A company wants to decrease their energy use by 13%. If their electric bill is currently $1,800 a month, what will their bill be if they are successful?

Answer:      [tex]\dfrac{11}{221}[/tex]

Step-by-step explanation:

We know that the total number of cards in a standard deck = 52

Then the number of ways to draw any two card = 52 x (52-1)

= 52 x 51 = 2652   [By Multiplicative principle]

Also , there are 12 face cards in a standard deck , so the number of ways to draw two face cards in succession = 12 x (12-1)

12 x 11= 132   [By Multiplicative principle]

Then, the probability of drawing 2 cards in succession (without replacement) from a standard deck and having them both be face cards would be

[tex]\dfrac{\text{ Number of ways to draw 2 face cards}}{\text{Total number of ways to draw two cards}}[/tex]

[tex]=\dfrac{132}{2652}=\dfrac{11}{221}[/tex]

Hence, the required probability is  [tex]\dfrac{11}{221}[/tex] .

Answer: 6m/s²

Step-by-step explanation:

Let

Initial Velocity be V_0 = 4m/s

Time be t = 3s

Final Velocity be V_n = 22m/s

Acceleration be A = (Final Velocity - Initial Velocity) / time

A = (V_n - V_0) / t

= (22 - 4) / 3

= 18/3

= 6m/s²

The average acceleration of the roller coaster is 6 m/s².

The average acceleration can be calculated by using the formula:

average acceleration = (final velocity - initial velocity) / time interval

In this case, the initial velocity is 4 m/s, the final velocity is 22 m/s, and the time interval is 3 seconds. So, the average acceleration is:

average acceleration = (22 m/s - 4 m/s) / 3 s = 6 m/s²

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Answer:

The answer to your question is      12n² + 6n - 3

Step-by-step explanation:

Polynomial

                   3(4n² + 2n - 1)

Distributive property, this property lets us multiply a sum by multiplying each term of the sum separately and if possible simplify like terms.

Solution

                 3(4n²) + 3(2n) - 3(1)

                 12n² + 6n - 3

In a normal distribution, the probability that a random variable X is equal or greater than the mean is always 0.5. Therefore, P(X ≥ 75) is 0.500.

In the context of normal distribution, when the value of the random variable X is equal to the mean, the probability is 0.5. So, in this case, the mean is 75. Hence, if asked the probability P(X ≥ 75), the answer would be 0.500. Remember that the area under the curve of a normal distribution indicates the probability, and when X = mean, it divides the area into equal halves, hence the probability is 0.5 or 50%.

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Answer:

  3/10

Step-by-step explanation:

Stephen works 6 hours of the total of 20 hours worked. If the chores are proportional to the time worked, then Stephen does 6/20 = 3/10 of the chores.

Answer:

0.1566

Step-by-step explanation:

We are given that probability of survival of computer chip for more than 500 temperature is

P(S)=0.42

Also, we are given that if the computer chips not survives then it was made by company A. So,

P( A/S')=0.73

We have to find the probability of computer chips  not survives and not made by company A i.e. P(A'∩S')=?

P(A/S') can be written as

P(A/S')=P(A∩S')/P(S')

where P(S')=1-P(S)=1-0.42=0.58

and P(A∩S')=P(A)-P(A∩S)

P(A/S')=P(A)-P(A∩S)/0.58

0.73*0.58=P(A)-P(A∩S)

P(A)-P(A∩S)=0.4234

P(A'∩S')=1-P(A∪S)=1-[P(S)+P(A)-P(A∩S)]=1-[0.42+0.42340]=0.1566

Thus, the probability of computer chips  not survives and not made by company A  is 15.66%.

