A 25 foot tall flagpole casts a 42 foot shadow. What is the angle the sun hits the flagpole?

Using the given radius we know that the length of the line BR is 6.5 units.

A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of such line segments.

The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."

The radius of a circle is the separation between its center and circumference.

Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.

So, according to the given image:

SP is the perpendicular bisector of line BA.

And line BA is 13 units.

SP intersects BA st R.

Then, the length of BR will be:

= 13/2

= 6.5

Therefore, using the given radius we know that the length of the line BR is 6.5 units.

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Mean of country A is $29600 and median $29000. Mean of country B is $49800 and median is $29000. Country B has greater income inequality. So option B is the correct answer.

Mean of incomes in country A = (9000+ 21000+ 29000 + 39000+ 50000)/5   =  $29600

Median income of country A = (5+1)/2 th term = 3rd term = $29000

Mean to median ratio = 29600/ 26000= 1.02

Mean income of country B = ( 9000+ 21000+ 29000+ 39000+ 151000)/5 = $ 49800

Median income = (n+1)/2 th term = (5+1)/2 = 3rd term = 29000

Mean to median ratio of country B = 49800/29000 = 1.71

Since mean and median are closer to each other, standard deviation is less. The mean to median ratio is greater for country B. So country B has greater income inequality.

If the income inequality has been increasing, then the mean-median ratio will increase, due to the extreme values, mean will increase. So option B is the correct answer.

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The solution is found by slope of the graph and the solution is 2,200.

Let x the amount of money per hour and y the total amount of money.

Studio A:-

Rents for 100 dollars plus 50 dollars per hour.

[tex]y= 100 + 50x[/tex]

So the slope is 50 and the y intercept is 100.

Studio B:-

rents for 50 dollars plus 75 dollars per hour.

[tex]y= 50 + 75x[/tex]

So the slope is 75 and the y intercept is 50.

ThrTh solution is 2200 , see the gragraphph.

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Complete question:- You and your friends decide to rent some studio time to make a CD. Big Notes Studio rents for $100 plus $50 per hour. Great Sounds Studio rents for $50 plus $75 per hour. Solve the system by graphic method.

Multiply each row of the first matrices of 3 x 3 order by the column of another matrix of 3 x 3 order, then add the result.

Therefore, to multiply  3 x 3 order matrices multiply each row of first matrix with each column of the second matrix.

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Generally, a size 1 diaper will weight around 8-14 lbs may it be for infants or adults.

By absorbing or containing waste materials to prevent soiling of outer clothing or the surrounding environment, diapers are a type of underwear that enable the wearer to urinate or defecate without using a toilet.

Diapers must be changed when they become soiled or wet, usually by a second person like a parent or caregiver. Skin issues around the diapered area can arise from failing to change a diaper as frequently as necessary.

Cloth or synthetic disposable materials are used to create diapers. Infants, toddlers who haven't learned to use the toilet, and kids who have bedwetting issues are the main groups of people who wear diapers. Adults who have incontinence or other conditions that call for their use may also do so.

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By using the current exchange rate for converting "Japanese Yen" to "US Dollar" , 500000 Yen is = 3729.12 USD .

To convert the amount of 500000 YEN to USD, we use the current exchange rate between the currencies  "Japanese Yen" and the "US Dollar" .

The exchange rate varies constantly due to fluctuations in the global financial markets ,

The current exchange rate of 1 US Dollar = 134.08 Japanese Yen  ,

We have to convert the amount 500000 yen to USD by dividing 500000 by 134.08  ;

⇒ 500000/134.08 = 3729.1169 USD ;

≈ 3729.12 USD .

Therefore, 500000 Japanese yen is approximately equal to 3792.12 US Dollars .

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(i) An exponential function to model this situation, [tex]A=2500(1.035)^n[/tex].

(ii) The value of the investment after 20 years A =$ 4,974.47 .

When the input variable x appears as an exponent in the formula f(x) = ax, an exponential function is indicated. Both the exponential function and the value of x have an impact on the exponential curve.

An essential mathematical function is the exponential function, which has the following formula:

f(x) = ax

When a>0 and a=1 are not true.

x can be any real number.

The exponential function is given as :

[tex]A=P(1+r)^n[/tex]

Where :

A = amount

P = principal

r = rate %

n = number of years

the situation can be modelled using an exponential function by substituting.

