May finds a house for a sale price of $355,000. She meets with her bank and finds a 30-year simple interest mortgage. If May accepts the mortgage, she would pay $798,750 in simple interest over the life of the loan. 1. How much is the interest rate of the mortgage? 2. How much would be her monthly mortgage payment? 3. If May decided to use a 15-year simple interest mortgage, how much would she save on interest charges?

Answer:

1) x = 6

2) x = 2√10 = 6.3

3) z = 19

4) x = 1

Step-by-step explanation:

1)

[tex]10x = 5(12)[/tex]

[tex]10x = 60[/tex]

[tex]x = 6[/tex]

2)

[tex] {x}^{2} = 10(4)[/tex]

[tex] {x}^{2} = 40[/tex]

[tex]x = 2 \sqrt{10} = 6.3[/tex]

3)

[tex](14 + 4)(14) = (z + 9)(9)[/tex]

[tex]18(14) = 9(z + 9)[/tex]

[tex]2(14) = z + 9[/tex]

[tex]28 = z + 9[/tex]

[tex]z = 19[/tex]

4)

[tex]2(4) = 8x[/tex]

[tex]8 = 8x[/tex]

[tex]x = 1[/tex]

The rate of change (slope) for a linear relationship can be found by taking the difference in the y-values divided by the difference in the corresponding x-values.

In this case, the change in y from x=1 to x=9 is 32-8=24, and the change in x is 9-1=8. Therefore, the rate of change is:

rate of change = (change in y) / (change in x) = 24/8 = 3

So the answer is A. 3.

The regular polygon with an exterior angle measuring 120 will have 3 equal sides. Thus, an equilateral triangle have three equal sidea and angles is a regular polygon.

Regular polygon: A regular polygon is both "equiangular" and "equilateral," meaning it has all sides that are the same length and interior angles that are the same size.

The following algorithm determines an ordinary polygon's exterior angle:

Exterior Angle = [tex]360 Degrees / Sides[/tex]

We can therefore make up an equation if the exterior angle measurement is [tex]120[/tex] degrees:

[tex]120 = 360/n[/tex] the number of sides being n

[tex]n (sides) = 360/120 = 3[/tex]

Three sides [tex]=[/tex] triangles are polygons with three sides.

An equilateral triangle is a regular three-sided polygon.

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Debbie sat for 9 tests with a total score of 756, based on her average of 84 marks for all tests.

The average refers to the quotient of the total value divided by the number of data items.

The average is also known as the mean.

The total number of marks obtained in x tests = 504

The additional number of tests taken = 3

The total number of marks obtained in x + 3 tests = 756

The number of marks obtained in 3 tests = 252 (756 - 504)

The average marks obtained in the 3 tests = 84 (252 ÷ 3)

The average marks obtained in x tests = 84

x = 6 (504 ÷ 84)

Therefore, the total number of tests taken = x + 3 = 6 + 3 = 9.

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Answer:

12.74

Step-by-step explanation:

To find the diameter of a circle with a given circumference, you can use the formula:

Circumference = π x diameter

where π (pi) is a mathematical constant approximately equal to 3.14159.

In this case, the circumference is given as 40. So we can rearrange the formula to solve for the diameter:

diameter = Circumference / π

Substituting the given values, we get:

diameter = 40 / π

To get the answer to the nearest hundredth, we can use a calculator or estimate π to a few decimal places. Let's use π ≈ 3.14.

diameter = 40 / 3.14

diameter ≈ 12.74

Therefore, the diameter of the circle to the nearest hundredth is approximately 12.74.

Step-by-step explanation:

Circumference = pi  * d

circumference / pi = d  =  40 / pi = 12.73 units

It will take approximately 13.6 years for the account value to reach $9000.

What is an account value?