Answer:

The answer to your question is width = 6 ft; length = 24 ft

Step-by-step explanation:

Data

Area = 144 ft²

width = w

length = l

The width is 1/4 of the length

Formula

Area = width x length = w x l

Length = 4 width     l = 4w

Process

1.- Substitute length in the first equation

                       Area = w(4w)

Simplify

                       Area = 4w²

2.- Solve for w

                      w = [tex]\sqrt{\frac{Area}{4}}[/tex]

Substitution

                      w = [tex]\sqrt{\frac{144}{4}}[/tex]

Simplification

                      w = [tex]\sqrt{36}[/tex]

Result

                      w = 6 ft

3.- Find l

                       l = 4(6)

                       l = 24 ft

Answer:

Experimental group

Step-by-step explanation:

In a  psychology experiment, the test gathering (or trial condition) alludes to the gathering of members who are presented to the free factor. These members get or are presented to the treatment variable.  

The free factor is changed in the exploratory gathering.

For example : A human test gathering could get another prescription, an alternate type of advising, or some nutrient enhancements

Answer: 352 miles

Step-by-step explanation:

At the point where the car overtook the bus, the car and the bus would have travelled the same distance.

Let x represent the distance covered by bus and the car before the car overtook the bus.

Let t represent the time taken by the bus to travel x miles.

The bus was traveling at 64 km an hour.

Distance = speed × time

Distance travelled by the bus in t hours would be

x = 64 × t = 64t

if the bus has a 1.5 hour Headstart, it means that the car started moving 1.5 hours after the bus has moved.

Therefore, time spent by the car would be t - 15 hours.

The car traveling at 88 km an hour

Distance covered by the car in t - 1.5 hours would be

x = 88(t - 1.5) = 88t - 132

Since the distance covered is equal, then

88t - 132 = 64t

88t - 64t = 132

24t = 132

t = 132/24

t = 5.5 hours

Therefore, the distance from the starting point when the car overtook the bus would be

x = 64 × 5.5 = 352 miles

Answer:

166.284 KJ

Step-by-step explanation:

We are given that

Mass of sled =70.9 kg

Displacement of sled=1.24 km

Coefficient of friction=[tex]\mu=[/tex]0.193

Acceleration due to gravity=[tex]g=9.8m/s^2[/tex]

We have to find the work done by the dogs in units KJ

Friction force=[tex]\mu mg[/tex]

Friction force =f=[tex]0.193\times 70.9\times 9.8=134.1N[/tex]

Force applied by team of dogs=Friction force

F=f=134.1 N

Work done=[tex]F\times s[/tex]

We have s=1.24 km=[tex]1.24\times 1000=1240m[/tex]

1 km= 1000 m

Work done=[tex]134.1\times 1240=166284 J[/tex]

1 KJ=1000J

Work done=[tex]\frac{166284}{1000}=166.284KJ[/tex]

Hence, the work done by the dogs=166.284 KJ

Answer:

The Inequality representing the number of hours she want to babysit to make a profit is [tex]5+3x>26[/tex].

Katie should babysit for more than 7 hours in order to make profit.

Step-by-step explanation:

Given:

Money spent on advertising = $26

Initial fee = $5

Hourly charge = $3

We need to find the number of hours she want to babysit to make a profit.

Solution:

Let the number of hours be 'x'.

Now we can say that;

The sum of Initial fee and Hourly charge  multiplied by number of hours should be greater than Money spent on advertising .

framing in equation form we get;

[tex]5+3x>26[/tex]

Hence The Inequality representing the number of hours she want to babysit to make a profit is [tex]5+3x>26[/tex].

On Solving the above Inequality we get;

Now Using Subtraction property of Inequality we will subtract both side by 5 we get;

[tex]5+3x-5>26-5\\\\3x>21[/tex]

Now Using Division Property of Inequality we will divide both side by 3 we get;

[tex]\frac{3x}{3}>\frac{21}{3}\\\\x>7[/tex]

Hence Katie should babysit for more than 7 hours in order to make profit.

Interpretation:

when x=7

Amount earned will be = [tex]5+3x=5+3\times7 =5+21=\$26[/tex]

Profit earned will be = Amount earned - Money spent on advertising = 26 -26 =0

when x= 8

Amount earned will be = [tex]5+3x=5+3\times8 =5+24=\$29[/tex]

Profit earned will be = Amount earned - Money spent on advertising = 29 -26 =$3

Hence at 7 hours of babysitting profit will be 0 and at 8 hours of babysitting profit will be $3.

