A 15-inch candle is lit and steadily burns until it is burned out. Let b represent the burned length of the candle (in inches) and let r represent the remaining length of the candle (in inches).
a. Write a formula that expresses r in terms of b.When 3.1 inches have burned from the candle, the remaining length of the candle is inches.
b. Graph the relationship between a and b

Answer:

(10, 11, 12, 13, 14, 15, 16)

Step-by-step explanation:

The minimum number of tables that the store has to sell in order to meet the requirements is given by:

[tex](25-t)*100+t*550=7,000\\(550-100)t=7,000-2,500\\t = 10\ tables[/tex]

The company must sell at least 10 tables.

Since the company already sold 9 chairs, and they can ship at most 25 items, they can sell at most 16 tables. Every integer number between the minimum and maximum is also possible:

(10, 11, 12, 13, 14, 15, 16).

Answer:

12,13,14,15,16

Step-by-step explanation:

\underline{\text{Define Variables:}}

Define Variables:

​

May choose any letters.

\text{Let }t=

Let t=

\,\,\text{the number of tables sold}

the number of tables sold

\text{Let }c=

Let c=

\,\,\text{the number of chairs sold}

the number of chairs sold

\text{\textquotedblleft at most 25 pieces"}\rightarrow \text{25 or fewer pieces}

“at most 25 pieces"→25 or fewer pieces

Use a \le≤ symbol

Therefore the total number of furniture pieces sold, t+ct+c, must be less than or equal to 25:25:

t+c\le 25

t+c≤25

\text{\textquotedblleft no less than \$7000"}\rightarrow \text{\$7000 or more}

“no less than $7000"→$7000 or more

Use a \ge≥ symbol

The store makes $550 for each table sold, so for tt tables, the store will make 550t550t dollars. The store makes $100 for each chair sold, so for cc chairs, the store will make 100c100c dollars. Therefore, the total revenue 550t+100c550t+100c must be greater than or equal to \$7000:$7000:

550t+100c\ge 7000

550t+100c≥7000

\text{Plug in }9\text{ for }c\text{ and solve each inequality:}

Plug in 9 for c and solve each inequality:

The store sold 9 chairs

\begin{aligned}t+c\le 25\hspace{10px}\text{and}\hspace{10px}&550t+100c\ge 7000 \\ t+\color{green}{9}\le 25\hspace{10px}\text{and}\hspace{10px}&550t+100\left(\color{green}{9}\right)\ge 7000 \\ t\le 16\hspace{10px}\text{and}\hspace{10px}&550t+900\ge 7000 \\ \hspace{10px}&550t\ge 6100 \\ \hspace{10px}&t\ge 11.09 \\ \end{aligned}

t+c≤25and

t+9≤25and

t≤16and

​

550t+100c≥7000

550t+100(9)≥7000

550t+900≥7000

550t≥6100

t≥11.09

​

\text{The values of }t\text{ that make BOTH inequalities true are:}

The values of t that make BOTH inequalities true are:

\{12,\ 13,\ 14,\ 15,\ 16\}

{12, 13, 14, 15, 16}

\text{(the final answer is this entire list)}

(the final answer is this entire list)

Answer:

Hello!

I believe your answer is:

4a(b+2c)

Step-by-step explanation:

I hope this worked for you!  Good luck!

answer will be 10cm² as i calculate it

Answer:

[tex] ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]

The confidence level is 0.98 and the significance is [tex]\alpha=1-0.98 =0.02[/tex] and [tex]\alpha/2 =0.01[/tex] and the critical value using the table is:

[tex]z_{\alpha/2}= 2.326[/tex]

And replacing we got:

[tex] ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex]\sigma = 425[/tex] represent the population deviation

[tex] n =22[/tex] the sample size

[tex]\bar X =1520[/tex] represent the sample mean

We want to find the margin of error for the confidence interval for the population mean and we know that is given by:

[tex] ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]

The confidence level is 0.98 and the significance is [tex]\alpha=1-0.98 =0.02[/tex] and [tex]\alpha/2 =0.01[/tex] and the critical value using the table is:

[tex]z_{\alpha/2}= 2.326[/tex]

And replacing we got:

[tex] ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76[/tex]

Answer:

Cable: 10%  Satellite: 40%  Streaming Service: 50%

Step-by-step explanation:

There are 10 friends  

1 has cable

4 have satellite

5 have streaming service  

Which means:

Cable is 10%

Satellite is 40%

Streaming Service is 50%

Answer:

Cable Television: 10%

Satellite Television: 40%

Streaming Service: 50%

Step-by-step explanation:

Cable television: [tex]\frac{1}{1+4+5} =\frac{1}{10} =\frac{10}{100}[/tex] or 10%

Satellite television: [tex]\frac{4}{1+4+5} =\frac{4}{10} =\frac{40}{100}[/tex] or 40%

Streaming service: [tex]\frac{5}{1+4+5} =\frac{5}{10} =\frac{50}{100}[/tex] or 50%

Answer:

(A) P (n,k) = n!/(n-k)! divided by 2

(B) C (n,3) = n!/(12)(n-3)!

