Determine the perimeter of the right triangle shown.

Answer:

38.88in²

Step-by-step explanation:

Area of shaded region = Area of square - Area of semi circle

First lets find the area of the square and semi circle

Area of square = s²

Where s = side length

Here we have a given side length of 8in

So s = 8

This means area = 8² = 64in²

Area of semicircle = (πr²)/2

Where r = radius

Here, the side length of the square and the diameter of the semicircle is shared meaning they are congruent. This means the diameter of the semicircle = 8in

To convert from diameter to radius we simply divide by 2

So radius = 8 / 2 = 4

Now we have Area = (πr²)/2

==> plug in r = 4 and π = 3.14

Area = (3.14(4)²))/2

==> simplify exponent

Area = (3.14(16))/2

==> multiply 3.14 and 16

Area = 50.24/2

==> simplify division

Area = 25.12in²

Area of shaded region

We now subtract the two areas

Area of shaded region = Area of square - Area of semi circle

Area of square = 64in² and Area of semicircle = 25.12in²

Area of shaded region = 64in² - 25.12in² = 38.88in²

Angle BCD is the same as angle FGH which is 122

Step-by-step explanation:

congruent means that they have the same angles.

so, the angle BCD = 122

The amount that hw must invest to achieve the goal when it will be compounded annualy is $68750

Given Information:

Principal Amount (P) = to be calculated

Rate of Interest (r) = 8 %

Time Period (t) = 6

Amount Received (A) = $110000

Number of times the interest is compounded quarterly (n) = 4

The Formula for the amount received when the principal (P) is compounded is given by,

[tex]A = P( 1 + \frac{r}{100n} )^{nt}[/tex]

Now, putting the values, we get:

[tex]110000 =P( 1 + \frac{8}{100*4} )^{4*6}[/tex]

P = $68750

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The error in the volume of the cube is gotten as; ±120 in³

In this type of situation, there could be maximum error, relative error and percentage error.

The maximum error is gotten by differentiating the volume equation.

The relative error is gotten by dividing the change in volume by the volume likewise change in length.

The percentage error is just converting the relative error to percentage. Thus;

Thus;

Volume of a cube is given by the formula;

V = x³

dV/dx = 3x²

dV = 3x²(dx)

We are given dx = 1/10

Thus;

dV = ±(3 * 20² × (1/10))

dV = ±120 in³

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The sample space in regard to the vacations is 24

Choice of 3 destinations: Cozumel (C), Jamaica (J), or Grand Caymans (G) =

3C1

A choice of 2 types of rooms: balcony (B) or inside view =  2C1

And a choice of 4 types of excursions: water sports (W), horseback riding (H), parasailing (P), or zip-lining (Z) = 4C1

Choosing only one of each, the sample space in regard to the vacations

Sample space = choice of destination x choice of room x choice of water sports

= 3C1 x 2C1 X 4C1

= 3 x 2 x 4 = 24

Therefore,  the sample space in regard to the vacations is 24

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Answer:

Step-by-step explanation:

the correct answer is A.

because if Kay has 5 pencils and it is given to Merry 1, it means that Kay still has 4 pencils.

Answer:

130 in standard form
100+30 in expanded form

Step-by-step explanation:

standard from is writing the sentence in a number fro example
three hundred seventy two is writen as 372 in standard for
expanded form is 300+70+2

Answer:

130 in standard form

In expanded form is100+30=1300

Step-by-step explanation:

For further example 4236

In standard form is 4236

In expanded form is 4000+200+30+6=4236

The percent of decrease is 4%.

One year, the population of a city was 215,000. Several years later it was 206,400.

To find out the percent decrease:

A fraction with denominator equals 100 to a percentage: 4%

Based on the given conditions, formulate: [tex]\frac{215000-206400}{215000}[/tex]

Calculate the sum or difference: [tex]\frac{8600}{215000}[/tex]

Cross out the common factor: [tex]\frac{1}{25}[/tex]

Multiply a number to both the numerator and the denominator: [tex]\frac{1}{25}* \frac{4}{4}[/tex]

Write as a single fraction: [tex]\frac{4}{25*4}[/tex]

Calculate the product or quotient: [tex]\frac{4}{100}[/tex]

Rewrite a fraction with denominator equals 100 to a percentage: 4%

Hence the answer is the percent of decrease is 4%.

