A triangle has two 90° angles and a side 12 centimeters in length.
Select True or False for each statement about this type of triangle.

The value of the length x is 2√70. Option C

To determine the value of the length of the triangle, we need to consider the different trigonometric identities, they are;

Now, using the Pythagorean theorem, we have;

17² = x² + 3²

Find the square values and substitute

289 = x² + 9

collect the like terms

x² = 289 - 9

Subtract the values

x² = 280

Find the square root of both sides

x = √280

Find the values

x = √4× 70

x = 2√70

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Part(2),

The volume of the snowcone is larger than the volume of the paper cup, the snowcone will overflow when it melts.

Part(3),

The difference in price per cubic inch is $0.0128/in³.

Part(4),

The volume of the cylinder with a radius of 8 inches and a height of 6 inches.

Part(2)

The volume of a cone is given by the formula V = (1/3)πr²h,

where r is the radius and h is the height. The volume of the snowcone is therefore V = (1/3)π(4 cm)²(12 cm) = 201.06 cubic cm.

V = (1/3)π(3 cm)²(12 cm) = 113.1 cubic cm.

Since the volume of the snowcone is larger than the volume of the paper cup, the snowcone will overflow when it melts.

Part(3)

To compare the cost per cubic inch of the two sizes of cereal boxes, we need to calculate the volume of each box and divide the cost by the volume.

The volume of the family-sized box is V = 3 in x 9 in x 12 in = 324 cubic inches.

The cost per cubic inch is therefore $6/324 in³ = $0.0185/in³.

The volume of the regular-sized box is V = 2 in x 8 in x 9 in = 144 cubic inches. The cost per cubic inch is, therefore, $4.50/144 in³ = $0.0313/in³.

The difference in price per cubic inch is $0.0313/in³ - $0.0185/in³ = $0.0128/in³.

Part(3)

The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

For the cylinder with a radius of 6 inches and a height of 8 inches, the volume is V = π(6 in)²(8 in) = 904.78 cubic inches.

For the cylinder with a radius of 8 inches and a height of 6 inches, the volume is V = π(8 in)²(6 in) = 1206.37 cubic inches.

Therefore, the volume of the cylinder with a radius of 8 inches and a height of 6 inches.

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The area of "shaded-region" formed between the two circles having radius as 14 and 6, is 160π square units.

The area of region between "two-circles" can be calculated as area of the "larger-circle" minus area of "smaller-circle".

The "larger-circle" is having radius of = 14 units;

The "smaller-circle" is having radius = 6 units;

So, we can find the area of the region as:

Area = π(14)² - π(6)²;

Area = π(196 - 36),

Area = π(160),

Therefore, area of the region between the two circles is 160π square units.

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The given question is incomplete, the complete question is

Find the area of the shaded region in the figure below if the radius of the outer circle is 14 and the radius of the inner circle is 6. Keep your answer in terms of π.

Mrs. Kenny can complete 5 projects with 1/4 of a pound of clay left over.

We know that,

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

To find out how many projects Mrs. Kenny can complete with 7/8 pound of clay, we need to divide 7/8 by 1/6:

= (7/8) ÷ (1/6)

To divide fractions, we need to invert the second fraction and multiply:

= (7/8) × (6/1)

Simplifying the fractions, we get:

(7 × 6)/(8 × 1) = 42/8 = 5 1/4

Thus, Mrs. Kenny can complete 5 projects with 1/4 of a pound of clay left over.

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Here cuz:

Frank got more cuz you see Graham has 1/3  and 3/4 and frank got 3/5 and 1/2 so he got more.

Hope This Helps Cuz!

Sample Response: Use the inverse operation to isolate the variable. Undo the subtraction of 4 by adding 4 to both sides of the equation. –4 + 4 = 0, and 9 + 4 is 13. The solution is q = 13. Check the solution by substituting 13 for q in the original equation, and then simplify. 13 – 4 is 9 and 9 = 9 is a true statement, so 13 is the solution.

