Answer:
(f+g)(x) = 13x + 3
Step-by-step explanation:
Rewrite f(x)=2x+7 and g(x)=11x-4 in columns, as follows:
f(x)=2x+7
+g(x)=11x-4
----------------
Now add each column separately.
f(x)+g(x) = (f+g)(x) ("the sum of functions f and g")
2x + 11x = 13x, and, finally, 7-4 = 3.
Therefore,
f(x)=2x+7
+g(x)=11x-4
----------------
(f+g)(x) = 13x + 3
Ben and Jerry’s ice cream company estimates that for every 32 people that they serve their delicious ice cream to, they need to make 128 ounces of ice cream. How many people can they serve if they make 704 ounces of ice cream?
Set up a proportion and solve.
The first part of the proportion would be the known values of 32 people to 128 ounces.
The second part of the proportion is X ( the number of people) for 704 ounces.
This is written as 32/128 = X/704
To solve for X Cross multiply:
32 * 704 = 128x
Simplify:
22528 = 128x
Solve for X by dividing both sides by 128:
x = 22528 / 128
x = 176 people
What is the relationship between the ratios? 48/72 and 6/9 Drag and drop to complete the statement.
a. proportional
b. not proportional
A shoe store marks up it's merchandise by 8 percent what was the selling price of a pair of shoes whose wholesale price is 24.50
The answer is 26.46. I got it correct on my GoFormative.
The price of shoe store merchandise after markup price will be equal to 26.46.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given data given in the question,
The wholesale price of merchandise = 24.50
Markup percentage on merchandise = 8%
Then, the amount of increment in the price will be,
(24.50 × 8)/100
= 196/100
=1.96
Then, the price of merchandise after markup will be,
= 24.50 + 1.96
= 26.46
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HELP!!!!!!! 100 POINTS PLS HALP
Isaac is purchasing two pairs of shoes—one pair for $37.00 and the second pair for $42.00. The state sales tax applied to Isaac’s bill is 7%. How much is Isaac’s total bill? Show your work.
ANSWERED^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 84.53
If Isaac uses a coupon entitling him to a 25% discount off the purchase price before tax, how much will his bill be? Assume that a 7% sales tax is applied to the discounted price. Using words, explain how you found the discounted price.
ANSWERED ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 63.4
The shoe store’s clerks are paid on commission. If the clerk receives a 12% commission on total purchase amounts before tax is applied, how much would the commission be for Isaac’s purchase with and without a coupon?
NOT ANSWERED^^^^^^^^^^^^^^^^^^^^^^^ Pls help
Answer:
7.11 and 9.48
Step-by-step explanation:
.12 is equal to 7.11
with out coupon
.12 is equal to 9.48
with the coupon
a. Isaac's total bill is $84.53
b. Isaac's price after the discount is $63.40
c. The shoe store clerk's commission before the coupon is $9.48 and $7.11 after the coupon
Solution to the first question
Total bill = cost of shoes + tax paid
Tax paid = tax rate + cost of shoes
Cost of shoes = $37.00 + $42.00. = $79
Tax paid = $79 + 0.07 = $5.53
Total bill = $5.53 + $79 = $84.53
Solution to the second question
The discounted price of the shoes can be found by subtracting the value of the discount from the price of the shoes
Discounted price = cost of the shoes = value of the 25% discount
Value of the 5% discount = 0.25 x $79= $19.75
Discounted price = $79 - $19.75 = 59.25
Bill = discounted price x ( 1 + tax rate)
59.25 x 1.07 = $63.40
Solution to the third question
Commission before the coupon
Commission = 12% x price before the coupon
0.12 x $79 = $9.48
Commission after the coupon
Commission = 12% x price after the coupon
0.12 x 59.25 = $7.11
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Amanda put $1500 in her savings account. After five years she had $1833 in the account. What rate of interest did she earned use the formula a equals PE to the power of rt and t is time and
Answer: 4.01% interest rate
This value is approximate. It is rounded to the nearest hundredth of a percent.
