Use the box method to distribute and simplify (-3x – 3)(5 + 4x²). Drag and drop the terms to the correct locations of the table.
Answers
Looking at the diagram, the box method has already been applied. The simplified answer would be gotten by adding up each term in the boxes while taking into consideration, the signs of each term. It becomes
- 15x - 15 - 12x^2 - 12x^3
Rearranging the terms in descending order of the exponents, it becomes
- 12x^3 - 12x^2 - 15x - 15 15x - 15 - 12x
Related Questions
coupon A:$18 rebate on a $95 bicycle couponB:15% off of a $95 bicycle
Answers
Coupon A gives the lower price,is $3.75 less than the price with coupon b
Explanation
Step 1
get the final price
a) Coupon A
$ 18 rebate on a $95 bycicle
so, the final price is
[tex]\begin{gathered} \text{final price=original price-discoutn} \\ \text{ final price=\$95 -\$18} \\ \text{ final price(a)=\$77} \end{gathered}[/tex]b) 15% off of a $95 bucycle
fint, the value for 15% of $95
[tex]15\text{ percent=}\frac{\text{15}}{100}=0.15[/tex]so, to know the value for 15% of $95,do:
[tex]\text{discount}=0.15\cdot95=14.25[/tex]the discount for coupon b is $14.25,
hence the final price is
[tex]\begin{gathered} \text{ Final price=\$95 -\$14.25} \\ \text{ Final price=80.75} \end{gathered}[/tex]Hence,
[tex]\text{ Final price(B)=\$ 80.75}[/tex]Step 2
compare the prices(difference)
[tex]\begin{gathered} \text{Price(a)}=77 \\ \text{Price(b)}=80.75 \\ \text{pric e(b)-price(a)=80.75-77=3.75} \end{gathered}[/tex]I hope this helps you
the answer to this equation no steps needed for me just needed a,b,c or d
Answers
Solution
- The solution steps are given below:
[tex]\begin{gathered} y\propto\frac{1}{x^2} \\ \\ \therefore y=\frac{k}{x^2} \\ where,\text{ }k\text{ is the constant of proportionality} \\ \\ when\text{ }x=1,y=\frac{7}{4} \\ \\ \frac{7}{4}=\frac{k}{1^2} \\ \\ \therefore k=\frac{7}{4} \\ \\ \text{ Thus, we can say} \\ y=\frac{7}{4x^2} \\ \\ \text{ Thus, when }x=3,\text{ we have:} \\ y=\frac{7}{4(3^2)} \\ \\ y=\frac{7}{4\times9} \\ \\ \therefore y=\frac{7}{36} \end{gathered}[/tex]Final Answer
The answer is
[tex]y=\frac{7}{4x^2};y(3)=\frac{7}{36}\text{ \lparen OPTION C\rparen}[/tex]which of the following is not a polynomial identityA) x²+y²=x²+2xy+y²B) x³+y³=(x+y) (x²-xy+y²)C) (x+y)² = x²+2xy+y²D) x²-y²= (x+y) (x-y)
Answers
The first option:
A)
x² + y² = x² + 2xy + y²
is not a polynomial identity because the right side of the equation corresponds to a binomial squared, which is given by:
(x + y)² = x² + 2xy + y²
and what you have left side of the given expression is x² + y² and not (x + y)² which is totally different.
Hence, x² + y² = x² + 2xy + y² is not a polynomial identity
what is slope of the line parallel to the given line(I know the steps no explanation just need work:)
Answers
Given the equation of the line :
[tex]4x-3y=-12[/tex]To find the slope, solve the equation for y:
[tex]\begin{gathered} 4x-3y=-12 \\ -3y=-4x-12 \end{gathered}[/tex]Divide both sides by -3 :
[tex]\begin{gathered} \frac{-3y}{-3}=\frac{-4x}{-3}-\frac{12}{-3} \\ \\ y=\frac{4}{3}x+4 \end{gathered}[/tex]So, the slope of the given line = 4/3
And the slope of the line parallel to the given line = 4/3
Because the parallel line have the same slopes
So, the answer is : slope = 4/3
Evaluate the expression when x=5 and z=7.25z+ xSimplify your answer as much as possible.
