The area of a circle is 616 cm². Find its circumference. Use π = 22/7
A) 88 cm
B) 44 cm
C) 88 cm²
D) 44 cm²
​

Answer:

9-16y

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use formula:

Factor:

The distributive law is the law to apply to have the following equivalence:

(¬p∨r)∧(¬q∨r)≡(¬p∧¬q)∨r.

Hence, the correct option is (D) Distributive law.

What is Distributive Law?

The distributive property is the most commonly used property of the number system.

Distributive law is the one which explains how two operations work when performed together on a set of numbers. This law tells us how to multiply an addition of two or more numbers.

Here the two operations are addition and multiplication. The distributive law can be applied to any two operations as long as one is distributive over the other.

This means that the distributive law holds for the arithmetic operations of addition and multiplication over any set.

For example, the distributive law of multiplication over addition is expressed as a(b+c)=ab+ac,

where a, b, and c are numbers.

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Answer:

m∡5 = 71°

Step-by-step explanation:

m∡8 = m∡6

m∡6 + m∡5 = 180

180 - m∡6 = m∡5

180 - 109 = 71

Answer:

the measurement of angle 5 is 71

Step-by-step explanation:

m∡8 = m∡6

M∡6 + m∡5 = 180

180 - m∡6 = m∡5

180 - 109 = 71

Hope this helps :)

The formula the capital gains yield = (pt 1 â pt)/dt is false.

The proper equation for  capital gains yield

return on investment = (pt - pt-1)/pt-1

where pt= cost of the resource at the conclusion of the holding period and pt-1 = cost at the start of the holding period.

 This equation communicates the rate increment (or diminish) within the cost of a resource over the holding period and could be a degree of speculation return due to changes within the cost of the resource. 

The term 'dt' in the original formula is not well defined and is not typically used in the context of calculating return on investment.  yield = (pt 1 â pt)/dt is false.

The proper equation for return on investment is:

return on investment = (pt - pt-1)/pt-1

where pt= cost of the resource at the conclusion of the holding period and pt-1 = cost at the start of the holding period.

 This equation communicates the rate increment (or diminish) within the cost of a resource over the holding period and could be a degree of speculation return due to changes within the cost of the resource. 

The term 'dt' in the original formula is not well defined and is not typically used in the context of calculating return on investment. 

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Answer:

It’s number 2 the values it 24

Step-by-step explanation:

maybe

Answer:

Step-by-step explanation:

You can't find an exact value, but you can find an simpler expression by using the distributive property.

a + 4bc + 2ab

And that is as much as it can be reduced.

The second option shows a pair of triangles which are congruent by the SSS congruence theorem.

The SSS (Side - Side - Side) congruence theorem states that if two triangles have three sides that are congruent to each other, then the two triangles are congruent by the SSS theorem.

The congruent sides for the second option are given as follows:

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Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

$1.50

I hope this helps!

Too easy XD I don’t remember how to do that T-T

Answer:

24

Step-by-step explanation:

8*3=24

Answer:

24

Step-by-step explanation:

We are supposed to replace 'x' with '3' and then evaluate.

==========================================

\(8x; x = 3\\\rule{150}{0.5}\\8(3)\\\\8 \times 3\\\\\boxed{24}\)

==========================================

Hope this helps!

The given geometric series is: 1/2, 3/4, 9/16, 27/64, …The common ratio is 3/2

Since the common ratio is greater than 1, the series diverges.

A geometric series is a sequence of numbers in which each term is obtained by multiplying the preceding term by a fixed number.

The sum of the first n terms of a geometric series is given by the formula:

Sn = a(1 - rn) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.

If the common ratio is greater than 1, the series is said to diverge to infinity, and the sum doesn’t exist.

If the common ratio is less than 1, the series converges to a finite value.

If the common ratio is equal to 1, the series either converges or diverges depending on the first term.

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a) By strong induction, any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

b) By strong induction, any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

c) By strong induction, any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

a. Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

Base case: For postage worth 8 cents, we can use two 4-cent stamps, which can be made using a combination of one 3-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 8, can be made from 3-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 8, we can use the induction hypothesis to make k cents using 3-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with a 5-cent stamp to get the same value. If the last stamp we added was a 5-cent stamp, we can replace it with two 3-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3-cent or 5-cent stamps.

b. Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

Base case: For postage worth 24 cents, we can use three 8-cent stamps, which can be made using a combination of one 7-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 24, can be made from 7-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 24, we can use the induction hypothesis to make k cents using 7-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 5-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with three 5-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 7-cent or 5-cent stamps.

c. Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

Base case: For postage worth 12 cents, we can use one 3-cent stamp and three 3-cent stamps, which can be made using a combination of two 7-cent stamps.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 12, can be made from 3-cent or 7-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 12, we can use the induction hypothesis to make k cents using 3-cent or 7-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with one 3-cent stamp and two 7-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3

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The following are the measures of angles and sides using the sine and cosine rules:

1). QR = 15, m∠P = 52°, m∠Q = 43°

2). BC = 21, DC = 10.4, m∠C = 22°

3). VX = 10.7, WX = 10.2, m∠V = 39°

4). HF = 18.4, m∠H = 28.7, m∠F = 15.3

The sine rule is a relationship between the size of an angle in a triangle and the opposing side. While the cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

1). Using the sine rule:

19/sin85 = 13/sunQ

Q = sin⁻¹[(13 × sin85)/19] {cross multiplication}

Q = 43

m∠P = 180° - (85 + 43) = 52°

QR = sin⁻¹[(19 × sin52)/sin85]

QR = 15.

2). m∠C = 180 + (19 + 139) = 22°

Using the sine rule:

BC = (12 × sin139)/sin22

BC = 21.

DC = (12 × sin19)/sin22

DC = 10.4

3). m∠V = 180 - (41 + 100) = 39°

Using the sine rule:

VX = (16 × sin41)/sin100

VX = 10.7

WX = (16 × sin39)/sin100

WX = 10.2

4). Using the cosine rule:

HF² = 7² + 13² - 2(7)(13)cos136°

HF = √338.8491

HF = 18.4

applying sine rule;

F = sin⁻¹[(7 × sin136)/18.4]

F = 15.3

m∠H = 180 - (15.3 + 136) = 28.7

Therefore, the measures of angles and sides using the sine and cosine rules are:

1). QR = 15, m∠P = 52°, m∠Q = 43°

2). BC = 21, DC = 10.4, m∠C = 22°

3). VX = 10.7, WX = 10.2, m∠V = 39°

4). HF = 18.4, m∠H = 28.7, m∠F = 15.3

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Answer:

The area of triangle VZX is 210 cm^2

Step-by-step explanation:

Here, we want to get the measure of the area of triangle VZX

From the given diagram, we have two explicit triangles making up triangle VWX

These are triangles VWZ and VZX

By adding the areas of both triangles, we can get the area of VWX

Mathematically, the area of VZX is the difference between the area of VWX and VZW

To get the area of VZW, we can use the formula for the area of a triangle

We have this as 1/2 * base * height

base = 35 cm and height = 28 cm

The area of VWZ is 1/2 * 35 * 28 = 490 cm^2

The area of triangle VZX is thus;

700 cm^2 - 490 cm^2 = 210 cm^2

Answer: 39k+40

Step-by-step explanation:

Distribute:−5(−6k−6)−(−9k−10)

                   30k+30-(9k-10)

                    30k+30+9k+10

Add the numbers: 30k+30+9k+10

                               30k+40+9k

Combine like terms: 30k+40+9k

                                  39k+40

there you go please Brainliest me

Thank you!!

The given expression is

First, we solve the subtraction

Now we subtract 2 on each side to get x-2

Let's solve the difference

Answer:

C because it's a quadratic equation and it can be solved by factorization and completing the square method and also general formula

We will apply the principle of similar triangles to solve this question

Given that

Method: Find side AC

We will use the Pythagoras theorem to evaluate AC

T

The probability that the mail arrival time is more than 20 minutes on a given day is 2/3.

It's nearly impossible to predict the outcomes of many events with a hundred percent certainty. However, we can still tell how likely the events are to happen.

Probability is how likely something is to happen. Probability can also mean a number that indicates the chance or likelihood that a particular event will occur. Probability is always between zero and one. Zero means impossible while one means certain. In most cases, the probability of something to happen is greater than zero and less than one.

Mathematically, we can express probability as P(A) = f/N where

Let P(A) represent the probability that the mail arrival time is more than 20 minutes on a given day, f represent the frequency (60 - 20), and N represent total number of possible outcomes, which is 60.

P(A) = (60 - 20)/60

P(A) = 40/60

P(A) = 4/6

P(A) = 2/3

There you have it! The probability is two-thirds.

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Answer:

5

Step-by-step explanation:

19-14=5

Answer:

\(\displaystyle k = 20\)

Step-by-step explanation:

We are given the function:

\(\displaystyle f(x) = 3x^3 - 2x + k\)

Where (x + 2) is a factor of f. And we want to determine the vale of k.

Recall that from the Factor Theorem, if (x - a) is a factor of a polynomial P(x), then P(a) must equal 0.

We can rewrite our factor as (x - (-2)). Hence, a = -2. Our polynomial is f. Since (x + 2) is a factor, then from the Factor Theorem, f(-2) must be 0.

Using this information, we can now determine k:

\(\displaystyle\begin{aligned} f(x) & = 3x^3 -2x + k \\ \\ f(-2) = 0 & = 3(-2)^3 -2(-2) + k \\ \\ 0 & = (-24) + (4) + k \\ \\ k & = 20 \end{aligned}\)

In conclusion, the value of k is 20.

Answer:

Step-by-step explanation:

As given that

Volume of jug=1 liter=1000ml  

also volume of one glass=200ml

and we poured out 4 glasses so total volume of 4 glasses will be,

4 glasses volume = 4*200ml =800ml

Step-by-step explanation:

ml to litres = divide by 1000

200/1000 = 0.2×4= 0.8ml

The rules AAS, ASA, SSS and SAS are congruence rule of triangle  and the each rules has been explained

The rules AAS, ASA, SSS and SAS are congruence rule of triangle

SSS rule is side-side-side rule, it states that if three sides of the one triangle and three sides of the other triangles are equal, then both triangles are congruent

SAS rule is side-angle-side rule, it states that if two sides and one included angles between the sides of the one triangle is equal to  the two sides and one included angles between the sides of the other triangle, then both triangles are congruent

ASA rule is angle-side-angle rule, it states that if two angles and one included side between the angle of the one triangle is equal to the two angles and one included sides between the angles of the other triangle, then both triangles are congruent

AAS rules is angle-angle-side rule, it states that if two angles and one non included sides of the one triangle is equal to the two angles and one non included sides of the another triangle, then both triangles are congruent

Therefore, the AAS, ASA, SSS and SAS are the rules of congruence of the triangle

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The simplified expression of the ∛4x / 5 is ∛4x / ∛5

Index laws are the rules for simplifying expressions involving powers of the same base number, these laws are also called Laws of indices.

Laws of indices provide us with rules for simplifying calculations or expressions involving powers of the same base. The indices are also known as powers or exponents.

It is represented in the form:

am = a × a × a ×……× a (m times)

we have the  law of indices formula:

\(\sqrt[a]{b}=b^\frac{1}{a}\)

∛4x / 5 = (4x/5)^1/3

Therefore,

∛4x / 5 = ∛4x / ∛5

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Step-by-step explanation:

csc(Theta) = 1/sin(Theta) = 3.2362

Answer:

C. 3.2362

Explanation:

Answer:

distance between them is

\(8 \sqrt{5} \: units\)

Step-by-step explanation:

by distance formula ,

\( \sqrt{(6 - ( - 10)) {}^{2} + (10 - 2) {}^{2} } \)

The covariance of x and y is 0. This means that x and y are uncorrelated, which means that they are independent or have no relationship.

To find the covariance of x and y, we need to use the formula for the covariance of two random variables:
Cov(x,y) = E[(x - E[x])(y - E[y])]
Since y is a standard normal random variable, E[y] = 0.
Now we need to find E[x], which means we need to find the expected value of x. We know that x = ay + z, where a is some constant. We can find the expected value of x by using the linearity of expectation:
E[x] = E[ay + z]
    = aE[y] + E[z]
    = 0 + 0
    = 0
Therefore, E[x] = 0.
Now we can simplify the formula for the covariance:
Cov(x,y) = E[xy] - E[x]E[y]
We can find E[xy] by using the fact that x and y are independent:
E[xy] = E[ayz] = aE[y]E[z] = 0
So we have:
Cov(x,y) = E[xy] - E[x]E[y] = 0 - 0*0 = 0

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if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter.

If the sample size is 28 and the population standard deviation is increased, there will be a direct impact on the confidence interval. This is because the confidence interval is calculated based on the sample mean and the standard deviation. If the population standard deviation is increased, it means that there is more variability in the population. This increase in variability will lead to wider confidence intervals.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. The width of the confidence interval is determined by the sample size, the standard deviation, and the level of confidence.
In this case, if the population standard deviation is increased, it means that the sample standard deviation will also increase. The sample mean will be relatively more variable than it would be if the population standard deviation was lower. This increase in variability will cause the confidence interval to become wider, as there is more uncertainty in the estimate of the population parameter.
In summary, if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter. It is important to note that increasing the sample size can help to reduce the impact of increased population standard deviation on the confidence interval, as a larger sample size provides more accurate estimates of the population parameter.

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Answer:

1/ 6

Step-by-step explanation:

Therefore, the required probability is 1/6.

Answer:

1/6

Step-by-step explanation:

Think of drawing 1 student at a time without replacement.

First drawing:

p(boy) = 6/10

Second drawing:

p(boy) = 5/9

Third drawing:

p(boy) = 4/8

p(3 boys) = 6/10 * 5/9 * 4/8 = 3/5 * 5/9 * 1/2 = 3/18 = 1/6

Answer: 1/6