The following two-way table shows the data for the students of two different grades in a school:

Member of Science Club Not Member of Science Club Total
Grade 7 20 2 22
Grade 8 20 8 28
Total 40 10 50

Based on the relative row frequency, the students of which grade are more likely to be members of the science club?


Grade 7

Grade 8

The students of both grades are equally likely to be members of the science club

No conclusion can be drawn about the chances of a student being a member of the science club

Answer:

Step-by-step explanation:

Solve each equation individually, using substitution or elimination.

A. x + 3y = 3

   2x - y = -2

Substitute:

2(3-3y) - y = -2

6-6y-y = -2

6-7y = -2

y = 8/7

plug it back in to the first equation:

x + 24/7 = 3

x = -0.4285, approximately, and since this rounds to -0.4 and 8/7 approximately equals 1.1,

A is your answer.

The system of equations has a solution of approximately (-0.4,1.1) is x+3y=3 and 2x-y=-2.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

here,
To determine whether (-0.4, 1.1) is the solution of which equation,
So, put the solution in the equation of Option A,
x+3y = 3
-0.4 + 3(1.1) = 3
2.9 ≈ 3

And,
2x-y=-2
2(-0.4) - 1.1 = -2
-0.8 - 1.1 = -2
-1. 9 ≈ -2

Thus, the system of equations has a solution of approximately (-0.4,1.1) is x+3y=3 and 2x-y=-2.

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Answer:

The answer is option B : $30,000.

Step-by-step explanation:

To avoid Primary Mortgage Insurance or PMI, one need to have the loan balance to be 80% or less of the home value.

Hence, Bella needs to deposit a down payment of at least 20% of $150,000

This value becomes:

[tex]0.20\times150000=30000[/tex] dollars

Therefore, the answer is option B : $30,000.

Answer:

B $30,000

Step-by-step explanation:

PMI then with the given amount is how we find the answer

Answer:

A = 3.4 cm

Step-by-step explanation:

The length of line segment AB is 3.4cm.

The area of octagon is given as 2a^2(1+sqrt{2})  

Where a is the side of octagaon. All sides of octagon are same.

As, 2a^2(1+sqrt{2}) = 54cm

Then, a^2 = 54/2(1+sqrt{2})

a^2 = 54/4.828

a^2 = 11.19

a = 3.4 cm

Answer:

B

Step-by-step explanation:

We can use the law of sines to form a proportion.

The law of sines state that any side length divided by the sin of the opposite angle measure will be equal.

Let's form a proportion.

[tex]\frac{25}{sin(90)}=\frac{b}{sin(35)}[/tex]

Simplify.

b ≈ 14.34

The value of b from the diagram is 14

From the given diagram we have the following

hypotenuse = 25

using the SOH CAH TOA identity, hence;

sin 35 = b/25

b = 25sin35

b = 14.34

The value of b from the diagram is 14.34

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Konichiwa~! My name is Zalgo and I am here to help you out today. The factorization of your equation is 4 (2a+b) (2a-b). If you do not understand this, it means 4 multiplied by 2a+b which is also multiplied 2a-b.

I hope that this helps! :P

"Stay Brainly and stay proud!" - Zalgo

(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Arigato~! XT)

Answer:

4(2a+b)(2a-b)

Step-by-step explanation:

Distributive property: A(B+C)=ab+ac

4²=4*4=16

4*4a²-4b²

Term of 4.

4 (4a²-b²)

Simplify, to find the answer.

4a²-b²= (2a+b)-(2a-b)

(2a+b)-(2a-b) is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

f(n) = 64(3/4)^(n-1).

Step-by-step explanation:

The common ratio  is  48/64 = 36/48 =  3/4.

For a GS  nth term = a1 r^(n-1) where r = the common ratio, a1 = the first term, and n = the number of peaks reached.

The axplicit function is   64(3/4)^(n-1).

Answer:

f(x) = 64(three-fourths) Superscript x minus 1

Step-by-step explanation:

A bouncing toy reaches a height of 64 inches at its first peak, 48 inches at its second peak, and 36 inches at its third peak. The explicit function is f(x) = 64(three-fourths) Superscript x minus 1

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}5x-3y=6\\x+y=2&\text{multiply both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}5x-3y=6\\3x+3y=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad8x=12\qquad\text{divide both sides by 8}\\.\qquad x=1.5\\\\\text{put the value of x to the second equation:}\\\\1.5+y=2\qquad\text{subtract 1.5  from both sides}\\y=0.5[/tex]

Answer:

Your answer would be A.) 5x − 3y = 6  and 6x − 2y = 8

Answer:

Step-by-step explanation:

The equation is simplified by combining "like" terms. The terms "2x" and "2x" are "like" not just because they are identical, but because the only variable (x) is raised to the same power (1) in each term. We can use the distributive property to help combine those terms:

  2x +2x = (x)(2+2) = 4x

Of course, the constants on the left can be simply added: 3 + 5 = 8.

