find the volume of the solid whose base is a circle of radius 5, if slices made perpendicular to the base are isosceles right triangles with one leg on the base.

Step-by-step explanation:

please answer this question quickly

Answer:

H<5

Step-by-step explanation:

u solve it as a normal equation but with the symbol <.

In summary, fy(a,b) is the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

The given expression represents the partial derivative of f(x, y) with respect to y, evaluated at (a, b):

fy(a,b) = lim┬(y→b)⁡〖[f(a,y) - f(a,b)]/(y - b)〗

Geometrically, this partial derivative represents the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

To see why this is the case, consider the following argument:

Let L be the limit in the expression given above.

Let h = y - b be the change in the y-coordinate from b to y.

Then, we can rewrite the limit as:

fy(a,b) = lim┬(h→0)⁡〖[f(a,b + h) - f(a,b)]/h〗

This expression represents the average rate of change of f(x, y) with respect to y over the interval [b, b + h].

As h approaches 0, this average rate of change approaches the instantaneous rate of change, which is the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

Therefore, fy(a,b) is the partial derivative of f(x, y) with respect to y, evaluated at (a, b).

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Examples of things in your house, dorm, or apartment that could be measured using square units are papers.

Examples of things in your house, dorm, or apartment that could be measured using cubic units are boxes, tin milk etc

Areas of two-dimensional objects are measured in square units while the areas of three-dimensional objects are measured in cubic units.

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Answer: Dimension of pool are length = 12 feet, width = 54 feet and depth = 6 feet.

Answer: 7%

(Hope this is right.)

Step-by-step explanation:

Let's solve this using the information we have and an equation.

Shane: $32,000 - (Given)

Theresa: 18,000+14x, if x=1,160 - (Given)

---------------------------------------------------------------

Step two: (Theresa) 14(1,160) =16,240 (Algebra)

Step three: (Theresa) 18,000+16,240=34,240 (Algebra, given.) - cost of Theresa's car.

---------------------------------------------------------------

Finally,

They're asking for how much more she paid for her car as a percentage of what Shane paid.

34,240-32,000=2,240 and

2,240/32,000=0.07

0.07x100=7

Answer 7% more than what Shane paid.

Answer: C

Step-by-step explanation:

I got this right

Answer:

y = 2x + 3

Step-by-step explanation:

The gradient (2x) is the same since the lines are parallel

The y-intercept(+3) is different however, since this line passes through co-ordinate (-1,3) It is +3 because in a co-ordinate the x and y co-ordinate is in this order (x,y). Therefore, the y number represents which y co-ordinate the line passed through the y axis.

Answer:

a = 55

Step-by-step explanation:

This angle is a right angle.

A right angle is equal to 90 degrees.

That means you have to subtract 90 and 35.

90 - 35 = 55

55° is the missing angle of the right angle.

Answer:

a = 55

Step-by-step explanation:

The whole image is a right angle which is 90 degrees. So subtract 35 degrees giving you the answer of 55 degrees

Set up ratios of height / shadow length:

8/6 = x/100

Cross multiply

6x = 800

Divide both sides by 6

X = 133.33 feet

The tower is 133.3 feet

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

We can see that the safety rail is a quarter of circle with radius equals 10yd. So it's lenght is:

The time it takes for 20% of the water to leak from a full vase is equal to 0.2 times the Volume of the Vase divided by 0.5 cubic inches per minute.

we need to use the formula,

Volume of Water Leaked = 0.5 cubic inches/min x time.

Since we want to find out the time it takes for 20% of the water to leak from a full vase, we can set up the equation as follows:

0.2 x Volume of Vase = 0.5 cubic inches/min x time

Solving for time, we get:

time = 0.2 x Volume of Vase / 0.5 cubic inches/min

Therefore, the time it takes for 20% of the water to leak from a full vase is equal to 0.2 times the Volume of the Vase divided by 0.5 cubic inches per minute.

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Answer:

24.1 minutes

Step-by-step explanation:

It would be 24.1 minutes because you would find the volume of the cone first: pi x radius squared times h/3 which gives you 60.32. Now, you multiply it by 0.2- which is the 20% of water that is to fall out. You would then get 12.064. Lastly, you would multiply this by 0.5 which is the rate that the water falls out of the cone and that gives you 24.128 which is rounded to 24.1 minutes. Hope that helped :)

Answer:

B. - ( -3, -2 )

Step-by-step explanation:

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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The correct option is B) Categorical

The variable X in this case is categorical. Categorical variables represent distinct categories or groups and do not have a numerical value associated with them. In this example, X represents different types of animals (cat, dog, pig, bear, lion), which are categories or groups.

