does anyone know how to find the volume by rotating the region based on what’s in the image i uploaded?

Answer:

3 and 5

Step-by-step explanation:

|x-4| = 1 is the same as x-4 = 1 and -x+4 = 1

x-4=1

x = 5

-x+4 = 1

-x = -3

x = 3

Answer:

[tex]3 \: {cm}^{2} [/tex]

Step-by-step explanation:

Given:

h (height) = 1,5 cm

b (base) = 4 cm

Find: A (area) - ?

[tex]a = \frac{1}{2} \times b \times h[/tex]

[tex]a = \frac{1}{2} \times 4 \times 1.5 = 3 \: {cm}^{2} [/tex]

The leading coefficient of the polynomial -4x^3+9  is -4.

The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

In this polynomial, -4x^3+9, the term with the highest degree is -4x^3, and the coefficient of this term is -4.

Therefore, the leading coefficient of the polynomial is -4.

The degree of a polynomial is the highest exponent of the variable in any of its terms. In this polynomial, the variable is x and the highest exponent is 3. So, the degree of this polynomial is 3.

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The area of the kitchen in square feet is 132[tex]ft^{2}[/tex]

To find the area of the rectangular kitchen, we need to multiply the length by the width.

The length of the kitchen can be found by subtracting the x-coordinates of the two points on the same vertical side. So, the length is 8 - (-3) = 11 feet.

The width of the kitchen can be found by subtracting the y-coordinates of the two points on the same horizontal side. So, the width is 4 - (-8) = 12 feet.

Therefore, the area of the kitchen is:

Area = Length x Width = 11 ft x 12 ft = 132 square feet

So the answer is 132[tex]ft^{2}[/tex].

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The factorization for 8i is 3x(5x+1)(x-2), which can also be checked by multiplying the factors and verifying that the result is equal to the original polynomial.

Polynomial     GCF Factored with GCF Factored TrinomiaL  Final  

9x^4 + 3x^3 -1222 1     NA                                   NA                                        

2x^2 + 3x - 9        1    NA     (2x-3)(x+3)                    (2x-3)(x+3)

15x^3 - 27x^2 - 6x 3x 3x(5x^2 - 9x - 2) not factorable 3x(5x+1)(x-2)

9a) Factorization from 8d: not factorable

9b) Factorization from 8h: (2x-3)(x+3)

9c) Factorization from 8i: 3x(5x+1)(x-2)

Note: The table shows the factoring process for each polynomial. In question 9, we just need to check the final factorization for each of the polynomials in question 8. The factorization for 8d is not factorable, so there is nothing to check. The factorization for 8h is (2x-3)(x+3), which can be checked by multiplying the factors and verifying that the result is equal to the original polynomial.

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The true statement about effect size is: The effect size is the extent to which the null or statistical hypothesis is false. Effect size is a measure used in research studies to quantify the magnitude of the difference between groups or the strength of an association between variables.

It helps determine the practical significance of the research findings, as opposed to the statistical significance.
When the effect size is small, detecting it is not necessarily easier, and a larger sample size may be required to achieve adequate statistical power. A larger effect size, on the other hand, might be easier to detect and might require a smaller sample size.
There is not just one type of effect size measure used in research studies. There are various measures of effect size, such as Cohen's d, Pearson's correlation coefficient (r), and odds ratio (OR), among others. Each type of effect size is suitable for different research designs and data types.

Choosing the appropriate effect size measure depends on the research question, the design of the study, and the type of data being analyzed.

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Based on both the mean and median values, we can conclude that Wide Awake typically sells more coffee per hour than Coffee Ground.

What are the mean and median?

The mean and median are two measures of central tendency that can be used to describe a set of data. The median is the middle value in the data set when the values are arranged in order from lowest to highest. If there are an even number of values, the median is the average of the two middle values.

To determine which coffee shop typically sells the most amount of coffee per hour, we need to compare the measures of center (mean and median) of the data for each shop.

Calculating the mean of each dataset, we get:

Mean of Coffee Ground = (1.5+20+3.5+12+2+5+11+7+2.5+9.5+3+5) / 12 = 6.5/2 = 5.42 gallons

Mean of Wide Awake = (2.5+10+4+18+4+3+6+5+2.5) / 9 = 56 / 9 = 6.22 gallons

Calculating the median of each dataset, we get:

Median of Coffee Ground = 4.25 gallons

Median of Wide Awake = 4.5 gallons

Comparing the measures of the center, we see that the mean value of coffee sold per hour at Coffee Ground is approximately 5.42 gallons, while the mean value of coffee sold per hour at Wide Awake is approximately 6.22 gallons.

Therefore, on average, Wide Awake sells more coffee per hour than Coffee Ground.

However, we also see that the median value of coffee sold per hour at Wide Awake is 4.5 gallons, while the median value of coffee sold per hour at Coffee Ground is 4.25 gallons.

This suggests that the middle value of coffee sold per hour is higher for Wide Awake than for Coffee Ground.

Therefore, based on both the mean and median values, we can conclude that Wide Awake typically sells more coffee per hour than Coffee Ground.

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The total number of possible three-digit numbers is not odd, does not contain 6, and has at least one repeated digit is 13,221,888.

To find the number of possible three-digit numbers we need to use the systematic approach method

Step 1:

we have to find the number of three-digit numbers that are not odd. Number of possible choices for the units digit (0, 2, 4, or 8)= 4

Number of possible choices for tens and hundreds of digits (0-9 excluding 6 = 9

the total number of three-digit numbers that are not odd is,

= 4 x 9 x 9

= 324.

Step 2:

Count the number of three-digit numbers that do not contain 6.

Number of possible choices for each digit (0-5, 7, 8, or 9) = 8

the total number of three-digit numbers that do not contain 6 is,

= 8 x 8 x 8

= 512.

Step 3:

Count the number of three-digit numbers that do not have distinct digits. The number of possible choices for the repeated digit and 9 choices for the other digit = 9

the total number of three-digit numbers that have a repeated digit is

= 9 x 9 = 81.

Step 4:

Find the intersection of the sets of numbers counted in Steps 1-3.

To do this, we multiply the number of choices in each set:

= 324 x 512 x 81

= 13,221,888.

Therefore, 13,221,888 possible three-digit numbers are not odd, do not contain 6, and have at least one repeated digit.

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If the pyramid is sliced horizontally (parallel to the base), the resulting cross section would be a regular pentagon with the same side length as the base of the pyramid

If the pyramid is sliced horizontally (parallel to the base), the resulting cross section would be a regular pentagon with the same side length as the base of the pyramid. This is because a horizontal slice would intersect all five sides of the pentagonal base at equal distances from the apex of the pyramid, resulting in a regular pentagon.

If the pyramid is sliced vertically through the top vertex (perpendicular to the base), the resulting cross section would be a triangle. The triangle's shape would depend on the height of the pyramid and the angle of the slice. The base of the triangle would be a regular pentagon, with the height of the pyramid as the altitude. The apex of the triangle would be the top vertex of the pyramid. The shape of the triangle would change depending on the angle of the slice, but it would always be an isosceles triangle since the slice passes through the apex, which is the vertex of the pyramid where all the edges meet.

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The first five terms are 2, 6, 18, 54, 162.

A number is a fundamental building block of mathematics.

Numbers are used for indexing, counting, measuring, and a variety of other tasks.

According to their characteristics, there are various sorts of numbers, including natural numbers, whole numbers, rational and irrational numbers, integers, real numbers, complex numbers, even and odd numbers, etc.

The resultant number can be calculated by using the fundamental arithmetic operations for integers.

Tally marks were formerly used before numbers.

Numbers are a crucial aspect of our daily lives, from the number of rounds we run around the race track to the number of hours we sleep at night, and much more.

According to our question-

a series where each subsequent term is obtained by multiplying the preceding one by a shared ratio.

The order is provided by:

a, ar, ar2, aar3, aar4, aar5,...

What is the nth term provided by-

a_n = ar^(n-1)

Second term = 6

a_2 = ar^(2-1)

6 = ar^1

6 = ar

Hence, The first five terms are 2, 6, 18, 54, 162.

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the first five terms of the geometric sequence can be either [tex]{2, 6, 18, 54, 162} or {-2, 6, -18, 54, -162}.[/tex]

Assume that "a" is the first letter of the geometric sequence and "r" is the common ratio.

According to the problem statement, the second term is 6. Therefore, we have:

[tex]ar = 6 .....(1)[/tex]

Similarly, the fourth term is 54, which gives us:

[tex]ar^3 = 54 .....(2)[/tex]

We must first determine the values of "a" and "r" in the geometric sequence. The two equations mentioned above can be solved simultaneously to achieve this.

The result of dividing equation [tex](2)[/tex] by equation [tex](1)[/tex] is

[tex]r^2 = 9[/tex]

When we square the two sides, we obtain:

r = ±3

Now, using equation (1), we can find the value of "a" as follows:

[tex]ar = 6[/tex]

Substituting r = 3, we get:

[tex]3a = 6[/tex]

[tex]a = 2[/tex]

Substituting [tex]r = -3[/tex], we get:

[tex]-3a = 6[/tex]

[tex]a = -2[/tex]

Therefore, the first term of the geometric sequence is either  [tex]2[/tex] or [tex]-2[/tex]  , and the common ratio is 3 or -3.

If the first term is 2 and the common ratio is 3, then the first five terms of the geometric sequence are: [tex]2, 6, 18, 54, 162[/tex]

The first five terms of the geometric sequence are as follows, if the common ratio is three and the first term is two:

[tex]-2, 6, -18, 54, -162[/tex]

So, the first five terms of the geometric sequence can be either [tex]{2, 6, 18, 54, 162} or {-2, 6, -18, 54, -162}.[/tex]

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The possible values of |x + 7| are:

-(x + 7), if x < -7

0, if x = -7

(x + 7), if x > -7

What is the inequality equation?

The expression |x + 7| represents the absolute value of x + 7. An inequality equation involving absolute value can be written as:

|x + 7| < a

where "a" is a positive constant. This inequality means that the distance between x + 7 and 0 on the number line is less than "a". In other words, x can be any value within "a" units of -7.

The possible values of |x + 7| depend on the value of x.

If x is negative, then |x + 7| will be equal to -(x + 7), which is negative.

If x is zero or positive, then |x + 7| will be equal to (x + 7), which is non-negative.

Therefore, the possible values of |x + 7| are:

-(x + 7), if x < -7

0, if x = -7

(x + 7), if x > -7

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Option A, For the aptitude puzzle, the number of ways each of people has the same number of internet friends is 60.

We want to count the number of ways that the 6 people can be internet friends with each other given that each person has the same number of internet friends and no one has an internet friend outside of the group.

Let k be the number of internet friends each person has. Since each person knows 5 other people in the group, we have 6k = 5 * 6, which means that k=5.

Thus, each person has 5 internet friends. We can choose these 5 friends in 5 to choose 5 times 4 choose 5 times 3 choose 5 times 2 choose 5 times 1 choose 5 = 1 × 0 × 0 × 0 × 0 = 0 ways since we can't choose 5 friends from fewer than 5 people.

Therefore, the answer is (A) 60.

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The question is -

Adam, Benin, Chiang, Deshawn, Esther, and Fiona have internet accounts. Some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. Each of them has the same number of internet friends. In how many different ways can this happen?

a. 60

b. 170

c. 290

d. 320

e. 660

Answer: 348 square meters

Step-by-step explanation:

To find the surface area of a rectangular prism, we need to calculate the area of each of the six faces and add them together. A rectangular prism has three pairs of opposite faces: the length (l) and width (w), the length (l) and height (h), and the width (w) and height (h).

Given dimensions: length (l) = 6m, width (w) = 4m, and height (h) = 15m

Area of the length and width faces (lw): 6m * 4m = 24m²

Since there are two opposite faces, the total area of these faces is 2 * 24m² = 48m².

Area of the length and height faces (lh): 6m * 15m = 90m²

Since there are two opposite faces, the total area of these faces is 2 * 90m² = 180m².

Area of the width and height faces (wh): 4m * 15m = 60m²

Since there are two opposite faces, the total area of these faces is 2 * 60m² = 120m².

Now, add the areas of all the faces together:

Surface area = 48m² (lw faces) + 180m² (lh faces) + 120m² (wh faces) = 348m²

The surface area of the rectangular prism is 348 square meters.

Answer:

the surface area of the rectangular prism is 348 square meters.

Step-by-step explanation:

The surface area of a rectangular prism can be found using the formula:Surface Area = 2lw + 2lh + 2whwhere l, w, and h are the length, width, and height of the prism.In this case, the dimensions of the rectangular prism are:l = 6m

w = 4m

h = 15m

Substituting these values into the formula, we get:

Surface Area = 2(6m)(4m) + 2(6m)(15m) + 2(4m)(15m)

Surface Area = 48m^2 + 180m^2 + 120m^2

Surface Area = 348m^2

The domain of f is [0, π/2]. The range of [tex]f^-1[/tex] is also [0, /2].

The domain of a function is the set of all possible values for the input variables (usually denoted as x) for which the function is defined. It is the set of all real numbers or other possible values that can be used as input to the function.

To find the inverse function [tex]f^-1[/tex] of f(x) = 2cos(2x), we follow these steps:

Step 1: Replace f(x) with y.

y = 2cos(2x)

Step 2: Swap x and y and solve for y.

x = 2cos(2y)

cos(2y) = x/2

2y = [tex]cos^(-1)[/tex](x/2)

y = (1/2)[tex]cos^(-1)[/tex](x/2)

Therefore, the inverse function of f is [tex]f^-1[/tex](x) = (1/2)[tex]cos^(-1)[/tex](x/2).

To find the range of f, we notice that the range of cos(2x) is [-1, 1]. Multiplying this by 2 gives us the range of f: [-2, 2].

To find the domain of [tex]f^-1[/tex], we notice that the range of [tex]cos^-1[/tex](x) is [0, pi]. Multiplying this by (1/2) and replacing x with x/2, we get the domain of [tex]f^-1[/tex]: [0, π/2].

To find the range of [tex]f^-1[/tex], we notice that the domain of f is [0, π/2]. Therefore, the range of [tex]f^-1[/tex] is also [0, /2].

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l will spend $58.40 on gas.

What is Multiplication?

Multiplication is an arithmetic operation that involves combining two or more numbers to produce a third number called the product. The symbol for multiplication is "×" or "*".

For example, if you have 3 apples and want to know how many apples you would have if you tripled the amount, you can multiply 3 by 3 to get the answer: 3 × 3 = 9. So, if you tripled the amount of apples you had, you would have 9 apples in total.

Multiplication can be thought of as repeated addition. For instance, 3 × 4 is the same as 3 + 3 + 3 + 3, which equals 12. In this example, 3 is added to itself four times.

Here given, a car holds 50 litres of gas and the price is 116.8 ($1.168) per litre.

We want to calculate the total cost of the gas.

We can find it by multiplying the number of litres by the price per litre

Total cost = [tex]50 \times 1.168[/tex]

Total cost = $58.40

Therefore, l will spend $58.40 on gas.

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Correct question is "Your car holds 50 litres

of gas. If the price is 116.8 ($1.168) per litre then how much money will you spend on gas?"

Brie saves $600 each month.

What is equation?

An equation is a  statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division

To determine how much money Brie saves each month, we need to subtract her expenses from her income.

Income = $3,000

Expenses = $1,400 + $700 + $200 + $100 = $2,400

Savings = Income - Expenses

Savings = $3,000 - $2,400

Savings = $600

Therefore, Brie saves $600 each month.

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10t + 4p ≤ 25 inequality shows the maximum number of tables and people Nathaniel can invite while staying within his budget.

What is inequality?

In mathematics, an inequality is a statement that two values or expressions are not equal, but rather that one is greater than or less than the other. An inequality is denoted by the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Let the number of tables Nathaniel buys be represented by t, and the number of people he invites be represented by p.

Then, the total cost can be expressed as:

Cost = 100t + 40p

Since Nathaniel does not want to spend more than 250, we can set up the inequality:

100t + 40p ≤ 250

We can simplify this inequality by dividing both sides by 10:

10t + 4p ≤ 25

This inequality shows the maximum number of tables and people Nathaniel can invite while staying within his budget.

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As, AD = BC, the given shape on the graph shows the rectangle found using distance formula.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.

From the given graph, The coordinates of A,B, C and D are-

A = (-3,1)

B = (0,3)

C = (4, -3)

D = (1, -5)

Find the distance AD and BC, if both are equal it forms a rectangle:

Using the distance formula:

d = √[(x2 - x1)² + (y2 - y1)²]

AD = √[(- 3 - 1)² + (1 + 5)²]

AD = √(16 + 36)

AD = √53

BC = √[(0 - 4)² + (3 + 3)²]

BC = √(16 + 36)

BC = √53

As, AD = BC, the given shape on the graph shows the rectangle found using distance formula.

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The perimeter of the rectangle is 38 feet, the predicted perimeter is 26 feet, the area of the rectangle is 30 square feet, and the predicted area is also 30 square feet.

The formulas for the perimeter and area of a rectangle are:

Perimeter = 2(length + width)

Area = length x width

In these formulas, "length" refers to the longer side of the rectangle, and "width" refers to the shorter side of the rectangle. The perimeter is the total length of the sides of the rectangle, and the area is the amount of space inside the rectangle.