[tex]A=2500(1+0.035)^n\\\\A=2500(1.035)^n[/tex]

(ii) when n = 20 , the Amount,

[tex]A=2500(1.035)^{20}[/tex]

A =$ 4,974.47

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The explanation is in the picture

Answer:

y = 4x + 3/4

Step-by-step explanation:

The slope intercept form is y = mx + b

Our equation is 4y - 12x = 4x + 3

4y - 12x = 4x + 3

4y = 16x + 3

y = 4x + 3/4

So, the answer is y = 4x + 3/4

2. 8.472 * 10^5 in standard form is

3. The scientific notation of 0.000067 is 6.7 * 10^-5

4. The division gives 4.455 * 10^3

Scientific notation is a way of expressing very large or very small numbers in a compact and convenient way.

In scientific notation, a number is written as a coefficient multiplied by a power of 10.

The coefficient is a number between 1 and 10 (or between -1 and -10 for negative numbers), and the power of 10 indicates the size of the number.

Calculator can be used to get numbers to scientific notation and in standard form

The required division can be performed using calculator to get 4.455 * 10^3

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The z-score associated with a 95% confidence level is approximately 1.96.

The z-score associated with a 95% confidence level is the value of the standard normal distribution that corresponds to an area of 0.95 to the left of the z-score.

Using a standard normal distribution table or calculator, we can find that the z-score associated with a 95% confidence level is approximately 1.96.

Therefore, if we want to calculate the z-score for a 95% confidence level, we can use the formula

z = invNorm(1 - α/2)

where α is the significance level (α = 0.05 for a 95% confidence level), and inv Norm is the inverse normal cumulative distribution function. Using this formula, we can calculate the z-score as:

z = inv Norm(1 - 0.05/2)

= inv Norm(0.975) ≈ 1.96

Therefore, the z-score is 1.96

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The solution to the system of inequalities is (80, 50).

At least two linear inequalities in the same variables make up a system of a linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

Given:

To raise money for the show,

the drama club is selling tickets.

Let x be the number of student tickets sold and y represents the number of adult tickets sold.

According to the question,

x + y ≤ 130

5x + 10y ≥ 900.

We have drawn a graph of the system of inequalities.

And the graph is given in the attached image.

Therefore, the solution is (80, 50).

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In the triangle the value for x is obtained as option B: 96°.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

Use the fact that the sum of the exterior angles of a triangle is always 360°.

Let the unknown exterior angle be x.

So, the equation will be -

130° + 134° + x = 360°

264° + x = 360°

x = 360° - 264°

x = 96°

Therefore, the value is obtained as 96°.

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Answer:25

Step-by-step explanation:

Answer:

11 containers of paint and 3 paint brushes

Step-by-step explanation:

The equation that can be used to determine the number of containers of paint, p, at each work station is p = 132 / (12 * 3) = 11. Therefore, each work station receives 11 containers of paint and 3 paint brushes

Sampling error refers to the difference between the results of a sample and the true characteristics of the population from which the sample was drawn.

In statistics, sampling error is a measure of the degree of uncertainty that arises when estimating the characteristics of a population based on a sample of that population. This error occurs due to the fact that it is not feasible to collect data from every individual in a population, so researchers must rely on samples.

Sampling error can arise from various sources, including biases in the sample selection process, variability in the characteristics of the population, and random chance. Understanding and quantifying sampling errors are important in order to assess the validity and reliability of statistical estimates and to draw accurate conclusions from data.

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To calculate the deposit, we need to add up the amounts of the two checks and the cash: $90.50 + $90.50 + $45.00 + $150.00 = $376.00. Therefore, the deposit is $376.00.

The problem asks us to calculate the deposit amount for two checks of $90.50 each, and cash of $45.00 and $150.00. To solve the problem, we simply add up the amounts of the checks and cash to find the total deposit amount. Adding $90.50 and $90.50 gives us $181.00, and adding this to the cash amounts of $45.00 and $150.00 gives us a total of $376.00. Therefore, the deposit amount is $376.00. This is the total amount of money that will be added to the account when the checks and cash are deposited.

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If the temperature decreased by 15°F, Pilar would expect to sell 15 fewer cups of hot chocolate.

What is an equation?

An equation is a statement that shows the equality of two expressions by using an equal sign (=). It expresses a mathematical relationship between two or more variables or quantities.