Therefore, the correct answer is B) Categorical.

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Answer:

learn what is binary system

add one by changing the last 0 into 1

Write another digit if all the numbers are one.

Use these rules to count to five.

Count to six.

Count to ten

Notice when new digits get added.

Practice with higher numbers.

hope this will help you and pls answer my questions also

Answer:

5^8/5^6 = 5^(8-6) = 5^2 = 25. Therefore, 5^8/5^6 simplified to a single power of 5 is 25.

Step-by-step explanation:

Answer:

the answer for that is 5^6-3 = 5^3 = 125

Step-by-step explanation:

The solution to the given initial-value problem is  x(t) = c1(e-ωt - eωt) = 2c1 sin ωt

The given initial-value problem is a second-order differential equation: d2x dt2 + ω2x = f0 sin ωt, x(0) = 0, x '(0) = 0

First, we can solve the homogeneous equation d2x dt2 + ω2x = 0 using the method of characteristic equation. The characteristic equation is r2 + ω2 = 0, which has two solutions r1 = -ω, r2 = ω.

The general solution to the homogeneous equation can be expressed as:

x(t) = c1e-ωt + c2eωt

Next, we can solve the non-homogeneous equation d2x dt2 + ω2x = f0 sin ωt. Since the right-hand side of the non-homogeneous equation has a sinusoidal form, we can use the method of variation of parameters to solve it.

The particular solution can be expressed as:

x(t) = A sin ωt + B cos ωt

By substituting the initial conditions, we can get:

A = 0, B = 0

Therefore, the solution to the given initial-value problem is:

x(t) = c1e-ωt + c2eωt

The constant c1 and c2 can be determined by the initial conditions:

x(0) = c1 + c2 = 0

x'(0) = -ωc1 + ωc2 = 0

Therefore, c1 = -c2 and c1 + c2 = 0.

Hence, the solution to the given initial-value problem is:

x(t) = c1(e-ωt - eωt) = 2c1 sin ωt

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When we are writing in expanded form we put zero (0) in the places in front of the digit given.

As we all know, zero (0) doesn't add any value or make any difference in the number while putting in front.

Hence, putting 0 in the front won't make any difference to the number

So, we put 0 in the front.

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Answer: Depends on the number!

Step-by-step explanation:

The digit to put in front of the given digit depends on the number. For example, if the given digit is an 8, then a 0 should be placed in front of it to indicate that it is a two-digit number. If the given digit is a 3, then a 0 should be placed in front of it to indicate that it is a three-digit number.

To find the power series representation of the product f(x)g(x), we can use the formula for multiplying power series.

Given that f(x) = 4x and g(x) = ∑(n=0 to ∞) (7^n)x^n, we can compute the product by multiplying each term of f(x) with each term of g(x) and combining like terms. The resulting power series representation will involve powers of x and coefficients that depend on the original coefficients of f(x) and g(x).

Let's start by expanding f(x)g(x) using the formula for multiplying power series:

f(x)g(x) = (4x)(∑(n=0 to ∞) (7^n)x^n)

Multiplying each term of f(x) by each term of g(x), we get:

f(x)g(x) = 4x(7^0)x^0 + 4x(7^1)x^1 + 4x(7^2)x^2 + ...

Simplifying each term, we have:

f(x)g(x) = 4x + 28x^2 + 196x^3 + ...

The resulting power series representation of the product f(x)g(x) involves powers of x, where the coefficient of each term depends on the original coefficients of f(x) and g(x). In this case, the coefficients are obtained by multiplying 4x with the corresponding terms of the power series (7^n)x^n, resulting in coefficients of 4, 28, 196, and so on.

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True.The range is a measure of dispersion that represents the difference between the highest and lowest scores in a dataset. In this case, the highest score is 9 and the lowest score is 2, so the range is simply 9-2=7.

