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The indicated real nth root(s) of a, where n=3 and a=27 is 3.


You need to find the indicated real nth root(s) of a, where n=3 and a=27. In other words, you need to find the real number(s) that, when raised to the power of 3, equal 27.

Here's a step-by-step explanation:

1. Identify the given values: n=3 and a=27.
2. Write the equation: x^n = a, where x is the real nth root you're trying to find.
3. Substitute the given values: x^3 = 27.
4. Solve the equation for x: x = 3, since 3^3 = 27.

Your answer is x = 3, which is the real 3rd root of 27.

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Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.

Since Daniel read 77 pages in $\frac{2}{5}$ of an hour, we can set up the proportion:

$\frac{77}{\frac{2}{5}} = x$

where $x$ is the number of pages he would read in 1 hour.

To solve for $x$, we can simplify the left side of the equation by multiplying both the numerator and denominator by 5, which gives:

$\frac{77 \times 5}{2} = x$

Simplifying this expression gives:

$192.5 = x$

Therefore, if Daniel continues reading at the same rate, he will read 192.5 pages in one hour. However, since the number of pages must be a whole number, we can round this answer to the nearest whole number to get:

$x \approx 193$

So, Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.

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Add the given numbers: -8 + 4 + (-2) = -6. So, the sum of -8, 4, and -2 is -6.

To represent -6 on a number line, we need to find its position relative to zero. Since -6 is negative, it will be located to the left of zero. We count 6 units to the left of zero on the number line to represent -6. Therefore, the number line that shows the sum of -8, 4, and -2 is:

o----+----+----+----+----+----+----+----+----+----o

-15 -10 -5 0 5 10 15 20 25 30

-6

So, the complete answer is:

The sum of -8, 4, and -2 is -6.

To represent -6 on a number line, locate 6 units to the left of zero.

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A. The distribution function F(x,y) is ¹¹/₁₈ + ¹/₁₂ x² - ¹/₁₈ y² + ¹/₁₂ xy

B. The marginal PDF of x is ¹/₂x + ¹/₆ + ¹/₁₂x² for 0≤x≤1 and for y is /₂y + ¹/₆ + ¹/₁₂y² for 0≤y≤2

C. P(0≤x≤1/2, 0≤y≤1/2) is ¹/₃₂ + ¹/₉₆ x² for 0≤x≤1/2

D. The joint PDF of u=2x-y and v=-x+y is f(u,v) = (1/27)(2u^2+2v^2-2uv)

a) To find the distribution function F(x,y), integrate the joint PDF over the appropriate limits.

F(x,y) = ∫∫f(u,v)dudv

The limits of integration are not specified, so, determine them from the limits of the variables x and y.

So,

F(x,y) = ∫∫f(u,v)dudv

= ∫∫f(x+y,x-y)dudv (substituting u = x+y and v = x-y)

= ∫∫(¹/₄(u²+v²)+¹/₆(u²-v²))dudv (substituting x and y back in terms of u and v)

The limits of integration for u and v can be found by solving for u and v in terms of x and y as follows:

u = x+y

v = x-y

x = (u+v)/2

y = (u-v)/2

0 ≤ x ≤ 1; 0 ≤ y ≤ 2

implies

0 ≤ (u+v)/2 ≤ 1; 0 ≤ (u-v)/2 ≤ 2

Solving the above inequalities gives the following limits:

0 ≤ u ≤ 2; -u ≤ v ≤ u;

Thus,

F(x,y) = ∫∫(¹/₄(u²+v²)+¹/₆(u²-v²))dudv

= ∫²₀ ∫ᵘ_(-u) (1/4(u²+v²)+¹/₆(u²-v²))dvdu

= ¹¹/₁₈ + ¹/₁₂ x² - ¹/₁₈ y² + ¹/₁₂ xy

b) To find the marginal PDF of x, integrate the joint PDF over all possible values of y:

f(x) = ∫f(x,y)dy

So,

f(x) = ∫²₀ (¹/₄x + ¹/₄y²/x + ¹/₆y) dy

= ¹/₂x + ¹/₆ + ¹/₁₂x² for 0≤x≤1

In the same way, find the marginal PDF of y, by integrating the joint PDF over all possible values of x:

f(y) = ∫f(x,y)dx

So,

f(y) = ∫¹₀ (¹/₄x²/y + ¹/₄y + ¹/₆xy) dx

= ¹/₂y + ¹/₆ + ¹/₁₂y² for 0≤y≤2

c) To find P(0≤x≤1/2, 0≤y≤1/2), integrate the joint PDF over the appropriate limits:

