A laundry detergent box measures 12 inches by 8 inches by 3 inches. What is the volume of two boxes of detergent?


Formula:


Plug in values


Solution:

The volume of the can of soup that the bear ate was approximately 4644.64 cubic inches.

To solve this problem, we need to make some assumptions about the can of soup. Let's assume that the can is cylindrical and that it is completely filled with soup. We also need to assume that the label covered the entire surface area of the can without any overlap.

The label is 22 inches tall and 9 inches wide, so it covered a total surface area of 22 x 9 = 198 square inches. Since the label completely covered the sides of the can without any overlap, we can use this surface area to find the surface area of the can itself.

The surface area of a cylinder is given by the formula A = 2πrh + 2πr², where r is the radius of the base of the cylinder, and h is the height of the cylinder. In this case, we know that the height of the cylinder is 22 inches (the height of the label), and the circumference of the base of the cylinder is 9 inches (the width of the label).

Using these values, we can solve for the radius of the cylinder:

9 = 2πr
r = 4.53 inches

Now we can use the formula for the surface area of a cylinder to solve for the volume of the can:

A = 2πrh + 2πr²
198 = 2π(22)(4.53) + 2π(4.53)²
198 = 634.26
A = πr²h
V = A x h/3
V = 634.26 x 22/3
V ≈ 4644.64 cubic inches

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Answer:

Its 12

Step-by-step explanation:

1.   Following PEMDAS, we first solve the equation inside the parentheses.

       -4(-2) = 8

       -12 ÷ 3 = -4

       -20 + 4 = -16

2.    Now, we have the following expression:

       8 + (-4) + (-16)

 3.  Again, following PEMDAS, we solve the equation inside the parentheses first.

       8 + (-4) + (-16) = 8 - 4 - 16

  4. Finally, we solve the equation from left to right.

       8 - 4 - 16 = 8 - (4 + 16)

       8 - (20) = -12

Therefore, the value of the expression is -12.

The equation in standard form for the circle with center (8,0) and radius 3/3 is (x - 8)² + y² = 1

To write the equation in standard form for the circle with center (8,0) and radius 3/3, we can use the following formula for a circle in standard form:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle and r is the radius. In this case, the center is (8,0) and the radius is 3/3, which simplifies to 1. Now, we can substitute the values of h, k, and r into the equation:
(x - 8)² + (y - 0)² = 1²

Since (y - 0) is just y, we can simplify the equation to:
(x - 8)² + y² = 1
So, the equation in standard form for the circle with center (8,0) and radius 3/3 is:
(x - 8)² + y² = 1
In summary, we used the standard form equation for a circle, substituted the given values for the center and radius, and simplified the equation to obtain the final answer.

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To solve the system of linear equations by elimination, we need to eliminate one of the variables by multiplying one or both equations by a constant so that the coefficients of one of the variables are equal in both equations. Then, we can subtract one equation from the other to eliminate that variable and solve for the remaining variable.

In this case, we can eliminate y by multiplying the first equation by -7 and the second equation by 6, so that the coefficients of y are equal in both equations:

-28x - 42y = -336

18x + 42y = 306

Adding these two equations together, we get:

-10x = -30

Dividing both sides by -10, we get:

x = 3

Now that we have solved for x, we can substitute this value into one of the original equations to solve for y. Using the first equation, we get:

4x + 6y = 48

4(3) + 6y = 48

12 + 6y = 48

Subtracting 12 from both sides, we get:

6y = 36

Dividing both sides by 6, we get:

y = 6

Therefore, the solution to the system of linear equations is x = 3 and y = 6.

Answer:

Please look at the picture provided to see the correct triangle because each figure has no a,b, or c. Thanks

Frank's monthly credit card payment for consolidating his credit cards will be $467.29.

Option C is the correct answer.

