A newscaster earns $31,800 and wants to invest 10% of his/her monthly salary to save for retirement in 24 years. If he/she invests this money at 5.5% compounded monthly, how much money will he/she have at retirement? a) How much will be saved each year? $ b) What will be the monthly deposit? $ c) What will be the amount in the account after 24 years? $

Frank used a total of 2 14/15 gallons of gas on Saturday and Sunday combined.

To find the total amount of gas Frank used on both days, we need to add the amount of gas he used on Saturday and Sunday.

First, we need to make sure that both quantities are in the same form. We can convert the mixed number 2 1/3 to an improper fraction by multiplying the whole number by the denominator and adding the numerator. This gives us:

2 1/3 = (2 x 3 + 1)/3 = 7/3

Next, we can add the two quantities by finding a common denominator. The lowest common denominator for 3 and 5 is 15. So, we can write:

7/3 gallons + 3 2/5 gallons = (35/15 + 9/15) gallons

= 44/15 gallons

To simplify the answer, we can express the mixed number as a whole number and a proper fraction by dividing the numerator by the denominator. This gives us:

44/15 = 2 14/15

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The measure of angle C is given as follows:

C = 106.6º.

The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:

c^2 = a^2 + b^2 - 2ab cos(C)

The side of length 9 is opposite to the angle C, hence the equation is given as follows:

9² = 4² + 7² - 2 x 4 x 7 x cos(C)

56cos(C) = -16

cos(C) = -16/56

C = arccos(-16/56)

C = 106.6º.

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The value of the angle C of the given triangle using law of cosines is: C = 106.6°

We usually make use of the Law of Cosines, if only one of which is missing: three sides and one angle. Thus, if the known properties of the triangle is SSS(side-side-side) or SAS (side-angle-side), this law is applicable.

This could be in the form of:

c² = a² + b² - 2ab Cos C

From the given triangles, we have:

a = 4

b = 7

c = 9

Thus:

9² = 4² + 7² - 2(4 * 7)cos C

81 = 16 + 49 - 56 cos C

56 cos C = -16

cos C = -16/56

cos C = -0.2857

C = cos⁻¹0.2857

C = 106.6°

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Answer:

1. 62

Step-by-step explanation:

The percent rate of each function given is:

[tex]f(t) = 1.18^t:16.99\%\\\\g(t) = 2^{-2t}:-9.1\%\\\\h(t) = 1.19^{\frac{t}{10} }:8.5\%\\\\k(t) = 0.13^t:-19.5\%[/tex]

A measure known as the percent rate of change quantifies the amount of change in a quantity over time and is given as a percentage of the initial number. It is frequently used to keep tabs on population growth, shifts in the financial markets, and other occurrences.

You must first determine the amount of change in the quantity (often done by deducting the beginning value from the final value) in order to compute the percent rate of change. To calculate the percent rate of change, divide this amount of change by the starting value, multiply the result by 100, and add a percent sign.

[tex]f(t) = 1.18^t:[/tex] 16.99% is the percent rate of change per unit (t). This increase is exponential.

[tex]g(t) = 2^{-2t}:[/tex] Approximately -9.1% of a percent rate of change per unit, t. The decline is exponential.

[tex]h(t) = 1.19^{\frac{t}{10} }:[/tex] The average percent rate of change for unit t is around 8.5 percent. This increase is exponential.

[tex]k(t) = 0.13^t:[/tex] t represents the percent rate of change, which is around -19.5% per unit. The decline is exponential.

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The length of the base is 15 feet and the height is 12 feet.

The three line fragments are known as the sides of the triangle, while the three places where they converge are known as the vertices of the triangle.

Let suppose, base of the triangle = x

Then, according to the problem, the height of the triangle is x - 3.

We know the area of triangle is,

[tex]A = \frac{1}{2}*b*h[/tex]  ;   here A is the area, h is the height and b is the base.

Put the given values,

[tex]90 = \frac{1}{2} *(x)*(x-3)[/tex]

Multiplying both sides by 2:

180 = x² - 3x

x² - 3x - 180 = 0

(x - 15)(x + 12) = 0

Therefore, either x - 15 = 0 or x + 12 = 0.

If x - 15 = 0, then x = 15, which is the length of the base of the triangle.

If x + 12 = 0, then x = -12, which is not a valid solution since the length of a side of a triangle cannot be negative.