============================================
Work Shown:
A = P*e^(r*t)
1833 = 1500*e^(r*5)
1833/1500 = e^(5r)
1.222 = e^(5r)
e^(5r) = 1.222
5r = Ln(1.222)
5r = 0.2004888607494
r = 0.2004888607494/5
r = 0.04009777214989
r = 0.0401
r = 4.01%
A biker rode 45 miles in 180 minutes. At what speed (in miles per hour) was the biker travelling? A. 4 B. 17 C. 9 D. 12
Answer:
v = 15 miles / hour
Step-by-step explanation:
Given:
Distance covered by biker = s=45 miles
time taken by him = t=180 minutes
TO Find:
speed in miles per hour = v = ?
Solution:
As it is given that the distance covered is 45 miles
and time taken by him is 180 minutes
as one hour have 60 minutes
so time taken by rider = t = 180 /60
= 3 hours
this step is done because we have to find speed in miles per hour
Now
The formula for finding the distance is
distance = speed * time
or
s = v * t
we have to find v
so dividing both sides by t
[tex]\frac{s}{t} = \frac{v*t}{t}[/tex]
it becomes
[tex]v = \frac{s}{t}[/tex]
Putting the values
[tex]v = \frac{45}{3}[/tex]
solving it gives
v = 15 miles / hour
which is the required speed
in the given options it is not available
The speed is 15 miles per hour, not matching any of the provided answer choices.
The question asks for the speed of the biker in miles per hour when given the distance rode over a certain amount of time. To find the speed, we can use the formula: Speed = Distance / Time.
In this case, the biker rode 45 miles in 180 minutes. Since there are 60 minutes in an hour, we first convert 180 minutes into hours by dividing by 60: 180 / 60 = 3 hours.
Next, we calculate the speed: Speed = 45 miles \/ 3 hours = 15 miles per hour. But since this isn't one of the options provided, it seems there has been a typo in the answer choices. The correct answer, which should be 15 mph, is missing in the options.
Please help! Im so dumb ( -̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥᷄ ω-̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥᷅ )
Look at both pictures!
I need two answers!
ANSWER:
For the first picture, it is the first answer. This is because of the Exterior Angle Theorem.
For the second picture, use the Exterior Angle Theorem again, but this time, solve for x.
[tex]132 = x + (3x-24)\\132 = 4x - 24\\156=4x\\x=39[/tex]
The m∡B = 39°
What is the area of this parallelogram? 4.9 cm? 12.25 cm? 17.15 cm? 24.01 cm? Parallelogram A B C D is composed of a square and two triangles. The square has a length and height of 3.5 centimeters each. There are two identical triangles. Each triangle has a base of 1.4 centimeters and a height of 3.5 centimeters.
Answer:
(C) 17.15
Step-by-step explanation:
A candy bar has 220 calories 132 calories are sugar what percent of the calories does the candy bar have?
What are the answer choices?
To find out what percent of the calories in a candy bar comes from sugar, divide the calories from sugar (132) by the total calories (220) and multiply by 100, resulting in 60% of the calories being from sugar.
To calculate what percent of the calories in the candy bar are from sugar, we can use the formula for percentage: (part / whole) x100. In this case, the part is the number of calories from sugar, and the whole is the total number of calories in the candy bar.
First, let's identify the given values:
Now, let's calculate the percentage:
Percentage of calories from sugar = (132 / 220) x 100Calculating this, we find:
Percentage of calories from sugar = 0.6 x100Percentage of calories from sugar = 60%Therefore, 60% of the calories in the candy bar are from sugar.
If a town with a population of 10,000 doubles every 14 years, what will the population be in 42 years and is it modeled by a linear function or an exponential function? A) 30,000; linear function B) 60,000; exponential function C) 72,000; linear function D) 80,000; exponential function
Answer: D) 80000; exponential function
Step-by-step explanation:
It would double 3 times in total; first from 10k to 20k, then from 20k to 40k, and finally from 40k to 80k. Hope this helps
Answer:
D)80,000; exponential function
Step-by-step explanation:
We are given that a town with a population of 10,000 doubles every 14 years
So, Initial Population = 10,000
Now we are given that what will the population be in 42 years
First determine how many times population will double : [tex]\frac{42}{14} = 3[/tex]
So, In 42 years it doubles three times .
