalent to 15/100 or 0.15

So just multiply $55,000 by 0.15.

After multiplying, you should get 8250.

So 8250 is your answer

Boba all the way, it is delicious and I can't live without it

Answer:

Perimeter of the entire shape is 114.24

Step-by-step explanation:

Use pi x diameter of the semicircle divided by 2 + the diameter to find the perimeter of one semicircle. There are 4 semi circles so you multiply this by 4. Then you take the perimeter of the inside 8x4 = 32. Add them all together to get 114.24

Answer:

Perimeter of the entire shape is 114.24

Step-by-step explanation:

Use pi x diameter of the semicircle divided by 2 + the diameter to find the perimeter of one semicircle. There are 4 semi-circles so you multiply this by 4. Then you take the perimeter of the inside 8x4 = 32. Add them all together to get 114.24