what are the real solutions

Final answer:

To calculate the length of the shadow cast by a 28-foot tree, we use proportional relationships, which yield a shadow length of approximately 11.2 feet.

Explanation:

Shadow Length Calculation

To find the length of the shadow cast by a 28-foot tree, we can use the concept of similar triangles. The relationship between the height of an object and the length of its shadow is proportional provided the sun's rays are coming at the same angle.

In this case, a 30-foot tree casts a 12-foot shadow.

We can set up a proportion to compare the two trees to find the unknown shadow length for the 28-foot tree.

Let's set up the proportion: Since the shadows are proportional to their respective tree heights, we can express this as follows:

(Shadow length of 28-foot tree) / 28 feet = 12 feet / 30 feet

By cross-multiplying and solving for the unknown shadow length, we would get:

Performing this calculation:

So, a 28-foot tree will cast a shadow that is approximately 11.2 feet long.

The correct answer is that the length of the shadow cast by a 28-foot tree is 11.2 feet.

To solve this problem, we can use the concept of similar triangles. The tree and its shadow form a right-angled triangle with the ground, and the angle of elevation of the sun is the same for both trees. Therefore, the triangles formed by the trees and their respective shadows are similar.

Let's denote the height of the first tree as [tex]\( h_1 = 30 \)[/tex] feet, the length of its shadow as [tex]\( s_1 = 12 \)[/tex] feet, the height of the second tree as [tex]\( h_2 = 28 \)[/tex] feet, and the length of its shadow as [tex]\( s_2 \)[/tex], which we want to find.

Since the triangles are similar, the ratios of the corresponding sides are equal:

[tex]\[ \frac{h_1}{s_1} = \frac{h_2}{s_2} \][/tex]

Substituting the known values:

[tex]\[ \frac{30}{12} = \frac{28}{s_2} \][/tex]

Now, we solve for [tex]\( s_2 \)[/tex] :

[tex]\[ s_2 = \frac{28 \times 12}{30} \][/tex]

[tex]\[ s_2 = \frac{336}{30} \][/tex]

[tex]\[ s_2 = 11.2 \][/tex]

-10 = -b/4

to get b multiply both sides by 4

-10 *4 = -40

since b already has the negative sign the 40 would be positive

 so b = 40

Mean annual growth rate in the asset’s value over the nine years is -3.8856%.

Given that an asset declines in value from $5000 to 3500 over the nine years.

To determine the mean growth rate over some period of time, compute the geometric mean of the growth factors. A growth factor less than one indicate negative growth.

The formula for the geometric mean over n periods is given by

[tex]y_n =\sqrt[n]{ {y_1 \times y_2 \times y_3 \times ......\times y_n}}[/tex]

Suppose an asset declined over nine years.

[tex]3500 = 5000\times({y_1 \times y_2\times y_3 \times ..\times y_9})[/tex]

[tex]{y_1 \times y_2\times y_3 \times ..\times y_9} = 3500/5000\\\ y_1 \times y_2\times y_3 \times ..\times y_9} = 0.7[/tex]

Then, the mean annual growth factor over these nine years is,

[tex]y_9 = \sqrt[9]{0.7}[/tex]

= 0.961144

Compute the mean annual growth rate in the asset’s value.

= (0.961144 - 1) 100%

= -3.8856%

Therefore, the mean annual growth rate in the asset’s value is -3.8856%.

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To find the mean annual growth rate of an asset declining from $5000 to $3500 over 9 years, you calculate the growth rate 'r' using the formula P(t) = P0 * e^(rt). The result is about -5.13%, indicating a depreciation in the asset's value.

To calculate the mean annual growth rate for an asset that declines in value, we can use the formula for the annual growth rate, which is P(t) = P0 * e(rt), where:

In this case, the value of the asset declines from $5000 to $3500 over 9 years. Therefore, we have:

First, we need to solve for r in the equation:

3500 = 5000 * e(9r)

By dividing both sides by 5000 and taking the natural logarithm, we get:

ln(3500/5000) = ln(e(9r))

ln(0.7) = 9r

r = ln(0.7)/9

Substitute the value of ln(0.7) and divide by 9:

r = -0.0512932942

Since the result is negative, it indicates a decline, and the annual growth rate is about -5.13%, reflecting a decrease in value.

Step-by-step explanation:

John always wears a shirt, pants, socks, and shoes. He owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts.

For example If John has 2 pants and 3 shirts

he make an combination of 1 pant with 3 shirts

and another pant with 3 shirts

so total of 6 combination he can make (2*3)= 6

To find the number of combination we multiply all the shirt, pants, socks, and shoes he have

12pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts.

12 * 3 * 5 * 5 = 900

So 900 different combination John can make

Combination helps us to find a number of ways. The number of ways John can wear an outfit is 900.

A combination helps us to find the number of ways something can be selected from a set. It is given by the formula,

[tex]^nC_r = \dfrac{n!}{r!(n-r) ! }[/tex]

where n is the total number of choices in the set, r is the number of choices we want.

Given to us

Number of pairs of socks = 12

Number of pairs of shoes = 3

Number of pants = 5

Number of shirts = 5

The number of ways John can wear an outfit can be found out using the combination of shirt, socks, pants, and shoes. Therefore,

Number of ways John can wear an outfit

= Number of ways John wears shocks x Number of ways John wears shoes x Number of ways John wears pants x Number of ways John wears a shirt

Number of ways John can wear an outfit

[tex]= ^{12}C_1 \times ^{3}C_1 \times ^{5}C_1 \times ^{5}C_1 \\[/tex]

= 900

Hence, the number of ways John can wear an outfit is 900.

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The cumulative distribution function (CDF) of u(n), when u(n) is the maximum of n independent uniformly-distributed random variables, is given by x^n. After standardization, as n approaches infinity, the CDF of the standardized variable converges to a standard normal distribution, as per the central limit theorem.

The subject matter relates to the field of statistics, specifically dealing with the concept of uniform distribution and standard normal distribution.

Let's denote the random variables as X1, X2, ..., Xn and they are uniformly distributed over [0, 1].Given that u(n) is the maximum of these random variables, the cumulative distribution function (CDF) of u(n) can be calculated as follows:

P(u(n) < x) = P(X1 < x, X2 < x, ..., Xn < x) = P(X1 < x) * P(X2 < x) * ... * P(Xn < x) = x^n

Given that Z = (u(n) - μ) / σ where μ is the mean and σ is the standard deviation. For the uniform distribution, μ = 0.5 and σ = √ (b - a)² / 12 = √1 / 12. Therefore, the standardized random variable Z can be calculated.

By the central limit theorem, as n increases, the standardized variable tends to a limiting value. Which means as n -> ∞ , the cumulative distribution function of Z = 1, the standardized variable converts to a standard normal distribution, and it poses bell-shaped curve form.

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A graph of the linear function y+2=3/2(x+4) is shown in the image attached below.

In Mathematics and Euclidean Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Based on the information provided about the graph of this line, we can reasonably infer and logically deduce that an equation or linear function that models it can be written as follows;

y - y₁ = m(x - x₁)

y+2=3/2(x+4)

y+2=3/2(0+4)

y(0) = 4

Next, we would use an online graphing tool to plot the given linear function for the values in its domain using table, as shown in the graph attached below.

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Answer:

The answer is C. Hope this helps.

Step-by-step explanation:

Answer:

B

C

E

Step-by-step explanation:

One-half bc sin60⁰

One-half a squared sin60⁰ ; if the two opposite sides posses the same parameters.

Start Fraction ab sin60⁰ Over 2 End Fraction

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

A triangle with equal angle and equal sides. The sum of an angle in a triangle is 180⁰  this implies that each angles have 60⁰

The area rule of triangle:

It states that the area of any triangle is equal to half the product of the lengths of the two sides of the triangle, multiplied by the sine of the angle.

Therefore, there are three options that defines the expressions to represent the area of triangle ABC:

One-half bc sin60⁰

One-half a squared sin60⁰ ; if the two opposite sides posses the same parameters.

Start Fraction ab sin60⁰ Over 2 End Fraction

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first step sum means addition so (12x+9y) +(-2y) = 12x +7y

second step subtract (4x -3y) from (12x+7y) 

need to use the distributive property:

12x +7y - 4x - -3y = 

12x + 7y - 4x +3y

 combine like terms

8x+10y

Answer has been edited.

Answer:

Subtract (4x − 3y) from the sum of (12x + 9y) and (−2y) is 8x + 10y .

Step-by-step explanation:

As given the expression

(12x + 9y) , (-2y) and (4x − 3y) .

First add the expression (12x + 9y) and (-2y) .

= (12x + 9y) - (2y)

First open the bracket

= 12x + 9y - 2y

= 12x + 7y

Now subtracted (4x − 3y) from 12x + 7y .

=  12x + 7y - (4x - 3y)

= 12x - 4x + 7y + 3y

= 8x + 10y

Therefore the Subtract (4x − 3y) from the sum of (12x + 9y) and (−2y) is 8x + 10y .

The total number of ways can first, second and third place can be assigned are:

                          6840

The total number of people that compete are: 20

Out of these 20 people we have to chose 3 people and also arrange them according to their ranks.

We know that when we have to choose and  arrange r items out of total n items then we need to use the method of permutation.

Hence, the formula is given by:

[tex]n_P_r=\dfrac{n!}{(n-r)!}[/tex]

Here we have:

n=20 and r=3

Hence, the number of ways first, second and third place can be assigned are:

[tex]{20}_P_3=\dfrac{20!}{(20-3)!}\\\\\\{20}_P_3=\dfrac{20!}{17!}\\\\\\{20}_P_3=\dfrac{20\times 19\times 18\times 17!}{17!}\\\\\\{20}_P_3=20\times 19\times 18\\\\\\{20}_P_3=6840[/tex]

         Hence, the answer is:

                 6840

Answer:

The correct answer is

1. 6,840

2. 342

3. 18

At a gymnastics meet, twenty gymnasts compete for first, second, and third place.

The only graph with a slope of 4/5 is;

Graph 2

The slope of the graph is simply rise divided by run or defined as the change in y-coordinates divided by the corresponding change in x-coordinate.

Thus; m = (y₂ - y₁)/(x₂ - x₁)

Graph 1; Let us pick two coordinates;

(1, 2) and (2, 3)

m = (3 - 2)/(2 - 1)

m = 1

Graph 2; Let us pick two coordinates;

(-1, 1 ) and (4, 5)

m = (5 - 1)/(4 - (-1))

m = 4/5

Graph 3; Let us pick two coordinates;

(-2,0) and (3, 2)

m = (2 - 0)/(3 - (-2))

m = 2/5

Graph 4; Let us pick two coordinates;

(1, 1) and (4, 5)

m = (5 - 1)/(4 - 1)

m = 4/3

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