Suppose when the price of gasoline is $3.50 per gallon the total amount of gasoline purchased in the United States is 6 million barrels per day. When the price of gas decreases to $3 per gallon the total amount of gasoline purchased is 8 million barrels per day. Based on these numbers and using the midpoint formula the percentage change in price is:

=========================================================

Work Shown:

The notation f(4) means we want to find f(x) when x = 4.

If x = 4, then we go for the middle definition since 4 makes [tex]3 \le x \le 10[/tex] to be true (ie, 4 is between 3 and 10)

Therefore,

f(x) = x^2 - 7 when [tex]3 \le x \le 10[/tex]

f(4) = 4^2 - 7

f(4) = 16 - 7

f(4) = 9

Answer:

f(4) = 9

Step-by-step explanation:

4 is between 3 and 10 so we use the middle function

f(4) = x^2 -7

     = 4^2 -7

     = 16 -7

    = 9

Answer:

b = 76°

Step-by-step explanation:

According to the inscribed angles proposition, the measure of an inscribed angle in a semicircle is said to be 90°.

Therefore, in the figure given, m<a = 90°

b = 180° - (90° + 14°) => sum of angles in a triangle.

b = 180° - 104°

b = 76°

Answer:

a. major arc

b. minor arc

c. semi circle

d. central angle

Answer:

0.32 grams

Step-by-step explanation:

ratio of weight of -copper, zinc, manganese, and nickel = 177:12:7:4

let the

weight of copper = 177x

weight of zinc = 12x

weight of manganese = 7x

weight of nickel = 4x

Total weight of this alloy in terms of x =  177x + 12x+ 7x + 4x = 300x

given weight of alloy = 8 grams

thus,

weight of this alloy in terms of x =given weight of alloy

300x = 8 grams

x = 8/300 grams =

weight of zinc = 12x = 12 * 8/300 grams = 96/300 grams = 0.32 grams

Answer:

84 women

Step-by-step explanation:

Using Algebra, we can apply the ratio of men and women, 4 and 3, in a format that can be used in an equation.

4x = men and the unknown variable that will solve the amount of men

3x = women and the unknown variable that will solve the amount of women

Now, we will use the other provided piece which is the total amount of employees, and we will put together an equation!

4x + 3x = 196

We will use this equation to solve for X by the process of addition and division.

4x + 3x = 196

7x = 196

196 ÷ 7 = 28

x = 28

Now we will use this variable and apply it for x to find the number of women.

3 x 28 = 84 women!

Checking the answer:

4 x 28 = 112 men

84 + 112 = 196

Therefore, this answer checks out.

Answer:

1) 0.3 ; 0.7

Step-by-step explanation:

Given the following :

Probability that product A launch : P(A) = 0.45

Probability that product B launch : P(B) = 0.60

Probability that both product launch : P(AnB) = 0.35

P(A alone) = p(A) - p(AnB)

P(A alone) = 0.45 - 0.35 = 0.1

P(B alone) = p(B) - p(AnB)

P(B alone) = 0.60 - 0.35 = 0.25

Probability that neither product will launch :

1 - [p(A alone) + p(B alone) + p(AnB)]

1 - [0.1 + 0.25 + 0.35]

1 - 0.7 = 0.3

Probability that at least one product will launch :

P(A alone) + p(B alone) + p(AnB)

0.1 + 0.25 + 0.35 = 0.7

Answer:

8+8 =16 not 0

Step-by-step explanation:

First she used associative property of addition. After that 8 + 8 = 16

but she wrote 0

she added them wrong

[tex]x+y=12\\\dfrac{x}{y+3}=\dfrac{1}{2}\\\\x=12-y\\2x=y+3\\\\2(12-y)=y+3\\24-2y=y+3\\3y=21\\y=7\\\\x=12-7=5\\\\\dfrac{x}{y}=\dfrac{5}{7}[/tex]

Answer:

Step-by-step explanation:

Use the Law of Sines for this. Set it up as follows:

[tex]\frac{sin(x)}{6}=\frac{sin(61)}{6.2}[/tex]  Cross multiply:

6.2sin(x) = 6sin(61) and solve for the term with the unknown in it:

[tex]sin(x)=\frac{6sin(61)}{6.2}[/tex]

Work on the right side first. Plug that into your calculator to get

sin(x) = .8464061682

Now the problem comes down to "what angle has a sine of .8464061682?" This requires the use of the inverse button on your calculator. Hit 2nd, then sin, and you will see on your screen:

[tex]sin^{-1}([/tex]

After that open parenthesis enter that big long decimal and hit equals. You should get an angle measure of 57.822 degrees. Not sure what you are rounding to.

Answer:

Salary after 5 year(A) = $60,485 (Approx)

Step-by-step explanation:

Given:

Staring salary(P) = $43,125

Growth rate(r) = 7%

Number of year (n) = (6-1) = 5

Find:

Salary after 5 year(A)

Computation:

[tex]A=P(1+r)^n \\\\ A = 43125(1+0.07)^5 \\\\ A = 60485[/tex]

Salary after 5 year(A) = $60,485 (Approx)

Answer:

By proportion :-

x/2.8 = 3/2.4

x = 3(2.8)/ 2.4

x= 3.5

Answer: C) 3.5

《OAmalOHopeO》

Answer:

HK = 42

HM = 23

MK = ??

23 + MK = 42

MK = 19

^^^ so you're correct :)

Let me know if this helps!

Answer:

Domain -5 ≤x<1

Range -4 ≤y<7

Step-by-step explanation:

The domain is the values that x takes

X goes from -5 included to 1 not included

-5 ≤x<1

The range is the values that y takes

y goes from -4 included to 7  not included

-4 ≤y<7

Answer:

Domain -5 ≤x<1

Range -4 ≤y<7

Please mark me as brainliest :)

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

The question doesn't ask you to find the area, it just ask for the expression that represents the area.

The area of rectangle is A=bh, where b and h are each of the side lengths.

Since we know the sides are (2x+7) and (5x+9), this means that the expression for the area of the rectangle is:

[tex](2x+7)(5x+9)[/tex]

To find the degree and classification, expand the factors:

[tex]=(2x+7)(5x+9)\\=(10x^2+18x+35x+63)\\=10x^2+53x+63[/tex]

Thus, this is a second degree quadratic expression

And from Part A, when we multiplied (2x+7)(5x+9), we got another polynomial (10x^2+52x+63). Thus, this rerepresents the closure property of polynomials, where multiplying a polynomial by another gets another polynomial.

.

Answer:

see below

Step-by-step explanation:

Part A

(2x+7) ( 5x+9)

Foil

first 2x*5x = 10x^2

outer: 2x*9 = 18x

inner: 7*5x= 35x

last: 7*9 = 63

Add together

10x^2 +18x+35x+63

10x^2+53x+63

Part B

This is a second degree polynomial called a quadratic

Part C

When we multiply two polynomials together, we get another polynomial.  This is the closure property for multiplication of polynomials

Answer:

100.5 ft^2

Step-by-step explanation:

First find the area of the rectangle

A = l*w

A = 12.16 * 6

A =72.96 ft^2

Then find the area of the triangle

A = 1/2 bh

The base is 12 ft - 6ft = 6ft

The height is 9.16 ft

A = 1/2 ( 9.16) * 6

A = 27.48 ft^2

Add them together

27.48+72.96

100.44 ft^2

Round to the nearest tenth

100.5 ft^2

Answer:

[tex]\huge \boxed{\mathrm{100.4 \ ft^2 }}[/tex]

Step-by-step explanation:

To find the area of the shape, we can add the area of the rectangle with the area of the triangle.

Area of rectangle :

base × height

6 ft × 12.16 ft

72.96 ft²

Area of triangle :

base × height × 1/2

(12 ft - 6 ft) × 9.16 ft × 1/2

6ft × 9.16 ft × 1/2

27.48 ft²

Adding the areas.

72.96 ft² + 27.48 ft²

100.44 ft²

≈ 100.4 ft² (rounded to nearest tenth)

Answer:

[tex]\Large \boxed{\mathrm{\bold{B. \ 9}}}[/tex]

Step-by-step explanation:

Plug in c = -4 and d = 10 for the expression.

1/4(-4³ + 10²)

Evaluate the expression.

