Find the area of the triangle below.

Using trigonometry and the tangent function, the height of the taller building, with a 42˚ angle of elevation from the smaller 32-foot building 35 feet away, is calculated to be approximately 63.514 feet. The formula tan(42˚) = (h₂ - 32) / 35 is utilized where tan(42˚) ≈ 0.9004. Solving this equation gives the height of the taller building.

The question asks: Two buildings are 35 feet apart. The elevation angle from the top of the smaller building to the top of the taller building is 42˚. The smaller building is 32 feet high. Find the height of the taller building.

To solve this problem, we will use trigonometry, specifically the tangent function, which relates an angle of a right triangle to the ratio of the opposite side to the adjacent side.

Let's denote the height of the smaller building as h₁ = 32 feet, the height of the taller building as h₂, and the horizontal distance between the buildings as 35 feet. The elevation angle from the top of the smaller building to the top of the taller building is 42˚.

First, we determine the difference in height (Δh) between the two buildings:

→ tan(θ) = opposite/adjacent

In this case:

→ tan(42˚) = (h₂ - h₁) / 35

We solve for the height difference:

→ (h₂- 32) = tan(42˚) * 35

Using a calculator to find tan(42˚):

→ tan(42˚) ≈ 0.9004

Substituting the value:

→ (h₂ - 32) = 0.9004 * 35

→ h₂ - 32 ≈ 31.514

Adding 32 to both sides:

→ h₂ ≈ 31.514 + 32

→ h₂ ≈ 63.514

Therefore, the height of the taller building is approximately 63.514 feet.

Answer:

18.84 km

Step-by-step explanation:

The formula for the circumference is 2πr. 6.28*3=18.84

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Final answer:

The circumference of the circle is approximately 18.84 kilometers.

Explanation:

The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle.

In this case, the radius of the circle is given as 3 kilometers.

So, the circumference of the circle is C = 2π(3) = 6π kilometers.

To find a numerical approximation for π, we can use the value 3.14.

Therefore, the circumference of the circle is approximately C = 6(3.14) = 18.84 kilometers. This calculation demonstrates a practical method to assess the distance around a circle based on its radius, providing a tangible measurement for the circle's outer boundary in a real-world context.

Answer:

The air is 38 degrees colder.

Step-by-step explanation:

To solve for this we must understand "key words" to understand which operation we are doing. The words in this are "how much colder" this signifies we must do subtraction.

33 - (-5) = 38.

The air is 38 degrees colder.

Answer:

Yes. parallel lines are known to have the same slope, but perpendicular lines will always have negative-reciprocal slopes.

This holds true for all lines that are not vertical or horizontal

This holds true for all lines that are not vertical or horizontal. A horizontal line has a slope of 0, and a vertical line has an undefined slope. These lines are perpendicular, but the rule of negative reciprocals does not apply because you cannot divide by zero.

Let’s prove that the product of the slopes of two perpendicular lines is -1.

Let’s consider two lines, Line 1 and Line 2, that are perpendicular to each other.

Line 1: Let’s say the slope of Line 1 is m1.

Line 2: Now, let’s consider Line 2 which is perpendicular to Line 1. Let’s say the slope of Line 2 is m2.

Since Line 1 and Line 2 are perpendicular, the angle between them is 90 degrees. Now, the tangent of the angle between two lines is equal to the absolute difference of their slopes divided by 1 plus the product of their slopes.

tan(90) = |m1 - m2| / (1 + m1*m2)

But we know that tan(90) is undefined, which implies that the denominator of the right side of the equation must be zero.

So, 1 + m1*m2 = 0, which implies that m1*m2 = -1.

Therefore, we have proved that the product of the slopes of two perpendicular lines is -1.

Answer:

12 1/2

Step-by-step explanation:

Answer:

the answer is -3

Step-by-step explanation:

To find the z-score corresponding to a blood pressure reading, you would use the formula:
[ z =fraction{(X -mu)}{sigma}]

where:
- \( X \) is the value for which you're calculating the z-score,
- \( \mu \) is the mean of the population, and
- \( \sigma \) is the standard deviation of the population.
Given the values from the question:
- \( X = 77 \) (the blood pressure score for which we're finding the z-score),
- \( \mu = 122 \) (the mean systolic blood pressure reading),
- \( \sigma = 15 \) (the standard deviation of the systolic blood pressure readings).
Now we can plug these values into the formula:
[ z = \fraction{(77 - 122)}{15} \]
[ z = \fraction{-45}{15} \]

[ z = -3 \]
So, the z-score corresponding to the blood pressure reading of 77 is -3. This means that a reading of 77 is 3 standard deviations below the mean systolic blood pressure reading for customers at the gym franchise.

