Can someone please help

Answer:

If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.

The given radical expression is (√x)^5. To rewrite it in rational exponent form, we need to express the square root (√) as a fractional exponent.

The square root (√) of x can be written as x^(1/2).

To raise x^(1/2) to the power of 5, we can multiply the exponents: (x^(1/2))^5 = x^(5/2).

Therefore, the radical expression (√x)^5 can be rewritten as x^(5/2) in rational exponent form.

In summary, (√x)^5 is equivalent to x^(5/2) in rational exponent form.

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Answer:

=81.64yd

Step-by-step explanation:

c=3.14d

c=(3.14)*(13+13)

=81.64yd

A circular park of radius 14 m has a road of 7 m width all around on its outside then the  area of the road is approximately 153.943 square meters.

The circular park has a radius of 14 m. This means that the diameter of the park is 2 x 14 = 28 m. The road around the park has a width of 7 m. This means that the total width of the park and the road is 28 + 7 + 7 = 42 m. The area of the circular park can be found using the formula for the area of a circle: Area of park =\(π x r^2 = π x 14^2 = 615.752 m^2\) (rounded to 3 decimal places)

The area of the park and the road can be found by calculating the area of the larger circle and subtracting the area of the park: Area of park and road =\(π x (r+7)^2 - π x r^2 = π x (14+7)^2 - π x 14^2 = π x 21^2 - π x 14^2 = π x (441 - 196) = π x 245 = 769.695 m^2\) (rounded to 3 decimal places)

To find the area of just the road, we need to subtract the area of the park from the area of the park and road: Area of road = Area of park and road - Area of park = 769.695 - 615.752 =\(153.943 m^2\) (rounded to 3 decimal places)

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Answer:  6 inches equals 0.16666667 yards, or about 0.2 yards.

Step-by-step explanation: 1 yard equals 36 inches. By that reasoning, we can divide 6 by 36, since we are trying to find out how many yards are in 6 inches.

6/36 = 0.16666667

The answer is 0.16666667 yards, or about 0.2 yards.

The total number of sides of a regular polygon with each exterior angle of measure 30 degrees is equal to 12.

Let us consider 'n' be the number of sides of the regular polygon.

Let 'y' be the measure of each of the exterior angle of regular polygon.

y = 30 degrees

Measure of each of the exterior angle of regular polygon 'y'

= ( 360° ) / n

⇒ n = ( 360° / y )

Substitute the value we get,

⇒ n = ( 360° / 30° )

⇒ n = 12

Therefore, the number of sides of a regular polygon with each of the exterior angle 30 degrees is equal to 12.

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The above question is incomplete, the complete question is:

How many sides does a regular polygon have when each exterior angle measures 30 degrees?

Answer:

FV= £13,131.66

Step-by-step explanation:

Giving the following information:

Initial Investment (PV)= £10,000

Interest rate (i)= 5.6%

Number of periods (n)= 5 years

To calculate the future value (FV), we need to use the following formula:

FV= PV*(1 + i)^n

FV= 10,000*(1.056^5)

FV= £13,131.66

Answer: !50 is the answer hope this helped

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

b+12 =16

-12. -12

b = 4

hope this helps

Julia needs to invest $4,901.43 every quarter for 4 years to have a down payment of $25,000. Checking the table of values, we see that the closest answer is $4,542.98, so that is the amount she needs to invest.

We can use the formula for the future value of an annuity with regular deposits to find the amount that Julia needs to invest now:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

where:

P = quarterly deposit

r = annual interest rate = 8%

n = number of compounding periods per year = 4 (quarterly)

t = number of years = 4

FV = future value of the annuity (i.e. the down payment)

We want to solve for P, which is the amount Julia needs to invest each quarter. Rearranging the formula, we get:

P = FV * (r/n) / ((1 + r/n)^(n*t) - 1)

Substituting the given values, we get:

P = 25,000 * (0.08/4) / ((1 + 0.08/4)^(4*4) - 1)

P ≈ $4,901.43

So Julia needs to invest $4,901.43 every quarter for 4 years to have a down payment of $25,000. Checking the table of values, we see that the closest answer is $4,542.98, so that is the amount she needs to invest.

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Given the odds in favor of event E as 16 to 4, the probability of event E is 4/5.The probability of event E is then the number of favorable outcomes divided by the total number of outcomes. So, P(E) = 16/20 = 4/5.

The odds in favor of event E are given as 16 to 4. To compute the probability of event E, we need to convert these odds into a fraction.

The odds in favor of E are 16 to 4, which means that for every 16 favorable outcomes, there are 4 unfavorable outcomes.

To find the probability, we add the number of favorable outcomes and the number of unfavorable outcomes together. In this case, 16 + 4 = 20.

The probability of event E is then the number of favorable outcomes divided by the total number of outcomes. So, P(E) = 16/20 = 4/5.

Therefore, the probability of event E is 4/5.In summary, given the odds in favor of event E as 16 to 4, the probability of event E is 4/5.

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Answer:

Go to the botom of the page

Step-by-step explanation:

Answer: 5

Step-by-step explanation: First we do (-4-(-7))^2 which is 9 and then

(8-4)^2 which is 16 so 9+16=25 and √25 = 5.

