In ΔF G H, ∠G is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. f=5, h=4

Answer:

Step-by-step explanation:

To solve the problem, we can use trigonometry and set up a right triangle with the ladder being the hypotenuse, the height being the opposite side, and the slide being the adjacent side. Then, we can use the tangent ratio to find the height of the ladder.

First, we need to convert the length of the slide from feet and inches to just feet. There are 12 inches in a foot, so 8 feet 3 inches can be written as:

8 + 3/12 feet = 8.25 feet

Next, we can use the tangent ratio:

tan(34°) = opposite/adjacent

where the opposite side is the height of the ladder, and the adjacent side is the length of the slide.

Plugging in the values we get:

tan(34°) = height/8.25

Solving for height, we get:

height = 8.25 x tan(34°)

Using a calculator, we can find that:

height ≈ 5.21 feet

Therefore, the height of the ladder leading to the top of the slide is approximately 5.21 feet.

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Answer:

Step-by-step explanation:

I will be using all caps for variables

Solve for L

V = LWH

/ WH  /WH

V/WH = L

Solve for H

V = LWH

/LW  /LW

V/LW = H

The partial derivative fy(0,π) of the function f(x, y) = cos(x^5 - 3y) is computed as follows:

The partial derivative fy(0,π) of the function f(x, y) = cos(x^5 - 3y) evaluated at (0, π) is 0.

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The slope of a line is its vertical change divided by its horizontal change, also known as rise over run. When you have 2 points on a line on a graph the slope is the change in y divided by the change in x. The slope of a line is a measure of how steep it is

The angular radius θ of the first dark ring for a point source being imaged by this telescope is 4.00 × 10^-5 degrees

The value of λ = 550 nanometer

The value of D = 0.96 m

We have to find the angular radius theta

The equation will be

sin θ = 1.22λ / D

Substitute the values in the equation

sin θ = 1.22 × (550 × 10^-9) / 0.96

Multiply the term in the numerator

sin θ = 6.71 × 10^-7 / 0.96

Divide the numbers

sin θ = 6.98 × 10^-7

θ = sin^-1 (6.98 × 10^-7)

θ = 4.00 × 10^-5

Therefore, the value of θ is 4.00 × 10^-5 degrees

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Answer:

e a resposta (d)

Step-by-step explanation:

Answer:

y=1 +4.75

Step-by-step explanation:

Answer:

4blue marble+9 green marble+5 red marble=18marble totle

1 marble probility=1/17

Answer:

8/3

Step-by-step explanation:

Slope:  

8 /3

y-intercept:  

( 0 , − 1 /3 )

Step-by-step explanation:

Answer:

\(\frac{7}{4}\)

Step-by-step explanation:

mixed fraction \(\frac{13}{6}\)

sum =\(\frac{13}{6}\) +\(\frac{1}{2}\) ( LCM)= 12

\(\frac{13}{6}\)×\(\frac{2}{2}\)  + \(\frac{1}{2}\)×\(\frac{6}{6}\)

\(\frac{26+2}{12}\)

\(\frac{28}{12}\) Simplify = \(\frac{7}{4}\)

The margin on the discounted bread is $2.33

Given,

In the question:

Your store cost on a loaf of bread is $0. 75,

and your retail price is $3. 85.

You are having a promotion which discounts the bread 20%.

To find the margin on the discounted bread.

Now, According to the question:

Given store cost on a loaf of bread is $0.75 and retail price is $3.85.

Discount is always given on retail price.

The amount of discount is 20%

Discount given on $3.85 = 20% of 3.85= .20(3.85)= 0.77.

Cost of bread after discount =3.85-0.77= 3.08

The discounted bread costs $3.08.

The difference in store cost and discounted cost = 3.08-0.75=$2.33

Hence, the margin on the discounted bread is $2.33

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Answer:

A

Step-by-step explanation:

Answer:

Zeros are at x=0 and x=3/2.

Step-by-step explanation:

f(x) = x(6x - 9)

x=0 and 6x -9 = 0

6x = 9

x = 3/2

Answer:

normal force decreases

Step-by-step explanation:

N=mgcosθ, and cosine decreases as theta increases

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Answer:

A) decreases

Step-by-step explanation:

As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.

Answer:

Um

Step-by-step explanation:

Its half of diameter

Are you thinking of circumference and area?

Answer:

Step-by-step explanation:

15% = 15/100 = .15

250 x .15 = 37.5

Answer:

37.5

Step-by-step explanation:

15%of 250 will be

15/100×250 = 75/2 = 37.5

Answer:

M/paws= (3x-3) and m/rqs

=(x+19).

the value of x is

Step-by-step explanation:

From Vieta's formulas, we have

\(3x^2 - 4x + 1 = 3 (x - \alpha) (x - \beta) \\\\ ~~~~~~~~~~~~~~~~~ = 3x^2 - 3 (\alpha + \beta) + 3\alpha\beta \\\\ \implies \begin{cases} \boxed{\alpha + \beta = \frac43} \\\\ \boxed{\alpha\beta = \frac13} \end{cases}\)

a) Note that

\((\alpha + \beta)^2 = \alpha^2 + 2\alpha\beta + \beta^2 \\\\ \implies \alpha^2 - \beta^2 = (\alpha+\beta)^2 - 2\alpha\beta - 2\beta^2\)

We have exact values for \(\alpha+\beta\) and \(2\alpha\beta\), but sadly not for \(-2\beta^2\). This means we'll need to solve for \(\beta\) explicitly.