To find the perimeter of the rectangle, we simply add up the lengths of all four sides:

Perimeter = 10 feet + 3 feet + 6 feet + 6 feet + 4 feet + 9 feet

Perimeter = 38 feet

To predict the perimeter, we could use the formula for the perimeter of a rectangle, which is:

Predicted Perimeter = 2(length + width)

We can find the length and width of the rectangle by finding the longest and shortest sides:

Length = 10 feet

Width = 3 feet

Therefore, the predicted perimeter would be:

Predicted Perimeter = 2(10 feet + 3 feet)

Predicted Perimeter = 26 feet

To find the area of the rectangle, we multiply the length by the width:

Area = 10 feet × 3 feet

Area = 30 square feet

To predict the area, we could use the formula for the area of a rectangle, which is:

Predicted Area = length × width

Using the same values for length and width as before, the predicted area would be:

Predicted Area = 10 feet × 3 feet

Predicted Area = 30 square feet

Therefore, the perimeter of the rectangle is 38 feet, the predicted perimeter is 26 feet, the area of the rectangle is 30 square feet, and the predicted area is also 30 square feet.

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The probability that the next piece of track Carly picks will be straight is 8/24 or 1/3

From the given information, Carly has picked 8 straight, 7 curved, 4 cross, and 5 switch tracks.

The total number of pieces of the track she has picked is 8 + 7 + 4 + 5 = 24

The probability that the next piece of track Carly picks will be straight is calculated as follows:

Probability = Number of straight tracks/Total number of tracks= 8/24= 1/3T

Therefore, the probability that the next piece of track Carly picks will be straight is 1/3.

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Answer: 1/3

Step-by-step explanation: i did this question and got it right

A sample size of at least 109 GPAs to estimate the population mean with a 90% confidence level

Confidence level = 90%

Standard deviation = 0.88

Mean = 0.1

Calculating the sample size -

[tex]n = [(zα/2σ) / E]^2[/tex]

The crucial value for a confidence level of 90%, denoted by z/2, may be determined using a typical normal distribution table or calculator, where n is the required sample size. The value of z/2 at a 90% degree of confidence is around 1.645. The problem statement specifies that the population standard deviation at 0.88 and that E is the most significant error of the sample mean from the population mean at 0.1.

Therefore, substituting the values -

[tex]n = [(1.645 x 0.88) / 0.1]^2[/tex]

n = 108.25

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Answer:

Step-by-step explanation:

Easy...

a=.5bh

so, .5*18*15= 135 in^2.

It looks like it has about four triangular sides, so just multiply that number four times.

135*4= 540

add the base

a=lw

=15*15

=225

540+225= 765 in^2

Let's hope.  A better photo next time would definitely help....;)

The ball is in the air for a total of 2 seconds.

We can use the fact that the time it takes for the ball to reach its maximum height is half of the total time the ball is in the air.

The initial vertical velocity of the ball is 32 ft/s and the acceleration due to gravity is -32 ft/s^2 (since it acts in the opposite direction to the initial velocity). We can use the kinematic equation:

y = y0 + v0*t + (1/2)at^2

Where

When the ball reaches its maximum height, its vertical velocity becomes 0. Therefore, we can use the equation:

v = v0 + at

To find the time it takes for the ball to reach its maximum height, since the vertical velocity at that point is 0.

v = v0 + at

0 = 32 - 32t

t = 1 second

So it takes 1 second for the ball to reach its maximum height. At this point, the vertical velocity of the ball is 0, so we can use the equation:

y = y0 + v0*t + (1/2)at^2

to find the maximum height:

y = 5 + 32(1) + (1/2)(-32)(1)^2

y = 21 feet

Now we can use the fact that the time it takes for the ball to fall back to the ground is the same as the time it took to reach its maximum height. Therefore, the total time the ball is in the air is:

2*1 second = 2 seconds

So the ball is in the air for a total of 2 seconds.

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Answer: The degree of (4by+2b-by) is 2, as it is a quadratic expression with the highest exponent of the variable being 2.

Step-by-step explanation: The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent of the variable is 2, which appears in the term 4by. Therefore, the degree of (4by+2b-by) is 2.

The clock that shows the time Mr. Walsh left his house to go to the store would be 3:42 pm.

Mr. Walsh's journey consisted of driving from his house to the store, shopping for 28 minutes, and then driving back home. The total time for his journey would be:

10 minutes (driving to the store) + 28 minutes (shopping) + 10 minutes (driving back home) = 48 minutes

If Mr. Walsh arrived home at 4:30 pm, and we subtract the 48 minutes it took for his entire journey, we can determine the time he left his house to go to the store:

4:30 pm - 48 minutes = 3:42 pm

Therefore, the clock that shows the time Mr. Walsh left his house to go to the store would be 3:42 pm.

