Using Cavalieri's principle, which of the following can be shown to have the same volume as a triangular prism with base area pi r² and height h?

The equation of the line in slope-intercept form is y = -11x + 29.

To find the slope of given points we are using the slope-intercept formulae

The line passing through the point are (x1, y1) and (x2, y2) is given by:

m = (y2 - y1) / (x2 - x1)

m is the slope of the line.

Putting all values in the above equation, we get:

m = (-15 - (-4)) / (4 - 3) = -11

So the slope of the line is -11

To write the equation of line the point-slope form of the equation we can use

y - y1 = m(x - x1)

Put all values into the equation

y - (-4) = -11(x - 3)

Simplifying, we get:

y + 4 = -11x + 33

Subtracting 4 from both sides, we get:

y = -11x + 29

So the equation of the line in slope-intercept form is y = -11x + 29.

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There were approximately 1131 blueberries in the box at first.

To find the total number of blueberries in the box at first, follow these

First, we need to add up the percentages of blueberries Gerry ate on Monday and Tuesday. On Monday, he ate 0.5 (or 50%) of the blueberries and on Tuesday, he ate 25% of the blueberries.

So, he ate a total of 50% + 25% = 75% of the blueberries.

Since Gerry ate 848 blueberries altogether, which is 75% of the total number of blueberries in the box, we can now set up a proportion to find the total number of blueberries:

(75% of the total number of blueberries) = 848]

We can express 75% as a decimal (0.75) and set up an equation:

0.75 × (total number of blueberries) = 848

Now, to find the total number of blueberries, divide both sides of the equation by 0.75:

(total number of blueberries) = 848 / 0.75

5. Solve for the total number of blueberries:

(total number of blueberries) = 1130.67

Since there can't be a fraction of a blueberry, we can round up to the nearest whole number:

There were approximately 1131 blueberries in the box at first.

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Question

Gerry picked 0.5 of the blueberries in a box on Monday and 25% of the blueberries on Tuesday. If he picked a total of 848 blueberries altogether, how many blueberries were in the box at first?

The employee's commission on the sales of clothing sold would be R360.

Thus, 5/7 path of the second mosaic Trent will complete in 1 hours.

A mixed number is a representation of both a whole number and a improper fraction. In most cases, it denotes a number that falls either between two whole numbers.

Divide the numerator and denominator to create a mixed number from an incorrect fraction. The solution here becomes the numerator, the remainder the denominator, and the denominator stays the same.

Given:

Time to complete simple mosaic = 2/5 hours.

Now, Time to complete second mosaic = (3 1/2)*2/5 hours.

Convert the 3 1/2 (given in mixed fraction into proper fraction).

= (3*2 + 1)/2

= 7/2

So, to complete second mosaic Trent took = (7/2)*(2/5) = 7/5 hours.

In 7/5  hours ---> 1 complete part.

In 1 hour --> 5/7 part complete

Thus, 5/7 path of the second mosaic Trent will complete in 1 hours.

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A semicircle rotated around its axis gives sphere, rectangle  rotated around its axis gives sphere . and a right triangle  rotated around its axis gives sphere

what is rectangle?

A rectangle is a four-sided flat shape with straight sides and four right angles. It is a type of parallelogram, with opposite sides equal in length and parallel to each other. The area of a rectangle can be calculated by multiplying its length and width, while its perimeter can be found by adding the lengths of all four sides.

In the given question,

A semicircle rotated around its axis gives sphere,

A  rectangle  rotated around its axis gives sphere .

A right triangle  rotated around its axis gives sphere

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Answer:

something time 4 is equal to x

Step-by-step explanation:

flip the question around

The number of negative real zeros is either 2 or 0.

How to use Descartes's rule ?

To use Descartes's rule to determine the possible number of real zeros of the polynomial function f(x) = 6x² - 9x - 6, we need to first find the sign changes in the coefficients of the polynomial.

The coefficient of the highest power of x is 6, which is positive. The coefficient of the next highest power of x is -9, which is negative. The coefficient of the constant term is -6, which is negative as well. So, there are two sign changes in the coefficients of the polynomial.

According to Descartes's rule, the number of positive real zeros of the polynomial f(x) is either equal to the number of sign changes in the coefficients or less than that by an even integer. In this case, there are two sign changes, so the number of positive real zeros is either 2 or 0.

Similarly, the number of negative real zeros of the polynomial f(x) is either equal to the number of sign changes in the coefficients or less than that by an even integer. In this case, there are two sign changes, so the number of negative real zeros is either 2 or 0.

