Dina has a mass of 50 kilograms and is waiting at the top of a ski slope that’s 5 meters high. the maximum kinetic energy she can reach when she skis to the bottom of the slope is joules. use pe = m × g × h and g = 9.8 m/s2. ignore air resistance and friction.

Answer:

The value of x is 15.75

Explanation:

Given that triangles A and B are similar.

Side lengths of triangle A are: 4.5, 7.0, and 5.25

Side lengths of triangle B are: 13.5, 21.0, and x

Since the triangles are similar, the following ratios are correct:

13.5/4.5 = 21/7 = x/5.25

3 = x/5.25

Multiply both sides of the equation by 5.25

x = 15.75

Measure of other angle is 133 if Two angles form a linear pair. One angle measure is 47° more than the other.

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. A linear pair is a pair of neighboring angles created by the intersection of two lines. 1 and 2 create a linear pair in the illustration. The same holds true for pairs 1, 2, 3, and 4. A linear pair's two angles are always supplementary, which means that the sum of their measurements is 180 degrees.

Given

Two angles form a linear pair.

One angle measure is 47° more than the other.

Other angle be x.

Sum of linear pair is 180.

x + 47 = 180

x = 180 - 47

x = 133

Measure of other angle is 133 if two angles form a linear pair. One angle measure is 47° more than the other.

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Answer:

\(p=11.2\)

Step-by-step explanation:

Given \(2.6(5.5p-12.4)=127.92\), distribute to remove the parentheses:

\(2.6\cdot 5.5p-2.6\cdot 12.4=127.92\)

Simplify:

\(14.3p-32.24=127.92\)

Add 32.24 to both sides:

\(14.3p=160.16\)

Divide both sides by 14.3:

\(p=\frac{160.16}{14.3}=\boxed{11.2}\)

The price that maximizes revenue is p = 120.

The price that maximizes revenue, we need to find the value of price (p) that corresponds to the maximum value of revenue (R). Revenue is calculated by multiplying the quantity (q) sold by the price (p), so we can express revenue as R = p × q.

Given the demand function q = -5p + 1200, we can substitute this expression for q into the revenue equation:

R = p × q

R = p × (-5p + 1200)

To find the price that maximizes revenue, we can take the derivative of the revenue function with respect to price (p), set it equal to zero, and solve for p.

dR/dp = -10p + 1200 = 0

Solving this equation for p:

-10p + 1200 = 0

-10p = -1200

p = -1200 / -10

p = 120

Therefore, the price that maximizes revenue is p = 120.

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The percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is  28.87%.

Given that the carrying capacity is directly proportional to the area, we can write:

C1 ∝ A1 = πr₁²

Since the carrying capacity is directly proportional to the area, we have:

C2 ∝ A2 = πr₂²

To find the percentage increase in diameter, we need to find the ratio of the increased area to the initial area and then express it as a percentage. Let's calculate this ratio:

(A2 - A1) / A1 = (πr₂² - πr₁²) / (πr₁²) = (r₂² - r₁²) / r₁²

We can also express the ratio of the increased carrying capacity to the initial carrying capacity:

(C2 - C1) / C1 = (60 - 36) / 36 = 24 / 36 = 2 / 3

Since the area and the carrying capacity are directly proportional, the ratios should be equal:

(r₂² - r₁²) / r₁² = 2 / 3

Now, let's substitute r = D/2 in the equation:

((D₂/2)² - (D₁/2)²) / (D₁/2)² = 2 / 3

(D₂² - D₁²) / D₁² = 2 / 3

Cross-multiplying:

3(D₂² - D₁²) = 2D₁²

3D₂² - 3D₁² = 2D₁²

3D₂² = 5D₁²

Dividing by D₁²:

3(D₂² / D₁²) = 5

(D₂² / D₁²) = 5 / 3

Taking the square root of both sides:

D₂ / D₁ = √(5/3)

To find the percentage increase in diameter, we subtract 1 from the ratio and express it as a percentage:

Percentage increase = (D₂ / D₁ - 1) × 100

Percentage increase = (√(5/3) - 1) × 100

Percentage increase = 28.87%

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Answer:

20

Step-by-step-explanation

There appears to be 2 lines intersecting eachother, and 150 degrees is on the opposite side to that of the expression. The expression 7x+10 equals a degree, since it is directly opposite to that of the 150 degrees we can use the vertical angles theorem. Although there are no congruent markings for the angles, it is safe to assume that they are congruent to each other with the information given. Vertical angles are angles opposite to each other by 2 intersecting lines. We can write the equation 7x+10=150 for finding x. Now, we solve for x. Inverse operations can be used to subtract 10 by both sides. 150-10=140, 7x=140, to move the x to the other side so that x is alone, we divide by 7 with the inverse operations. Leaving the x alone gives us to what x is, 140/7=20! x=20 Good luck and have a great time

We can use the radical rules to simplify the product 3(4x2). To start, we simplify 4 to its square root, which equals 2. Next, we employ the power property of radicals, which asserts that (a,m) = (a(m/2)), to simplify the cube root (x2) by using it. In this instance, (x2) = x.

We now get 3 * 2 * x, which simplifies to 6x when the simpler terms are combined.The result is that the product 3(4x2) has the simplest form (6x).We can dissect the constituent parts and use the radical-simulation principles to simplify the product 3(4x2).In the beginning, we may reduce the square root of 4 to 2: 3(2x2).Then, since it contains a square (2) and a cube root (), we can reduce them as follows:

3 * 2 * x^(²/³)Taking the square root before the cube root is shown by the exponent 2/3. We may calculate the exponent by reducing it to: 3 * 2 * x(2/3)The terms are then combined when we multiply the coefficients: 6 * x(2/3)As a result, 6x(2/3) is the product of 3(4x2) in its simplest form.

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Answer:

2/5 is the answer man ooooo

Answer:

\(\frac{1}{25}\)

Step-by-step explanation:

So when you have a negative exponent, it means reciprocal.

\(5^{-2}\) will now be \(\frac{1}{5^2}\)

Now find the squared 5. 5 * 5 is 25.

So, your answer is 1/25

Hope this helps !!

-Ketifa

The maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is 1.771 ounces.

The maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight can be calculated using the formula:

Margin of error = Z-score x (population standard deviation / square root of sample size)

Here, the Z-score for a 90% confidence level is 1.645 (obtained from a standard normal distribution table). The population standard deviation is given as 5.7 ounces, and the sample size is 28.

Plugging in these values, we get:

Margin of error = 1.645 x (5.7 / sqrt(28))
= 1.645 x (1.076)
= 1.771

Therefore, the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is 1.771 ounces. This means that we can be 90% confident that the true population mean turtle weight lies within the range of (60 - 1.771) to (60 + 1.771) ounces, or 58.229 to 61.771 ounces.

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The probability of selecting all bottles of the same variety is P(A) = 6/46656 = 0.00013.

The probability of selecting two bottles of each variety when randomly selecting 6 bottles can be calculated using the formula P(A) = n(A) / n(S), where n(A) is the number of possible ways to select two bottles of each variety and n(S) is the total number of possible ways to select 6 bottles. In this case, n(A) is equal to 6! / (2!2!2!) = 90 and n(S) is equal to 6^6 = 46656. So, the probability of selecting two bottles of each variety is P(A) = 90/46656 = 0.0019.

The probability of selecting all bottles of the same variety when randomly selecting 6 bottles can be calculated using the same formula. In this case, n(A) is equal to 6, which is the number of ways to select 6 bottles of the same variety, and n(S) is equal to 46656. So, the probability of selecting all bottles of the same variety is P(A) = 6/46656 = 0.00013.

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Answer: 75 Grapes

Step-by-step explanation:

14 grapes left + 39 grapes Ana ate + 22 grapes Xan ate = Original 75 grapes in the bag

Answer:

There were 75 grapes in the bag before the trip

Step-by-step explanation:

First, you will need to add up all the grapes that they ate.

39+22=61

Then, you need to add the left over grapes and the grapes that both of them ate all together.

61+14=75

So, they had 75 grapes in the bag before the trip.

The probability that at least one child would draw the nickel too small is: P(X ≥ 1) = 1 - P(X = 0).

b) To find the probability that exactly 4 children would draw the nickel too small, we can use the binomial probability formula. The formula is: P(X = k) = (nCk) * (p^k) * (q^(n-k)), where n is the number of trials, k is the number of successes, p is the probability of success, and q is the probability of failure.

In this case, n = 8 (as 8 children are chosen), k = 4 (as exactly 4 children drawing the nickel too small), p = 0.15 (as the probability of a child drawing the nickel too small), and q = 1 - p = 1 - 0.15 = 0.85.

So, the probability that exactly 4 children would draw the nickel too small is: P(X = 4) = (8C4) * (0.15^4) * (0.85^(8-4)).

c) To find the probability that at least one child would draw the nickel too small, we can use the complement rule. The probability of at least one success is equal to 1 minus the probability of no success.

The probability of no success (all children drawing the nickel of the right size) is given by: P(X = 0) = (8C0) * (0.15^0) * (0.85^8).

Therefore, the probability that at least one child would draw the nickel too small is: P(X ≥ 1) = 1 - P(X = 0).

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Answer:

(0,-2)

Step-by-step explanation:

Based on the information about the APR, Andy would pay $878.48 more than Brett.

From the information, Brett and Andy applied for the same credit card from the same bank. The bank checked both of their FICO scores, Brett had an excellent credit rating, and Andy had a poor credit rating. Brett was given a card with an APR of 12.6%. Andy was given a card with an APR of 21.1%.

Brett's finance charge for the year would be $10,449.63 * 12.6%:

= $1320.47.

Andy's finance charge for the year would be $10,449.63 * 21.1%:

= $2198.95.

Andy would pay $2198.95 - $1320.47 = $878.48 more than Brett.

Therefore, Andy would pay $878.48 more than Brett.

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Answer:

14 tests

Step-by-step explanation:

10 1/2 divided by 3/4 s 14 tests

Answer:

14

Step-by-step explanation:

if you set it up as a porportion, 10.5/.75, and you find that in order to make .75 equal to one, you multiply by 1.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333...

10.5*1.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333...=14

Hope I helped.  

The required specific energy increases with increasing depth and the water surface profile will be rapidly varied.

To determine the type of water surface profile for different depths in the rectangular channel, we can use the concept of specific energy and Manning's equation.

The specific energy (E) is given by the equation:
E = y + (V² / (2g)) + (Sf * x)

Given values:
Width of the rectangular channel (b) = 2.45 m
Discharge (Q) = 2.83 m³/sec
Bed slope (Sf) = 0.003
Manning's roughness factor (n) = 0.015

For each depth, we can calculate the velocity (V) using Manning's equation and then determine the specific energy (E) using the equation mentioned above.

Depth 1 (y₁ = 1.52 m):

First, let's calculate the velocity (V₁) using Manning's equation:\(V_1 = (1/n) * (R_1^{2/3}) * (S_f^{(1/2)})\)

The hydraulic radius (R₁) can be calculated as:
R₁ = (b * y₁) / (b + 2y₁) = (2.45 * 1.52) / (2.45 + 2 * 1.52) ≈ 0.678 m

Substituting the values
\(V_1= (1/0.015) * (0.678 ^{2/3}) * (0.003^{1/2})\) ≈ 2.81 m/s

Now, let's calculate the specific energy (E₁) using the equation:
E₁ = y₁ + (V₁² / (2g)) + (Sf * x)

Substituting the values:
E₁ = 1.52 + (2.976² / (2 * 9.81)) + (0.003 * x)

The above expression shows, the specific energy increases with increasing depth, and the water surface profile will be rapidly varied.

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Given question is incomplete, the complete question is:
2.45-m wide rectangular channel with a discharge of 2.83 m³/sec. has a bed slope of 0.003 and Manning's roughness factor of 0.015. What is the type of water surface profile for depths of 1.52 m, whether it is rapidly varied or not?

b) h = \(tan \theta\)  x 17 is the required equation.

c) The height of the streetlight is 20.4 ft.

The height of the person is 6 ft.

The distance at which the person is standing from the streetlight = 12 ft.

The distance at which the person's shadow appears = 5ft.

a) Hence, we can make the following diagram.

The right triangle below gives a visual representation of the problem. It shows the known quantities and a variable 'h' to indicate the height of the streetlight.

b) Let's now find an equation trigonometric function involving the unknown quantity 'h'.

from the below diagram, we can say that,

\(tan \theta\) = h/base

base= 12+5=17

hence we have, \(tan \theta\) = h/17

h = \(tan \theta\)  x 17 is the required equation.

c) Now we have to find the height of the streetlight.

firstly let's find the value of \(\theta\),

\(\theta\) = tan 6/5.

\(tan^{-1}\)(6/5) = 50.2°

hence, tan 50.2 = h/17

                   1.20 = h/17

                         h= 1.20 x 17

                         h= 20.4 ft.

Hence, the height of the streetlight is 20.4 ft.

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Answer

I think it would be -6 but im not sure

Explanation

I looked at google and i think it is this.

Answer:

When a figure is scaled by a scale factor greater than 1, the copy is larger than the original. When the scale factor is less than 1, the copy is smaller. This means that triangles and are scaled copies of each other.

Step-by-step explanation:

We accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

We have given: μ = 14, x bar = 16, n = 40, s = 6,  α = 5%, = 0.05

To test μ0 : μ = 14   Vs  H1: μ > 14

Test statistics = (X bar - μx)√n / sx = (2 x 6.3245) / 6 = 2.1081

So, P value = 0.021

Conclusion: There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

P value for the hypothesis test

n = 50, x bar = 420, sx = 81, μ = 400,

To test:  H0: μ 400    Vs   H1:  μ > 400

It is right tail test

Test statistics =  (X bar - μx)√n / sx = (420 - 400) √50 / 81 =

z = 1.7459

P value = 0.04093

Declsion: We reject H0 is p value < α

Here α = 0.05

Hence P value < α

Conclusion: We accert H1 alternative that is result is population mean greater than 400.

Hence, we accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

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Answer:

D. Square

It is the only one with all right angles and sides the same length

Answer:

=69

=69+66

=135

-unequal

-dependent

Answer:

christian closest-0.5 is the distance he traveled which is less than 8 and 6

Step-by-step explanation:

Freddie is the fastest because christian travles .1 miles every 2 minutes being the slowest  and .8 is greater than .66666

Answer:

a. Christian

b. Freddie

Step-by-step explanation:

a.

y = mx + b

m is the slope. It represents the speed of walking.

b is the y-intercept. It represents the distance from the school at time 0. Time 0 is when a person leaves his home, so the higher b is the farther from the school the person lives.

Freddie: y = -0.8x + 8

b = 8

Freddie lives 8 miles from school.

Christian: (0, 0.5); b = 0.5

Christian lives 0.5 miles from school.

Trevor: (0, 6) from the graph. b = 6; Trevor lives 6 miles from school.

a. Answer: Christian

b.

Each slope is the speed.

Freddie: m = -0.8

Christian: m = (0.4 - 0.5)/(2 - 0) = -0.1/2 = -0.05

Trevor: m = rise/run = -2/3 = -0.666...

The fastest speed is the slope with the highest absolute value.

b. Answer: Freddie

Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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Answer:

B. Decreasing

Step-by-step explanation:

From the table, we can see that as variable x increases, variable y decreases relatively.

If the data points are plotted on a scatter plot, the trend line would be sloping downwards from our left to our right. This shows that the trend line is decreasing because the sloping downwards from the left to the right shows implies a decrease.

Answer:

The first one

because 8 - 3 = 5 and is not less than it

hope this helps :)

Step-by-step explanation:

The system of linear equation of the line are y=2x-5 when (2,-1) is a solution of the first equation but not for the second equation.

Given that,

We have to find the system of linear equation in which (2,-1) is a solution of the first equation but not for the second equation and (5,5) is a solution for system of equation.

We know that,

To find the system of equation we have a formula that is

y=mx-mx₁+y₂

Here m is slope

m=-1-5/2-5

m=-6/-3

m=2

The equation is

y=2x-2(5)+5

y=2x-10+5

y=2x-5

Therefore, The system of linear equation of the line are y=2x-5 when (2,-1) is a solution of the first equation but not for the second equation.

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Answer:

see explanation

Step-by-step explanation:

Given

2x + 3y = 4 ( subtract 2x from both sides )

3y = - 2x + 4 ( divide all terms by 3 )

y = - \(\frac{2}{3}\) x + \(\frac{4}{3}\)

To determine if the point (2, 1) lies on the line, substitute x = 2 into the right side of the equation and if the value obtained equals the y- coordinate of the point then it lies on the line.

y = - \(\frac{4}{3}\) + \(\frac{4}{3}\) = 0 ≠ 1

Ths (2, 1) does not lie on the line

The value of x in the intersecting chords MO and OL is determined as 12.1.

The value of x is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

arc ML = 2 x m∠MOL

From the diagram, we have, m∠MOL = 60⁰

The value of x is calculated as follows;

arc ML = 2 x m∠MOL

12x - 25 = 2 (60)

12x - 25 = 120

12x = 120 + 25

12x = 145

x = 145/12

x = 12.1

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Answer:$60.94

Step-by-step explanation:

49.87+11.07(the total of tax plus tip)=60.94