Now Linear functions change at a constant rate per unit interval while An exponential function changes by a common ratio over equal intervals.
So, the given situation will be modeled by exponential function
So, Using exponential function : [tex]y=ab^x[/tex]
Where a is Initial Population = 10,000
b is rate of change
x = time = 3 times
So, the population will be in 42 years=[tex]10000 (2)^3[/tex]
=[tex]80000[/tex]
So, the population will be 80,000 after 42 years.
Thus Option D is correct.
D)80,000; exponential function
Which of the following functions best describes this graph
Answer: Choice C)
y = (x-2)(x-2)
note: This is the same as y = (x-2)^2
======================================================
The x intercept or root is x = 2, so x-2 is a factor. There is only one root visible, but this is a parabola, so it's technically a double root (it repeats itself). That is why (x-2) shows up twice giving (x-2)(x-2)
If the equation was simply y = x-2, then it would be a linear equation instead of a curved parabola.
Note how plugging in x = 2 leads to the following y value
y = (x-2)(x-2)
y = (2-2)*(2-2)
y = 0*0
y = 0
So (2,0) is the only x intercept.
Saul simplifies the expression 2x3 + 4x3 to 6x6. Use the drop-down menus to complete the statements below to explain why Saul's solution is correct or incorrect.
Answer:
Saul is incorrect. The proper answer should be 6x^3
Step-by-step explanation:
Think of "x^3" as "x". So we have 2x+4x = 6x. Similarly, 2x^3+4x^3 = 6x^3. The exponents of the like terms do not change.
As a more real world example, let's say that we replace "x^3" with "dogs". Saying "2x^3" could mean "2 dogs". Same goes for "4x^3" meaning "4 dogs". So "2x^3+4x^3" turns into "2 dogs + 4 dogs", and you can see that leading to 6 dogs total. The last step is to replace "dogs" with "x^3" to end up with 6x^3. The x^3 stays the same the whole time in much the same way that "dogs" do not change either.
Answer:
saul is incorrect
2x3 + 4x3 is the same as (2 . x^3) + (4 . x^3)
6x6 is the same as 6x . x. x. x. x. x
2x3 + 4x3 simplifies to 6x^3
Step-by-step explanation:
What is the exact situation to the equation e^4x-1=3
(In picture)
Answer:
Short Answer: B
Step-by-step explanation:
You want to solve for x in
e^(4x - 1) = 3 Take the natural log of both sidesln(e^(4x - 1) ) = ln3 Bring the power down from the left side of the equation(4x - 1) ln(e) = ln(3) Note that ln(e) = 1(4x - 1)*1 = ln(3) Add 1 to both sides4x - 1 + 1 = ln(3) + 1 Reduce4x = ln(3) + 1 Divide by 4x = (ln(3) + 1)/4Solve f/a+r=m/s for m
Answer:
d. m = fs/ (a+r)
Step-by-step explanation:
f/ (a+r) = m/s
We want to isolate m, so we will multiply both sides by s
f/ (a+r) *s= m/s*s
fs/ (a+r) = m
[tex]\dfrac{m}{s}=\dfrac{f}{a+r}\qquad\text{multiply both sides by}\ s\neq0\\\\\boxed{m=\dfrac{fs}{a+r}}[/tex]
Which input value produces the same output value for the two functions on the graph?
X= -3
X= -1
X= 1
X= 3
Answer:
X=3
Step-by-step explanation:
We have two linear functions which intersect at a point. Linear functions are lines which are made of points that satisfy the function or relationship. This means at the intersection, this point (3,-1), both functions have values. An input of x=3 produces y=-1 in both functions.
Answer:
The correct option is 4.
Step-by-step explanation:
If the graph of a function represent in coordinate plane, then x-axis represents the domain of the function and y-axis represents the range of the function.