(C) C (n,k) = n!/(n-k)!(k!)

Step-by-step explanation:

Permutation deals with order or arrangement or position of objects. Where this does not matter, we use the Combination formula.

We divide by 2 in all cases, because no 2 chosen chairs should be adjacent.

For (B), n=10

C (n,3) = n!/(n-3)!(3!) divided by 2

3! = 3×2×1 = 6

The expression divided by 2 means it will be multiplied by 1/2

Hence 6×2 = 12

And we arrive at

C (n,3) =n!/(12)(n-3)!

Here is the full question:

When a species has several variants of a phenotype passed on from generation to generation, we can form a hypothesis about the genetics of the trait based on Mendelian theories of genetic inheritance. For example, in a two-gene dominant epistatic model, the first gene masks the effect of the second gene, leading to the expression of three phenotype variants. Crossing the dominant and recessive homozygote lines would result in a second generation represented by a mix of dominant, intermediate, and recessive phenotype variants in the expected proportions: and respectively, also called a 12:3: 1 ratio.

Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2: 131 white squash, 34 yellow squash, and 10 green squash. Are these data consistent with a 12: 3: 1 dominant epistatic model of genetic inheritance( white being dominant)?

The null hypothesis for the chi-square goodness-of-fit test is                

Answer:

The null  hypothesis for the chi-square goodness-of-fit test is :

[tex]\mathbf{H_o:p_{white} = \frac{12}{16}, p_{yellow} = \frac{3}{16}; p_{green} = \frac{1}{16} }[/tex]

Step-by-step explanation:

The objective of this question is to state the null hypothesis for the  chi-square goodness-of-fit test.

Given that:

There are three colors associated with this model . i,e White , yellow and green and they are in the ratio of 12:3:1

The total number of these color traits associated with this model = 12 + 3 + 1 = 16

Thus ;

The null  hypothesis for the chi-square goodness-of-fit test is :

[tex]\mathbf{H_o:p_{white} = \frac{12}{16}, p_{yellow} = \frac{3}{16}; p_{green} = \frac{1}{16} }[/tex]

Answer:

Option(B) is the correct answer to the given question.

Step by Step Explanation

We know that

[tex]A\ =\ P \ *(\ 1+\ \frac{r}{n} \ ) ^{nt}[/tex]

Here A=amount

r=15.98%=0.1598

n=365

t=1

Putting these values into the equation

[tex]A\ =\ P \ *(\ 1+\ \frac{0.1598}{365} \ ) ^{365}[/tex]

[tex]A\ =\ P \ *(\ 1+\ 0.000437) ^\ { 365}[/tex]

[tex]A\ =\ P \ *(\ 1.000437 ) ^{365}[/tex]

[tex]A\ =1.17288 P[/tex]

Now we find the interest

I=[tex]1.17288P\ -P\\=\ 0.17288P\\\ ~ 0.1720P[/tex]

Therefore effective interest rate of the last year can be determined by

[tex]\frac{0.1720P}{P}[/tex]

=0.1720 *100

=17.20%

Answer:

17.32%

Step-by-step explanation:

Answer:

1:0.4641

Step-by-step explanation:

We are told that the scale of the model with respect to the real world is 0.1 cubic meter. This means that for every 1 cubic meter in the real world the model represents 0.1.

They tell us that the real world volume is 100,000, that if we assume a cube, we have to:

V = l ^ 3

l = 100000 ^ (1/3)

l = 46.41

46.41 meters would be each side, now the volume of the model would be:

100,000 * 0.1 = 10,000

Which means that its sides would be:

V = l ^ 3

l = 100000 ^ (1/3)

l = 21.54

We calculate the scale of the sides:

21.54 / 46.41 = 0.4641

Which means that for every 1 meter in the real world the model represents 0.4641 meters.

Answer:

P(odd number) = 0.5

Step-by-step explanation:

There are 90 members in the set (10, 11, 12, .. , 97, 98, 99)

When we have an even number of consecutive numbers, the number of even numbers equals the number of odd numbers. This means that half of the numbers in this set are even and half of them are odd.

So the probability of P(odd number) = 0.5

Answer:

540

Step-by-step explanation:

Since the surface area is 408, we can set up the equation

2*9*6 + 2*r*9 + 2*r*6 = 408

108 + 30r = 408

30r = 300

r = 10

The volume is length * width * height

9*6*10 = 540

Answer:

$976

Step-by-step explanation:

Straight time pay= $15.25(hourly rate) × 40(hours worked)= $610

Overtime Rate = 15.25×2= $30.50

Overtime Pay= $30.5 × 12 (Hours worked overtime)= $366

Total Pay= Basic wage + Overtime Wage = $976

Answer:

52% probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: A puppy is adopted.

