A solar water heater costs about $6240 to install (after rebates). A traditional gas water heater costs about $850 and costs about $320 per year to run. The average annual cost to run the solar water heater is about $75

Create total cost functions for each of the water heaters as a function of the number of years that the heater is used

so the area A is no more than 10, namely A ⩽ 10 , it could be 10 or less, but no more than that.

let's recall the area of a triangle is A = (1/2)bh

[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=4\\ h=2x-3 \end{cases}\implies A=\cfrac{1}{2}(4)(2x-3) \\\\[-0.35em] ~\dotfill\\\\ A\leqslant 10\implies \cfrac{1}{2}(4)(2x-3)\leqslant 10\implies 2(2x-3)\leqslant 10\implies 4x-6\leqslant 10 \\\\\\ 4x\leqslant 16\implies x\leqslant \cfrac{16}{4}\implies x\leqslant 4 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{maximum height of the triangle}}{2(4)-3}\implies 8-3\implies 5[/tex]

when x = 4 is the maximum height, since x ⩽ 4, so it could be 4 at most, could be less than 4 or equals but never higher.

Answer: 17.5cm

Steps: 70m = 700cm

40cm = 40cm

700cm/40cm

=17.5cm

vous êtes les bienvenus, baisers cher!

Answer:

40 cm

Step-by-step explanation:

She has one ribbon of 40 cm and another ribbon of 70 m

First, we have to change 70 m to cm, to do this we know that 1m = 100 cm

so we multiply 70*100 = 7,000 cm.

Now we have to find the longest length she can cut the ribbons in centimeters.

To do this we have to find the Greatest Common Factor of 40 and 7000 to know what is the longest length she can cut the ribbons.

To find the Greatest Common Factor we have to find the factors for each number:

Factors of 40:

1, 2, 4, 8, 10, 20, 40

Factors of 7000

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40

The Greatest Common Factor is 40, so she can have pieces of 40 cm long.

Answer:

Option 3 is the best option that compares the pair of intersecting rays with the angle

Step-by-step explanation:

The definition of angle says that an angle is a shape that is produced by the intersection of two rays that have a common end point.

A ray is a line segment that has only one end point and is extended infinitely in a unique direction

So Yeah. :) Hope I've helped

Answer:

f(- 3) = 5

Step-by-step explanation:

The absolute value always returns a positive value, that is

| - a | = | a | = a

Given

f(x) = | x - 2 |

To evaluate f(- 3) substitute x = - 3 into f(x)

f(- 3) = | - 3 - 2 | = | - 5 | = 5

Answer: Option 'b' is correct.

Step-by-step explanation:

Since we have given that

Average marks in Homework = 95

Average marks in Quiz = 90

Average marks in Test = 87

According to question, we have that the teacher weights homework at 20%, Quizzes at 20%, Test at 40%, and the final exam at 20%

Total score in the class = 90

So, Score of homework is given by

[tex]0.2\times 95\\\\=19[/tex]

Score of Quiz is given by

[tex]0.2\times 90\\\\=18[/tex]

Score of test is given by

[tex]0.4\times 87\\\\=34.8[/tex]

So, it becomes,

[tex]19+18+34.8+x=90\\\\71.8+x=90\\\\x=90-71.8\\\\x=18.2[/tex]

So, minimum grade Anna can make on the final is given by

[tex]\dfrac{20}{100}\times y=18.2\\\\y=\dfrac{18.2}{0.2}\\\\y=91[/tex]

Hence, Option 'b' is correct.

1. 14 can be divided by 7 ( 14/7 = 2) so 7/14 reduces to 1/2

2. Both 6 and 9 can be divided by 3: 6/9 reduces to 2/3

3. 3/8 cannot be reduced, they do not have a common multiple, so this stays 3/8

4. Both 16 and 20 can be divided by 4, so this reduces to 4/5

On solving the equation -(6x+7)+8=19, we get value of x = -3.

To solve the equation -(6x+7)+8=19, we will first simplify each side of the equation and then solve for x. Here's how to do it step-by-step:

Distribute the negative sign across the parenthesis: -6x - 7 + 8 = 19.

Combine like terms on the left side: -6x + 1 = 19.

Subtract 1 from both sides: -6x = 18.

Divide both sides by -6 to find the value of x: x = -3.

The data obtained from both questions is qualitative and discrete. The highest level of measurement for the data is ordinal.

