PROBLEM SOLVING The profit P (in millions of dollars) for a shoe manufacturer can be modeled by P= -21x3 + 46x where x
is the number (in millions) of shoes produced. The company now produces 1 million shoes and makes a profit of $25 million, but it
would like to cut back production. What lesser number of shoes could the company produce and still make the same profit?

Answer:2

Step-by-step explanation:

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Answer:

27.4%

Step-by-step explanation:

Step one:

given

original cost $69

seling price $52

Required

The percent reduction

Step two:

% reduction= change in price/original price*100

% reduction= 69-52/62*100

% reduction=17/62*100

% reduction= 0.274*100

% reduction= 27.4%

Answer:

Step-by-step explanation:

here you go mate'

step 1

X / 2 + 1 > 3  equation

step 2

X / 2 + 1 > 3  simplify the equation

step 3

1/ 2 + 1 > 3  subtract the number at the front

1 / 2 + 1 (-1)> 3(-1)

step 4

1/2x>2  multiply

answer

x>4

Denominators= 4 and 6

LCM of 4 and 6 => 12

So, the least common denominator of the given fractions is 12.

Hope it helps!

Answer:

12

Step-by-step explanation:

1/4 and 5/6

4, 8, 12

6, 12

Answer:

42:14

42 cats and 14 fish

Answer:

3:1

Step-by-step explanation:

42 : 14 ---> 42/14 = 21/7 = 3/1 ---> 3 : 1

Answer:

[tex]\dfrac{31}{2}+\dfrac{27}{2}i[/tex]

Step-by-step explanation:

The given complex number is:

[tex]z=\dfrac{(2+3i)(4-7i)(1+i)}{(1^2-i^2)}[/tex]

Firstly we can solve (2+3i)(4-7i)(1+i)

= 2(8)+2(-7i)+4(3i)+3i(-7i²)× (1+i)

= (16-14i+12i-21i²i)× (1+i)

Since, i² = -1

= (16-14i+12i-21(-1)i)× (1+i)

= (16-14i+12i+21)× (1+i)

= (29-2i)(1+i)

= 31+27i

Denominator : (1-i²)

= (1-(-1))

= 2

[tex]\dfrac{(2+3i)(4-7i)(1+i)}{(1^2-i^2)}=\dfrac{31+27i}{2}\\\\=\dfrac{31}{2}+\dfrac{27}{2}i[/tex]

Hence, the correct answer is [tex]\dfrac{31}{2}+\dfrac{27}{2}i[/tex].

Answer:

slope = - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 5x + 9 ← is in slope- intercept form

with slope m = - 5

Answer:

$23.75

Step-by-step explanation:

5.50*2=11

4.25*3=12.75

11.00+12.75=23.75

Answer:

The answer is 1.2

Step-by-step explanation:

Answer: See explanation

Step-by-step explanation:

You didn't really say what you want to know but let me explain.

The gross domestic product of an economy is the value of the goods and.d services that are being produced in such an economy. The gross domestic Product is used to know how well an economy is doing

Per capita gross domestic product (GDP) is a used to know the economic output of a particular country per person. It is calculated by dividing the GDP of such an economy by the population.

For example, let us say the GDP of a country is $800,000,000 and the population is 3,500,254. Therefore, the per capita GDP would be:

= $800,000,000 / 3,500,254

= $228.56 per person

Answer:total market value of goods and services produced within a year divided by total population

Step-by-step explanation:

basic defenition

Answer:

using a scale of 2", is another way to say, "is going to grab the original, and blow it up to 2 times as large".

so, the resulting copy is twice as large as the original.