Regarding the second question, to find out how many more cups of hot chocolate Pilar would expect to sell if the temperature decreased by 15°F, we can plug in t = 15 into the equation c = -t + 120 and calculate the difference between the original value of c and the new value.

c(Original) = -15 + 120 = 105

c(New) = -(15+15) + 120 = 90

The difference is:

c(New) - c(Original) = 90 - 105 = -15

Therefore, if the temperature decreased by 15°F, Pilar would expect to sell 15 fewer cups of hot chocolate.

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Answer:

2(8x−5+x^2 )

Step-by-step explanation:

2(3x−1+x^2+5x−4)

2((3x+5x)+(−1−4)+x^ )

2(8x−5+x^2 )

Answer: look at the image for the answer and explanation

Step-by-step explanation:

The remaining angles of the parallelogram are 60°, 120°, and 120°.

In a parallelogram, opposite angles are equal and consecutive angles are supplementary. This means that:

- Angle A = Angle C
- Angle B = Angle D
- Angle A + Angle B = 180°
- Angle C + Angle D = 180°

Given that angle A = 60°, we can use the above properties to find the remaining angles:

- Angle C = Angle A = 60°
- Angle B + Angle A = 180° => Angle B + 60° = 180° => Angle B = 180° - 60° = 120°
- Angle D = Angle B = 120°

Therefore, the remaining angles of the parallelogram are 60°, 120°, and 120°.

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So, in response to the above question, we can state that As a result, equation Alden paid interest of $816.75 for the month of January.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

We must first estimate the monthly mortgage payment using the monthly mortgage payment table in order to compute the amount of interest paid for the month of January.

The table shows that the monthly payment per $1,000 borrowed for a 30-year loan at 4% interest is $4.77. So, the following formula may be used to determine Alden's mortgage payment each month:

$275,000 / $1,000 = 275

$275 x $4.77 = $1,311.75 (monthly mortgage payment) (monthly mortgage payment)

Alden's January mortgage payment included $495 towards the principle, with the balance going to interest. The amount of interest paid can be determined as follows:

$1,311.75 - $495 = $816.75

As a result, Alden paid interest of $816.75 for the month of January.

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Therefore , the solution of the given problem of equation comes out to be y = (-1/5)x + 4 is the required equation.

The equivalent sign (=) is used in arithmetic equations to signify the equality of two propositions. It is shown that it is possible to compare various numerical factors by using mathematical techniques, which have served as manifestations of reality. For instance, the equal sign divides the number 12 even the solution y + 6 = 12 in two distinct portions. How many characters also are present from either end of such a character can be calculated. Conflicting symbol readings are prevalent.

Here,

The given equation of line j is y+5=5(x+5) which can be rewritten in slope-intercept form as y = 5x + 20.

Since line k is perpendicular to line j, the slope of line k will be the negative reciprocal of the slope of line j. The slope of line j is 5, so the slope of line k will be -1/5.

We are also given that line k includes the point (5,3). We can use this point and the slope of line k to find the equation of line k using point-slope form:

y - 3 = (-1/5)(x - 5)

Simplifying and rearranging, we get:

y = (-1/5)x + 4

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The volume of a right circular cone is given by the formula V = (1/3)*pi*r²*h, where r is the radius, h is the height, and pi is the constant 3.14. When the radius is multiplied by a factor of x, the volume will be multiplied by a factor of x².

Therefore, when the radius is multiplied by a factor of x. The volume changes by x².

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Answer: 3.2t − 2.4

Step-by-step explanation:

Add −3.6 and 1.2

Then, add −1.9t and 5.1t

3.2t − 2.4

The inequality that represents the value of x is x ≥ -10.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

y ≤ -6 (x - 18) - 2

Substitute y = 46

So,

46 ≤ - 6 (x - 18) - 2

46 ≤ - 6x + 108 - 2

46 ≤ 6x + 106

46 - 106 ≤ 6x

-60 ≤ 6x

-10 ≤ x

Thus,

The inequality of x is x ≥ -10.

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To solve this system of equations by elimination, we need to eliminate one of the variables (either x or y) by adding or subtracting the equations.

In this case, we can eliminate x by multiplying the first equation by 2 and subtracting it from the second equation:

2x - 6y = 12    (original second equation)

-2(x - 3y = 7)  (original first equation multiplied by -2)

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

0x - 12y = -2

Now we have a new equation, 0x - 12y = -2, that relates only to y. Solving for y, we get:

0x - 12y = -2

-12y = -2

y = 1/6

Substituting this value of y back into either of the original equations, we can solve for x:

x - 3y = 7

x - 3(1/6) = 7

x - 1/2 = 7

x = 7 + 1/2

x = 15/2

Therefore, the solution to the system of equations is x = 15/2 and y = 1/6.