Step-by-step explanation:

–4 + 4 = 0, and 9 + 4 is 13. The solution is q = 13. check it by taking 13 for q in the original equation, and then simplify. 13 – 4 is 9 and 9 = 9 is a true statement, 13 is the answer

The esteem of the annuity is roughly $21,713.22.

The intrigued (interest) earned on the annuity is roughly $14,513.22.

A. To discover the esteem of the annuity, we are able utilize the equation:

PV = C * ((1 - (1 + r)^(-n)) / r)

where PV is the display esteem of the annuity, C is the intermittent store, r is the intrigued rate per period, and n is the entire number of periods.

In this case, C = $120, r = 4.5%/2 = 0.0225 (since the intrigued is compounded semiannually), and n = 2 * 30 = 60 (since there are 2 periods per year for 30 a long time).

Stepping in these values, we get:

PV = $120 * ((1 - (1 + 0.0225)^(-60)) / 0.0225) ≈ $21,713.22

In this manner, the esteem of the annuity is roughly $21,713.22.

B. The intrigued earned on the annuity would be the overall esteem of the annuity short the entire sum stored over the 30-year period. The full sum kept would be:

Add up to Stores = $120 * 2 * 30 = $7,200

So the intrigued earned would be:

Intrigued = $21,713.22 - $7,200 = $14,513.22

In this manner, the intrigued earned on the annuity is roughly $14,513.22.

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The students' line that will be parallel to line d is the line with the same slope as d

The rules are given as

This means that the equations of the function are

Carly: y = x + 2

Ramil: y = 2x + 1

If the slope of line d is 1, Carly's line will be parallel to line d and if the slope of line d is 2, Ramil's line will be parallel to line d

This is because parallell lines have equal slopes

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The name of the shape Kimberly forms by connecting the points is a plane shape

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

A shape is formed by connecting points

As a general rule; shapes formed by connecting points are referred to as plane shapes, and examples of them are:

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The error that was made in finding the area of the circle is that diameter was used for radius. The correct area of the circle is: 113.10 ft²

The formula for area of a circle is expressed as:

A = πr²

where:

A is Area

r is radius

From the given circle, we are given the diameter as 12.

But radius = diameter/2 = 12/2

radius = 6

Thus, the error is that they used the diameter as radius.

Correct area of circle = π * 6²

= 36π

= 113.10 ft²

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-3x+y=-1 matches  m=3, (1, 2)

-3x+y=-1 matches  m=3, (1, 2) by point slope form

(5, 2)(6, 5) this matches with y=3x-13 b slope intercept form

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

m=3, b=2

Slope is 3 and y intercept is 2

This matches with equation y-3x=2

Now m=3, (1, 2)

Let us find equation in point slope form

y-2=3(x-1)

y-2=3x-3

-3x+y=-1

So -3x+y=-1 matches  m=3, (1, 2)

(5, 2)(6, 5) this matches with y=3x-13 by slope intercept form

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The correlation coefficient for the data shown in the table is: B. -1.

In order to calculate or determine the correlation coefficient for the data shown in the table (see attachment), we would have to determine the slope of the line based on the points as follows;

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (10 - 15)/(5 - 0)

Slope (m) = -5/5

Slope (m) = -1.

Slope (m) = (5 - 10)/(10 - 5)

Slope (m) = -5/5

Slope (m) = -1.

In this context, we can reasonably infer and logically deduce that there is a negative correlation between the data and the correlation coefficient is -1.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The product of the matrices is [24].

Given is a row matrix and a column matrix, we need to find the product of both,

So,

A = [-3, 3, 0]

B = [tex]\left[\begin{array}{ccc}-3\\5\\-2\end{array}\right][/tex]

Now, the product will be =

AB = [-3, 3, 0] ×  [tex]\left[\begin{array}{ccc}-3\\5\\-2\end{array}\right][/tex]

AB = [9 + 15 + 0]

AB = [24]

Hence the product of the matrices is [24].