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The value of h in the parallelogram is 4 feet

The area of the parallelogram = b × h

Where b is the base of the parallelogram

h is the height of the parallelogram

One side of the parallelogram = 6 feet

The second side of the parallelogram = 8 feet

If the base of the parallelogram is 6 feet

The area = 6 × h

If the base of the parallelogram is 8 feet

Then the area of the parallelogram = 8 × 3

= 24 square feet

In both cases the area will be equal, then the equation will be

6h = 24

h = 24 / 6

h = 4 feet

Hence, the value of h in the parallelogram is 4 feet

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The numbers arranged in increasing order are D < C < A < E < B.

We are given a set of five numbers. The numbers are represented by the variables A, B, C, D, and E. The numbers need to be calculated. The numbers are solved below.

A = 2*1/2*4*1/6 = 2/3 = 0.667

B = 12*128 = 1,536

C = 1*8*1/5² = 8/25 = 0.32

D = 4*(-1)/2*(-1)*8*(-1) = -16

E = 3*√2*4*1/4 = 3√2 = 4.24

We need to arrange the numbers in increasing order. Ascending order refers to the arrangement of numbers in increasing order, from least to greatest. The numbers in ascending order are given below :

-16 < 0.32 < 0.667 < 4.24 < 1,536

The increasing order of the corresponding variables is : D < C < A < E < B.

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Step-by-step explanation:

it is totally simple : you need to put the x-value into every place of the x-variable, and then we calculate.

and then the same for the next x-value. and the next. ...

-2

-2×-2 + 9 = 4 + 9 = 13

0

-2×0 + 9 = 0 + 9 = 9

2

-2×2 + 9 = -4 + 9 = 5

4

-2×4 + 9 = -8 + 9 = 1

Answer:

1 and 3

Step-by-step explanation:

discriminant = 16 - 4 * 1 * 3 = 16 - 12 = 4

x1 = (4 + √4)/2 = (4+2)/2 = 6/2 = 3

x2 = (4 - √4)/2 = (4-2)/2 = 2/2 = 1

the answer is a, -π/8

Answer:10

Step-by-step explanation:

1.20 + (4.75 × x) = 48.701.20 + 4.75x = 48.70Collect like terms 4.75x = 48.70 - 1.204.75x = 47.50Divide both side by 4.754.75x/4.75 = 47.50/4.75.x = 10

The side x of the right triangle is 235.72 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be found using trigonometric ratios or Pythagoras theorem depending on the sides and angles given.

Hence, let find the value of x in the combine right triangles.

Therefore,

tan 28 = opposite / adjacent

tan 28 = 105 / l

cross multiply

l = 105 / tan 28

l = 105 / 0.53170943166

l = 197.479781832

l = 197.50

tan 70 = 105 / a

a = 105 / tan 70

a = 38.2168804325

a = 38.22

Therefore,

x = 197.50 + 38.22

x = 235.72 units

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If Clara lives 12 floors above Darren, Clara lives on the 16 floor while Darren lives on the 4 floors.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

Given that Darren and Clara reside in a towering structure, this is expected. Twelve stories above Darren, Clara resides. One day, Darren climbed the stairs from his apartment to Clara's and went to see her. He was halfway up, on the eighth floor.

Suppose Darren and Clara live on x and y number of floor respectively.

If Clara lives 12 floors above Darren.

x-y=12

If in halfway he is on the 8th floor the total number of floors in the building will be 16.

As a result, we can say that Clara lives on the 16 floors while Darren lives on the 4 floor.

Thus, if Clara lives 12 floors above Darren, Clara lives on the 16 floors while Darren lives on the 4 floors.

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The price of each bag of apples is $3.5 and price of  each bag of potatoes is $2.

Given:

a person can buy two bags of apples and two bags of potatoes for $11 at a farmers market the same person by two bags of apples and three bags of potatoes for $13.

Let x be the apples and y be the potatoes.

