A boy 1.2m tall stands 6m away from the foot of a vertical lamp pole 4.2m long. If the lamp is at the tip of the pole, calculate
I. the length of the shadow the boy cast at the lamp
II. angle of elevation of the lamp from the boy correct to the nearest degree.​

Answer:

it would be the ones where there are two lines not touching

Step-by-step explanation:

Francisca prefers less rainfall, she might choose City B, as it generally has fewer rainy days during the two-week period.

Here are the results for the number of rainy days during a two-week period over the past 10 years for the two cities:

City A:

Year 1: 8 rainy days

Year 2: 10 rainy days

Year 3: 7 rainy days

Year 4: 9 rainy days

Year 5: 6 rainy days

Year 6: 10 rainy days

Year 7: 8 rainy days

Year 8: 9 rainy days

Year 9: 7 rainy days

Year 10: 6 rainy days

City B:

Year 1: 4 rainy days

Year 2: 5 rainy days

Year 3: 6 rainy days

Year 4: 4 rainy days

Year 5: 5 rainy days

Year 6: 7 rainy days

Year 7: 3 rainy days

Year 8: 6 rainy days

Year 9: 5 rainy days

Year 10: 4 rainy days

Based on this information, Francisca can compare the number of rainy days between the two cities to make her decision. If she prefers less rainfall, she might choose City B, as it generally has fewer rainy days during the two-week period. However, other factors such as temperature, attractions, or personal preferences may also influence her decision.

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The initial height of the skydiver can be determined by looking at the graph that is 4000ft.  

A slope is a measure of the steepness or incline of a line. It is a ratio of the vertical change to the horizontal change between two points on a line, or surface. It is usually expressed as a ratio, a percentage, or an angle.      

The graph begins at a height of 4000ft, showing that this is the initial height of the skydiver. The graph is a line with a negative slope, indicating that the height is decreasing as time passes. This is due to the acceleration due to gravity, which causes the skydiver to fall at a faster rate. The fact that the line is linear also demonstrates that the rate of acceleration is constant. Therefore, we can conclude that the skydiver’s initial height was 4000ft.

At the initial height of 4000ft, the graph has a value of 0 for time. As time increases, the height decreases, showing that the skydiver has fallen. This is expected, as gravity is always acting on the skydiver, causing them to accelerate downward. The graph shows that the skydiver’s height decreases by 10ft per second of time, indicating that the skydiver is falling at a rate of 10ft/s. Therefore, the initial height of the skydiver can be concluded to be 4000ft.

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The number of each type of coins are as follows:

q = 15 quarters.

d = 30 dimes.

n = 25 nickels.

In order to solve this word problem, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Let d represent the number of dimes.

Let q represent number of quarters.

Let n represent number of nickels.

Let T represent total number of coins.

Note: 1 quarter is equal to 0.25 dollar, 1 nickel is equal to 0.5 dollar, and 1 dime is equal to 0.1 dollar.

Translating the word problem into an algebraic equation, we have;

Dimes; d = 2q     .....equation 1.

Nickels; (70 - (q + 2q)) = (70 - 3q)     .....equation 2.

Total coins; T = n + d + q

0.5(70 - 3q) + 2q(0.1) + q(0.25) = 8.00

Multiplying all through by 100, we have:

5(70 - 3q) + 2q(10) + q(25) = 800

350 - 15q + 20q + 25q = 800

350 + 30q = 800

30q = 800 - 350

30q = 450

q = 450/30

q = 15 quarters.

For the number of dimes, we have:

Dimes, d = 2q

Dimes, d = 2(15)

Dimes, d = 30 dimes.

For the number of nickels, we have:

Nickels, n = (70 - 3q)

Nickels, n = (70 - 3(15))

Nickels, n = (70 - 45)

Nickels, n = 25 nickels.

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Answer:

I don't see any answer options, and the equation doesn't look correct.

I'll assume the equation is meant to be:

Step-by-step explanation:

(2x/5 - 9) = 9

2x/5  = 18

2x  = 90

x = 45

if the modified equation is correct.