We can use the formula for compound interest to solve this problem:

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

where A is the final amount, P is the principal or initial amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

We want to find t, so we can rearrange the formula as:

t = (1/n) × log(A/P) / log(1 + r/n)

Substituting the given values:

P = $3200

r = 8% = 0.08

A = $9000

n = 1 (interest is compounded annually)

Using a calculator:

t = (1/1) × log(9000/3200) / log(1 + 0.08/1)

t ≈ 13.6

Rounding to the nearest tenth of a year, it will take approximately 13.6 years for the account value to reach $9000.

What is an interest ?

Interest is the cost of borrowing money, or the compensation paid by a borrower to a lender for the use of money. When you borrow money, you are usually required to pay back the amount borrowed (the principal) plus an additional amount of money, which is calculated as a percentage of the principal and represents the interest.

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they spent a total of $215.76 including tax and tip.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Therefore, the total cost per person without tax and tip would be:

$28 + $30 = $58

Since there were three people, the total cost without tax and tip would be:

$58 × 3 = $174

The sales tax would be 4% of the total cost:

$174 × 0.04 = $6.96

The tip left was about 5 times the amount of tax, so:

Tip = $6.96 × 5 = $34.80

Therefore, the total cost including tax and tip would be:

$174 + $6.96 + $34.80 = $215.76

So, they spent a total of $215.76 including tax and tip.

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An equation that represents the transformed function include the following: A. y = |1/4x|.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.

Since the vertex of the two absolute value functions is located at points (0, 0), we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin as follows:

y = |1/4x|

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The sample size was 1000 Americans, and 20% of the survey respondents reported owning 2 pets. To calculate the number of Americans who own 2 pets, we can use the formula (20/100) x 1000 = 0.20 x 1000 = 200. However, we cannot directly conclude that 20% of all Americans own 2 pets.

The 1000 Americans that were polled in this case make up the sample. This indicates that a sample rather than the complete American population was used to get the data on pet ownership.

A statistic, which is a quantitative description of the sample, is the finding that 20% of survey respondents reported having two pets. It is crucial to remember that while this statistic provides useful information about the sample, it cannot be used to draw conclusions about the full population without additional research or inference.

Based on the poll, we can apply the following calculation to get the proportion of Americans who own two pets:

Number of Americans who own 2 pets = (Percent of survey respondents who own 2 pets / 100) x Sample size

Plugging in the given values, we get:

Number of Americans who own 2 pets = (20 / 100) x 1000

= 0.20 x 1000

= 200

As a result, we may assume that 200 Americans possess 2 pets based on the poll results. However, as this would entail assuming the representativeness of the sample and the generalizability of the results, we cannot immediately conclude that 20% of all Americans own 2 pets.

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Step-by-step explanation:

The length and the width of the rectangle are LEGS of a RIGHT triangle

    the 91 yards is the hypotenuse .....so you can use the Pythagorean Theorem for right triangles

    hyp^2  =  leg1^2   + leg2^2

     91^2   = 35^2 +   width^2

      91^2 - 35^2  = width^2

          7056 = width^2  

                 then width = sqrt (7056) = 84 yards

Rounding to the nearest whole number, the previous number of Covid patients before 2 hours was 39,991.

A population's growth rate gauges how much a quantity's worth has increased in percentage terms.

To find the number of Covid patients before 2 hours, we need to apply the 5% growth rate for 2 hours to the current number of patients (44,100 at 8:00 am).

First, we can find the growth factor by adding 1 to the percentage growth rate expressed as a decimal:

1 + 0.05 = 1.05

Next, we can raise the growth factor to the power of the number of hours of growth:

1.05² = 1.1025

Finally, we can divide the current number of patients by the growth factor to find the previous number of patients:

44,100 / 1.1025 = 39,990.91

Rounding to the nearest whole number, the previous number of Covid patients before 2 hours was 39,991.

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The total number of unique ways in which the type of monsters can be collected by the collector as per the conditions are 6.

The monster collector wants to catch 22 little monsters.

The combination in one case is given by the formula,

C(n, a) = ⁿCₐ = n!/(n-a)!(a)!

Now the question says he intends to catch at least two of each type.