Answers
We are given the expression
[tex]\frac{5z+x^2}{x}[/tex]and are asked to evaluate it when x=5 and z=7. For this, we simply replace the given values on the original expression, like this:
[tex]\frac{5(7)+(5)^2}{5}[/tex]And now we simplify it as much as possible:
[tex]\frac{35+25}{5}=\frac{60}{5}=12[/tex]i need help with question 36 (make sure to read the the information above the graph)
Answers
Given:
[tex]\begin{gathered} x+2y>6 \\ -2x+3y\leq6 \end{gathered}[/tex]Required:
To solve the given inequality by graphing.
Explanation:
The graph of the above inequality is,
Now, the solution is shaded in the graph.
Final Answer:
The solution by using the graph is,
Over the past 7 days, Ms.Burge found that the temperature outside had dropped a total of 28 degrees. What is the average temperature per day?
Answers
Remember that the average or mean is the ratio between the sum of all numbers involve and the total number of items there.
In this case, the total is 28 degrees, and the total number of days is 7, we just have to divide.
[tex]\bar{x}=\frac{28}{7}=4[/tex]Therefore, the average temperature per day is 4 degrees.Find the composition of transformations thatmap ABCD to EHGF.Reflect over the [? ]-axis, then translate(x+[ ], y+[ ]).Note: Enter x ory for axis.BсGH2DE124-3-2-10Enter
Answers
Let's complete the transformation from ABCD to EHGF.
Let's first determine the coordinates of the two figures.
Figure ABCD:
A : -5, 2
B : -3, 4
C : -2, 4
D : -1, 2
Figure EHGF:
E : 4, 1
H : 2, 3
G : 1, 3
F : 0, 1
Reflecting ABCD over the y - axis, we get:
P (x, y) = P' (-x, y)
For ABCD:
A : -5, 2 = A' : 5, 2
B : -3, 4 = B' : 3, 4
C: -2, 4 = C' : 2, 4
D: -1, 2 = D' : 1, 2
Let's now complete the translation,
(x + S), (y + T)
Where,
S = translation at x-axis
T = translation at y-axis
We get,
A' : 5, 2 = E : 4, 1 → S, T = 4 - 5, 1 - 2 = -1, -1
B' : 3, 4 = H : 2, 3 → S, T = 3 - 4, 3 - 4 = -1, -1
C' : 2, 4 = G : 1, 3 → S, T = 1 - 2, 3 - 4 = -1, -1
D' : 1, 2 = F: 0, 1 → S, T = 0 - 1, 1 - 2 = -1, -1
Therefore, we can say that the translation is (x + _, y + _) = (x + (-1), y + (-1)) = x - 1, y - 1
two hundred million thirty five
Answers
The given number is two hundred million thirty five.
As you can observe, this number has hundred millions, tens, and units. Specifically, it has 2 hundred million, 3 tens and 5 units. We write each part as a sum, as follows
[tex]200,000,000+30+5[/tex]Then we add, so the number is
[tex]200,000,035[/tex]Create a real life word problem that represents a partial variation and has a constant of variation of 4
Answers
We and a problem with a constant of variation of 4.
We can think as following:
Kate wants to make a party and make candies for her guests. She intent to make at least 15 candies and an additional of 4 candies for each guest. Thetermine the total number of candies, c, that Kate must make according to the total numer of guests, g.
Answer: c = 4g + 15
mean=100 sd=20 determine the probability that random student scores below 70 on the pax test. above 112 on the pax test, and random student scores between 85 and 115 on the pax test
Answers
For this problem, we are given the mean and standard deviation of a certain test. We need to determine a probability of a random sample to be in a few values.
The first value we need to determine is the probability of the random sample being below 70. The first step we need to take is to determine the z-score of this value, which can be calculated with the following expression:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]For the value of 70, we have:
[tex]Z=\frac{70-100}{20}=\frac{-30}{20}=-1.5[/tex]Now we need to find this value on the z-table, which is:
[tex]P(Z<-1.5)=0.0668[/tex]Therefore we can determine that the probability of a value to be below 70 is 6.68%.
Now we need to determine the probability of a value above 112. We need to determine the z-score once again:
[tex]Z=\frac{112-100}{20}=\frac{12}{20}=0.6[/tex]The z-table only tells us values below the z-score, so we need to subtract the result from 1, which is shown below:
[tex]P(Z>0.6)=1-P(Z<0.6)=1-0.7275=0.2725[/tex]The probability of the value being greater than 112 is 27.25%.