The data obtained from the first question, "What has been your experience with American products?", is qualitative as it involves responses categorized into below average, average, above average, and good to excellent. The data from the second question, where a supervisor gives a summary evaluation rating, is also qualitative, with choices ranging from poor to excellent.

Both sets of data are discrete since they are categorized into distinct choices. The highest level of measurement for these data is ordinal since the choices have a specific order but do not have equal intervals between them.

Answer:

The number of adults tickets sold was 894 and the number of children tickets sold was 335

Step-by-step explanation:

Let

x ----> the number of adults tickets sold

y ----> the number of children tickets sold

we know that

x+y=1,229 -----> equation A

35x+27y=40,335 ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (894,335)

see the attached figure

therefore

The number of adults tickets sold was 894 and the number of children tickets sold was 335

To solve for the number of adult and child Broadway show tickets sold, we set up and solve a system of equations. After calculation, we find that 894 adult tickets and 335 child tickets were sold.

The question asks to determine the number of adult and child tickets sold when tickets to a Broadway show cost $35 for adults and $27 for children, with a total of 1229 tickets sold for a total amount of $40335. This is a typical example of a system of equations problem.

Step-by-Step Solution:

Let x be the number of adult tickets sold and y be the number of child tickets sold.

We have two equations:

To solve the system, multiply the first equation by -27 to eliminate y:

Add this result to the second equation:

Divide by 8 to find x:

Substitute x = 894 into the first equation to find y:

Therefore, 894 adult tickets and 335 child tickets were sold.

Answer:

Step-by-step explanation:

There are two parts to this problem:

As you can learn from any speed limit sign, speed is in units of distance per time--miles per hour in the US. To compute speed, you divide distance by time.

If we were to use the given numbers directly, dividing distance in miles by time in seconds, our speed would have units of miles per second. In order to change the units to the ones asked for by the problem statement, we need to make one of two conversions.

For the first part, we need to convert miles to feet, so our speed is in feet per second instead of miles per second. For the second part, we need to convert seconds to hours, so the speed is in miles per hour.

__

Any units conversion can be done using a conversion factor that is a fraction that has a value of 1. That is, its numerator is equal to its denominator.

For the conversion from miles to feet, we want to cancel units of miles and leave units of feet. The operation on units looks like ...

  [tex]\dfrac{miles}{second}\times\dfrac{feet}{mile}=\dfrac{feet}{second}[/tex]

The units of miles in the numerator cancel the units of miles in the denominator, so we're left with feet per second, as we want. In order to make the conversion factor have a value of 1, it must be ...

  (5280 ft)/(1 mi) . . . . . . numerator equal to denominator

(a) Express the speed in ft/s:

(2.5 mi)/(37.895 s) × (5280 ft)/(1 mi) = 2.5·5280/37.895 ft/s ≈ 348.331 ft/s

__

(b) For the conversion to miles per hour from miles per second, we need to cancel the units of seconds in the denominator and replace them with hours. The conversion factor for that is ...

  (3600 s)/(1 h) . . . . . . numerator equal to denominator

(2.5 mi)/(37.895 s) × (3600 s)/(1 h) = 2.5·3600/37.895 mi/h ≈ 237.498 mi/h

Answer:

h(- 8) = - 8

Step-by-step explanation:

To evaluate h(- 8) substitute x = - 8 into h(x), that is

h(- 8) = [tex]\frac{(-8)^2+3(-8)}{4(-8)+27}[/tex]

        = [tex]\frac{64-24}{-32+27}[/tex]

       = [tex]\frac{40}{-5}[/tex] = - 8

Answer:

  6

Step-by-step explanation:

The largest factor that is common to all these numbers is 6. That is the number of pencil boxes Lana can fill.

  18 = 6×3

  24 = 6×4

  36 = 6×6

___

Each of her six (6) pencil boxes will have 3 pencils, 4 erasers, and 6 crayons.

Answer:

Option c.

Step-by-step explanation:

In 2017, Moreno Cheeses had a net income of $42,390, paid preferred dividends of $6,000.

value of the shares = Net income - preferred dividends

                                = 42,390 - 6,000

                                = $36,390

To find their earnings per share = [tex]\frac{\text{Value of the shares}}{\text{total number of shares}}[/tex]

= [tex]\frac{36,390}{1,8000}[/tex]

= $2.02 per share

Option c) $2.02 per share

Answer:

6 quarters, 3 dimes, and 12 nickles

Step-by-step explanation:

Let's say Q is the number of quarters, D is the number of dimes, and N is the number of nickles.

