Answer:
x = -3 x=8
Step-by-step explanation:
(x+3)(x-8)=0
Using the zero product property
x+3 =0 x -8 = 0
x = -3 x=8
tank contains 20002000 liters (L) of a solution consisting of 112112 kg of salt dissolved in water. Pure water is pumped into the tank at the rate of 1212 L/s, and the mixturelong dash—kept uniform by stirringlong dash—is pumped out at the same rate. How long will it be until only 88 kg of salt remains in the tank?
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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lled a 12:3:112:3:1 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 F2:131F2:131 white squash, 3434 yellow squash, and 1010 green squash. Are these data consistent with a 12:3:112:3:1 dominant epistatic model of genetic inheritance( white being dominant)? The null hypothesis for the chi‑square goodness‑of‑fit test is
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]
The function s(t) represents the position of an object at time t moving along a line. Suppose s (1 )equals 62 and s (5 )equals 102. Find the average velocity of the object over the interval of time [1 comma 5 ].
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
if the base of a right angled triangle is 4cm and its area is 20cm^2, find its height
answer will be 10cm² as i calculate it
Probability allows one to measure effectively the risks in selecting one alternative over the others.
True
False
A random two digit number (10-99) is drawn. Find P(odd number)
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
Please answer this correctly
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
For all the people that have to do algebra and dont want to do it yourself there is a website or you can download it on your phone its called*** MATH PAPA*** ****IT SHOWS YOU STEP BY STEP AND GIVES YOU THE ANSWER*** Just input the equation
Factories fully 4ab + 8ac
Answer:
Hello!
I believe your answer is:
4a(b+2c)
Step-by-step explanation:
I hope this worked for you! Good luck!
A computer has a price tag of $300. The store is giving you a 15% discount for the computer. Find the discount AND final price of the computer.
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
(a) There are $n$ chairs in a row. Find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent.
(b) There are 10 chairs in a circle, labelled from 1 to 10. Find the number of ways of choosing 3 of these chairs, so that no two chosen chairs are adjacent.
(c) There are $n$ chairs in a circle, labelled from 1 to $n.$ Find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent.
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)!
Which expression is equivalent to 2 (5) Superscript 4?
2 times 5 times 4
2 times 5 times 5 times 5 times 5
2 times 4 times 4 times 4 times 4 times 4
10 times 10 times 10 times 10
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).
What are the rules of exponents?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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An animal shelter has a 65% adoption rate for puppies. Of all puppies in the shelter, 75% live to be 7 years or older. Of the puppies who are adopted, 80% live to be 7 years or older. What is the probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
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
X 8.2.79
Question Help
A dietitian at a hospital wants a patient to have a meal that has 64 grams of protein, 29 grams of carbohydrates, and 72.5 milligrams of vitamin A The hospital food
service tells the dietitian that the dinner for today is salmon steak, baked eggs, and acorn squash. Each serving of salmon steak has 40 grams of protein, 10 grams
carbohydrates, and 1 milligram of vitamin A. Each serving of baked eggs contains 20 grams of protein, 2 grams of carbohydrates, and 20 miligrams of vitamin A
Each serving of acom squash contains 4 grams of protein, 20 grams of carbohydrates, and 32 milligrams of vitamin A How many servings of each food should the
dietitian provide for the patient?
Answer:
steak: 1/2baked eggs: 2acorn squash: 1Step-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.
nu
a. Write the equation of a line through the points (-4,- 10) and (8,5) in slope-intercept form.
b. Write the equation in standard form Ax+By = C, where A, B, and C are integers and A>0.
ents
Thoquution
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
The height of a ball t seconds after it is thrown upward from a height of 6 feet and with an initial velocity of 80 feet per second is f (t) = -16t2 + 80t + 6. (a) Verify that f(2) = f(3).
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.
Gia is painting her wall. 1 liter of paint can cover 10 square metres. She has a rectangular wall that measures 4 metres by 5 meters. How many liters of paint will Gia need to cover her wall?
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.
An architect creates a scale model. The volume of the scale model is 0.1 cubic meters. The volume of the real-world
building is 100,000 cubic meters. What is the ratio of corresponding sides from model to real world?
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.
Dorothy Kaatz, a computer programmer, earns a regular hourly rate of
$15.25 and earns double that when she works overtime. Kaatz usually works
40 regular hours and 12 hours overtime while she's trying to update the
company's systems before the month's end. What is her straight-time pay?
What is her overtime pay? What is her total pay?
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
An article reported the following data on oxidation-induction time (min) for various commercial oils:87 105 130 160 180 195 135 145 213 105 145151 152 136 87 99 92 119 129(a) Calculate the sample variance and standard deviation. (Round your answers to three decimal places.)s^2 = ________. min^2s = ________. min(b) If the observations were reexpressed in hours, what would be the resulting values of the sample variance and sample standard deviation? Answer without actually performing the reexpression. (Round your answer to three decimal places.)s^2 =______ hr^2s = ______hr
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
Solve for x.
6(x - 2) = 4
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
For a certain drug, the rate of reaction in appropriate units is given by Upper R prime (t )equalsStartFraction 2 Over t plus 1 EndFraction plus StartFraction 1 Over Start Root t plus 1 End Root End Fraction where t is time (in hours) after the drug is administered. Find the total reaction to the drug over the following time periods.
a. From t=1 to t=12.
b. From t=12 to t=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
what is the diagonal of asquare with length 3cm
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
Find the lengths of g, h, and j. Round answers to the nearest tenth. (marking brainliest for correct)
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
Please answer this correctly
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%
A field is in the shape of a rectangle 5/6 mile long and 3/4 mile wide. What is the area of the field? *
Area = length x width
Area = 5/6 x 3/4
= (5x3) / (6x4)
= 15/24
= 5/8 square miles
A credit card had an APR of 15.98% all of last year, and compounded interest daily. What was the credit card's effective interest rate last year?
A.
17.32%
B.
17.20%
C.
16.96%
D.
16.62%
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:
Which equation can be used to find mMN
Answer:
Its depending on the angle
The weekly salaries of sociologists in the United States are normally distributed and have a known population standard deviation of 425 dollars and an unknown population mean. A random sample of 22 sociologists is taken and gives a sample mean of 1520 dollars.
Find the margin of error for the confidence interval for the population mean with a 98% confidence level.
z0.10 z0.05 z0.025 z0.01 z0.005
1.282 1.645 1.960 2.326 2.576
You may use a calculator or the common z values above. Round the final answer to two decimal places.
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]
An online furniture store sells chairs for $100 each and tables for $550 each. Every day, the store can ship at most 25 pieces of furniture and must sell no less than $7000 worth of chairs and tables. If 9 chairs were sold, determine all possible values for the number of tables that the store must sell in order to meet the requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
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)