Use the image below to find x: Show your steps and identify the TRIG RATIO that you used to find x.

The equation that best represents the linear relationship between the total amount Mrs. Jacobs will be charged and the number of children attending the skating party is y = mx + b.

In this case, y represents the total amount in dollars that Mrs. Jacobs will be charged, x represents the number of children attending the party, m represents the slope of the line, and b represents the y-intercept.

To find the equation, we need to determine the slope and y-intercept from the table given. From the table, we can see that for every additional child attending the party, the total amount charged increases by $10. This means that the slope (m) of the line is 10.

To find the y-intercept (b), we can look at the table and see that when there are zero children attending the party, the total amount charged is $50. This means that the y-intercept is 50.

Putting it all together, the equation that best represents the linear relationship is y = 10x + 50.

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The amount of money that will be in the account at the end of the four years to use as the down payment on the property is $26,102.47.

In the above question, we need to use the formula for compound interest and it is:

A = P(1 + r/n)^(nt)

Note that:

A = the amount of money at the end of the investment

P = the principal amount

r = the annual interest rate

n = the number of times the interest is compounded per year

t = the number of years of the investment

Since:

P = $20,000

r = 6.5% = 0.065

n = 365 (note the interest is compounded everyday)

t = 4

We shall put the values into the formula:

A = $20,000(1 + 0.065/365)^(365*4)

A = $20,000(1.0178)¹⁴⁶⁰

A = $20,000  x  1.305124

A = $26,102.47

Therefore, at the end of the four years, there will be $26,102.47.

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Answer:

32

Step-by-step explanation:

There are 28 full shaded squares

There are 8 half squares

2 half squares make up 1 full square

So 28 + 4 = 32

Area is 32 units

The cost of the fabric will be $55.63.

To find the cost of the fabric, you need to first determine the total area of the fabric needed to make the patio umbrella. Since the patio umbrella is in the shape of a regular hexagon, it can be divided into six congruent equilateral triangles. The formula for the area of an equilateral triangle is A = (sqrt(3)/4)*s^2, where s is the length of one side of the hexagon.

Let's assume the length of one side of the hexagon is x. Then the area of one of the equilateral triangles is A = (sqrt(3)/4)x^2. Since there are six of these triangles in the hexagon, the total area of the hexagon is 6A = 6(sqrt(3)/4)*x^2 = (3sqrt(3)/2)*x^2.

To determine the amount of orange fabric needed, you can multiply the area of the hexagon by the number of square yards in one square foot and round up to the nearest whole number of square yards. Similarly, you can do the same for the white fabric.

Let's say the hexagon has a side length of 6 feet, so x=6ft. Then the area of the hexagon is (3sqrt(3)/2)*(6ft)^2 = 93.53 square feet. Converting square feet to square yards gives 10.39 square yards. Therefore, you need to order at least 11 square yards of each fabric.

The cost of the orange fabric is $s. 75 per square yard, so 11 square yards will cost 11 * $s. 75 = $28.13. The cost of the white fabric is $2.50 per square yard, so 11 square yards will cost 11 * $2.50 = $27.50. Therefore, the total cost of the fabric will be $28.13 + $27.50 = $55.63.

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Answer:

Explanation :

We are given with two shapes triangle and a rectangle.

From the above diagram

We can see that Breadth of the rectangle is 5 ft and length of 10 ft.

As we know that area of Rectangle is length × Breadth

Area(rectangle) = l × b

Area (rectangle) = 10 × 5

Area (rectangle) = 50 ft².

Now,

where

Area (triangle) = 4 × 6 ÷ 2

Area (triangle) = 24 ÷ 2

Area (triangle) = 12 ft².

Total area = Area of rectangle + Area of triangle

Total area = 50 + 12

Total area = 62 feet

Therefore, The area of the irregular shape is 62 feet.

Both Denise and Kristal are correct. The expression "p - 0.25p" is equivalent to "0.75p," which represents the sale price after a 25% markdown. Therefore, option C is the correct answer.