Now, the simplified form of the equation is ...

  4x + 8 = 16

__

To solve this, we note that all the numerical values are multiples of 4, the x-coefficient. Then we can divide all of them by 4 to give ...

  x + 2 = 4

You know the value of x already at this point, since you're familiar with your addition facts. However, to complete the solution algebraically, we subtract 2 from both sides of the equation:

  x = 2

_____

Comment on this solution

You will usually get instruction to "separate the variable terms from the constant terms," so the simplified equation would usually have 8 subtracted from both sides to give ...

  4x = 8

Then, you would divide by the x-coefficient to get x=2.

I elected to do it the way shown above for a couple of reasons:

For this case we have that if and it varies directly with x, we can write the equation as:

[tex]y = kx[/tex]

Where:

k: It is the constant of proportionality.

According to the table:

[tex]-3 = k (1)[/tex]

Clearing k:

[tex]k = -3[/tex]

Then,[tex]y = -3x[/tex]

Answer:

Option C

Answer:

y varies directly with x

[tex]k = -3[/tex]

The equation is:

[tex]y = -3x[/tex]

Step-by-step explanation:

We can say that and it varies directly with x if it is fulfilled that

[tex]y = kx[/tex]

Where k is a constant known as the constant of variation.

So

[tex]\frac{y}{x} = k[/tex]

This means that if y varies with x then the division of y between x should always be equal to a constant value k.

We must test this for the values shown in the table

[tex]\frac{-3}{1} = -3[/tex]

[tex]\frac{-9}{3} = -3[/tex]

[tex]\frac{-15}{5} = -3[/tex]

The quotient of [tex]\frac{y}{x}[/tex] is always equal to [tex]-3[/tex]. Then [tex]k = -3[/tex] and the variation of y with x is direct

The equation is:

[tex]y = -3x[/tex]

ANSWER

Option D.

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} [/tex]

The new function is

[tex]g(x) = f(5x)[/tex]

This implies that,

[tex]g(x) = {(5x)}^{2} [/tex]

This gives us:

[tex]g(x) = {25x}^{2} [/tex]

We can that the graph of g(x) will shrink by a factor of 25 compared to f(x).

The graph will open upwards and shrink towards the y-axis.

Answer:

The answer is D

Step-by-step explanation:

* Lets revise some transformations

- A horizontal compression is the squeezing of the graph toward

 the y-axis.

- If the graph is y = f(x) and its image is y = f(k•x)

∴ The graph is horizontally compressed if k > 1 that means divide

   each of its x-coordinates by k.

∴ The graph is horizontally stretched if 0 < k < 1, that means divide

   each of its x-coordinates by k.

* Now lets solve the problem

∵ f(x) = x²

∵ g(x) = f(5x)

- Substitute the value of x in f(x) by 5x

∴ f(5x) = (5x)²

∴ g(x) = (5x)²

∵ The image of f(x) = x² is g(x) = (5x)²

∴ k = 5

∵ 5 > 1

∴ The graph of f(x) is compressed horizontally

- divide each x-coordinates of the points on the graph by 5

∴ The graph becomes narrow to the y-axis

- Look to the attached graph for more understanding

# The red graph is f(x) = x²

# The blue graph is g(x) = (5x)²

* The answer is the last graph D

Answer:

Anything you own that has value and can be turned into cash.

Step-by-step explanation:

Unless there is a passage that refers to the word, the second option would be the best answer due to Google's online dictionary.

Answer:

∠2 = 52°

Step-by-step explanation:

Since 1 angle = 90° then the sum of the other 2 angles = 90°, that is

∠2 + ∠3 = 90 ← substitute values

3x + 1 + 2x + 4 = 90

5x + 5 = 90 ( subtract 5 from both sides )

5x = 85 ( divide both sides by 5 )

x = 17

Hence

∠2 = 3x + 1 = (3 × 17) + 1 = 51 + 1 = 52°

Step-by-step answer:

If one is constrained to move to the right, or up, or diagonally upwards (i.e. remain in the first quadrant), then

there are three choices at A.

