Answer:
a) f(x) = (x + 6)(x + 2)(x – 3)
b) [tex]f(x) = x^3 + 5x^2 - 12x - 36[/tex]
Step-by-step explanation:
We have to find the polynomial with zeroes as -6, -2, and 3.
Roots are those values of x for which the polynomial is zero.
a) f(x) = (x + 6)(x + 2)(x – 3)
[tex]f(x) = (x + 6)(x + 2)(x -3)=0\\\Rightarrow x+6 = 0, x+2 = 0, x-3 = 0\\\Rightarrow x = -6,x = -2, x = 3[/tex]
b)
[tex]f(x) = x^3 + 5x^2 - 12x - 36 \\\text{It can be factored as}\\f(x) = (x+6)(x-3)(x+2) = 0\\\Rightarrow (x+6)=0,(x-3)=0,(x+2)=0\\\Rightarrow x = -6, x = 3, x = -2[/tex]
c) f(x) = (x – 6)(x – 2)(x + 3)
[tex]f(x) = (x - 6)(x - 2)(x + 3) =0\\\Rightarrow (x -6)(x -2)(x + 3) = 0\\\Rightarrow (x -6)=0,(x -2)=0,(x + 3)=0\\\Rightarrow x = 6, x = 2, x = -3[/tex]
d)
[tex]f(x) = x^3 - 5x^2 - 12x + 36\\f(x) = (x-2)(x+3)(x-6)=0\\\Rightarrow (x-2) = 0, (x+3)=0,(x-6)=0\\\Rightarrow x =2, x = -3, x = 6[/tex]
Use the distributive property to remove the parentheses
(4n^2+2n-1)3
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
A different class is made up of 66% women and has 23 women in it. What is the total number of students in the class?
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.
What is percent?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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For what value of a does (one-seventh) Superscript 3 a + 3 Baseline = 343 Superscript a minus 1?
–1
0
1
no solution
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:
:)
There are 39 chips number from 1 to 39 placed in a barrel one chip is randomly pulled from the barrel what is the probability that the number on the chip is greater than or equal to 18
Find angle A in the following triangle.
A. 50.67
B. 49.23
C. 48.19
D. 51.89
A machine is supplied energy at a rate of 4,000 W and does useful work at a rate of 3,760 W. What's the efficiency of the machine? A. 92 percent B. 97 percent C. 96 percent D. 94 percent
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%
A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many squa
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.
Katie is starting a babysitters sitting business. She spent $26 to make signs to advertise. She charges her initial fee of five dollars and then three dollars for each hour of service right in Solve inequality to find the number of hours she want to babysit to make a profit interpret the solution any quality
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.
John and Monica are paid $41.25 for their work. John worked 2.5 hours, and Monica worked 3 hours. They split the money according to the amount of time each of them worked. How much is John's share of the money?
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.
Explanation: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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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, how many miles you have travelled at 12:20
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
Research participants drank either caffeinated or decaffeinated beverages in a study of the effects of caffeine on anxiety levels. Those who received the caffeinated drinks were assigned to the ________ group.
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
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars. R, that he is reimbursed and the number of miles, m, he drives in one day. Interpret the slope of the equation.
Answer:
The slope, 0.575, means that the total amount Bruce is reimbursed in one day increases by 0.575 of a dollar for each mile he drives on that day.
Step-by-step explanation:
The slope of equation R=0.575m+42 represents the rate of change of reimbursement with respect to miles driven. Thus, for each additional mile driven, the reimbursement increases by $0.575. This means that the slope essentially represents the reimbursement rate per mile.
Explanation:The equation R=0.575m+42 given in the question is a linear equation in the form of y = mx + b. In this equation R is the dependent variable symbolizing the reimbursement amount in dollars, m is the independent variable symbolizing the miles driven, 0.575 is the slope, and 42 is the y-intercept.
The slope in this case, 0.575, interprets as the rate of change of the reimbursement amount with respect to the miles driven. That is, for each additional mile driven, the reimbursement Bruce receives increases by $0.575. Hence, the slope or 'm' is actually the reimbursement rate per mile for Bruce's travels.
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A car traveling at 88 km an hour over takes a bus traveling at 64 km an hour if the bus has a 1.5 hour Headstart how far from the starting point does the car over take the bus
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
What is the probability of drawing 2 cards in succession (without replacement) from a standard deck and having them both be face cards?
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] .
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?
1) The probability that she will get a job offer from neither company is 0.3.2) The probability that she will get a job offer from exactly one of the two companies is 0.5.