Therefore, the length of the base of the triangle is 15 feet.

The height of the triangle (x - 3), so the height is: (15 - 3) = 12 feet.

Hence, the length of the base is 15 feet and the height is 12 feet.

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The answers are A = 46% and B = 20%.

Given that, a table of data, each cell in the table shows the number of cars in that category.

A) The probability that the car's total repair cost is less than $10000 =

86 / (86+35+67) x 100 = 86/188 x 100 = 46%

B) The probability that the car's purchase was more than $40,000 =

40 / (40+86+71) x 100 = 40/197 x 100 = 20%

Hence, the answers are A = 46% and B = 20%.

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Answer:

x < 0, x > 2

Step-by-step explanation:

|1-x| > 1

(x-1)^2 > 1

x^2 -2x + 1 > 1

x^2 - 2x > 0

x(x-2) > 0

Using the graph of y=x(x-2), x(x-2)> 0 when

x < 0, x > 2

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The perimeter of the square garden is 36 feet, which means that each side of the square is 36/4 = 9 feet long. Therefore, the total cost of the fences is $92.

The length of the outer fence, which is 2 feet away from the garden, is equal to the perimeter of a larger square with sides that are 2 feet longer than the sides of the original garden.

So, the length of the outer fence is 4(9+2) = 44 feet.

The length of the inner fence, which is around the perimeter of the garden, is equal to the perimeter of the original square garden, which is 4(9) = 36 feet.

The total length of both fences is the sum of the lengths of the inner and outer fences:

36 + 44 = 80 feet.

The cost of the fences is the total length of both fences multiplied by the cost per foot:

80 x $1.15 = $92.

Therefore, the total cost of the fences is $92.

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It will take 14.14 seconds for the object to return to the ground.

We know that the height is modeled by the quadratic equation:

h(t)=-5t^2+120t+17

The object will return to the ground when its height is zero, so we only need to solve the quadratic equation:

0 = -5t^2+120t+17

Using the quadratic formula we will get.

[tex]t = \frac{-120 \pm \sqrt{120^2 - 4*-5*17} }{2*-5} \\\\t = \frac{-120 \pm 121.4 }{-10}[/tex]

We only care for the positive solution:

t = (-120 - 121.4)/-10 = 14.14

It will take 14.14 seconds.

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Complete question:

"The height of an object is launched into the air given by the function h(t)=-5t^2+120t+17 where t is the time in seconds. How long takes for the object to hit the ground?"

Answer:

55

Step-by-step explanation:

The first we need to do is find the other angle measures. The left angle must be supplementary with 110, so it must measure 70. The right angle must be supplementary with 125, so it must measure 55. The sides of an angle add up to 180, so 180-70-55= 55

The angle of x is 55°.

There is 180° in a triangle. First, we need to calculate the angles of the other two sides. A straight line also forms 180°. Therefore the first angle will be

180 - 110= 70°

The second angle will be

180 - 125 = 55°

Angles of the triangle excluding x will be

70 + 55  =  125°

Since there is 180° in a triangle, x will be

180 - 125=  55°

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Answer: ∠EFA and/or ∠CFB

Step-by-step explanation:

Adjacent: In order to classify adjacent the 2 angles need to have a common side and common vertex

Starting Angle: ∠CFE

Possible Adjacents: ∠ EFA and/or ∠CFB

The production of biodiesel would be the least likely to impact the price of electricity. Biodiesel is not commonly used as a fuel source for electricity generation, so changes in its production would not significantly affect the overall supply and demand of electricity. On the other hand, the price of a barrel of oil, the cost of a ton of coal, and a fire in a gas pipeline could all impact the price of electricity, as these are commonly used fuel sources for electricity generation.

If glass contains 320 cm³ of milk, the mass of the milk is 330 g, the density of the milk is approximately 1031 kg/m³.

Density is defined as the mass per unit volume of a substance. To find the density of milk in kg/m³, we need to convert the given volume and mass to the appropriate units.

