on june 10, 2010 the boston globe reported that in the six years between 2006 and 2012 boston firefighters received raises of 2%, 2.5%, 3%, 3.5%, 2.5%, and 1.5%.

Based on the given parameters, the amount of the investment after 4 years is $1030

The given parameters about the compound interest are

Principal Amount, P = $1000

Interest Rate, R = 0.85%

Time, t = 4

Number of times, n = 1 i.e. annually

Compound interests are different from simple interest, and they are calculated using the following compound interest formula

CI = P(1 + R/n)^nt - P

To calculate the amount, we have:

A = P + CI

So, the equation becomes

A = P + P(1 + R/n)^nt - P

Evaluate the like terms

A = P(1 + R/n)^nt

Substitute the known values in the above equation

A = 1000 * (1 + 0.85%/1)^(1 * 4)

Express 0.85% as decimal

A = 1000 * (1 + 0.0085/1)^(1 * 4)

Evaluate the sum

A = 1000 * (1.0085/1)^(1 * 4)

Evaluate the exponent

A = 1000 * 1.03

Evaluate the product

A = 1030

Hence, the value of the investment is $1030

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Answer:

x=10

Step-by-step explanation:

48=6x-12

60=6x

x=10

The quadratic function in the standard form containing the point (-7, 5) and vertex (1, 9) is y = (-1/16)(x - 1)² + 9.

The vertex form of a quadratic function with vertex (h, k) is written as

y = a(x - h)² + k, where (x, y) denotes a point on the parabola. Real integers a, h, and k are also included.

Given:

Point (x, y) = (-7, 5)  

Vertex (h,k) = (1, 9)

The general equation of quadratic function in vertex form is:

 y = a(x - h)² + k

To solve for a, substitute the given point (x,y) = (-7,5) into the equation.

5 = a(-7 - 1)² + 9

a(-8)² = -4

a = -4 /64

a = -1/16

Therefore, the required quadratic function is,

 y = (-1/16)(x - 1)² + 9

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Answer: the second one

Step-by-step explanation:

commutative is like

A+b=b+A

So 4+(-6)=-6+4

Which is like 4-6=-6+4

Answer:

[tex]g(x)=2x+3[/tex]

Step-by-step explanation:

[tex]g(x)=\frac{1}{2}(4x+6)=2x+3[/tex]

Answer:

=2s−4

Step-by-step explanation:

−4s−3+6s−1

=−4s+−3+6s+−1

Combine Like Terms:

=−4s+−3+6s+−1

=(−4s+6s)+(−3+−1)

=2s+−4

Answer:

=2s−4

Answer:

3528

Step-by-step explanation:

35280 divided by 10 is 3528. To check your work, multiply 3528 by 10. The answer is 35280.

Hope this helps! :)

Answer:

- 4° F

Step-by-step explanation:

substitute C = - 20 into the formula

F = ([tex]\frac{9}{5}[/tex] × - 20 ) + 32 = (9 × - 4) + 32 = - 36 + 32 = - 4° F

FOR A RECIPROCAL OF FRACTION WE SWAP POSITIONS. WHATEVER WAS IN THE NUMERATOR BECOMES THE DENOMINATOR AND WHAT WAS IN THE DENOMINATOR BECOMES THE NUMERATOR.

THIS MEANS THAT AS A RESULTS WE HAVE

[tex] \frac{b}{b - 1} [/tex]

ATTACHED IS THE SOLUTION.

For the function x³ - 6x² + 11x - 6, we have that:

a) The x-intercepts are: x = 1, x = 2, x = 3.

b) The y-intercept is of y = -6, while the end behavior is that it decreases to the left and increases to the right.

The function is given as follows:

f(x) =  x³ - 6x² + 11x - 6

x - 3 is a factor of the function, meaning that x = 3 is a x-intercept and the function can be written as follows:

x³ - 6x² + 11x - 6 = (x - 3)(ax² + bx + c)

Then we have to build a system of equations to find the coefficients as follows:

x³ - 6x² + 11x - 6 = ax³ + (b - 3a)x² + (c - 3b)x - 3c.

Then the coefficients are given as follows:

Then the factor is given by:

x² - 3x + 2.

Hence the other intercepts of the polynomial are found when:

x² - 3x + 2 = 0

(x - 2)(x - 1) = 0.

x - 2 = 0 -> x = 2.

x - 1 = 0 -> x = 1.

The y-intercept is the value of f(x) when x = 0, that is, f(0), hence:

f(0) = 0³ - 6(0)² + 11(0) - 6 = -6.

For the end behavior, we need to find the limits as x goes to infinity, hence:

When the limit goes to infinity, we consider only the term with the highest exponent of the polynomial.

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3x+x+(x+12)=152

<AOD =<COB(VERTICAL OPPOSITE ANGLES)

[tex]5x+12=152\\5x=152-12\\5x=140\\\frac{5x}{5} =\frac{140}{5} \\x=28[/tex]

x=28°

be reminded that <COB IS MADE OF ALOT OF BRANCH ANGLES THAT WE HAD TO ADD TO GET IT

i.e <COE,<EOF AND <FOB

7-(-4) is 4 units from 7 in the negative direction. See the explanation and the linear scale attached.

The direction being referred to is the direction of the number on a numerical scale or Linear Scale.

In the attached linear scale, we can see that the arrow stops at 11. This is arrived at by expanding the bracket:

7 - (-4)

the subtraction signs cancel out each other creating a positive sign. Hence we have:

7 + 4

= 11.

Hence, 11 is 4 units away from 7 in the negative direction. That is going toward zero is negative or a reduction hence, to get to 7 you need to go toward the negative section of the scale.

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Answer:

Number

Step-by-step explanation:

48 divided by 100 equals .48

Answer:

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. 

Answer:

1 to 100,000

Step-by-step explanation:

There are 100,000 cm in a km

86 = 1p + 5n

n = p + 4

86 = 1p + 5(p + 4)

86 = 1p + 5p + 20

66 = 6p; p = 11

86 = 1(11) + 5n

86 = 11 + 5n

75 = 5n; 15 = n

11 pennies, 15 nickels

11(1) + 15(15) = 11 + 75 = 86

Considering that a transversal line cuts two parallel lines, the relations between the angles are given as follows:

1. Corresponding angles.

2. Alternate exterior angles.

3. Consecutive interior angles.

Angles 1 and 3 are corresponding angles, as they are both at the same position relative to their lines, j for angle 1 and m for angle 3, being cut by the transversal line t.

Angles 4 and 8 are alternate exterior angles, as:

Inverse positions in both senses, left/right and up/down, hence alternate exterior angles.

Angles 2 and 3 form a supplementary pair inside the same region, between the two lines being cut by the transversal, hence they are consecutive interior angles.

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Answer:

d

Step-by-step explanation:

Pythagorean theorem : a2 + b2 = c2

Here, ‘a’ is the vertical side i.e. wall

‘b’ is the base side i.e. bottom = 5 m

‘c’ is the hypotenuse i.e. the ladder = 10 m

If b = 5 m, c = 10 m

Then, a2 = c2 - b2 = (10 x 10) - (5 x 5) = 75

a = √75 = 8.66 m

The the top of the ladder is at 8.66 m.

Answer:

3 Feet

Step-by-step explanation:

Issac's Kitchen Area - 54 sqft

Issac's Pantry Area - 54/9 = 6 sqft (His pantry is 9x smaller than his kitchen)

[tex]area = length * width[/tex]

Here we have the total area and the width, so we can substitute for finding the length:

[tex]6 = length * 2\\ \\ = > \frac{6}{2} = length\\ \\ = > length = 3[/tex]

Hence is pantry is 3 feet long.

In order to solve this quadratic equation by completing the square, let's analyse the coefficient b by comparing the equation with the standard form:

We have b = -12. In order to be a perfect square, the coefficient c needs to be (-12/2)^2 = (-6)^2 = 36

We already have 30, so we just need to add 6:

The equation that can be used to get the number of men if the total number of people who attended was 2400 is x + 3x + x + 240 = 2400.

It should be noted that from the information given, in the health camp the number of children was three times the number of men and the number of men was 240 less than the number of women.

Number of men = x

Number of children = 3x

Number of women = x + 240

Total number of people = 2400

The appropriate equation will be:

x + 3x + x + 240 = 2400

5x + 240 = 2400

Collect like terms

5x = 2400 - 240

5x = 2160

Divide

x = 2160 / 5

x =432

Therefore, the total number of men is 432 men.

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Answer:  [tex]\text{y} \ge 2[/tex]

Reason:

The lowest point on the graph occurs when y = 2. This is a closed endpoint so it's included with the graph. So either y = 2 or y > 2, both of which combine to get the answer shown above.

The relationship will be a solid line .

How to find the relationship between the given amounts?

Given:

The amount of one lunch =$4

The amount of the school lunch card=$100

Let, the amount remaining on the card= b

Let the number of lunches to buy  = a

The equation is given by,

b = 100 - 4a

When 1 lunch is bought ,a= 1 ;

b= 100 - 4(1) = 96

When 2 lunches are bought ,a= 2;

b= 100 - 4 (2)= 92

When 3 lunches are bought ,a= 3;

b= 100 - 4 (3)= 88

When 4 lunches are bought ,a= 4;

b= 100 - 4 (4)= 84

Since ,the decrease is gradual and same, the relationship will be a solid line.

The complete question is:

What is the relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card. Is the relationship a solid line or a set on unconnected points?

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2 teaspoon of cinnamon need if he uses 3 cups of yogurt

By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part to part ratio, whereas the second is a part to whole ratio. The relationship between two separate entities or organizations is shown by the part-to-part ratio. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio describes how one group compares to another. For instance, five people enjoy reading books out of every ten persons. Since the ratio of the component to the total is 5:10, 5 out of every 10 persons enjoy reading.

Given that :Sandeep is making fruit dip for a party. His recipe calls for 1/2 of a teaspoon of cinnamon and 3/4 of a cup

of yogurt.

[tex]0.5 : 0.75 = x : 3[/tex]

x = 2

2 teaspoon of cinnamon need if he uses 3 cups of yogurt

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Answer: x= -5

Step-by-step explanation: Zero is x

f(-5)= -15 +7= -8

f(-5)= -1 - 7 = -8

Answer is -8

Answer:

51

Step-by-step explanation:

I may have made a mistake somewhere along the way but if not then it is 51 gallons.

The way i did this was to multiply 20 minutes by 3 to equal an hour, then multiply that by 24 to equal a day, then multiply that by 365 to equal a year.

That gives you the numbers you need to multiply the ounce by. So first multiply 1/4 by 3 to get 3/4. Next you multiply 3/4 by 24 to get 72/4 or 18. Then you multiply 18 by 365 to get 6570 ounces in a year. Finally you translate that to gallons and you get 51.328125, which rounds down to 51.

Alsooo, i wouldnt mind a good old brainliest if im correct :)

Answer: y=-4x+30

Step-by-step explanation: put into point slope form y-y1=m(x-x1). M is out slope with the given point (7,2) 7 is out x and 2 is our y. Give us y-2=-4(x-7) once done distribute yo get y-2=-4x+28. Add the 2 from the left to the right. to get y=-4x+30

Answer: 9,800

Step-by-step explanation:

She should save 9,800 yearly.

2/10 = 20/100 ; 20%

20% = 0.2

0.2 x 49,000

(which is 20% of 49,000)

= $9,800

Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots.  you  disagree with Katies statement because the function has four real roots

Katie is studying the polynomial  and determines the polynomial has three real roots. Do you agree or disagree with Katie's statement? Explain your reasoning.

the complete question is

Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots. Do you agree or disagree with Katies statement? Explain your reasoning.

Write properties of function:

x intercept/zero: [tex]x_{1}[/tex] = 3/2 ; [tex]x_{2}[/tex] = 4 ; [tex]x_{3}[/tex] = -[tex]\sqrt{3}[/tex] ;  [tex]x_{4}[/tex] = [tex]\sqrt{3}[/tex]

Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots.  you  disagree with Katies statement because the function has four real roots

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