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The area of the curve in the first quadrant is A = 2/7 units²

Given data ,

Let the region described is bounded by the curves y = x^(2/5) and y = 1 be in the first quadrant

Now , the point of intersection of these two curves is given by

x^(2/5) = 1

x = 1^5

So the two curves intersect at x = 1

Now , the area of the curve is given by y = x^(2/5) is the lower curve and y = 1 is the upper curve in the given interval [0, 1]

And , the , integral is used to find the area

∫[from 0 to 1] (1 - x^(2/5)) dx

∫(1 - x^(2/5)) dx = x - (5/7)x^(7/5) + C

Evaluated from 0 to 1, we get:

[(1 - (5/7)(1^(7/5))) - (0 - (5/7)(0^(7/5)))]

Simplifying further, we get:

[(1 - 5/7) - 0] = 2/7 units²

Hence , the area of the region bounded by the curves y = x^(2/5) and y = 1 in the first quadrant is 2/7 square units

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The proportion when completed for the triangles is a/c = h/b

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

The right triangles

The first expression in the proportion is a/c

This proportion represents leg/hypotenuse expression

Using this as a guide, we can make use of the following proportion

h/b

So, the complete equation is a/c = h/b

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Answer:

B' = (-8, -1)

C' (-1, 1)

Step-by-step explanation:

In your question, we are given A which is translated -3 units on the X axis, and translated -5 units on the Y axis.

Using this translation on points B and C we get B' = (-8, -1) and C' (-1, 1).

B = (-5, 4)

      -3, -5

B' = (-8, -1)

C = (2, 6)

     -3, -5

C' = (-1, 1)

After the vertical stretch by factor 3 the function becomes g(x)=3x².

The given function is f(x)=x² is vertically stretched by the factor 3.

When we stretch a function vertically, we multiply the base function by its scale factor. Hence, we have g(x) = 3·f(x). Let’s make sure to distribute 3 to each of the term in f(x).

Here, g(x)=3×x²

g(x)=3x²

Therefore, after the vertical stretch by factor 3 the function becomes g(x)=3x².

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Answer:

V = π(5.1^2)(7.1) + (1/3)π(5.1^2)(8.6)

= 184.671π + 74.562π

= 259.233π cubic feet

= about 814.4 cubic feet

Answer:

C

Step-by-step explanation:

because i did it in school and got it correct sorry if im wrong any way

When someone aged 20 sets up an IRA retirement account with an APR of 5% and deposits $65 at the end of each month, when he retires at age 65, the account will have a future value of $131,718.42.

b) Compared to the total deposit he made over time ($35,100.00), he generated a total compounded interest of $96,618.42.

The future value can be determined using an online finance calculator, which compounds the interest at 5% over a period of 540 months or 45 years.

Number of years = 45 years (65 - 20)

N (# of periods) = 540 months (45 years x 12)

I/Y (Interest per year) = 5%

PV (Present Value) = $0

PMT (Periodic Payment) = $65

Results:

Future Value (FV) = $131,718.42

Sum of all periodic payments = $35,100.00 ($65 x 540 months)

Total Interest = $96,618.42

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The equation of the straight line shown in the given graph is x = -2

From the question, we are to determine the equation the given straight line in the graph

To determine the equation of the line, we will use the given two points on the line

The given points are (-2, 2) and (-2, -3)

Using the formula,

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

Substitute the given points

(y - 2) / (x - (-2)) = (-3 - 2) / (-2 - (-2))

(y - 2) / (x + 2) = -5 / (-2 + 2)

(y - 2) / (x + 2) = -5 / 0

Cross multiply

0 × (y - 2) = -5 × (x + 2)

0 = -5x - 10

Add 5x to both sides

0 + 5x = -5x + 5x - 10

5x = -10

Divide both sides by 5

5x / 5 = -10/5

x = -2

Hence, the equation is x = -2

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Part(A),

The value of the mean is 27.1, the value of the mode is 12 and median is 27.5.

