Answer:
n = 9 is the value in the replacement set is a solution to the equation [tex]3(n+7)=48[/tex]
Step-by-step explanation:
Given an equation: [tex]3(n+7)=48[/tex] .....[1]
Replacement set: {8, 9, 10}
For n = 8
Substitute in equation [1], we get;
[tex]3(8+7)=48[/tex]
[tex]3(15)=48[/tex]
[tex]45=48[/tex] False.
Similarly, For n = 9
Substitute in equation [1], we get;
[tex]3(9+7)=48[/tex]
[tex]3(16)=48[/tex]
[tex]48=48[/tex] True.
for n = 10
Substitute in equation [1], we get;
[tex]3(10+7)=48[/tex]
[tex]3(17)=48[/tex]
[tex]51=48[/tex] False.
Therefore, the value in the replacement set is a solution to this equation [tex]3(n+7)=48[/tex] is, 9
Answer:
9
Step-by-step explanation:
A delivery company purchased a new delivery truck for $43,200. The depreciated value of the truck can be estimated by the number of t years in service. If the the truck depreciates at a rate of $7,200 per year, which of the functions ƒ(t) could be used to estimate the truck's depreciated value after t years?
Answer:
[tex]f(t)=43,200-7200t[/tex]
Step-by-step explanation:
We have been given that a delivery company purchased a new delivery truck for $43,200. The depreciated value of the truck can be estimated by the number of t years in service. The truck depreciates at a rate of $7,200 per year.
This means that after t years truck will depreciate 7200t. To find the truck's depreciated value after t years we will subtract 7200t from the cost of new delivery truck (43,200).
[tex]f(t)=43,200-7200t[/tex]
Therefore, the function [tex]f(t)=43,200-7200t[/tex] could be used to estimate the truck's depreciated value after t years.
The depreciated value of the truck after t years can be estimated by the linear function ƒ(t) = 43200 - 7200t, reflecting a straight-line depreciation method at a rate of $7,200 per year.
To estimate the depreciated value of the delivery truck after t years, we can use a linear equation which reflects a straight-line depreciation method. Since the truck cost $43,200 and depreciates at a rate of $7,200 per year, the equation representing the depreciated value of the truck after t years would be ƒ(t) = 43200 - 7200t. This equation starts with the initial value of the truck and subtracts the depreciation cost multiplied by the number of years the truck has been in service.
Depreciation is a way businesses can allocate the cost of a physical asset over its useful life. In this case, each year the truck is in service, it loses $7,200 in value. After one year, the value of the truck would be $43,200 - $7,200, which equals $36,000, and you would continue to subtract $7,200 for each additional year to determine the truck's value at any given time.
a new car has a sticker price of 20950 while the invoice price paid was 18750. what is the dealer markup
11.73%
Step-by-step explanation:
If you need 3 hot dogs for every 5 people and 1,200 people show up how many hot dogs would you need
Answer:
I'd say about 720 hotdogs.
Step-by-step explanation:
Please help on this one ?
Answer:
A
Step-by-step explanation:
The expansion of (x +y)⁴ is ...
... x⁴ +4x³y +6x²y² +4xy³ +y⁴
The expansion coefficients are 1, 4, 6, 4, 1; the sum of exponents is always 4, and there are 5 terms.
It takes 12 hours for a single hose to fill a large vat. When a second hose is added, the vat can be filled in 4 hours. How many hours are required for the second hose working alone to fill the vat?
6 hours
Step-by-step explanation:The two hoses together take 1/3 the time (4/12 = 1/3), so the two hoses together are equivalent to 3 of the first hose.
That is, the second hose is equivalent to 2 of the first hose. Two of the first hose could fill the vat in half the time one of them can, so 6 hours.
The second hose alone can fill the vat in 6 hours.
_____
The first hose's rate of doing work is ...
... (1 vat)/(12 hours) = (1/12) vat/hour
If h is the second hose's rate of doing work, then working together their rate is ...
... (1/12 vat/hour) + h = (1/4 vat/hour)
... h = (1/4 - 1/12) vat/hour = (3/12 -1/12) vat/hour = 2/12 vat/hour
... h = 1/6 vat/hour
so will take 6 hours to fill 1 vat.
The second hose can fill the vat alone in 6 hours, calculated by subtracting the work rate of the first hose from their combined work rate.
Explanation:The question is about the time it would take for the second hose to fill the large vat alone, given that the first hose takes 12 hours alone, but together they take 4 hours. We are not given any info about the hose size or flow rate, so those don't need to be involved here.
We can analyze this problem in terms of work done. We know that one hose can fill the vat in 12 hours, so its work rate is 1/12 of the vat per hour. When we add the second hose, the vat is filled in 4 hours. The combined work rate of both hoses is 1/4 of the vat per hour.
To find the work rate for the second hose, we subtract the work rate of the first hose from the combined work rate: 1/4 - 1/12 = 1/6. This means the second hose can fill the vat in 6 hours alone.
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Three different golfers played a different number of holes today. Rory played 9 holes and had a total of 42 strokes. Jordan played 18 holes and had a total of 79 strokes. Rickie played 27 holes and had a total of 123 strokes. Which golfer had the lowest number of strokes per hole? Choose 1 answer:
Answer:
See below
Step-by-step explanation:
The units are stokes per hole or strokes / hole
Rory: 42/9 = 4.66667Jordan: 79/18 = 4.38889 <<< AnswerRickie: 123/27 = 4.5555Jordan had the lowest number of strokes / hole followed by Rickie and finally Rory.
Answer:
Jordan had the lowest number of strokes per hole
Step-by-step explanation:
1) Total holes played by Rory = 9
Total strokes of Rory = 42
Number of stroke per hole: Rory
[tex]\frac{42 strokes}{9 hole}=4.667 strokes/hole[/tex]
2)Total holes played by Jordan = 18
Total strokes of Jordan = 79
Number of stroke per hole: Jordan
[tex]\frac{79 strokes}{18 hole}=4.389 strokes/hole[/tex]
3) Total holes played by Rickie = 27
Total strokes of Rickie = 123
Number of stroke per hole: Rickie
[tex]\frac{123 strokes}{27 hole}=4.556 strokes/hole[/tex]
4.667 strokes/hole > 4.556 strokes/hole > 4.389 strokes/hole
Rory > Rickie > Jordan
Jordan had the lowest number of strokes per hole
What are the next three terms of 50,150,450,1350,...
Answer: 4,050, 12,150, 36,450
Step-by-step explanation: multiply each following number by 3
Answer:
4050; 12150; 36450
Step-by-step explanation:
[tex]a_5 = 50.3^4 \\\ a_5 = 4050 \\\ a_6 = 50.3^5 \\\ a_6 = 12150 \\\ a_7 = 50.3^6 \\\ a_7 = 36450[/tex]
I hope I helped you.
NEED HELP ASAP!!!
WILL CHOOSE THE BRAINLIEST!!!!
You need a 70% alcohol solution. On hand, you have a 200 mL of a 35% alcohol mixture. You also have 90% alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution?
Add 350 mL of the 90% alcohol mixture to obtain a 70% alcohol solution.
Let V be the volume of the 90% alcohol solution needed
Set up the equation
The final mixture volume will be 200 + V mL.
- The total amount of alcohol in the final mixture should be 70% of the total volume.
Calculate the total amount of alcohol
- Amount of alcohol from 200 mL of 35% solution: 0.35 * 200 = 70 mL.
- Amount of alcohol from V mL of 90% solution: 0.90 * V mL.
Total amount of alcohol in the final solution
- Total alcohol = 70 + 0.90V mL.
Set up the equation for the final concentration
- Final concentration: 70%
0.70 *(200 + V) = 70 + 0.90V
Solve the equation
0.70 * (200 + V) = 70 + 0.90V
140 + 0.70V = 70 + 0.90V
140 - 70 = 0.90V - 0.70V
70 = 0.20V
V = 70 / 0.20 = 350 mL.
Nancy is 5 yrs younger than her brother stan last year she was half as old as he was how old are they both
Answer: 11 and 6
Step-by-step explanation:
I think this is it because she is 5 years younger and last year she was half of his age so he was 10 then you have to add another year to their age because that was last year, 5+1=6, 10+1=11. but im not completely sure so if you can wait for someone else or if you agree go ahead and answer it.
We'll call the ages n and s
Nancy is 5 yrs younger than her brother Stan
n = s - 5
Last year she was half as old as he was
n - 1 = (1/2) ( s - 1 )
We substitute for n
s - 5 - 1 = (1/2) (s - 1)
2s - 12 = s - 1
s = 11
n = s - 5 = 6
Answer: Nancy is 6, Stan is 11
Check:
Clearly they're five years apart. Last year they were 5 and 10, half, good.
C = F Based on the given information, choose the similarity statement that you would use to say ABC~DEF. If you could NOT conclude the triangles similar, then choose NOT. AA SAS SSS NOT
Answer:
Might not be congruent
Step-by-step explanation:
You don't have enough information
Answer with explanation:
It is given that,In ΔABC and Δ DEF
∠C =∠F⇒⇒[Given]
To prove that two triangles are similar, we can use following Similarity axiom which are
a.→ AA
b.→S AS
c.→SSS
→Ratio of sides of two triangles should be proportional while proving similarity of two triangles.
But, Here between two triangles , only one angle is congruent ∠C and ∠F.So, we can't conclude that these two triangles that is, ΔABC and Δ DEF are similar.
Option D:→ Not
divide. simplify your answer (2x^4-6x^3+4x^2-3x)*(2x)
Answer:
[tex]x^3-3x^2+2x-\frac{3}{2}[/tex]
Step-by-step explanation:
We can divide polynomials by other polynomials by dividing each term by the denominator. Remember, when we divide a variable by itself, we must change the exponent in our answer according to exponent rules.
[tex]\frac{ (2x^4-6x^3+4x^2-3x)}{2x}=\frac{2x^4}{2x} -\frac{6x^3}{2x} +\frac{4x^2}{2x} -\frac{3x}{2x} =x^3-3x^2+2x-\frac{3}{2}[/tex]
Answer:
3/2
Step-by-step explanation:
If Tonya bought 1/6 pounds of bologna and 3/8 pounds of ham and 2/4 pound turkey and that cost $5.99 what is the total number of pounds of meat processed
Answer:
25/24 pounds of total meat processed.
Step-by-step explanation:
We have been given pounds of bologna and 3/8 pounds of ham and 2/4 pound turkey
And we need to find the total number of pounds of meat processed.
The total number will be calculated by finding their sum of all the meats which is
1/6+3/8+2/4
Taking LCM of (6,8,4)=24 hence, we get:
1/6+3/8+2/4= 25/24
Sue buys material for a costume she buys 1.75 yards of red material. . She buys 1.2times as much yards of material. How many yards of blue material will she need
Answer:
2.1 yards of blue material will she need.
Step-by-step explanation:
As per the given statement: Sue buys material for a costume she buys 1.75 yards of red material.
As she bought 1.75 yards of the red material.
For blue material she bought 1.2 times as much as yard of the red material.
"times" represents multiply
Blue material she will need = [tex]1.2 \times 1.75 = 2.1 yards[/tex]
therefore, 2.1 yards of blue material will she need.
The number of students at Marita`s school decreased to 90% of last year's number. Last year, there were 1,500 students. How many students are there this year
Answer:
1350
Step-by-step explanation:
We can write a proportion to find the total amount in the school this year using the information given. A proportion is two equivalent ratios set equal to each other. If 10% has decreased, then 90% is now left.
[tex]\frac{10}{100}=\frac{y}{1500}[/tex]
We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.
10(1500)=100(y)
15000=100y
y=150
Y is the number of students who are now gone. We subtract 1500-150=1350
The distance from the school to the corner is 0.9 kilometers. How many meters is this?
Trevor and Marissa together have 26 t-shirts to sell. If marissa has 6 fewer t shirts than trever, how many t shirts does Trevor have
The centre of each semicircle is on DC.
Work out the area of the shaded region.
Give your answer correct to 3 significant figures.
The shaded region, which is approximately 251.74 cm².
For the area of the shaded region, we need to calculate the area of a trapezium and the area of two semicircles.
