find the measure of each angle indicated​

To find the distance from the ranger's station to the forest fire, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of depression to the forest fire, the height of the ranger's station above the ground, and the distance from the ranger's station to the forest fire to form a right triangle.

We can then use the tangent function to find the distance from the ranger's station to the forest fire as follows:

tan(35°) = opposite/adjacent

opposite = tan(35°) * adjacent

opposite = tan(35°) * 100 feet

opposite = 0.7392 * 100 feet

opposite = 73.92 feet

Therefore, the distance from the ranger's station to the forest fire is approximately 74 feet. To the nearest tenth of a foot, this is 73.9 feet.

The value of the composite function is (hog)(x) = 3x²- 13.

What is a composition function?

Function composition is an operation used in mathematics that takes two functions, f, and g, and creates a function, h = gof, such that h(x) = g. The function g is applied in this operation on the outcome of applying the function f to x.

The functions are g(x)=x²-5 and h(x) = 3x + 2

The composition function (hog)(x) can be written as (hog)(x) =h(g(x))

Putting g(x)=x²-5 in (hog)(x) =h(g(x)):

(hog)(x) =h(x²-5)

Now putting x= (x²-5) in h(x) = 3x + 2:

h(x²-5) = 3(x² - 5) + 2

h(x²-5) = 3x² - 15 + 2

h(x²-5) = 3x² - 13

Therefore (hog)(x) = 3x² - 13.

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By using proportionality, it can be calculated that-

a) Constant of proportionality that relates the length of paver in the model and the actual length is k = [tex]\frac{4}{3}[/tex]

[tex]y = \frac{4}{3}x[/tex] is the required equation which relates the length of paver in the model and the actual length of the paver

b) Area of the rectangle = [tex]\frac{1}{3}[/tex] sq.feet

Constant of proportionality that relates the area of paver in the model and the actual area is k = [tex]\frac{9}{16}[/tex]

What is proportionality?

Suppose there are two quantities. Proportionality indicates that if there is a change in the value of one quantity, the value of other quantity also changes but maintaining a constant ratio

Proportionality can be direct or inverse

Direct proportion

Two quantities are said to be in direct proportion if on increasing the value of one quantity, the value of other quantity also increases and vice versa.

For example cost of a commodity and quantity of a commodity are in direct proportion

Inverse proportion

Two quantities are said to be in inverse proportion if on increasing the value of one quantity, the value of other quantity decreases and vice versa.

For example Number of men and number of days taken by those men to complete a job.

Length of paver in the model = [tex]\frac{2}{3}[/tex] ft

Actual length of paver = [tex]\frac{1}{2}[/tex] ft

Let the constant of proportionality be k

[tex]\frac{2}{3} = \frac{1}{2}k[/tex]

k = [tex]\frac{2}{3} \div \frac{1}{2}[/tex]

k = [tex]\frac{4}{3}[/tex]

Let y be the length of paver in the model and x is the actual length

[tex]y = \frac{4}{3}x[/tex] is the required equation which relates the length of paver in the model and the actual length of the paver

b) Area of the model = [tex]\frac{1}{2}\times \frac{3}{8} = \frac{3}{16}[/tex] sq. feet

Actual area = [tex]\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}[/tex] sq.feet

Let the constant of proportionality be l

[tex]\frac{3}{16} = \frac{1}{3}l[/tex]

l = [tex]\frac{3 \times 3}{16}\\[/tex]

l = [tex]\frac{9}{16}[/tex]

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The intrest will be X=1293000/79057.

Interest is the price of  you pay to borrow money or it is  cost you charge to lend money.

Based on the given condition we know that

{P=14374

{R=3.3%

{I=7758

Formulate and substitute

Substitute {P=14374

                 {R=3.3%

                 {I=7758

These are into formula I=Prt

7758=14374rt

We have to solve the equation

14374×0.033x=7758

Multiply

474.342x=7758

Devide both sides

X = 7758/474.342

By calculating we can get

X =1293000/79057

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Answer:m,m,

Step-by-step explanation:

Answer:

Zeros:

Step-by-step explanation:

Given quadratic polynomial:

[tex]x^2+x -20[/tex]

The zeros of a function f(x) are the x-values that satisfy the equation f(x)=0.  

