g(x) = x2 – 5x + 2.

Answer:

a) [tex]V(t) = 24 - 2t[/tex]

b) As t increases from 3 to 6, v varies from 18 gallons to 12 gallons.

Step-by-step explanation:

The volume of the tank in terms of the time can be described by the following equation:

[tex]V(t) = V(0) - at[/tex]

In which V(0) is the initial volume and a is the hourly decrease rate.

a. Write a formula that expresses v in terms of t.

The tank initially contains 24 gallons of water, which means that [tex]V(0) = 24[/tex]

Drains at a constant rate of 2 gallons per hour, so [tex]a = 2[/tex]

Then

[tex]V(t) = V(0) - at[/tex]

[tex]V(t) = 24 - 2t[/tex]

b. As t increases from 3 to 6, v varies from _________ to _________

[tex]V(t) = 24 - 2t[/tex]

[tex]V(3) = 24 - 2*3 = 18[/tex]

[tex]V(6) = 24 - 2*6 = 12[/tex]

So as t increases from 3 to 6, v varies from 18 gallons to 12 gallons.

Answer:

f(x) = x³ - 2x²

=>

f(i) = i³- 2i²

Hope this helps!

:)

Answer:

111.60

Question:

Ania bought two books in a bookstore and paid 37.20, and Jurek paid three times more for his. How much did Jurek pay?

Step-by-step explanation:

This is a question on multiplying decimals by natural numbers.

Number if books bought by Ania = 2

Cost for the two books = 37.20

Jurek paid = 3 times the amount Ania paid

Amount Jurek paid = 3×37.20

To multiply decimals with whole numbers, first multiply without the decimals

3×3720 = 11160

3 has no decimal place

37.20 has 2 decimal place

Therefore the answer would be in two decimal place = 111.60

So 3× 37.2= 111.60

Answer: obtuse and scalene

Step-by-step explanation:

Answer:

Obtuse And Scalene

Step-by-step explanation:

trust me!

Answer:

Step-by-step explanation:

In a survey of 1,000 adults living in a big city, 540 participants said that they prefer to get news from the Internet, 330 prefer to watch news on TV, and 130 are rarely interested in the current news. We want to test if the proportion of people getting the news from the Internet is more than 50%. By generating the randomization distribution, we find that the p-value is 0.0057. Choose the correct statement interpreting the p-value.

A.If the proportion of people getting the news from the Internet is not equal to 0.5 then there is a 0.0057 chance of seeing the sample proportion as extreme as the survey results.

B. If the proportion of people getting the news from the Internet is not equal to 0.54 then there is a 0.0057 chance of seeing the sample proportion as extreme as the survey results.

C. If the proportion of people getting the news from the Internet is equal to 0.54 then there is a 0.0057 chance of seeing the sample proportion less extreme compared to the survey results. р

D. If the proportion of people getting the news from the Internet is equal to 0.54 then there is a 0.0057 chance of seeing the sample proportion as extreme as the survey results.

E. If the proportion of people getting the news from the Internet is equal to 0.5 then there is a 0.0057 chance of seeing the sample proportion as extreme as the survey results.

The correct interpretation of P value will be:

if the proportion of people getting the news from internet is equal to 0.5 then there is a 0.0057 chance of seeing the sample proportion as extreme as survey results.

Answer:

The minimum score that she must earn to get admitted is 523.

Step-by-step explanation:

As the scores are normally distributed, we can calculate the probability using the z-score.

The distribution has a mean of 420 and a standard deviation of 80.

We have to calculate the z-score z* that satisfies:

[tex]P(z>z^*)=0.1[/tex]

This happens for z*=1.28155.

Then, we can calculate the score as:

[tex]X=\mu+z\cdot\sigma=420+1.28155\cdot 80=420+102.524=522.524[/tex]

Answer:

  42.67%

Step-by-step explanation:

The annual growth factor for interest at annual rate r compounded quarterly is ...

  (1 +r/4)^4

You want that value to be 1.5:

  1.5 = (1 +r/4)^4

  1.5^(1/4) = 1 +r/4

  (1.5^(1/4) -1) = r/4

  4(1.5^(1/4) -1) = r ≈ 0.426728

The rate r must be about 42.67%.

_____

Comment on the wording

We interpreted the problem to mean the end-of-year amount is 1.5 times the beginning-of-year amount. That is, it is "1.5 times the amount invested."

The word "more" is typically used when addition is involved. For example, "25% more" means 25% of the original is added to the original. We occasionally see "more" where "x times more" is intended to mean "x times", rather than "x times the amount, added to the original amount."