Given data: AB = 28 cm , DC = 12cm and h = 14 cm
The formula for the Area of Trapezium:
Area of trapezium = 1/2 × (AB + DC) × h
Substituting the given values:
Area of trapezium = 1/2 × (28 + 12) × 14 = 280 cm²
The formula for the Area of a Semicircle:
Area of semicircle = πr²/2
Given that the radius r is 3 cm:
Area of two semicircles = 2 × π × 3²/2 = 28.26 cm²
Area of the Shaded Region:
Area of shaded region = Area of trapezium - Area of two semicircles
Area of shaded region = 280 - 28.26 ≈ 251.74 cm²
Therefore, the area of the shaded region is approximately 251.74 cm².
Carlos swam to the bottom of a pool that is 12 ft deep. What is the opposite of Carlos's elevation relative to the surface
Answer:
The opposite of Carlos's elevation would be +12ft.
Step-by-step explanation:
This question is using positive and negative integers to represent elevation and descending. The surface of the pool would represent an elevation of 0, where we are level. However, when Carlos descends (swims to the bottom) of the pool, he is at an elevation of -12 because he is below the surface. The opposite of -12 would be +12. So the opposite of where Carlos is -12ft below the surface of the water would be +12 foot above the surface of the water.
Consider the function f(x)=−23x+1.
What is f(3)?
Please help! Urgent!
What is the measure of angle B?
-78°
-92°
-102°
-282°
What is the value of x in the equation 2^2x = 2^3?
A.) x = 1.5
B.) x = 3
C.) x = 64
D.) x = 0.28
Answer:
B
Step-by-step explanation:
Find h(x) if it is known that h(x+5)=3x+18.
[tex]h(x+5)=3x+18\\\\h(x)=mx+b\to h(x+5)=m(x+5)+b=mx+5m+b\\\\\text{Therefore we have}\ m=3\ \text{and}\\\\5m+b=18\to5(3)+b=18\\\\15+b=18\qquad\text{subtract 15 from both sides}\\\\b=3\\\\Answer:\ \boxed{h(x)=3x+3}[/tex]
To find the function h(x) when given h(x+5)=3x+18, we substitute x with (x-5) in 3x+18 to make h(x) = 3x+3.
Explanation:To find the function h(x), we need to replace (x+5) in the equation with x. The given equation is h(x+5)=3x+18.
We know that if we substitute x+5 with x in h(x+5), we must also substitute the x in 3x+18 with (x-5) to keep the equation and function consistent.
So, we replace x with (x-5) in 3x+18, and our new equation will be 3(x-5)+18.
This simplifies to 3x - 15 + 18, which further simplifies to 3x+3.
Consequently, the function h(x) = 3x+3.
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Phyllis Doran worked at Symmes Medical Center for 7 1/2 hours on Monday and from 8:00 a.M. Until 1:00 p.M. On Tuesday What is the total number of hours she worked
Final answer:
Phyllis Doran worked a total of 12.5 hours between Monday and Tuesday at Symmes Medical Center.
Explanation:
Phyllis Doran worked a total of two different shifts across Monday and Tuesday. On Monday, she worked for 7 1/2 hours. On Tuesday, she started at 8:00 a.m. and finished at 1:00 p.m., which is a 5-hour shift.
To find the total number of hours Phyllis worked, we add the hours from both days together.
Monday: 7.5 hours
Tuesday: 5 hours (since 1:00 p.m. is 5 hours after 8:00 a.m.)
Now, we sum these up:
Total hours worked = 7.5 hours + 5 hours = 12.5 hours.
So, Phyllis Doran worked a total of 12.5 hours between Monday and Tuesday at Symmes Medical Center.
The latest online craze is a new game, Khan on Seven. You get 100 points for playing the game. In addition, you get 50 points for each seven-letter word you are able to make with the ten letters you are given. The game leader currently has 17,950 points. Sal wants to break the record, and needs 18,000 points or more to do so. Write an inequality to determine how many seven-letter words, ww, Sal will need to make to break the record.
Answer:
x is greater than or equal to 358
Step-by-step explanation:
1. Subtract 100 from 18,000
2. Divide by 50 to get your number of seven letter words
Please help!!