Answer:0.2
Step-by-step explanation: Let the two companies be A and B
Pa = probability of getting a job offer from only company A
Pb = probability of getting a job offer from only company B
Pbb = probability of getting a job offer from both companies
Pn = ProbabityProbability of getting a job from neither companies
The relation could be combined using :
Pbb+Pa+Pb+Pn=1
Pn = 0.3
(Pa + Pb) =probability of offer from exactly one of A or B = 0.5
Pbb + 0.5 + 0.3 = 1
Pbb+0.8=1
Pbb=1-0.8
Pbb = 0.2
A small plane is flying a banner in the shape of a rectangle. The area of the banner is 144 square feet . The width of the banner is 1/4 the length of the banner. What are the dimensions of the banner?
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
If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then P(X ≥ 75) is:a. 0.500b. 0.250c. 0.125d. 0.975e. 0.625
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.
Explanation: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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A team of dogs drags a 70.9 kg sled 1.24 kmover a horizontal surface at a constant speed.The coefficient of friction between the sledand the snow is 0.193.The acceleration of gravity is 9.8 m/s2.Find the work done by the dogs.Answer in units of kJ.
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
Find the midpoint of (5,9) and (-1,9)
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)
A roller coaster starts down the slope at 4 m/s. But 3 seconds later at the bottom of the slope it's speed is 22 m/s. What is the average acceleration?
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.
Explanation: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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A company repaid a long-term debt during the year. They will report this as an (increase/decrease) in the activities section on the statement of cash flows.
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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The first term in an arithmetic sequence is 1 , and the second term is 2. The difference between each pair of consecutive terms in the sequence is 1 2/5.
A) True
B) False
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]
Given: The coordinates of rhombus WXYZ are W(0, 4b), X(2a, 0), YO, -4b), and Z(-2a, 0).
Prove: The segments joining the midpoints of a rhombus form a rectangle.
As part of the proof, find the midpoint of XY
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
A geologist found two underground wells that contained large deposits of water. The first well was 46 2/3 meters below the surface. The second well had more water, and was 77 5/6 meters deeper than the first well. How deep below the surface was the second well?
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.
n a reliability test there is a 42% probability that a computer chip survives more than 500 temperature cycles. If a computer chip does not survive more than 500 temperature cycles, then there is a 73% probability that it was manufactured by company A. What is the probability that a computer chip is not manufactured by company A and does not survive more than 500 temperature cycles?
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%.
A box contains 80 balls numbered from 1 to 80. If 11 balls are drawn with replacement, what is the probability that at least two of them have the same number?
Final answer:
The student's question is about finding the probability that at least two of the 11 balls drawn with replacement from a box of 80 uniquely numbered balls are the same. We use the complement rule to find the probability of all balls being unique and subtract this from 1 to find the desired probability.
Explanation:
The student is asking about the probability of drawing at least two balls with the same number when 11 balls are drawn with replacement from a box containing 80 uniquely numbered balls. To solve this, we can use the complement rule, which states that the probability of an event occurring is equal to one minus the probability of the event not occurring.
The probability of drawing 11 unique balls in a row with replacement from 80 can be calculated by multiplying the probabilities of drawing a unique ball at each draw after the first. For the first ball, the probability is 80/80 (since any ball can be drawn), for the second ball it's 79/80 as one unique ball is already drawn, for the third it's 78/80, and so on until the eleventh ball.
The probability of drawing 11 unique balls is therefore (80/80) * (79/80) * (78/80) *...* (70/80). The probability of at least two balls having the same number is 1 minus this product, which represents the probability of all balls being unique.
I have 8 flavors of ice cream and 4 different toppings. How many different ice cream sundaes can I make if I choose one flavor of ice cream and only one topping?
Keith drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Keith drove home, there was no traffic and the trip only took 5 hours. If his average rate was 21 miles per hour faster on the trip home, how far away does Keith live from the mountains? Do not do any rounding.
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.
A recent survey reported that out of 50 teenagers, 9 said they get most of their news from a newspaper. At this rate, how many out of 300 teenagers would you expect to get their news from a newspaper?
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.
A model of a car is available in 4 colors (black blue silver and white.) and 3 body styles(coupe sedan and wagon) there are also 2 engines to choose from , (16 cylinders, called V6 and four cylinder called l4) what is the probability of choosing a vehicle that is V6 sedan
Answer:
Step-by-step explanation:
P=1/2 *1/3=1/6