P(0≤x≤1/2, 0≤y≤1/2) = ∫∫f(x,y)dxdy

So,

P(0≤x≤1/2, 0≤y≤1/2) = ∫¹₀ ∫^(1/2)_0 (¹/₄x² + ¹/₄y²/x + ¹/₆xy) dydx

= ¹/₃₂ + ¹/₉₆ x² for 0≤x≤1/2

d) To find the joint PDF of u=2x-y and v=-x+y, express x and y in terms of u and v and then apply transformation formula.

From the given equations, solve for x and y in terms of u and v as follows:

x = (u+v)/3

y = (v-u)/3

Now, find the Jacobian of the transformation:

J = ∂(x,y)/∂(u,v) =

| ∂x/∂u ∂x/∂v |

| ∂y/∂u ∂y/∂v |

=

| 1/3 1/3 |

| -1/3 1/3 |

So, |J| = 2/9

Using the transformation formula for joint PDFs:

f(u,v) = f(x(u,v), y(u,v)) |J|

Substituting x and y in terms of u and v:

f(u,v) = f((u+v)/3, (v-u)/3) (2/9)

Substituting the given joint PDF for f(x,y), we get:

f(u,v) = (¼((u+v)/3)² + ¼((v-u)/3)² + ⅙((u+v)/3)((v-u)/3))(2/9)

Simplify:

f(u,v) = (1/27)(2u²+2v²-2uv)

So, the joint PDF of u=2x-y and v=-x+y is:

f(u,v) = (1/27)(2u²+2v²-2uv)

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Answer:

Step-by-step explanation:

To determine the total cost of the laptop each month if you make no payments, we need to calculate the balance on the credit card after each month, including the simple interest charged.

Starting balance = $550

Month Balance Interest Total Cost
0 $550 $0 $550
1 $616 $66 $616 + $66 = $682
2 $689.92 $73.92 $689.92 + $73.92 = $763.84
3 $770.15 $80.23 $770.15 + $80.23 = $850.38
4 $857.09 $86.94 $857.09 + $86.94 = $944.03
5 $951.19 $94.10 $951.19 + $94.10 = $1045.29

To calculate the balance for each month, we multiply the previous balance by 1.12, which represents the 12% interest charged. For example, for month 1, the balance is $550 * 1.12 = $616.

To calculate the interest charged each month, we subtract the previous balance from the new balance. For example, for month 1, the interest charged is $616 - $550 = $66.

To calculate the total cost each month, we add the new balance to the interest charged.

For example, for month 1, the total cost is $616 + $66 = $682.

Note that if you make no payments on the credit card, the balance will continue to grow each month due to the interest charged.

It is always advisable to make at least the minimum payment each month to avoid high interest charges and potential late fees.

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Answer:

A, C, F

Step-by-Step:

The amplitude is whatever the coefficient is behind the trig function

Her profit when 0 people attend is -$50 and each person pays 10

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

y = 10x - 50.

The graph is added as an attachment

This means that

x = 0

So, we have

y = 10(0) - 50.

y = -50

She made a loss of 5-

This represents her profit when 0 people attend

This represents the slope of the function

The slope of the function is 10

So, each person pays 10

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The size of three angles of the triangle are 55 degrees, 55 degrees, and 15 degrees. The three consecutive odd numbers are 9, 11, and 13 and three consecutive even numbers are 32, 34, and 36.

1.To find the size of each angle in the triangle, we know that the sum of all angles in a triangle is 180 degrees. So we can set up an equation:

(2x + 5) + (2x + 5) + (x - 10) + 65 = 180

Simplifying and solving for x, we get:

5x + 55 = 180

5x = 125

x = 25

Now we can substitute x back into the expressions for each angle and simplify:

2x + 5 = 55 degrees

2x + 5 = 55 degrees

x - 10 = 15 degrees

Therefore, the three angles of the triangle are 55 degrees, 55 degrees, and 15 degrees.