Therefore, to find the zeros of the given function, set it to zero and solve for x.

Factor the quadratic:

[tex]\implies x^2+x-20=0[/tex]

[tex]\implies x^2+5x-4x-20=0[/tex]

[tex]\implies x(x+5)-4(x+5)=0[/tex]

[tex]\implies (x-4)(x+5)=0[/tex]

[tex]\boxed{\begin{minipage}{8.4 cm}\underline{Zero Product Property}\\\\If $a \cdot b = 0$ then either $a = 0$ or $b = 0$ (or both).\\\end{minipage}}[/tex]

Apply the Zero Product Property:

[tex]\implies x-4=0 \implies x=4[/tex]

[tex]\implies x+5=0 \implies x=-5[/tex]

Therefore, the zeros of the given quadratic polynomial are:

Answer: You should add the equation

Step-by-step explanation: I see here that you already have perfect 3x and -3x, so the best way is to add them and eliminate the x to find the y first and then put the y back in the equation and solve for the x!

If you can, please give me a Brainliest, I only need one more to become an Ace, thank you!

The situation which can be used to represent the dot plot is "Henry has 15 classmates and each has between 0 and 6 pets".

The correct answer option is option C

A dot plot graph is a graph plotted by using small spots to represent data.

Henry has 15 classmates and each has between 0 and 6 pets

Each dot represent a pet

Consequently, the dot plot represent Henry's situation of having 15 classmates and each has between 0 and 6 pets

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1a

f is inversely proportional to d² so when d is d f=10N and when d is doubled F is 5/2N

1bi K=Fd²

1bii

since K=fd² when d is 3cm and F is 2N k=18

then when d=5

F is 18/25N

Answer:

  see below

Step-by-step explanation:

You want examples of use of the rules of logarithms:

  [tex]\begin{array}{ll}\vphantom{\dfrac{M}{gN}}1.&\log_b{(MN)}=\log_b{(M)}+\log_b{(N)}\\2.&\log_b{\left(\dfrac{M}{N}\right)}=\log_b{(M)}-\log_b{(N)}\\\vphantom{\dfrac{b}{g}}3.&\log_b{(M^a)}=a\cdot\log_b{(M)}\end{array}[/tex]

The point of these is that M and N and 'a' and 'b' can be anything. (Generally, 'b' will be a positive number greater than 1.) For the purpose here, we can let M ∈ {x^3y, (1+r)}, N ∈ {(x-4), r/n}, a ∈ {4, -3}, b ∈ {2, e}.

Using these values in various combinations, your examples could be ...

  [tex]\log_2{((x^3y)(x-4))}=\log_2{(x^3y)}+\log_2{(x-4)}\\\\\ln{((1+r)(r/n))}=\ln{(1+r)}+\ln{(r/n)}\\\\ \log_2{((x^3y)(r/n))}=\log_2{(x^3y)}+\log_2{(r/n)}[/tex]

  [tex]\log_2{\left(\dfrac{x^3y}{x-4}\right)}=\log_2{(x^3y)}-\log_2{(x-4)}\\\\\\\ln{\left(\dfrac{1+r}{r/n}\right)}=\ln{(1+r)}-(\ln{(r)}-\ln{(n)})\\\\\\ \log_2{\left(\dfrac{x^3y}{r/n}\right)}=\log_2{(x^3y)}-(\log_2{(r)}-\log_2{(n)})}[/tex]

  [tex]\ln{(x^3y)^4}=4\ln(x^3y)=4(3\ln{(x)}+\ln{(y)}=12\ln{(x)}+4\ln{(y)}\\\\\log_2{(1+r)^{-3}}=-3\log_2{(1+r)}\\\\\log_2{(x^3y)^{-3}}=-3\log_2{(x^3y)}=-9\log_2{(x)}-3\log_2{(y)}[/tex]

Answer:

$337.50

Step-by-step explanation:

To find the total cost of the uniforms, you will need to find the unit price of the shirts and the unit price of the shorts and then multiply each by the number of shirts and shorts, respectively.

The unit price of the shirts is the total cost divided by the number of shirts, or $180 / 15 shirts = 12/shirt.

The unit price of the shorts is

$12/shirt - $1.50/shirt = 10.5/shirt.

Since the coach bought the same number of shirts and shorts, the total number of shirts and shorts is 15 shirts + 15 shorts = 30 shirts and shorts.

The total cost of the shirts is $12/shirt * 15 shirts = $12*15 = 180.

The total cost of the shorts is $10.5/shirt * 15 shirts = 157.5

The total cost of the uniforms is the sum of the cost of the shirts and the cost of the shorts, or $180 + 157.5= 337.5.

Therefore, the total cost of the uniforms for the team is $337.5.

The reason for why the confidence intervals help researchers attain their purpose of using a sample to understand a population is given below .

In the question ,

we have been asked how does the confidence interval help researchers to attain the purpose of using a sample to understand a population ,

we know that , the confidence interval is calculated from an estimate of how far away our sample mean is from actual population mean .

the confidence interval are useful because ,

(i) by calculating the confidence intervals around any data we collect, we have additional information about the likely values we are trying to estimate .

(ii) they make data analyses richer and help us to make more informed decisions about the research questions .

Therefore , the reason how confidence interval helps is mentioned above.

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Answer:

the slope is 0.5 or 1/2

Step-by-step explanation:

3x - 6y = 90

-6y = -3x + 90

y = 0.5x + 90

Answer:

slope= 1/2

Step-by-step explanation:

3x-6y=90

rewrite the equation into slope intercept form

y=1/2x-15

subtracting is the same as adding the opposites

y=1/2x+(-15)

since the equation is written in slope intercept form, y=mx+b, identify the slope of the line as the coefficient next to the variable x

y=1/2x+(-15), m=1/2

identify the y intercept of the lines as the constant term

y=1/2x+(-15),m(slope)=1/2,b=-15

Theoretical Probability because its what should happen but experimental is what happens

What is Probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

it is binomial probability p=3/15 = 1/5 = 0.2

or at the very least geometric

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Answer:

Step-by-step explanation:

d

Answer:

d

Step-by-stedp explanation:

The inequality best represents the possible ways the team can score more than 60 points.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that, the Mid-High JV Team is playing in the state championship for football.

In order to beat their all-time points in a season record, they need to score more than 60 points in the game.

Considering a field goal (f) scores 3 points, a touchdown (t) scores 6 points, and a touchdown with an extra point (p) scores 7 points.

We need to find the inequality best represents the possible ways the team can score more than 60 points.

3f+6t+7p>60

Hence, 3f+6t+7p>60 is the inequality best represents the possible ways the team can score more than 60 points.

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According to the intermediate value theorem, every continuous function is a Darboux function.

Given that,
To discuss, what is Intermediate Value Theorem.

Darboux's theorem asserts that for a function f(x) that is differentiable on the domain [a, b], there exists some point c on the open interval (a, b) such that f′(c).

Here,
The intermediate value theorem is defined as that if the function is a continuous function over a domain [a, b] with domain values f(a) and f(b) at the interval's endpoints, then the function takes any value between f(a) and f(b) at any point inside the range.

Thus, According to the intermediate value theorem, every continuous function is a Darboux function.

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Answer:

DF= 16m

JH= 14m

GJ= 19m

Step-by-step explanation:

turn the triangles until they overlap each other

since they are congruent, the measure of one angle will be the same for the other one

Answer:

DF= 16m    JH= 14m     GJ = 19m

Step-by-step explanation:

We know the two figures are equal to each other. So to find the missing sides just refer to the other figure with the included side.

Answer: 75 degrees

Step-by-step explanation:

Answer:

65 sq.inches

Step-by-step explanation:

To find the total surface area of a box, you need to calculate the area of each of its faces and add them together. In this case, the box has three faces with dimensions 5 inches by 7 inches, and three faces with dimensions 5 inches by 3 inches.

The total surface area of the box is therefore:

(5 * 7) * 2 + (5 * 3) * 2 = 35 + 30 = 65 square inches

This means that you will need 65 square inches of gift wrap to cover the box.

Hope this helps you

Answer: 142 squared inches of gift wrap

Step-by-step explanation:

To find how many square inches of gift wrap you would need, you would use the formula for the surface area of the box (rectangle)

Now plug the numbers in from the  given dimensions

Now solve...

