Help, please! Find the VOLUME of this complex shape.

Answer:

16

Step-by-step explanation:

To solve this problem, you need to follow the order of operations (PEMDAS):

First, you need to solve the parentheses: 2+2 = 4

Next, you need to solve the multiplication: 2 x 4 = 8

Finally, you need to solve the division: 8 ÷ 2 = 16

To graph the parametric path x = t^2, y = (t - 1)(t^2 - 4) on a Slope-Direction diagram, we need to plot points by evaluating the expressions for different values of t within the given interval [-3, 3].

First, let's calculate the coordinates for several values of t:

For [tex]t = -3: x = 9, y = 0[/tex]

For[tex]t = -2: x = 4, y = 6[/tex]

For [tex]t = -1: x = 1, y = 0[/tex]

For [tex]t = 0: x = 0, y = -4[/tex]

For[tex]t = 1: x = 1, y = 0[/tex]

For[tex]t = 2: x = 4, y = 6[/tex]

For [tex]t = 3: x = 9, y = 0[/tex]

Plotting these points on the Slope-Direction diagram, we can observe the shape of the curve. The path starts at (9, 0), moves downward to (4, 6), reaches the lowest point at (0, -4), and then goes back up to (4, 6) and (9, 0).

To find the length of the curve given by (2cost - cost2t, 2sint - sin2t) over the interval 0 ≤ t ≤ π/2, we can use the arc length formula:

L = ∫√(dx/dt)² + (dy/dt)² dt

First, calculate the derivatives of x and y with respect to t:

dx/dt = -2cost - 2costsin2t

dy/dt = 2cost - 2sintcos2t

Next, square and add these derivatives:

(dx/dt)² + (dy/dt)² = 4cost² + 4costsin2t + 4cost² + 4sint²cos²2t

Simplify the expression:

(dx/dt)² + (dy/dt)² = 8cost² + 4costsin2t + 4sint²cos²2t

Now, integrate the square root of this expression over the given interval 0 ≤ t ≤ π/2 to find the length of the curve:

L = ∫√(8cost² + 4costsin2t + 4sint²cos²2t) dt, from 0 to π/2

Evaluating this integral will provide the final answer for the length of the curve.

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1)

When the points (1, 150) and (6, 900) are used:

a)

Slope of line is 150.

Given points,

(1, 150) and (6, 900)

Slope of a line passing from two points:

Slope = y2 - y1 / x2 - x1

Slope = 900 - 150 / 6 - 1

Slope = 150

b)

Equation of line :

Y = mx + c

m = slope of line

c = y intercept

Here,

Slope =150

Hence the equation of line is:

y = 150x

c)

For every TV ad, CD sales increased by about 150 as the slope of line is + 150 which indicates the increase in  sales of CD .

2)

When the points (1, 100) and (8, 800) ae used:

a)

Slope of line is 100.

Given points,

(1, 100) and (8, 800)

Slope of a line passing from two points:

Slope = y2 - y1 / x2 - x1

Slope = 800 - 100 / 8 - 1

Slope = 100

b)

Equation of line :

Y = mx + c

m = slope of line

c = y intercept

Here,

Slope =100

Hence the equation of line is:

y = 100x

c)

For  every magazine ad, CD sales increased by about 100, as the slope of line is + 100 which indicates the increase in  sales of CD .

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Answer:

[tex]11\frac{7}{10}[/tex]

Step-by-step explanation:

[tex]\displaystyle 3\frac{1}{4}+\biggr(3\frac{1}{4}+5\frac{1}{5}\biggr)\\\\3\frac{5}{20}+3\frac{5}{20}+5\frac{4}{20}\\\\(3+3+5)+\biggr(\frac{5}{20}+\frac{5}{20}+\frac{4}{20}\biggr)\\\\11+\frac{14}{20}\\\\11\frac{7}{10}[/tex]

Again, make sure all denominators are the same by using the least common denominator (in this case it's 20 since 5*4=20).

The coordinates of the image of triangle ABC would be A (-1, -1), B (3, 2), and C (4, -6)  after translation, and if the original coordinates are A(-3,2) B(1,5) C(2,-3).

We know that,

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

Let assume A(-3,2) B(1,5) and C (2,-3) are original coordinates

The following translation is being used: (x, y) ⇒ (x + 2, y - 3)

First, take your x-coordinates and add them by two because it is the translation utilized to solve for your x-coordinate.

You would receive the following for yours x's: A (-1, y ) B (3, y) C (4, y)

Next, remove three from each of your y-coordinates because it is the translation being utilized to solve for your y-coordinate.

You would receive the following for your y's: A (x, -1) B (x, 2) C (x, -6)

Finally, you would take each one and put it together, or piece it together.

Hence, the coordinates of the image of triangle ABC after translation would be A (-1, -1), B (3, 2), and C (4, -6).

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To find the range of a data set, we subtract the minimum value from the maximum value.

Given the data set: 47, 38, 72, 56, 40, 64, 30, 80, 66, 51

The minimum value is 30, and the maximum value is 80.

Range = Maximum value - Minimum value

= 80 - 30

= 50

Therefore, the range for the data set is 50.

To find the interquartile range (IQR), we need to determine the values of the first quartile (Q1) and the third quartile (Q3) and then calculate the difference between them.

First, we need to order the data set in ascending order:

30, 38, 40, 47, 51, 56, 64, 66, 72, 80

To find Q1, we take the average of the values at the 25th and 26th positions (since it falls between 38 and 40):

Q1 = (38 + 40) / 2

= 78 / 2

= 39

To find Q3, we take the average of the values at the 75th and 76th positions (since it falls between 66 and 72):

Q3 = (66 + 72) / 2

= 138 / 2

= 69

Now, we can calculate the interquartile range (IQR):

IQR = Q3 - Q1

= 69 - 39

= 30

Therefore, the interquartile range (IQR) for the given data set is 30.

The debt will be cleared in approximately 158 months.

The monthly installment starts at Rs. 10,000 and increases by Rs. 100 each month. We can set up an arithmetic progression to represent the installment amounts:

10,000, 10,100, 10,200, ...

The nth term of this arithmetic progression can be calculated using the formula:

an = a1 + (n-1)d

where:

an = nth term of the sequence

a1 = first term of the sequence

d = common difference between the terms

In this case, a1 = 10,000 and d = 100.

Now we need to find the value of n such that the sum of the first n terms of the sequence exceeds or equals Rs. 622,500.

The sum of the first n terms of an arithmetic sequence can be calculated using the formula:

Sn = (n/2)(2a1 + (n-1)d)

We need to solve the equation:

Sn >= 622,500

Substituting the values, we have:

(n/2)(2*10,000 + (n-1)*100) >= 622,500

Simplifying the equation, we can solve for n:

n^2 + 199n - 614000 = 0

Using the quadratic formula, we find that:

n ≈ 157.37 or n ≈ -356.37

Since we cannot have a negative number of months, we take n ≈ 157.37. Therefore, it will take approximately 158 months (rounded up) to clear the debt.

Hence, the debt will be cleared in approximately 158 months.

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To find an expression representing the width of the rectangular garden, we need to use the given information about the area and length of the garden.

The formula for the area of a rectangle is:

Area = Length × Width

We are given that the area of the garden is x^2 - 36, and the length is x^2 - 2x - 24.

Let's substitute these values into the formula:

x^2 - 36 = (x^2 - 2x - 24) × Width

To isolate the width, we divide both sides of the equation by (x^2 - 2x - 24):

Width = (x^2 - 36) / (x^2 - 2x - 24)

Therefore, an expression representing the width of the garden is:

Width = (x^2 - 36) / (x^2 - 2x - 24)

Answer:

To calculate the time it will take to pay off the account, we can use the formula for the future value of an annuity:

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

Where:

PV = Present value (current balance)

PMT = Payment amount per period

r = Interest rate per period

n = Number of periods

In this case:

PV = $14,790

PMT = $570

r = 0.0097 (0.97% expressed as a decimal)

n = ?