2. Let's call the first odd number x. Then the next two consecutive odd numbers would be x + 2 and x + 4. We know that the sum of these three numbers is 33, so we can set up an equation:

x + (x + 2) + (x + 4) = 33

Simplifying and solving for x, we get:

3x + 6 = 33

3x = 27

x = 9

Therefore, the three consecutive odd numbers are 9, 11, and 13.

3. Let's call the first even number x. Then the next two consecutive even numbers would be x + 2 and x + 4. We know that the sum of these three numbers is 102, so we can set up an equation:

x + (x + 2) + (x + 4) = 102

Simplifying and solving for x, we get:

3x + 6 = 102

3x = 96

x = 32

Therefore, the three consecutive even numbers are 32, 34, and 36.

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The system of inequalities in the graph is the one in option A.

y ≥ (-2/5)x - 2/5

y ≥ (3/2)*x - 1

Here we can see the graph of a system of inequalities, on the graph we can see two lines.

The first one is a line with a positive slope, it has an y-intercept of -1, the shaded region is above that line,  and it is a solid line, so one of the inequalities is:

y ≥ a*x - 1

Where a is positive.

The second line has a negative slope, and we can see that the shaded region is also above the line, so this second inequality is like:

y ≥ line with negative slope.

It is easy to identify the correct option because there is only one with these properties, which is the first option:

y ≥ (-2/5)x - 2/5

y ≥ (3/2)*x - 1

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Answer:

Step-by-step explanation:

Let's call the two angles in the ratio of 4:13 "x" and "y".

We know that the sum of all three angles in a triangle is always 180 degrees.

So, we can set up an equation:

10 + x + y = 180

We also know that x and y are in a ratio of 4:13, which means we can write:

x = 4k

y = 13k

where "k" is a constant that we need to find.

Substituting these expressions for x and y into the equation, we get:

10 + 4k + 13k = 180

17k = 170

k = 10

Now we can find the values of x and y:

x = 4k = 4(10) = 40

y = 13k = 13(10) = 130

Therefore, the measures of the two angles in the ratio of 4:13 are 40 degrees and 130 degrees, respectively.

Using the nth-term test for divergence on the series ∑ 1/n+13 is inconclusive. However, by comparing the series to the divergent harmonic series, we can conclude that ∑ 1/n+13 is also divergent.

We can use the nth-term test for divergence to determine the convergence or divergence of the series

lim n → ∞ (1/n+13) = 0

Since the limit of the nth term is 0, the nth-term test is inconclusive, and we cannot determine the convergence or divergence of the series using this test.

However, we can use the comparison test to show that the series diverges. We can compare the given series to the harmonic series, which we know diverges

1/1 + 1/2 + 1/3 + ...

Since each term of the given series is less than the corresponding term of the harmonic series, the given series must also diverge. Therefore, the series ∑ 1/n+13 is divergent.

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Answer: Linear Function: y = -10x + 15    Exponential Function:  

y = 15(1/3)(to the power of x)

Step-by-step explanation:

Linear Function:

First we need to find the slope by using the slope equation: (y2 - y1)/(x2 - x1)

In which, it should be (5 - 15)/(1 - 0)

So, we know that the slope is -10, and we already know that the y-intercept is 15, so, we are going to plug it in to the slope-intercept formula, which is

y = mx + b,

In which, it would become y = -10x + 15

Exponential Function =

The exponential function is y = ab(to the power of x)

Let's list out the points onto the equation, 15 = ab(0) and 5 = ab(1)

Know let's solve for each variable.

1. 15 = ab(0)

2. 15/b(0) = a

3. 15 = a

Know we know that a is 15, we can solve for b.

1. 5 = (15)b(1)

2. 5/15 = b(1)

3. 1/3 = b

Know we know that b is equal to 1/3, let's plug it into the equation.

y = 15(1/3)(to the power of x)

Answer:

24 - x would mean the air, or empty space in the bottle not being used by the water in the bottle.

Question:

"Create an equation that shows how much space is not taken up by water in a 24 once water bottle if it currently has x ounces of water."

OR

"A standing garden bed has x cubic feet in the box.  It can hold 24 cubic feet, counting from the bottom to very top.  How much empty space is there from the top of the dirt in the box to the very top of the box?"

Based on the linear regression formula y = 1.3485x + 840.51, you can calculate the monthly rental price (y) for a one-bedroom apartment by plugging in the square footage (x) of the apartment.

The linear regression formula for the 15 similar one-bedroom apartments is y = 1.3485x + 840.51, where x represents the square footage and y represents the monthly rental price. This means that for every square foot increase in the apartment size, the monthly rental price is predicted to increase by $1.35.

The y-intercept of the formula is $840.51, which represents the predicted monthly rental price for an apartment with 0 square footage (this is not possible in reality, but is used in the formula for mathematical purposes). To get the rental price, round your answer to the nearest whole number. For example, if an apartment has 500 square feet, you'd calculate: y = 1.3485(500) + 840.51 ≈ 1344.76, which rounds to $1,345 as the monthly rental price.

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If using the method of completing the square to solve the quadratic equation number 1 be added to both side of the equation to be added to "complete the square".

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. The requirement that the coefficient of x² be a non-zero term (a 0) is necessary for an equation to qualify as a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term.

Add 1 to both sides of the equation to get:

[tex]x^2+4x+4=1[/tex]

The left hand side is now a perfect square:

[tex]x^2+4x+4=(x+2)^2[/tex]

So we have:

[tex](x+2)^2=1[/tex]

Hence:

[tex]x+2=\pm\sqrt{1} =\pm1[/tex]

Subtract 2 from both ends to get:

x = -2 ± 1

That is:

x = -3 or x = -1.

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We will use the Poisson distribution, which is a probability distribution that models the number of events occurring in a fixed interval of time or space, given the average rate of occurrence and assuming that the events are independent and randomly distributed.

For this problem, we will assume that the number of days with 0.01 inch or more precipitation in Lewiston, Idaho, follows a Poisson distribution with parameter λ = 8.7.

(a) To find the probability that there are exactly 9 days with 0.01 inch or more precipitation, we can use the Poisson probability mass function:

P(X = k) = e^(-λ) * λ^k / k!

where X is the random variable representing the number of days with 0.01 inch or more precipitation, λ is the parameter of the Poisson distribution, and k is the number of events we are interested in.

Plugging in the values, we get:

P(X = 9) = e^(-8.7) * 8.7^9 / 9! ≈ 0.151

Therefore, the probability that there are exactly 9 days with 0.01 inch or more precipitation is approximately 0.151.

(b) To find the probability that there are at most 9 days with 0.01 inch or more precipitation, we can use the cumulative distribution function of the Poisson distribution:

P(X ≤ k) = ∑i=0^k e^(-λ) * λ^i / i!

Plugging in the values, we get:

P(X ≤ 9) = ∑i=0^9 e^(-8.7) * 8.7^i / i! ≈ 0.503

Therefore, the probability that there are at most 9 days with 0.01 inch or more precipitation is approximately 0.503.

(c) To find the probability that there are more than 9 days with 0.01 inch or more precipitation, we can subtract the probability of having 9 or fewer days from 1:

P(X > 9) = 1 - P(X ≤ 9) ≈ 0.497

Therefore, the probability that there are more than 9 days with 0.01 inch or more precipitation is approximately 0.497.

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Answer:

a. x = 68

b. x = 55

c. x = 18

Step-by-step explanation:

Formula

Inscribed angle = Central angle/2

a.

x = 136/2

x = 68

b.

x = ( 360 - 150 - 100 )/2

= 110/2

x = 55

c.

x = 18

Andres brought the most milk, and Carlos brought the least milk.

To find out the student who bought the most milk, you need to convert the liters decimals so that they can be compared evenly.

Andrés brought 2²

= 2 x 2

= 4 liters of milk.

Bruno brought 13/4:

= 13 / 4

= 3.25 liters of milk.

Carlos bought 1. 16 liters and Daniel bough 1. 3 liters.

This shows that Andres bought the most milk and Carlos bought the least amount.

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The account that will give Grady at least a 5% annual yield is Account C

We can use the formula for compound interest to compare the three investment accounts and find the one that will give Grady at least a 5% annual yield:

FV = PV × (1 + r/n)^(n*t)

where FV is the future value, PV is the present value, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.

