Use the diagram shown If AD = 25. BF = 10, and DF = 10, then what is the value of AB?

if the volume is known, you can calculate the radius using the formula and the given values and it is =1.7853

To find the radius (r) of a right cylinder with a given height (h) of 10 and an unknown volume (V), additional information is needed to solve the problem. Without knowing the value of the volume, it is not possible to determine the exact value of the radius. The volume of a right cylinder is calculated using the formula V = \(\pi r^{2h}\), where π is a constant value approximately equal to 3.14159.

However, if you have the value of the volume (V), you can rearrange the formula to solve for the radius (r). For example, if the volume is given as V = 100 cubic units, you can use the formula V = πr^2h and substitute the known values to find the radius. Rearranging the formula, we get r = √(V / (πh)), where √ denotes the square root.

By plugging in the values of V = 100 and h = 10 into the formula, we can calculate the radius as r = √(100 / (π × 10)). Simplifying further, r ≈ √(10 / π) ≈ √(10 / 3.14159) ≈ √(3.1831) ≈ 1.7853

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Answer:

the y-intercept is 22 spaces higher.

Step-by-step explanation:

I don't know, what special operations you want to express with 3(5)x.

as it is written this simply means

3×5×x

no exponents or other special things are visible.

but it should not matter.

whatever is the first function is unchanged the first part of the second function.

so, the only difference is the "+ 22" part.

and that simply means that all y values (the functional result values) are increased by 22.

you know that "f(x) =" has the same meaning as "y =".

and with that also the y-intercept (the y value when x = 0, and therefore the point, where the curve intersects the y-axis) is increased by 22 spaces.

Answer:

F and C

Step-by-step explanation:

CUZ AAS means angle angle side

Answer:

see explanation

Step-by-step explanation:

for the triangles to be congruent by the angle- side- angle (ASA postulate )

if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle ( included side is the side between the vertices of the two angles ) , then the triangles are congruent.

given

∠ B ≡ ∠ D and AB ≡ PD

then the included sides are AB and PD

the other 2 angles for congruency are ∠ A ≡ ∠ P

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

By the AAS postulate

If two angles and a non included side of one triangle are congruent to the corresponding parts of the other triangle, then the triangles are congruent

for AAS then ∠ C ≡ ∠ F

We are given a path c, and a vector field f. The path c is defined by r(t) = (t³, t², -2t) for 0 ≤ t ≤ 1. The vector field f = (-4sin x, 5cos y, 10xz). We are required to evaluate the line integral ∫cf ⋅ dr using the given information.To evaluate the line integral, we use the following formula:∫cf ⋅ dr = ∫abf(r(t)) ⋅ r'(t) dt.

Here, we can see that r(t) is already in vector form, so we don't need to convert it. We just need to find r'(t).Differentiating r(t) with respect to t, we get:r'(t) = (3t², 2t, -2)Substituting the given values of f and r'(t), we get:∫cf ⋅ dr = ∫₀¹ (-4sin t³, 5cos t², -20t³) ⋅ (3t², 2t, -2) dt= ∫₀¹ (-12t⁴ sin t³ + 10t cos t² - 20t⁴) dt= (-3t⁴ cos t³ + 5t³ sin t² - 5t⁵) from 0 to 1= -3 cos 1 + 5 sin 1 - 5The final answer is -3 cos 1 + 5 sin 1 - 5.

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Answer:

Which expressions are equivalent?

3x - 7y and -7y + 3x

3x - 7y and 7y -3x

3x - 7y and 3y - 7x

3x - 7y and -3y + 7x

=

A.) 3x - 7y and -7y + 3x

A sequence is said to be bounded if its terms are limited to a certain value. The sequences that are bounded are  Option a, option c, option e.

Let's go through the sequences and determine which ones are bounded:

a) an = cos(n): The cosine function oscillates between -1 and 1. As n increases, cos(n) will continue to fluctuate between these values. Therefore, an = cos(n) is bounded.

b) an = 7n: This sequence grows without bound as n increases. As n gets larger, the terms of the sequence become arbitrarily large. Thus, an = 7n is not bounded.

c) an = (-8)^n: When -8 is raised to an even power, the result is a positive number, and when it is raised to an odd power, the result is a negative number. In both cases, the magnitude of the number increases without bound as n increases. Therefore, an = (-8)^n is not bounded.

d) an = n/(6n + 1): To determine the behavior of this sequence, we can take the limit as n approaches infinity:

lim(n→∞) n/(6n + 1) = 1/6.