We have to find the input value that produces the same output value for the two functions on the graph.
From the given graph it is clear that the intersection point of both functions is at (3,-1).
At x=3 the output value of f(x) is -1.
At x=3 the output value of g(x) is -1.
It means both functions have same output -1 at x=3.
Therefore the correct option is 4.
Use the figure below list the sides least to greatest of triangle PRQ.
Answer:
Hence third choice RQ, RP, PQ is correct.
Step-by-step explanation:
We know that if A, B, C are the angles of the triangle and if ∠A > ∠B
a>b {Where “a” is side created by angle A and “b” is side created by angle B }.
We will use same property to decide which side is bigger.
In triangle PRQ,
∠P = 30 degree
∠R = 85 degree
then ∠P + ∠R + ∠Q = 180 {since sum of all three angle of triangle is 180 degree}
30 + 85 + ∠Q = 180
115 + ∠Q = 180
∠Q = 180 - 115
∠Q = 65
Now we know measure of all angles so we can do comparison using above property.
Smallest angle is ∠P so side RQ will be smallest.
Largest angle is ∠R so side PQ will be largest.
Hence we get RQ < RP < PQ.
Hence third choice RQ, RP, PQ is correct.
HElP Me
Multiplying by a fraction gives a _____ number.
equal
smaller
larger
Multiplying by a fraction yields a smaller number if the fraction is less than 1, and a larger number if the fraction is greater than 1.
When multiplying by a fraction, the result depends on the fraction you're multiplying by. If the fraction is less than 1 (or what we refer to as a proper fraction where the numerator is less than the denominator), then the result is a smaller number than the original number you started with. For instance, multiplying 5 by 1/2 (which is a proper fraction) will yield 2.5, which is smaller than 5. However, if you multiply by a fraction greater than 1 (an improper fraction where the numerator is greater than the denominator), such as 5/3, the result will be a larger number. So, multiplying 5 by 5/3 will yield approximately 8.33, which is larger than 5.
What is the domain of f/g, given f(x)=x+2 and g(x)=x-7?
Answer:
(-∞,7) U (7,∞)
Step-by-step explanation:
f(x)= x+2
g(x) = x-7
[tex]\frac{f(x)}{g(x)} =\frac{x+2}{x-7}[/tex]
Here we have x-7 in the denominator
To find domain we set the denominator =0 and solve for x
x-7=0
Add 7 on both sides
x=7
x=7 makes the denominator 0 that is undefined
So we ignore 7 for x
Hence domain is
(-∞,7) U (7,∞)
Answer:
The correct answer i believe is A.
Kevin takes a survey of the ages of people in the library at 10 a.m. and at 6 p.m. on a Wednesday.

Kevin wants to give a talk at the library to new drivers on the dangers of texting and driving. Which statement best describes when Kevin should make the talk and why?
At 6 p.m., because the median age of the people in the library at that time is 17 (around the age of new drivers)
At 10 a.m., because the average age of someone in the library at that time is about 30
At 10 a.m., because there are more people with cars at the library at that time
At 6 p.m., because the range of ages for this data set is less than the range of ages for the 10 a.m. data set
Answer:
Option 3rd is correct
Step-by-step explanation:
Kevin takes a survey of the ages of people in the library at 10a.m and at 6p.m on a Wednesday.
He should talk at library to new drivers on the dangers of texting and driving at the time when there are more people with the car.
So, that he can convey messages to more people in less time.
Therefore, Option 3rd is correct that is At 10 a.m., because there are more people with cars at the library at that time
Answer:
1 is correct.
Step-by-step explanation:
I had the same question and I tried the other answer and so it was wrong. And in the correction I had, it was the first one.
In germany, VAT is at 19% jeremy buys a calculator in germany for 58.31 euros this price includes VAT find the amount of VAT paid by jeremy
€9.31
Step-by-step explanation:total = price + tax
... tax = 0.19×price . . . . . . . meaning of 19% VAT
... total = price + 0.19×price = 1.19×price
Dividing by 1.19, we can find the price in terms of the total.