We have,

To calculate the monthly credit card payment for consolidating Frank's credit cards, we can use the formula for the monthly payment on a loan:

[tex]M = P (r (1 + r)^n) / ((1 + r)^n - 1),[/tex]

where M is the monthly payment, P is the total loan amount (sum of all credit card balances), r is the monthly interest rate, and n is the number of months.

First, let's calculate the total loan amount:

Total loan amount = $2,380 + $4,500 + $1,580 + $900 = $9,360.

Next, let's calculate the monthly interest rate:

Monthly interest rate = APR / 12 = 18% / 12 = 1.5%.

Now, let's calculate the monthly payment using the formula:

[tex]M = $9,360 \times (0.015 (1 + 0.015)^{24}) / ((1 + 0.015)^{24} - 1).[/tex]

Using a calculator, we can compute the value of M:

M ≈ $467.286.

Rounding to the nearest cent,

Frank's monthly credit card payment for consolidating his credit cards will be $467.29.

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Answer: 55%

Step-by-step explanation:

To find the percentage of 11/20, we can use the following formula:

Percentage = (Numerator ÷ Denominator) × 100

Substituting the values from 11/20 into the formula, we get:

Percentage = (11 ÷ 20) × 100

Percentage = 0.55 × 100

Percentage = 55%

Therefore, the percentage of 11/20 is 55%.

Answer:

Solution: 11/20 as a percent is 55%

Step-by-step explanation:

First, convert the fraction into a decimal by dividing the numerator by the denominator:

11/20 = 0.55

If we multiply the decimal by 100, we will get the percentage:

00.5 * 100 = 55

We can see that 11/20 is percentage is 55.

The dimensions of the garden last year were 15 feet by 4 feet.

Let the length of the garden last year be L feet, and the width be W feet. We are given that the area of the garden last year was 60 square feet:

L * W = 60

This year, the garden is 1 foot wider and 3 feet shorter than last year's garden:

Length: L - 3

Width: W + 1

The area of the garden remains the same:

(L - 3) * (W + 1) = 60

Now we have two equations with two variables:

L * W = 60

(L - 3) * (W + 1) = 60

We can solve this system of equations using substitution or elimination. Let's use substitution. From equation 1, we can write L as:

L = 60 / W

Now substitute this expression for L in equation 2:

(60 / W - 3) * (W + 1) = 60

Simplify and solve for W:

60 + 60 / W - 3W - 3 = 60

Combine like terms:

60 / W - 3W = 3

Multiply both sides by W to eliminate the fraction:

60 - 3W² = 3W

Move all terms to one side:

3W² + 3W - 60 = 0

Divide the equation by 3:

W² + W - 20 = 0

Factor the quadratic equation:

(W + 5)(W - 4) = 0

The possible values for W are -5 and 4. However, since width cannot be negative, W must be 4 feet. Now, use the expression for L to find the length:

L = 60 / W = 60 / 4 = 15 feet

So, the dimensions of the garden last year were 15 feet by 4 feet.

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The given question is related to a regression line, where the equation is given as y = 1425 + 19.87x.

Slope of the equation is 19.87 and the intercept of the equation is 1425.

In part (a), step 2, we can explain that the slope in the least square regression equation is the coefficient of x and represents the average increase or decrease in y per unit of x.

Therefore, the slope value here is b = 19.87, which means that the average consumption of natural gas per day by Joan will decrease by 19.87 cubic feet per degree Fahrenheit over a month.

In part (b), step 1, we can explain that the y-intercept is a constant value in the least square regression equation that represents the average value of y when x is 0. Here, the intercept value is m = 1425, which means that when the temperature is 0 degrees Fahrenheit, the average consumption of natural gas per day is 1425 cubic feet.

This value has significance in this scenario because it indicates that a temperature of 0 degrees Fahrenheit is a possible temperature for which the natural gas consumption has been calculated.

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The probability of flipping a coin and getting tails at least once in four flips is 15/16 or approximately 0.94. (option d).