=============================================================

Explanation:

For now, focus solely on the orange boxplot. The first quartile Q1 is the left edge of the box, which is at 3.5; while the value of Q3 is 7.5 (right edge of the box). The interquarile range (IQR) is ...

IQR = Q3 - Q1

IQR = 7.5 - 3.5

IQR = 4

This is basically the width of the box. Ignore the whiskers when it comes to the IQR.

Let A = 4 as we'll use it later.

---------------------------------

Find the IQR for the blue box plot

Q1 = 6 = left edge of the blue box

Q3 = 9.5 = right edge of the blue box

IQR = Q3 - Q1

IQR = 9.5 - 6

IQR = 3.5

Let B = 3.5 as we'll use it later

---------------------------------

Subtract the values of A and B to find the difference of the IQR values

A - B = 4 - 3.5 = 0.5

Answer:

no you are definetly not allowed

Step-by-step explanation:

because if you dont have a brain you are certainly not educated

Answer:

What type of question is that?

Brainly is a platform where students and other educators gain knowledge while distributing old knowledge to people who need it. If you don't have a brain then I don't know what to tell you but get some help.

Answer:

The perimeter of the quarter-circle is 200 cm.

Step-by-step explanation:

Given that the angle of quarter-circle is 90°. So using Length of Arc formula, you are able to find the length of curve :

[tex]arc = \frac{θ}{360} \times 2 \: \pi \: r[/tex]

Let r be radius = 56 cm,

Let θ = 90°

[tex]arc = \frac{90}{360} \times 2 \times\pi \times 56[/tex]

[tex] = \frac{1}{4} \times 2 \times \pi \times 56[/tex]

[tex] = \frac{1}{2} \times \pi \times 56[/tex]

[tex] = 28\pi \: cm[/tex]

We have already found the arc. Next we have to add up together to find the perimeter :

[tex]p = 56 + 56 + 28\pi[/tex]

[tex]p = 112 + 28\pi[/tex]

[tex]p = 200 \: cm \: (3s.f)[/tex]

Answer:

You can divide a circle into smaller portions. A part of a circle is called an arc and an arc is named according to its angle. Arcs are divided into minor arcs (0° < v < 180°), major arcs (180° < v < 360°) and semicircles (v = 180°). When diameters intersect at the central of the circle they form central angles.

Step-by-step explanation:

Answer:

You can divide a circle into smaller portions. A part of a circle is called an arc and an arc is named according to its angle. Arcs are divided into minor arcs (0° < v < 180°), major arcs (180° < v < 360°) and semicircles (v = 180°). When diameters intersect at the central of the circle they form central angles.Arc Of A Circle. The arc of a circle is a portion of the circumference of a circle. Measure an arc by two methods: 1) the measure of the central angle or 2) the length of the arc itself.

Step-by-step explanation:

(happy to help)

Answer:

The MAD is: 2

Step-by-step explanation:

First, you add all the terms together. So we get 49.

Then, we divide 49 by the amount of terms. There are 7 terms, so we do 49/7.

We get 7. Now we have to find out the distance between each point and the mean, which is seven.

Now, we add all the distances together. We get 14.

Now, we divide 14 by the amount of terms, which is 7. 14/7 is 2.

The answer is b.

The correct option is b. The mean absolute deviation of the data set is 2.

