Mike saves $2,000 at a yearly simple interest rate of 2%, he earns $280 in interest for how many years did he save this money

Answer:

100° and 40°

Step-by-step explanation:

In an isosceles, 2 interior angles are equal.

If one angle is 40°, another one of its angles must be also 40°.

Fact of a triangle

Sum of interior angles of a triangle is 180°.

Let the unknown angle be x.

x + 40° + 40° = 180°

x + 80° = 180°

x = (180 - 80)°

x = 100°

So, the other angle is 100°

Hence,

100° and 40° are the possible measures for the other two triangles.

The slope of the line AB and the perpendicular bisector are reciprocal to each other and the equation of the line is 3y + - 4x = 18.  

A line is known as a perpendicular bisector when it divides a specified line segment in half, by creating a 90° angle at the intersection.

The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler.

On both sides of the line segment being divided, it forms a 90° angle.

Here we have

On the grid below segment AB is shown with endpoints A(-1,-1) and B(7,5). It's midpoint M. The coordinates of M (3, 2).  

Slope from A(-1,-1) and B(7,5)  

=> [ 5 + 1]/[7 + 1 ] = 6/8 = 3/4

When we draw a perpendicular bisector of AB on the grid. It will pass through the point (0, 6)  

The slope of the perpendicular bisector i.e from (0, 6) to (3, 2)  

=> [2 - 6]/[3 - 0] = - 4/3

Let the equation of the bisector is y = mx + c

=> y = (-4/3)x + c

=> 3y = - 4x + 3c           [ ∵ Slope = -4/3 ]

As we know the bisector will pass through (3, 2)

=> 3(2) = -4(3) + 3c

=> 3c = 12 + 6

=> 3c = 18

Hence, the required equation of the line is 3y = - 4x + 18  

Therefore,

The slope of the line AB and the perpendicular bisector are reciprocal to each other and the equation of the line is 3y + - 4x = 18.  

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Answer: To solve the equation -3(x+2)^2-4 = 5 by factoring, we can follow these steps:

Move all the terms to one side of the equation by adding 3(x+2)^2 and 4 to both sides: -3(x+2)^2-4+3(x+2)^2+4 = 5+3(x+2)^2

Combine like terms: 3(x+2)^2 = 5

Take the square root of both sides of the equation: (x+2)^2 = 5/3

Isolate x+2 on one side of the equation by taking the square root of both sides: x+2 = ±sqrt(5/3)

Solve for x by subtracting 2 from both sides of the equation: x = ±sqrt(5/3) - 2

So the solutions to the equation -3(x+2)^2-4 = 5 by factoring is x = ±sqrt(5/3) - 2.

It's important to note that the square root of a fraction is a positive and negative solution, so the solutions are x = sqrt(5/3) - 2 and x = -sqrt(5/3) - 2

Step-by-step explanation:

In order to leave an equal space between shelves, the distance between each shelf should be 9 feet 10 inches.

1. The floor-to-ceiling clearance is 9 feet 10 inches.

2. Each shelf is 10 inches thick.

3. To leave an equal space between shelves, the distance between each shelf should be the same as the floor-to-ceiling clearance, which is 9 feet 10 inches.

In order to ensure that there is an equal space between each of the shelves, the distance between each shelf should be 9 feet 10 inches. This is because the floor-to-ceiling clearance is 9 feet 10 inches, and the thickness of each shelf is 10 inches.

Therefore, in order to have an equal space between shelves, the total distance between each shelf should be 9 feet 10 inches. This is the best way to ensure that each shelf is equally spaced from the next.

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The probability that a death will result from an accident is 0.105, or 10.5%.

Given:

In foggy conditions, 25% of accidents result in fatalities.

Rain-related accidents result in fatalities in 12.5% of cases.

In sunny weather, 5% of accidents result in fatalities.

To find : The probability that a death will result from an accidents

The likelihood that a death will ensue from an accident

5% of 60%(sunny) (sunny)

25% of 20%(foggy) (foggy)

12.5% of 20%(rainy) (rainy)

Probability = 0.05 x 0.6 x 0.25 x 0.125 x 0.22

Chance is 0.105

Chance is 10.5%.

There is a 10.5% chance that a fatal accident may occur.

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Answer: 12/48 = 25%

Step-by-step explanation: If the unit rate that characterizes my juice reflects its concentration, then there are 36 + 12 = 48 ounces of matter in total. The orange juice mix that we add is 12 ounces of mix, therefore the concentration is 12/48 = 25%.

Answer:

The gravitational force acting on the 6-kg bowling ball at the top of the 120-meter tall building is approximately 58.64 Newtons.

Step-by-step explanation:

Work Shown:

|x - 5| < 3

-3 < x-5 < 3

-3+5 < x-5+5 < 3+5

2 < x < 8

The graph will have open circles at 2 and 8, then shade between the open circles. The open circles indicate "do not include this endpoint". This is why choice A is the final answer.

The radius of such a cylinder will be 8 and height=8/3.

What is a cylinder?

Cylinder is one of the basic 3d shapes, in geometry, which has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center. The line segment joining the center of two circular bases is the axis of the cylinder. The distance between the two circular bases is called the height of the cylinder. LPG gas-cylinder is one of the real-life examples of cylinders.

Since, the cylinder is a three-dimensional shape, therefore it has two major properties, i.e., surface area and volume. The total surface area(TSA) of the cylinder is equal to the sum of its curved surface area and area of the two circular bases. The space occupied by a cylinder in three dimensions is called its volume(V).

V=πr²h and TSA=2πr²+2πrh where r=radius and h=height.

Now,

In any case, we can let the radius of the inscribed cylinder be x

. That must therefore mean that the height of the cylinder is 8−4/6x

. This makes the volume of the cylinder

V=πx^2(8−2/3x)=π(8x^2−2/3*x^3)

To find the maximum volume of the cylinder we take the derivative of V

with respect to x

and set it to 0

dV/dx=π(16x−2x^2)=0⇒16x−2x^2=2x(8−x)=0

x=0  leads to a trivial case, which leaves us with x=8

. This means that the height is 8−2/3*8=8/3

, and the volume is therefore

V=π⋅8^2⋅8/3

V=512/3π.

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The number of student tickets sold are 109.

As per the given data a high school drama department sold 238 tickets for their performance.

An adult ticket cost $6. 75.

A student ticket cost $3. 50.

Let the number of adult tickets be x.

Let the number of student tickets be y.

Then we know that the total number of tickets is 238.

x + y = 238 ... (1)

If we multiply the cost of a ticket by the number of tickets we can also get the total.

6. 75x + 3. 50y = 1252. 25(....... (2))

Now we have two equations and two unknowns and we can find the value for these unknowns

Lets use substitution method.

x + y = 238

x = 238 - y

Substitute x = 238 - y in equation (2)

6. 75(238 - y) + 3. 50y = 1252. 25

1606.5 - 6.75y + 3. 50y = 1252. 25

- 3.25y = - 354.25

3.25y =  354.25

y = 109

Substitute y = 109 in equation (1)

x + 109 = 238

x = 129.

Therefore number of student tickets are 109.

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According to the equation of the trend line the population will reach 52900 in 27831 years.

A mathematical statement known as an equation is a combination of two expressions joined together by the equal sign.

The equation of the trend line is:

y = 1.9x + 21

where, y is the population and x indicate the year.

To find the number of years in which the population reach 52900, substitute y = 52900.

y = 1.9x + 21

52900 = 1.9x + 21

52900 - 21 = 1.9x

52879/ 1.9 = x

x = 27831

Hence, according to the equation of the trend line the population will reach 52900 in 27831 years.

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The standard deviation of the household income will be increased by $5,000.

The standard deviation is a measure of variation from the mean that takes spread, dispersion, and spread into account. The standard deviation reveals a "typical" divergence from the mean. It is a popular measure of variability since it retains the original units of measurement from the data set.

standard deviation is increased by 5x/100 = 0.05x

Change in standard deviation = $5000

There is little variety when data points are near to the mean, and there is a lot of variation when they are far from the mean. How much the data differ from the mean is determined by the standard deviation. Standard deviation, which is based on all data, is the most often used metric for measuring dispersion. As a result, the standard deviation's value can be affected by even a slight change in one number.

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The z score that corresponds to the 90th percentile is 1.28. Option D

A z-score (also called a standard score) gives you an idea of how far from the mean a data point is. But more technically it’s a measure of how many standard deviations below or above the population mean a raw score is.

The 90th percentile refers to the value above 90 percent of the data. This is illustrated in the figure.

Therefore, using a z-table (also attached) or a technology, we can solve that  getting the  z=1.28.

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She needs to go to the swimming pool about 14 times for it to be worth paying the membership fee.

To determine how many times you need to go to the swimming pool to make the membership fee worth paying, you can use the following formula:

Number of visits = membership fee / (cost without the membership - cost with membership)

Plugging in the values, we get:

Number of visits = $50 / ($5 - $3.50)

The savings from the membership's lower entrance price will have surpassed the cost of the membership after 14 visits.

Hence, she needs to go to the swimming pool about 14 times for it to be worth paying the membership fee.

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Answer:

55°

Step-by-step explanation:

For the line including the 110°, the angle of the supplementary angle is 70° which is the 'non-equivalent' length of the isosceles triangle. Then do:

(180°-70°)/2 = 55° to get x

Answer:

Supplementary angles, x = 55

Step-by-step explanation:

Supplementary angles: straight line means both angles add up to 180, this if the outside angle is 110 then the inside angle is 180° - 110° = 70°

Since it is an isosceles triangle, it means both angles are equal to x therefore

[tex]180 - 70 = 2x\\110 = 2x\\\frac{110}{2} = x\\x = 55[/tex]

The expression that shows John's score will be 2x + 9.

It is vital to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

In this case, Mai has a score of x while John has 9 more than twice mai's score.

The expression for this relationship will be:

= (2 × x) + 9

= 2x + 9

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Complete question

Mai has a score of x. John has 9 more than twice mai's score. Illustrate the expression for Johnsc score.

The frequency table has been created in the attachment

Given that 56 respondents did not belong to any clubs, we know that the number of 7th graders who belong to zero clubs is 56.

Given that twice as many 7th graders belonged to one club as no clubs, we can set up the equation:

x = 2 * 56

Given that 10 fewer 7th graders belonged to more than one club than no clubs, we can set up the equation:

y = 56 - 10

Given that twice as many 8th graders belonged to one club as more than one club, we can set up the equation:

z = 2*w

Now we have the following system of equations:

x = 2 * 56

y = 56 - 10

z = 2*w

x+z = 150

y+w = 150

By solving the above system of equations we get:

x = 112

y = 46

z = 112

w = 56

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The linear equation parallel to y=(2/3)x+1 that passes through (3, 0) is:

y = (2/3)*x - 2

A general linear equation can be written in the slope-intercept form as:

y = m*x + b

Where m is the slope and b is the y-intercept.

Particularly, two linear equations are parallel only if both equations have the same slope and different y-intercepts.

Then a line parallel to:

y = (2/3)*x + 1

Is of the form:

y = (2/3)*x + b

And we want this line to pass through the point (3, 0), replacing these values we will get:

0 = (2/3)*3 + b

0 = 2 + b

-2 = b

Then the linear equation is:

y = (2/3)*x - 2

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The equation of the line in slope intercept form is y = -2.65x + 25.

The x-intercept means when the gift card has a balance of zero dollars.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore. let's find the slope of the line using (2, 19.7) and (4, 14.4).

Hence,

m = slope = 14.4 - 19.7 / 4 - 2

m = - 5.3 / 2

m = - 2.65

Therefore, let's find the y-intercept using (2, 19.7).

y = -2.65x + b

19.7 = -2.65(2) + b

b = 19.7 + 5.3

b = 25

Therefore, the equation of the line is y = -2.65x + 25.

The x-intercept is the value of x when y = 0.

Hence,

0 = -2.65x + 25

-25 = -2.65x

x = -25 / -2.65

x = 9.4

The x-intercept means the gift card has zero balance. At this point the medium cup of coffee is 9.4 .

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A geometric sequence begins with 72, 36, 18, 9, is Of(n) is 72(2)+1.

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Answer:

f(n) = 72(0.5)n−1

Step-by-step explanation:

Got right.

Correct option is D, the fraction of area of square region ABCD is 1/4.

A + B + C = D + E + F since diagonal QS divides the square into two equal portions.

We can see that the areas of regions A and F must be equal because they have the exact same measurements and form. Similar reasoning leads us to the conclusion that the areas of regions D and C are equal.

As a result, it follows that the size of regions E and B must likewise be equal. Due to the fact that URPT is a parallelogram, its area equals (base)(height)=(1)(2)=2.

Area of region E = Area of region B = 1 as a result.

The percentage of the square PQRS's area is represented by the darkened region 1/4 is a fraction.

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Complete question -

According to the information in the table, the value of B is 50 (option B)

To find the value of B we must calculate the constant, for that we have to perform the following operation:

In this case, we use the values of another column to identify the constant that applies to all the values in the table and the result is the following:

Additionally, to find the value of B we must perform the following operation:

According to the above, the correct answer would be 50 (option B).

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The relative frequencies for the car riders are given as follows:

A relative frequency is obtained with the division of the number of desired outcomes by the number of total outcomes.

The total number of car riders is given as follows:

78.

The number in each grade is given as follows:

Hence the relative frequencies are given as follows:

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Heat loss, according to Newton's cooling curve, is exponential. Like a half-life, it operates.

Cake temperature and ambient temperature varied by 140 F. The cake has lost half of that difference after 30 minutes, thus that is the half-life. It will shed another half or 35 F in the next 30 minutes, bringing the temperature to 105 F. It will shed 17.5 F in about 30 minutes, leaving 87.5 F.

The temperature is between the last two, at 100 F, so it will be between an hour and an hour and a half. You get an interpolated result of about an hour and ten minutes.

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The transformation represented by the figure is (c) translation

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

The figure

On the figure, we have the following

A figure and its translated image

When a shape is translated to form another, then the transformation is a translation

Hence, the transformation is translation

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After solving, 1.53 pints of blue paint she used to paint her bedroom walls.

Irene uses 6.1 pints of white paint and blue paint to paint her bedroom walls.

3/4 of this amount is white paint, and the rest is blue paint.

The combined amount of blue and white paint = 6.1 pints

Quantity of white paint applied to bedroom walls = 3/4

Quantity of blue paint applied to bedroom walls = 1 - 3/4

Quantity of blue paint applied to bedroom walls = 4/4 - 3/4

Quantity of blue paint applied to bedroom walls = (4 - 3)/4

Quantity of blue paint applied to bedroom walls = 1/4

Hence, 

Blue paint were used to paint the bedroom's walls = 1/4 × 6.1

Blue paint were used to paint the bedroom's walls = 1.53

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The complete question is:

Irene uses 6. 1 pints of white paint and blue paint to paint her bedroom walls. 3/4 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?

4 cups of mayonnaise should be used if 1 cup of pecans is used.

As per the given data:

A recipe calls for  [tex]$1\frac{1}{2}[/tex] cups of mayonnaise and [tex]$\frac{3}{8}[/tex] cups of pecans.

First, convert the mixed fraction to an improper fraction.

[tex]$1\frac{1}{2}[/tex] cups of mayonnaise = [tex]$\frac{3}{2}[/tex]

Here we have to determine how much mayonnaise should be used if 1 cup of pecans is used.

This can be determined by using the unitary method.

We may determine the value of one unit from the value of many units and the value of many units from the value of one unit using the unitary technique.

The ratio of the amount of pecans comparing reality and the recipe is:

[tex]$= \frac{1}{\frac{3}{8} }[/tex]

= [tex]$\frac{8}{3}[/tex]

To find the amount of mayonnaise that should be added:

= [tex]$\frac{8}{3}[/tex] × [tex]$\frac{3}{2}[/tex]

= 4

Therefore 4 cups of mayonnaise is required.

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A graph of the ordered pairs (time, distance) for the rows in the ratio table is shown in the image attached below.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/10

Constant of proportionality, k = 0.2

When time x = 20, the distance (y) is given by:

y = 20(0.2)

y = 4 miles.

When time x = 30, the distance (y) is given by:

y = 30(0.2)

y = 6 miles.

When time x = 40, the distance (y) is given by:

y = 40(0.2)

y = 8 miles.

Next, we would use an online graphing calculator to plot the ordered pairs as shown in the graph attached below.

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You can "find algebraically" if a function is even, odd, or neither by taking it, substituting -x for x, simplifying it, and then comparing the results to what you had initially.

The function is even if it is exactly the same as what you started with (that is, if f(-x) = f (x), with all the signs remaining the same. The function is odd if it is exactly the opposite of what you started with (that is, if f(-x) = -f(x), with all the signs switched.

The function is neither even nor odd if the outcome is neither exactly the same nor exactly the opposite (that is, neither having all the same words but with all the signs reversed).

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The system of equations are:

15 + x = y

13 + 2x = y

The weight of the package is 2 pounds.

The delivery cost for both services is 17$.

Here is a system of equations you can use to represent the cost of the two courier services:

First courier: 15 + x = y

Second courier: 13 + 2x = y

Where x is the weight of the package in pounds and y is the total cost of delivery.

We know that the two courier services are equivalent in terms of cost, so we can set the two equations equal to each other:

15 + x = 13 + 2x

then we can subtract 15 from both sides

x = 13 + 2x -15

x = -2 + 2x

then we can subtract x from both sides

-x = -2

then we can divide both sides by -1

x = 2

The package weighs 2 pounds, and the delivery cost for both services is 15 + 2 = 17$.

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