This is represented mathematically because the has twenty small sample container assemblies. Collector can only access non-unique types. They are small monsters with attributes of water, fire and grass.

C(3, 2) = 3!/(2!(3-2)!)

= 3!/2! x1!

= 3

He also intends to catch at least three fire monsters.

(3-1)!)

= 3!/1!x2!

= 3

The number of different combinations is therefore 6.

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The total number of muffins the bakeries make each day is 36,552.

As per the given information, A muffin company owns 6 bakeries. Each

bakery makes 6,092 muffins per day.

To find out how many muffins in total the bakeries make each day, you

should multiply the number of bakeries by the number of muffins each

bakery makes per day.

Identify the number of bakeries (6) and the number of muffins per bakery

(6,092).

Multiply the number of bakeries by the number of muffins per bakery (6 × 6,092).

Therefore, each day, bakers produce a total of 36,552 muffins.

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The probability that all of the customers will give him a tip is 3/100 or 0.03 or 3%.

Based on the table presented, Steve simulated the situation by rolling a six-sided die 5 times. Each time an odd number appears, it represents a tip. This table shows the results of 100 trials: number of times an odd number appears 0 1 2 3 4 5 number of trials 2 15 33 31 16 3.

The customer leaves a tip 50% of the time, we can calculate the probability by multiplying the probability of a single tip (0.5) by itself 5 times.

Probability = (0.5) * (0.5) * (0.5) * (0.5) * (0.5)

Probability = 0.03125

From the table presented, it can be concluded that Steve got all of the five customers tipping him in 3 trials. Therefore, the probability that all of the customers will give him a tip is 3/100 or 0.03 or 3%.

The probability that an event will occur is the ratio of the number of ways that the event can occur to the number of total possible outcomes. In this scenario, the probability of a customer giving Steve a tip is 0.5.

Since the customer either gives a tip or doesn't.

In other words, there are two possible outcomes (gives a tip or doesn't give a tip) and only one outcome results in a tip (gives a tip).

Therefore, the probability of getting a tip from one customer is 1/2 or 0.5.

Since there are five customers, the probability of all five customers giving Steve a tip is calculated by multiplying the probability of each customer giving a tip.

This is because the occurrence of each event is independent of the others.

Therefore, the probability of all five customers giving Steve a tip is:

0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.03125 or 3.125%.

From the table presented, it can be concluded that Steve got all of the five customers tipping him in 3 trials.

Therefore, the probability that all of the customers will give him a tip is 3/100 or 0.03 or 3%.

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A rational inequality for which -2 < x < 1 is the solution is (3x - 1)/(x + 2) > 2.

An inequality that incorporates one or more rational expressions—that is, expressions that can be expressed as the quotient of two polynomial expressions—is referred to as a rational inequality. The same techniques used to resolve other kinds of inequalities, such as graphing, testing intervals, or algebraic manipulation, can also be used to resolve rational inequalities. The denominator of a rational expression cannot, however, equal zero, hence extra care must be made to identify and rule out any values of the variable that would do so, as these values would render the expression undefinable.

A rational inequality for which -2 < x < 1 is the solution is:

(3x - 1)/(x + 2) > 2

In the equation when,

For x -2, the inequality holds because both the denominator and the numerator are negative.

When -2 x 1, the inequality is true since both the denominator and the numerator are positive.

When x > 1, the denominator and numerator are both positive, but the expression's value is less than 2, rendering the inequality untrue.

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The value for x is 10. The solution has been obtained by using the triangle similarity theorem.

What is triangle similarity theorem?

The triangle that comes from the intersection of two sides of a triangle by a segment parallel to one of the sides is equivalent to the original triangle, and the segment that splits the two sides it intersects is proportionate.

In the given figure, a line is parallel to the base of the triangle.

So, as per triangle similarity theorem, the other sides are proportional to each other.

From this, we get

⇒ [tex]\frac{12}{x}[/tex] = [tex]\frac{18}{15}[/tex]

Now, we will solve the equation for x to obtain the required value.