Step-by-step explanation:

Answer: A picture is photocopied by using a scale factor of 2. Each side of the photocopy of the picture is

enlarged by a factor of 2.

enlarged by a factor of One-half.

reduced by a factor of 2.

reduced by a factor of One-half

Step-by-step explanation:

Answer:

[tex]6s - \frac{3}{4}=3(2s - \frac{1}{4})[/tex]

Step-by-step explanation:

Given

[tex]6s - \frac{3}{4}[/tex]

Required

Factorize

[tex]6s - \frac{3}{4}[/tex]

Express 6s as 3 * 2s

[tex]3 * 2s - \frac{3}{4}[/tex]

Express 3/4 as 3 * 1/4

[tex]3 * 2s - 3 * \frac{1}{4}[/tex]

Factorize:

[tex]3(2s - \frac{1}{4})[/tex]

Hence:

[tex]6s - \frac{3}{4}=3(2s - \frac{1}{4})[/tex]

Answer:

D

Step-by-step explanation:

There are 5 ways to prove congruence:

1. SSS (3 sides)

Not applicable here

2. SAS (side-angle-side)

This requires a side, then an angle in between, and another side. This cannot be met with angles (as we currently have side-angle) so none of these are possible

3. ASA (angle-side-angle)

This is a side between angles, so if we squished line AC between angles C and A, and angle A=angle O, this would be true -- B is one answer

4. AAS (angle-angle-side)

Similar to option 3, but would be with angles T and G instead,

D is another answer

5. hypotenuse leg (only in right triangles)

The reason T and G fit AAS is because we hit angle T, then angle C, then side CA, all congruent with G, D, and DO in that order.

Answer:

5p+4>14 (A)

Step-by-step explanation:

Open dot means that the value is not included.

Answer:

$11.80

Step-by-step explanation:

3*$1.10 = $3.30

price without tax,

= 38.70-3.30

= 35.40

Cost of each CD,

= 35.40/3

= 11.80

Answer:

11.80 dollars

Step-by-step explanation:

Well, first I would multiply 1.10 by 3 which is 3.30 then subtract 38.70 - 3.30 and get 35.40, and finally divide 35.40 by 3 to get 11.80

Answer:

b) [tex]d[/tex] = 84 miles

c) [tex]h[/tex] = 14.3 hours

Step-by-step explanation:

Given that:

The speed of Colton is constant while riding a bike.

Formula for speed is given as:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

If speed is constant, then we can deduct that:

[tex]Distance \propto Time[/tex]

Time = 3.5 hours

Distance = 49 miles

Therefore, the speed will be equal to:

Speed = [tex]\frac{49}{3.5}[/tex] = 14 miles/hr

b) Given that:

Time = 6 hours, then we have to find the distance to be hiked if the speed is same.

[tex]14 = \dfrac{d}{6}\\\Rightarrow d = \bold{84}\ miles/hr[/tex]

c) Given that:

Distance = 200 miles

Number of hours = [tex]h[/tex]

To find, the value of [tex]h[/tex].

[tex]14 = \dfrac{200}{h}\\\Rightarrow h = \dfrac{200}{14}\\\Rightarrow h = \bold{14.3}\ hours[/tex]

Answer:

2cos(330º)

Step-by-step explanation:

both equal to √3

Expressing 4cos2(165°) – 2 as a single trignometric function, it will be written as : 2cos(330º)

Trigonometric function can be defined as real functions in mathematics that forms a relationship between an angle of a right-angled triangle to the ratio of the length of two sides.

Trigonometric function is very important as it is mostly concerned with functions of angles and their application in calculation

In conclusion, to express 4cos2(165°) – 2 as a single trignometric function, it will be written as : 2cos(330º)

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Answer:

16. this would be "base" but that isn't an option...

17.  R, exponent

24. F, term

4x and –3(–x) are negative.

Answer:

a)

x      -3         -2         -1         0          1            2         3

y       0          8          6         0         -4           0        18

b)

see in the table, at x = {-3; 0; 2}, y = 0

=> x = {-3; 0; 2} is the solutions of the equation x³ + x² - 6x = 0

Step-by-step explanation:

a) 0 and 6  will be written in the given blank spaces.

b) The value of x for the given equation is 0, -3 and 2.

It is a method for finding the values of variable, by substituting the value of one variable to get the another.