Now we need to find the probability of the score to be between 85 and 115. We need to find both Z-scores:
[tex]\begin{gathered} Z(85)=\frac{85-100}{20}=\frac{-15}{20}=-0.75\\ \\ Z(115)=\frac{115-100}{20}=\frac{15}{20}=0.75 \\ \end{gathered}[/tex]So we need to find the two values on the Z-table and subtract them. We have:
[tex]P(-0.75The probability of the random value being between 85 and 115 is 54.68%.Question 6 Clare volunteers at a local library during the summer. Her work includes putting labels on 750 books. How many minutes will she need to finish labeling all books if she takes no breaks and labels 15 books a minute Question 7 Suppose Clare labels the books at a constant speed of x books per minute. Write an equation that represents the relationship between her labeling speed and the number of minutes it would take her to finish labeling.
Answers
Clare is going to need 50 minutes to label 750 books
1) Gathering the data
750 books
15 books per minute
2) Let's set a proportion for that, considering the fact that her speed is constant
15 books ----------------------1 minute
750 -------------------------------x
15x = 750
x= 50 books
3) Clare is going to need 50 minutes to label 750 books.
connie is packing for a trip. she has 16 pairs of shoes. if she has room to pack 7 pairs, how many ways can she choose which shoes to take?
Answers
Combinatorics
If Connie had only 7 pairs of shoes and she has room for 7 pairs of shoes, then she has only one way to take her shoes.
If she had 8 pairs of shoes, then she can select any group of shoes that leaves one pair out. This makes 8 possible ways to choose.
When the number of pairs of shoes goes up, then the counting gets more complex. That is when combinatorics is a useful tool.
If we have a total of n elements to select m, where the order of selection is not important, then the total number of selections is given by:
[tex]C_{n,m}=\frac{n!}{(n-m)!\cdot m!}[/tex]Where the sign (!) is the factorial of a number.
Connie has n=16 pairs of shoes and she will take m=7 from them, thus the number of possible ways or combinations is:
[tex]\begin{gathered} C_{16,7}=\frac{16!}{(16-7)!\cdot7!} \\ C_{16,7}=\frac{16!}{(9)!\cdot7!} \end{gathered}[/tex]Expanding the factorial down to match the greatest factorial in the denominator:
[tex]C_{16,7}=\frac{16\cdot15\cdot14\cdot13\cdot12\cdot11\cdot10\cdot9!}{(9)!\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex]Simplifying and calculating:
[tex]C_{16,7}=\frac{57,657,600}{5,040}=11,440[/tex]Connie can choose in 11,440 ways the shoes to choose
The vertex of this parabola is at (-2,5). Which of the following could be its equation? (-2,5) -5 O A. y = 3(x-2)2-5 O B. y = 3(x-2)2 + 5 O C. y= 3(x+ 2)2-5 BE E EIE O D. y=3(x + 2)2 + 5 anter
Answers
The base equation of a parabola is F(X) = X^2 + C
if we make F(X+2) it means the chart will move 2 units to the left
on the other hand, if the make F(X) + 5, it means the chart will displace 5 units upwards
As a result, from the given chart, our equation would be: y = 3(x+2)^2 + 5
I need help with this question my answer was 2 but I for sure
Answers
Given
Distance = 30 km
Time = 1 1/2 hours = 3/2 hours
Find
rate in km per hour
Explanation
we need to find the rate in km per hour.
as we now the rate is also called a speed
so , speed = distance/time
[tex]\begin{gathered} rate=\frac{distance}{time} \\ \\ rate=\frac{30}{\frac{3}{2}} \\ \\ rate=\frac{30\times2}{3} \\ \\ rate=\frac{20km}{h} \end{gathered}[/tex]Final Answer
Therefore, the rate of ship is 20km/hr
so , the correct option is 1.
One type of dog treat, Barker, contains 3 oz and sells for $1.95. DogYum contains 3.25 and sells for $2.10.Which is less expensive, per ounce?A. DogYum is less expensive, per ounceB. Barker is less expensive, per ounce
Answers
Solution
- We are told that dog treats, Barker and DogYum cost $1.95 for 3 oz and $2.10 for 3.25 oz respectively and we are required to find out which is more expensive per ounce.
- In order to find the more expensive dog treat, we need to find the cost per ounce for each item. The cost per ounce is given by the formula below:
[tex]\frac{\text{Cost of dog treat (In Dollars)}}{\text{Weight of dog treat (In Oz)}}[/tex]- The dog treat with the larger cost per oz is the more expensive item.
- Thus, let us calculate the cost per oz for both items.
DogYum:
[tex]\begin{gathered} \frac{\text{Cost of DogYum}}{\text{Weight of DogYum}}=\frac{2.10}{3.25}=0.646 \\ \\ \text{Thus, the cost per oz of the DogYum treat is \$0.646/oz} \end{gathered}[/tex]Barker:
[tex]\begin{gathered} \frac{\text{ Cost of Barker}}{\text{Weight of Barker}}=\frac{1.95}{3}=0.65 \\ \\ \text{Thus, the cost per oz of the Barker treat is \$0.65/oz} \end{gathered}[/tex]- We can observe that Barker is marginally more expensive than DogYum. We can confirm this by simply subtracting the cost per oz for both treats.
[tex]\text{Barker - DogYum}=0.65-0.646=0.004[/tex]Final Answer
The answer is:
DogYum is less expensive, per ounce
A telemarketers computer selects phone numbers at random. The telemarketer has recorded the number of respondents in each age bracket for one evening in the following table. What is the probability that the next respondent will be between 18 and 25? Enter a fraction or round your answer to four decimal places, if necessary.Under-18 =1818-25=2526-35=4636-45=56Over 45=54
Answers
The probability P of an event e can be found using the formula:
[tex]P(an\text{ event e occurring\rparen= }\frac{Number\text{ of occurrence of an event}}{Total\text{ number of occurrence}}[/tex]Required: The probability that the next respondent will be between 18 and 25
Number of respondents between the ages of 18 and 25 = 25
Total number of respondents :
[tex]\begin{gathered} =\text{ 18 + 25 + 46 + 56 + 54} \\ =\text{ 199} \end{gathered}[/tex]Hence, the probability of a selecting a respondents in the age range 18 to 25 is:
[tex]\begin{gathered} P\text{ = }\frac{25}{199} \\ =\text{ 0.125628} \\ \approx\text{ 0.1256} \end{gathered}[/tex]Answer: 0.1256
This is a graph of the relationship between millimeters of rainfall and umbrella sales. In your own words, explain what happens to umbrella sales as the amount of rainfall changes.
Answers
On the graph, the x axis represents rainfall while the y axis represents number of umbrella sold. We can see that as the amount of rainfall is increasing, the number of umbrellas sold is increasing. This is shown by the line moving upwards in the positive direction. the relationship between the amount of rainfall and the number of a umbrellas sold is a positive association.
Question 1 (Essay Worth 10 points)(03.03 MC)A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:f(d) = 11(1.01)dPart A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points) Source StylesFormat ◢ Question 2 (Essay Worth 10 points)(03.02, 03.03, 03.04 MC)The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Marco is studying the change in the amount of money in two accounts, A and B, over time.The amount f(x), in dollars, in account A after x years is represented by the function below:f(x) = 1,264(1.09)xPart A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)Part B: The table below shows the amount g(r), in dollars, of money in account B after r years:r (number of years)1234g(r) (amount in dollars)1,3751,512.501,663.751,830.13Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer. (5 points)
Answers
A biologist studying the growth of a particular species of algae and later designed a model equation for the growth
F(d) = 11(1.01)d
Where, f(d) is in mm and d is days
QUESTION A
F(d) = 11(1.01)d
f(d) = 11.79 mm
Substitute f(d) = 11.79 mm into the model equation
11.79 = 11(1.01)d
11.79 = 11 * 1.01 * d
11 .79 = 11.11 x d
11.79 = 11.11d
Divide both sides by 11.11
11.79/11.11 = 11.11d/11.11
d = 11.79/11.11
d = 1.061
Thde reasonable domain to plot the growth function is 1.061 < d > 1.061
3x - 4y = 10Add a Com6x + y = 38andMediac-9% +12y = -30Save9x - 3y = 48These systems are said to be equivalent. Both of the equations in the secondsystem came from the first system somehow,Two questions: How was the first equation is the second system formed fromthe first system? And how was the second equation in the second systemformed from the first system?
Answers
First solution
[tex]\begin{gathered} \text{The first equation in the second system (Equation 2.1),} \\ \text{was formed by multiplying (Equation 1.1) by -3} \end{gathered}[/tex][tex]\begin{gathered} \text{proof:} \\ -3\text{ (3x - 4y= 10) = -9x + 12y = -30} \end{gathered}[/tex]Second solution
The second equation in the second system (Equation 2.2) was formed by adding both equations in the first system.