First, we need to convert the volume from cm³ to m³. Since 1 m = 100 cm, 1 m³ = (100 cm)³ = 1,000,000 cm³. Therefore, we can convert 320 cm³ to m³ by dividing by 1,000,000:

320 cm³ ÷ 1,000,000 = 0.00032 m³

Next, we need to convert the mass from grams to kilograms. Since 1 kg = 1000 g, we can convert 330 g to kg by dividing by 1000:

330 g ÷ 1000 = 0.33 kg

Now that we have both the mass and volume in appropriate units, we can calculate the density by dividing the mass by the volume:

Density = mass ÷ volume = 0.33 kg ÷ 0.00032 m³ ≈ 1031 kg/m³

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The area of the figure is 45 square millimeters.

What is Area?

Area is a measure of the size or extent of a two-dimensional surface or shape. It is usually expressed in square units such as square meters , square feet , square centimeters , square inches , etc. The area of a shape or surface can be calculated by multiplying the length of one side or dimension by the length of an adjacent side or dimension, or by using specific formulas depending on the shape.

The figure can be broken down into a rectangle (5 mm x 7 mm) and two right triangles (with legs 2 mm and 3 mm, respectively).

Area of rectangle = length x width = 5 mm x 7 mm = 35 square mm

Area of each triangle = 1/2 x base x height = 1/2 x 2 mm x 4 mm = 4 square mm

1/2 x 3 mm x 4 mm = 6 square mm

Total area of the figure = area of rectangle + area of two triangles = 35 square mm + 4 square mm + 6 square mm = 45 square mm.

Therefore, the area of the figure is 45 square millimeters.

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The investment will be worth approximately $3,326 after 9 years.

The interest that is paid on both the initial investment and any interest that has been paid on that investment in previous periods is called compound interest.

The investment's future value can be determined using the formula for compound interest:

[tex]A = P * (1 + \frac{r}{n})^{nt}[/tex]

where, A = future value of the investment, P = principal (initial investment), r = annual interest rate, n = number of times, interest compounded per year, and t = number of years.

In this case, given values:

P = $2200 (the initial investment or principal)

r = 4.7% (the annual interest rate expressed as a decimal)

n = 1 (interest is compounded annually)

t = 9 (the investment is held for 9 years)

putting the values,

[tex]A = 2200 * (1 + \frac{0.047}{1} )^{1*9}[/tex]

[tex]A = 2200 * (1.047)^9[/tex]

A = $3326.16

Therefore, the investment will be worth approximately $3326 after 9 years.

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The investment will be worth approximately $3,326 after 9 years.

The interest that is paid on both the initial investment and any interest that has been paid on that investment in previous periods is called compound interest.

The investment's future value can be determined using the formula for compound interest:

[tex]A = P * (1 + \frac{r}{n})^{nt}[/tex]

where, A = future value of the investment, P = principal (initial investment), r = annual interest rate, n = number of times, interest compounded per year, and t = number of years.

In this case, given values:

P = $2200 (the initial investment or principal)

r = 4.7% (the annual interest rate expressed as a decimal)

n = 1 (interest is compounded annually)

t = 9 (the investment is held for 9 years)

putting the values,

[tex]A = 2200 * (1 + \frac{0.047}{1} )^{1*9}[/tex]

[tex]A = 2200 * (1.047)^9[/tex]

A = $3326.16

Therefore, the investment will be worth approximately $3326 after 9 years.

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Answer: 4/21

Step-by-step explanation: 1 1/3 =4/3 3 1/2x2= 7

If perimeter of rectangle is denoted as "18x+6" and width is denoted as "2x+5", then the expression for length of the rectangle will be .

The "Perimeter" of a rectangle is known as the "total-distance" around the outside of rectangle.

Let  length of rectangle be denoted by "L". The formula for the "peri-meter" for rectangle is : P = 2(length + width),

The "peri-meter" is = "18x + 6", and "width" is "2x + 5".

Substituting these values into the formula,

We get,

⇒ 18x + 6 = 2(L + 2x + 5),

⇒ 18x + 6 = 2L + 4x + 10,

⇒ 18x - 4x - 10 - 6 = 2L,

⇒ 14x - 16 = 2L,

⇒ 7x - 8 = L,

Therefore, the expression for the length of the rectangle is "7x - 8".

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The value of arctan(√2) for the equation tan(x/2 - π/2) = √2 in the form x=π +πn is given by arctan(√2) = π/4 + πn, where n is an integer.