On solving, we get

⇒ 18x = 12 * 15

⇒ 18x = 180

⇒ x = 10

Hence, the value of x is 10.

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Answer:

16/25

Step-by-step explanation:

64/100 which simplifies to 16/25 if the asked for the simplified answer

Answer:

D

Step-by-step explanation:

(my trick to calculate percentage) to calculate 1% of 70 we do 70/100= 0.7, then we multiply 0.7 with the percent which is 80, so 0.7*80=56

therefor the answer is 56!

Answer:

D. 56

Step-by-step explanation:

80% can also be said as 80/100 and then multiply that with the total value of the thing you need to find.

So in this case its 70.

Now 70x(80/100) [remember the BODMAS rule] solve the bracket first.

80/100 = .8 x 70 = 56

hence the option D

Answer:

1/21

Step-by-step explanation:

you do 1/7 divided by 3, because she distributes 1/7 liters of juice to 3 students. We can infer that its dividing because it says distribute.

A histogram of the average age for every possible combination of cases from the population is referred to as a scatter plot

A scatter plot matrix is a plot that presents all feasible scatter plots for a given collection of variables in a matrix structure. It is helpful for investigating the connections between related factors in a collection. A scatter plot matrix is not a histogram that shows the average age for every mix of instances drawn from the community.

Instead, it is referred to as a sampling distribution or a distribution of sample means. This kind of histogram displays the range of means for all conceivable community samples of a specific number. It is a crucial idea in statistics because it aids in understanding a population's characteristics based on a subset of data.

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Two clusters can be seen in the scatterplot, and their factors are connected. Y increases, but the growth is gradual, as x increases in the bottom one. As x rises in the upper cluster, y rises as well, but more quickly.

A collection of points plotted on a horizontal and vertical axis is known as a scatter plot. Because they can display the degree of link, if any,between the values of measured quantities or phenomena, scatter plots are crucial in statistics. Scatter graphs are used for showing data points on an axis that is vertical and horizontal to show how much one element influences another.

Data visualisation that demonstrates the connection between various variables is known as a scatter plot. To show this data, different components of information are positioned between an x- and y-axis. This type of data visualisation takes its name from the way that each of the information points appears to be "spread" across the graph.

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The complete question attached below,

Answer:

a) [tex] \frac{4}{5} [/tex]

b) [tex] \frac{3}{35} \: \: larger[/tex]

.

Step-by-step explanation:

Given:

[tex] \frac{4}{5} \: and \: \frac{5}{7} [/tex]

a) In order to find the larger fraction, we have to make their denominator the same (it's 35 (multiply both fractions' denominators) in this case)

[tex] \frac{4 \times 7}{35} = \frac{28}{35} [/tex]

[tex] \frac{5 \times 5}{35} = \frac{25}{35} [/tex]

[tex] \frac{28}{35} > \frac{25}{35} [/tex]

.

b) In order to find how much larger it is, we have to subtract the smaller fraction from the larger one (find the difference):

[tex] \frac{28}{35} - \frac{25}{35} = \frac{3}{35} [/tex]

The value of angle EFG is 151°.

What is angle?

An angle is a measure of the amount of rotation or turn between two lines, rays, or planes that meet at a common point called the vertex. The unit of measurement for angles is degrees or radians.

An angle is formed when two rays share a common endpoint, known as the vertex. The rays are often referred to as the arms or legs of the angle. The angle is measured in degrees, with a full circle measuring 360 degrees.

Angles can be classified according to their size. An acute angle measures less than 90 degrees, a right angle measures exactly 90 degrees, an obtuse angle measures more than 90 degrees but less than 180 degrees, and a straight angle measures exactly 180 degrees.

Angles can also be complementary or supplementary. Two angles are complementary if their sum is equal to 90 degrees, and they are supplementary if their sum is equal to 180 degrees.

Angles are used in many fields, including mathematics, physics, engineering, and architecture. They are used to measure distances, calculate trajectories, and design buildings and structures.