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Let's represent the cost of a cup of corn as 'c' and the cost of a taco as 't'.

From the first statement, we know that:

2c + 4t = 19 (equation 1)

From the second statement, we know that:

3c + 2t = 14.5 (equation 2)

We can solve this system of equations using elimination or substitution. Here, we'll use substitution.

Rearranging equation 2, we get:

3c = 14.5 - 2t

Dividing both sides by 3, we get:

c = 4.83 - 0.67t

Now we can substitute this expression for 'c' into equation 1:

2(4.83 - 0.67t) + 4t = 19

Simplifying, we get:

9.66 - 0.34t = 19

Subtracting 9.66 from both sides, we get:

-0.34t = 9.34

Dividing both sides by -0.34, we get:

t = -27.47 ≈ $-2.75

Since a negative price for a taco doesn't make sense, we made an error somewhere. Checking our calculations, we can see that we made a mistake in the expression for 'c'. It should be:

c = (14.5 - 2t)/3

Substituting this expression for 'c' into equation 1:

2[(14.5 - 2t)/3] + 4t = 19

Multiplying both sides by 3:

2(14.5 - 2t) + 12t = 57

Expanding and simplifying:

29 - 4t + 12t = 57

8t = 28

t = 3.5

Therefore, the tacos cost $3.50.

we don't have enough information to determine the exact lengths of the streamers or the distance from the center of the floor to where the second streamer is attached.

Sure, I'd be happy to help! Based on the information you provided, we know that Belle is hanging two streamers of different lengths at the peak of the ceiling for her brother's surprise birthday party. The center of the floor is directly underneath the ceiling peak.

We also know that the distance along the floor from the center of the room to where the first streamer is attached is 6 feet.

Since the second streamer is attached to the floor further from the center of the floor than the first streamer, we can infer that the second streamer is longer than the first streamer.
I hope this helps! Let me know if you have any other questions.

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To find the surface area of a pyramid with a square base, we need to find the area of the square base and the area of each triangular face, then add them together.

The area of the square base is the square of the length of one of its sides. In this case, the side length is 10 inches, so the area of the base is:

[tex] \rm A_{base} = 10^2 = 100 \text{ square inches}[/tex]

To find the area of each triangular face, we need to find the height of the pyramid. The height of the pyramid is the perpendicular distance from the apex (the top of the pyramid) to the base. To find the height, we can use the Pythagorean theorem, since we know the length of the slant height (15 inches) and half the length of the base (5 inches):

[tex] \rm{h = \sqrt{15^2 - 5^2} = \sqrt{200} = 10\sqrt{2} \text{ inches}}[/tex]

Now we can find the area of each triangular face using the formula:

[tex] \rm{A_{face} = \frac{1}{2} \times \text{base} \times \text{height}}[/tex]

where the base is the side length of the square base, and the height is the height of the pyramid. In this case, we have:

[tex] \rm{A_{face} = \frac{1}{2} \times (10 \text{ inches}) \times (10\sqrt{2} \text{ inches}) = 50\sqrt{2} \text{ square inches}}[/tex]

Finally, we can find the surface area of the pyramid by adding the area of the base and the area of the four triangular faces:

[tex] \rm{A_{total} = A_{base} + 4A_{face} = 100\text{ square inches} + 4(50\sqrt{2} \text{ square inches}) \approx 314.16 \text{ square inches}}[/tex]

Therefore, the surface area of the pyramid is approximately 314.16 square inches.

The fraction equivalent to 3/8 with a numerator and denominator product of 216 is 9/24.

To find the fraction equivalent to 3/8 with a numerator and denominator product of 216, follow these steps:

Set up an equation for the product of the numerator and denominator:

x × y = 216.

Since the fraction is equivalent to 3/8, you can write another equation: x / y = 3/8.

Solve for x in terms of y in the second equation:

x = (3/8) × y.

Substitute this expression for x in the first equation:

(3/8) × y × y = 216.

Solve for y: [tex]y^2 = (8/3) × 216.[/tex]

Simplify the equation: y^2 = 576.

Find the square root of both sides: y = 24.

Now, find x using the equation x = (3/8) × y:

x = (3/8) × 24.

Simplify the expression:

x = 9.

So, the fraction equivalent to 3/8 with a numerator and denominator product of 216 is 9/24.

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