2.16x+4.40(16-x) = 2.44(16)

2.16x+70.40-4.40x = 39.04

-2.24x = -31.36

x= 14

So, there are 14 packets of the sweet pepper seeds at 2.16 and 16-14 = 4 packets of the hot pepper seeds at 4.40

Square feet of rectangle = 50 x 10 = 500 square feet.

The perimeter of the rectangle is 50 + 50 + 10 + 10 = 120 feet.

Change to a square: 120/4 = 30

The square would have a side length of 30 feet.

Area of the square = 30 x 30 = 900 square feet.

The square is 900. - 500 = 400 square feet more.

Answer: you would have travelled 500 miles.

Step-by-step explanation:

Distance travelled = speed × time

Japanese bullet trains travel at an average speed of 150 miles per hour.

If you take the bullet train and leave Tokyo at 9:00 AM, by 12:20, it would be noon. The time that you would have spent would be

12:20 - 9:00 = 3 hours 20 minutes.

Converting to hours, it becomes

3 + 20/60 = 3 + 1/3 = 10/3 hours

Therefore, the number of miles that you would have travelled would be

10/3 × 150 = 500 miles

Divide the number of women by the percentage of women:

23 / 0.66 = 34.84

Round the answer as needed.

The total number of students in the​ class is 35.

In mathematics, a percent is a number or ratio expressed as a fraction of 100. It is often denoted using percentage sign "%".

Now it is given that,

Percentage of women in the class = 66%

Number of women = 23

Let x be the total number of students in the class.

Now, Since Number of women = 23

Therefore,

x of 66% = 23

or, 66x/100 = 23

or, 66x = 23*100

or, x = 2300/66

or, x = 34.84

⇒ x ≈ 35

Thus, the total number of students in the​ class is 35.

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Answer:

The answer to your question is  (2, 9)

Step-by-step explanation:

Data

A (5, 9)

B (-1, 9)

Formula

Xm = [tex]\frac{1 + x2}{2}[/tex]

Ym = [tex]\frac{y1 + y2}{2}[/tex]

Substitution

Xm = [tex]\frac{5 - 1}{2}[/tex]

Xm = [tex]\frac{4}{2} = 2[/tex]

Ym = [tex]\frac{9 + 9}{2} = \frac{18}{2} = 9[/tex]

Midpoint = (2, 9)

Answer:

Step-by-step explanation:

P=1/2 *1/3=1/6

Answer:

∴ MNOP is Rectangle

midpoint of XY (N) : (a , - 2b)

Step-by-step explanation:

W (0 , 4b)   X ( 2a , 0)   Y (0 , -4b)   Z (-2a , 0)

M (midpoint of WX) : ( (0 + 2a)/2 , (4b + 0)/2)  i. e. (a , 2b)

N (midpoint of XY) : ( (2a + 0)/2 , (0 - 4b)/2)  i. e. (a , - 2b)

O (midpoint of YZ) : ( (0 - 2a)/2 , (- 4b + 0)/2)  i. e. (- a , - 2b)

P (midpoint of ZW) : ( (0 - 2a)/2 , (4b + 0)/2)  i. e. (- a , 2b)

MN: length = 2b + 2b = 4b     MN segment perpendicular to x axis (slope undefined)

NO: length = a + a = 2a     NO segment parallel to x axis (slope = 0)

OP: length = 2b + 2b = 4b     OP segment perpendicular to x axis (slope undefined)

PM: length = a + a = 2a     NO segment parallel to x axis (slope = 0)

MN = OP and MN // OP and MN ⊥ PM

NO = PM and NO // PM and NO ⊥ OP

∴ MNOP is Rectangle

midpoint of XY (N) : (a , - 2b)

please draw graph to prove

Answer:

Number of Small Cones Sold=22

Number of Large Cones Sold=34

Step-by-step explanation:

Suppose,

Number of Small Cones Sold: s

Number of Large Cones Sold: l

For the condition that, larges cones sold were 12 more than small ones, equation would be

[tex]s-l=12....................................... (i)[/tex]

and for the total revenue condition of $163

[tex]2*s+3.5*l=163.........................(ii)[/tex]

By solving equation (i) and (ii) simultaneously, we get

s=22

and

l=34

Hence, small cones sold would be 22 and large cones sold would be 34.