Answer:

0.83

0.63

Step-by-step explanation:

P(V or W) = P(V) + P(W) − P(V and W)

P(V or W) = 0.47 + 0.37 − 0.01

P(V or W) = 0.83

P(not W) = 1 − P(W)

P(not W) = 1 − 0.37

P(not W) = 0.63

a. the probability that the computer contains either a virus or a worm or both is 0.83

b. The probability that the computer does not contain a worm is 0.63.

(a)

The probability is

P(V or W) = P(V) + P(W) − P(V and W)

P(V or W) = 0.47 + 0.37 − 0.01

P(V or W) = 0.83

(b) The probability is

P(not W) = 1 − P(W)

P(not W) = 1 − 0.37

P(not W) = 0.63

Learn more about the probability here: https://brainly.com/question/16096170

Answer:

The answer is A (1,-3/2)

Step-by-step explanation:

Add both x coordinates, divide by 2

Add both y coordinates, divide by 2

Answer:

hope this helps you

Answer:

Omar can put together 6 outfits.

66.67% probability of Omar’s outfits including a red T-shirt or red shorts

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

-How many different outfits can Omar put together?

For each t-shirt, that are two options of shorts.

There are 3 t-shirts.

3*2 = 6

Omar can put together 6 outfits.

What is the probability of Omar’s outfits including a red T-shirt or red shorts?

Red t-shirt and red shorts

Red t-shirt and black shorts

Green shirt and red shorts

Yellow shirt and red shorts

4 desired outcomes.

4/6 = 0.6667

66.67% probability of Omar’s outfits including a red T-shirt or red shorts

Answer: 600 of the 500ml energy drinks be sold be sold at $45

Step-by-step explanation:

The linear relationship between the price (p) of 500ml soft drink and the number sold (x) is expressed as

x = ap + b

At N$20 she sells 1500 of the 500ml soft drinks. This means that the first equation would be

1500 = 20a + b - - - - - - - - -1

the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. This means that the new quantity sold is 1500 - 200 = 1300

The price at which they were sold is

20 + (50/100 × 20) = $30

The second equation would be

1300 = 30a + b - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

200 = - 10a

a = 200/- 10 = - 20

Substituting a = - 20 into equation 2, it becomes

1300 = 10 × - 20 + b

1300 = - 200 + b

b = 1300 + 200 = 1500

The linear relationship becomes

x = - 20p + 1500

If x = 600, then

600 = - 20p + 1500

- 20p = 600 - 1500 = - 900

p = - 900/ - 20

p = $45

Answer:

a= 2/5

b= -3/5

Step-by-step explanation:

We need to multiply the numerator and denominator by -i (conjugate) to cancel out i in the denominator

[tex]\frac{(3+2i)(-i)}{5i(-i)}[/tex]

This simplifies to:

[tex]\frac{-3i+-2i^{2} }{-5i^{2} }[/tex]

This further simplifies to:

[tex]\frac{-3i +2}{5}[/tex]

Can be rewritten as:

[tex]\frac{2}{5} +-\frac{3}{5} i[/tex]

a = 2/5

b = -3/5

Answer: the answer is A 5 units

The length of L'L in the dilated figure is 5 units.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Dilation is the increase or decrease in size of a figure.

Triangle JKL was dilated by 1/3 with M as the center of dilation to form J'K'L'.

Given that ML' = 2.5 units, hence:

L'L = (2.5 * 3) - 2.5 = 5 units

The length of L'L in the dilated figure is 5 units.

Find out more on transformation at: https://brainly.com/question/1620969

Answer:

4s< 32

Step-by-step explanation:

Congruent sides mean they are all the same length

Let the length be s

Perimeter means add the sides

s+s+s+s < 32

4s< 32

Answer:

4s>32

Step-by-step explanation:

your welcome dears

Answer:

he will be 25

Step-by-step explanation:

36 monthly payments left/12 payments a year = 3 years. 22 + 3 = 25

Answer:

d) 50

Step-by-step explanation:

40 + 90 + p = 180

p = 50

Answer:

The lines would intersect at: (6, -4)

Step-by-step explanation:

I graphed both lines.

Answer:

(4,-2)

Step-by-step explanation:

The equation for the graphed line is [tex]y=\frac{1}{2} x-4[/tex] as it has a slope of [tex]\frac{1}{2}[/tex] and a y-intercept of -4.

Now that we have the two equations, we can set them equal to each other to find the x-value at which they intersect

[tex]\frac{1}{2} x-4=-x+2[/tex]

First, we can add 4 to each side

[tex]\frac{1}{2} x=-x+6[/tex]

Then we can add x to each side

[tex]\frac{3}{2} x=6[/tex]

Now we need to divide both side by [tex]\frac{3}{2}[/tex], which is the same thing as multiplying by [tex]\frac{2}{3}[/tex]

[tex]x=6*\frac{2}{3} \\\\x=\frac{12}{3} \\\\x=4[/tex]

Now that we have the x-value, we can plug it into one of the equations to see the y-value for where they intersect.