By factorizing, we have

\(3x^2 - 4x + 1 = (3x - 1) (x - 1) = 0 \\\\ \implies x = \dfrac13 \text{ or } x = 1\)

Then the value of \(\alpha^2-\beta^2\) depends on which is chosen to be the larger root, and

\(\alpha^2 - \beta^2 = \dfrac1{3^2} - 1^2 = \boxed{-\dfrac89} \text{ or } \alpha^2 - \beta^2 = 1^2 - \dfrac1{3^2} = \boxed{\dfrac89}\)

While we're at it, we can also immediately find

\(\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = \left(\dfrac43\right)^2 - 2\cdot\dfrac13 = \dfrac{10}9\)

b) Combine fractions to get

\(\dfrac2{\alpha^2} + \dfrac2{\beta^2} = \dfrac{2\beta^2 + 2\alpha^2}{\alpha^2\beta^2} \\\\ ~~~~~~~~~~~~~ = 2 \cdot \dfrac{\alpha^2 + \beta^2}{(\alpha\beta)^2} \\\\ ~~~~~~~~~~~~~ = 2\cdot \dfrac{\frac{10}9}{\left(\frac13\right)^2} \\\\ ~~~~~~~~~~~~~ = \boxed{20}\)

c) Combine fractions again.

\(\dfrac2{\alpha^2} - \dfrac2{\beta^2} = 2 \cdot \dfrac{\beta^2 - \alpha^2}{(\alpha\beta)^2} \\\\ ~~~~~~~~~~~~~ = -2\cdot \dfrac{\pm\frac89}{\left(\frac13\right)^2} \\\\ ~~~~~~~~~~~~~ = \boxed{\pm16}\)

I'll start first by finding the slope of the line at t = 2 mins up to t = 6 mins, t = 6 mins up to t = 8 mins, and t = 14 mins up to t = 20 mins.

For the first interval (2 mins to 6 mins), we have the coordinates (2, 7) and (6, 5). The slope of the line is

For the second interval (6 mins up to 8 mins), we have the coordinates (6, 5) and (8,0). The slope of the line is

For the last interval (14 mins up to 20 mins), we have the coordinates (14,0) and (20,9). The slope of the line is

The x-axis of the given graph pertains to time while its y-axis pertains to distance from home. Let's try to make a story about a person from work going home and will prepare something before going outside again.

For the first 2 mins, the person walks out of his office and will go to his car. Since he is still in the office, the distance from home does not change for the first two minutes.

For the next 4 mins (2 mins to 6 mins interval), he starts driving going home at a rate of 1/2 miles per minute. Because of traffic, he is driving slower than his usual driving speed. Upon passing away from the traffic, the person now travels at a rate of 5/2 miles per minute for 2 mins (6 to 8 mins interval). At the 8th minute mark, he is already home. He prepared something at home during the 8 min to 14 min interval time. After the preparation, he went again outside for some business trip, traveling at the speed of 9/6 miles per minute.

The probability of picking three red bulbs with replacement is 0.3456.

The probability of picking three red bulbs without replacement is 0.2211.

(a) With replacement:

If the bulbs are selected with replacement, the probability of selecting a The no. of the red bulb is 60

Probability for red bulb = 60/100 = 0.6

The number of green bulb = 40

Probability of  green bulb = 40/100 = 0.4.

Using the binomial probability formula:

P (X = 3) = (4 choose 3) * (0.6)^3 * (0.4)^1

= 4 * 0.216 * 0.4

= 0.3456

(b) Without replacement:

If the bulbs are selected without replacement, the probability of selecting a red bulb on the first draw is 60/100 = 0.6

The probability of selecting a red bulb on the second draw is 59/99,

The probability of choosing a red bulb on the third draw, given that the preferably two draws were red, is 58/98.

The probability of selecting a green bulb on the 4th draw is 40/97.

the probability will be:

P(3R, 1G) = (60/100) * (59/99) * (58/98) * (40/97)

= 0.2211

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The probability to answer 5 questions correctly from 14 true or false questions is 0.1222

The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:

P(x)= nCx × p^x × q^(n-x)

Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.

n = 14 (total number of questions)

p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).

To find P(5), we substitute these values in the formula

P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222

Therefore, the answer is option D, 0.1222.

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There are 57 different ways a person can vote for the regional judges.

To determine the number of different ways a person can vote for regional judges, we can use the concept of combinations. In this case, we want to find the number of ways to choose a certain number of judges from a total of 6 candidates.

Since voters can choose to vote for 0, 1, 2, 3, or 4 judges, we need to find the sum of all the possible combinations for each number of judges.

For choosing 0 judges, there is only one possible combination (choosing none).