To find the mean absolute deviation (MAD) of the data set [tex]\(\{8, 5, 12, 4, 5, 8, 7\}\)[/tex], follow these steps:

1. Calculate the mean (average) of the data set.

[tex]\text{Mean} = \frac{\sum \text{data points}}{\text{number of data points}} \\\\\text{Mean} = \frac{8 + 5 + 12 + 4 + 5 + 8 + 7}{7} = \frac{49}{7} = 7[/tex]

2. Find the absolute deviations from the mean for each data point.

[tex]|8 - 7| &= 1 \\|5 - 7| &= 2 \\|12 - 7| &= 5 \\|4 - 7| &= 3 \\|5 - 7| &= 2 \\|8 - 7| &= 1 \\|7 - 7| &= 0 \\[/tex]

3. Calculate the mean of these absolute deviations.

[tex]\text{Mean Absolute Deviation} = \frac{\sum \text{absolute deviations}}{\text{number of data points}} \\\\\text{Mean Absolute Deviation} = \frac{1 + 2 + 5 + 3 + 2 + 1 + 0}{7} = \frac{14}{7} = 2[/tex]

So, the mean absolute deviation of the data set is: b. 2

Answer:

5.2

Step-by-step explanation:

Answer:

5.2

Step-by-step explanation:

just did it

Answer:

Biological weathering is the actual molecular breakdown of minerals. There are things called lichens (combinations of fungi and algae) which live on rocks. Lichens slowly eat away at the surface of rocks. The amount of biological activity that breaks down minerals depends on how much life is in that area

Step-by-step explanation:

Answer:

390

Step-by-step explanation:

99+98+97+96=390

Answer:

394

Step-by-step explanation:

The largest number is 100 since it says none greater than 100.  We can have 100

The next number is 99 since it is not equal to 100 and is the next largest number

The next number is 98 since it is not equal to 100 or 99 and is the next largest number

The last number is 97 since it is not equal to 100 or 99 or 98 and is the next largest number

The sum of the 4 numbers is

100+99+98+97 =394

Answer: B.  −4(3n+5)

Step-by-step explanation:

Factor out the common term 4.

−4(3n+5)

Answer:

???

Step-by-step explanation:

I don’t know the answer, sorry. I made this post on accident.

here is the graph for anyone needing it and the answer is C

Answer:

a more b same c less d same

Step-by-step explanation:

his per pound is 75 cents

Ed charges $3.75 for 5 pounds of cabbage, which makes his unit rate $0.75 per pound. To compare his unit rate with other farmers, calculate each of their unit rates and compare them to Ed's. Farmers work with a "going rate" like most agricultural markets, which reflects the competitive nature of the industry.

To determine whether the unit rate charged for cabbage by other farmers is less than, equal to, or greater than the unit rate charged by Ed, it is necessary to calculate Ed's unit rate first. Ed charges $3.75 for 5 pounds of cabbage, which means the unit rate is $3.75 ÷ 5 pounds = $0.75 per pound.

Once we have Ed's unit rate, we can compare it with the rates provided by other farmers. Without the rates from other farmers included in the question, the specific comparison cannot be completed. However, if another farmer is charging a different price for a quantity of cabbage, you would calculate their unit rate the same way and compare it to Ed's $0.75 per pound. If the unit rate of another farmer is less than $0.75, then they charge less than Ed. If it is greater than $0.75, they charge more than Ed. If it is equal to $0.75, then they charge the same as Ed.

Understanding unit rates is crucial as it helps consumers make informed decisions and ensures that farmers like Ed maintain competitiveness within the market, similar to the conditions agricultural growers face. Farmers generally adhere to a "going rate", which represents a price point that is influenced by supply and demand within a competitive market.

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Answer:

b = 3

Step-by-step explanation:

All you need to do is subtract 3 from both sides, like so:

6 = 3 + b

-3  -3

________

3 = b

Answer:

B = 3

Step-by-step explanation:

6  =  3 + b, subtract the 3 from 6

6 - 3 = b

3 = b

Answer:

2137 kg

Step-by-step explanation:

The number of fish the fisherman harvest in the first five days is

512 kg.

Given,

A fisherman harvested 350 kg of fish on Monday.

From Monday to Friday, the amount of fishes, be harvested increased by

10% per day.

We need to find the total amount of fish the fisherman harvest in the

first five days.

Round your answer to the nearest whole number.

We multiply the required percentage with the given amount.

Example:

10% of 500 = 10/100 x 500 = 10 x 5 = 50

We have,

Each day 10% increases.

