Solve for x
Your answer must be simplified
-3 < x - 10

Answer:

70 ft

Step-by-step explanation:

To find the height of the building, we can use the trigonometric relationship between the angle of elevation, the distance from the object, and the height of the object.

In this case, we have a right triangle formed by the observer, the top of the building, and the base of the building. Therefore, we can use the tangent trigonometric ratio, since the height of the building is the opposite the angle of elevation, and the distance between the observer and the building is the side adjacent the angle.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]

Let "x" be the height of the building.

Let "d" be the initial distance from the observer to the building.

The angle of elevation changes from 15° to 30° as the observer advances 140 feet toward the building.

(See the attachment for a visual representation).

Based on this information, we can set up the following equations:

[tex]\tan 15^{\circ}=\dfrac{x}{d}[/tex]

[tex]\tan 30^{\circ}=\dfrac{x}{d-140}[/tex]

Rearrange both equations to isolate d:

[tex]d=\dfrac{x}{\tan 15^{\circ}}[/tex]

[tex]d=\dfrac{x}{\tan 30^{\circ}}+140[/tex]

Solve this system of equations by the method of substitution.

[tex]\dfrac{x}{\tan 15^{\circ}}=\dfrac{x}{\tan 30^{\circ}}+140[/tex]

[tex]\dfrac{x}{\tan 15^{\circ}}-\dfrac{x}{\tan 30^{\circ}}=140[/tex]

[tex]\dfrac{x\tan 30^{\circ}-x \tan 15^{\circ}}{\tan 30^{\circ}\tan 15^{\circ}}=140[/tex]

[tex]\dfrac{x(\tan 30^{\circ}- \tan 15^{\circ})}{\tan 30^{\circ}\tan 15^{\circ}}=140[/tex]

[tex]x=\dfrac{140\tan 30^{\circ}\tan 15^{\circ}}{\tan 30^{\circ}- \tan 15^{\circ}}[/tex]

[tex]x=\dfrac{140\cdot \frac{\sqrt{3}}{3}(2-\sqrt{3})}{\frac{\sqrt{3}}{3}- (2-\sqrt{3})}[/tex]

[tex]x=\dfrac{\dfrac{140(2\sqrt{3}-3)}{3}}{\dfrac{4\sqrt{3}-6}{3}}[/tex]

[tex]x=\dfrac{140(2\sqrt{3}-3)}{2(2\sqrt{3}-3)}[/tex]

[tex]x=\dfrac{140}{2}[/tex]

[tex]x=70[/tex]

Therefore, the height of the building is exactly 70 feet.

Answer:

percentage = 528/ 3,300*100= 16%

Step-by-step explanation:From the pie chart we can see that saving are 528 dollars, so

now we need to calculate total from the given pie chart, which is

3,300 dollars. So percentage is savings( 528 dollars) divided by total( 3,300 dollars) and then finally multiply by 100

Answer: B

Step-by-step explanation:

Answer:

B. 81 / 100

Step-by-step explanation:

9 / 11 = 0.82

81 / 100 = 0.81

8 / 9 = 0.89

80 / 99 = 0.80

Hope this helps! :)

Answer:

3:2

Step-by-step explanation:

60,636.048 people are french speakers when the population is 5,053,004 and only 1.2% are the french speakers.

Percentages are basically fractions with a denominator of 100. We use the percent symbol (%) beside a number to indicate that it is a percentage. A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is one hundredth part; thus, 100 percent represents the entire amount.

To manually calculate percentages, follow these steps:

1. Determine the number's initial format to be converted to a percentage.

The decimal or fraction format of the number to be converted to a percentage can be used. The next mathematical process to be performed on the number will be determined by the initial format.

2. Perform a mathematical calculation on the number to be converted to a percentage.

If the number to be converted to a percentage is a decimal number, such as 0.57, you may not need to proceed to the next step.

3. Multiply the result by 100.

To convert a decimal number, such as 0.57, to a percentage, simply multiply it by 100.

here we need to calculate 1.2% of 5053004

(1.2*5053004)\100

=60636.048

60636.048 people speak french in the country with population of 5053004.

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One of the terms equals 0.85, so do the other two:

sample size

proportion

probability

How can sample size be determined?

to calculate the sample size in five easy steps

Calculating sample size requires knowledge of or estimation of three or four factors:

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write out the given data for Team A

STEP 2: Find the mean

Hence, the mean of the data for production team A is 37375

Answer:

x = 3

Step-by-step explanation:

x + .12x = 3.36  Combine like terms

1.12x = 3.36  Divide both sides of the equation by 1.12

x = 3

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

Work Shown:

12% = 12/100 = 0.12

x + 12% of x = x + 0.12x = 1.12x = 3.36

1.12x = 3.36

x = 3.36/1.12

x = 3

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

Check:

12% of 3 = 0.12*3 = 0.36

x + 12% of x = 3 + 12% of 3 = 3 + 0.36 = 3.36

Or you could say 1.12x = 1.12*3 = 3.36

The answer is confirmed.