Plugging in the values, we can solve for n:

14,790 = 570 * ((1 - (1 + 0.0097)^(-n)) / 0.0097)

Let's solve this equation to find the value of n:

((1 + 0.0097)^(-n)) = 1 - (14,790 * 0.0097) / 570

((1 + 0.0097)^(-n)) = 0.9742105

Taking the logarithm of both sides:

-n * log(1.0097) = log(0.9742105)

n = log(0.9742105) / log(1.0097)

Using a calculator, we find that n is approximately 28.56.

Therefore, it will take approximately 28.56 months (or 28 months and 17 days) to pay off the account.

Step-by-step explanation:

Answer:

64 inches.

Step-by-step explanation:

To find the amount of inches in 5 1/4 feet, you must first multiply 12 by 5 because there are 12 inches in one foot.
12x5=60.

The next step in order to complete the equation would be to find how many inches are in 1/4 of a foot.
To find how many inches are in 1/4 of a foot you must divide 12 by 4.
12 divided by 4= 4.

Now, you must as the two numbers together to get the total number of inches.
60+4=64.

This, 64 is your final answer.

Hope this helps! :)

Answer:

a) -73°C, -15°C, -12°C, 0°C, 16°C, 37°C, 96°C

a) 96°C, 37°C, 16°C, 0°C, -12°C, -15°C, -73°C

b) -36°C, -15°C, -7°C, -1°C, 0°C, 20°C, 23°C

b) 23°C, 20°C, 0°C, -1°C, -7°C, -15°C, -36°C

Hello!

abc * cd

= a * b * c * c * d

= abc²d

[tex] \bold{abc \: \: by \: \: cd}[/tex]

[tex] \bold{(abc) \cdot(cd)}[/tex]

[tex] \sf{abc {}^{1 + 1} d}[/tex]

[tex] \sf{abc {}^{2} d}[/tex]

The general rule for multiplication of monomials says that: multiply the coefficients and then write the letters of the factors in alphabetical order. Each letter is given an exponent equal to the sum of the exponents it has in the factors. The sign of the product result will be given by the Law of Signs.

The total cost T of the floor algebraically is T = c x (3√3/2) x s²

We have,

To express the total cost T of the floor of the hexagonal gazebo algebraically, we need to consider the area of the hexagonal floor and the cost per square unit of flooring.

The area of a regular hexagon can be calculated using the formula:

Area = (3√3/2) x s²

Where s is the side length of the hexagon.

To find the total cost, we multiply the area by the cost per square unit of flooring (c):

T = c x Area

Substituting the area formula into the equation:

T = c x (3√3/2) x s²

Now, we have expressed the total cost T algebraically in terms of the side length s and the cost per square unit of flooring c.

Thus,

The total cost T of the floor algebraically is T = c x (3√3/2) x s²

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The difference in overall loss or gain between sell at the current day's high price or low price is found tp be the difference in overall gain as $280.10

The third option is correct.

High price value: 115 shares * $105.19 per share = $12,084.85

Low price value: 115 shares * $103.25 per share = $11,858.75

High price value: 30 shares * $145.18 per share = $4,355.40

Low price value: 30 shares * $143.28 per share = $4,298.40

The overall value at high price:

$12,084.85 + $4,355.40

= $16,440.25

The overall value at low price:

$11,858.75 + $4,298.40

= $16,157.15

In conclusion, the difference in overall gain or loss:

$16,440.25 - $16,157.15 = $280.10

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The number of cars Captain's Autos sold in total that week is 160.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that:

Now,

Let's call the total number of cars sold during the week "x".

We know that the number of cars sold on Monday and Tuesday is 25% of the total number of cars sold during the week. So we can write:

[tex]\sf 22 + 18 = 0.25x[/tex]

Simplifying, we get:

[tex]\sf 40 = 0.25x[/tex]

Dividing both sides by 0.25, we get:

[tex]\bold{x = 160}[/tex]

Hence, by the unitary method the answer will be 160.

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The Puyer Corporation has budgeted fixed selling and administrative expenses of $73,860 for February.

This includes advertising of $51,960, executive salaries of $21,900, and other expenses of $9,900.