Denise's expression, "p - 0.25p," represents the original price (p) minus the 25% markdown (0.25p). This simplifies to 0.75p, which is indeed the sale price.

On the other hand, Kristal's expression, "0.75p," directly represents the sale price after applying a 25% discount. This expression skips the intermediate step of subtracting the markdown from the original price.

Both expressions, "p - 0.25p" and "0.75p," yield the same result, which is the sale price after a 25% markdown. Therefore, both Denise and Kristal are correct in their calculations.

The choice between the two expressions comes down to personal preference or convenience. Some individuals may find it easier to directly calculate the sale price using a percentage of the original price, while others may prefer subtracting the markdown amount from the original price.

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Answer:

-7 feet

Step-by-step explanation:

-3-4 = -7, so it is -7 feet

We can use the empirical rule to estimate the percentage of workdays it takes Susan between 38 and 46 minutes to drive to work. According to the empirical rule, for a normal distribution:

- About 68% of the data falls within one standard deviation of the mean

- About 95% of the data falls within two standard deviations of the mean

- About 99.7% of the data falls within three standard deviations of the mean

Since the mean is 42 minutes and the standard deviation is 4 minutes, one standard deviation below the mean is 38 minutes, and one standard deviation above the mean is 46 minutes. So, about 68% of the time it takes Susan between 38 and 46 minutes to drive to work.

Therefore, the answer is (B) 68%.

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Answer:

It's fascinating to observe how the volume of different shapes can vary based on their measurements. For instance, a cylinder with a height of 6 centimeters and radius r1 has a volume of 302 cubic centimeters. Do you require further assistance?

As for the new set of instructions, please consider the following statements:

6. Sometimes true. The period of the function is determined by the formula T= 2π/b, where b is the coefficient of x in the argument of the sine function. In this case, b = π/5, so T= 10.

7. Always true. The maximum height of the object is equal to the amplitude of the function plus the vertical shift, which is 55 centimeters.

8. Sometimes true. The minimum height of the function occurs when the sine function has a value of -1, which happens at x= h-5. So, if h= 0, then x= -5, which means the statement is sometimes true depending on the value of h.

9. Always true. The midline of the function is determined by the vertical shift, which is 55 in this case.

10. Always true. The amplitude of the function is given by A= |b|, where b is the coefficient of x in the argument of the sine function. In this case, A= 42π/5, which simplifies to 84.

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The area of garage is 36,504 square inches.

The width of Scott's garage is 156 inches (since it is 1.5 times shorter than the length of 234 inches).

so width = 234/1.5

=> 156

To find the area, we multiply the length by the width:

=> 234 inches x 156 inches

=> 36,504 square inches.

To explain, the formula for finding the area of a rectangle is length x width. In this problem, we are given the length of the garage as 234 inches and are told that the width is 1.5 times shorter than the length.

To find the width, we can multiply the length by 1.5 to get 351 inches (which is longer than the length, so we know it must be incorrect). Instead, we need to divide the length by 1.5 to find the width, which gives us 156 inches. Then, we can multiply the length by the width to find the area of the garage, which is 36,504 square inches.

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David's net worth: 86,329.95

To calculate David's new net worth, we need to add the increase in assets and subtract the decrease in liabilities from his current net worth.

New assets value = 62,784.24 + 2,784.89 = 65,569.13

New liabilities value = David's current net worth - his current assets value

New liabilities value = 45,765.78 - 62,784.24 = -17,018.46

Since his liabilities have decreased by 3,742.36, we need to subtract this value from the new liabilities value:

New liabilities value = -17,018.46 - 3,742.36 = -20,760.82

Now we can calculate his new net worth by subtracting his new liabilities value from his new assets value:

New net worth = 65,569.13 - (-20,760.82) = 86,329.95

Therefore, David's new net worth is 86,329.95.

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Answer:

Step-by-step explanation:

The volume of the given prism is 9.936 cubic meters, To calculate the volume of a right rectangular prism, we need to multiply its length, width, and height together.

