2


How much water will a cone hold that has a diameter of 6 inches and a height of 21 inches.


Use 3. 14 for 7 and round your answer to the nearest whole number.


A 66 cubic inches


B 198 cubic inches


C) 594 cubic inches


D 2374 cubic inches

Answer:

the negative

Step-by-step explanation:

if you do -5 to the second power it will give you -25 and if you do (-5) it will give you 25.

The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

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Answer:

7

Step-by-step explanation:

42/6=7

The density is:

D = 10g/2mL = 5 g/mL

The correct option is the first one.

Remember that density is defined as the quotient between mass and volume.

We know that the mass of the solid is 10.0 grams.

And the volume of the solid is given by the difference between the volume of the water alone (15.0 mL) and the water with the solid (17 mL).

V = 17mL - 15mL = 2mL

Then the density is:

D = 10g/2mL = 5 g/mL

The correct option is the first one.

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Serafin risks his life to help Tobe when he is in danger of drowning in the river in "Saving Tobe" because he is the person who is most qualified to attempt to save Tobe.

In the story "Saving Tobe," Serafin risks his life to save Tobe because he is a great swimmer and knows how to swim in that river. He is aware of the fact that if he doesn't do anything about it, Tobe will die. Furthermore, he understands that if Tobe dies, the community will be shaken because Tobe is an integral part of the community. Serafin also realizes that he is the only one capable of saving Tobe and that if he doesn't act quickly, Tobe will perish.In addition, Serafin's actions are motivated by the fact that he sees himself in Tobe. Tobe reminds him of his younger self. Serafin also remembers how hard it was for him when he lost his brother to the river. He believes that he could have done something about it but was powerless at that time. Serafin now has the opportunity to do something about it, and he takes the chance.

In conclusion, Serafin risks his life to save Tobe because he understands the gravity of the situation, is the most qualified to perform the rescue, and sees himself in Tobe. Serafin is motivated by the prospect of saving Tobe's life and preventing the community from being shattered. He is also motivated by the opportunity to make amends for his previous failure to save his brother.

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The probability P(t > -3.56) for a t-distribution with 3 degrees of freedom is approximately 0.930.

To find P(t > -3.56) for a t-distribution with 3 degrees of freedom, we need to calculate the cumulative probability up to -3.56 and subtract it from 1.

Since the t-distribution is symmetric around 0, we can find the probability P(t < -3.56) and then subtract it from 1.

Using statistical software or a t-table, we can find the cumulative probability for -3.56 in the t-distribution with 3 degrees of freedom. However, since the software is not available here, I will provide you with the general steps to calculate it.

The cumulative distribution function (CDF) of the t-distribution with ν degrees of freedom is denoted as F(t; ν). We need to find F(-3.56; 3).

To calculate this, we can use the t-distribution CDF formula or look it up in a t-table.

Alternatively, you can use a statistical software or online calculators to obtain the probability directly. Many statistical software packages and online resources provide the functionality to calculate probabilities for specific t-distribution values.

Remember that the CDF provides the probability of observing a value less than or equal to the given value. To find the probability of observing a value greater than -3.56, we subtract the CDF from 1:

P(t > -3.56) = 1 - P(t < -3.56)

Please use a t-table, statistical software, or online calculator to find the cumulative probability for -3.56 in the t-distribution with 3 degrees of freedom, and then subtract it from 1 to obtain the desired probability.

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The complete question is:

Consider a t-distribution with 3 degrees of freedom. Find P(t>-3.56).

Answer:

The answer is A. 0

Step-by-step explanation:

If you graph the equation it shows a straight horizontal line and that makes it zero

Answer:

A) 0

or m = 0

Step-by-step explanation:

Slope is zero, because it's just a straight horizontal line.

You can tell when you graph it or by the fact that they both have the same y-value, in this case -5.

I hope this helps :)

the height of the box is 9 inches

Answer:

solution given:

total surface area of a box=160 square inches

let length, width, and height be l,b, and h respectively.

according to the question:

l=2b

∴b =\(\frac{l}{2}\)

l=h-4

∴ h=l+4

we have

total surface area of a box=160 square inches

2(lb+lh+bh)=160

\(2(l*\frac{l}{2}+l(l+4)+\frac{l}{2}*(l+4))=160\)

\(2*\frac{l^2+2l^2+8l+l^2+4l}{2}=160\)

\(4l^2+12l=160\)

\(4(l^2+3l)=160\)

\(l^2+3l=\frac{160}{4}\)

\(l^2+3l-40=0\)

doing middle term factorization

\(l^2+(8-5}l-40=0\)

\(l^2+8l-5l-40=0\)

taking common from each two terms

l(l+8)-5(l+8)=0

(l+8)(l-5)=0

either

l=-8[neglected as length is always positive]

or

l=5

now

b=\(\frac{5}{2} =2.5\)

h=5+4=9

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) ∠WVZ and ∠VWX are right angles & VX = = WZ      Given

2) WV = VW                                                                      Reflexive property

3) ΔWVZ ≅ ΔVWX                                                           HL

4) ∠Z = ∠X                                                                       CPCT

CPCT --> Corresponding parts of congruent triangle.

The degree of curvature, by the arc definition, for a circular curve of radius 500 ft is approximately 0.11.

When it comes to a circular curve, the degree of curvature is defined as the central angle subtended by a 100-foot arc length.

In other words, the degree of curvature is the amount of angle subtended by a 100-foot arc.

This definition is also applicable to circular curves that are larger or smaller than 100 feet in length, with no changes required.

The formula for calculating the degree of curvature (D) is:D = 57.3/r

where r is the radius of the curve in feet. Here, the radius of the curve is 500 ft.

Using this formula, we can determine the degree of curvature as:D = 57.3/500D = 0.1146 ≈ 0.11

Therefore, the degree of curvature, by the arc definition, for a circular curve of radius 500 ft is approximately 0.11.

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The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.

To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.

The formula for calculating the standard error is:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.

Plugging in the values:

Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)

\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)

≈ 0.0131

Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.

Margin of Error = z * Standard Error

= 1.96 * 0.0131

≈ 0.0257

Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:

Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100

= (0.0257 / 0.64) * 100

≈ 4.0%

Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.

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The equation of each of the lines are:

1. y = 1/3x - 1

2. y = 3x + 1

3. y = 2/3x - 1

4. y = 3x

5. y = -2/3x - 1

6. y = 1/3x - 1

7. y = -3x + 2

To write the equation of a line, find the following:

1. Slope (m) = rise/run = 1/3

y-intercept (b) = -1.

To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:

y = 1/3x - 1

2. Slope (m) = rise/run = 3/1 = 3

y-intercept (b) = 1.

To write the equation, substitute m = 3 and b = 1 into y = mx + b:

y = 3x + 1

3. Slope (m) = rise/run = 2/3

y-intercept (b) = -1.

To write the equation, substitute m = 2/3 and b = -1 into y = mx + b:

y = 2/3x - 1

4. Slope (m) = rise/run = 3/1 = 3

y-intercept (b) = 0.

To write the equation, substitute m = 3 and b = 0 into y = mx + b:

y = 3x

5. Slope (m) = rise/run = -2/3

y-intercept (b) = -1.

To write the equation, substitute m = -2/3 and b = -1 into y = mx + b:

y = -2/3x - 1

6. Slope (m) = rise/run = 1/3

y-intercept (b) = -1.

To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:

y = 1/3x - 1

7. Slope (m) = rise/run = -3/1 = -3.

y-intercept (b) = 2.

To write the equation, substitute m = -3 and b = 2 into y = mx + b:

y = -3x + 2

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Answer:

approximately 6.6 yards :)  

Step-by-step explanation:

Answer:

6.6

Step-by-step explanation:

take pi as 3.14

formula for circumfurence is 2*pi*r

so 2r=20.724/pi

2r=6.6

since diameter is 2 radius, the diameter is 6.6

Answer:

9 x 5 = 45

Step-by-step explanation:

An example: Tom worked for 5 hours today, for each hour, he earned $9, how much money did he earn in total?

$9 x 5 hours of work = $45 for 5 hours

the size of the wedge for aqua pencils is 43°

Given:

A table showing the pencil collection

To find:

the portion that represents the aqua pencils in degree

The total number of pencils = 23 + 106 + 62 + 47 + 32

The total number of pencils = 270

In degrees:

Total angle in a circle = 360°

Size of the wedge for aqua = number of aqua pencils/total pencils × 360°

To the nearest degree, the size of the wedge for aqua pencils is 43°

Sam's height is 1.8 meters.

The angle A'OB' = 112.8337°.

We assume the height of Sam, that is, AC or BD to be x meters.

From the given figure, we can say that the triangle A'CA is similar to the triangle A'OP, and the triangle B'CB is similar to B'OP.

Thus, for:

Triangles A'CA and A'OP, we can write:

CA/PO = AA'/PA',

or, x/6 = 2.1/(AP + 2.1),

Triangles B'DB and B'OP, we can write:

DB/PO = BB'/PB',

or, x/6 = 3.6/(BP + 3.6).

Thus, we get:

2.1/(AP + 2.1) = 3.6/(BP + 3.6),

or, 2.1BP + 7.56 = 3.6AP + 7.56,

or, 2.1BP = 3.6AP.

But, AP + BP = 13.3,

or, BP = 13.3 - AP.

Substituting this, we get:

2.1(13.3 - AP) = 3.6AP,

or, 27.93 - 2.1 AP = 3.6AP,

or, 2.1AP + 3.6AP = 27.93,

or, 5.7AP = 27.93,

or, AP = 27.93/5.7 = 4.9.

Substituting AP = 4.9 in x/6 = 2.1/(AP + 2.1), we get:

x/6 = 2.1(4.9 + 2.1),

or, x/6 = 2.1/7,

or, x = 2.1*6/7 = 1.8.

Thus, Sam's height = 1.8 meters.

Substituting AP = 4.9 in AP + BP = 13.3, we get:

4.9 + BP = 13.3,

or, BP = 13.3 - 4.9 = 8.4.

In triangle, A'OP,

tan ∠A'OP = A'P/PO,

or, ∠A'OP = tan ⁻¹(A'P/PO) = tan ⁻¹((A'A + AP)/PO) = tan ⁻¹((2.1 + 4.9)/6) = tan ⁻¹ (7/6) = 49.3987°.

In triangle B'OP,

tan ∠B'OP = B'P/PO,

or, ∠B'OP = tan ⁻¹(B'P/PO) = tan ⁻¹((B'B + BP)/PO) = tan ⁻¹((3.6 + 8.4)/6) = tan ⁻¹ (12/6) = tan ⁻¹ 2 = 63.4349°.

Now, ∠A'OB' = ∠A'OP + ∠B'OP = 49.3987° + 63.4349° = 112.8337°.

Thus, the angle A'OB' = 112.8337°.

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For the complete question, refer to the attachment.

Answer:

Whats the question?

Step-by-step explanation:

Yes, that's correct. In the slope-intercept form, the equation of a line is given as y = mx + b where m is the slope of the line.

The variable "m" represents the slope of the line, which is a measure of how steep the line is. It is calculated as the ratio of the change in the y-coordinate to the change in the x-coordinate, also known as the rise over the run.

A line with a positive slope will rise as it moves to the right, while a line with a negative slope will fall as it moves to the right. A line with a slope of zero is a horizontal line and one with an infinite slope is a vertical line.

The variable "b" is the y-intercept, which is the point where the line crosses the y-axis. It is the value of y when x = 0.

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Answer: C

Step-by-step explanation:

area of rectangle = (5--2) × (2--2) = 7 × 4 = 28

area of triangle = ((12-5) × (6--6)) ÷ 2 = (7 × 12) ÷ 2 = 84 ÷ 2 = 42

total area = 28 + 42 = 70

Answer:

135°

Step-by-step explanation:

a supplementary angle is equal to 180°. since you already have the measure of ZA, all you need to do is subtract 45°, the measure of ZA, from 180°, the total measure of a supplementary angle, in order to figure out the measure of ZB.

180 - 45 = 135, therefore the measure of ZB = 135°.

Answer:

m=18g

Step-by-step explanation:

Because the total miles add up by the 18miles for each gallon of gas. Which is found by multiplying each gallon of gas to mph per gallon of gas.

You use the "truncated" keyword when you know only one end of a range (either the upper or lower end). Truncated searches allow you to find results within a specified range by including an unknown value on one side.

The keyword that you use when you know only one end of a range is called "range." This term is used in various contexts, including mathematics, statistics, and computer programming, where it represents a set of values that fall between two specified limits. For instance, in statistics, a range is a measure of dispersion that reflects the spread of a dataset from its lowest to highest value. If you only know one end of the range, say the upper end, you can estimate the lower end by subtracting the width of the range from the upper limit. Conversely, if you only know the lower end, you can obtain the upper end by adding the range width to the lower limit. In computer programming, range is a function that generates a sequence of integers or floating-point numbers between two given values. The range function is useful when you want to loop through a set of values without having to specify each value individually. For example, if you want to print all even numbers between 0 and 10, you can use the range function with a step of 2 to generate the sequence 0, 2, 4, 6, 8, 10. In conclusion, the keyword "range" is used when you know only one end of a range, and it helps you estimate the other end based on the width of the range. Whether you are dealing with statistical data or programming algorithms, understanding the concept of range is crucial for making accurate calculations and solving problems efficiently.