[tex]y=-x+2\\\\y=-(4)+2\\\\y=-2[/tex]

This means that the coordinates for the intersection of these two lines would be [tex](4,-2)[/tex]

3/4, 6/8, 9/12, 12/16 , 15/20, 18/24, 21/28, 24/32 , 27/36, 30/40, 33/44, 36/48 , 39/52, 42/56, 45/60, 48/64 , 51/68, 54/72, 57/76, 60/80, ect..

I hope this is what you are looking for :)

Answer:

Step-by-step explanation:

[tex]2xsin(2y)dx-(x^2+10) cosy dy =0\\\\\frac{2x}{x^2 + 10}dx= \frac{cosy}{sin(2y)}[/tex]

Take integration both side (apply substitution for the left hand side, apply sin(2y) = 2 sin(y) cos(y) for the right hand side) you will have the condition.

Problem solved

Answer:1232m^3

Step-by-step explanation:

1/3 *22/7*7^2*24

1232m^3

Answer:

$25

Step-by-step explanation

If oliver had $43 before his birthday he was given (+) an amount of money, in order to find out  how much money was given you need to reverse the equation (-) $68-$43= $25

Answer: 363 cm squared

Step-by-step explanation:

So we can split the shape into 1 triangle and 3 rectangles.

We can start with the top right rectangle which is a 4 by 5.

4*5 = 20 cm squared

We can now do the horizontal rectangle. We need to find the dimensions firs by subtracting 4 from 31 to find the length and add 4 and 5 to find the height.

This means the dimensions are 27 by 9.

27 * 9 = 243 cm squared

Now the final square toward the bottom left will be a 10 by 7.

10 * 7 = 70 cm squared.

Now for the final piece is the triangle in the bottom left. We need to first find the height which we can determine by taking the the right hand side values of 10 , 4 and 5 and adding those together then subtracting that number by 13 to get the missing length that will add to 6 to find the height.

10 + 4 + 5 = 19

19 - 13 = 6

6 + 6 = 12

Now that we have the height and base of the triangle we solve for the area.

0.5 * 5 * 12 = 30 cm squared

Now we add all the areas together to find the total area.

20 + 243 + 70 + 30 = 363 cm squared

Answer:

C

Step-by-step explanation:

Measure of Arc FED = 51+79

= 130°

Since the measures of arcs and angles are the same

Hence

<FED = 130°

Answer:

m = - 5

Step-by-step Explanation:

[tex]-3(1-5m)=-38+8m \\ \\ - 3 + 15m = - 38 + 8m \\ \\ 15m - 8m = 3 - 38 \\ \\ 7m = - 35 \\ \\ m = \frac{ - 35}{7} \\ \\ \huge \purple{ \boxed{m = - 5}}[/tex]

Answer:

-5

Step-by-step explanation:

Answer:

$5,882

Step-by-step explanation:

To calculate the money Lindsay needs today, you can use the following formula to calculate the present value:

PV=FV/(1+i)^n

PV= present value

FV= future value= $8,000

i= interest rate= 8%

n= number of periods= 4

PV= 8,000/(1+0.08)^4

PV=8,000/1.08^4

PV=8,000/1.36

PV= 5,882

According to this, Lindsay will need to have $5,882 in the account today so she will have enough to pay for the repairs in four years.

Answer: The graph is:

9514 1404 393

Answer:

Step-by-step explanation:

In step 1 Angela used the distributive property to eliminate both sets of parentheses. In step 2, she found each of the products she indicated in step 1. In step 3, she combined like terms.

Answer:

the answer is a,d,e

Step-by-step explanation:

Complete Question:

Dustin is buying carpet for the living room. If the length of the room is 21 ft and the width

is 11 ft, how many square feet of carpet does he need to buy?

Answer:

231 ft²

Step-by-step explanation:

==>GIVEN:

Length of room (L) = 21 ft

Width of room (W) = 11 ft

==>REQUIRED:

Square feet of carpet to be bought = area of the rectangular room

==>SOLUTION:

The room to be covered with carpet is rectangular in shape. In order to ascertain the square feet of carpet to be bought, we need to calculate the area of the room by using the formula for area of rectangle.

Thus, area of rectangle (A) = Length (L) × Width (W)

A = 21 × 11

A = 231 ft²

Square feet of carpet to be bought = 231 ft²

Answer:

[tex] \sqrt{3} - 1[/tex]

Step-by-step explanation:

[tex](1 + \sqrt{3} )(2 - \sqrt{3} ) \\ 2 - \sqrt{3} + 2 \sqrt{3} - 3 \\ = \sqrt{3} - 1[/tex]