Therefore, the possible number of real zeros of the polynomial function f(x) = 6x² - 9x - 6 is either 2, 0, or 2 complex zeros. To determine the exact number of real zeros and complex zeros, we may need to use other methods, such as the quadratic formula, factoring, or graphing.

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Answer: 8

Step-by-step explanation: a triangle has a total of 180 adding all the angles

Answer:

8°

Step-by-step explanation:

The sum of the three interior angles in a triangle is always 180°.

Third angle = 180 - (88 + 84) = 8

[tex] \:\:\:\:\:\: \:✰ [/tex]Let the maximum length of a soccer field for play by under-8-year-olds be 'x yards ' then the maximum length of a soccer field for international play will be (x + 80) yards.(For solving this problem we have to assume the soccer field as rectangular-shaped.)

As per question, the total length of these two categories of soccer fields is 160 yards. Which states -

[tex] \:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \underline{ x + (x + 80) = 160}\\[/tex]

[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf x + x + 80 = 160\\[/tex]

[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf 2x + 80 = 160 \\[/tex]

[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf 2x = 160 - 80\\[/tex]

[tex]\:\:\:\:\:\:\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf 2x = 80\\[/tex]

[tex] \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf x = \cancel{\dfrac{80}{2}}\\[/tex]

[tex] \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \underline{ x = 40}\\[/tex]

The measure of angle B is indeed 70°, and the two angles are Supplementary

Step 1: Understand supplementary angles
Supplementary angles are two angles whose sum equals 180 degrees. In other words, if two angles are supplementary, then their measures add up to 180°.

Step 2: Set up the equation
Let's say you have two supplementary angles, angle A and angle B. You know the measure of angle A, but you need to find the measure of angle B. To do this, you can set up the following equation:

angle A + angle B = 180°

Step 3: Insert the known angle measure
Since you know the measure of angle A, you can insert its value into the equation. For example, if angle A measures 110°, the equation would be:

110° + angle B = 180°

Step 4: Solve for the unknown angle
Now, you can solve the equation to find the measure of angle B. Using the example above:

110° + angle B = 180°

Subtract 110° from both sides:

angle B = 70°

Step 5: Verify your answer
To make sure your answer is correct, you can add the measures of angle A and angle B together. If they equal 180°, then your answer is correct. In this example:

110° + 70° = 180°

So, the measure of angle B is indeed 70°, and the two angles are supplementary.

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Answer:

Since the absolute value of any real number is a positive, the range is all the real numbers less than or equal to 0. We can see this by placing x = 1 and hence getting 0.Mar

Step-by-step explanation:

Answer:

I am sorry but I cant find the graph !

Can you please resend your question with the picture of the graph

thank you

Step-by-step explanation:

Answer:

a) 6°C

b) upward

Step-by-step explanation:

I don't know if you mean  this  type

a) The range of temperatures is the difference between the maximum and the minimum temperatures. From the graph we can see that:

maximum temperature: 18 °C

minimum temperature: 12 °C

Then:

range of temperatures: 18-12 = 6°C

b) The trend is upward because, given any temperature, the next one is higher.

Answer: b. 18

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Step-by-step explanation:

A reasonable prediction of the population of South Carolina in 2018, based on the trend shown in the table, is approximately 3.71 million people.

What is population?

Population refers to the total number of individuals, typically humans, living within a specific geographic area, such as a city, state, or country. It is an important measure for studying the demographics and characteristics of a given region or community. Population can also be used to analyze trends and patterns in areas such as healthcare, education, employment, and economics.

Based on the trend shown in the table, we can assume that the population of South Carolina is increasing linearly over time. To make a prediction of the population in 2018, we can use linear regression to estimate the slope and intercept of the line that best fits the data, and then use that line to extrapolate to the year 2018.

Using the data from the table, we can calculate the slope and intercept of the line of best fit as:

slope = 1.84

intercept = 4.92

Using these values, we can predict the population of South Carolina in 2018 as:

population_2018 = slope * 2018 + intercept

population_2018 = 1.84 * 2018 + 4.92

population_2018 = 3710.16 (rounded to two decimal places)

Therefore, a reasonable prediction of the population of South Carolina in 2018, based on the trend shown in the table, is approximately 3.71 million people.

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We can conclude that the answer is that the quotient of 28 and 0.48 is undefined, and it cannot be compared to 56.

The method of dividing two numbers that gets us the answer is called a quotient. Divide 8/2 to get 4, which is an example of a quotient.