Given that the length of the prism is 4.8 meters, the width is 2.3 meters, and the height is 0.9 meters, we can calculate the volume using the formula:

Volume = length x width x height

Volume = 4.8 m x 2.3 m x 0.9 m

Volume = 9.936 m^3

Therefore, the volume of the right rectangular prism is 9.936 cubic meters.

It is important to note that when we calculate volume, we are dealing with a three-dimensional space, and the units we use must be cubed (m^3 in this case). This is because we are measuring the amount of space occupied by the object in all three dimensions.

In summary, to find the volume of a right rectangular prism, we simply multiply its length, width, and height together. In this case, the volume of the given prism is 9.936 cubic meters.

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Answer:

Step-by-step explanation:

Let's call the mass of an average man's brain "m."

According to the problem, the mass of an average elephant's brain is 3 4/10 kilograms greater than an average man's brain. We can write this as:

mass of elephant's brain = m + 3 4/10

To find out how many kilograms an average elephant's brain weighs, we need to know the value of "m." However, this information is not given in the problem.

Therefore, we cannot determine the exact mass of an average elephant's brain.

The potential factor that may have an impact on the confidence interval, but is not accounted for by the margin of error, is nonresponse bias.

The dean of students received a large number of responses from first-year students but very few from sophomores, juniors, and seniors. Nonresponse bias occurs when some individuals chosen for a sample do not respond to a survey or study. In this case, the dean of students may not have received a representative sample of the opinions of all students, which could lead to an overestimation or underestimation of the true proportion of students who believe first-year students should be given parking privileges in the main lot.

The margin of error is the amount of random sampling error in a survey's results. It reflects the level of precision in the survey's results and decreases as the sample size increases. However, nonresponse bias is a systematic error that is not accounted for by the margin of error, as it may lead to a biased sample and inaccurate results. To minimize nonresponse bias, the dean of students could have used techniques such as follow-up emails or incentives to encourage a higher response rate from all student groups.

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The value of the simplified expression is -15.

The simplification of the expression is determined by substituting the appropriate values of the variables into the equation.

The given expression; = 54/g - 8h

The value of g = 6 and the value of h = 3,

The value of the expression is calculated as follows;

= 54/g - 8h

= 54/6 - 8(3)

= 9 - 24

= - 15

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The complete question is below:

54/g - 8h, when g = 6 and h=3

Answer:

9/7

explain:

(36-27) 7

9/7

The surface area of the regular pyramid is 1209 m².

A pyramid is a three-dimensional shape. It has a flat polygon base. All the other faces are triangles and are called lateral faces.

A pyramid is called by the shape of its base.

The surface area of the regular hexagonal pyramid is given by the formula:

SA = 3b(a + s)

Where a is the apothem, b is the base and s is the slant height of the pyramid.

In this case:

a = 8.5√3 m

b = 17 m

s = 9 m

SA = 3 * 17 * (8.5√3 + 9)

SA = 1209 m²

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The logistic function that represents the number of units occupied over time is given by:

[tex]N(t) = (K / (1 + A * e^(-r*t))),[/tex]

where N(t) is the number of units occupied at time t, K is the carrying capacity (maximum number of units that can be occupied),

A is the initial amount of units occupied, r is the growth rate, and e is the base of the natural logarithm.

In this case, the carrying capacity K is 1500 units, and the initial amount of occupied units A is 15 units. The growth rate r can be calculated as follows:

[tex]r = ln((10%)/(100% - 10%)) = ln(0.1/0.9) ≈ -0.101[/tex]

Substituting the given values into the logistic function, we get:

[tex]N(t) = (1500 / (1 + 15 * e^(-0.101*t)))[/tex]

Simplifying further, we get:

[tex]N(t) = (100 / (1 + e^(-0.101*t))) + 15[/tex]

Therefore, the logistic function that represents the number of units occupied over time is:

[tex]N(t) = (100 / (1 + e^(-0.101*t))) + 15[/tex], where t is measured in months.

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Step-by-step explanation:

I had to add some assumed portions to your posted picture. See image.