Answer:

Decrease and financing section

Step-by-step explanation:

The cash flows statement categorizes activities into 3 groups namely; Operating, Investing and Financing.

Operating activities captures the changes to current assets and liabilities such as inventory, trade payables and trade receivables, net income, depreciation etc.

Investing has elements such as sale and purchase of fixed asset. While financing dealings with elements around equity changes and long term debts.

As such the payment of long term debt will be reported in the financing activities section as a decrease because it results in the out flow of cash.

Repayment of a long-term debt during the year is reported as a decrease in the cash flows from financing activities section on the statement of cash flows. This reflects the money used to repay the debt.

When a company repays a long-term debt during the year, it is reported as a decrease in the cash flows from financing activities section on the statement of cash flows.

This decrease reflects the outgoing funds used to repay the debt. For example, in the case of Singleton Bank's change in business plan, their balance sheet would reflect the change in assets from the repayment of a loan, such as the one to Hank's Auto Supply for $9 million.

As a result, there would be a corresponding decrease in cash flows from financing activities by the same amount in the statement of cash flows. The decrease would indicate the outflow of money used to retire the long-term debt.

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Answer:

Out of  300 teenagers 54 would be expected to get their news from a newspaper.

Step-by-step explanation:

Given:

A recent survey reported that out of 50 teenagers, 9 said they get most of their news from a newspaper.

Now, at this rate, out of 300 teenagers to find the number of teenagers to get their news from a newspaper.

So, as given 9 out of 50 teenagers said they get most of their news from a newspaper.

Thus, 9 : 50 is the ratio.

At this rate, out of 300 teenager.

Let the number of teenagers to get their news from a newspaper be [tex]x.[/tex]

Thus, the ratio is [tex]x:300.[/tex]

Now, to get the number of teenagers we set proportion:

[tex]\frac{9}{50} =\frac{x}{300}[/tex]

So, to solve by using cross multiplication method:

[tex]\frac{9}{50} =\frac{x}{300}[/tex]

By cross multiplying we get:

[tex]2700=50x[/tex]

Dividing both sides by 50 we get:

[tex]54=x[/tex]

[tex]x=54.[/tex]

Therefore, out of  300 teenagers 54 would be expected to get their news from a newspaper.

Answer:The efficiency is (d).94%

Step-by-step explanation:

The efficiency:

E=100× (output/input)

So the input is 4000W and the out put is 3760W

From the above formula

E=100×(3760/4000)

E=376000/4000

E=94%

Answer:

  a = 0

Step-by-step explanation:

I find a graphing calculator useful for such questions. It shows the solution to be a = 0. For the graph, we have rewritten the equation from

  (1/7)^(3a+3) = 343^(a-1)

to

  (1/7)^(3x+3) -343^(x-1) = 0 . . . . . this graphing calculator likes x for the independent variable

__

If you recognize that 343 is the cube of 7, you might solve this by taking logarithms to the base 7.

 (7^-1)^(3a+3) = (7^3)^(a-1)

Equating exponents of 7*, we get ...

  -(3a+3) = 3(a -1)

  -3a -3 = 3a -3 . . . . . eliminate parentheses

  0 = 6a . . . . . . . . . . . add 3+3a

  0 = a . . . . . . . . . . . . divide by 6

_____

* Equating exponents of 7 is the same as taking logarithms to the base 7. Here, we use the rules of exponents ...

  1/a^b = a^-b

  (a^b)^c = a^(bc)

Answer:

B. 0

Step-by-step explanation:

:)

Answer:

B) False                  

Step-by-step explanation:

We are given the following in the question:

The first term in an arithmetic sequence is 1.

[tex]a_1 = a =1[/tex]

The second term in an arithmetic sequence is 2.