Answer:

VD; DV

Step-by-step explanation:

you can name the line in two ways

VD or DV

they are the two endpoints of the line

they are the same line

Answer: 3x^2−3x

Step-by-step explanation:

1.) Distribution

2.) Combine like Terms

3.) Combine like Terms.. again

4.) Common Factor

5.) GET UR SOLUTION!!

The average number of customers contacted each day is 13. We used the basic average method which is explained below.

The formula for calculating the average is:

Sum of all the observations ÷ Total number of observations

So, according to the formula

Sum of all the observations = People contacted on (Monday+ tuesday+wednesday+thursday+friday)

= 15+12+14+11+13

= 65

Number of observations = 5

So putting values in the formula, we get

65÷5

= 13

Hence, the average number of customers contacted is 13.

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The length of the unknown side of the triangle using similar triangle ratio concept is; x = 24

We want to find the length of the unknown side of the similar triangles.

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. Thus, we can say that if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

From the given triangle ADE which is divide into a similar triangle ABC with an unknown side x, we can use the concept of similar triangle ratios to get the unknown value of x as;

6/x = 8/(x + 8)

Cross multiply to get;

6(x + 8) = 8x

6x + 48 = 8x

8x - 6x = 48

2x = 48

x = 48/2

x = 24

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The value of x (hypotenuse) using the Pythagorean Theorem is 5 units.

So, the formula of the Pythagorean Theorem:

Where a (AC) = 4 and b (CB) = 3 as the given figure is symmetric and so line CB will be equal to 3.

Now,

Therefore, the value of x using the Pythagorean Theorem is 5 units.

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The most appropriate choice for probability will be given by-

Probability of not getting two cans of coke is  [tex]\frac{49}{52}[/tex]

What is probability?

Probability of an event is the chance of occurance of that event.

Probability is calculated by Number of favourable outcomes divided by total number of outcomes

Here,

Number of lemonades in a cooler = 16

Number of sprite in a cooler = 5

Number of cans coke in a cooler = 10

Number of cans of root beers in a cooler = 9

Total number of refreshments = 16 + 5 + 10 + 9

                                                  = 40

Probability of getting a can of coke in the first draw = [tex]\frac{10}{40}[/tex]

                                                                                       = [tex]\frac{1}{4}[/tex]

Probability of getting a can of coke in the second draw = [tex]\frac{9}{39}[/tex]

                                                                                              = [tex]\frac{3}{13}[/tex]

Probability of getting two cans of coke in the two draws = [tex]\frac{1}{4} \times \frac{3}{13}[/tex]

                                                                                              = [tex]\frac{3}{52}[/tex]

Probabilty of not getting two cans of coke in the two draws = [tex]1-\frac{3}{52}[/tex]

                                                                                                   = [tex]\frac{52-3}{52}[/tex]

                                                                                                   = [tex]\frac{49}{52}[/tex]

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Using equation;

The monthly payment is 67.5 dollars

The hours of labour that is required to replace the water pump is 4 hours

The purchase of the large TV including finance charges is 1615 dollars . A down payment of 400 dollars was paid. The remainder was paid in 18 monthly instalment payment.

Therefore, using equation,

let

x = amount paid each month

The monthly payment can be found as follows:

1615 = 400 + 18x

1615 - 400 = 18x

1215  = 18x

divide both sides by 18

x = 1215 / 18

x = 67.5 dollars

Therefore,

monthly payment = 67.5 dollars

The cost of replacing a water pump was 465 dollars. This include 145 dollars for water pump plus 80 dollars per hour for labour .

The number of hours for labour that was used to replace the water pump can be calculated as follows:

Using equation,

465 = 145 + 80h

where

h = number of hours for labour

465 - 145 = 80h

320 = 80h

h = 320 / 80

h = 4 hours

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Answer:

Approximately $18 each month.

Step-by-step explanation:

This is quite simple. So, we know that there are 12 months in a year. And we know that in a year, the store has given out discounts totaling up to $216. All we have to do is divide the total number by how many months there are in a year.

[tex]216\div12=18[/tex]

This means that the store gives out $18 of discounts per month.

(Also, you don't seem college level)

The distance between the point (-1,0) and (7,6) is 10.

Distance between the points:

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by

d=√((x2 – x1)² + (y2 – y1)²).

Given,

(−1,0) and (7,6).

Here we need to find the distance between these points.

Apply the values on the formula , in order to solve it,

d = √(7 - (-1))² + (6 - 0)²

When we simplify it, then we get,

d = √(7 + 1)² + (6)²

d = √(8)² + 36

d = √64 + 36

d = √100

d = 10

Therefore, the distance is 10.