Answer:

0

Step-by-step explanation:

If c=0

that expression also equals 0

Answer:

485.42

Step-by-step explanation:

multiply by using` long multiplication

Answer:

= -24 * 1/4

-24/4

= -6

Hope this helps you. Do mark me as brainliest.

Answer:

27

Step-by-step explanation:

divide 81 by 3 :p

Answer:

Step-by-step explanation:

81nBdivided by 3 is 28

Answer:

(x,y)=(24,-7)

Step-by-step explanation:

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer:

(2) The statement is true.

-1 < r < 1

Answer:

uwuwhwhwnwjwjwiwieiwiwjwjjejeejjwje

Step-by-step explanation:

euwwuwjw

The student should stand at 2L/9 you will see it tip over so as to weigh of 60kg.

Due to the fact that mass is the quantity of matter contained in an item and does not change with gravity, mass is always the same. As long as the amount of matter in an object doesn't change, its mass will remain constant. In contrast, an object's weight refers to the force of gravity acting on it.

No matter where you are in the cosmos, you have the same mass since mass is a measurement of how much matter is in an object. But because weight measures the force between an object and the body it is resting on, it fluctuates (whether that body is the Earth, the Moon, Mars, et cetera).

Given : A mass of student 40 kg

length is represented by l

Position of the pivot point from the board = l/3

The student should stand at 2L/9 you will see it tip over so as to weigh of 60kg.

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The probability is approximately a 3.51% chance that an elite athlete has a maximum oxygen uptake of at least 73.3 ml/kg.

To find the probability that an elite athlete has a maximum oxygen uptake of at least 73.3 ml/kg, we need to use the concept of z-scores and the standard normal distribution.

Step 1: Calculate the z-score
The z-score measures how many standard deviations a particular value is away from the mean. In this case, we want to find the z-score for 73.3 ml/kg using the formula:

z = (x - μ) / σ

where x is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.

In this case:
x = 73.3
μ = 62.5
σ = 7.2

Substituting these values into the formula:
z = (73.3 - 62.5) / 7.2

Step 2: Look up the z-score
Once we have the z-score, we can use a standard normal distribution table or a calculator to find the probability associated with that z-score. The probability corresponds to the area under the normal distribution curve to the right of the z-score.

In this case, we want to find the probability of an elite athlete having a maximum oxygen uptake of at least 73.3 ml/kg, which means we want to find the probability to the right of the z-score.

Step 3: Calculate the probability
Using a standard normal distribution table or a calculator, we find that the z-score of 73.3 ml/kg is approximately 1.826.

The probability to the right of this z-score can be calculated by subtracting the cumulative probability from 1.

P(Z > 1.826) = 1 - P(Z < 1.826)

From the standard normal distribution table, the cumulative probability associated with a z-score of 1.826 is approximately 0.9649.

So, the probability that an elite athlete has a maximum oxygen uptake of at least 73.3 ml/kg is:

P(Z > 1.826) = 1 - 0.9649 = 0.0351

Therefore, the probability is approximately 0.0351 or 3.51%.

In conclusion, there is approximately a 3.51% chance that an elite athlete has a maximum oxygen uptake of at least 73.3 ml/kg.

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Answer:

MUN= (0,1,2,4,5,7)

Step-by-step explanation:

M=(0,2,7) N=(1,2,4,5) what's MUN?

Given data

​M=(0,2,7)

N=(1,2,4,5)

"MUN" is translated as M union N, hence we want to combine all elements

of M and N together

MUN= (0,1,2,4,5,7)

The z scοre is negative the actual probability would be

1-0.7995 = 0.2005

What is the probability?

A number that expresses hοw likely it is that an event will occur is called the probability of οccurrence. It is written as a number from 0 to 1, or frοm 0% to 100%, in percentage notation. The probability of an event occurring increases with probability.

here,

mean = 20.20

standard deviatiοn = 2.60

we knοw that,

Z scοre = (X-mean)/standard deviation

fοr X = 18:

Z scοre = (18-20.20)/2.6 = -0.8461

nοte that the z score is negative because the measured value is less than the mean value.

fοr Z score 0.8461 probability is 0.7995

and since the z scοre is negative the actual probability would be

1-0.7995 = 0.2005

a. For nοt within 1 hour of the population mean

We apply the formula here and we get the value οf P.

P(19.20>x>21.20) = P(19.20-20.20/2.60√18) > X-μ/σ√n >21.20-20.20/2.60√18

P(19.20>x>21.20) = P(-1.63>z>1.63)

Now, we find the value οf z.

P(19.20>x>21.20) = P(z>1.63) + P(z<-1.63)

P(19.20>x>21.20) = 0.0516 + 0.0516

P(19.20>x>21.20) = 0.1032

b. Fοr 20. 0 to 20. 5 hours

P(20<x<20.5) = P(20-20.20/2.60√18) < X-μ/σ√n<20.50-20.20/2.60√18

P(20<x<20.5) = P(-0.33<z<0.49)

Nοw, we find the value of the z-score and we get

P(20<x<20.5) = P(z<0.49) - P(z<-0.33)

P(20<x<20.5)  = 0.6879 - 0.2707

P(20<x<20.5)  = 0.3172

c. Fοr at least 22 hours

We apply the t-test fοrmula here and we get

P(x≥22) = P(X-μ/σ√n≥22-20.20/2.60√18)

Nοw, we find the value of z.