As n gets larger, the ratio n/(6n + 1) approaches the constant value of 1/6. Therefore, an = n/(6n + 1) is bounded.

e) an = 1/12^n: As n increases, the term 1/12^n becomes arbitrarily small. It will never be negative or exceed a certain value, such as 1. Therefore, an = 1/12^n is bounded.

So, the sequences that are bounded are:

an = cos(n)

an = n/(6n + 1)

an = 1/12^n

The sequences that are not bounded are:

an = 7n

an = (-8)^n

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The total number of cups of chocolate is A = 12 cups

Given data ,

To find the total number of cups of hot chocolate that Stanley made, we need to add together the amounts of milk, cream, and melted chocolate.

6 cups of milk

1 pint of cream (1 pint = 2 cups)

On simplifying the equation ,

4 cups of melted chocolate

Now , the total number of cups is A

where A is

6 cups of milk + 2 cups of cream + 4 cups of melted chocolate = 12 cups of hot chocolate

Hence , Stanley made 12 cups of hot chocolate

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Answer:

r = \(2\sqrt{5}\)

\((x - 3)^{2} + ( y - 2)^{2} = 20\)

Is this a live test question or a homework question?

Step-by-step explanation:

the radius is the distance between (3, 2) and (5, -2)

\(r^{2}\) = \({(3 - 5)^{2} + (2 + 2)^{2} }\)

    =  \((-2)^{2} + 4^{2}\)

    =  4 + 16 = 20

r = \(\sqrt{20 } = 2\sqrt{5}\)

Equation of circle:   \((x - 3)^{2} + ( y - 2)^{2} = 20\)

Answer:

Radius: \(2\sqrt{5}\)

Equation of circle: \((x-3)^2+(y-2)^2=20\)

Step-by-step explanation:

The radius of a circle is equal to the distance between the center of the circle and any point on the circle. Therefore, we have:

\(r=\sqrt{(5-3)^2+(2-(-2))^2},\\r=\sqrt{2^2+4^2},\\r=\sqrt{20}=\boxed{2\sqrt{5}}\)

The equation of a circle with radius \(r\) and center \((h, k)\) is given by:

\((x-h)^2+(y-k)^2=r^2\).

What we know:

Substituting known values, we get:

\((x-3)^2+(y-3)^2=(2\sqrt{5})^2,\\\boxed{(x-3)^2+(y-2)^2=20}\)

Step-by-step explanation:

x

x+2

x+4

x+6

x+8

these are the 5 consecutive odd integers.

when starting with an odd number as x, with every added 2 we get again an odd number.

the sum of the last 3 integers is 3 more than the sum of the 2 greatest :

x+4 + x+6 + x+8 = x+6 + x+8 + 3

we can subtract (x+6) abd (x+8) from both sides :

x + 4 = 3

x = -1

so, the 5 numbers are

-1

1

3

5

7

3 + 5 + 7 = 15

5 + 7 + 3 = 15

correct.

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

We have,

Let's analyze each of the given statements to determine whether they are identities:

tan x = sin x / cos x:

This is an identity.

It is known as the fundamental identity of trigonometry, as it holds true for all values of x (except when cos x is equal to 0).

tan x cos x = sin x:

This is not an identity.

It is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

cos x = tan x sin x:

This is not an identity.

Similar to the previous statement, it is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

sin x / tan x = cos x:

This is an identity.

It can be derived from the fundamental identity by dividing both sides by cos x, resulting in sin x / cos x = cos x / cos x, which simplifies to sin x / tan x = cos x.

Thus,

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

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Step-by-step explanation:

m<AEC= 180-152= 28°

m<CEB= 180-28=152°

m<FEC= 90+28=118°

Answer: 500 people don't read both.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

a) ✔️

This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.

b) ❌

There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.

c) ❌

This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.

d) ❌

This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.

A consumer advocacy group suspects that a local supermarket's 750 grams of sugar actually weigh less than 750 grams. The group took a random sample of 20 such packages, weighed each one, and found the mean weight for the sample to be 746 grams with a standard deviation of 8 grams. Using 10% significance level, would you conclude that the mean weight is less than 750 grams.

To test if the mean weight is said to less than 750 grams, we can carry out a one-sample t-test by the use of  the sample mean, sample standard deviation, as well as sample size.

The null hypothesis =  750 grams,

The  alternative hypothesis=  less than 750 grams.

so we need to calculate the test as:

t = (746 - 750) / (8 / √(20)) = -2.236

Next, we have to find the critical t-value for a one-tailed test with 19 degrees of freedom (so  n-1 =19)

When you a t-distribution table, the critical t-value to be -1.734.

Therefore, know that -2.236 < (less than) -1.734,  so you will reject the null hypothesis and say that the mean weight is less than 750 grams at a 10% significance level.

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Answer:

Frame B has the shorter width.

Step-by-step explanation:

The area of a rectangle is given by length×width. If the two have a maintained area of 45 in², then length and width are inversely proportional, meaning if one goes up, the other must go down. Since Frame B has a larger length than Frame A and both frames have the same area, Frame B must have a shorter width to accommodate for its larger length.

The probability density function for a normal distribution N(68, 5) reaches its maximum height at x = 68, which is the mean of the distribution. The function does not touch the x-axis at μ±30.

The probability density function (PDF) for a normal distribution is bell-shaped and symmetrical around its mean. In this case, the mean (μ) is 68, and the standard deviation (σ) is 5.

(a) To find the x value at which the PDF reaches a maximum, we look at the mean of the distribution, which is 68. The PDF is highest at the mean, and as we move away from the mean in either direction, the height of the PDF decreases. Therefore, the x value at which f(x) reaches a maximum is x = 68.

(b) The PDF of a normal distribution does not touch the x-axis at μ±30. The x-axis represents the values of x, and the PDF represents the likelihood of those values occurring. In a normal distribution, the PDF is continuous and never touches the x-axis. However, the PDF becomes close to zero as the values move further away from the mean. Therefore, the probability of obtaining values μ±30, which are 38 and 98 in this case, is very low but not zero. So, the PDF does not touch the x-axis at μ±30, but the probability of obtaining values in that range is extremely small.

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Answer:

uh?

Step-by-step explanation:

Answer:

w = 30ft

1200 / 40 = 30

Answer:

Yes, it is a real number.

Step-by-step explanation:

All numbers are real numbers.

Out of the given functions, g(x), h(x), and k(x) satisfy the extreme value theorem, and guarantee the existence of an absolute maximum and minimum value over the given interval.

Now, let's apply the extreme value theorem to the given functions:

f(x) = ln(1 - x) over [0,2]: This function is not continuous on the given interval since it is undefined at x = 1. Therefore, the extreme value theorem does not apply to this function.

g(x) = ln(1 + x) over [0,2]: This function is continuous on the given interval, and its derivative is always positive, which means it is an increasing function. Therefore, the absolute minimum value occurs at x = 0 and the absolute maximum value occurs at x = 2. Hence, the extreme value theorem applies to this function.

h(x) = √1 - x over [1,4]: This function is continuous on the given interval, and its derivative is always negative, which means it is a decreasing function. Therefore, the absolute maximum value occurs at x = 1 and the absolute minimum value occurs at x = 4. Hence, the extreme value theorem applies to this function.

k(x) = 1/√1 - x over [1,4]: This function is continuous on the given interval, and its derivative is always negative, which means it is a decreasing function. Therefore, the absolute maximum value occurs at x = 1 and the absolute minimum value occurs at x = 4. Hence, the extreme value theorem applies to this function.

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Answer:

109 inch

Step-by-step explanation:

we know that

\(tan\theta=\frac{Perp}{Base} \\\theta=70\\Base=40 in\)

So,

\(tan(70)=\frac{Perp}{40} \\\\2.747=\frac{Perp}{40} \\\\2.747\times40=Perp\\\\Perp=109\quad in\)

So, length of lamppost is 109 inch

The value of x in miles is 18 miles.

The beach is x miles away from home.  