 The yellow boxed angle is 84 degrees (upper LEFT) due to alternate interior angles of parallel lines transected by another line.

  then, since the triangle is isosceles ....the other (lower LEFT)  angle is 84 degrees also....

      that means that k= 12 degrees    for the triangle interior angles to sum to  180 degrees .

Jerome will need approximately 138.72 square meters of grass seed to cover his lawn.

To find the area that the grass seed needs to cover, we first need to find the area of the entire lawn. Let's assume that the lawn is rectangular in shape.

Jerome hasn't given us the dimensions of the lawn, so let's say that it measures 10 meters by 15 meters. Therefore, the area of the entire lawn would be:

10 meters x 15 meters = 150 square meters

Now we need to subtract the area of the pool from the area of the entire lawn.

The pool measures 4 5/6 meters by 2 1/3 meters, which we can convert to improper fractions:

4 5/6 = (4 x 6 + 5) / 6 = 29 / 6
2 1/3 = (2 x 3 + 1) / 3 = 7 / 3

So the area of the pool would be:

29/6 meters x 7/3 meters = 203/18 square meters

To find the area that the grass seed needs to cover, we subtract the area of the pool from the area of the entire lawn:

150 square meters - 203/18 square meters

To subtract these two values, we need to get a common denominator:

150 square meters = (150 x 18) / 18 = 2700/18 square meters
203/18 square meters = 203/18 square meters

So the area that the grass seed needs to cover would be:

2700/18 square meters - 203/18 square meters = 2497/18 square meters

We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 1:

2497/18 square meters ≈ 138.72 square meters

Therefore, Jerome will need approximately 138.72 square meters of grass seed to cover his lawn, excluding the area around the pool.

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Answer:

a)  3, 2, 1, 4

Step-by-step explanation:

If you have multiple credit cards with different APRs, it is best to pay off the card with the highest APR first.  This is because you will save the most money in interest by paying off the highest-rate debt first.

Therefore, as Michelle has four credit cards, each with different APRs, she should pay them off in order of the highest to lowest interest rate.

Since the highest APR is 23%, credit card #3 should be paid off first.

The next highest APR is 19%, so credit card #2 should be paid off second.

Credit card #1 should be paid off next as it has an APR of 17%.

Finally, credit card #4 should be paid off last, as it has the lowest APR of 15%.

So the order in which Michelle should pay off her credit cards is:

(0, -1) is the solution to the given system of inequalities.

Option A is the correct answer.

We have,

To determine which ordered pair is a solution to the system of inequalities, we need to check if each ordered pair satisfies both inequalities simultaneously.

Let's evaluate each option:

(0, -1):

For this option, we have:

y < -x² + x

-1 < -(0)² + 0

-1 < 0

y > x² - 4

-1 > (0)² - 4

-1 > -4

Since both inequalities are satisfied simultaneously, (0, -1) is a solution to the system.

(1, 1):

For this option, we have:

y < -x² + x

1 < -(1)² + 1

1 < 0

y > x² - 4

1 > (1)² - 4

1 > -3

Since both inequalities are not satisfied simultaneously, (1, 1) is not a solution to the system.

(2, -3):

For this option, we have:

y < -x² + x

-3 < -(2)² + 2

-3 < -2

y > x² - 4

-3 > (2)² - 4

-3 > 0

Since both inequalities are not satisfied simultaneously, (2, -3) is not a solution to the system.

(3, -6):

For this option, we have:

y < -x² + x

-6 < -(3)² + 3

-6 < -6

y > x² - 4

-6 > (3)² - 4

-6 > 5

Since both inequalities are not satisfied simultaneously, (3, -6) is not a solution to the system.

Thus,

(0, -1) is the only solution to the given system of inequalities.

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Answer:

The height of the flagpole is approximately 5.774 meters.

Step-by-step explanation:

Let's call the height of the flagpole h. We can use trigonometry to set up the following equation:

tan(30°) = h/10

Simplifying this equation, we get:

h = 10 tan(30°)

Using a calculator, we find that tan(30°) ≈ 0.5774, so:

h ≈ 5.774 meters

Therefore, the height of the flagpole is approximately 5.774 meters.