Divide. 2 5/8 ÷ 2 1/2 Enter your answer, as a mixed number in simplest form, in the box.
The simplest form of [tex]2\frac{5}{8}[/tex] ÷ [tex]2 \frac{1}{2}[/tex] is [tex]1\frac{1}{20}[/tex] .
Simplification: Consider,[tex]2\frac{5}{8}[/tex] ÷ [tex]2\frac{1}{2}[/tex]
write the mixed fraction to improper fraction
= [tex]\frac{21}{8}[/tex] ÷ [tex]\frac{5}{2}[/tex]
Now change the division sign to the multiplication sign by writing the second number as [tex]\frac{2}{5}[/tex] .
= [tex]\frac{21}{8}[/tex] × [tex]\frac{2}{5}[/tex]
= [tex]\frac{21}{20}[/tex]
Write the above improper fraction into a mixed fraction.
= [tex]1\frac{1}{20}[/tex]
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If there are 150 students surveyed and 23% is English 30% Science 15% Social Studies and Music is 12% What would the percent be for math be?
Answer:
it would be 20%
Step-by-step explanation:
out of 100% you would subtract the 23%, 30%, 15% and, 12% and you would get 20%
Factor the trinomial below
6x^2-9x-6
A. 3(2x+1)(x-2)
B. 3(2x=6)(x-1)
C. 3(2x+2)(x-1)
D. 3(2x+1)(x-6)
For this case we must factor the following expression: [tex]6x ^ 2-9x-6[/tex]
We test the options:
Option A:
[tex]3 (2x + 1) (x-2) =[/tex]
We apply distributive property for the first parenthesis:
[tex](6x + 3) (x-2) =[/tex]
We apply distributive property of the form:
[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]
[tex]6x ^ 2-12x + 3x-6 =[/tex]
Different signs are added and the sign of the major is placed.
[tex]6x ^ 2-9x-6[/tex]
So, [tex]3 (2x + 1) (x-2) = 6x ^ 2-9x-6[/tex]
Answer:
Option A
Rick carries a balance on his credit card each month. Today is the first day of the new, 28-day billing cycle. The current balance is $2,360 and the APR is 21%. Rick is buying a friend an expensive gift that costs $1,500 that he plans to put on his credit card. This will be his only purchase this month. How much in finance charges can he save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle?
Answer:
$ 25.31 finance charges he can save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle
Step-by-step explanation:
In the beginning of Month , ADB will be on the total amount of balance and the purchase that means ADB = 0.21 (2360 + 1500)/12
= $ 67.55
ADB at the end of the month
Part of 2360 for 27 days = (2360 x 27)/28 = $ 2275.71
Part of 3860 for 1 day = (3860 x 1)/28 = $ 137.85
So the total becomes $ 2275.71 + $ 137.85 = $ 2413.56
So , ADB will be $ 2413.56 x (0.21)/12
= $ 42.23
Difference in the finance charges at the beginning and at the end of the month is
$ 67.55 - $ 42.23
= $ 25.31
Which expression is equivalent to 5x - 5x + 3x - 3x?
A) -16x
B) -4x
C) 4x
D) 0 what the answer
The simplification form of the expression 5x - 5x + 3x - 3x is 0 option (D) is correct.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The linear expression is:
= 5x - 5x + 3x - 3x
After simplification:
= 0 + 3x - 3x
= 0
All terms are canceled out,
Thus, the simplification form of the expression 5x - 5x + 3x - 3x is 0 option (D) is correct.
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A restaurant automatically charges a 20% gratuity if a party has 6 or more people. How much gratuity is added to a party of 6 on and $141 bill?
Answer:
The gratuity added is $28.2 .
Step-by-step explanation:
As given
A restaurant automatically charges a 20% gratuity if a party has 6 or more people.
The bill of the party is $141.
20% is written in the decimal form.
[tex]= \frac{20}{100}[/tex]
= 0.20
Gratuity is added to a party = 0.20 × 141
= $28.2
Therefore the gratuity added is $28.2 .
Answer: The gratuity added is $28.2.