To determine the probability of flipping a coin and getting tails at least once in four flips, we can use a probability table. The table shows all the possible outcomes of flipping a coin four times.

Flip 1 Flip 2 Flip 3 Flip 4

Outcome 1 H H H H

Outcome 2 H H H T

Outcome 3 H H T H

Outcome 4 H H T T

Outcome 5 H T H H

Outcome 6 H T H T

Outcome 7 H T T H

Outcome 8 H T T T

Outcome 9 T H H H

Outcome 10 T H H T

Outcome 11 T H T H

Outcome 12 T H T T

Outcome 13 T T H H

Outcome 14 T T H T

Outcome 15 T T T H

Outcome 16 T T T T

In the table, H represents heads, and T represents tails. There are 16 possible outcomes when flipping a coin four times. We can see that getting tails at least once is possible in 15 of these outcomes: Outcome 2, Outcome 3, Outcome 4, Outcome 6, Outcome 7, Outcome 8, Outcome 10, Outcome 11, Outcome 12, Outcome 14, Outcome 15, and Outcome 16.

Therefore, the probability of flipping a coin and getting tails at least once in four flips is the number of outcomes where tails appear at least once divided by the total number of outcomes, which is 15/16 or approximately 0.94. (option d).

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To determine how many triangles are represented by the angles a=120 degrees, a=250 degrees, and b=195 degrees, we need to use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

First, we need to determine which angle corresponds to which side. Let's assume that angle a is opposite to the longest side, and angle b is opposite to the shortest side. Therefore, we have: a = 250 degrees (longest side) a = 120 degrees b = 195 degrees (shortest side) Next, we need to use the triangle inequality theorem to determine which combinations of sides can form a triangle. For any two sides a and b, the third side c must satisfy the following condition: c < a + b Using this condition, we can determine the valid combinations of sides: - a + b > c: This is always true, since a and b are the longest and shortest sides, respectively. - a + c > b: This is true for all values of c, since a is the longest side. - b + c > a: This is true only when c > a - b.

Substituting the given values, we get: c > a - b c > 250 - 195 c > 55 Therefore, any side c that is greater than 55 can form a triangle with sides a and b. We can use this condition to count the number of valid triangles: - If c = 56, then we have one triangle. - If c = 57, then we have two triangles (c can be either adjacent side). - If c = 58, then we have three triangles (c can be any of the three sides). Continuing this pattern, we can count the number of triangles for each value of c: c = 56: 1 triangle c = 57: 2 triangles c = 58: 3 triangles c = 59: 4 triangles c = 60: 5 triangles c = 61: 6 triangles c = 62: 7 triangles c = 63: 8 triangles c = 64: 9 triangles c = 65: 10 triangles c = 66: 11 triangles c = 67: 12 triangles c = 68: 13 triangles c = 69: 14 triangles c = 70: 15 triangles c > 70: 16 triangles (since all three sides can form a triangle) Therefore, there are 16 possible triangles that can be formed with the given angles and side lengths.

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The triangle has two sides with equal lengths (AB and AC) and one side with a different length (BC). This makes it an isosceles triangle.

Triangle ABC has vertices A(0,0), B(0,3), and C(3,0).

To determine the type of triangle, we can find the lengths of the sides using the distance formula:

AB = sqrt((0-0)^2 + (3-0)^2) = sqrt(0 + 9) = 3

BC = sqrt((3-0)^2 + (0-3)^2) = sqrt(9 + 9) = sqrt(18) = 3√2

AC = sqrt((3-0)^2 + (0-0)^2) = sqrt(9 + 0) = 3

The triangle has two sides with equal lengths (AB and AC) and one side with a different length (BC). This makes it an isosceles triangle.

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Answer:

.15(180) - .10(180) = .05(180) = 9

9 more people voted for split pea soup than for potato soup.