To estimate the quotient of 28 and 0.48, we can round 0.48 to the nearest whole number and 28 to the nearest ten.

0.48 is closer to 0 than 1, so we round it down to 0.

We just round up to 30 because 28 is nearer to 30 than 20.

Now we have:

28 ÷ 0.48 ≈ 30 ÷ 0 = undefined

Any number divided by zero is undefined, so the quotient is not a real number. It is not greater or less than 56, because it does not exist.

Therefore, the answer is that the quotient of 28 and 0.48 is undefined, and it cannot be compared to 56.

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Step-by-step explanation:

To find the width of the border, we first need to calculate the area of the picture.

Area of the picture = length x width = 8 in x 11 in = 88 in²

Let the width of the border be "x".

The new length of the picture will be 11+2x, and the new width will be 8+2x.

The total area of the new picture with the border will be:

total area = (11+2x) x (8+2x) = 108 in²

Expanding this equation gives:

88 + 22x + 16x + 4x² = 108

Simplifying and rearranging the terms, we get:

4x² + 38x - 20 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 4, b = 38, and c = -20.

Plugging in these values, we get:

x = (-38 ± sqrt(38² - 4(4)(-20))) / 2(4)

x = (-38 ± sqrt(1936)) / 8

x = (-38 ± 44) / 8

The two possible solutions are:

x = 1.5 or x = -5

Since a negative width for the border does not make sense, the width of the border should be 1.5 inches.

The Maximum no. of fish is 200 thousands.

How to find the fish count from the function?

Let say the function is

[tex]P(x)=-2(x-9)^2+200\\\\[/tex]

Differentiating w.r.t x, we get

[tex]\\\\P'(x) = -4(x-9)\\\\for\ maximum\ value\ of\ x,\ P'(x) =0\\\\x=9\\\\So,\ put\ value\ of\ x\ in\ equation, we get\\\\P(x) = 200[/tex]

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The condition that requires further analysis of the data  for slope inference is the independence of errors.

In this scenario, we have to determine the condition that requires further analysis of the data. We know that there are five conditions that need to be satisfied to perform the linear regression.

The five conditions are: Linearity, Homoscedasticity, Normality of residuals, Independence of errors. And the last one is: Independence of errors is the fifth condition that requires further analysis of the data to confirm that it is satisfied or not. The independence of errors condition is that there should be no pattern in the residuals.

Residuals are the differences between the actual values and the predicted values. The independence of errors is important because it ensures that the errors are random and not influenced by any other variable.

The independence of errors condition can be checked by plotting the residuals against the predicted values. If there is a pattern in the residuals, then the independence of errors condition is not satisfied. So, in order to satisfy the fifth condition for slope inference, the independence of errors condition must be satisfied.

*Complete question:  Which is the fifth condition requires further analysis of the data to confirm that this condition for inference has been satisfied the same way that four conditions for slope inference have been satisfied?

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[tex] \: [/tex]

To determine which bus is the most consistent, we need to compare the interquartile ranges (IQR) and ranges of the two data sets.

Bus 47 has an IQR of 8 and a range of 8.

Bus 14 has an IQR of 6 and a range of 6.

The IQR is a better measure of variability than the range because it is less sensitive to outliers. In this case, we can see that Bus 14 has a smaller IQR, indicating that the travel times for Bus 14 are more consistent.

Therefore, Bus 14 is the most consistent bus in terms of travel times.

Mega Movies hosted a film premiere on Friday night. They charged $9 for adults and $5 for children. Therefore, the equation is written as 11 children; 120 adults  went to the premier.

Let children be x and adult be y

As the cost of the entry fee is in the ratio of 9 to 6

so, 9x+5y= 1135 ----------------- (1)

and x +y = 131  ------------------- (2)

Multiplying equation (2) by 9, we get:

9x + 9y = 1179

Now, subtracting equation (2) and (1), we get:

9x + 9y = 1179

9x+5y= 1135

⇒ 4y = 44

⇒ y = 11

Now putting y = 11 in equation  (1) , we get:

   9x+5y = 1135  

⇒ 9x + 5× 11 = 1135

⇒ 9x = 1080

⇒ x = 120

Therefore, 11 children; 120 adults  went to the premier.

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V(t) = -$266.67t + $28,500 is the linear model that captures this situation.

What is a linear model?

In mathematics, a linear model is a mathematical function that has a constant rate of change between two variables. The general form of a linear model is given by:

y = mx + b

where "y" and "x" are variables, "m" is the slope of the line, and "b" is the y-intercept (the point where the line crosses the y-axis).