1/4(-64 + 100)

1/4(36)

36/4 = 9

Answer:

[tex]\huge\boxed{B. \ \ 9}[/tex]

Step-by-step explanation:

1/4 (c³ + d²)

Given that c = -4 and d = 10

1/4 ( -4³ + 10²)

1/4 ( -64+100)

1/4 ( 36 )

=> 9

Answer:

Center: (9,3)

Radius: 9 units

Step-by-step explanation:

[tex]x^{2} -y^{2} -18x-6y+9=0[/tex]

[tex]x^{2} -18x+81+y^{2} -6y+9=-9+81+9[/tex]

[tex](x-9)^{2} +(y-3)^{2} =81[/tex]

Center: (9,3)

[tex]r^{2} =81[/tex] → [tex]r=9[/tex]

Radius : 9 units

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

OAmalOHopeO

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

Answer:

27/10

Step-by-step explanation:

You want to get a common denominator in order to add them together.

First:

    Convert the whole numbers to fractions, 4 = 8/2

         4 1/2 = 9/2

     And 1 = 10/10

         1 8/10 = 18/10

Then find the common denominator:

The least common multiple of 2 and 10 is 10. So:

convert 9/2 to a denominator of 10 : 9*5 / 2*5 = 45/10

Subtract:

45/10 - 18/10 = 27/10

Answer:

27/10

Step-by-step explanation:

1. Change the mixed fractions to improper fractions

9/2 -9/5

2. Find the LCD, 10

3. multiply to get the denominator to 10

45/10 - 18/10

4. Deal with the numerators 45-18=27

5. 27/10

Answer: is brainly broken for u too??

Step-by-step explanation:

Answer:

2(x -2)² = 0

Step-by-step explanation:

2(x² - 4x - 4) = 0

2(x -2)² = 0

x = 2

Answer:

[tex]2(3x-2)(x+2)=6x^2-8x-8[/tex]

The factored form of [tex]6x^2-8x-8=0[/tex] is [tex]2(3x-2)(x+2)=0[/tex]

Step-by-step explanation:

[tex]6x^2-8x-8=0[/tex]

The way the quadratic equation was given, we can't have a factored form in the format: [tex](ax-b)(cx+d)[/tex]

First, divide both sides by 2

[tex]3x^2-4x-4=0[/tex]

Now, it is about thinking. From the equation, we will get something in the format:  [tex](ax-b)(cx+d)[/tex]

Let's expand this: [tex](ax-b)(cx+d) = acx^2+adx-bcx-bd[/tex]

From here, we can give some values for those variables, based on the quadratic equation [tex]3x^2-4x-4=0[/tex]:

[tex](3x-b)(x+d) = 3\cdot 1\cdot x^2+3dx-b\cdot 1 \cdot x-bd= \boxed{3x^2+3dx-bx-bd}[/tex]

Once we want the middle term to be -4 and bd to be 4, we can easily evaluate the other variables.

[tex](3x-2)(x+2) = 3\cdot 1\cdot x^2+3(2)x-(2)\cdot 1 \cdot x-(2)(2)= \boxed{3x^2+6x-4x-4}[/tex]

Therefore,

[tex](3x-2)(x+2)=3x^2-4x-4[/tex]

But we are not ready yet!

This is the factored form of [tex]3x^2-4x-4=0[/tex], to get the factored form of the problem equation, just multiply the factored form we got by 2.

[tex]2(3x-2)(x+2)=6x^2-8x-8[/tex]

Answer:

12

Step-by-step explanation:

Because you add 8 to the 40 which is 48 then divide equaling 12

Answer:

12

Step-by-step explanation:

40+8=48

48/4=12

Answer:

x = (4y-6)/17

where x is the  number of pens each student got.

Step-by-step explanation:

No. of boxes = 4

no. of pen in 1 box = y

total no, of pens in 4 box =  No. of boxes *no. of pen in 1 box = 4y

No. of pen took away by Jaden's teacher = 6

no. of pens left = 4y - 6

This, 4y - 6 pen has to be divided among 17 students.

Let  each student get x pen

thus, total no. of pen got by 17 student  = 17x

This, 17x should be equal to total no. of pens available which is 4y-6

17x = 4y-6

=> x = (4y-6)/17

Thus, expression to represent  number of pens each student got

is x = (4y-6)/17

Answer:

4y-6/17

Step-by-step explanation:

Jaden’s teacher had 4 boxes of pens that each contained y pens.

Number of boxes of pen = 4

Number of pens per box = y

Total number of pens = 4 x y = 4y

She took 6 pens out of one of the boxes told her 17 students to divide the remaining pens equally among themselves.

Total number of pens left = 4y - 6

Number of students = 17

Answer:

associative property

The solution is,  property is shown in the matrix addition below is

associative property.

Here, we have,

The property shown in the given matrix addition is associative property.

Let's define associative property first,

The Associative Property of Addition for Matrices states :

Let A , B and C be m×n matrices .

Then, (A+B)+C=A+(B+C) .

Associative Law of Addition of Matrix:

Matrix addition is associative. This says that, if A, B and C are Three matrices of the same order such that the matrices B + C, A + (B + C), A + B, (A + B) + C are defined then A + (B + C) = (A + B) + C.

Since P and Q are of the same order and pij = qij then, P = Q.

Here, from the given information,

we get, A , B and C be 4×1 matrices,

and,  (A+B)+C=A+(B+C)

So, The solution is,  property is shown in the matrix addition below is

associative property.

To learn more on matrix click:

brainly.com/question/30646566

#SPJ7

Answer:

Approximately 17 stars

Answer:

3x +10y  is greater than or equal to 250.

Step-by-step explanation:

The question asks us to write an inequality which shows that both nylon and canvas added should be greater than or equal to 250.

Since we don't know the number of nylon backpacks and canvas backpacks the company makes, we used the variables "x" and "y" to represent the number of backpacks they made from each style.

Answer:

3n + 10c > 250

Step-by-step explanation:

I confirmed it in grandpoint

Answer:9/5

Step-by-step explanation:

Answer:

the question seems incomplete or maybe am unable to solve it

Answer:

the number line with the clear circles

Step-by-step explanation:

Answer:

Cody should run approximately 19.978 meters along the shore before jumping into the water in order to save the child.Thus,

Step-by-step explanation:

Consider the diagram below.

In this case we need to minimize the time it takes Cody to save the child.

Total time to save the child (T) = Time taken along the shore (A) + Time taken from the shore (B)

The formula to compute time is:

[tex]time=\frac{distance}{speed}[/tex]

Compute the time taken along the shore as follows:

[tex]A=\frac{x}{4}[/tex]

Compute the time taken from the shore as follows:

[tex]B=\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}[/tex]

Then the total time taken to save the child is:

[tex]T=\frac{x}{4}+\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}[/tex]

Differentiate T with respect to x as follows:

[tex]\frac{dT}{dx}=\frac{d}{dx}[\frac{x}{4}]+\frac{d}{dx}[\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}][/tex]

    [tex]=\frac{1}{4}-\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}[/tex]

Equate the derivative to 0 to compute the value of x as follows:

                              [tex]\frac{dT}{dx}=0[/tex]

[tex]\frac{1}{4}-\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}=0\\\\\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}=\frac{1}{4}\\\\4\cdot (40-x)=1.1\cdot [\sqrt{70^{2}+(40-x)^{2}}]\\\\\{4\cdot (40-x)\}^{2}=\{1.1\cdot [\sqrt{70^{2}+(40-x)^{2}}]\}^{2}\\\\16\cdot (40-x)^{2}=1.21\cdot [70^{2}+(40-x)^{2}}]\\\\16\cdot (40-x)^{2}-1.21\cdot (40-x)^{2}=5929\\\\14.79\cdot (40-x)^{2}=5929\\\\(40-x)^{2}=400.88\\\\40-x\approx 20.022\\\\x\approx 40-20.022\\\\x\approx 19.978[/tex]

Thus, Cody should run approximately 19.978 meters along the shore before jumping into the water in order to save the child.

Answer:

three terms

Step-by-step explanation:

3x + 2y + 8z

Since we cannot simplify

There are three terms

3x, 2y, 8z

Answer:

Step-by-step explanation:

5x - 9 <= 21

5x <=30

x <= 6