The variable cost per Deb sold is $2.50. If the company sells 16,900 Debs in February, then the total budgeted selling and administrative expenses will be $89,760.

The total budget spending is given as:

$73,860 + (16,900 * $2.50) = $89,760

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Answer:

  A.  82 cm

Step-by-step explanation:

You want the perimeter of the L-shaped figure that is 12.5 cm high and 28.5 cm wide.

The top two horizontal line segments have the same total length as the bottom horizontal line segment. We don't need to figure what the missing length is, because we only need their total for the perimeter.

The right side two vertical line segments have the same total length as the left vertical line segment. As with the horizontal segments, we don't need to figure out the missing length, because we only need their total for the perimeter.

The perimeter is the sum of horizontal line segments plus the sum of vertical line segments:

  2(28.5 cm) + 2(12.5 cm) = 57 cm + 25 cm = 82 cm

The perimeter of the figure is 82 cm.

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Answer:

A

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{\boxed{x = 10}}[/tex]

Step-by-step explanation:

To solve the equation [tex]5x = 50[/tex] and find the value of [tex]x[/tex], we need to isolate [tex]x[/tex] on one side of the equation.

Step 1: Divide both sides of the equation by 5.

[tex]\frac{5x}{5} = \frac{50}{5}[/tex]

Step 2: Simplify this expression

[tex]x = 10[/tex]

Therefore, the solution to the equation [tex]\boldsf{5x = 50}[/tex] is [tex]x = 10[/tex].

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Answer:

(x - 1/8) * 1/4 = 1/16

x - 1/8 = 1/16

x = 1/16 + 1/8

x = 3/8

If x = -2 is a zero with a multiplicity of one, x = 3 is a zero with a multiplicity of two, and x = 1 is a zero with a multiplicity of one, then the polynomial can be written in factored form as:

[tex]f(x) = (x + 2)(x - 3)^2(x - 1)[/tex]

To find the polynomial in expanded form, we can use the distributive property and the rules of exponents:

[tex]f(x) = (x + 2)(x - 3)(x - 3)(x - 1)\\= (x^2 - x - 6)(x - 3)(x - 1)\\= (x^3 - 4x^2 + 3x + 18)(x - 1)\\= x^4 - 5x^3 + 6x^2 + 4x + 18[/tex]

Therefore, the polynomial that has a lead coefficient of one and exactly three distinct zeros, with x = -2 as a zero with multiplicity of one, x = 3 as a zero with multiplicity of two, and x = 1 as a zero with multiplicity of one, is:

[tex]f(x) = x^4 - 5x^3 + 6x^2 + 4x + 18[/tex]

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The probability that spinner one will land on four, and spinner two will land on blue is (1/24) x (2/24) = 1/288, or approximately 0.3%.

Megan has two spinners with one spinner divided into six equal parts, while the second spinner is divided into four equal parts. The probability that spinner one will land on four, and spinner two will land on blue is required.

The fundamental principle of probability states that the probability of an event happening is the number of favorable outcomes to the total number of outcomes.

To find the probability, it is essential to determine the total number of outcomes by multiplying the number of sections on each spinner.

The total number of outcomes = (Number of sections in spinner one) x (Number of sections in spinner two)

Number of sections in spinner one = 6Number of sections in spinner two = 4Total number of outcomes

= 6 x 4 = 24

The number of outcomes that will result in spinner one landing on four is one, and the number of outcomes that will result in spinner two landing on blue is two.

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Answer:

Approximately 2.5% of the data is greater than 34.

Step-by-step explanation:

To solve this problem, we need to use the empirical rule (also known as the 68-95-99.7 rule) for a normal distribution. This rule states that about 68% of values lie within 1 standard deviation of the mean, about 95% of the values lie within 2 standard deviations of the mean, and about 99.7% of the values lie within 3 standard deviations of the mean.

The mean of the dataset is 27, and the standard deviation is 3.5.

34 is exactly 2 standard deviations away from the mean (since 27 + 2*3.5 = 34). According to the empirical rule, about 95% of the data falls within this range. This means that about 5% of the data is outside of this range.