Distance is a numerical description of how far apart two objects are. Therefore,

The distance between beach and his home is x miles. He travelled to and fro at a distance of 36 miles. Therefore,

Travelling to and fro simply means he travelled back and forth. Therefore,

x = 36 / 2

x = 18 miles

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When a procedure meets all of the conditions of a binomial distribution except the number of trials is not fixed, the geometric distribution can be used.

Given that subjects are randomly selected for a health survey, the probability that someone is a universal donor (with group O and type Rh negative blood) is 0.14.

We have to find the probability that the first subject to be a universal blood donor is the seventh person selected.Using the formula mentioned above:\(P(7) = 0.14(1 - 0.14)6= 0.0878\)

The probability is 0.0878. Option C is correct.

Now, let's solve the next part.Assuming that different groups of couples use a particular method of gender selection and each couple gives birth to one baby.

This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5.

Assuming that the groups consist of 24 couples.

(a)Find the mean and the standard deviation for the numbers of girls in groups of 24 births:

Let X be the number of girls in a group of 24 births.

\(X ~ B(24, 0.5)Mean:μ = np= 24 * 0.5= 12\)Standard deviation:\(σ = `sqrt(np(1-p))`= `sqrt(24*0.5*0.5)`= `sqrt(6)`≈ 2.449\) (rounded to one decimal place).

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Based on the computed 95% confidence interval, we can conclude that we are 95% confident that the true population mean falls within the range of 12.65 to 25.65.

A confidence interval is a range of values that provides an estimate of the true population parameter. In this case, we are interested in estimating the population mean (μ). The 95% confidence interval, as mentioned, is given as 12.65 ≤ μ ≤ 25.65.

Interpreting this confidence interval, we can say that if we were to repeat the sampling process many times and construct 95% confidence intervals from each sample, approximately 95% of those intervals would contain the true population mean.

The confidence level chosen, 95%, represents the probability that the interval captures the true population mean. It is a measure of the confidence or certainty we have in the estimation. However, it does not guarantee that a specific interval from a particular sample contains the true population mean.

Therefore, based on the computed 95% confidence interval, we can conclude that we are 95% confident that the true population mean falls within the range of 12.65 to 25.65.

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Answer:

Yes I think

Step-by-step explanation:

I went through the braces process a few years ago and I got an expander. Your separator is probably making room for something meaning your teeth will probably move. Im no professional so Id say call into the office tomorrow or asap. And for the pain use whatever pain meds they allow (normally ibprophen ot tylenol) (sorry for spelling)

Without redefining any global objects, changing the definition of the exp y function, or creating new objects, you can calculate the fourth power of eleven using the exp y function by calling exp y(11), which will give you the result of 14641.

To calculate the fourth power of eleven using the expy function without redefining the global objects x or y, changing the definition of the expy function, or creating any new objects, you can follow these steps:

1. First, we need to understand the expy function. The expy function calculates the exponential value of the variable y. In this case, y represents the power to which we want to raise a number.

2. To calculate the fourth power of eleven, we can use the expy function with y set to 4 and the number 11 as the input. This can be done by calling the expy function with the value of 11 as the argument, like this: expy(11).

3. The expy function will then raise the input number (11) to the power of the variable y (4). In other words, it will calculate 11^4.

4. The result of the calculation will be the fourth power of eleven, which is 14641.

So, without redefining any global objects, changing the definition of the exp y function, or creating new objects, you can calculate the fourth power of eleven using the exp y function by calling exp y(11), which will give you the result of 14641.

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Answer:

Yes, it is a polynomial, and the degree is 5

Step-by-step explanation:

A polynomial is a combination of terms separated using + or − signs and normally have exponents. So, this equation is a polynomial. The degree is just the highest exponential value, which is 5 because -5y is being raised to the 5th power

Answer:

I would usually do a guesstimate of this. For example, if I had to plot 0.5 somewhere, I would do it between the 0 and the 1 because the number on the left is a 0, and it's halfway to reaching 1.

Step-by-step explanation:

Step-by-step explanation:

The given mass of the Earth is 5.972 × 10²⁴

The given mass of the Jupiter is 1.898 × 10²⁷

Now,

1.898 × 10²⁷ ÷ 5.972 × 10²⁴

= 0.3178 × 10³ = 317.8

Thus, Jupiter is 317.8 heavier than Earth