Equation is equal to,

tan(x/2 - π/2) = √2

By using the identity for tangent of half angle,

tan(x/2 - π/2)

= 1/cot(x/2 - π/2)

= 1/(-tan(x/2))

So the equation becomes,

1/(-tan(x/2)) = √2

Multiplying both sides by -1, we get,

tan(x/2) = -1/√2

            = -√2/2

Now use the inverse tangent function (arctan) to find x/2,

arctan(-√2/2) = -π/4

Since x/2 - π/2 = -π/4, we have,

⇒ x/2 = -π/4 + π/2

         = π/4

The solutions for x are x = π/2 + 2πn, where n is an integer.

Now let us find the value of arctan(√2),

arctan(√2) is the angle whose tangent is √2.

Since tan(π/4) = √2, we have,

arctan(√2) = π/4 + πn, where n is an integer.

Therefore, the value of arctan(√2) in the form x=π +πn is equal to

arctan(√2) = π/4 + πn, where n is an integer.

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A. 0.3015; fail to reject the null hypothesis

The test statistic is z = 0.52 and p-value (0.3015) is greater than the significance level (0.05)

Given data ,

Under the premise that the null hypothesis is true, the p-value is the likelihood of witnessing a test statistic that is as severe as the one computed or even more extreme. The p-value of a right-tailed test is the likelihood of seeing a test statistic that is higher than or equal to the computed test statistic.

We can compare the test statistic to the critical value or use a conventional normal distribution table to calculate the p-value given that the test statistic is z = 0.52 and the significance threshold is 0.05

Looking up the p-value corresponding to z = 0.52 in a standard normal distribution table or using a calculator, we find that the p-value is approximately 0.3015.

Since the p-value (0.3015) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Hence , 0.3015; fail to reject the null hypothesis

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Any value between 5.3 cm and 11.7 cm (exclusive) could be the length of the third side of the triangle which is 6.7cm in the given options.

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for a triangle with sides a, b, and c, where c is the longest side, the following inequality holds:

a + b > c

This means that the length of any side of a triangle must be less than the sum of the lengths of the other two sides. This theorem is fundamental in geometry and is used in many proofs and applications.

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, the length of the third side must be greater than the difference between the other two sides and less than their sum.

Let's apply this rule to the given triangle. We have two sides of length 3.2 cm and 8.5 cm.

To be a valid triangle, the length of the third side must satisfy the following inequality:

8.5 cm - 3.2 cm < third side < 8.5 cm + 3.2 cm

5.3 cm < third side < 11.7 cm

Therefore, any value between 5.3 cm and 11.7 cm (exclusive) could be the length of the third side of the triangle. So it's 6.7cm.

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Answer:Supplementary

Step-by-step explanation:

The two angles add up to 180

Answer:

supplementary since 136+44= 180 and any angles that sum up to 180 are supplementary

Answer:

Yes, point A on the graph represents a pair of possible values of m and w because it satisfies the equation w = 2.5m + 5.

To confirm this, we can substitute m = 20 into the equation to get:

w = 2.5(20) + 5

w = 50 + 5

w = 55

So the coordinates of point A are (20, 55), which represents a possible value of m and w that satisfies the equation.

The measure of angle x is  23⁰.

The value of arc angle y is 45.5⁰.

The value of arc angle z is 116⁰.

The measure of angle x, y and z is calculated as follows;

∠mEGF = ¹/₂ (arc EF - arc DC ) (intersecting chord theorem)

33 = ¹/₂ (89 - x )

2(33) = 89 - x

66 = 89 - x

x = 89 - 66

x = 23⁰

The value of arc angle z is calculated as follows;

89 + 132 + 23 + z = 360 (sum of angles of a circle)

244 + z = 360

z = 360 - 244

z = 116⁰

The value of angle y is calculated as follows;

∠mGEF = ¹/₂(z) (intersecting chord theorem)

∠mGEF =  ¹/₂(116)

∠mGEF = 58⁰

∠mEFG = 180 - (58 + 33) = 89

y + 89 + y = 180 (sum of angles on a straight line)

2y + 89 = 180

2y = 91

y = 91/2

y = 45.5⁰

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The measure of angle x is  23⁰.

The value of arc angle y is 45.5⁰.

The value of arc angle z is 116⁰.

The measure of angle x, y and z is calculated as follows;

∠mEGF = ¹/₂ (arc EF - arc DC ) (intersecting chord theorem)

33 = ¹/₂ (89 - x )

2(33) = 89 - x

66 = 89 - x

x = 89 - 66

x = 23⁰

The value of arc angle z is calculated as follows;

89 + 132 + 23 + z = 360 (sum of angles of a circle)

244 + z = 360

z = 360 - 244

z = 116⁰

The value of angle y is calculated as follows;

∠mGEF = ¹/₂(z) (intersecting chord theorem)

∠mGEF =  ¹/₂(116)

∠mGEF = 58⁰

∠mEFG = 180 - (58 + 33) = 89

y + 89 + y = 180 (sum of angles on a straight line)

2y + 89 = 180

2y = 91

y = 91/2

y = 45.5⁰

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The number of scoops of seeds needed to fill three bird feeders is 13 1/7 scoops of seeds .

To calculate the total seed quantity required to fill all three feeders, begin by computing the volume for the first two dispensers: each can hold 5 and five-twelfths cups of seeds.

Next, this text assumes an understanding that one scoop of seeds holds approximately 1 and one-sixth cups of product. Using this information, we determine how many scoops are needed to satisfy all three bird feeders' capacity.

By multiplying the first fraction's value with the reciprocal of the second fraction helps you divide fractions accurately:

(46 / 3) x (6 / 7) = (46 x 6) / (3 x 7) = 276 / 21

276 / 21 = 13 3/21

13 3/21 = 13 1/7 scoops

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Answer:

96

Step-by-step explanation:

8 times 12 = 96

The width of the rectangular section of Clark's backyard is 3.9 meters.

Area of the rectangular section is 11.31 sq meters.

length of rectangular section is 2.9 meters.

For a rectangular section the formula for area is equal to the product of length and width of the rectangular section.

                  Area = length * width

Rectangle: It is a 4 sided structure with two equal opposite sides It also has 4 right angles and sum of all angles is equal to 360°.

here,

                 width = [tex]\frac{area}{length}[/tex] = [tex]\frac{11.31}{2.9} =3.9[/tex] meters.

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The average rate of change of the function f(x) = x² on the interval [3, 3 + h] is given as follows:

h + 6.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

The function in this problem is given as follows:

f(x) = x².

Then the outputs are obtained as follows:

The change in the output is given as follows:

h² + 6h + 9 - 9 = h² + 6h.

The change in the input is given as follows:

3 + h - 3 = h.

Hence the rate is:

r = (h² + 6h)/h.

r = h(h + 6)/h

r = h + 6.

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The value of the thickness of each record if the volume of the carton is 100π is,

⇒ 2.78 inches

We have to given that;

Karen can fit 25 vinyl records of diameter 12 in. inside a cylindrical carton with the same diameter.

We know that;

Volume of cylinder is,

⇒ V = πr²h

Hence, We get;

100π = π × (12/2)² × h

100 = 36h

h = 100 / 36

h = 50/18

h = 2.78 inches

Thus, The value of the thickness of each record if the volume of the carton is 100π is,

⇒ 2.78 inches

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The solution of the system of equations is x = -5/17 and y = -16/17.

To do this, we can use a method called substitution. In this method, we solve one equation for one variable in terms of the other variable, and then substitute this expression into the other equation. This results in a new equation with only one variable, which can be solved to find the value of that variable. Once we know the value of one variable, we can substitute it into either equation to find the value of the other variable.

Let's apply this method to your system of equations:

5x - y/2 = -1 (Equation 1)

3x - 2y = 1 (Equation 2)

First, we'll solve Equation 1 for y in terms of x:

5x - y/2 = -1

y/2 = 5x + 1 (Add y/2 to both sides)

y = 10x + 2 (Multiply both sides by 2)

Now we substitute this expression for y into Equation 2:

3x - 2(10x + 2) = 1 (Substitute y = 10x + 2)

3x - 20x - 4 = 1

-17x = 5

x = -5/17

Now that we know the value of x, we can substitute it into either Equation 1 or Equation 2 to find the value of y. Let's use Equation 1:

5x - y/2 = -1

5(-5/17) - y/2 = -1

-25/17 - y/2 = -1

y/2 = -1 + 25/17

y/2 = -8/17

y = -16/17

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Complete Question:

What is the solution of the system of equations:

5x - y/2 = -1

3x - 2y = 1