[tex]a_2 = 2[/tex]

Difference between each pair of consecutive terms in the sequence

[tex]=a_2-a_1\\= 2 - 1\\= 1[/tex]

Statement:

The difference between each pair of consecutive terms in the sequence is [tex]1\frac{2}{5}[/tex]

Thus, the given statement is false since the  difference between each pair of consecutive terms in the sequence is equal to difference between first an second term of arithmetic sequence which is 1 not [tex]1\frac{2}{5}[/tex]

Answer:

Second well was  [tex]103 \frac{3}{6}\ m[/tex] deep below the surface.

Step-by-step explanation:

Given:

Depth of First well = [tex]46\frac{2}{3}\ m[/tex]

[tex]46\frac{2}{3}\ m[/tex] can be Rewritten as [tex]\frac{140}{3}\ m[/tex]

Depth of First well = [tex]\frac{140}{3}\ m[/tex]

Also Given:

The second well had more water, and was [tex]77\frac{5}{6}\ m[/tex]  deeper than the first well.

[tex]77\frac{5}{6}\ m[/tex] can be Rewritten as [tex]\frac{467}{6}\ m[/tex]

Hence We can say that;

Depth of second well is equal to  [tex]\frac{467}{6}\ m[/tex] plus Depth of First well.

framing in equation form we get;

Depth of second well = [tex]\frac{467}{6}+\frac{77}{3}[/tex]

Now the denominators are common so we can solve the numerators

now to solve the fractions we need to make the denominator common we will use L.C.M we get;

Depth of second well = [tex]\frac{467\times1}{6\times1}+\frac{77\times2}{3\times2}= \frac{467}{6}+\frac{154}{6}[/tex]

Now the denominators are common so we can solve the numerators.

Depth of second well = [tex]\frac{467+154}{6}=\frac{621}{6}\ m \ \ OR\ \ 103 \frac{3}{6}\ m[/tex]

Hence Second well was [tex]103 \frac{3}{6}\ m[/tex] deep below the surface.

John worked for a portion of the total hours, so he should get a proportionate share of the payment. His share of the total hours is 2.5/5.5, so his share of the total payment is (2.5/5.5) times $41.25, which is about $18.75.

The subject of this question is Mathematics, specifically a scenario about division and ratios. To find out how much money John gets, we need to know the total number of hours worked and how this correlates to the total payment.

John and Monica collectively worked for 2.5 + 3 = 5.5 hours. John worked 2.5 out of these 5.5 hours.  So, the proportion of time John worked is 2.5/5.5. Then, multiply this proportion (2.5/5.5) by the total payment of $41.25 to get John's share.

John's share is thus (2.5/5.5) * $41.25 ≈ $18.75.

This approach represents a principle of fair division, where the money is divided according to the proportion of hours worked by each person.

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Answer:

Keith live 280 miles far way from the mountains.

Step-by-step explanation:

Consider the provided information.

Keith drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took  8  hours.

Let the distance is D and average rate or speed is x miles.

[tex]Distance =Speed\times Time[/tex]

Substitute the respective values.

[tex]D=x\times 8\\D=8x[/tex]

When Keith drove home, there was no traffic and the trip only took  5

hours. The average rate was  21  miles per hour faster on the trip home,

The average rate or speed during return is x+21 miles.

Substitute the respective values in the above formula.

[tex]D =(x+21)\times 5\\D=5x+105[/tex]

Equate both the equations.

[tex]5x+105=8x\\3x=105\\x=35[/tex]

Substitute the value of x in [tex]D=8x[/tex]

[tex]D=8(35)\\D=280[/tex]

Hence, Keith live 280 miles far way from the mountains.

Final answer:

To find the distance Keith lives from the mountains, we need to set up and solve an equation using the given information about the trip duration and rates.

Explanation:

To find the distance Keith lives from the mountains, we can use the formula:

Distance = Rate * Time

Let's assume the rate Keith drove to the mountains is r. Therefore, the distance to the mountains would be 8r. We also know that on the return trip, Keith's rate was 21 miles per hour faster, so his rate on the return trip would be r + 21. The distance on the return trip would be 5(r + 21).

Since the distance to and from the mountains is the same, we can set up the equation:

8r = 5(r + 21)

Solving this equation will give us the value of r, and therefore, the distance Keith lives from the mountains.