Here given,

[tex]\angle EFH = {44}^{o} [/tex] and

[tex] \angle \: HFG = {107}^{o} [/tex]

Here

[tex]\angle EFG = \angle EFH + \angle HFG \\ \angle EFG = {44}^{o} + {107}^{o} \\ = {151}^{o} [/tex]

So, required value of angle EFG is 151°.

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The UCR (Uniform Crime Reporting) is B. not a truly reliable measure.

The UCR is a program established by the FBI in 1930 to collect and analyze crime statistics from law enforcement agencies across the United States. Although it provides useful data and insights into crime trends, it is not without its limitations. One significant issue with the UCR is that it relies on voluntary reporting from law enforcement agencies, meaning that some areas may not provide complete or accurate data. This can lead to an underrepresentation of certain crimes or inconsistencies in reporting across jurisdictions.

Another limitation is that the UCR only includes reported crimes, excluding any unreported criminal activity. This means that the data does not necessarily provide a comprehensive picture of all crimes occurring in a given area. Additionally, the UCR uses a hierarchy rule, meaning that if multiple crimes are committed during a single incident, only the most severe crime is counted. This can result in an undercounting of less severe but still significant crimes.

In summary, although the UCR provides valuable information on crime trends and patterns, it is not a truly reliable measure due to its reliance on voluntary reporting, exclusion of unreported crimes, and hierarchy rule. Therefore, the correct option is B.

The question was incomplete, Find the full content below:

it is fair to say that the ucr is: group of answer choices

A. A mutually exclusive measure

B. Not a truly reliable measure

C. An exhaustive measure

D. All of the above

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The angles with a common reference angle of 340° are:

To find an angle in each quadrant with a common reference angle of 340°, we need to determine the reference angle of 340° and then find angles in each quadrant with that same reference angle.

The reference angle of 340° is found by subtracting the nearest multiple of 360°, which is 0°, from 340°. Therefore, the reference angle of 340° is 20°.

Quadrant I:

To find an angle in quadrant I with a reference angle of 20°, we simply take the reference angle itself, which is 20°.

Quadrant II:

To find an angle in quadrant II with a reference angle of 20°, we need to add the reference angle to 180°, which gives us 200°.

Quadrant III:

To find an angle in quadrant III with a reference angle of 20°, we need to subtract the reference angle from 180°, which gives us 160°.

Quadrant IV:

To find an angle in quadrant IV with a reference angle of 20°, we need to subtract the reference angle from 360°, which gives us 340° (which is the original angle we started with).

Therefore, the angles in each quadrant with a common reference angle of 20° are:

The complete question is:-

Find an angle in each quadrant with a common reference angle with 340°, from 0°≤θ<360°

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Answer:

42 students would be expected to pick an orange

Answer:

Need to be more specific. What units?

Step-by-step explanation:

The area of the shaded square is 4 square centimeters, and the radius of the circle is approximately 1.41 cm.

To find the area of the shaded square and the radius of the circle, we will follow these steps:
Step 1: Identify the dimensions of the square.
From the student question, we know that the square has sides of 2 cm each.
Step 2: Find the area of the square.
The area of a square can be calculated using the formula:

Area = side × side.
In this case, the area of the square is:

2 cm × 2 cm = 4 square centimeters.
Step 3: Find the diagonal of the square.
The diagonal of a square can be found using the Pythagorean theorem:

diagonal² = side² + side².
In this case, the diagonal² = 2 cm² + 2 cm² = 4 cm² + 4 cm² = 8 cm².
Taking the square root of both sides, we get: diagonal = √8 cm ≈ 2.83 cm.
Step 4: Find the radius of the circle.
Since the circle is inscribed in the square, its diameter is equal to the diagonal of the square.

Thus, the radius of the circle is half the diagonal.
Radius = diagonal ÷ 2 ≈ 2.83 cm ÷ 2 ≈ 1.41 cm.

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