It is important to note that the range only considers the extreme values in the dataset and does not take into account the distribution of the scores. Therefore, it should be used in conjunction with other measures of dispersion, such as the standard deviation, to fully understand the variability of the dataset.the range refers to the difference between the largest and smallest values in a set of data. It is a measure of dispersion that helps to provide an idea of how much variation exists in the dataset. To calculate the range, one simply subtracts the smallest value from the largest value

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Answer:

p=7

Step-by-step explanation:

use inverse operation

add 6 to both sides

you get

-3p=-21

divide -3 from both sides

p=7

Answer:

p=7

Step-by-step explanation:

Answer:c hope that helps <3

Step-by-step explanation:

The equation which is representing the given scenario is w = -3p + 1160 so option (C) will be correct.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Let's say the equation representing is

y = mx + c

Where m is the slope associated with the given points.

Given that,

80 people ⇔ 920 ounce

120 people ⇔ 800 ounce

Slope m = (800 - 920)/(120- 80) = -3

So,

y = -3x + c

Now putting (80,920)

920 = -3(80) + c

c = 1160

So,

y = -3x + 1160

Corresponding to it w = -3p + 1160

Hence "The equation which is representing the given scenario is w = -3p + 1160".

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y + 3 = (-4/3)(x - 6) is the equation of the line that passes through the point (-6, 3) and has slope of -4/3.

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Answer:

C

Step-by-step explanation:

Answer:

(b)

Step-by-step explanation:

The statements that best describe the bowling scores data are:

- The MAD best describes the variability (C)

- The IQR best describes the spread (D)

Based on the given data in the table, the following statements can be made:

- There are no outliers in the data set, as all the scores fall within a reasonable range.

- The mean can be calculated as:

Mean = \(\frac{121 + 159 + 146 + 132 + 149}{5}\)

          = 141.4,

but it may not be the best measure of central tendency due to the small size of the data set and the presence of outliers in larger data sets.

- The MAD (Median Absolute Deviation) can be calculated as the median of the absolute deviations from the median, which are:

|121 - 146| = 25,

|159 - 146| = 13,

|146 - 146| = 0,

|132 - 146| = 14,

|149 - 146| = 3.

The median of these values is 13, so the MAD is 13.

This describes the variability of the data well, as it takes into account the distance of each score from the median.

- The IQR (Interquartile Range) can be calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of the data set. To do this, we need to first find the median of the lower half of the data set (Q1) and the median of the upper half of the data set (Q3). Ordering the data set from lowest to highest, we have:

               121, 132, 146, 149, 159.

Q1 is the median of the lower half, which is:

Median = \(\frac{121 + 132}{2}\)  = 126.5.

Q3 is the median of the upper half, which is

Median = \(\frac{149 + 159}{2}\) = 154.

The IQR is then:

IQR = Q3 - Q1

       = 154 - 126.5

       = 27.5.

This describes the spread of the data well, as it captures the middle 50% of the data set.

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For power lines p and m to adhere to the statement "Power lines are not allowed to intersect," the necessary relationship between them is that they must be parallel to each other and not intersect.

When power lines intersect, it can lead to dangerous situations such as power outages, electrical fires, and accidents.

To ensure the safe and efficient operation of the power grid, power lines are designed and installed in a way that they do not intersect with each other.

This helps to prevent any potential hazards and ensures the uninterrupted flow of electricity. Therefore, the relationship between power lines p and m should be that they do not intersect.

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It is essential to ensure that power lines, like p and m, do not intersect to maintain a safe and reliable electrical infrastructure.

The relationship between power lines p and m is that they should not intersect.

This is because intersecting power lines can lead to dangerous situations, such as electrical hazards and power outages.

To understand why power lines should not intersect, let's consider an example. Imagine two power lines, p and m, running parallel to each other.

If they were to intersect, the electrical currents flowing through the lines would mix and cause a short circuit. This can result in power failures, damage to the power lines, and even fires.

To prevent these risks, power lines are designed and installed in a way that they do not cross paths.

They are carefully planned and spaced apart to maintain a safe distance from each other.

The standard clearance between power lines is usually around 150 feet (or 45 meters), which helps minimize the chances of them intersecting.

In addition to safety concerns, intersecting power lines can also create problems with the transmission and distribution of electricity.

When power lines intersect, the electrical currents can interfere with each other, causing disruptions and affecting the overall efficiency of the power system.

Therefore, it is essential to ensure that power lines, like p and m, do not intersect to maintain a safe and reliable electrical infrastructure.

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