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The ratios are shown equivalent as by simplification done below.

Ratio is the representative of comparison of part of things in a complete thing. Equivalent ratios are collection of ratios that show same comparison. As per the given question, the equivalent ratios are calculated as follows -

First column -

Ratio = 6:2

Dividing both the parts of ratio by 2

Ratio = 3:1

Second column -

Ratio = 9:3

Dividing both the parts of ratio by 3

Ratio = 3:1

Third column -

Ratio = 12:4

Dividing both the parts of ratio by 4

Ratio = 3:1

Fourth column -

Ratio = 15:5

Dividing both the parts of ratio by 5

Ratio = 3:1  

Similarly, for rest of the columns, division by 6, 7 and 8 of both parts of ratio will give the result 3:1. Hence, the given rations are shown as equivalent ratios, by simplifying into 3:1.

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The probability distribution of the variable X, representing the total number of towels drawn from the bag until a red towel is obtained, follows a geometric distribution. The mean of variable X can be calculated as 7/2, and the variance can be calculated as 35/4.

In given , the variable X represents the total number of towels drawn from the bag until a red towel is obtained. Since towels are drawn without replacement, this situation follows a geometric distribution. The probability distribution of X can be calculated as follows:

P(X = k) = (3/7)^(k-1) * (4/7)

where k represents the number of towels drawn.

To calculate the mean of variable X, we can use the formula for the mean of a geometric distribution, which is given by:

mean = 1/p = 1/(4/7) = 7/4 = 7/2

For the variance of variable X, we can use the formula for the variance of a geometric distribution:

variance = (1 - p) / p^2 = (3/7) / (4/7)^2 = 35/4

Therefore, the mean of variable X is 7/2 and the variance is 35/4. These values provide information about the average number of towels drawn until a red towel is obtained and the variability around that average.

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The asymptotes of the original function f(x)=10x and the transformed function g(x) remain the same.

The transformation of reflecting the graph of f(x)=10x about the x-axis followed by shifting it left 12 units creates the new function g(x). The reflection about the x-axis results in the graph of g(x) being upside down compared to the graph of f(x). The shift left 12 units means that the entire graph of g(x) is shifted to the left on the x-axis by 12 units.

However, the transformation does not have any effect on the asymptotes of the function. Asymptotes are vertical or horizontal lines that a function approaches but never touches. They are determined by the behavior of the function as it approaches infinity or negative infinity. Reflecting the graph about the x-axis or shifting it left or right does not change the behavior of the function as it approaches infinity or negative infinity.

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Step-by-step explanation:

The given equation is :

4(3x+2)=4(2x+3)+4x

Solving LHS, = 12x+8

Solving RHS, = 8x+12+4x

So,

12x+8 = 8x+12+4x

12x + 8 = 12x +12

12x cancel out from both sides, the given equation becomes not defined.

Answer:

45

Step-by-step explanation:

by the definition of an isocoles triangle, defined by having two congruent sides,  (p-s, r-s), angles SPR and SRP are congruent. by the triangle sum theorem, (internal angles + to 180˚) 90˚ + 2a = 180˚. 2a =90, a = 45

Answer:

Step-by-step explanation:

greater than 1   ,  is your teacher just giving you brain teaser questions?  these seem like they are .. "out in the weeds"  type of questions,  not really useful math   :/  

Answer:

Step-by-step explanation:

n + 1 = 4(n - 8)

n + 1 = 4n - 32      [Multiply 4 times (n-8)]

1 = 3n - 32           [Subtract 1n from both sides]

33 = 3n               [Add 32 to both sides]

3n = 33

CHECK:

Does n + 1 = 4(n - 8) when n = 11?

n + 1 = 4(n - 8)

11 + 1 = 4(11 - 8)

11 + 1 = 4(3)

12 = 12   YES

The probability of choosing an r or an a is 0.7143. A single letter from the word aardvark is chosen.

The probability of choosing an r or an a from the word aardvark can be calculated as follows:

First, calculate the total number of letters in the word aardvark.

Aardvark is a seven-letter word. As a result, there are seven letters available.

Next, calculate the number of r's and a's in the word aardvark.

There are five letters that are either an r or an a in aardvark.

As a result, there are two r's or three a's in aardvark.

So, the probability of choosing an r or an a is:

\(P("r" or "a") = \frac{number of r's or a's in aardvark}{total number of letters in aardvark} \\ = 5/7\\=0.7143\)

The probability of choosing an r or an a is 0.7143.

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