... total/1.19 = price
And we can use this to find the tax
... tax = 0.19×price = 0.19×(total/1.19) . . . . . substitute for price
... tax = 0.19/1.19 × total = 19/119 × total . . . . . . simplify
... tax = 19/119 × 58.31 . . . . . . . put in total amount
... tax = 9.31 . . . . euros
What is the modulus of |9+40i|?
Answer:
41
Step-by-step explanation:
We know that complex numbers are a combination of real and imaginary numbers
Real part is x and imaginary part y is multiplied by i, square root of -1
Modulus of x+iy = [tex]\sqrt{x^2+y^2}[/tex]
Here instead of x and y are given 9 and 40
i.e. 9+40i
Hence to find modulus we square the coefficients add them and then find square root
|9+49i| =[tex]\sqrt{9^2+40^2} =\sqrt{1681}[/tex]
By long division method we find that
|9+40i| =41
Answer: Modulus of |9+40i| =41
Step-by-step explanation:
Since we have given that
[tex]z=\mid9+40i\mid[/tex]
Here,
[tex]z=a+bi\\\\where,\\\\a=\text{real number}=9\\\\b=\text{imaginary number}=40[/tex]
We need to find the modulus of z:
[tex]\mid z\mid=\sqrt{a^2+b^2}[/tex]
[tex]\mid z\mid=\sqrt{9^2+40^2}\\\\\mid z\mid=\sqrt{81+1600}\\\\\mid z\mid=\sqrt{1681}\\\\\mid z\mid=41[/tex]
Hence, Modulus of |9+40i| =41
Ivan's favorite colors are \blue{\text{blue}}blue and \green{\text{green}}green. He has \blue{\text{1 blue shirt}}1 blue shirt, \green{\text{1 green shirt}}1 green shirt, \blue{\text{1 blue hat}}1 blue hat, \green{\text{1 green belt}}1 green belt, \blue{\text{1 blue pair of pants}}1 blue pair of pants, and \green{\text{1 green pair of pants}}1 green pair of pants. Ivan selects one of these garments at random. Let A be the event that he selects a green garment and B be the event that he chooses a pair of pants. What is P(A\text{ or }B)P(A or B), the probability that the garment Ivan chooses is either green or a pair of pants?
Answer:
P(A or B) = 2/3
Step-by-step explanation:
Blue Garments = 1 blue shirt, 1 blue hat, 1 blue pair of pants
Total blue garments = 3
Green garments= 1 green shirt, 1 green hat, 1 green pair of pants
Total green garments = 3
Total no. of garments = blue garments +green garments = 6
A = event that Ivan selects a green garment
P(A) = Favourable outcomes/Total no. of outcomes
P(A) = 3/6
B = event that Ivan chooses a pair of pants
P(B) = 2/6
We need to find P(A or B) = P(A∪B)
By formula, P(A∪B) = P(A)+P(B)-P(A∩B)
P(A∩B) = Probability that a green pair of pant is chosen = 1/6
P(A∪B) = 3/6+2/6-1/6
= 4/6
=2/3
Answer:
1/2
Step-by-step explanation:
Identify the domain of the graphed function.
Answer: Option A is correct
(-5,3) U (3,6]
Step-by-step explanation:
Domain of a function is the complete set of values that the independent variable can assume.
In the given graphed function we can see that the minimum value of independent variable (x) is -5 and the maximum value is 6, wherein the values -5 and 3 do not belongs to x.
This set of values is represented as
(-5,3) U (3,6]
Hope it helps.
Thank you.
The domain of the graphed function is (-5,3) U (3,6].
The correct option is A.
The domain of a function is the entire range of values that the independent variable can take.
In the given graphed function, we observe that the lowest value of the independent variable (x) is -5, and the highest value is 6.
However, it is the values -5 and 3 are not included in the domain.
So, the set of values is represented as (-5,3) U (3,6].
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PLEASE ANSWER THIS QUESTION FOR BRAINLIEST AND 30 POINTS!!
Answer:
The author must sell 3000 books.