Part(B),

Tennis players should report the median value to show they are less prepared for the tournament.

Part A:

To calculate the mean, we need to find the sum of all the data values and divide by the total number of values:

Sum of the data = 12 + 12 + 29 + 20 + 22 + 26 + 31 + 31 + 40 + 68 = 271

Number of data values = 10

Mean = sum of the data/number of data values

Mean = 271 / 10

Mean = 27.1

Therefore, the mean time spent practicing is 27.1 minutes.

To find the median, we need to arrange the data in order from smallest to largest:

12, 12, 20, 22, 26, 29, 31, 31, 40, 68

There are 10 data values, so the median is the average of the two middle values:

Median = (26 + 29) / 2

Median = 27.5

Therefore, the median time spent practicing is 27.5 minutes.

To find the mode, we need to identify the data value that occurs most frequently. In this case, there are two modes:

Mode = 12 and 31

Therefore, the modes for the time spent practicing are 12 and 31 minutes.

To find the range, we need to subtract the smallest data value from the largest data value:

Range = largest data value - smallest data value

Range = 68 - 12

Range = 56

Therefore, the range of time spent practicing is 56 minutes.

Part B:

Based on the scenario, it is more appropriate for the tennis players to report the median value to show they are less prepared for the tournament. This is because there is one outlier value of 68, which is much larger than the other data values.

The mean is affected by outliers and may not represent the typical amount of time spent practicing for the tournament. On the other hand, the median is not affected by outliers and represents the middle value of the data set, which is a more accurate measure of the typical amount of time spent practicing.

Therefore, tennis players should report the median value to show they are less prepared for the tournament.

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Answer:

The answer is

1) x²=5²+6²

2)Volume

3)39.7ft

Step-by-step explanation:

KL=4-(-1)=5

KJ=3-(-3)=6

JL=x

using pythagoras theorem

x²=5²+6²

3)using pythagoras theorem

opp²=hyp²-adj²

let opp be y

y²=40²-5²

y²=1600-25

y²=1575

y=39.7ft

The sum of the sequence is 9828

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

First term, a = 12

Common ratio, r = 4

The sum of a finite geometric series is

Sn = a(1 - r^n)/(1 - r)

substitute the known values in the above equation, so, we have the following representation

Sn = 12 * (1 - 4^6)/(1 - 6)

Evaluate

Sn = 9828

Hence, the sum is 9828

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The different committees possible are 10,584. Option A is the answer.

Тhe number оf wаys tо choosе 4 men out оf 9 is givеn by 9C4, which is:

9C4 = (9!)/(4!5!)

= 126

Similаrly, the number оf wаys tо choosе 6 wоmen out оf 9 is givеn by 9С6, which is:

9С6 = (9!)/(6!3!)

= 84

So the tоtal number оf wаys tо choosе a committее consisting оf 4 men and 6 wоmen is:

126 * 84 = 10,584

Тherefore, the аnswer is (А) 10,584.

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Answer: Therefore, the probability of not landing on blue when spinning the spinner once is 62.5%.

Step-by-step explanation:  There are 8 sections on the spinner, and 3 of them are blue. Therefore, the probability of landing on blue is:

P(blue) = 3/8 = 0.375

The probability of not landing on blue is the complement of the probability of landing on blue:

P(not blue) = 1 - P(blue) = 1 - 0.375 = 0.625

To convert this probability to a percentage, we can multiply by 100:

P(not blue) = 0.625 x 100% = 62.5%

The measure of angle 3 is 95°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

When we have two parallel lines and they are intersected by a transversal , the angles on the parallel lines are corresponding and equal.

Therefore angle 3 = angle 7

angle 7 = 180-(angle 6) (angles on a straight line)

angle 7 = 180-85

= 95°

angle 3 = angle = 7 = 95°

Therefore the value of angle 3 is 95°

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Answer:

Step-by-step explanation: