Why is the expression 5(3x + 2) equivalent to 15x + 10 A. The 5 has been divided into each term in the parenthesis B. The 5 was distributed using the Distributive Property C. The 5 was distributed using the Associative Property D. The expressions are not equal

Answer:

y = 15

Step-by-step explanation:

Given: y varies directly with x, x=4 when y=20

To find:  y when x = 3

Solution:

As y varies directly as x, it means that as x increases, y also increases by the same factor.

As y varies directly with x,

\(y=kx\)

Here, k is a constant

As x = 4 when y = 20,

\(20=4k\\k=\frac{20}{4}=5\\\Rightarrow y=5x\)

Put x = 3

\(y= 5(3) = 15\)

Answer:

YOU L HAHA

Step-by-step explanation:

LOS ER

The correct Option is A. Equation that can be used to find the number of dogs in the shelter is StartFraction 60 divided by 2 Over 100 divided by 2 EndFraction = StartFraction 30 Over 50 EndFraction.

In order to do that, we first need to determine the number of dogs in the shelter.

We can do that by multiplying the total number of animals by 60% (0.60):60% of 50 = (60/100) × 50 = 30

Therefore, there are 30 dogs in the shelter.

Now, we can look at the answer choices to see which equation can be used to find the number of dogs in the shelter.

A. (60/2 ÷ 100/2) = 30/50This equation simplifies to (30 ÷ 50) = 0.6, which is the decimal equivalent of 60%. T

his equation is correct.

B. (100 × 2 ÷ 50 × 2) = 200/100

This equation simplifies to 1, which is not the correct answer.

C. (50 ÷ 1 ÷ 60 ÷ 1) = 50/60

This equation simplifies to 5/6, which is not the correct answer.

D. (60 × 2 ÷ 50 × 2) = 120/100

This equation simplifies to 6/5, which is not the correct answer.

Therefore, the equation that can be used to find the number of dogs in the shelter is A. (60/2 ÷ 100/2) = 30/50.

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The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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Answer:

look at the domain, where the line is on the x-axis

Step-by-step explanation:

Answer:

A. \(n=100\)
B. \(k=0\)

Step-by-step explanation:

A. The equation "110% n = 11" can be solved as follows:

110% n = 11

To solve for n, we need to get rid of the percentage sign (%). We can do this by dividing both sides of the equation by 110%, or 0.110 (since 110% is equivalent to 1.1 in decimal form).

(110% n) / 110% = 11 / 110%

n = 11 / 0.110

n = 100

So, the solution for n in the equation "110% n = 11" is n = 100.

B. The given equation is:

(328 x 128) x k = 328 x (82 x 128) x k

To solve for k, we can simplify the equation using the properties of multiplication.

Step 1: Perform the multiplications inside the parentheses:

41984 x k = 328 x 10576 x k

Step 2: Rearrange the equation by applying the associative property of multiplication:

41984 x k = 328 x (10576 x k)

Step 3: Divide both sides of the equation by 328:

(41984 x k) / 328 = 10576 x k

Step 4: Cancel out the common factor of k on the left-hand side:

(41984 / 328) x k = 10576 x k

Step 5: Simplify the left-hand side:

128 x k = 10576 x k

Step 6: Subtract 10576 x k from both sides of the equation to isolate k:

128 x k - 10576 x k = 0

Step 7: Factor out k on the left-hand side:

k x (128 - 10576) = 0

Step 8: Simplify further:

k x (-10448) = 0

Step 9: Divide both sides of the equation by (-10448):

k = 0

So, the solution for k in the equation "(328 x 128) x k = 328 x (82 x 128) x k" is k = 0.

Answer:

can you put the actual question in the question plz?

Step-by-step explanation:

The students that are in the seventh grade is 60.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Let the students that are in the seventh grade be x.

Since 12 students in the Environmental Club represent 20% of the students in the seventh grade. This will be:

20% × x = 12

0.2x = 12

Divide

x = 12 / 0.2

x = 60

Therefore, there are 60 students.

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Answer:

11

Step-by-step explanation:

we know this because there are 5 people saying they have 3 and 6 people saying they have between 4-7

The correct answer is "Oy-axis" as it represents the line of reflection for triangle DEF to triangle D'EF.

To determine the line of reflection that maps triangle DEF to triangle D'EF, we can examine the coordinates of the corresponding vertices.

Given that E' is located at (10, 4) and the corresponding vertex E in triangle DEF is at (-10, 4), we can observe that the x-coordinate of E' is the negation of the x-coordinate of E.

This suggests that the line of reflection is the y-axis. A reflection across the y-axis results in a transformation where the x-coordinate of each point is negated while the y-coordinate remains the same.

Since "Oy-axis" indicates the line of reflection from triangle DEF to triangle D'EF, it is the appropriate response.

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Answer:

\(\huge\boxed{9-\dfrac{2}{x}=9-2:x}\)

Step-by-step explanation:

Nine minus:

\(9-...\)

the quotient of two and a number x:

\(2:x=\dfrac{2}{x}\)

together

\(9-\dfrac{2}{x}\)

Answer:

A

Step-by-step explanation:

there's an invisible power of one next to the x, so there is one solution. same way that if there was a power of 2 to the x, there would be 2 solutions

The current market price for the bond is $870 the yield to maturity is 14.13%

The approximate yield to maturity of this bond is 11.25%, which is above the annual coupon rate of 10% by 1.25%. You can then use this value as the rate (r) in the following formula: C = future cash flows/coupon payments. r = discount rate (the yield to maturity)

knowing that:

the formula is:

\(P = (C / (1 + r))^1 + (C / (1 + r))^2 + ... + (C + F) / (1 + r)^n\)

Putting the values:

\($870 = (130 / (1 + r))^1 + (130 / (1 + r))^2 + ... + (130 + 1,000) / (1 + r)^13\)

Using the math we find that the percentage is  approximately 14.13%;

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Answer:

As baby porcupine is backed into cactus, so the spines of cactus will feel like spines of mother porcupine. So the baby porcupine will give  call to its mother.

Step-by-step explanation

He said hi Ma.

Answer:

X=4

Step-by-step explanation:

Answer:

2x - 3 = 5

+3 +3

2x = 5 + 3

2x = 8

÷2 ÷2

× = 4

Applying the sine rule the value of side w is calculated to be 6.2

The size of w is calculated using the sine rule which states that the ratio of a side and the opposite angles are equal

the formula is

Sin A / a = Sin B / b = Sin C / c

applying the formula for the problem

Sine W / w = Sine X / x

plugging in the values

Sine 38 / w = Sine 84 / 10

cross multiplying

w = 10 x Sin 38 / Sine 84

x = 6.185

x =  6.2 to the nearest tenth

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The number of terms of the Maclaurin series for eˣ that should be used to estimate \(e^{0.1}\) to within 0.00001 is 4.

Taylor’s inequality:

If Rn( x ) = 0

Rn(x)=0

Rn​(x)=0.

The given function is eˣ

Thus, all the derivatives of eˣ is eˣ itself.

Suppose that, the nth derivative of eˣ is eˣ

To estimate the value of \(e^{0.1}\) substitute the value of x as 0.1.

Note that Taylor series is called Maclaurin series when a=0.

Usually, Maclaurin series will starts with n=2.

Increase the value of n until the reminder is less than 0.00001.

By Taylor’s inequality,

If | \(f^{n}\)(0.1) | = \(e^{0.1}\)≤ M then | Rₙ(x) |≤\(\frac{M}{(n+1)!}\) \(|0.1-0|^{n+1}\)

Substitute the value of n as 2. Then,

\(|R2(x)|\)≤\(\frac{M}{(2+1)!} |0.1-0|^{2+1}\)

≤ \(\frac{e^{0.1}}{3!} |0.1|^{3}\)

≤ \(\frac{e^{0.1}}{6} 0.001\)

≤ 0.00018

Since \(|R2(x)|\) ≥ choose the value of n as 3. Then,

\(|R3(x)|\) ≤\(\frac{M}{(3+1)!} |0.1-0|^{3+1}\)

≤ \(\frac{e^{0.1}}{4!} |0.1|^{4}\)

≤ \(\frac{e^{0.1}}{24} 0.0001\)

≤ 0.0000046

Therefore, \(|R3(x)|\) ≤ 0.00001

That is, n=3 satisfies the inequality.

So, by adding the 4 terms (when n=0,1,2,and 3) of the Maclaurin series, it

is possible to estimate the value of \(e^{0.1}\) to within 0.00001.

Thus, the number of terms of the Maclaurin series for eˣ that should be used to estimate \(e^{0.1}\) to within 0.00001 is 4.

The number of terms of the Maclaurin series for eˣ that should be used to estimate \(e^{0.1}\) to within 0.00001 is 4.

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Answer:

Step-by-step explanation:

THE ANSWER TO YOUR QUESTION IS C.

Answer:

Step-by-step explanation:

Given,

Length of the rectangle = 5m 20cm = 5.2m

Breadth of the rectangle = 3.5m

Therefore,

Perimeter of the rectangle

= 2(Length + Breadth)

= 2(5.2m + 3.5m)

= 2 × 8.7m

= 17.4m

Hence,

Area of the given rectangle is 17.4 sq.m (Ans)

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

In a right triangle, the legs \(l_1\) and \(l_2\) are related with the hypotenuse \(h\) by the Pythagorean Theorem, given below:

\(h^2 = l_1^2 + l_2^2\)

In this problem:

Applying the Pythagorean Theorem:

\(h^2 = l_1^2 + l_2^2\)

\(9^2 + x^2 = (x + 1)^2\)

\(81 + x^2 = x^2 + 2x + 1\)

\(2x + 1 = 81\)

\(2x = 80\)

\(x = \frac{80}{2}\)

\(x = 40\)

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Answer:

\(KH = 55\)

Step-by-step explanation:

Given

See attachment

Required

Find KH

From the attachment:

\(GD = 13\)   \(DE = 7\)

\(HI = 29.4\)

To find KH, we make use of the following equivalent ratio:

\(GD : DE = KH : HI\)

Substitute values for GD, DE and HI

\(13 : 7 = KH : 29.4\)

Convert to fractions

\(\frac{13}{7} = \frac{KH}{29.4}\)

Make KH the subject

\(KH = \frac{13}{7} * 29.4\)

\(KH = \frac{13* 29.4}{7}\)

\(KH = \frac{382.2}{7}\)

\(KH = 54.6\)

\(KH = 55\) --- approximated

Answer:

3 to 8 = 6 to 16 = 30 to 80

Step-by-step explanation:

Each time you multiply both numbers of a ratio by the same number, you get an equivalent ratio.

3 to 8

Multiply both 3 and 8 by 2:

6 to 16

Multiply both 3 and 8 by 10:

30 to 80

3 to 8 = 6 to 16 = 30 to 80

Answer:

Huh!! What is this question supposed to mean?

Answer:

Jim ran 144 miles

Step-by-step explanation:

Since Kate ran 72 miles (12x6), Jim ran 144 miles (72x2)

Answer:

9

Step-by-step explanation:

Plug in 6 to x, since this is the x-value in the ordered pair.

\(3(6)+2y=36\\18+2y=36\\2y=18\\y=9\)

Answer:

(6, 9)

Step-by-step explanation:

3x + 2y = 36

Substitute 6 into the equation to get the output.

3(6) + 2y = 36

Multiply 3 and 6.

18 + 2y = 36

Subtract 18 from both sides.

2y = 18

Divide both sides by 2.

y = 9

The ordered pair when x = 6 is

(6, 9)

SOLUTION

It is given that the diametr of the circle is 6 yd.

Since radius is half of diameter, It follows that the radius is 3 yd.

Therefore the area of the circle is:

Therefore the area of the circle is 28.26 square yard.

The circumference of the circle is:

Therefore the circumference of the circle is 18.84 yd.

There are 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters and 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.

The prοduct οf all pοsitive integers less than οr equal tο a given pοsitive integer and denοted by that integer and an exclamatiοn pοint. Thus, factοrial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factοrial zerο is defined as equal tο 1.

If the chοice matters (i.e., the οrder οf the chοsen οbjects matters), then there are 3 pοssible chοices fοr the first οbject and 2 pοssible chοices fοr the secοnd οbject.

Thus, there are 3 * 2 = 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters.

If the chοice dοes nοt matter (i.e., the οrder οf the chοsen οbjects dοes nοt matter), then there are 3 chοοse 2 = 3!/((3-2)!*2!) = 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.

Therefοre,  there are 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters and 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.

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\(0.35 \times 4\)

We can see that there are \(2\) sets of grids which each set contains \(100\) grids. We can see one of the set has all of its grids shaded. We can also see that the other set has its \(40\) grids shaded. The ratio of all the total shaded grids of the \(2\) sets to the number of grids of \(1\) set is \(\frac{140}{100}\\\) which we can write it in Decimal as \(1.4\).

We know that the product of \(0.35\) and \(4\) is also \(1.4\). So, \(0.35 \times 4\) is the product that matches the shading on grids.

Answer:

Let's start by finding out how many muffins were there in total before the ogre stole 20 of them. Let's call that number "x".

If 5/8 of them were left after the ogre stole 20, then 3/8 of them were taken.

So we can set up an equation:

x - 20 = 3/8x

To solve for x, we can start by multiplying both sides by 8 to get rid of the fraction:

8(x - 20) = 3x

8x - 160 = 3x

Now we can solve for x by subtracting 3x from both sides:

5x - 160 = 0

5x = 160

x = 32

So there were originally 32 muffins.

Now we can find out how many are left:

5/8 of 32 = 20

So there are 20 muffins left.

Step-by-step explanation:

Answer:

9207 divided by 4 = 2301 with a remainder of 3

Step-by-step explanation:

  (check the attached document)