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Answer:      (-4,-8)

Step-by-step explanation:

1000 hours in day can be converted in to by a formula dividing the the 1000 hours by 24 is 41.66 days.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

As 1 Hour is equal to 0.0416666666667 Days, you must multiply 1000 by 0.041666666666667 to convert hours to days. The outcome is as follows:

1000 hr × 0.041666666666667 = 41.667 d

1000 hr = 41.667 d

We come to the conclusion that one thousand thousand hours is equal to 41.7667 days:

41.667 days are equivalent to 1000 hours.

Hence, using the conversion method above, you can figure out how many days there are in 1000 hours.

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The percentage increase in the area of Server A to get the area of the Net Area is 460%.

What is area ?

Area is a measure of the amount of surface a two-dimensional shape or figure occupies. It is usually measured in square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²).

a. To find the actual length of the court, we can use the given scale of 1 inch representing 8 feet. From the drawing, the length of the court is approximately 10.5 inches. Therefore, the actual length of the court is:

Actual length = 10.5 inches x 8 feet/inch = 84 feet

b. Receiver A has a length of approximately 2.5 inches and a width of approximately 1 inch. Therefore, the actual dimensions of Receiver A are:

Actual length = 2.5 inches x 8 feet/inch = 20 feet

Actual width = 1 inch x 8 feet/inch = 8 feet

c. The Net Area has a length of approximately 3.5 inches and a width of approximately 2 inches. Therefore, the actual dimensions of the Net Area are:

Actual length = 3.5 inches x 8 feet/inch = 28 feet

Actual width = 2 inches x 8 feet/inch = 16 feet

d. To find the percentage of the area of Server B to the area of Server A, we need to calculate the area of each server. From the drawing, Server A has an area of approximately 2.5 inches x 0.5 inches = 1.25 square inches, and Server B has an area of approximately 1 inch x 1 inch = 1 square inch. Therefore, the percentage of the area of Server B to the area of Server A is:

(Area of Server B / Area of Server A) x 100%

= (1 square inch / 1.25 square inches) x 100%

= 80%

e. The perimeter of Receiver B is approximately (1 inch + 2.5 inches + 1 inch + 2.5 inches) = 7 inches, and the perimeter of the Net Area is approximately (3.5 inches + 2 inches + 3.5 inches + 2 inches) = 11 inches. Therefore, the ratio of the perimeter of Receiver B to the perimeter of Net Area is:

Perimeter of Receiver B / Perimeter of Net Area

= 7 inches / 11 inches

= 7/11

f. The area of Receiver B is approximately 2.5 inches x 2.5 inches = 6.25 square inches, and the area of the Net Area is approximately 3.5 inches x 2 inches = 7 square inches. Therefore, the ratio of the area of Receiver B to the area of Net Area is:

Area of Receiver B / Area of Net Area

= 6.25 square inches / 7 square inches

= 0.893

g. Receiver B and Net Area are not similar rectangles, as they have different dimensions.

h. To find the percentage increase in the area of Server A to get the area of the Net Area, we can calculate the area of Server A and the Net Area, and then find the percentage increase. From the drawing, Server A has an area of approximately 1.25 square inches, and the Net Area has an area of approximately 7 square inches. Therefore, the percentage increase in the area of Server A to get the area of the Net Area is:

[(Area of Net Area - Area of Server A) / Area of Server A] x 100%

= [(7 square inches - 1.25 square inches) / 1.25 square inches] x 100%

= 460%

Therefore, The percentage increase in the area of Server A to get the area of the Net Area is 460%.

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To solve for theta in the equation 3sin(theta) = sin(theta) + 1:

First, we can simplify the equation by subtracting sin(theta) from both sides:

2sin(theta) = 1

Then, we can isolate sin(theta) by dividing both sides by 2:

sin(theta) = 1/2

Using the unit circle or a calculator, we can find the two possible solutions for theta:

theta = pi/6 + 2npi or theta = 5pi/6 + 2npi, where n is an integer.

Answer:-1

Step-by-step explanation:

When you multiply exponents that have the same bases you add the exponent. You subtract the exponents when you divide.

x^9=x^y*x^10  the blank box is -1.