If the standard quota for how many new schools will open in the 5 boroughs are:
Bronx: 20.73
Brooklyn: 10.12
Queens: 35.46
Manhattan 25.16
Staten Island 5.44

Use Jefferson's plan to apportion the Bronx quota.

You can solve with many ways but I'll do this one instead. Move 12 to the left side and change from positive to negative.

\(2x^2-2x-12=0\\\)

Then divide by 2 whole equation.

\(\frac{2x^2-2x-12}{2}=\frac{0}{2}\)

Simplify, as we get  \(x^2-x-6=0\)

We can either use Quadratic Formula or Factoring the Polynomials. It depends but since the polynomial aren't that hard to factor because it doesn't have that many numbers in value. So using factoring will be faster.

From \(x^2-x-6=0\) we can factor as -

\((x-3)(x+2)=0\\x-3 =0, x+2=0\\x=3, x=-2\\(x=3,-2)#\)

Thus, the value of x is 3 or -2. So x = 3, -2 is the answer.

Note that we can also use Quadratic Formula to solve the equation, however that will take longer than factoring then solve the equation.

Answer:

Store number 1 has the best discount.

Step-by-step explanation:

Find how much of a discount you get from each store. For number 1 you find 30% of $150 by turning the percent to a decimal and multiplying, for number 2 you would subtract 150 - 30, and for number 3 you subtract 150 - 1/5. When all of this is done you get the greatest discount of $45 off from store number 1.

Point-Slope Equation of the Line

If we are given the slope of the graph (m) and one point through which it passes (h,k), we can write the equation of the line as follows:

y - k = m (x - h)

Now substitute the values of m=2 and (h,k) = (5,2):

y - 2 = 2 (x - 5)

Operating:

y - 2 = 2x - 10

Adding 2 to both sides:

y = 2x - 8

Now we have the equation of the line, you can set any value for x and get the corresponding value of y and draw your graph.

Let's select x = 1, the value of y is

y = 2*1 - 8 = -6

Thus, the other point can be (1,-6)

With these points, you can plot them and draw the graph as shown below:

Answer:

x = 2

Step-by-step explanation:

Let the number be x

When we multiply a number by 6 and subtract it by 5, we would get 7.

On multiplication of number x with 6 it will be 6x.12

On subtraction of 5 it will be 6x - 5

6x - 5 = 7

6x = 7 + 5  

6x = 12

x = 12/6

x = 2

Answer:

The number is 2

Step-by-step explanation:

Let the number be n

Multiply the number by 6 = 6n

Subtract 5 from the number , 6n - 5

And we get 7

So , the expression : 6n - 5 = 7

                                6n = 7 + 5

                                6n = 12

                                  n = 2

Answer:

1. 1 in 5

2. There are 5 colors it could land on, and orange is one of them.

3. 40 different combinations

4. There are 5 colors with 8 corresponding numbers. 5x8=40

Step-by-step explanation:

1) 20%

2) Assuming that on the spinner with color, every section has an equal share, then the probability of landing on orange is \(\frac{1}{5}\) or 20%. This is because, the orange section is one of the five equal sections, or \(\frac{1}{5}\) or the spinner. \(\frac{1}{5}\) in decimal form is 0.2, to convert to a percent, multiply by 100. Hence one gets, 20%.

3) 40

4) There are 5 sections on the spinner with color, hence 5 possible outcomes when one spins the spinner. On the black and white spinner, there are 8 sections, hence 8 possible outcomes when one spins the spinner. To find the total number of outcomes resulting from the two events, one must multiply the total outcomes from one event by the total outcome of the other event. When one does this, they get that there are 40 possible events.

Step-by-step explanation:

after simplifying they look like

I) -5x + 13

II) 11x - 17

III) 9x + 13

IV) 4x + 10

V) 9x + 13

VI) -4x + 10

VII) -5x + 13

VIII) 11x - 17

so, clearly, IV and VI are not the same (equivalent).

Answer:

the answer is 51.75

Step-by-step explanation:

Answer:

x = 26

Step-by-step explanation:

Since s║t and r is a transversal, consecutive interior angles add to 180

⇒ 2(x + 15) + (3x + 20) = 180

⇒ 2x + 30 + 3x + 20 = 180

⇒ 5x + 50 = 180

⇒ 5x = 180 - 50

⇒ 5x = 130

⇒ x = 130/5

⇒ x = 26

Answer:

x=26

Step-by-step explanation:

Given:

s || t

2(x+15) + (3x+20) = 180°

Since the sum of co interior angle is 180°

Opening bracket

2x + 30 + 3x + 20 =180

Solving like terms

5x+50= 180

subtracting both side by 50

5x=180-50

5x = 130

dividing both side by 5.

\(\tt x=\frac{130}{5}\)

x = 26

Therefore value of x is 26.

Answer:

1 cm and 18 cm

2 cm and 9 cm

3 cm and 6 cm

Step-by-step explanation:

We need to find the factors of 18
which are; 1,18; 2,9; 3,6
So therefore we'd pick:
1 cm and 18 cm

2 cm and 9 cm

3 cm and 6 cm

Answer:

B) There is one unique solution, (2, 1).

Attached is a graph of the system of equations.

Step-by-step explanation:

Given system of equations:

\(\begin{cases} 3x+6y=12 \\ 3x+2y=8\end{cases}\)

Types of Solutions to a System of Equations

Using a graphing calculator, we can find the solution(s) to the given system of equations. To find the solution(s), we need to look at the point where the lines intersect; this is called the point of intersection.

Answer:

B: There is one unique solution, (2, 1)

Step-by-step explanation:

Took the test.

Answer:

x = 4

Step-by-step explanation:

3x + 2 = 14

→ 3x = 14 - 2

→ 3x = 12

→ x = 12/3

→ x = 4

````````````````````````

The crime that is often alcohol related is domestic violence. That is option D.

Domestic violence is defined as an abusive relationship that exist between two or more individuals that are closely related by blood or marriage.

The causes of domestic violence include the following:

Therefore, alcohol intake can lead to domestic violence because it can cause the abusive partner to have a reduction in cognitive and physical functions that impair self-control, with the consequent effect of reducing the ability to resolve conflicts nonviolently.

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Answer:

124

Step-by-step explanation:

You can find this answer by simply multiplying 62 by 2. lol

Therefore, the total annual premium to insure the wood house and its contents would be $2,055.

An equation is a statement that two mathematical expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to represent relationships between quantities and can be solved to find the value of the unknown variable.

Here,

We need to first determine the building area rating for the location of the wood house. Let's assume that the wood house is located in a rural area. Then, the building area rating for wood construction is 0.80 for building coverage and 0.91 for contents coverage. To calculate the annual premium for building coverage, we can use the following formula:

Annual premium = (building value / 100) * annual premium per $100 of coverage

For a wood house worth $200,000, the annual premium for building coverage would be:

Annual premium = (200,000 / 100) * 0.80

= $1,600

Similarly, to calculate the annual premium for contents coverage, we can use the same formula:

Annual premium:

= (contents value / 100) * annual premium per $100 of coverage

Assuming a contents value of $50,000, the annual premium for contents coverage would be:

Annual premium = (50,000 / 100) * 0.91

= $455

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Answer:

D. Bank charges a large fee for bouncing a check is not an example of overdraft protection.

Step-by-step explanation:

Overdraft protection is a service offered by banks that allows you to link your checking account to another account, such as a savings account or a line of credit. If you overdraw your checking account, the bank will automatically transfer funds from the linked account to cover the shortfall, which helps you avoid overdraft fees and other penalties.

Option A is not an example of overdraft protection as it refers to earning interest on money in your savings account, which is a separate service.

Option B refers to additional fees collected by the bank when you bounce a check, which is a penalty for not having sufficient funds in your account to cover the check.

Option C refers to an ATM machine providing you with cash, which is a basic function of an ATM and is not related to overdraft protection.

Answer:4 dimes = 40 cents

1 nickel 3 pennies =8 cents

5 quarters and 1 dime = $1 and 35 cents

step explanation:

The ratio of the sides of the small box and the medium box is 1:3

The ratio of the area of the bases of the small box and the medium box is 1:9.

The ratio of the volumes of the small box and the medium box is 1:27.

The volume of a medium box is 5832 cubic inches.

What is a cube?

The solid shape of a cube has six square faces. Because every square face has the same side length, each face is the same size. A cube has 8 vertices and 12 edges. Each vertex is the intersection of three cube edges.

Given that a cube-shaped small packaging box has a volume of 216 cubic inches.

Assume the length of sides is a.

The volume of a cube is side³.

The volume of the small box is a³.

Thus,

a³ = 216

a³ = 6³

a = 6

The length of the small box is 6.

The area of the base of small box is 6×6  = 36 square inches.

The dimensions of a medium box are tripled in length, width, and height.

Thus the length of the medium box is 3×6 = 18 inches.

The area of the base of the medium box is 18×18 = 324 square inches.

The volume of cube medium box is 18×18×18 = 5832 cubic inches.

The ratio of the sides of small box and medium box is

6:18 = 1:3

The ratio of the area of bases of small box and the medium box is

36:324 = 1:9

The ratio of the volumes of small box and the medium box is

216:5834 = 1:27

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Answer:

We failed to reject H₀

t < 2.06

1.5 < 2.06

We do not have significant evidence at significance level α=0.05 to show that the mean G.P.A. of CC students transferring to Sac State is above 3.3

Step-by-step explanation:

Set up hypotheses:

Null hypotheses = H₀: μ = 3.3

Alternate hypotheses = H₁: μ > 3.3

Determine type of test:

Since the alternate hypothesis states that mean G.P.A. of CC students transferring to Sac State is above 3.3, therefore we will use a upper-tailed test.

Select the test statistic:  

Since the sample size is very small (n < 30) therefore, we will use t-distribution.

Determine level of significance and critical value:

Given level of significance = 5% = 0.05

Since it is a upper tailed test,

At α = 0.05 and DF = n – 1 =  25 - 1 = 24

t-score =  2.06

Set up decision rule:

Since it is a upper tailed test, using a t statistic at a significance level of 5%

We Reject H₀ if t > 2.06

Compute the test statistic:

\($ t = \frac{\bar{x}-\mu}{\frac{s}{\sqrt{n} } } $\)

\($ t = \frac{ 3.45- 3.3 }{\frac{0.5}{\sqrt{25} } } $\)

\(t = 1.5\)

Conclusion:

We failed to reject H₀

t < 2.06

1.5 < 2.06

We do not have significant evidence at significance level α=0.05 to show that the mean G.P.A. of CC students transferring to Sac State is above 3.3

The greatest common factor of 15 , 50 and 25 is A = 5

The Greatest Common Divisor is the highest number that divides exactly into two or more numbers. It is also expressed as GCF

Given data ,

Let the greatest common factor of the numbers be represented as A

Let the first number be a = 15

Let the second number be b = 50

And , the third number be c = 25

Now , the factors of 15 = 1 , 3 , 5 and 15

The factors of 50 = 1 , 2 , 5 , 10 , 25 and 50

The factors of 25 = 1 , 5 , and 25

Therefore, the GCF is 5

Hence , the greatest factor is 5

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The measure of the arc or angle is:

m∠NLM = 60 deg

From the given figure, line LN is the diameter. Thus, the measure of arc LN is 180° (semicircle).

Thus, we can say:

arc NM + arc ML = 180°

(3x + 21) + (8x + 16) =  180°

11x + 37 = 180

11x = 180 - 37

11x = 143

x = 143/11

x = 13

arc NM = 8x + 16

put x = 13:

arc NM = 8(13) + 16 = 120°

Recall that:

The measure of inscribed angle is half the measure of its intercepted arc. That is:

m∠NLM = 1/2 * 120°

m∠NLM = 60°

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Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

Answer:

156 M

Reasoning you add How far He has walked from his starting point

Step-by-step explanation:

Answer: 156 m here u go

Answer:

if you mean 206 divided by 6 than the answer will 34.3 (rounded)

Step-by-step explanation:

I used a calculator

Answer:

c

Step-by-step explanation:

it's a property of powers, when the base is the same (-5) , you need to

sum the powers when both terms are multiplyng

subtract the powers when both terms are dividing (numerator power minus denominator power, in that order)

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Answer:

98.64

Step-by-step explanation:

Answer: 98.640

Step-by-step explanation:

The hundredth place is 4 so u look to the right where the next digit is. Then you have to look if the next digit is 5 or more or 5 or less. 3 is 5 or less so u look back to the left where the 4 is and u leave that same but make the 3 a 0 and then u will get 98.640.

Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property

From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.

In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.

Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

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