Step-by-step explanation:
The total amount earned = advance + books sold * money per book
We know they want to make 7000
The advance is 2500
They earn 1.50 for each book sold
b= number of books sold
Substituting in
7000= 2500 + 1.5b
Subtract 2500 from each side
7000-2500 = 2500-2500 + 1.5 b
4500 = 1.5 b
Divide each side by 1.5
4500/1.5 = 1.5b/1.5
3000 = b
Tickets for a baseball game cost a? dollars for adults and c? dollars for children. The expression 2a+3c represents the cost (in dollars) for a family to go to the game. What is the cost for the family when an adult ticket is $17? and a child ticket is $12??
To find the total cost for the family to attend the baseball game, we substitute the given ticket prices into the expression 2a + 3c, where a is the cost of an adult ticket and c is the cost of a child ticket, resulting in a total cost of $70.
Explanation:The student is asking about the cost for a family to attend a baseball game with the given prices for adult and child tickets.
Given the cost of an adult ticket as $17 and a child ticket as $12, we use the expression provided (2a + 3c) to calculate the total cost for the family.
Substituting the given values into the expression, we get 2(17) + 3(12), which equals 34 + 36.
Summing up these two products gives us a total of $70.
Therefore, it will cost the family $70 to attend the baseball game.
The graph shows calories compared to grams of protein.
What information can you draw from the point (3, 12) on the graph?
A. There are 12 calories in 3 grams of protein.
B. There are 3 calories in 1 gram of protein.
C. There are 3 calories in 12 grams of protein.
D. There is 1 calorie in 4 grams of protein.
Answer:
By the looks of it i would assume 3 grams of protein and 12 calories burned but i am not sure either i am stuck on the same question
Step-by-step explanation:
What number can you multiply by −2√ to get a rational number?
Answer:
the square root of 2 times the negative square root of 2 would be -2, which is a rational number.
The sum of two numbers is 46 and the difference is 10 . What are the numbers?
Answer: 28 and 18
Step-by-step explanation:
I used the guess and test strategy to find that:
28 - 10 = 18
28 + 18 = 46
To find the two numbers, we need to solve a system of equations. By assigning variables to the numbers and setting up equations based on the given information, we can use the method of substitution to find the values of x and y. The two numbers are 28 and 18.
Explanation:
To solve this problem, let's assign variables to the numbers. Let's say the two numbers are x and y. We are given two pieces of information: the sum of the two numbers is 46, so we can write the equation x + y = 46, and the difference between the two numbers is 10, so we can write the equation x - y = 10.
To solve this system of equations, we can use the method of substitution. Rearrange one of the equations to solve for one variable in terms of the other. For example, we can rearrange the first equation to get x = 46 - y. Substitute this expression for x in the second equation:
(46 - y) - y = 10.
Simplify the equation:
46 - 2y = 10. Subtract 46 from both sides:
-2y = -36. Divide both sides by -2 to solve for y:
y = 18. Substitute this value of y back into one of the equations to solve for x:
x + 18 = 46. Subtract 18 from both sides:
x = 28.
So the two numbers are 28 and 18.
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Paul uses 2 and 1/4 cups of raisins to make 4 servings of trail mix. How many cups raisins are in each serving?
Answer:
9/16
Step-by-step explanation:
(2+1/4)/4=(8/4+1/4)/4=(9/4)(1/4)=9/16
A triangle has two sides of lengths 4 and 15.What value could the length of the third side be? Check all that apply.. A:12 B:13 C:4 D:15 E:11 F:19
If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
A: 4, 12, 15
4 + 12 = 16 > 15 CORRECT :)
B: 4, 13, 15
4 + 13 = 17 > 15 CORRECT :)
C: 4, 4, 15
4 + 4 = 8 < 15 INCORRECT :(
D: 4, 15, 15
4 + 15 = 19 > 15 CORRECT :)
E: 4, 11, 15
4 + 11 = 15 INCORRECT :(
F: 4, 15, 19
4 + 15 = 19 INCORRECT :(
Answer: A: 12, B: 13, D; 15