Giving you the answer of 142 squared inches of gift wrap

Hope this is correct and helpful! ^^

By cross multiplication, the result for each pair of rational numbers are listed below:

Cross multiplication is a property involving multiplication and division between the terms of two rational numbers of the form:

a / b = c / d

Where a, b, c, d are real numbers. Combinations between a numerator and a denominator are multiplications and combinations between two numerators and two denominators are divisions. Now we proceed to solve on each case:

Case 11

4 / x = 2 / 7

4 · 7 = 2 · x

28 = 2 · x

x = 14

Case 12

19 / 10 = x / 12

19 · 12 = 10 · x

228 = 10 · x

x = 114 / 5

Case 13

(x - 1) / 6 = 13 / 19

(x - 1) · 19 = 13 · 6

(x - 1) · 19 = 78

x - 1 = 78 / 19

x = 1 + 78 / 19

x = 97 / 19

Case 14

5 / 17 = 19 / (x + 4)

5 · (x + 4) = 19 · 17

x + 4 = 323 / 5

x = 318 / 5

Case 15

10 / (2 · x - 9) = 20 / 9

10 · 9 = 20 · (2 · x - 9)

90 / 20 = 2 · x - 9

27 / 2 = 2 · x

27 / 4 = x

x = 27 / 4

Case 16

12 / 18 = (3 · x + 4) / 15

2 / 3 = (3 · x + 4) / 15

10 = 3 · x + 4

3 · x = 6

x = 2

Case 17

(x - 20) / 3 = (x - 11) / 18

18 · (x - 20) = 3 · (x - 11)

18 · x - 360 = 3 · x - 33

15 · x = 327

x = 109 / 5

Case 18

6 / (x + 16) = 7 / (3 · x + 3)

6 · (3 · x + 3) = 7 · (x + 16)

18 · x + 18 = 7 · x + 112

11 · x = 94

x = 94 / 11

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Answer: yes you can.

Step-by-step explanation:

The greatest possible integer that could be in this set is 43.

The group of 15 different integers in this instance has a range of 25 and a median of 25. The greatest value that can be entered will be limited by that range.

With a median of 25, we can deduce that 7 numbers fall within the range of 25 and above, and 7 numbers fall within this range.

We must increase the smallest value in order to increase the largest value. Here's how to accomplish it:

18 19 20 21 22 23 24 25

With 18 as the lowest value and a range of 25, 43 would be the highest value.

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Answer:

8

Step-by-step explanation:

The number 80 is called the numerator or dividend, and the number 9 is called the denominator or divisor.

The quotient (integer division) of 80/9 equals 8; the remainder (“left over”) is 8.

80 is the dividend, and 9 is the divisor.

The values of a and b in the expression x³ + ax³ + bx - 3 are a = 1 and b = -17

From the question, we have the following parameters that can be used in our computation:

x^3+ax^3+bx-3

Rewrite properly

So, we have

x³ + ax³ + bx - 3

The expression has a factor of x - 3

This means that

(3)³ + a(3)³ + b(3) - 3 = 0

So, we have

27 + 27a + 3b - 3 = 0

Evaluate the like terms

27a + 3b = -24

Divide by 3

9a + b = -8

The expression has a remainder of 15 when divided by x + 2

This means that

(-2)³ + a(-2)³ + b(-2) - 3 = 15

So, we have

-8 - 8a - 2b - 3 = 15

Evaluate the like terms

-8a - 2b = 26

Divide by -2

4a + b = -13

So, we have

9a + b = -8

4a + b = -13

Subtract the equations

5a = 5

Divide

a = 1

Recall that 4a + b = -13

So, we have

4(1) + b = -13

So, we have

b = -13 - 4

Evaluate

b = -17

Hence, the values are 1 and -17

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Answer:

  MN = 50

Step-by-step explanation:

You want the length of the base segment MN in triangle MNO, where MN is marked 41+3x and parallel midsegment PQ is marked 49-8x.

The midsegment is half the length of the parallel base segment. That means the base segment is double the length of the midsegment:

  MN = 2·PQ

  41 +3x = 2(49 -8x)

  41 +3x = 98 -16x

  19x = 57 . . . . . . . . add 16x-41

  x = 3

  MN = 41 +3x = 41 +3·3 = 50

The length of MN is 50 units.