Event B: The puppy lives 7 or more years.

An animal shelter has a 65% adoption rate for puppies

This means that [tex]P(A) = 0.65[/tex]

Of the puppies who are adopted, 80% live to be 7 years or older.

This means that [tex]P(B|A) = 0.8[/tex]

What is the probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(A)*P(B|A)[/tex]

[tex]P(A \cap B) = 0.65*0.8[/tex]

[tex]P(A \cap B) = 0.52[/tex]

52% probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years

Answer:

v = 10

the average velocity of the object over the interval of time [1, 5 ] is 10 units per unit time

Step-by-step explanation:

Given;

function​ s(t) represents the position of an object at time t moving along a line.

s(1) = 62 at t1 = 1

s(5) = 102 at t5 = 5

Velocity v = distance/time

Average velocity v over time t is;

v = ∆s/∆t

v = [s(5) - s(1)]/[t5 - t1]

Substituting the given values;

v = (102 - 62)/(5 - 1)

v = 10

the average velocity of the object over the interval of time [1, 5 ] is 10 units per unit time

Answer:

j=13, g=20.8, h=24

Step-by-step explanation:

The overall shape given and the shape within, are both right triangles. With right triangles, you are allowed to use the pythagorean theorem formula ([tex]a^{2} + b^{2} = c^{2}[/tex]) in order to solve for some sides. In this case, that would be j and h. The five in the smaller triangle is represented by b and the 12 is the hypotenuse so it is represented by c. When you plug in those numbers in the pythagorean theorem formula, you will find the value of j to be 13. When looking at this, we see that 12 is the second greatest value in the right triangle values that we just found, so we know the the opposing angle for that one will be 60 degrees. The 5's opposing side is therefore 30 degrees. When subtracting 90 and 30, we get 60, so therefore you can use the 30 60 90 formula to find the sides of the bigger triangle. The 60 degrees represents g. This formula will be [tex]a\sqrt{3}[/tex]. The a is 12 since it is the smallest value. So therefore, g is [tex]12\sqrt{3}[/tex], which is 20.8. Now that we have this side, we can just use the pythagorean theorem formula to find the remaining side. Therefore, h is going to be 24

Answer:

a) 8.13

b) 4.10

Step-by-step explanation:

Given the rate of reaction R'(t) = 2/t+1 + 1/√t+1

In order to get the total reaction R(t) to the drugs at this times, we need to first integrate the given function to get R(t)

On integrating R'(t)

∫ (2/t+1 + 1/√t+1)dt

In integration, k∫f'(x)/f(x) dx = 1/k ln(fx)+C where k is any constant.

∫ (2/t+1 + 1/√t+1)dt

= ∫ (2/t+1)dt+ ∫ (1/√t+1)dt

= 2∫ 1/t+1 dt +∫1/+(t+1)^1/2 dt

= 2ln(t+1) + 2(t+1)^1/2 + C

= 2ln(t+1) + 2√(t+1) + C

a) For total reactions from t = 1 to t = 12

When t = 1

R(1) = 2ln2 + 2√2

≈ 4.21

When t = 12

R(12) = 2ln13 + 2√13

≈ 12.34

R(12) - R(1) ≈ 12.34-4.21

≈ 8.13

Total reactions to the drugs over the period from t = 1 to t= 12 is approx 8.13.

b) For total reactions from t = 12 to t = 24

When t = 12

R(12) = 2ln13 + 2√13

≈ 12.34

When t = 24

R(24) = 2ln25 + 2√25

≈ 16.44

R(12) - R(1) ≈ 16.44-12.34

≈ 4.10

Total reactions to the drugs over the period from t = 12 to t= 24 is approx 4.10

Answer:

Step-by-step explanation:

Mean = (87 + 105 + 130 + 160 + 180 + 195 + 135 + 145 + 213 + 105 + 145 + 151 152 + 136 + 87 + 99 + 92 + 119 + 129)/19 = 129

Variance = (summation(x - mean)²/n

Standard deviation = √(summation(x - mean)²/n

n = 19

Variance = [(87 - 129)^2 + (105 - 129)^2 + (130 - 129)^2+ (160 - 129)^2 + (180 - 129)^2 + (195 - 129)^2 + (135 - 129)^2 + (145 - 129)^2 + (213 - 129)^2 + (105 - 129)^2 + (145 - 129)^2 + (151 - 129)^2 + (152 - 129)^2 + (136 - 129)^2 + (87 - 129)^2 + (99 - 129)^2 + (92 - 129)^2 + (119 - 129)^2 + (129 - 129)^2]/19 = 23634/19 1243.895 min

Standard deviation = √1243.895 = 35.269 min

60 minutes = 1 hour

Converting the variance to hours,

Each division would have been divided by 60². 60² can be factorized out

Variance = 23634/60² = 6.565 hours

Converting the standard deviation to hours, it becomes

√6.565 = 2.562 hours

Answer:

3√2

Step-by-step explanation:

If you draw the diagonal, you have a 45°45°90° triangle.