That is;
(Equation 2.2) = (Equation 1.1) + (Equation 1.2)
[tex]\begin{gathered} \text{proof:} \\ 3x\text{ -4y = 10 } \\ +\text{ 6x + y = 38} \\ (3x+6x)\text{ + (-4y+y) = 10+38} \\ 9x\text{ -3y = 48} \end{gathered}[/tex]The function y =30+5x represents the cost y (in dollars) of having your dog groomed and buying x for extra services . can u please just do C (graph the function using six values of it's domain
Answers
Problem
The function y =30+5x represents the cost y (in dollars) of having your dog groomed and buying x for extra services . can u please just do C (graph the function using six values of it's domain
Solution
Part a
For this case a linear function is given by: y = mx+b
If we compare the function y =30 +5x we can see that we have the sam efunctional form and we can conclude that yes is a linear function with m = 5 and b =30
Part b
For this part since we have a linear function the domain is given by:
D= [0,1,2,3,4,5}
Then the domain is discrete
Part c
For this case we have the following solution:
Situation:Holly wants to save money for anemergency. Holly invests $1,000 in anaccount that pays an interest rate of6.25%
Answers
Given data:
Amount of money invested, P = $1000
Interest rate, r = 0.0625
Total money in the account, A = 5500
Now, to find the years use simple interest rate formula that is
[tex]A=P(1+rt)[/tex]Therefore, t will become
[tex]t\text{ = (A/P}-1\text{)/r}[/tex]Putting the values we get,
[tex]t=(\frac{5500}{1000}-1)\text{ / 0.0625}[/tex][tex]\begin{gathered} t=(5.5-1)\text{ / 0.0625} \\ t=\frac{4.5}{0.0625} \\ t=72 \end{gathered}[/tex]Thus, it will take 72 years for the account to reach 5500.
the recursive rule is a1=__and a n-1 for n> __.the explicit rule is a n= ___(__)n-1
Answers
We are required to find both the recursive rule and the Explicit rule for the values given in the table.
Recursive rule:
To get the recursive rule, we need to find the common ratio.
The common ratio (r) is found by dividing the 2nd term by the 1st term, or the 3rd term by the 2nd term, or the 4th term by the 3rd term, and so on.
We can generalize and say the common ratio is also the division of the nth term by the (n-1)th term.
Let us put these facts into mathematical expressions:
[tex]\begin{gathered} Let,_{}_{} \\ a_1=\text{first term} \\ a_2=\text{Second term} \\ a_3=\text{third term} \\ \text{...} \\ a_n=\text{nth term} \\ \\ \text{common ratio (r)=}\frac{a_1}{a_2}=\frac{a_3}{a_2}=\frac{a_4}{a_2}\ldots=\frac{a_n}{a_{n-1}} \\ \\ \text{if a}_1=1,a_2=3_{} \\ \therefore r=\frac{a_2}{a_1}=\frac{3}{1}=3 \end{gathered}[/tex]Thus, we can now write the recursive formula as:
[tex]\begin{gathered} \frac{a_n}{a_{n-1}}=\text{common ratio (r)} \\ \\ \therefore\frac{a_n}{a_{n-1}}=3 \\ \\ \therefore a_1=1,a_n=3a_{n-1}\text{ for n}\ge1 \end{gathered}[/tex]Explicit rule:
To get the rule, we need to recognize the pattern:
[tex]\begin{gathered} \text{when n = 1} \\ a_1=1=3^0 \\ \\ \text{When n = 2} \\ a_2=3=3^1 \\ \\ \text{When n= 3} \\ a_3=9=3^2 \\ \\ \text{When n= 4} \\ a_4=27=3^3 \\ \\ \text{When n = 5} \\ a_5=81=3^4 \end{gathered}[/tex]We can see a pattern developing and from that, we can generalize:
[tex]\begin{gathered} a_1=3^0 \\ a_2=3^1 \\ a_3=3^2 \\ a_4=3^3 \\ a_5=3^4 \\ \ldots \\ a_n=3^{n-1} \end{gathered}[/tex]Thus, the explicit rule is:
[tex]\begin{gathered} a_1=1 \\ a_n=1\times3^{n-1} \end{gathered}[/tex]R's sleep log: 8.5 8 9.5 9 7.5 8.5B's sleep log 6.5 7 7.5 6.5 12 7.5which statement is NOT true about the data provided?a. both sets of data have an interquartile range of 1b. both measures of center for R's data have a value of 8.5c. the shape of both data distributions are non-symmetricd. the IQR of B's data is best used to describe the spread because of the outlierR's sleep log: 8.5 8 9.5 9 7.5 8.5B's sleep log 6.5 7 7.5 6.5 12 7.5
Answers
Answer
C. The shape of both data distributions are non-symmetric
Step-by-step explanation
Ordering both data sets from least to greatest, we get:
R's sleep log:7.5 8 8.58.5 99.5
B's sleep log: 6.5 6.577.57.512
We can see that B's data is concentrated at the lower values (12, the maximum, is an outlier). Then, the shape of B's data distribution is non-symmetric. But, in R's data every value is equidistant from the other ones, in consequence, the shape of R's data distribution is symmetric.
