A university law school accepts 3 out of every 13 applicants. If the school accepted 243 ​students, find how many applications they received.

Thank you anyone who helps =)

Answer:

2x+6y=-2 x is -3y-1 and 5x-3y=31 x is 3y+31/5

Step-by-step explanation:

5x−3y=31

Add 3y to both sides.

5x=31+3y

The equation is in standard form.

5x=3y+31

Divide both sides by 5.

5

5x =  5

3y+31

​Dividing by 5 undoes the multiplication by 5.

x=  5

3y+31

​

Answer:

The answer is 13.

Step-by-step explanation:

(b) Find the value of 2a + b: Remember that 2a means 2 × a. Replacing a by 4 and b by 7 gives 2×4 + 7.

Two possible values for 2a - b are 4i√2 and -4i√2, where 'i' is the imaginary unit.

To find the value of 2a - b, we need to eliminate 'b' from the two equations given.

Given equations:

1. 2a + b = 4

2. ab = -3

Let's solve for 'a' and 'b' using these equations.

Step 1: Solve for 'b' in terms of 'a' from equation (1).

2a + b = 4

b = 4 - 2a

Step 2: Substitute the value of 'b' from step 1 into equation (2).

a(4 - 2a) = -3

[tex]4a - 2a^2 = -3[/tex]

Step 3: Rearrange the equation to a quadratic form:

[tex]2a^2 - 4a + 3 = 0[/tex]

Step 4: Solve the quadratic equation for 'a'. You can use the quadratic formula:

a = [ -(-4) ± √([tex](-4)^2[/tex] - 4*2*3) ] / (2*2)

a = [ 4 ± √(16 - 24) ] / 4

a = [ 4 ± √(-8) ] / 4

a = [ 4 ± 2i√2 ] / 4

a = 1 ± i√2

Now we have two possible values for 'a': a = 1 + i√2 and a = 1 - i√2, where 'i' is the imaginary unit (√(-1)).

Step 5: Find the corresponding values of 'b' using the equation b = 4 - 2a.

For a = 1 + i√2:

b = 4 - 2(1 + i√2) = 4 - 2 - 2i√2 = 2 - 2i√2

For a = 1 - i√2:

b = 4 - 2(1 - i√2) = 4 - 2 + 2i√2 = 2 + 2i√2

Now we have two sets of values for 'a' and 'b':

1. a = 1 + i√2, b = 2 - 2i√2

2. a = 1 - i√2, b = 2 + 2i√2

Step 6: Calculate the value of 2a - b for each set of values:

For a = 1 + i√2, b = 2 - 2i√2:

2a - b = 2(1 + i√2) - (2 - 2i√2)

        = 2 + 2i√2 - 2 + 2i√2

        = 4i√2

For a = 1 - i√2, b = 2 + 2i√2:

2a - b = 2(1 - i√2) - (2 + 2i√2)

        = 2 - 2i√2 - 2 - 2i√2

        = -4i√2

So, the two possible values for 2a - b are 4i√2 and -4i√2, where 'i' is the imaginary unit.

To know more about imaginary unit, refer here:

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Complete Question:

If 2a + b = 4 and ab = -3, what is the value of 2a - b

Answer:

Your answer is in the Step by Step

Step-by-step explanation:

4=32x

We move all terms to the left:

4-(32x)=0

We move all terms containing x to the left, all other terms to the right

-32x=-4 x=-4/-32 x=1/8

Answer:

the answer is x=1/8

in the decimal form, it's x=0.125

Step-by-step explanation:

isolate the variable by dividing each side by a factor that doesn't contain the variable

hope this helps.

may I  please get a brainliest:)

The fraction of each piece of a cake is 1/6.

Given that, Joe has four birthday cakes to share with his 24 guests joe doesn't eat cake.

We need to find what fraction is each piece of cake.

A fraction represents a part of a whole or, more generally, any number of equal parts. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Now, 4 cakes are shared among 24 guests.

So, 24/4=6

Thus, each cake needs to divide into 6 slices.

Therefore, the fraction of each piece of a cake is 1/6.

To learn more about the fractions visit:

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Answer:

15/22

Step-by-step explanation:

Answer:

Graph using a table of values.

x      y

-2    -6

-1      -1

0       4

1         9

2       14

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hey niy

Answer:

-y= -4x -4

y= 4x +4

slope is 4

Step-by-step explanation:

Answer:

(3 x 20) + 9 = 69

4 x 100) + 20 = 420

Answer:

(3x20) + 9 is 69

(4x100) + 20 is 420

Answer:

(6³×2^6)÷2³=6³×2^(6-3)=6³×2³=(6×2)³=12³is your answer(1728)

1688 to the nearest hundred would be 1700

Answer:

The answer is 1700

Step-by-step explanation:

Have a great day.

Answer:

0.0011 = 0.11% probability of selling less than 3 properties in one week.

Step-by-step explanation:

For each property, there are only two possible outcomes. Either they are sold, or they are not. The chance of selling any one property is independent of selling another property. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A real estate agent has 17 properties that she shows.

This means that [tex]n = 17[/tex]

She feels that there is a 50% chance of selling any one property during a week.

This means that [tex]p = 0.5[/tex]

Compute the probability of selling less than 3 properties in one week.

This is

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{17,0}.(0.5)^{0}.(0.5)^{17} \approx 0[/tex]

[tex]P(X = 1) = C_{17,1}.(0.5)^{1}.(0.5)^{16} = 0.0001[/tex]

[tex]P(X = 2) = C_{17,2}.(0.5)^{2}.(0.5)^{15} = 0.0010[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0.0001 + 0.0010 = 0.0011[/tex]

0.0011 = 0.11% probability of selling less than 3 properties in one week.

Answer:

Yes it is, You can rearrange the expression to find that  y is uniquely determined in terms of  x, therefore a function.

Step-by-step explanation:

Answer:

y=-3/4x-5

Step-by-step explanation:

m=y2-y1/x2-x1

m=1-(-5)/-8-0

m=1+5/-8

m=6/-8

m=-3/4

y-y1=m(x-x1)

y-(-5)=-3/4(x-0)

y+5=-3/4x

y=-3/4x-5

Answer:

Revenue = 1020x  +  118y

Step-by-step explanation:

Revenue = 1020x  +  118y

This is an important question to understand. You will use it very shortly when you try and solve 2 equations with 2 unknown. Just to show you what that means, Suppose the revenue is

Revenue = 5808

and 11 items total were sold

x + y = 11                          Total number of items sold

1020x + 118y= 5808        Revenue

is the kind of problem you will be solving.

Step-by-step explanation:

a computer sell for $1020

x computer will sell for $1020x

a hard drive sell for $118

y hard drive will sell for $118y

The revenue equals $1020x + $118y

Answer:

Among the four choices, [tex](x + 5)[/tex] is the only one that is not a linear factor of this polynomial function.

Step-by-step explanation:

Let [tex]a[/tex] denote some constant. A linear factor of the form [tex](x - a)[/tex] is a factor of a polynomial [tex]f(x)[/tex] if and only if [tex]f(a) = 0[/tex] (that is: replacing all [tex]x[/tex] in the polynomial [tex]f(x) \![/tex] with the constant [tex]a\![/tex] would give this polynomial a value of [tex]0[/tex].)

For example, in the second linear factor [tex](x - 2)[/tex], the value of the constant is [tex]a = 2[/tex]. Verify that the value of [tex]f(2)[/tex] is indeed [tex]0[/tex]. (In other words, replacing all [tex]x[/tex] in the polynomial [tex]f(x) \![/tex] with the constant [tex]2[/tex] should give this polynomial a value of [tex]0\![/tex].)

[tex]\begin{aligned}f(2) &= 2^3 - 5\times 2^2 - 4 \times 2 + 20 \\ &= 8 - 20 - 8 + 20 \\ &= 0 \end{aligned}[/tex].

Hence, [tex](x - 2)[/tex] is indeed a linear factor of polynomial [tex]f(x)[/tex].

Similarly, it could be verified that [tex](x - 5)[/tex] and [tex](x + 2)[/tex] are also linear factors of this polynomial function.

Rewrite the first linear factor [tex](x + 5)[/tex] in the form [tex](x - a)[/tex] for some constant [tex]a[/tex]: [tex](x + 5) = (x - (-5))[/tex], where [tex]a = -5[/tex].

Calculate the value of [tex]f(5)[/tex].

[tex]\begin{aligned}f(5) &= (-5)^3 - 5\times (-5)^2 - 4 \times (-5) + 20 \\ &= (-125) - 125 + 20 + 20 \\ &= -210\end{aligned}[/tex].

[tex]f(5) \ne 0[/tex] implies that [tex](x - (-5))[/tex] (which is equivalent to [tex](x + 5)[/tex]) isn't a linear factor of this polynomial function.

Answer:

332.5º

Step-by-step explanation:

To convert radians to degrees, you multiply the radians by 180/π.

133π/72 • 180/π

We can see that the π's will cancel out. Therefore, we have:

133/72 • 180

Multiply.

133/72 • 180 = 23940/72

Simplify.

665/2 = 332.5

Your answer is:

332.5º

Hope this helps!

Answer:

332.5 º is the answer

Step-by-step explanation:

...

Answer:

I think it's 75°

Step-by-step explanation:

sorry if I was wrong

Answer:

75 %

Step-by-step explanation:

jane is 1,116 years old.

Step-by-step explanation:

first you have to subtract 1345 minus 116. Which will give you 1229. Then you subtract that by 113.

Answer:

$66.08

Step-by-step explanation:

Judy bought two things, a hat and sunglasses. So, the total money spent is:

$44.67 + $110.76 = $155.43

She has $89.35 in her checking account and spent $155.43 on the two items.

So that means she spent more than she has in the account. To find how much she needs to put in her checking account, we're going to subtract how much money she spent and how much she has in her account.

$89.35 - $155.43 = -$66.08

Therefore, she needs to put in $66.08 into her account to pay off her debt at the end of the month.

[tex](2^{\frac{1}{2}})^n=\frac{2^x}{2^{3y}}\\2^{\frac{1}{2}n}=2^{x-3y}\\\frac{n}{2}=x-3y\\n=2x-6y[/tex]

Answer:

Step-by-step explanation:

It’s 20

Answer:

x= y/10

Step-by-step explanation:

recheck ans:

(2)= y/10

20= y

Answer:

x > -20

Step-by-step explanation:

-x < 20

When dividing by negative numbers, flip the inequality.

x > -20

inclusive -> open circle

greater than -> to the right

open circle at -20 going to the right

Answer:

The point moves 3 units down and 3 units to the right

Step-by-step explanation:

Answer:

Step-by-step explanation:

perimeter = 4(10x) = 40x units

if x = 12, perimeter = 480x units

The next point she plots on the graph is (2,9)

The function is given as:

f(x) = 25(Three-fifths)^x

Rewrite properly as:

f(x) = 25(3/5)^x

The first point has an x value of 1.

So, the next would be x = 2

This gives

f(2) = 25(3/5)^2

Evaluate the product

f(2) = 9

So, we have:

(2, 9)

Hence, the next point she plots on the graph is (2,9)

Read more about exponential functions at:

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Step-by-step explanation:

1) Simplify what's inside the parentheses first which is ( 11 + 2) Simplify 11 + 2 to 13.

[tex]13 - 7[/tex]

2) Simplify 13 - 7 to 6.

[tex]6[/tex]

Therefor, the answer is 6.