A line's slope is the ratio of change in y (vertical) to change in x. (horizontal). It denotes the pace at which y changes in relation to x. If the slope is upward, theIf the value is positive, the line ascends from left to right, while if it is negative, the line descends from left to right. A horizontal line has a slope of zero, but a vertical line has an indeterminate slope.

A line's y-intercept is the value of y when x is zero. It denotes the point at where the line intersects the y-axis.

We can build a linear model to characterise the car's value decline over time. Let V(t) be the car's worth t years after 2005. Then, using the two data points provided, we can construct two equations:

V(0) = $28,500 (the initial value in 2005)

V(3) = $27,700 (the value in 2008, 3 years later)

Because we are assuming

Because we have a straight line, we can write:

V(t) = mt + b

where m is the slope (annual rate of change) and b is the y-intercept (initial value).

We may use the two equations above to obtain the values of m and b:

V(0) = m(0) + b = $28,500 => b = $28,500

V(3) = m(3) + b = $27,700 = 3m + $28,500 = $27,700 = $27,700 = m = -$266.67/year

As a result, the linear model that best describes this circumstance is:

V(t) = -$266.67t + $28,500

This model reveals that the car's value depreciates at a rate of $266.67 per year, with a starting value of $28,500 in 2005. This methodology can be used to determine the worth of an automobile in any year after 2005.

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Keilantra's headphones were less than the original price by 37%, rounded to the nearest whole number.

To find out the percentage that Keilantra's headphones were less than the original price, we need to compare the discounted price to the original price, and express the difference as a percentage of the original price.

Let's start by calculating the discounted price. Keilantra bought headphones for $34 and received a 40% discount using a coupon code:

Discounted price = Original price - Discount

Discount = 40% of Original price

Discounted price = Original price - 40% of Original price

Discounted price = 60% of Original price

Substituting the values given, we can calculate the discounted price as:

Discounted price = 0.6 x $34

Discounted price = $20.40

Now we need to apply the 5% processing fee to the discounted price:

Final price = Discounted price + Processing fee

Processing fee = 5% of Discounted price

Final price = Discounted price + 5% of Discounted price

Final price = 1.05 x Discounted price

Substituting the value we found for the discounted price, we get:

Final price = 1.05 x $20.40

Final price = $21.42

Now we can calculate the percentage that Keilantra's headphones were less than the original price:

Percentage discount = ((Original price - Final price) / Original price) x 100%

Percentage discount = (($34 - $21.42) / $34) x 100%

Percentage discount = (12.58 / 34) x 100%

Percentage discount = 0.37 x 100%

Percentage discount = 37%

Therefore, Keilantra's headphones were less than the original price by 37%, rounded to the nearest whole number.

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18.84 feet farther is it around the outer edge of the path than around the inner edge.

Given:

A circular path 3 feet wide has an inner diameter of 450 feet.

Use 3.14 for [tex]\pi[/tex].

Now, to find how much farther is it around the outer edge of the path than around the inner edge.

Width of the circular path = 3 feet.

Inner diameter of circular path = 450 feet.

So, to get the inner radius we divide the inner diameter of circular path by width of circular path:

[tex]450\div3[/tex]

[tex]=150 \ \text{feet}[/tex]

[tex]\text{r} = 150 \ \text{feet}[/tex].

Now,

Thus, the outer radius is:

[tex]150+3[/tex]

[tex]=153 \ \text{feet}[/tex]

[tex]\text{r} = 153 \ \text{feet}[/tex].

Now, we get the circumference of inner edge and outer edge:

[tex]\bold{Circumference \ of \ inner \ edge} = \bold{2\pi r}[/tex]

[tex]\text{Circumference of inner edge} = 2\times3.14\times150[/tex] [tex]\text{Circumference of inner edge}=942 \ \text{feet}.[/tex]

[tex]\bold{Circumference \ of \ outer \ edge} = \bold{2\pi r}[/tex]

[tex]\text{Circumference of outer edge} = 2\times3.14\times153[/tex]                                                

[tex]\text{Circumference of outer edge}=960.84 \ \text{feet}.[/tex]

Now, to get how much farther is it around the outer edge of the path than around the inner edge:

[tex]\text{Circumference of outer edge - circumference of inner edge}[/tex].

[tex]960.84-942[/tex]

[tex]=18.84 \ \text{feet}.[/tex]

Therefore, 18.84 feet farther is it around the outer edge of the path than around the inner edge.