Since the normal distribution is symmetrical, the data outside of 2 standard deviations is equally split between values that are too large and too small. Hence, about half of this 5%, or 2.5%, is greater than 34.

Therefore, approximately 2.5% of the data is greater than 34.

Answer:

$6.00

Step-by-step explanation:

In order y find the cost of one muffin, we divide the price of 6 muffins by 6.

$3.00 / 6 = $0.50

Therefore, the cost of one muffin is $0.50.

To find the price per dozen, we multiply the cost of one muffin by 12.

$0.50 * 12 = $6.00

Therefore, the price per dozen muffins is $6.00.

Answer:

B. $5.99

Step-by-step explanation:

Let's start by finding the total cost of the sodas. We know that there were 5 sodas and each cost $0.75, so the total cost of the sodas is:

5 * $0.75 = $3.75

Next, we need to subtract the cost of the sodas from the total cost before tax to find the cost of the pizzas:

$33.70 - $3.75 = $29.95

Finally, we can divide the cost of the pizzas by the number of pizzas to find the cost of each pizza:

$29.95 ÷ 5 = $5.99

Therefore, the cost of each pizza pie was $5.99. Answer choice B is correct.

About 95% of the housing Prices are between (µ - 2σ) and (µ + 2σ).About 99.7% of the housing prices are between (µ - 3σ) and (µ + 3σ)

Given that housing prices in a small town are normally distributed with a mean of µ. We are to use the empirical rule to complete the following statement.

The empirical rule states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean,

and approximately 99.7% of the data falls within three standard deviations of the mean.Since we do not have information about the standard deviation of the housing prices,

we cannot provide exact values for the empirical rule. However, we can make some general statements:

About 68% of the housing prices are between (µ - σ) and (µ + σ).

About 95% of the housing prices are between (µ - 2σ) and (µ + 2σ).About 99.7% of the housing prices are between (µ - 3σ) and (µ + 3σ)

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Answer:

[tex]( { \frac{ {r}^{2} }{s} })^{3} = \frac{ {r}^{2 \times 3} }{ {s}^{1 \times 3} } = \frac{ {r}^{6} }{ {s}^{3} } [/tex]

Answer:  C  200 times larger

Step-by-step explanation:

If you want to compare Edmond to Tulsa

Edmond = 1.6 x 10^3

Tulsa  = 3.3 x 10^5

10 to the power of anything means 1 and what ever that power is, that's how many 0's you put on.

Ex. 10^3 = 1000

10^5 = 100000

So Edmond = 1.6 x 1000

Tulsa = 3.3 x 100000

If you multply by 10's 100's etc.  the amount of 0's you have is how many you will move your decimal point

So Edmond = 1600

Tulsa = 330000

You can see that when comparing edmond to tulsa it got a lot larger.  200 times larger.

Answer:

The bottom one

Step-by-step explanation:

Notice that the graph is an upward opening parabola and passes through the x-axis at the x-intercepts x=1 and x=-4. These are our zeroes that allow f(x)=0 by the Zero Product Property.

The polynomial f(x) with real coefficients and the given zeros is:

f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)

To form a polynomial with degree 5 and the given zeros, we can start by writing the factors corresponding to each zero.

The zero 3 gives us the factor (x - 3).

The zero -i gives us the factor (x + i) since complex zeros always come in conjugate pairs.

The zero 9+i gives us the factor (x - (9+i)).

Now, we can multiply these factors together to obtain the polynomial:

f(x) = (x - 3)(x + i)(x - (9+i))

Next, we simplify the expression:

f(x) = (x - 3)(x + i)(x - 9 - i)

Expanding the product, we have:

f(x) = (x^2 + xi - 3x - 3i)(x - 9 - i)

Multiplying further:

f(x) = (x^3 - 9x^2 - ix^2 + xi - 3x^2 + 27x + 3ix - 3xi - 27i - 3x + 27 + 3i)

Combining like terms:

f(x) = x^3 - (9 + i)x^2 - 3x^2 + (x - 3 - 3i)x + 27x + (27 + 3i)

Simplifying:

f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)

The polynomial f(x) with real coefficients and the given zeros is:

f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)

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