For Account A:

APR = 4.95%, compounded monthly

r = 0.0495

n = 12

t = 1

FV = PV × (1 + r/n)^(nt)

FV = PV × (1 + 0.0495/12)^(121)

FV = PV × 1.050452

To get at least a 5% annual yield, we need FV/PV ≥ 1.05

1.050452/PV ≥ 1.05

PV ≤ 1.000497

Therefore, Account A will not give Grady at least a 5% annual yield.

For Account B:

APR = 4.85%, compounded quarterly

r = 0.0485

n = 4

t = 1

FV = PV × (1 + r/n)^(nt)

FV = PV × (1 + 0.0485/4)^(41)

FV = PV × 1.049375

To get at least a 5% annual yield, we need FV/PV ≥ 1.05

1.049375/PV ≥ 1.05

PV ≤ 1.000351

Therefore, Account B will not give Grady at least a 5% annual yield.

For Account C:

APR = 4.75%, compounded daily

r = 0.0475

n = 365

t = 1

FV = PV × (1 + r/n)^(nt)

FV = PV × (1 + 0.0475/365)^(3651)

FV = PV × 1.049038

To get at least a 5% annual yield, we need FV/PV ≥ 1.05

1.049038/PV ≥ 1.05

PV ≤ 1.000525

Therefore, Account C will give Grady at least a 5% annual yield.

Therefore, the account that will give Grady at least a 5% annual yield is Account C.

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The cost to manufacture 2000 headphones as the number of headphones varies inversely with the cost of manufacture is $32

Let x = number of headphones

y = cost of manufacturing headphones

The cost of manufacturing a certain type of headphones is inversely proportional to the number of headphones.

The equation for inversely proportional is

x₁ y₁ = x₂ y₂

x₁ = 8000 , y₁ = 8 , x₂ = 2000 y₂ = ?

Putting the value in the equation we get ,

8000 × 8 = 2000 × y₂

64000/2000 = y₂

y₂ = 32

Cost of manufacturing 2000 headphones is 32 .

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There will be a total of 7 rows for nails and 6 rows for screws, making 13 rows in total.

To solve it, we need to find the greatest common divisor (GCD) of the number of boxed nails (42) and boxed screws (36). This will tell us the greatest number of boxes that can be displayed in one row without mixing nails and screws.

Step 1: List the factors of each number.
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Step 2: Find the greatest common divisor (GCD) by identifying the largest factor they have in common.
- The largest common factor is 6.

So, the greatest number of boxes that can be displayed in one row is 6.

Next, we'll find out how many rows will there be if the manager puts the greatest number of boxes in each row.

Step 3: Divide the total number of boxed nails and boxed screws by the GCD.
- Rows for nails: 42 ÷ 6 = 7
- Rows for screws: 36 ÷ 6 = 6

Therefore, there will be a total of 7 rows for nails and 6 rows for screws, making 13 rows in total.

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Knowing that tan(x) = 3/5 and using a trigonometric identity, we will get that:

tan(2x) = 1.875

There is a trigonometric identity we can use for this, we know that:

[tex]tan(2x) = \frac{2tan(x)}{1 - tan^2(x)}[/tex]

So we only need to knos tan(x), which we already know that is equal to 3/5, then we can replace it in the formula above to get:

[tex]tan(2x) = \frac{2*3/5}{1 - (3/5)^2}\\\\tan(2x) = \frac{6/5}{1 - 9/25} \\tan(2x) = 1.875[/tex]

That is the value of the tangent of 2x.

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The measure of angle W in the kite WXYZ is 0 degrees.

To find the measure of angle W in the kite WXYZ, we can use the properties of kites. In a kite, the two opposite angles formed by the intersection of the diagonals are equal. Let's denote the measure of angle W as "x."

Step 1: Start with the given information that WXYZ is a kite.

Step 2: Recall that the diagonals of a kite intersect at right angles. Let's label the intersection point of the diagonals as point P.

Step 3: Draw the diagonals WX and YZ, which intersect at point P.

Step 4: Recognize that angles WXP and ZYP are congruent. Therefore, the measure of angle WXP is also x.

Step 5: Observe that the sum of the angles in a triangle is 180 degrees. Since triangle WXP is a triangle, we can write the equation: x + 90 + 90 = 180.