P(x≥22) = P(z≥2.94)

P(x≥22) = 0.0016

d. Fοr not more than 21 hours.

P(x<21) = P(X-μ/σ√n<21-20.20/2.60√18)

We find here the value οf P for x<21 and we get

P(x<21) = P(z<1.31)

Now, we find the value οf the z- score.

P(x<21) = 0.9049

Hence, a. 0.1032

b.  0.3172

c. 0.0016

d. 0.9049

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Complete question is,

Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average time spent working per week of 18 randomly selected college students who old part-time jobs during the school year is.

Therefore, we need to add approximately 0.0526 gallons of water (which is equivalent to about 6.63 fluid ounces) to 1 gallon of pure antifreeze to obtain a solution that is 95% antifreeze.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of one or more variables, coefficients, and constants, and it can include mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign, indicating that they have the same value. The goal of solving an equation is to determine the value of the variables that make the equation true. Equations are used in many areas of mathematics and science to model real-world phenomena and solve problems.

Here,

Let's assume that we need to add x gallons of water to 1 gallon of pure antifreeze to obtain a solution that is 95% antifreeze. We know that the final solution will contain 1 gallon of antifreeze, and that this will be 95% of the total solution (the remaining 5% will be water). So, we can write:

1 gallon of antifreeze = 95% of (1 gallon of antifreeze + x gallons of water)

We can simplify this equation by converting 95% to a decimal:

0.95 × (1 gallon of antifreeze + x gallons of water) = 1 gallon of antifreeze

Now we can solve for x by isolating it on one side of the equation. First, let's distribute the 0.95:

0.95 gallons of antifreeze + 0.95x gallons of water = 1 gallon of antifreeze

Next, let's isolate x by subtracting 0.95 gallons of antifreeze from both sides:

0.95x gallons of water = 0.05 gallons of antifreeze

Finally, we can solve for x by dividing both sides by 0.95:

x = 0.05 gallons of antifreeze ÷ 0.95

x ≈ 0.0526 gallons of water

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Answer:

9.4 pound of raisin and 10.6 pound of peanut is required to make 20 pound of product

Step-by-step explanation:

The cost of raisins is $2.5 per pound and the cost of peanut per pound is $3.50.

Let r represent the number of raisin pound and p represent the number of peanut pound. Since 20 pounds of a new product that consists of peanuts and raisins need to be produced, it can be represented by the equation:

p + r = 20             (1)

The new product would cost $3.03, therefore:

3.5p + 2.5r = 3.03(20)

3.5p + 2.5r = 60.6          (2)

We have to solve equation (1) and (2) simultaneously. First multiply (1) by 2.5 to get 2.5p + 2.5r = 50. Subtract  2.5p + 2.5r = 50 from equation (2):

p = 10.6 pound

Put p = 10.6 in equation (1)

10.6 + r = 20

r = 20 - 10.6 = 9.4

r = 9.4 pound

9.4 pound of raisin and 10.6 pound of peanut is required to make 20 pound of product

Answer:

p + r = 20

\(\frac{3.50p+2.50r}{20}\) = 3.03

Step-by-step explanation:

The total cost of the product when the peanuts and raisins are combined is:

3.50p + 2.50r

To obtain the per pound cost, this expression needs to be divided by the number of total pounds, 20.

\(\frac{3.50p+2.50r}{20} =3.03\)

**KA's explanation**

Answer:

Given that a worker earns a 3% increase in her annual salary for each of 5 years, and they plan to continue working in their position for an additional N years, if they continue to earn a 3% increase in their annual salary, to determine what statement could describe the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year the following calculation should be performed:

1 + 0.03 (interest rate) ^ N (number of years) = final interest rate

1.03 ^ N = Final interest rate

Thus, for example, if it were invested for 5 years, the equation would operate as follows:

1.03 ^ 5 = X

1.16 = X

The total percent increase in their annual salary from the first year to the last year is \((1.03)^n\).

A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

As it is given that the annual salary of the worker increases at a rate of 3%. therefore, the salary of the worker increases compounded at a rate of 3% annually. Therefore, the salary of the worker after n number of years can be written as,

\(A = P(1+\dfrac{r}{100})^n\)

where A is the final salary of the worker, P is the initial salary of the worker, r is the rate at which the salary is increasing, and n is the number of years.

Substituting the values in the formula,

\(A = P(1+\dfrac{3}{100})^n\\\\A = P(1.03)^n\)

Hence, the total percent increase in their annual salary from the first year to the last year is \((1.03)^n\).

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Answer:

3a - 7.5

Step-by-step explanation:

4.5a−1.5(a+5)

4.5a - 1.5a - 7.5

3a - 7.5

So, the answer is 3a-7.5