2x + 2y = 11

2x + 3y = 13

on solving:

2x + 2y - 2x - 3y = 11 - 13

2y - 3y = -2

-y = -2

y = 2

2x + 2y = 11

2x + 2*2 = 11

2x + 4 = 11

2x = 7

x = 7/2

x = 3.5

Therefore The price of each bag of apples is $3.5 and price of  each bag of potatoes is $2.

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Answer:

Apples cost $3.50, potatoes cost $2.

Step-by-step explanation:

If you only add one bag of potatoes and the price jumps two dollars, then the potatoes cost two dollars each. We can substitute this into the equation, which can be solved to find apple price.

The quantity of items tha must be made for supply to equal demand is 2050 items

Demand simply means a consumer's desire to buy goods and services without any hesitation and pay the price for it.

To calculate the unit of quantity Q that must be made for demand to be equal to supply, we equate the demand and supply equation.

From the question,

For Demand

From Supply,

When supply is equal to demand

Solve for P

Substitute the values of P into equation 1

Hence, the quantity of items tha must be made 2050 items.

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The calculation of the required financial ratios for Sunland Company is as follows:

The return on assets is 6%.

The Asset Turnover is 2.06 times.

The profit margin is 2.9%.

Financial ratios express the numerical relationships of two or more financial statement elements.

Financial ratios are used to make comparisons of the financial performance or position of companies from one year to another (trend analysis) and between companies or the industry average.

Net sales $11,257.9

Net earnings $327.9

Total assets, ending = $5,560.0

Total assets, beginning = $5,370.0

Average assets = (Beginning total assets + Ending total assets) ÷ 2

= $5,465 ($5,560 + $5,370)/2

Return on assets = Net earnings/Average total assets x 100

= 6% ($327.9/$5,465 x 100)

Asset Turnover = Net Sales/Average total assets

= 2.06x ($11,257.9/$5,465)

Profit margin = Net earnings/Net Sales x 100

= 2.9% ($327.9/$11,257.9 x 100)

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Answer:

Rational x Irrational = Irrational

Step-by-step explanation:

6 is a rational number.  It can be written as an integer over and integer [tex]\frac{6}{1}[/tex]

[tex]\pi[/tex] is irrational.  This is a number that never repeats or terminates, so it can not be written as an integer over and integer.

Answer:  Choice B

Rational x Irrational = Irrational

==============================================

Reason:

6 = a rational number

3pi = an irrational number

18pi = an irrational number

Anything involving pi is irrational. The value 6 is rational because 6 = 6/1.

pi is irrational since we cannot write it as a ratio of two integers. We can get approximations like 22/7, but we can't nail down the exact value of pi with a fraction.

Answer:

The y-intercept is when $x=0$ so $y=32\frac{ft}{s}*0-\frac{1}{2}*9.8*0^2=0$, so the ball starts on the ground. The maximum height is when $v=0$, so $0=32\frac{ft}{s}-9.8t$ and solving for $t$ we get $t=\frac{32}{9.8}=3.265s$, and plugging this back in for $y$ we get $y=32\frac{ft}{s}*3.265s-\frac{1}{2}*9.8*3.265^2=156.205 ft$. So the ball will be at its maximum height of 156.205 ft at 3.265 seconds.

Step-by-step explanation:

The $y$-intercept is $-1$.  The maximum height of the baseball is when $y=0$; that is when $x=\ln(4)$.  Here is a sketch of the path.

From the $y$-intercept, we see that the baseball starts at height $y=-1$.  It reaches a maximum height at $x=\ln(4)$; that is, $y=0$.  From there, it falls and reaches the ground at $x=2\ln(4)$; that is, $y=-1$ again.

a) The maximum height of the ball is 100 feet.

b) The velocity of the ball on its way up is +16 feet per second.

c) The velocity of the ball on its way down is - 16 feet per second.

A free fall is an uniformly accelerated motion experimented by a particle due to the effects of gravity. The position of the ball (s) in time (t), in seconds, is described by a quadratic equation.

a) First, we find the maximum height reached by the ball:

s(t) = 80 · t - 16 · t²

16 · t² - 80 · t + s(t) = 0

Then, by using the discriminant:

(- 80)² - 4 · 16 · s(t) = 0

64 · s(t) = (- 80)²

s(t) = 100 ft

b) Second, find the function velocity by derivatives:

v(t) = 80 - 32 · t

Third, find the time related to the position s(t) = 96 ft:

s(t) = 80 · t - 16 · t²

100 = 80 · t - 16 · t²

16 · t² - 80 · t + 96 = 0

Then, by quadratic equation:

t = 3 s or t = 2 s.