To solve a polynomial equation, first write it in standard form. Once it is equal to zero, factor it and then set each variable factor equal to zero.

a). We have, an equation

[tex]y = x^{3}+x^{2} -6x[/tex]

so, at x = -3

[tex]y = -3^{3} +(-3)^{2} -6(-3)[/tex] =  -27+9+18 = 0   (substitute x = -3 in the given equation)

at x = -1

y = [tex]-1^{3} +(-1)^{2} -6(-1) = -1+1+6 = 6[/tex]

Hence, 0 and 6 will we written the blank spaces of the given table.

b). We have an equation

[tex]x^{3} +x^{2}-6x = 0[/tex]

⇒ [tex]x(x^{2} +x-6)=0[/tex]

⇒ [tex]x (x^{2} +3x-2x-6)=0[/tex]

⇒ [tex]x(x(x+3)-2(x+3))=0[/tex]

⇒ [tex]x(x+3)(x-2)=0[/tex]

⇒ [tex]x = 0,-3 and 2[/tex]

Hence, 0, -3 and 2 are the solutions of the given equation.

Learn more about substitution method  here:

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Step-by-step explanation:

The angle at B is the same as the angle at E so equate them to each other to find x

2x+4=40°

2x=40-4

2x=36

x=36/2=18

Answer:

We conclude that 520 tickets will be sold in the first 5 hours of the tickets go on sale.

Hence, option A is true.

Step-by-step explanation:

Given that the tickets to a concert went on sale at 10 a.m. by 12 p.m.

Given that the tickets sold in 2 hours = 208

Thus,

Unit rate = 208 tickets / 2 hours

              = 104 tickets per hour

Therefore,

Tickets sold in the first 5 hours of the tickets go on sale:

104 × 5 = 520 tickets

Therefore, we conclude that 520 tickets will be sold in the first 5 hours of the tickets go on sale.

Hence, option A is true.

Answer: x = 4

Step-by-step explanation:

first, we calculate it.

-x = 8 - 3x

then, we move the variable to the left.

-x + 3x = 8

then, we collect like terms.

2x = 8

finally, we divide both sides.

x = 4

Answer:

To write 65/100 as a decimal you to divide numerator by the denominator of the fraction.

We divide now 65 by 100 what we write down as 65/100 and we get 0.65.

And finally we have:

65/100 as a decimal equals 0.65

Step-by-step explanation:

Answer:

Felicia needs 3.17 minutes to run once around the track

Step-by-step explanation:

Subtraction

Shaq is known to run once around the track in 8.07 minutes. Felicia runs once around the track in 4.90 less than Shaq.

We don't know how long does it take Felicia to run once around the track, but we can find it by subtracting the time done by Shaq with the difference between their relative times.

Felicia takes 8.07 min - 4.90 min = 3.17 min.

Felicia needs 3.17 minutes to run once around the track

Answer:

y=36

Step-by-step explanation:

using that 63° angle there on the right, we know that the other angle for a 180° total is 117°.

Now we have to figure out y using that total of 117

(4y-27)=117

4y-27=117

4y=144

y=36

Now if we substitute y...

(4y-27)=117

(4(36)-27)=117

(144-27)=117

(117)=117

Answer: Choice A) The value of s(x) depends on the value of x, since s is a function of x.

The outer letter s tells us what the function's name is. It's the dependent variable and it might be handy to tie it to the y variable. The x is the independent variable. It changes freely without relying on what s happens to be.

Answer:  A. The value of s(x) depends on the value of x, since s is a function of x.

Step-by-step explanation: s(x) is the output of the function when a given value of x is calculated according the operations in the function.

Answer:

y=−3

Step-by-step explanation:

(−2)(5)−7y=11

−10+−7y=11

−7y−10=11

Step 2: Add 10 to both sides.

−7y−10+10=11+10

−7y=21

Step 3: Divide both sides by -7.

−7y

−7

=

21

−7

Answer:

wHaT?

Step-by-step explanation: