An architect wants to draw a rectangle with a diagonal of 25 centimeters. The length of the rectangle is to be 10 centimeters more than twice the width. What dimensions should she make the rectangle?

Answer:

Set your calculator to Degree mode.

a² = 17² + 20² - 2(20)(17)cos(89°)

a² = 677.13236

a = 26.0 in.

sin(89°)/26.02177 = (sin B)/17

sin B = 17sin(89°)/26.02177

B = 40.8°

C = 50.2°

Step-by-step explanation:

x = amount of shares for $6.25

y = account of shares for $6.50

x + y = 500

x×6.25 + y×6.5 = 3218.75

x = 500 - y

(500 - y)×6.25 + y×6.5 = 3218.75

3125 - y×6.25 + y×6.5 = 3218.75

0.25×y = 93.75

y = 375

x = 500 - 375 = 125

so, he bought

375 shares of $6.50

125 shares of $6.25

The probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes is only 0.02%.

P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X = k) = (100 choose k) * 0.078^k * (1 - 0.078)^(100-k)

P(X <= 4) = (100 choose 0) * 0.078^0 * (1 - 0.078)^(100-0) + (100 choose 1) * 0.078^1 * (1 - 0.078)^(100-1) + (100 choose 2) * 0.078^2 * (1 - 0.078)^(100-2) + (100 choose 3) * 0.078^3 * (1 - 0.078)^(100-3) + (100 choose 4) * 0.078^4 * (1 - 0.078)^(100-4)

Using a calculator or software, we can find that:

P(X <= 4) = 0.000203

This means that the probability is 0.02%.

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Charges for TV advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is the percentage of population of 110 million TV households.The CBS television show 60 minutes recently had a rating of 7.8, indicating that 7.8% of the household were tuned to that show.An advertiser conducts an independent survey of 100 households and finds that only 4 were tuned to 60 minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes.Does the result suggest that the rating of 7.8 is too high?

Answer:  $4,000

Step-by-step explanation:

If the total earnings were $40,000 and the base pay was $10,000, then the commission earned would be $40,000 - $10,000 = $30,000.

Since the commission rate is 40%, we can set up the equation:

40% x Total Sales = Commission Earned

We know that the commission earned is $30,000, and we also know that 15 cars were sold. Therefore, we can solve for the average price of each car:

40% x Total Sales = Commission Earned

40% x (15 x Price per Car) = $30,000

6 x Price per Car = $30,000

Price per Car = $5,000

However, this is just the average price per car. Since the commission is based on the total sales, we need to calculate the actual commission earned on each car:

Commission per Car = 40% x Price per Car

Commission per Car = 40% x $5,000

Commission per Car = $2,000

Therefore, the total earnings of $40,000 divided by the number of cars sold (15) gives the amount earned per car:

Amount earned per Car = Total Earnings / Number of Cars Sold

Amount earned per Car = $40,000 / 15

Amount earned per Car = $4,000

Answer:

the answer is 1,2 and 4 hope it helps

Answer:

5

Step-by-step explanation:

No, Savannah is incorrect. Doubling the length, width, and height of a right rectangular prism will not double its surface area.

Surface area is the total area of an object's exposed faces, including any external surface area. It is a measure of the size of a surface and is usually expressed in square units such as square meters or square centimeters. Surface area is a two-dimensional measurement, since it only takes into account the area of a surface, and not its thickness or volume.

The surface area of a right rectangular prism is calculated by multiplying the length by the width and then multiplying that number by two and adding the two products together.

For example, the surface area of a right rectangular prism with a length of 15 cm, a width of 10 cm, and a height of 5 cm is calculated as follows:

Surface area = (15 cm * 10 cm) + (15 cm * 5 cm) = 150 cm2 + 75 cm2 = 225 cm2

Doubling the length, width, and height of this right rectangular prism would give us a prism with a length of 30 cm, a width of 20 cm, and a height of 10 cm. The surface area of this new prism would be calculated as follows:

Surface area = (30 cm * 20 cm) + (30 cm * 10 cm) = 600 cm2 + 300 cm2 = 900 cm2

As you can see, doubling the length, width, and height of the right rectangular prism does not double its surface area - the surface area has increased by four times (900 cm2/225 cm2 = 4).

In conclusion, doubling the length, width, and height of a right rectangular prism does not double its surface area; rather, it increases the surface area by a factor of four.

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No, Savannah is incorrect. Doubling the length, width, and height of a right rectangular prism will not double its surface area.

Surface area is the total area of an object's exposed faces, including any external surface area. It is a measure of the size of a surface and is usually expressed in square units such as square meters or square centimeters. Surface area is a two-dimensional measurement, since it only takes into account the area of a surface, and not its thickness or volume.

The surface area of a right rectangular prism is calculated by multiplying the length by the width and then multiplying that number by two and adding the two products together.

For example, the surface area of a right rectangular prism with a length of 15 cm, a width of 10 cm, and a height of 5 cm is calculated as follows:

Surface area = (15 cm * 10 cm) + (15 cm * 5 cm) = 150 cm2 + 75 cm2 = 225 cm2

Doubling the length, width, and height of this right rectangular prism would give us a prism with a length of 30 cm, a width of 20 cm, and a height of 10 cm. The surface area of this new prism would be calculated as follows:

Surface area = (30 cm * 20 cm) + (30 cm * 10 cm) = 600 cm2 + 300 cm2 = 900 cm2

As you can see, doubling the length, width, and height of the right rectangular prism does not double its surface area - the surface area has increased by four times (900 cm2/225 cm2 = 4).

In conclusion, doubling the length, width, and height of a right rectangular prism does not double its surface area; rather, it increases the surface area by a factor of four.

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The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.

The base will be calculated as:-

tan(38.6) = P / B

tan(38.6) = 67.7 / B

B = 67.7 / tan(38.6)

B = 54.8 ft

The height will be calculated as:-

Cos(42.4) = B / H

H = 84.8 / Cos(42.4)

H = 114.83 ft

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x=62 bec 180-118=62.

Step-by-step explanation:

180=118-x

180-118=x

x=62

Answer:

To get the population of the bacteria at a time t, we just plug in the given value of t

so in this case, we will put 5 in the place of t

f(t) = \(e^{t}\)

f(5) = \(e^{5}\)

we know that the value of e is about 2.7. So the population of the bacteria after 5 hours will be 2.7 to the power 5

which will be equal to:

b) 148.413

note: using 2.7 in the calculation will give slightly different answer since it is an estimated value, i suggest using 'e' in the actual calculation

Answer:

The total number of branches = total possibilities = the denominator of a probability.

So the second choice is correct.

Let me know if this helps!

Answer:

Step-by-step explanation: answer B (the denominator of a probability)

Answer:

b. false

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

A P E X

The solution of the system of equations are x = 7 and y = 77

Given data

y = 9x + 14

y = 6x + 35

solving using substitution method to solve the simultaneous equation we have

y = 9x + 14  equation 1

y = 6x + 35  equation 2

equating the both equations will give

9x + 14  = 6x + 35

9x - 6x = 35 - 14

3x = 21

x = 7

plugging x = 7 into equation 1

y = 9x + 14

y = 9 * 7 + 14

y = 63 + 14

y = 77

The solution of the system of equations are x = 7 and y = 77

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Answer:

8m-10=8-m

We move all terms to the left:

8m-10-(8-m)=0

We add all the numbers together, and all the variables

8m-(-1m+8)-10=0

We get rid of parentheses

8m+1m-8-10=0

We add all the numbers together, and all the variables

9m-18=0

We move all terms containing m to the left, all other terms to the right

9m=18

m=18/9

m=2

Another way to write the compound inequality is 2 ≤ y+3 < 6. The 1st option is the answer

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

Given: y + 3 ≥ 2 and y + 3 < 6

To write these in another way, change the inequality sign of one of the inequalities by rearranging. That is:

y + 3 ≥ 2 can be rewritten as 2 ≤ y+3. Thus, we have:

2 ≤ y+3 and y + 3 < 6

Combine the two:

2 ≤ y+3 < 6

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Answer:

A.18.9285714286

B.18 remainder 39

Step-by-step explanation:

0 1 8

4 2 7 9 5

 − 0    

   7 9  

 − 4 2  

   3 7 5

 − 3 3 6

     3 9

From the given information, the measure of DEF is 81°

From the question, we are to determine the measure of DEF

From the given information,

DEF and RST are complementary angles. This means they sum up to 90°

Thus,

(3(-5 + 2x)) + (x - 7) = 90

(3(-5 + 2x)) + (x - 7) = 90

(-15 + 6x) + (x - 7 ) = 90

-15 + 6x + x - 7 = 90

6x + x = 90 + 15 + 7

7x = 112

x = 112/7

x = 16

Then, substitute the value of x to determine the measure of DEF

(3(-5 + 2x))

= (3(-5 + 2(16)))

= (3(-5 + 32))

= (3(27))

= 81°

Hence, the measure of DEF is 81°

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Answer:

Step-by-step explanation:

Let the number of games be x

Inequality:

Since there should be more than 0 left, another inequality for it:

So 13 < x < 15, which leaves us with 14

Answer:

The calculated value Z = 1.8368 < 1.96 at 0.05 level of significance

The null hypothesis is accepted

The samples have been drawn from the same Population

Step-by-step explanation:

Step(i):-

Given first sample size 'n₁' = 49

Mean of the first sample 'x₁⁻ = 609.86

Standard deviation of the sample S₁ = 55.96 calories

Given first sample size 'n₂' = 78

Mean of the first sample 'x₂⁻ = 641.02

Standard deviation of the sample S₂ = 109.14 calories

Step(ii):-

Null hypothesis : H₀: x₁⁻ = x₂⁻

Alternative Hypothesis : H₁: x₁⁻ ≠ x₂⁻

Level of significance ∝ = 0.05

Test statistic

\(Z = \frac{x^{-} _{1}-x^{-} _{2} }{\sqrt{S.D^2(\frac{1}{n_{1} } }+\frac{1}{n_{2} } }\)

where

 \(S.D^{2} = \frac{n_{1} S^2_{1}+ n_{2} S^2_{2} }{n_{1} + n_{2} -2}\)

 \(= \frac{49 X (55.96)^2+ 78X(109.14)^2 }{49 + 78 }\)

 σ² =  8660.357

Step(iii):-

Test statistic

\(Z = \frac{x^{-} _{1}-x^{-} _{2} }{\sqrt{S.D^2(\frac{1}{n_{1} } }+\frac{1}{n_{2} } }\)

\(= \frac{ 609.86-641.02 }{\sqrt{8660.357(\frac{1}{49 } }+\frac{1}{78 } ) }\)

\(Z = \frac{-31.16}{16.9638} = -1.8368\)

|Z| = |-1.8368| = 1.8368

The tabulated value Z₀.₉₅ = 1.96

The calculated value = 1.8368 < 1.96 at 0.05 level of significance

The null hypothesis is accepted

Final answer:-

The samples have been drawn from the same Population

Answer: 0.2

happy learning

Answer:

2.3 pounds

Step-by-step explanation:

First, the mean is equal to the sum divided by the number of numbers.

There are four packages, so there are four numbers. Let's say the fourth package has a weight of x. We can then write

mean = sum / number of numbers

2.5 = (1.8+3.2+2.7+x)/4

multiply both sides by 4 to remove the denominator

10 = 1.8+3.2+2.7+x

10 = 7.7 + x

subtract 7.7 from both sides to isolate the x

x = 2.3 pounds

Answer:

Total pay=$288.64

Step-by-step explanation:

Giving the following information:

Hourly rate= $8.125

Number of hours worked= 35.525

To calculate the total pay of the week, we need to use the following formula:

Total pay= hourly rate * number of hours worked

Total pay= 8.125*35.525

Total pay=$288.64

Answer:

15

Step-by-step explanation:

Answer:

x = 7.

Step-by-step explanation:

I am assuming the numbers are angles.

50 + 80 + 8x - 6 = 180

8x - 6 = 180 - 130  = 50

8x = 56

x = 7.

Answer: The expression inside the parentheses can be simplified as follows:

24/16 + 3/3 = 3

So, the expression becomes:

6/11 - 3/12 = 6/11 - 1/4

Now we can subtract the two fractions:

6/11 - 1/4 = 6/11 - 4/11 = 2/11

So the final answer is 2/11.

Step-by-step explanation:

Solution

For this case we have the following data:

30, 40, 39, 36, 30

Representing the ages (in years) of the 5 doctors at a local clinic

these values represent an entire population, and we want to find the standard deviation of the population

1) First we need to calculate the mean

2) Now we can find the population variance like this:

3) Calculate the population standard deviation

then the answer would be:

4.29

The distance that Mr. Stein drove can be represented by the expression: \(140 - x\)

A mathematical phrase made up of one or more variables, constants, and arithmetic operations like addition, subtraction, multiplication, and division is known as an algebraic expression. Exponentiation and other mathematical operators could also be present.

Let's assume that Mr. Smith drove "x" miles before Mr. Stein took over the driving.

Then, the total distance they traveled is 140 miles.

So, the distance that Mr. Stein drove can be represented by the expression:

140 - x

Therefore, This is because if Mr. Smith drove "x" miles, then the remaining distance that needed to be covered by Mr. Stein would be the difference between the total distance of 140 miles and the distance already driven by Mr. Smith.

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The inverse equation to the one given in this exercise is:

\(y = 2(\sqrt{7 + x} + 1)\)

To find the inverse, we have to exchange x and y and then isolate y.

In this problem, the equation is:

2(x - 2)² = 8(7 + y).

Exchanging x and y:

2(y - 2)² = 8(7 + x)

Now we work to isolate y:

(y - 2)² = 4(7 + x).

To isolate y, we apply the square root to both sides, hence:

\(\sqrt{(y - 2)^2} = \sqrt{4(7 + x)}\)

\(y - 2 = 2\sqrt{7 + x}\)

\(y = 2\sqrt{7 + x} + 2\)

\(y = 2(\sqrt{7 + x} + 1)\)

Hence the inverse equation to the one given is:

\(y = 2(\sqrt{7 + x} + 1)\)

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