Answer:

f(x)=x² → g(x)=4x²-5

Parent Function: y=[tex]x^{2}[/tex]

Horizontal Shift: None

Vertical Shift: Down 5 Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: Stretched

The correct answer is B. 11 inches.

The following equation is given using the PEMDAS order of operations and we get the solved expression as -1.

BODMAS, also known as PEMDAS, is an acronym used to remember the order of operations in mathematics. The letters in the acronym stand for:

B - Brackets

O - Order (exponents and roots)

D - Division

M - Multiplication

A - Addition

S - Subtraction

BODMAS tells us about the order in which to perform mathematical operations in an expression. This is important because performing the operations in the wrong order can give us a different answer than what is intended.

We start by evaluating 6(6), which is 36. Next, we combine 36 and 18 to get 54.

Finally, we subtract 55 from 54 to get -1.

Therefore, the answer to the expression 6(6) + 18 - 55 is -1, not 118.

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Answer:

X=85°

Step-by-step explanation:

35°+x°=120° [Exterior angle of a triangle is equal to the sum of the interior opposite angles]

x=120°-35°

x=85°

The volume of the solid obtained by rotating the region about the y-axis is 3036π cubic units.

How to find the volume by rotating the region?

To find the volume of the solid obtained by rotating the region enclosed by the graphs of y=27-x, y=3x-9, and x=0 about the y-axis, we need to use the method of cylindrical shells.

Here the region is bounded by the graphs of y=27-x, y=3x-9, and x=0. We can see that the region is a trapezoid with vertices at (0, -9), (6, 9), (18, 9), and (27, 0).

Next, we need to determine the height and radius of each cylindrical shell. The height of each shell is the difference between the y-coordinates of the top and bottom of the shell. The radius of each shell is the x-coordinate of the shell.Let's consider a shell with x-coordinate x. The height of the shell is given by (27 - x) - (3x - 9) = 36 - 4x. The radius of the shell is x. The volume of the shell is given by 2πrhΔx, where Δx is the thickness of the shell.

Therefore, the total volume of the solid is given by:

[tex]V = \int0^6 2πx(36 - 4x)dx + \int6^18 2πx(9)dx + \int18^27 2πx(27 - x - 9)dx[/tex]

Simplifying and evaluating the integral, we get:

V = 2π(216) + 2π(243) + 2π(243/2) = 3036π

Therefore, the volume of the solid obtained by rotating the region about the y-axis is 3036π cubic units.

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Rotating the area about the y-axis yields a solid with a volume of 3036 cubic units.

The cylindrical shell method must be used to determine the solid's volume after rotating the region enclosed by the graphs of

y=27-x, y=3x-9, and x=0 about the y-axis.

In this case, the graphs of y=27-x, y=3x-9, and x=0 define the region's boundaries. The region is a trapezium, as can be seen, with vertices at (0, -9), (6, 9), (18, 9), and (27, 0).

The height and radius of each cylindrical shell must then be determined. Each shell's height is determined by the difference between its top and bottom y-coordinates.

Each shell's x-coordinate corresponds to its radius.Consider a shell with the coordinates x and y. (27 - x) - (3x - 9) = 36 - 4x gives the height of the shell. The shell has a radius of x. 2rhx, where x is the shell's thickness, gives the volume of the shell.

As a result, the solid's entire volume can be calculated using:

When we simplify and assess the integral, we obtain:

V = 2π(216) + 2π(243) + 2π(243/2)

  = 3036π

As a result, the region's volume after being rotated about the y-axis is 3036 cubic units.

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Therefore, the inequality simplifies to u ≤ 27.

Inequality refers to the state of being unequal or the existence of disparities or differences between individuals, groups, or regions. This can manifest in various forms, including economic inequality, social inequality, and political inequality. Economic inequality, for example, may refer to the unequal distribution of wealth or income among different individuals or groups in a society. Social inequality may refer to differences in access to education, healthcare, or other resources, based on factors such as race, gender, or social class. Political inequality may refer to disparities in political power or representation, where some.

The inequality 25 ≥ u - 2 can be simplified by adding 2 to both sides to isolate the variable "u":

25 + 2 ≥ u - 2 + 2

27 ≥ u

Therefore, the inequality simplifies to u ≤ 27.

This means that any value of u that is less than or equal to 27 will make the inequality true. For example, u could be 27, 10, -5, or any number less than or equal to 27. However, if u is greater than 27, the inequality will be false.

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