From the information in the problem, we can write three equations:

25Q + 10D + 5N = 240

N = 2Q

Q = 2D

Solve the system of equations using substitution.

25(2D) + 10D + 5(2Q) = 240

50D + 10D + 10Q = 240

60D + 10(2D) = 240

60D + 20D = 240

80D = 240

D = 3

Q = 6

N = 12

There are 6 quarters, 3 dimes, and 12 nickles.

Answer with Step-by-step explanation:

The exponential growth function is given by

[tex]N(t)=N_oe^{mt}[/tex]

where

[tex]N(t)[/tex] is the population of the bacteria at any time 't'

[tex]N_o[/tex] is the population of the bacteria at any time 't = 0'

'm' is a constant and 't' is time after 7.00 a.m in hours

Assuming we start our measurement at 7.00 a.m as reference time  t = 0

Thus we get[tex]N(0)=N_oe^{m\times 0}\\\\12=N_o[/tex]

Now since it is given after 5 hours the population becomes 14 mg thus from the above relation we get

[tex]12\times e^{m\times 5}=14\\\\e^{5m}=\frac{14}{12}\\\\m=\frac{1}{5}\cdot ln(\frac{14}{12})\\\\m=0.031[/tex]

Thus the population of bacteria at any time 't' is given by

[tex]N(t)=12e^{0.031t}[/tex]

Part a)

Population of bacteria after another 5 hours equals the population after 10 hours from start

[tex]N(10)=12e^{0.031\times 10}=16.361mg[/tex]

Part b)

Population of bacteria at 7:00 p.m is mass after 12 hours

[tex]N(1)=12e^{0.031\times 12}=17.41mg[/tex]

Part c)

Population of bacteria at 8:00 p.m is mass after 1 hour

[tex]N(1)=12e^{0.031\times 1}=12.3378mg[/tex]

Part d)

Differentiating the relation of population with respect to time we get

[tex]N'(t)=\frac{d(12\cdot e^{0.031t})}{dt}\\\\N'(t)=12\times 0.031=0.372e^{0.031t}[/tex]

Thus we can see that the percentage increase varies with time initially the percentage increase is 37.2% but this percentage increase increases with increase in time

Part 4)

Since there are 24 hours in 1 day thus the percentage increase in the population is

[tex]\frac{N(24)-N_o}{N_o}\times 100\\\\=\frac{25.25-12}{12}\times 100=110.42[/tex]

Thus there is an increase of 110.42% in the population each day.

Answer:

The error that Adam could have made is added 45 to the depth of

submarine instead of adding -45

Step-by-step explanation:

* Lets explain how to solve the problem

- A submarine traveling 200 meters below the surface of the ocean

- Increases its depth by 45 meters

- Adam says that the new location of the submarine is -155 meters

- We need to know the error of Adam

∵ We consider the surface of the ocean is the zero level

∵ The submarine is 200 meters below the surface of the ocean

∵ Below means negative

∴ The depth of submarine is -200 meters

∵ It increases the depth by 45 meters

- That means it travels down another 45 meters

∵ Down means negative

∴ The depth of submarine = -200 + (-45) = -245 meters

∴ The depth of submarine is 245 below the surface of the ocean

- Adam could thought that the submarine traveled up for 45 meters

 then he add 45 to -200

∵ -200 + 45 = -155 meters

∴ The error that Adam could have made is added 45 to the

   depth of submarine instead of adding -45

Final answer:

Adam incorrectly subtracted the increased depth from the initial depth, but the correct method is to add the increased depth to the initial negative depth, resulting in a depth of -245 meters.

Explanation:

The error Adam made in his calculation is that he subtracted the increased depth from the initial depth, instead of adding it. When a submarine dives deeper from any initial depth below sea level, we must add the increase to the existing negative depth.

The submarine was originally at -200 meters (below the surface), and then it went 45 meters deeper. Thus, the correct new depth is -200 meters - 45 meters = -245 meters.

Answer: B.1.96.

Step-by-step explanation:

The critical z-value used for [tex](1-\alpha)[/tex] confidence interval istwo tailed value with the significance level of [tex](\alpha)[/tex] i.e.[tex]z_{\alpha/2}[/tex] from the standard normal distribution table for z.

Given : Level of confidence : [tex]1-\alpha=0.95[/tex]

Significance level : [tex]\alpha:1-0.95=0.05[/tex]

By using the standard normal distribution table for z,

The z-value = [tex]z_{0.05/2}=z_{0.025}=1.96[/tex]

The correct Z value to use in obtaining a 95% confidence interval for the mean length of cut sheet insulation using a known standard deviation is 1.96.