Step 6: Simplify the equation: x + 180 = 180.

Step 7: Subtract 180 from both sides: x = 0.

Step 8: Analyze the result. The measure of angle W, denoted by x, is equal to 0 degrees.

Therefore, the measure of angle W in the kite WXYZ is 0 degrees.

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P(X ≤ 1) = P(X = 0) + P(X = 1) ≈ 0.901

So the probability that at most 1 customer in the sample orders for delivery is approximately 0.901, rounded to three decimal places.

To solve this problem, we can use the binomial distribution since we have a fixed number of trials (6) and each trial can result in one of two outcomes (ordering for delivery or not).

Let X be the number of customers in the sample who order for delivery. Then X follows a binomial distribution with parameters n = 6 and p = 0.11 (the probability of ordering for delivery).

We want to find the probability that at most 1 customer orders for delivery. This can be written as:

P(X ≤ 1) = P(X = 0) + P(X = 1)

To calculate these probabilities, we can use the binomial probability formula:

P(X = k) = (n choose k) *[tex]p^k[/tex]*[tex](1 - p)^(n - k)[/tex]

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.

Using this formula, we can calculate:

P(X = 0) = (6 choose 0) * 0.11^0 * [tex]0.89^6[/tex] ≈ 0.530

P(X = 1) = (6 choose 1) * 0.11^1 * 0.89^5 ≈ 0.371

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The area for the first shape is  16,000 square feet, the area for the second shape is 2,400 square feet. The total area of both shapes added together is 18,400 square feet.

To find the area of the first shape, which is a rectangle that is 160 feet tall and 100 feet wide, we can use the formula:

Area = length x width

So, for the first shape, the area is:

Area = 160 ft x 100 ft

Area = 16,000 square feet

To find the area of the second shape, which is a rectangle that is 60 feet long and 40 feet wide, we can use the same formula:

Area = length x width

So, for the second shape, the area is:

Area = 60 ft x 40 ft

Area = 2,400 square feet

To find the total area of both shapes added together, we simply add the two areas:

Total Area = 16,000 square feet + 2,400 square feet

Total Area = 18,400 square feet

Therefore, the total area of both shapes added together is 18,400 square feet.

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Using the properties of exponents:

5. The value of x is 9

6. The value of b is -4

7. The value of n is 0

From the question, we are to calculate the value of the exponent in each question

5.

8² · 8ˣ = 8¹¹

Applying the multiplication law of indices, this can be written as

8² ⁺ ˣ = 8¹¹

Equate the powers

2 + x = 11

Solve for x by subtracting 2 from both sides

2 - 2 + x = 11 - 2

x = 9

6.

5⁷ · 5ᵇ = 5³

Applying the multiplication law of indices, this can be written as

5⁷ ⁺ ᵇ = 5³

Equate the powers

7 + b = 3

Solve for b by subtracting 7 from both sides

7 - 7 + b = 3 - 7

b = -4

7.

x¹² · xⁿ = x¹²

Applying the multiplication law of indices, this can be written as

x¹² ⁺ ⁿ = x¹²

Equate the powers

12 + n = 12

Solve for n by subtracting 12 from both sides

12 - 12 + n = 12 - 12

n = 0

Hence, the value of n is 0

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Answer: 129275775.0

Step-by-step explanation:

129275775.0

whenever there is a whole number, the decimal is at the end of the number.

Step-by-step explanation:

4% tax is .04 in decimal:

($  50  + 30 ) * .04    = 3.20 tax    

The value of ∠APB = 180°. It is a straight line.

Given the information, we can deduce that the line passing through the center O of circle C2 and point A also passes through point B, as AB is the intersection of the two circles.

Now, consider the line segment AP. Since PAT is tangent to circle C1 at point A, we know that ∠APT = 90°. Additionally, since AB is a diameter of circle C1, we know that ∠ABP = 90°.

Using these angles, we can see that ∠APB is equal to the sum of ∠APT and ∠ABP. Therefore,

∠APB = ∠APT + ∠ABP = 90° + 90° = 180°.

So, we have shown that ∠APB is a straight line.

To know more about circles, refer to the link below:

https://brainly.com/question/11253017#

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