I
3. (5 points) Herman and Rosie need to wash the walls on the side of the school. Herman
has a power washer, which could complete the job in 10 hours. Rosie has a manual
scrubber, which could complete the job in 15 hours. in
they work together, how many hours
will it take them to clean the wall?
Answers
Answer:
It would take them 6 hours. Six hours is 3/5 of Herman’s required time. 6 hours is 2/3 of Rosie’s, so 3/5 +2/5= the project being complete.
23 pointsThe length of a rectangular box is 1 inch longer than twice the width (x).The height is 5 inches.which is the volume (y) function
Answers
y = 5x ( 2x + 1)
Explanations:Let the width of the rectangular box be x
Let the length be L
Let the height be H
Let the volume be y
The length of the rectangular box is 1 inch longer than twice the width (x)
L = 2x + 1
The Height is 5 inch
H = 5
The volume of a rectangular box is:
Volume = Length x Width x Height
y = LHx
y = (2x + 1) (5) (x)
y = 5x (2x + 1)
drag two number lines to the box where the shade parts best compare 1/6 and 1/4
Answers
Given the fractions 1/6 and 1/4
We need to compare between them
The two number lines will be:
By comapring between them : 1/6 < 1
There are two bags containing only white and blue marbles.BagA has 11 white marbles and 9 blue marbles.Bag B has 6 white marbles and 2 blue marbles
Answers
from Least likely to Most likely
Event 3,
Event 1,
Event 4,
Event 2
STEP-BY-STEP EXPLANATION
BAG A contains:
no of white marbles = 11
no of blue marbles = 9
Total marbles in Bag A
= 11 + 9 = 20
Prob. of choosing a white marble in Bag A
= 11 / 20
Prob. of choosing a blue marble in Bag A
= 9 / 20
BAG B contains:
no of white marbles = 6
no of blue marbles = 2
Total marbles in Bag B
= 6 + 2 = 8
Prob. of choosing a white marble in Bag B
= 6 / 8
Prob. of choosing a blue marble in Bag B
= 2 / 8.
Event 1: Choosing blue marble from Bag B
= 2 / 8 = 0.25
Event 2: Choosing white marble from Bag B
= 6 / 8 = 0.75
Event 3: Choosing purple marble from Bag A
= 0 / 20 = 0
Event 4: Choosing white marble from Bag A
= 11 / 20 = 0.55.
Hence, from Least likely to Most likely we have Event 3, Event 1, Event 4, Event 2.
Hello, May I please get some assistance with this homework question? I posted an image below. Question A has already been answered, but do need help with the other questions. Q2 (part b)
Answers
ANSWER
• (g o f)(x) = ,16x² + 24x + 9
,• B., the domain of g o f is all real numbers
EXPLANATION
The composition is,
[tex](g\circ f)(x)=g(f(x))[/tex]This means that, to find the composition, we have to replace x with f(x) in the function g(x),
[tex]g(f(x))=(f(x))^2[/tex]Now, replace f(x) with its expression,
[tex]g(f(x))=(4x+3)^2[/tex]We can expand this binomial squared to write it in standard form. The composition is,
[tex](g\circ f)(x)=16x^2+24x+9[/tex]As we can see, this is a polynomial function. Therefore, the domain is all real numbers.
Stefan can pick forty bushels of apples in12 hours. One day his friend Gabriellahelped him and it only took 6.67 hours.Find how long it would take Gabriella todo it alone.
Answers
Stefan picks up 40 bushels of apples in 12 hours.
With the helo of gabriela they do so th 6.67 hours. We can represent this in the following table:
Bulshels of apples Hours
40 6.67
We need to multiply these number by 2, so that we can know how much time it would take for Gabriella to pick 40 alone.
Bulshels of apples Hours
40 6.67
80 13.34
Now, since picking 80 together takes 13.34 hours, and we know that tefan picks up 40 in 12 hours, the other 40 where picked up by Gabriella in:
[tex]13.34-12=1.34[/tex]Answer: 1.34 Hours