The part of the surface area equation are

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

SA = B + 1/2Pl

In the equation, we have

Part 1 = B

Part 2 = P

Part 3 = l

When the above parts are labelled, we have

Part 1 = B = Base area

Part 2 = P = Perimeter of base

Part 3 = l = Height of pyramid

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Considering the figures the scale factor is 1/4

Area of parallelogram QRST

= 9 square units

Area of parallelogram Q'R'S'T'

= 144 square units

The scale factor is solved using a reference side say QR and Q'R'

with QR = 12 and Q'R' = 3

the relationship is

QR * scale factor = Q'R'

12 * scale factor = 3

scale factor = 3/12 = 1/4

Area of parallelogram QRST

= base * height

= 3 * 3

= 9 square units

Area of parallelogram Q'R'S'T'

= 12 * 12

= 144 square units

The relationship between the areas are

9 square units * ( scale factor)² = 144

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The distance between points E and B is (2/3)*AB, or (2/3)*(7+x) units.

Since the dotted line is the perpendicular bisector of side AB, it means that it cuts the line AB into two equal halves. Thus, the distance between points E and the dotted line is equal to the distance between point A and the dotted line.

We know that the distance between points E and A is 7 units, and since the dotted line bisects AB, the distance between point A and the dotted line is equal to the distance between point B and the dotted line. Let's call this distance 'x'.

Therefore, we have two equal distances (7 units and 'x') that add up to the length of AB. This means that:

AB = 7 units + x

However, we also know that the dotted line is the perpendicular bisector of AB, meaning that it forms right angles with both A and B. This creates two right-angled triangles, AED and BED, where DE is the perpendicular line from point E to AB.

Using Pythagoras' theorem, we can find the length of DE in terms of 'x':

(DE)² + (AE)² = (AD)²

(DE)² + (7)² = (AB/2)²

(DE)² + 49 = (AB²)/4

(DE)² = (AB²)/4 - 49

(DE)² = (AB² - 196)/4

(DE)² = (x²)/4

DE = x/2

Therefore, the distance between points E and B is equal to the length of DE plus the distance between point B and the dotted line, which is also equal to 'x'. Therefore, the distance between points E and B is:

EB = (x/2) + x = 1.5x

We can substitute this into the equation we found earlier:

AB = 7 units + x

AB = 7 units + (2/3)*EB

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The number written as a percentage is:

772.5666118%

To do this, just multiply the number by 100%.

For example, for any number A, the percentage form of A is:

p = A*100%

Here the number is  7.725666118, then the percentage form of this number will be:

N =  7.725666118*100% = 772.5666118%

That is the number as a percentage.

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The mean of the temperatures shown is -39.4°F.

What is the mean temperature?

The average mean air temperature throughout a specific time period, typically a day, a month, or a year, as measured by a thermometer that has been properly exposed. The mean temperature is often calculated for the year and for each month in climatological tables.

Date:   Low temperature:

January 1   -42°F

January 2 -31°F

January 3  -40°F

January 4  -40°F

January 5  -44°F

Mean = Total sum of all 5 days temperature / total number of days

Mean = -42  - 31 - 40 - 40 - 44 / 5

= -197 / 5

= - 39.4°F

Hence, the mean of the temperatures shown is -39.4°F.

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The volume of the part of the ball p < 5 that lies between the cones φ = π/4 and φ = π/3 is 0.

To express the volume of the part of the ball p < 5 that lies between the cones φ = π/4 and φ = π/3, we first need to determine the limits of integration in spherical coordinates.
Since the ball has radius 5, we know that the limits on ρ are 0 and 5.

For the limits on φ, we know that the region of interest lies between the cones φ = π/4 and φ = π/3, which correspond to angles of 45 degrees and 60 degrees, respectively.

Therefore, the limits on φ are π/4 and π/3.
For the limits on θ, we know that the region of interest extends all the way around the ball, so the limits on θ are 0 and 2π.
Using these limits, we can express the volume of the region of interest as:
V = ∫∫∫E ρ sin φ dρ dθ dφ
where,

E is the region of interest defined by the limits on ρ, θ, and φ that we just determined.
Substituting the limits and the volume element in spherical coordinates,
Integrating with respect to θ, we have:
V = 0
Therefore, the volume of the part of the ball p < 5 that lies between the cones φ = π/4 and φ = π/3 is 0.

This result suggests that there may be an error in the problem statement or that the region of interest is not well-defined.

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Percentage of lifetime cost that was interest = $407.

Let's begin by finding the monthly payment that Hillary made to pay off her laptop over two and a half years.

If she paid off the $804 balance with identical monthly payments, then the total amount she paid is equal to the balance plus the interest:

Total amount paid = balance + interest

We can use the formula for the present value of an annuity to solve for the monthly payment, where PV is the present value (in this case, $804), r is the monthly interest rate (which we can find from the APR), n is the total number of payments (30 months), and PMT is the monthly payment:

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

We can solve this equation for PMT:

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

The monthly interest rate is the annual percentage rate divided by 12, and the number of payments is the number of years times 12:

r = 0.1127 / 12 = 0.009391667

n = 2.5 * 12 = 30

Using these values, we get:

PMT = 804 * 0.009391667 / (1 - (1 + 0.009391667)^(-30)) = $33.00

So Hillary made 30 monthly payments of $33.00 to pay off her laptop.

Next, we can calculate the cost of electricity over six years. There are 365 days in a year, and 2 leap years in the six-year period, for a total of 6*365+2 = 2192 days.

At $0.27 per day, the total cost of electricity is:

2192 * $0.27 = $592.64

Now we can calculate the total cost of the laptop over six years.

Hillary paid $33.00 per month for 30 months, or a total of 30 * $33.00 = $990.00. She also paid $592.64 for electricity. Therefore, the total cost of the laptop is:

$990.00 + $592.64 = $1582.64

The interest she paid on her credit card is the difference between the total amount she paid and the cost of the laptop:

Interest = Total amount paid - Cost of laptop

Interest = $990.00 + interest on $804 balance - $804 - $592.64

Simplifying this expression, we get:

Interest = $185.36 + interest on $804 balance

To find the interest on the $804 balance, we can use the formula for compound interest, where P is the principal (in this case, $804), r is the annual interest rate (11.27%), and t is the time in years (2.5 years):

A = P*(1 + r/n)^(n*t)

Here, we can set the number of compounding periods per year, n, to 12 since the interest is compounded monthly. Substituting the given values, we get:

A = $804*(1 + 0.1127/12)^(12*2.5) = $1026.12

So the interest on the $804 balance is:

Interest on $804 balance = $1026.12 - $804 = $222.12

Plugging this value into our expression for Interest, we get:

Interest = $185.36 + $222.12 = $407.48

Finally, we can find the percentage of the lifetime cost of the laptop that was interest:

Percentage of lifetime cost that was interest = Interest / Total cost of laptop * 100%

Percentage of lifetime cost that was interest = $407.

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This is an example of an experiment. In an experiment, researchers manipulate the independent variable (in this case, the presence or absence of an electrical impulse) to determine its effect on the dependent variable (the number of repetitions the subjects can lift a weight).

The researcher randomly assigned subjects to either receive the electrical impulse or not, which is a key feature of experimental design.

By doing so, the researcher can ensure that any differences observed between the two groups are due to the manipulation of the independent variable, rather than any pre-existing differences between the groups.

In contrast, an observational study merely observes existing characteristics or behaviors of a population, without any manipulation or control of variables.

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The price of the stereo system after the discount and markup is $691.20.

The markup price represents the price after adding a percentage of the discounted price.

The markup can be determined using the markup factor, which increases 100% by the markup percentage.

The discount offered on the stereo system = 20%

Original sales price of the system = $720

Discount factor = 0.8 (1 - 0.2)

Discounted price = $576 ($720 x 0.8)

Markup percentage after the discount = 20%

Markup factor = 1.2 (1 + 0.2)

Marked up price = $691.20 ($576 x 1.2)

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Answer:

I can definitely help you with that math problem! Given the information about the bicycle wheel, we need to find the function that models the height of a spot on the edge of the wheel. We know that the wheel has a diameter of 26 inches, which means the radius is half of that, or 13 inches. Isabelle rides the bike so that the wheel makes two complete rotations per second, which means the period of the function is 1/2 second (since it takes half a second for the wheel to complete one rotation).

Using the formula for a sinusoidal function, we can write the function as h(t) = A sin(2π/B (t - h)) + k, where A is the amplitude, B is the period, h is the horizontal shift, and k is the vertical shift. We can determine the values of these parameters as follows:

- Amplitude: The amplitude is half the distance between the highest and lowest points of the function. Since the radius of the wheel is 13 inches, the highest and lowest points are 26 inches apart. Therefore, the amplitude is 13 inches.

- Period: We know that the period is 1/2 second, so B = 2π/1/2 = 4π.

- Horizontal shift: The function starts at its highest point, so there is no horizontal shift. Therefore, h = 0.

- Vertical shift: The center of the wheel is at a height of 13 inches above the ground, so the vertical shift is also 13 inches.

Putting it all together, we get the function h(t) = 13 sin(4πt) + 13, which corresponds to option C. This function models the height of a spot on the edge of the wheel as Isabelle rides the bike. I hope this explanation helps! Let me know if you have any other questions or if there's anything else I can assist you with.

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(a) The greatest amount of snowfall in any of the cities = 50 inches.

(b) The data is most concentrated in the second quarter (Q₂), ranging from 6 inches to 20 inches.

(c) The data is most spread out in the fourth quarter (Q₄), ranging from 32 inches to 50 inches.

A box plot is a type of graphical representation that summarizes the distribution of a dataset based on the five-number summary: the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value.

A box plot consists of a rectangular box, which spans from Q1 to Q3, with a vertical line inside it representing the median. The length of the box represents the interquartile range (IQR), which is the range between Q1 and Q3.

Whiskers, which are lines extending from the top and bottom of the box, indicate the range of the dataset outside of the IQR.  

Here we have

Jyllina created this box plot representing the number of inches of snow that fell this winter in different nearby cities

The data ranges from 4 to 50 inches

4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

(a) The greatest amount of snowfall in any of the cities will equal the highest value which is 50 inches.

(b) The data is most concentrated in the second quarter (Q₂), which ranges from 6 inches to 20 inches.

This can be inferred from the fact that the box plot shows the smallest range between the minimum and maximum values, as well as the smallest size of the box, which represents the interquartile range (IQR).

(c) The data is most spread out in the fourth quarter (Q₄), which ranges from 32 inches to 50 inches.

This can be inferred from the fact that the box plot shows the largest range between the minimum and maximum values, as well as the largest size of the box, which represents the IQR.

Additionally, the whiskers, which represent the range of values outside the IQR, are also the longest in this quarter, indicating that there are more extreme values in this range compared to the other quarters.

Therefore,

(a) The greatest amount of snowfall in any of the cities = 50 inches.

(b) The data is most concentrated in the second quarter (Q₂), ranging from 6 inches to 20 inches.

(c) The data is most spread out in the fourth quarter (Q₄), ranging from 32 inches to 50 inches.

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Complete Question:

The expression that shows the temperature at sunset in terms of T is 3T/2.

Let's call the temperature at sunrise T. According to the problem statement, the temperature tripled from sunrise to noon, so the temperature at noon is 3T.

Then, from noon to sunset, the temperature halved, so the temperature at sunset is (1/2) of the temperature at noon, or (1/2)(3T), which simplifies to 3T/2. Therefore, the expression that shows the temperature at sunset in terms of T is 3T/2.