At the next position, whichever path one has taken, there are also three choices.

At the following position, there are no more choices.

Therefore, there are 3*3 = 9 different paths.

Answer:

23

Step-by-step explanation:

plug and chug: 5(4)+3=20+3=23

Hello There!

The answer would be "23"

When we have an expression like this, the "x" next to a number means that we multiply the number next to the variable by it.

In this case, if "x" equals 4, then we multiply 5 by 4 and we get a product of 20 and we add 3 to get a sum of 23.

Have A Great Day!

Be Safe!

TheBlueFox

Answer:

(y + 14)(y - 14)

Step-by-step explanation:

A difference of squares has the general form

a³ - b² and factors as

(a + b)(a - b)

Given

y² - 196

y² = (y)² ⇒ a = y and 196 = 14² ⇒ b = 14

y² - 196

= y² - 14² = (y + 14)(y - 14) ← difference of squares

Answer:

option B

Step-by-step explanation:

Paul bought 6 pounds of hamburger. He used 3 1/ 2  pounds to make burgers. Paul says he has 2 1/ 2  pounds of hamburger left.

To find out pounds of hamburger left we subtract 3  1/2 from 6 pounds

[tex]3 \frac{1}{2} =\frac{3*2+1}{2}=\frac{7}{2}[/tex]

Now we subtract the fraction from 6

[tex]6 - \frac{7}{2} = \frac{12}{2} - \frac{7}{2} =\frac{5}{2}[/tex]

Now we convert 5/2 into mixed fraction

[tex]\frac{5}{2} = 2\frac{1}{2}[/tex]

Paul's answer is correct. because when we add [tex]3\frac{1}{2} + 2\frac{1}{2}[/tex] we will get 6

Answer:

Step-by-step explanation:

volume of a pyramid is V=(lwh)/3

For this case we have that by definition, the volume of a pyramid is the third part of the volume of a prism that has the same area of the base and equal height.

Thus:

[tex]V = \frac {b * h} {3}[/tex]

Where:

b: It is the area of the base

h: It's the height

Answer:

[tex]V = \frac {b * h} {3}[/tex]

Answer:

Step-by-step explanation:

In math, a term is a combination of coefficients, constants and /or variables, each combination being separated by either a + sign or a - sign.

A term's definition provides an explanation of its meaning, often found in dictionaries but should also consider context and usage for a well-rounded understanding. Terms are often constructed from roots, prefixes, and suffixes that each convey a portion of the term's complete meaning. In textbooks, 'Key Terms' are important words paired with their definitions, as used in context.

The definition of a term refers to the explicit and clear explanation of what a particular term or word represents or means. This explanation is often found in dictionaries, but for full comprehension, it's important to also consider context and usage. While a dictionary provides a basic description based on common usage of a term, sometimes this common usage might lack precision or accuracy. It becomes essential to reflect on the term's meaning within a larger understanding of the world.

Consider anatomical terms used in biology, their definitions are composed of roots, prefixes, and suffixes - each part offering a piece of the term's overall meaning. For example, 'hypertension' is made from hyper- which means high and -tension which means pressure. Together it represents abnormally high blood pressure.

Meanwhile, in the context of a school textbook, 'Key Terms' are words of importance that are highlighted (usually in bold) and then followed by a definition. This way, the term syntax is given in the context in which it is used in the text. This makes understanding easier and seamless.

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[tex]\bf 40a^2+20a-30=(-1)(15a^3+30)\implies 40a^2+20a~~\begin{matrix} -30 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=-15a^3~~\begin{matrix} -30 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \\\\\\ 40a^2+20a=-15a^3\implies 15a^3+40a^2+20a=0\implies 5a(3a^2+8a+4)=0 \\\\\\ 5a(3a+2)(a+2)=0\implies a= \begin{cases} 0\\ -\frac{2}{3}\\ -2 \end{cases}[/tex]

Answer:

3x²

Step-by-step explanation:

Note that when adding, as long as the variables have the same power, you can combine the numbers together.

The sum of 3x² + 7x² = 10x² is correct.

If you used -3x², then it will be wrong, because -3x² + 7x² = 4x².

~

Answer:

x = 3

Step-by-step explanation:

Given

[tex]\sqrt{-x+4}[/tex] = x - 4 ( square both sides )

- x  4 = (x - 4)² ← expand

- x + 4 = x² - 8x + 16 ( subtract - x + 4 from both sides )

0 = x² - 7x + 12 ← in standard form

0 = (x - 3)(x - 4) ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions

x = 3 : [tex]\sqrt{-3+4}[/tex] = [tex]\sqrt{1}[/tex] = 1

right side = 3 - 4 = - 1

left side ≠ right side ⇒ extraneous solution

x = 4 : [tex]\sqrt{-4+4}[/tex] = 0 and right side = 4 - 4 = 0

left side = right side ⇒ x = 4 is the solution

Answer:

B

Step-by-step explanation:

Answer:

60 m2

Step-by-step explanation:

Since they are congruent SQ=MP, NM=RQ, RS=NP. The formula to find the area of a triangle is  1/2 bh. So you do 8 times 15 divided by 2. 8 times 15 is 120. 120 divided by 2 is 60 m2.

Answer:60m^2

Step-by-step explanation:

MNP is a triangle and area of a triangle = 1/2* base *height

From the figure height = 15 and base = ?

So we solve for the base using Pythagoras theorem

.: MP = square root of 17^2 - 15^2

MP = 8m =the base

Area of MNP = 1/2*8*15

Area = 60m^2

For this case we must simplify the following expression:

[tex]\sqrt {\frac {2160x ^ 8} {60x ^ 2}}[/tex]

We rewrite the expression:

[tex]\sqrt {\frac {60 * 36 * x ^ 8} {60x ^ 2}} =[/tex]

We eliminate common terms:

[tex]\sqrt {\frac {36 * x ^ 8} {x ^ 2}} =[/tex]

For division of powers of the same base, the same base is placed and the exponents are subtracted:

[tex]\sqrt {36x ^ {8-2}} =\\\sqrt {36x ^ {6}} =[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]6x ^ {\frac {6} {2}} =\\6x ^ 3[/tex]

Answer:

Option C

Answer:

usually means establishing a series of equal monthly payments that will provide

a principal payment that will cause the unpai principal balance to decrease each month so that the principal balance will be zero at the time of the final payment

Answer:

To amortize a loan refers to equal and periodic payments (monthly in most of the cases), on which the lender runs some interest ratio due to the amortization.

In other words, it means that the total amount of money the lender is going to "give" you is divide in smaller amount of moneys, which he is gonna lend you periodically, monthly. For example, if you need a $60,000 loan, and your lender propose to lend that money with a 4% of annual interest, that means he is gonna give your $1771.4 per month, he won't give you the whole money, instead he amortize the loan and give your a certain quantity based on the interest rate.

Hello There!

50*50 is 2,500

Answer:

1000

Step-by-step explanation:just multiply

We can notice that 731.8 is the Greatest among all numbers because 731 is always greater than 730

Now consider the remaining numbers : 730.38 , 730.1 , 730.63

★  730.1 can be written as 731.10

As the Number part of remaining numbers is same (730), we need to consider the decimal parts of the numbers in order tell which number is greatest among them

★ Decimal part of 730.38 is 38

★  Decimal part of 730.10 is 10

★  Decimal part of 730.63 is 63

As 63 > 38 > 10 :

We can say that : 730.63 > 730.38 > 730.10

So, Arrangement of given numbers from greatest to least is :

★  731.8 > 730.63 > 730.38 > 730.10

For this case we must simplify the following expression:[tex]7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {16x}) - 3 (\sqrt [3] {8x})[/tex]

We rewrite:

[tex]16x = 2 ^ 3 * 2x\\8x = 2 ^ 3 * x[/tex]

We rewrite the expression:

[tex]7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {2 ^ 3 * 2x}) - 3 (\sqrt [3] {2 ^ 3 * x}) =[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, taking the terms of the radical:

[tex]7 (\sqrt [3] {2x}) - 3 (2 \sqrt [3] {2x}) - 3 (2 \sqrt [3] {x}) =\\7 \sqrt [3] {2x} -6 \sqrt [3] {2x} -6 \sqrt [3] {x} =[/tex]

We add similar terms:

[tex]\sqrt [3] {2x} -6 \sqrt [3] {x}[/tex]

Answer:

Option C

Answer:

B

Step-by-step explanation:

In the composition of f and g, the equation is telling us to place the function f inside g. Observing in B that f is (x + 4), then this can be put in place of the x in 3x^2, making it 3(x + 4)^2 and finally the minus 5.

Answer:

3x + 7y = 31

-3x - 2y = -1

____________________

5y = 30

y = 6

____________________

3x + 42 = 31

3x = -11

x = - 11/3

____________________

x = -11/3; y = 6