In triangle ABC, Aat the top of the triangle, B at 90° and C at the third end, angle C = 21°, the hypotenus = 15m,find BC = y the unknown side

The potential energy of the drum at A is: PE = 490 J.

The potential energy of the drum at A can be calculated using the equation: PE = mgh, where m is the mass of the drum (10kg), g is the acceleration due to gravity (9.8 m/s2), and h is the height of the incline (5m).

Therefore, the potential energy of the drum at A is:

PE = 10kg x 9.8 m/s2 x 5m

PE = 490 J.

Potential energy is a type of stored energy that an object has due to its position or state. It is the energy that an object has because of its position relative to other objects, its own internal stresses, its electric charge, or other factors.

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Answer:

Law of sines

Step-by-step explanation:

i took the test

The law of sines can be used to calculate the side h. Hence, option B is correct.

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

For triangle FGH, angles F and G are known, as is the length of side h. The sin angle is the ratio of the perpendicular to the hypotenuse we can calculate one side by using the sine angle.

Hence, Hence, option B is correct.

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Answer:

0.58

Step-by-step explanation:

58/100 = 0.58

Since hundred has two zeros, it moves forward twice and hence the decimal point ends in front of the 5 making is 0.58

The average velocity for the [3,4] is 27m/s and for [4,5] is 37m/s

The average velocity can be found by taking the derivative of the position function and evaluating it at the midpoint of the interval.

The average velocity on the interval [3,4] is given by (s(4) - s(3)) / (4 - 3), which is equal to (s(4) - s(3)) / 1. Using the position function, s(t) = 5t^2 - 8t + 13, we find that s(4) = 5(4²) - 8(4) + 13 = 61 and s(3) = 5(3²) - 8(3) + 13 = 34. Therefore, the average velocity on the interval [3,4] is (61 - 34) / 1 = 27 m/s.

The average velocity on the interval [4,5] is given by (s(5) - s(4)) / (5 - 4), which is equal to (s(5) - s(4)) / 1. Using the position function, s(t) = 5t² - 8t + 13, we find that s(5) = 5(5²) - 8(5) + 13 = 98 and s(4) = 5(4²) - 8(4) + 13 = 61. Therefore, the average velocity on the interval [4,5] is (98 - 61) / 1 = 37 m/s.

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Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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Step-by-step explanation:

500=2x

x= 250....ppl can get water

250==2x

125....ppl can get water now

Answer:

Step-by-step explanation:

44.4--0.4=-44

The expressions are given as;

1. The factored form of g(x) is g(x) = 1/(x-6)

2. The LCD of g(x) and h(x) is (x-6)(x+8)

3. The LCD of h() and p(x) is (x-6)(8x + 32)

Functions are simply defined as laws, equations or rules showing the relationship between two variables.

These variables are termed;

From the information given, we have that;

g(x) = (x + 8)/x² + 2x - 48

Factorize the denominator of the function;

x²+ 8x - 6x - 48

group in pairs

x(x + 8) - 6(x + 8)

Then,

g(x) = x + 8/(x-6)(x+ 8)

g(x) = 1/(x-6)

The lowest common denominator of the functions g(x) and h(x) is;

g(x) = x + 8/(x-6)(x+ 8)

h(x) = 6x - 36/x-6

LCD = (x-6)(x+8)

The LCD of h(x) and p(x) is given as;

p(x) = x² - x - 20/8x + 32

= (x-6)(8x + 32)

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The given system of equations has no solution.

What is substitution method?

In order to solve a system of equations, the substitution approach is typically utilized in mathematics. The first equation involving the variable must be solved using this procedure before the variable's value is substituted in the second equation.

Consider, the given system of equations,

y + 7 = 3x          ..(1)

6x - 2y = 12             ..(2)

From equation (1),

y = 3x - 7.

Substitute value of (y) in inequation (2),

6x - 2(3x - 7) = 12

6x - 6x - 14 = 12

            -14 = 12

It is not possible to solve -14 = 12.

Therefore, the given system of equations has no solution.

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In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.

Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.

We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)

Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!

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This question is incomplete

Complete Question

Joe needs to transfer 28 quarts of oil into gallons containers joe calculated that he needs 112 containers but he made a mistake in his calculations identify and correct his error

Joe's error:

28 quarts × 4 quarts/ 1 gallon

= 28 quarts/1 × 4 quarts/ 1 gallon

= (28 × 4)/ ( 1 × 1) = 112 gallons

Answer:

7 gallons is the correct answer

Joe needs to transfer 28 quarts of oil into 7 gallons

Step-by-step explanation:

Joe's error:

28 quarts × 4 quarts/ 1 gallon

= 28 quarts/1 × 4 quarts/ 1 gallon

= (28 × 4)/ ( 1 × 1) = 112 gallons

Correcting Joe's error, we have:

4 quarts = 1 gallon

28 quarts = x

Cross Multiply

4 quarts × x = 28 quarts × 1 gallon

x = 28 quarts × 1 gallon/ 4 quarts

x = 7 gallons

= 28 quarts/x gallons × 1 gallon/4 quarts

= (28 × x)/ ( 1 /4) = 7 gallons

Therefore, Joe needs to transfer 28 quarts of oil into 7 gallons

Answer: Domain: (-∞, 0) U (0, ∞)

Step-by-step explanation:

\(\frac{12}{x} *-8x^{3}\)

\(=-96x^2\)

Domain: (-∞, 0) U (0, ∞)

Yes, the student can use the first equation to replace the second equation and create a new system that has the same solution.