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Assuming that the trail is a total of "x" miles, we can set up the following equation to solve for "x":

816 = 0.48x

To solve for "x", we can divide both sides by 0.48:

x = 1700

Therefore, the total length of the trail is 1700 miles.

Answer:

Step-by-step explanation:

false i think

Answer:

True

Step-by-step explanation:

If two prisms are similar, their corresponding dimensions are proportional.

Let's assume that the ratio of the corresponding lengths of the smaller prism to the larger prism is k:1, where k is a constant.

Then the ratio of the corresponding surface areas of the smaller prism to the larger prism is [tex](k^2):1[/tex], because the surface area of a prism is proportional to the square of its length.

In this problem, the surface area of the smaller prism is not given.

However, we can find the ratio of the corresponding lengths of the smaller prism to the larger prism using the fact that they are similar.

The height of the smaller prism can be found as follows:

[tex]7/5 = h/L[/tex]

where h is the height of the smaller prism and L is the length of the larger prism.

Solving for h, we get:

[tex]h = (7/5)L[/tex]

The ratio of the corresponding lengths of the smaller prism to the larger prism is 7:5.

The ratio of the surface areas of the smaller prism to the larger prism is:

[tex](7/5)^2 : 1 = 49/25 : 1[/tex]

We know that the surface area of the larger prism is [tex]90 m^2.[/tex]

Let's denote the surface area of the smaller prism by A. Then we can set up an equation:

(49/25)A = 90

Solving for A, we get:

A = (25/49) * 90 = 45/7 ≈ 6.4

The surface area of the smaller prism is approximately [tex]6.4 m^2.[/tex]

(Note: The units of the surface area are not provided for the smaller prism, so I assumed the same units as the larger prism.

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To find the measure of angle 1 when AB is tangent to circle P at point B, we must consider some properties of tangents and circles.

A tangent line to a circle is a line that touches the circle at exactly one point, known as the point of tangency. In this case, line AB is tangent to circle P at point B. A crucial property of tangents is that they are perpendicular to the radius of the circle at the point of tangency. Therefore, the radius PB of circle P is perpendicular to tangent AB at point B.

Now, let's examine angle 1. If angle 1 is the angle formed by the tangent AB and the radius PB at point B, then it is a right angle due to the aforementioned property. In this case, the measure of angle 1 is 90 degrees.

However, if angle 1 is not directly formed by the tangent and radius, more information is needed to determine its measure. For example, if angle 1 is an angle inside the circle, you would need to know the measure of other angles or lengths of chords within the circle to calculate it.

In summary, if angle 1 is formed by tangent AB and radius PB at point B, its measure is 90 degrees because tangents are perpendicular to the radius at the point of tangency. If angle 1 is not formed by the tangent and radius, additional information is required to determine its measure.

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The entire expression is factored completely as: 5x2(x4 + 4)(x2 + 2)(x2 - 2)

Part A:

To factor out the greatest common factor, we need to find the largest number that divides evenly into both terms. In this case, the greatest common factor is 5x2.

5x10 − 80x2

= 5x2 (x8 - 16)

Therefore, we can rewrite the expression as 5x2(x8 - 16).

Part B:

To factor the entire expression completely, we need to use the difference of squares formula, which states that:

a2 - b2 = (a + b)(a - b)

In this case, we can rewrite the expression as:

5x2(x8 - 16) = 5x2[(x4)2 - (4)2]

Notice that x8 can be rewritten as (x4)2, and 80 can be factored into 4 x 20, which gives us 16 when squared.

Using the difference of squares formula, we can factor the expression further:

5x2[(x4 + 4)(x4 - 4)]

The expression (x4 + 4) cannot be factored further, but (x4 - 4) can be factored using the difference of squares formula again:

5x2[(x4 + 4)(x2 + 2)(x2 - 2)]

Therefore, the entire expression is factored completely as: 5x2(x4 + 4)(x2 + 2)(x2 - 2)

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