For choosing 1 judge, there are 6 possible combinations (choosing one out of the six candidates).

For choosing 2 judges, there are \(C(6, 2) = 15\) possible combinations. This is calculated using the combination formula, which  \(C(n, r)\)represents the number of combinations of choosing r items from a set of n items.

For choosing 3 judges, there are \(C(6, 3) = 20\) possible combinations.

For choosing 4 judges, there are \(C(6, 4) = 15\) possible combinations.

To find the total number of different ways a person can vote, we sum up the number of combinations for each scenario:

\(1 + 6 + 15 + 20 + 15 = 57\)

Therefore, there are 57 different ways a person can vote for the regional judges.

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The lateral and surface area of the given shape above in terms of π would be = 48π yd²:120π yd². That is option A.

To calculate the lateral surface area of the cylinder the formula below is used:

Lateral surface area = 2πrh

where;

r = diameter/2 = 12/2 = 6 yd

h = 4 yd

Lateral surface area = 2 ×π × 6×4 = 48π yd²

To calculate the surface area of the cylinder the following formula is used:

Surface area = 2πrh + 2πr²

r = diameter/2 = 12/2 = 6 yd

h = 4 yd

surface area = (2×π×6×4)+(2×π×36)

= 48π+72π

= 120π yd²

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Answer:

For a confined, constant volume of gas, the ratio

P

T

is therefore constant (i.e.,

P

T

=

k

). If the gas is initially in “Condition 1” (with P = P1 and T = T1), and then changes to “Condition 2” (with P = P2 and T = T2), we have that

P

1

T

1

=

k

and

P

2

T

2

=

k

, which reduces to

P

1

T

1

=

P

2

T

2

Answer:

y = x + 8

Step-by-step explanation:

b = 5 - (1)(-3)

b = 5+3

y = x+8

In summary, the derivative of v(t) = 4t³e^5t is v'(t) = 4t²e^5t(3 + 5t), which was obtained by applying the product rule, calculating the derivatives of the individual functions, and factoring the result.

To take the derivative of v(t) = 4t³e^5t using the product rule, follow these steps:

1. Identify the two functions: f(t) = 4t³ and g(t) = e^5t
2. Calculate the derivatives: f'(t) = 12t² and g'(t) = 5e^5t
3. Apply the product rule: v'(t) = f'(t)g(t) + f(t)g'(t)

So, v'(t) = 12t²e^5t + 4t³(5e^5t) = 12t²e^5t + 20t³e^5t.

Now, simplify and factor the result:

v'(t) = e^5t(12t² + 20t³) = 4t²e^5t(3 + 5t).

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f(4) = 3 and f'(4) = m, where m is the slope of the tangent line to the function f(x) at the point (4, 3).

Since the tangent line passes through (4, 3), we can use the point-slope form of a linear equation to determine the equation of the tangent line. Let the equation of the tangent line be y = mx + b, where m is the slope of the tangent line. We know that the slope of the tangent line is equal to the derivative of f(x) evaluated at x = 4, so m = f'(4).

Substituting the point (4, 3) into the equation of the tangent line, we get 3 = 4m + b.

Since the tangent line also passes through (0, 2), we can substitute these coordinates into the equation of the tangent line to get 2 = 0m + b.

From the above two equations, we can solve for b, which gives us b = 2.

Now we have the equation of the tangent line as y = mx + 2, and we know that it represents the function f(x) at the point (4, 3). Therefore, f(4) = 3.

Finally, we can determine f'(4) by substituting the value of m into the equation of the tangent line. So f'(4) = m.

In summary, f(4) = 3 and f'(4) = m, where m is the slope of the tangent line to the function f(x) at the point (4, 3).

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The theoretical yield is typically determined based on the stoichiometry of the reaction and the limiting reagent.

The percentage yield is calculated by comparing the actual yield (the amount of product obtained in the experiment) to the theoretical yield (the amount of product that should have been obtained based on stoichiometry). The formula for percentage yield is:

Percentage Yield = (Actual Yield / Theoretical Yield) x 100%

To calculate the theoretical yield of a soap, you would need specific information regarding the reaction and the quantities involved. Since I don't have the specific details of your soap production process, I am unable to provide an accurate calculation for the theoretical yield. The theoretical yield is typically determined based on the stoichiometry of the reaction and the limiting reagent.

However, I can provide a general explanation of the percentage yield and the discrepancies that may occur.

The percentage yield is calculated by comparing the actual yield (the amount of product obtained in the experiment) to the theoretical yield (the amount of product that should have been obtained based on stoichiometry). The formula for percentage yield is:

Percentage Yield = (Actual Yield / Theoretical Yield) x 100%

Discrepancies between the actual yield and the theoretical yield can occur due to various reasons, such as incomplete reactions, side reactions, loss of product during purification or separation processes, or experimental errors. Other factors like impurities, environmental conditions, and equipment limitations can also contribute to the differences between the actual and theoretical yields.

It is important to analyze the factors that may affect the yield and take steps to optimize the process to improve the percentage yield. Regular calibration of equipment, careful handling of reactants, and purification techniques can help minimize discrepancies and increase the overall yield.

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