Fourth, evaluate the function velocity:

v(2) = 80 - 32 · 2

v(2) = 16

v(3) = 80 - 32 · 3

v(3) = - 16

The velocity of the ball when s(t) = 96 ft on its way up is 16 feet per second.

c) The velocity of the ball when s(t) = 96 ft on its way down is - 16 feet per second.

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True statement are:

A. This graph is not a function because the value x = 3 is assigned to

more than one y-value.

D. This graph is a function because the value of x is the same for

every value of y.

Given,

In the question:

To see the graph :

Mark all the statement that are true.

Now, According to the question:

From the graph,

Equations are expressions of two mathematical expressions t such as two numbers, functions. An equality between quantities and operations, usually with an equal sign "=".

Functions is a correspondences between two sets that are not empty each element in the set of input values can corresponds to a element in a set of output values that is unique.

Hence, True statement are:

A. This graph is not a function because the value x = 3 is assigned to

more than one y-value.

D. This graph is a function because the value of x is the same for

every value of y.

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The distance it should take my classmate to ride the bicycle at each speed to burn 575 calories would be = 13.2m for first speed and 11.3m for the second speed.

A fitness program is defined as the program that is adequately organised for the purpose of maintaining proper healthy calories.

The period he plans to ride the bicycle for a day = 60minutes.

For the first speed,

8 cal/ min = 11mph

To convert to hour,

8 × 60 =480

He burns 480cal per hour in 11mph speed

If 480cal = 11 mph

575 cal = X

make X the subject of formula;

X = 575×11/480

X = 6325/480

X = 13.2 m

For the second speed;

12.75 cal/ min = 15mph

To convert to hour,

12.75 × 60 =765cal

He burns 765cal per hour in 11mph speed.

If 765cal = 15mph

575 cal = y

make y the subject of formula;

y = 575 × 15/765

y = 8625/765

y = 11.3 m

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The coordinates of T' are, T'(-3, -1).

What is rotation?

A rotation is a transformation in which each point of a preimage is turned through a predetermined angle and direction around a fixed point. The center of rotation is the fixed point. The term for the amount of rotation is the angle of rotation, and it is expressed in degrees. Measure the specified angle in the anticlockwise direction using a protractor.

Given: Triangle RST has vertices R(1, 1), S(1, 4), and T(3, 1).

We have to find the coordinates of T' after counterclockwise rotation of 180°.

Since, The rule for a rotation by 180° about the origin is (x, y) → (−x, −y).

So, the coordinates R(1, 1), S(1, 4) and T(3, 1) changes to R'(-1, -1), S'(-1, -4) and T'(-3, -1).

Therefore, the coordinates of T' are T'(-3, -1).

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Answer:

13

Step-by-step explanation:

if b = 5, then 3(5) - 2 = 15 - 2 = 13

Using the table, the average daily balance of the credit card for the August 1 through August 31 billing period is $705.

The average daily balance refers to the computed total balance divided by the number of days in the billing cycle.

The computed total balance is the sum of closing balance multiplied by the number of days covered in the billing cycle before the next credit card transaction or activity.

Day   Activity     Adjustment     Closing Balance  No. of days     Total

1           --                     --                      950                     7            $6,650

8       Payment           −600                350                     8              2,800

16      Purchase         +300                650                     8              5,200

24     Purchase         +250                900                     8              7,200

Total                                                                             31           $21,850

Average daily balance = $705 ($21,850/31)

Thus, the average daily balance on the credit card is $705.

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Answer:

5/16

Step-by-step explanation:

This is a geometric sequence

aₙ=a₁*rⁿ⁻¹

a₆=10*.5⁶⁻¹

a₆=10*.5⁵

a₆=10*(1/2)⁻⁵

a₆=10*1/32

a₆=10/32=5/16