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Answer:

Step-by-step explanation:

−2x−y−2z−4x−2y+3z

Combine −2x and −4x to get −6x.

−6x−y−2z−2y+3z

Combine −y and −2y to get −3y.

−6x−3y−2z+3z

Combine −2z and 3z to get z.

−6x−3y+z

DIFFERENTIATE W.R.T. X

−6

hello

to solve this problem, we need the formula of length of an arc

t find the value of angle JM, we should take into cognizance that the sum of angles in a circle is equal to 360 degree and angle on a straight line is equal to 180 degree

now we know the value of angle jm, let's find the length of the radius

with all the necessary informations or data required, we can now proceed to solve for the length of arc jm

from the calculations above, the length of the arc is equals to 12.87 miles

Answer:

12.9

Step-by-step explanation:

Answer:

6 pieces of candy will be left.

Step-by-step explanation:

45×2 = 90

20×3 = 60 +

15×4 = 60

Ttl. of candies= 210

Candies ÷ people

210 ÷ 12 = 17.5

17-12= 5.5 (round to the tenth) 5.5-> 6

210-6= 204

you'll get 6 as the difference which is your answer.

Becca works for the Humane Society and had to buy food for the dogs. She bought 5 1/2 pounds of dog food. She feeds each dog about one-third of a pound. How many dogs can she feed? ​

_______________________________________________________

Food ÷ amount of food per dog

5 1/2 pounds of dog food ÷ 1/3

5 1/2 ÷ 1/3 = (10/2 +1/2) ÷ 1/3 = 11/2 ÷ 1/3 = 11/2 x 3/1 = 33/ 2

33/ 2 = 16 1/5 = 16.5

_______________________________________

Can you see the updates?

___________________________________

Answer

She can feed 16.5 (16) dogs with 5 1/2 pounds of dog food

_________________________________________

Do you have any questions regarding the solution?

The correct connections for AC will be option b) AB+3.7 = 1.5. Two expressions joined by the equals symbol ("=") form an equation.

Hence, The correct connections for AC will be option b) AB+3.7 = 1.5.

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Value of x is 16/91

How to Find value of x  ?

In question

(8/7)/(13/9) = x / (2/9)

72/91 =x/(2/9)

182* (72/91) = 182* (x/(2/9))

2 *72 = 819 * x

144 = 819 * x

(144/819) = 819 *x / 819

X = 16/91

The value of x is 16/91

Definition of Fraction :

There are in total six types of fractions such as:

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Using the binomial distribution, the probabilities are given as follows:

1) Three girls in a family of five children: 0.3125 = 31.25%.

2) At least two boys in a family of seven children: 0.9375 = 93.75%.

3) Total of 15 when four dice are thrown:  0.1080 = 10.80%.

4) At least two left-handed people in a group of 7: 0.1497 = 14.97%.

5) At least five of them have the same birth date: 0%.

The formula for the probability of x successes is:

[tex]P(X = x) = C(n,x).p^{x}.(1-p)^{n-x}[/tex]

[tex]C(n,x) = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

A children is equally as likely to be a boy or a girl, hence the parameters are given as follows:

n = 5, p = 0.5.

The probability is P(X = 3), hence:

P(X = 3) = C(5, 3) x (0.5)³ x (0.5)² = 0.3125 = 31.25%.

The parameters are:

n = 7, p = 0.5.

The probability of at least two boys is:

P(X >= 2) = 1 - P(X < 2).

In which:

P(X < 2) = P(X = 0) + P(X = 1).

Then:

This one is simple probability, number of desired outcomes divided by the number of total outcomes.

When 4 dice are thrown, we have that:

Hence the probability is:

p = 140/(6^4) = 0.1080 = 10.80%.

The parameters are:

n = 7, p = 0.1.

Hence, similarly to item 2:

The parameters are:

n = 75, p = 1/365 = 0.0027.

Then the probability is:

P(X >=5) = 1 - P(X < 5).

In which:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).

Using a calculator, it is found that P(X < 5) = 1, hence the probability is of 0%, as P(X >=5) = 1 - 1 = 0.

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If the bank deposit paying simple interest grew from an initial amount of $1100 to $1265 in 6 months, then the interest rate is 30%

The initial amount = $1100

The  final amount = $1265

So simple interest = 1265-1100

= $165

Time period = 6 months = 6/12 years

We know

Simple interest I = P×r×t

Where P is the initial amount

r is the interest rate

t is the time period

Substitute the values in the equation

165 = 1100×r×(6/12)

165 = 550×r

r = 165/550

r = 0.3

r = 30%

Hence, If the bank deposit paying simple interest grew from an initial amount of $1100 to $1265 in 6 months, then the interest rate is 30%

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I am going to draw a picture to ilustrate the solution

Now, we are going to use the trigonometric functions for the right triangle on the left to calculate h

Now we use the formula for the area of a triangle