The Z value to use in obtaining the 95% confidence interval for the mean length cut by a machine (which is distributed normally) is 1.96. This is because a 95% confidence interval excludes 5% of the probability, with 2.5% in each tail of the normal distribution. The critical Z value for 0.025 in one tail is roughly 1.96, which is the standard score that corresponds to the 97.5th percentile of the standard normal distribution.

The quality control engineer, who is working on automatically cut sheet insulation, found a mean of 12.25 feet from a sample of 75 cuts. Given the known standard deviation of 0.20 feet, using the Z value of 1.96 will allow for the construction of the desired confidence interval around the sample mean. This critical value enables us to estimate the range in which the true population mean is likely to fall with 95% certainty.

Final answer:

You need to pull out 6 socks to guarantee a pair of one color, 11 socks to guarantee two pairs, and 7 socks to be certain you have a pair of black socks.

Explanation:

To guarantee that you have a pair of one color when selecting from a mix of 10 pairs of socks (5 black and 5 blue), you must consider the worst-case scenario. This occurs when you alternatively pick one of each color. Therefore, after picking 5 black and 4 blue socks, the next sock you pick will guarantee a pair. So, you need to pull out 6 socks to ensure a pair of one color (5 of one color and 1 of the other).

To have two good pairs, you would continue this pattern. After the first pair is secured with 6 pulls, you would possibly pick the alternating color for the next 4 pulls, and then any subsequent sock would complete a second pair of one color. In total, this would require pulling out 11 socks to ensure two pairs.

To be certain you have a pair of black socks, prepare for the possibility of pulling out all 5 blue socks first. After these 5, the next 2 socks you pull out will be black, giving you at least one pair of black socks. Therefore, you would need to pull out 7 socks to be certain.

To determine the size of Dylan's collection, we multiply Jayden's collection (800 cards) by 1/10. The result is that Dylan has 80 baseball cards in his collection.

In this problem, Jayden has a collection of 800 baseball cards. His brother Dylan has a collection that is 1/10 as large. To find out how many cards Dylan has, we perform a simple multiplication problem: we multiply Jayden's collection (800 cards) by the fraction representing Dylan's collection size (1/10).

Therefore, Dylan has 800 * 1/10 = 80 baseball cards.

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Answer with Step-by-step explanation:

We are given that six integers 1,2,3,4,5 and 6.

We are given that sample space

C={1,2,3,4,5,6}

Probability of each element=[tex]\frac{1}{6}[/tex]

We have to find that [tex]P(C_1),P(C_2),P(C_1\cap C_2) \;and\; P(C_1\cup C_2)[/tex]

Total number of elements=6

[tex]C_1[/tex]={1,2,3,4}

Number of elements in [tex]C_1[/tex]=4

[tex]P(E)=\frac{number\;of\;favorable \;cases}{Total;number \;of\;cases}[/tex]

Using the formula

[tex]P(C_1)=\frac{4}{6}=\frac{2}{3}[/tex]

[tex]C_2[/tex]={3,4,5,6}

Number of elements in [tex]C_2[/tex]=4

[tex]P(C_2)=\frac{4}{6}=\frac{2}{3}[/tex]

[tex]C_1\cap C_2[/tex]={3,4}

Number of elements in [tex](C_1\cap C_2)=2[/tex]

[tex]P(C_1\cap C_2)=\frac{2}{6}=\frac{1}{3}[/tex]

[tex]C_1\cup C_2=[/tex]{1,2,3,4,5,6}

[tex]P(C_1\cup C_2)=\frac{6}{6}=1[/tex]

Answer:

C is your answer

Step-by-step explanation:

Answer:

I think she is incorrect she need to change all the fractions to the same denominators

Step-by-step explanation:

We are going to change all the fractions to 64

9/64 stays the same

5/32 multiply 2    then 10/64

1/16 multiply by 4 then 4/64

1/8 multiply by 8  then 8/64

Now we can order then

5/32 > 9/64 > 1/8 > 1/16 This is the right order

She was wrong.

The order of the list from least to greatest is 1/16 < 1/8 < 9/64 < 5/31.

Ascending order means to arrange numbers in increasing order, that is, from smallest to largest.

Now the given sizes of sets of screws are,

9/64, 5/32, 1/16, 1/8

Now We shall convert the values into decimals for simplicity.