To do this, the student must multiply the second equation by a number that will make the coefficients of the x terms the same. In this case, the student must multiply the second equation by 4. This will result in a new equation of 16x + 20y = 72.

The student can then add this equation to the first equation, resulting in a new equation of 28x + 28y = 112. The student can then use this equation and the first equation to create a new system that has the same solution as the original system.

This new system will be 12x + 8y = 40 and 28x + 28y = 112. By solving this new system, the student can find the same solution as the original system.

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Answer:

maximum height is 80 feet

8 seconds until it hits ground

Step-by-step explanation:

-5t(t - 8) = 0

-5t= 0;  t = 0  (this represents the beginning of the throw)

t-8=0;  t = 8   (this represents the end of the throw)

To find maximum height, find the vertex of the graph,

you can use -b/2a to find 't' and then substitute that value back into the function to find h(t)

x = -40÷2(-5)

x = -40/-10

x = 4

h(4) = -5(4²)+40(4)

h(4) = -5(16) + 160 which is 160 - 80 = 80

The process to show the vector field V(x,y,z) as conservative is show  below and the scalar potential f is \(f(x,y,z) =xyz^{2} + e^{\pi }\)   .

A Vector field can be called as conservative if we are able to find the potential function "f" , whose gradient is field .

The Gradient is vector that is made from partial derivatives of potential function .

The Vector function is given as , V(x,y,z) = \((yz^{2} )i + (xz^{2} )j + (2xyz)k\) ,

So , we can write the partial derivatives function of potential function as :

\(\frac{\partial f}{\partial x} = yz^{2}\) ; \(\frac{\partial f}{\partial y} = xz^{2}\) ; \(\frac{\partial f}{\partial z} = 2xyz\),

On Antidifferentiating any of the above three partial derivatives ,

we get ; \(f=xyz^{2} + C\) , here the constant C can take any value ,

so , we take C as \(e^{\pi }\) .

Therefore , the potential Function is \(f(x,y,z) =xyz^{2} + e^{\pi }\) .

The given question is incomplete , the complete question is

Show that the vector field defined by the vector function V(x,y,z) = (yz²)i + (xz²)j + (2xyz)k is conservative by finding a scalar potential f .

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Answer:

x = 135

Step-by-step explanation:

The angles are vertical angles and vertical angles are equal

125 = x-10

Add 10 to each side

125+10 = x

135 =x

Answer: The absolute value inequality will be |x| ≥ -2.

Step-by-step explanation: gl :)

Answer:

more simple here da answer but this answer is from the person above i just putted the answer

The absolute value inequality will be |x| ≥ 6

A picking list is used by forklift drivers to let them know how much of each item to get from specific storage areas in a distribution center.

Explanation:

A picking list is a document that is used by forklift drivers and other warehouse personnel to identify the specific items and quantities that need to be picked from specific storage locations in a distribution center.

The picking list typically contains information such as the item number, description, location, and quantity needed for each item. It may also include other details such as the customer's name, order number, and delivery date.

The purpose of the picking list is to ensure that the correct items are picked in the correct quantities, and that they are picked from the correct storage locations. This helps to ensure that orders are filled accurately and efficiently, and that inventory levels are properly managed.

Once the items are picked, the picking list may be used to update inventory records and to generate packing slips or other shipping documents. The picking list is an essential tool in the warehouse and distribution process, and it helps to ensure that customers receive the correct products on time.

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Answer:

179 + 49+ 139 = 367

Step-by-step explanation:

khan academy

khan academy is a site used for students to learn

Let's add the fractions to determine how many miles Rami run:

Therefore Rami run 2 11/24 miles. (In decimal approximation this is 2.4583 miles)

Answer:

I think both angle formed is equal bcz of corresponding angle property

We need two things to write the recursive formula

\(a\) is the first value of this sequence. For this set of values, \(a = 1\), since \(1\) appears first.

\(d\), the common difference, is \(d = t_{3} - t_{2} = t_{2} - t_{1}\). Basically it's just the the higher term minus the previous terms. To solve for \(d\),

So regardless of what terms you choose, the common difference will be the same. Now the general formula for a recursive function is

where \(n\) is the \(nth\) term. Let's substitute for \(a\) and \(d\) in this formula.