The two legs are 3, so the hypotenuse is 3√2

Answer:

f(2) = f(3) = 102 ft

Step-by-step explanation:

The height f at t = 2 seconds is given by:

[tex]f(t) = -16t^2 + 80t + 6\\f(2) = -16*2^2 + 80*2 + 6\\f(2)=-64+160+6\\f(2)=102\ ft[/tex]

The height f at t = 3 seconds is given by:

[tex]f(t) = -16t^2 + 80t + 6\\f(3) = -16*3^2 + 80*3 + 6\\f(3)=-144+240+6\\f(3)=102\ ft[/tex]

For both t =2 and t =3, the expression results in a height of 102 ft, therefore f(2) = f(3) = 102 ft.

Answer:

b

Step-by-step explanation:

The given expression can be rewritten as 2 × 5 × 5 × 5 × 5 and is equal to 1250. The correct option is (B).

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

The given expression is 2 × 5⁴.

It can be simplified using the rule of indices as follows,

The expression 5⁴ can be written as 4 times 5 as below,

5⁴ = 5 × 5 × 5 × 5.

Then, the expression can be evaluated as

⇒ 2 × 5 × 5 × 5 × 5

⇒ 1250

Hence, the expression can be simplified to obtain 1250.

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The time taken in draining salt so that only 88 kg of salt remains in tank will be 35.71 sec.

It is given that a tank contains 2000 liters of a solution consisting 112 kg of salt is dissolved in water. Pure water is then pumped at rate of 12 L/sec.

We have to find out that how long it will take to drain out salt such that only 88kg of salt remains in tank.

What will be the amount of water flow ; if a water flows for 4 hours at constant speed of 120 liter /hour ?

The amount of water flow will be 120 liter / hour × 4 hour or 120 × 4 liter or 480 liters.

As per the question ;

In 2000 liters solution there is 112 kg salt.

The pumping speed of water into tank = 12 L/s

The salt pumping per second will be ;

= ( 12L/s × 112kg salt ) / 2000 L

= 0.672 Kg salt/sec

This means that 0.672 kg per second salt comes out .

It should be found that the amount of salt that must be drained so that only 88 kg of salt remain.

So , the amount of salt drained out will be ; (x kg)

⇒ 112kg salt - x kg salt = 88 kg salt

⇒ x kg salt = 112 - 88

⇒ x kg salt = 24 kg

The time taken until only 88 kg of salt remains in the​ tank will be ;

= 24 / 0.672

= 35.71 sec

Thus , the time taken in draining salt so that only 88 kg of salt remains in tank will be 35.71 sec.

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Answer:

2 liters of paint.

Step-by-step explanation:

First we nned to know to total area of the wall by using the formula A = lw

A = 4*5 = 20m²

then we given 1 liter cover 10 m², 20 m² = 2 liters of paint.

Answer:

5x - 4y = 20

Step-by-step explanation:

First find slope

(5- -10)/(8- -4) = 15/12 = 5/4

(y - 5) = 5/4 (x - 8), multiply everything by 4 so you don't have fractions

4y - 20 = 5x - 40

5x - 4y = 20

Area = length x width

Area = 5/6 x 3/4

= (5x3) / (6x4)

= 15/24

= 5/8 square miles

Answer:

Discount = $45

Final = $255

Step-by-step explanation:

First you would multiply $300 by .85. (You do this because your only paying for 85% of the computer) to get the final price

$255

In order to get the discount amount you would subtract 300 by 255 to get

$45

Answer:

Step-by-step explanation:

Let s, b, a represent the numbers of servings of steak, baked eggs, and acorn squash, respectively. Then the equations we want to solve are ...

  40s +20b +4a = 64 . . . . grams of protein

  10s +2b +20a = 29 . . . . grams of carbohydrate

  1s +20b +32a = 72.5 . . . milligrams of vitamin A

There are any number of calculators or web sites that will solve this system of equations for you. The solution is ...

  s = 0.5

  b = 2

  a = 1

The dietitian should provide 1/2 serving of steak, 2 servings of baked eggs, and 1 serving of acorn squash.

Answer:

Its depending on the angle

Answer:

8/3

Step-by-step explanation:

6(x-2)=4

x-2=4/6

x= 8/3

Answer:

x = 8/3

Step-by-step explanation:

Use Distributive Property

6(x-2) = 4

6x -12 = 4

add 12 on both sides

6x = 16

Divide by 6

x = 8/3

In decimal form: 2.667