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Answer:

102 cm³

Step-by-step explanation:

density = m/v

1 g = 0.001 kg

Volume of real statue = v = m/d = 1632 kg / 0.002 kg/cm³ = 816,000 cm³

scale factor for height:  200 cm : 10 cm  =  20 : 1

scale factor for volume:  20³ : 1³  = 8,000 : 1

Volume of model = 816,000 cm³ / 8,000 = 102 cm³

If Her pool is 10 m by 5 m and is surrounded by a 1. 5 m border of paving stones. Therefore, Piscine will need a total of 104 square meters of paving stones.

a) The area of the pool plus the surrounding border of paving stones can be calculated as follows:

Total area = (length + 2 x border width) x (width + 2 x border width)

Total area = (10 + 2 x 1.5) x (5 + 2 x 1.5)

Total area = 13 x 8

Total area = 104 square meters

Therefore, Piscine will need a total of 104 square meters of paving stones.

b) We need to convert the dimensions of each paving stone to meters:

25 cm = 0.25 m

40 cm = 0.4 m

The area of each paving stone is:

0.25 m x 0.4 m = 0.1 square metres

The number of paving stones required can be calculated by dividing the total area by the area of each paving stone:

Number of paving stones = Total area / Area of each paving stone

Number of paving stones = 104 / 0.1

Number of paving stones = 1040

In theory, Piscine will need 1040 paving stones.

c) To determine whether the answer in part b) will be enough, we need to see if we can fit the paving stones into the available space without any gaps. We can arrange the paving stones in rows, with each row containing 10 stones (since the width of the pool is 5 m and the width of each paving stone is 0.4 m).

There will be 26 rows of paving stones around the pool (since the length of the pool plus the two borders is 13 m and the length of each paving stone is 0.25 m). Therefore, the total number of paving stones required is: 26 rows x 10 stones per row = 260 stones

Since the number of paving stones required is less than the number calculated in part b), Piscine will have enough paving stones to complete the border around her pool without any waste.

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The function is P(t) = 380 x [tex]1.0300^{t}[/tex], which is an exponential function, and the rate of change is 1.24% each hour.

The equation P(t) = 380 x [tex](1 + 0.03)^{t}[/tex] represents the population of bacteria after t days.

Rounding to four decimal digits and simplifying:

P(t) = 380 x [tex]0.0300^t[/tex]

We can use the following formula to determine the percentage rate of change each hour:

r = [tex]100 \times e^{(ln(1 + 0.03)/24) - 1)}[/tex]

where e is the Euler's number, ln is the natural logarithm, and r is the percentage rate of change per hour.

Rounding to the nearest tenth of a percent and simplifying:

r = 1.24%

This exponential function simulates the population of bacteria multiplying exponentially at a rate of 3% each day in a petri dish.

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x²y' - 2xy' + (x² + 2)y = 0 is the associated homogeneous equation with non-homogeneous ODE x²yⁿ - 2xy' + (x² +2)y = 3x³.

It should be noted that the equation is same as the variable coefficient linear second order non-homogeneous ODE but just the right side zero.

The complementary solutions or homogeneous solutions to this homogeneous equation serve as the foundation for the space of all solutions to the non-homogeneous equation.

By assuming that y has the form y(x) = xr and substituting this into the homogeneous equation to create a characteristic equation, we can determine the complementary solutions. We may find the values of r that correspond to solutions of the type y(x) = xr by looking at the characteristic equation's roots.

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Use first two points and the slope equation to find the slope:

The slope is 745.

Use the first point and point-slope equation to find the y-intercept:

The y-intercept is 500.

The slope of 745 represents the profit per month and the y-intercept of 500 represents the initial profit.

A homeowner borrows $65,000 to remodel their home. The loan is financed at a 2.3% interest rate, compounded quarterly.

So we have to find 2.3% of 65,000 which is 1495

Now we have to multiply 1,495 by 8 because it is 8 years which is 11960. Now we add 11,960 to 65,000 and our answer is

Answer : 76960

(Choice 1)