Substitute the values into the appropriate formula and solve for x.

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.

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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Answer:

[tex]\textsf{1.} \quad 4x \leq 25[/tex]

[tex]\textsf{2.} \quad x \leq 6.25[/tex]

3.  See attachment.

Step-by-step explanation:

Given information:

If the baseballs cost $4 each and x is the number of baseballs, then 4x represents the total cost of the baseballs.

The maximum amount of money available to spend on the baseballs is $25.

Therefore, the inequality to represent this is:

[tex]\large\boxed{4x \leq 25}[/tex]

Solve the inequality by dividing both sides by 4:

[tex]\implies \dfrac{4x}{4} \leq \dfrac{25}{4}[/tex]

[tex]\implies x \leq 6.25[/tex]

Note:  As x represents the number of baseballs you can buy, and as you cannot buy part of a baseball or negative baseballs, the real solution is 0 ≤ x ≤ 6.

To graph  x ≤ 6.25  on a number line:

To graph  0 ≤ x ≤ 6  on a number line:

Answer:

Average Rate of Change

Functions are relationships that exist between two variables. Graphing them allows us to observe and predict their behavior. The graph of a function is a line or curve where we can determine random values directly and identify a set of results through it.

The rate of change is one of the calculations we can determine from a graph. It is the change of the function per unit. It is deriving from the slope of the line formed in the interval. The formula for determining the rate of change is:

r

c

=

y

2

−

y

1

x

2

−

x

1

P

1

=

(

−

1

,

0

)

P

2

=

(

3

,

12

)

We use the average exchange rate formula:

r

c

=

y

2

−

y

1

x

2

−

x

1

We substitute the values, obtaining:

r

c

=

12

−

0

3

−

(

−

1

)

Solving, we obtain:

r

c

=

12

4

=

3

The average rate of change of

g

when

x

varies from

−

1

to

3

is:

R

c

=

3

The equation that can be used to determine the price, in dollars, of any watermelon based on the number of pounds is p = 0.7w

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the price of a watermelon that weights 9.3 pounds is $6.51, the cost per pound of watermelon will be:

= $6.51 / 9.3

= $0.7

Therefore, the equation is p = (0.7 × w) = 0.7w

where P = price

w = pound of watermelon

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Answer:

Step-by-step explanation:

[tex]2\sqrt{35[/tex]

The experimental probability that the next man to walk by will have a beard is 2/3

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

Men with beard = 4

Men without beard = 2

This means that

P(Beard) = Beard/Total

Substitute the known values in the above equation, so, we have the following representation

P(Beard) = 4/6

Simplify

P(Beard) = 2/3

Hence the probability is 2/3

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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: 75 degrees

Step-by-step explanation:

For a taxable income of $1,80,900, the effective tax rate is 21.11%.

Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.

Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.

To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.

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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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By setting up the equation and solving and simplifying  the equation, the possible number of hours Frank can trim tree is 5.43 hours, round off the hour that will be 6 hours.

Algebraic simplification is the process of rewriting an algebraic expression in a simpler form, without changing its value.

An algebraic expression is a combination of numbers, variables, and arithmetic operations that can be evaluated to a specific numerical value.

let the required number of hours be h,

so setting up the equation,

7h + 9 = 47

Then we can subtract 9 from both sides to isolate h:

7h + 9 - 9 = 47 - 9

7h = 38

Dividing both sides by 7 gives us:

7h/7 = 38/7

h = 5.43

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The algebraic expression is [tex]\frac{7}{10}m-\frac{1}{3}m+2m[/tex] = [tex]\frac{71m}{30}[/tex]

What do you mean by an algebraic expression?

Algebraic expression is the idea of ​​using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here. An algebraic expression can be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor.

Given expression:

[tex]\frac{7}{10}m-\frac{1}{3}m+2m[/tex]

= [tex]\frac{21m-10m+60m}{30}[/tex]

= [tex]\frac{71m}{30}[/tex]

Therefore, [tex]\frac{7}{10}m-\frac{1}{3}m+2m[/tex] = [tex]\frac{71m}{30}[/tex]

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The expression for the situation regarding the wedding singer is 15 + 60x.

The independent variable is the travel expense.

The dependent variable is the amount per hours.

It ie important to note that an expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Let the number of hours be x

Since the wedding singer is paid $60 per hour plus $15 for travel expenses, the expression will be:

= 15 + (60 × x)

= 15 + 60x

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The least to greatest or increasing order of the given data set will be 0.1375,0.25,5/8,11/16 thus, option (C) is correct.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given data set,

The value of 5/8 = 0.625 and 11/16 = 0.6875

Thus, 0.1375 < 0.25 < 5/8 < 11/16

Hence "The least to greatest or increasing order of the given data set will be 0.1375,0.25,5/8,11/16".

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Her commission rate is 7.44%.

What is commission rate?

The payment that is either a fixed amount or a percentage of a sale is the commission rate. When they make a sale, people in commission-based professions like insurance brokers, real estate agents, and car salespeople are compensated.

The parameters given are;

The amount Mary earns annually = $28,000

The amount Mary grossed during a week = $658.00

The amount Mary had sold during the week to make the amount grossed during the week = $1673.19

Given that Mary makes $28,000 per year

Therefore;

The amount Mary earns per week = Amount earned per year/52

The amount Mary earns per week =  $28,000/52 = $538.46

The amount extra she made on commission = $658.00- $538.46= $119.54

The commission rate = Commission earned/(Amount of merchandise sold)×100

The commission rate = 119.54/1673.19 × 100 = 7.14%

Her commission rate = 7.44%

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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]

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: yes you can.

Step-by-step explanation:

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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The possible ways a basketball team could score 24 points, without making any free throws are given below.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Three types of points:

Free throws - 1 point

2 - points.

3 - points.

Now,

The different ways to have a score of 24 points without making any free throws.

Case 1:

2 x 12 = 24 points.

Case 2:

3 x 8 = 24 points.

Case 3:

2 x 6 = 12 and 3 x 4 = 12

12 + 12 = 24 points.

Case 4:

2 x 9 = 18 and 3 x 2 = 6

18 + 6 = 24 points

Case 5:

2 x 3 = 6 and 3 x 6 = 18

6 + 18 = 24 points

Similarly, we can have many possible ways.

We have to make sure that the points add to 24 points.

Thus,

The possible ways a basketball team could score 24 points, without making any free throws are given above.

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Answer:

The different ways to have a score of 24 points without making any free throws.

Case 1:

2 x 12 = 24 points.

Case 2:

3 x 8 = 24 points.

Case 3:

2 x 6 = 12 and 3 x 4 = 12

12 + 12 = 24 points.

Case 4:

2 x 9 = 18 and 3 x 2 = 6

18 + 6 = 24 points

Case 5:

2 x 3 = 6 and 3 x 6 = 18

6 + 18 = 24 points

Step-by-step explanation:

Because i know

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 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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Answer:

idek

Step-by-step explanation:

Answer:

Juliana uses 1/2 amount of sugar

Emiliano uses 3/2 amount of sugar

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.

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.