Answer:

20

Step-by-step explanation:

Since the triangles are similar, we can use ratios to solve

12        ?

----- = -------

3         5

Using cross product

12*5 = 3?

60 = 3?

Divide each side by 3

60/3 = 3?/3

20 = ?

The unknown side is 20

Answer:

20

Step-by-step explanation:

Since the triangles are similar, all the side lengths can be multiplied by a scale factor,

12/3 = 4, so the scale factor is 4, which

5 x 4 = 20, so the missing side length is 20

Based on the numbers that the decimal contains, and the positioning of the numbers, the number can be found to be 0.54123.

The 0 is in the tens place which means that it is the only number to the left of the decimal point.

The fifth digit to the right of the decimal sign is smaller than the first which means that it cannot be 5.

The number in the thousandth(3rd place) is the smallest number which makes it 1.

The number in the ten thousandths(4th) place is half the value of the number in the hundredths place(2nd) which means that the hundredths number can only be 4 and the ten thousandth number is 2.

The decimal is therefore:
= 0.54123

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Answer:

BC= 5 units

Step-by-step explanation:

Answer:

1. Hush

Step-by-step explanation:

Answer:

The answer should be D.) Desired.

Step-by-step explanation:

The definition of soothing is "having a gently calming effect",

A.) Hush, which in most cases is negative,

B.) Flaming, does not sound gentle OR calming,

B.) Fired usually comes from a negative impact, so your answer MUST and SHOULD be, D.) Desired.

The table has a greater rate of change.

The rates of change are equal.

In the given problem, we have a table showing the relationship between x and y values. By comparing the change in y with the change in x, we can determine the rate of change. Looking at the table, we observe that for every increase of 1 in x, there is a corresponding increase of 1 in y. Therefore, the rate of change for this table is 1.

The slopes are equal.

The equation has a greater slope.

In problem 2, we are given a linear equation in the form y = mx + b, where m represents the slope. The given equation is y = 2x + 7, which means the slope is 2. To compare the rates of change, we compare the slopes. If the slopes are equal, the rates of change are equal. In this case, the slopes are equal to 2, so the rates of change are the same.

The function rule has a greater slope.

The slopes are equal.

In problem 3, we are told that as x increases by 1, y increases by 3. This information gives us the rate of change between x and y. The slope of a function represents the rate of change, and in this case, the slope is 3. Comparing the slopes, we find that they are equal, as both have a value of 3. Therefore, the rates of change are the same.

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Answer:

y=14

Step-by-step explanation:

y+6=20

To find y, you need to isolate y. In order to do this, subtract 6 from both sides.

Answer: 86m cubed

Step-by-step explanation:

The Volume of green house is 54 m³

A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism=Length X Width X Height

A company makes a greenhouse that is shaped like a rectangular prism on bottom and a half cylinder on top.

Given;

Base = 3m x 9m

Height of house = 2 m

Find: Volume of green house

Volume of green house = 3m x 9m x 2m

Volume of green house = 54 m³

Therefore, the Volume of green house is 54 m³

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Answer:

17

Step-by-step explanation:

PLS GIVE BRAINLIEST

Repost your question. Separate your words, variables and numbers correctly. Otherwise, it makes no sense.

Answer:

20

Step-by-step explanation:

We already have our first value 3.4 and the second value 17. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

Step 1 ---> 3.4 = 17% × Y

Step 2 ---> 3.4 = 17/100 × Y

Multiplying both sides by 100 and dividing both sides of the equation by 17 we will arrive at:

Step 3 ---> Y = 3.4 × 100/17

Step 4 ---> Y = 3.4 × 100 ÷ 17

Step 5 ---> Y = 20

Finally, we have found the value of Y which is 20 and that is our answer.

The expression for sin(θ + ϕ), we get sin(θ + ϕ) = (-15 - 8sqrt(24))/85 under the conditions.

Using the trigonometric identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b), we have:

sin(θ + ϕ) = sin(θ)cos(ϕ) + cos(θ)sin(ϕ)

We are given that sin(θ) = 15/17 with θ in Quadrant I, so we can use the Pythagorean identity to find cos(θ):

cos(θ) = sqrt(1 - sin^2(θ)) = sqrt(1 - (15/17)^2) = 8/17

We are also given that cos(ϕ) = -5/5 with ϕ in Quadrant II, so we can use the Pythagorean identity again to find sin(ϕ):

sin(ϕ) = -sqrt(1 - cos^2(ϕ)) = -sqrt(1 - (5/5)^2) = -sqrt(24)/5

Substituting these values into the expression for sin(θ + ϕ), we get:

sin(θ + ϕ) = (15/17)(-5/5) + (8/17)(-sqrt(24)/5) = (-15 - 8sqrt(24))/85

Therefore, sin(θ + ϕ) = (-15 - 8sqrt(24))/85 under the given conditions.

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Answer:

its $375.70

Step-by-step explanation:

i guessed and got it right. good luck guys. love u. remeber to eat n drink water and try to spend some time outside if you can! i know its hard rn but we can do it! im proud of u all

The value of Erica's approximate monthly payment is $375.70. The correct option is C .

Rate of Interest is the rate at which a loan is borrowed or the rate at which an investment gives return .

It is given that

Student Loan Total =  $29,158

Rate of Interest = 9.4 %

Time Period = 10 years

The monthly payment is given by

\(\rm \dfrac{F p(i) }{ ( 1 - ( 1 + i )^{-n})}\)

Substituting the values in the equation

\(\rm = \dfrac{29158* (0.094/12) }{ ( 1 - ( 1 + (0.094/12) )^{-12*10})}\)

= $ 375.70

Therefore,The value of Erica's approximate monthly payment is $375.70. The correct option is C.

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Given:

The circle graph shows how Ann's family budgets a total of $91,000 for the year.

Required:

To find the percentage of utilities, food and transportation.

Explanation:

The percentage of utilities is:

The percentage of food is :

The percentage of transportation is:

Final Answer:

The series in question converges.

If a series converges to a value as its terms approach to infinity, it is said to be convergent. If a series does not converge to a value but instead keeps on rising or dropping as the terms of the series go to infinity, it is said to be divergent.

The geometric sequence is as follows:

10 - 4 + 1.6 - 0.64 +...

If the common ratio of the series is between -1 and 1, then a geometric progression will be convergent.

The common ratio in this case is

r = -4/10

r = -0.4, or -1 -0.4 1.

The presented series is hence convergent.

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In a dataset or graph, outliers are extreme values that greatly deviate from the dominant pattern of values.

In order to identify the outlier, search for a value that is significantly greater or smaller than all the other values. Due to its extreme size compared to all other numbers, the number 267 is an outlier.

a value that "lies outside" (i.e., is significantly smaller or substantially bigger) most of the other values in a set of data For instance, both 3 and 85 in the scores 25, 29, 3, 32, 85, 33, 27 and 28 are "outliers".

A data point that is an outlier in a data graph or dataset you are dealing with is one that is extraordinarily high or extraordinarily low in comparison to the nearest data point and the rest of the nearby coexisting values. Outliers in a dataset or graph are extreme values that stand out significantly from the main pattern of values.

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To find the expected value of the probability distribution, we need to multiply each value by its corresponding probability, then add up the results. So, we have:

0 * 0.3 + 1 * 0.25 + 2 * 0.3 + 3 * 0.15 = 0 + 0.25 + 0.6 + 0.45 = 1.3

Therefore, the expected value of the probability distribution is 1.3.

To find the standard deviation of the probability distribution, we need to use the formula:

σ = sqrt(∑(x-μ)²p)

Where σ is the standard deviation, μ is the expected value, x is each value, and p is its corresponding probability.

So, we have:

σ = sqrt((0-1.3)² * 0.3 + (1-1.3)² * 0.25 + (2-1.3)² * 0.3 + (3-1.3)² * 0.15)

σ = sqrt(0.69 * 0.3 + 0.09 * 0.25 + 0.49 * 0.3 + 1.69 * 0.15)

σ = sqrt(0.207 + 0.0225 + 0.147 + 0.2535)

σ = sqrt(0.63)

σ = 0.79

Therefore, the standard deviation of the probability distribution is 0.79.

the expected value of the probability distribution is 1.3 and the standard deviation is 0.79.

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a. The frequency response of the system is given by \(H(\omega) = \frac{1}{j\omega + 2}\), and its Bode plot is a straight line with a slope of -20 dB/decade and a constant magnitude of 0.5.

b. The Fourier transform of the output Y(omega) is given by Y(omega) = H(omega) X(omega), which simplifies to \(Y(\omega) = \frac{1}{j\omega + 2 - je^{-j\omega t}\omega}\).

To obtain the frequency response, we take the Laplace transform of the differential equation and solve for:

\(\frac{Y(s)}{X(s)}\)

Which gives:

\(H(s) = \frac{1}{s + 2}\)

Substituting s = j*omega gives us the desired frequency response H(omega). The Bode plot of H(omega) is obtained by plotting the magnitude and phase of H(omega) on a logarithmic frequency scale, where the magnitude plot has a slope of -20 dB/decade and a constant magnitude of 0.5.

To obtain this expression, we use the fact that the Fourier transform of \(e^{-t}u(t)\) is  \(\frac{1}{j\omega+1}\), and apply the frequency response obtained in part a.

Finally, we simplify the expression by using the identity:

\(e^{-j\omega t} = \cos(\omega t) - j\sin(\omega t)\)

The resulting expression for Y(omega) can be used to compute the magnitude and phase of the output as a function of frequency.

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Answer:

16

Step-by-step explanation:

since he needs 32 points to get to 75 points,

soo you just dividi the points you need by the points you get by every question since it's 2 for every question you just need half of the question needed to get to 32 points soo divide it by 2 and the answer you get is 16.

The rational model of decision-making is considered prescriptive in that it describes how managers should make decisions, rather than how they actually make them.

The rational model is based on the assumption that decision-makers are rational and will always make the best possible decision based on a careful analysis of all available information.

According to this model, decision-making is a logical, sequential process that involves the following steps: identifying the problem, generating alternative solutions, evaluating the alternatives, selecting the best solution, and implementing and monitoring the chosen solution.

However, in reality, decision-making is often influenced by a variety of cognitive biases, emotions, and other factors that may lead to less than optimal decisions. Therefore, while the rational model provides a useful framework for decision-making, it is important to recognize its limitations and to be aware of the ways in which actual decision-making may deviate from this idealized model.

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Thus, the obtained area of sector for the given circle is found as 43.96 in².

Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle assessment and radius measurement are both crucial for solving circle-related difficulties.

The curved portion that runs along the circle's perimeter and joins the ends of a two radii that make up a sector is known as the sector arc.

given data:

Formula for the area of sector:

area of sector = Ф /360 * (πr²)

area of sector = 140/360 * (3.14 *6²)

area of sector = 7/18 * 3.14 *36

area of sector = 43.96 in²

Thus, the obtained area of sector for the given circle is found as 43.96 in².

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Answer:

75 cm

Step-by-step explanation:

using the conversion

1 m = 100 cm , then

2 m = 2 × 100 cm = 200 cm , then

\(\frac{3}{8}\) of 2 m

= \(\frac{3}{8}\) × 200 cm

= 0.375 × 200 cm

= 75 cm

We get that proportional relationship pass trough (0,0) and has the form of

y=kx. So the answer is

y=4x

Answer:

1−cos2A=43

⟹cos2A=1−43

⟹cos2A=44−3

⟹cos2A=41

⟹sec2A=4

⟹secA=±2

sorry if wrong

The value of angle 1 is 122°.

The value of angle 5 is 58°

The angle of angle 8 is 58°

The angle of angle 14 is 122°

The angle 18 is 58°

It should be noted that this information deals with angles. It should be noted that the value of angle on a straight line is 180°.

In this situation, the value of angle 1 will be:

= 180° - 58°

= 122°

Also it should be noted that vertically opposite angles are equal. Therefore, angle 5 will be 58°.

In this situation, it should also be noted that alternate angles are the same. Hence, Thai gives the value of the angles for angles 8, 14 and 18.

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