\(t_{n} = 1 + (n - 1) \times -3\\t_{n} = 1 + -3(n - 1)\\t_{n} = 1 - 3(n - 1)\)

So the recursive formula is \(t_{n} = 1 - 3(n -1)\)

The given box plot answers are,

a) 6

b) 5

c)3

d) 5

What is box plot?

   A suitable graphical representation of the concentration of the data is provided by box plots, often known as box-and-whisker plots or box-whisker plots. They also demonstrate how remote the extreme numbers are from the bulk of the data. Five numbers are used to create a box plot: the minimum value, first quartiles, median, third quartile, and maximum value.

Here in the given box plot middle line value is called median .Then ,

Median = 6

Now the maximum quartile = 8

The minimum quartile = 3

Now IQR is difference between the minimum and maximum quartile.

Then ,

=> IQR = 8-3 =5

Therefore the answers are

a) 6

b) 5

c)3

d) 5

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Answer:

KL = 10

Step-by-step explanation:

Given:

 \(JL=26\)

 \(KL=3x+7\)

 \(JK=8x+8\)

From inspection of the given diagram:

\(JK+KL=JL\)

Substitute the given values into the found equation and solve for x:

\(\implies 8x+8+3x+7=26\)

\(\implies 11x+15=26\)

\(\implies 11x+15-15=26-15\)

\(\implies 11x=11\)

\(\implies \dfrac{11x}{11}=\dfrac{11}{11}\)

\(\implies x=1\)

Substitute the found value of x into the expression for KL:

\(\implies KL=3(1)+7\)

\(\implies KL=3+7\)

\(\implies KL=10\)

Formula we use,

→ JK + KL = JL

Now the value of x will be,

→ (8x + 8) + (3x + 7) = 26

→ 11x + 15 = 26

→ 11x = 26 - 15

→ x = 11/11

→ [ x = 1 ]

Then the value of KL will be,

→ 3x + 7

→ (3 × 1) + 7

→ 3 + 7 = 10

Hence, the value of KL is 10.

Here is the code:

# Define the urns

urn1 <- c("black", "gold")

urn2 <- c("white", "gold")

# Define the sample space

sample_space <- expand.grid(urn1 = urn1, urn2 = urn2)

# Exact probability of getting same color

exact_prob <- sum(sample_space$urn1 == sample_space$urn2) / nrow(sample_space)

# Set seed for reproducibility

set.seed(123)

# Simulation

n_sims <- c(10, 100, 10000)

for (n in n_sims) {

 same_color <- replicate(n, {

   ball1 <- sample(urn1, size = 1)

   ball2 <- sample(urn2, size = 1)

   ball1 == ball2

 })

 sim_prob <- mean(same_color)

 cat(paste0("Number of simulations: ", n, "\n"))

 cat(paste0("Simulation probability: ", sim_prob, "\n"))

 cat(paste0("Exact probability: ", exact_prob, "\n\n"))

}

The output will give you the simulation probability and the exact probability for each number of simulations. You can compare these values to see how close the simulation is to the exact answer.

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The forecasts for periods 11 through 15 are: F11 = 297.4, F12 = 296.7, F13 = 297.1, F14 = 296.9, F15 = 297.0

Given: Smoothing constant α = 0.45, Forecast for period 10 = 297

We need to calculate the forecasts for periods 11 through 15 using the essential smoothing forecast method.

The essential smoothing forecast is given by:Ft+1 = αAt + (1 - α)

Ft

Where,

At is the actual value for period t, and Ft is the forecasted value for period t.

We have the forecast for period 10, so we can start by calculating the forecast for period 11:F11 = 0.45(297) + (1 - 0.45)F10 = 162.35 + 0.45F10

F11 = 162.35 + 0.45(297) = 297.4

For period 12:F12 = 0.45(At) + (1 - 0.45)F11F12 = 0.45(297.4) + 0.55(297) = 296.7

For period 13:F13 = 0.45(At) + (1 - 0.45)F12F13 = 0.45(296.7) + 0.55(297.4) = 297.1

For period 14:F14 = 0.45(At) + (1 - 0.45)F13F14 = 0.45(297.1) + 0.55(296.7) = 296.9

For period 15:F15 = 0.45(At) + (1 - 0.45)F14F15 = 0.45(296.9) + 0.55(297.1) = 297.0

Therefore, the forecasts for periods 11 through 15 are: F11 = 297.4, F12 = 296.7, F13 = 297.1, F14 = 296.9, F15 = 297.0 (All values rounded to two decimal places)

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Answer:

F. 619 in. cubed

Step-by-step explanation:

volume for rectangular prism

12 x 7 x 4

= 336

volume of cylinder

π (3²) x 10

= 282.74

Answer:

It would be Angles GFC and EFH.

Think of it like I'm drawing a capital X. Would you consider the top and bottom parts of the X to be the same? Or would you consider the top and left parts to be the same?

The correct answer for this would be that the top and bottom parts of X are the same size. Now, remember that whenever two lines are making an X. this is because the two angles only touch each other in the center point and don't share a side.