Monday:

350 kg of fishes

Tuesday:

350 x 10%

= 350 x 10/100

=350 x 1/10

= 35

The number of fishes:

= 350 + 35

= 385 kg

Wednesday:

385 x 10%

= 385 x 1/10

= 38.5

The number of fishes:

= 385 + 38.5

= 423.5 kg

Thursday:

423.5 x 10%

= 423.5 x 1/10

= 42.35

The number of fishes:

= 423.5 + 42.35

= 465.85 kg

Friday:

465.85 x 10%

= 465.85 x 1/10

= 46.585

The number of fishes:

= 465.85 + 46.585

= 512.435 kg

Rounding to the nearest whole number we get,

= 512 kg

Thus the number of fish the fisherman harvest in the first five days is

512 kg.

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Answer:

D

Step-by-step explanation:

Given that the segment is an angle bisector then the ratio of sides and base are equal, that is

[tex]\frac{10}{4}[/tex] = [tex]\frac{18}{x}[/tex] ( cross- multiply )

10x = 72 ( divide both sides by 10 )

x = 7.2 → D

Answer:

260

Step-by-step explanation:

divide 3,648 by 14

this equals 260.57

Because he is putting the same amount of candy in each bag, you would round down. He is not going to put a fraction of candy in a bag so he would be able to make 260 bags with some candy left over.

Therefore, Mr. Fox was able to make 260 treat bags with 14 pieces of candy in each.

To solve the problem, we need to determine how many treat bags of 14 pieces each can be made from 3,648 candies. This is a simple division problem where the total number of candies is divided by the number of candies per treat bag.

Here is the step-by-step solution:

1. Start with the total number of candies Mr. Fox has, which is 3,648.

2. Determine the number of candies per treat bag, which is given as 14.

3. Divide the total number of candies by the number of candies per treat bag to find out how many treat bags can be made.

4. Perform the division: [tex]\( \frac{3,648}{14} = 260 \)[/tex].

Mr. Fox was able to make 260 treat bags.

Answer:

B. 0.602%

Step-by-step explanation:

Probability is essentially (# times specific event will occur) / (# times general event will occur). Here, we have a few specific events: draw a quarter, draw a second quarter, draw a penny, and draw another penny. The general event will just be the number of coins there are to choose from.

The probability that the first draw is a quarter will be 4 / (4 + 8 + 9) = 4/21.

Since we've drawn one now, there's only 21 - 1 = 20 total coins left. The probability of drawing a second quarter is: (4 - 1) / (21 - 1) = 3/20.

The probability of drawing a penny is: 9 / (20 - 1) = 9/19.

The probability of drawing a second penny is: (9 - 1) / (19 - 1) = 8/18.

Multiply these four probabilities together:

(4/21) * (3/20) * (9/19) * (8/18) = 864 / 143640 ≈ 0.602%

The answer is B.

Answer:

0.602%

Step-by-step explanation:

Total coins:

8+9+4 = 21

Quarter, Quarter, Penny, Penny:

4/21 × 3/20 × 9/19 × 8/18

4/665 × 100

0.6015037584%

Answer:

500 x 0.8 = 400 would be your answer

Step-by-step explanation:

The answer is 5500 meters.

i.e. 5500 meters is shorter than 6 km.

Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind.

Here, we have,

6 kilometers=6000m.

because, 1 kilometer=1000 meters

6000>5500

Hence,  5500 meters is shorter than 6 km.

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Answer:

9.83

Step-by-step explanation:

x2 + 4x- 59 = 0 +59

x2 + 4x = 59

6x=59

6x/6 = 59/6

x=9.83

Answer:

B

Step-by-step explanation:

Answer:

I'm positive that the

answer is B 8

Answer:

b=-3

Step-by-step explanation:

Let's solve your equation step-by-step.

−11b+7=40

Step 1: Subtract 7 from both sides.

−11b+7−7=40−7

−11b=33

Step 2: Divide both sides by -11.

−11b /−11 = 33 /−11

b=−3

Answer:

The correct answer is b=(-3)

Step-by-step explanation:

First you subtract 7 from both sides and you willl get -11b=33. Then you divide both sides by -11 and you will get b=33/-11. Then you simplifty your answer and you will get b=(-3).

                              ^^Hope this helps!^^