So,

9/64 = 0.1406

5/32 = 0.1562

1/16 = 0.0625

1/8 = 0.125

So, arranging them from least to greatest :

0.0625 < 0.125 < 0.1406 < 0.1562

So, the required order of sizes of sets of screws are,

1/16 < 1/8 < 9/64 < 5/31

Thus, The order of the list from least to greatest is 1/16 < 1/8 < 9/64 < 5/31.

To learn more about least to greatest:

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Answer:

y= 2/3x + 3

Step-by-step explanation: I suggest to look up slope intercept calculator it really helps.

Answer:

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

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 )

Rearrange - 2x + 3y = 9 into this form

Add 2x to both sides

3y = 2x + 9 ( divide all 3 terms by 3 )

y = [tex]\frac{2}{3}[/tex] x + 3 ← in slope- intercept form

Answer:

31

Step-by-step explanation:

Let number of ten dollar bills be x .

So, number of five dollar bills = 2 x

Total amount of money in the cash register = 620 dollars

Amount of money in total cash as a result of  five dollar bills = 2 x × 5 = 10 x  dollars

Amount of money in total cash as a result of  ten dollar bills =  x × 10 = 10 x dollars

According to question ,

Total amount of money in the cash register = Amount of money in total cash as a result of  five dollar bills +  Amount of money in total cash as a result of  ten dollar bills

⇒ 620 = 10 x + 10 x

⇒ 620 = 20 x

⇒ x = [tex]\frac{620}{20}[/tex] = 31

So, number of ten dollar bills = 31

Final answer:

By setting up an algebraic equation based on the information provided, we can determine there are 31 ten dollar bills in the cash register.

Explanation:

To solve the question: A cash register contains only five dollar and ten dollar bills. It contains twice as many five's as ten's and the total amount of money in the cash register is 620 dollars. How many ten's are in the cash register? we need to use algebra.

Let's let x represent the number of ten dollar bills. Since the register contains twice as many five dollar bills as ten dollar bills, we can represent the number of five dollar bills as 2x.

The value of the ten dollar bills is 10x dollars, and the value of the five dollar bills is 5(2x) = 10x dollars. The total amount of money in the cash register is the sum of these values, which equals 620 dollars. So, we have the equation:

10x + 10x = 620

Simplifying, this becomes 20x = 620. Dividing both sides by 20 gives us x = 31.

Therefore, there are 31 ten dollar bills in the cash register.

Answer:

Sheila is 0.61 meters taller than her son.

Step-by-step explanation:

First, you would convert 109 cm into meters. Once converted, Sheila's son would be 1.09. Then you would subtract 1.09 from 1.7 to find your answer!

Step-by-step explanation:

3y-x-5=0

3y=x+5

y=(x+5)/3

y= (1/3)*x + (5/3)

The general equation of y is:

y=mx+b

where:

slope=m

b= y intercept

so, slope is (1/3) and y intercept is (5/3)

and x intercept=0, when you star to graphic you can see that the only option for have y=(5/3) is necessary that the value of x=0. Or:

y intercept= (1/3)*x +(5/3) =(5/3)

(5/3)-(5/3)=(1/3)x

0=(1/3)*x

0/(1/3)=x

x=0.

Answer:

x = -8(-43)

x = 344 is the solution

Answer:

Remember that if you want the area on a rectangle you have to think, lengh x width. In this case, the correct answer is C.

Step-by-step explanation:

There is something wrong in this, because 20 is not 2 meters than its width.

Answer:

[tex]\dfrac{x}{4}[/tex]

C is correct.

Step-by-step explanation:

At a picnic,

Number of adults is 3 times as number of children.

Number of women is twice as number of men.

Total number of men, women and children at the picnic be x

Let number of children be c

Let number of men be m

Let number of women be w

# Number of women is twice as number of men, w = 2m

# Number of adults is 3 times as number of children, w + m = 3c

      2m + m = 3c     (∴  w=2m )

                c = m

Total number of men, women and children at the picnic be x

∵       c + m + w = x

     m + m + 2m = x

                    4m = x

Number of men, [tex]m=\dfrac{x}{4}[/tex]

Hence, The total number of men will be  [tex]\dfrac{x}{4}[/tex]

Answer:

y = 3x - 4

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 )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line

m = [tex]\frac{2+4}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3

Note the line crosses the y- axis at (0, - 4) ⇒ c = - 4

y = 3x - 4 ← equation of line