[tex]\bf \begin{array}{ccll} inches¢s\\ \cline{1-2} 17&51\\ 33&x \end{array}\implies \cfrac{17}{33}=\cfrac{51}{x}\implies 17x=33\cdot 51\implies x = \cfrac{33\cdot 51}{17} \\\\\\ x = 33\cdot \cfrac{51}{17}\implies x = 33\cdot 3\implies x = 99[/tex]
Final answer:
To find the cost of 33 inches of wire, we calculate the cost per inch from the given 17 inches costing 51 cents, which is 3 cents per inch, and then multiply by 33 inches to get a total cost of 99 cents.
Explanation:
The student is asking to determine the cost of 33 inches of wire based on the given rate of 17 inches costing 51 cents. To solve this, we can set up a proportion where we compare the given inches of wire to the given cost and then find the cost for the desired inches of wire.
Step-by-Step Calculation:
First, we determine the cost per inch of wire by dividing the total cost by the total length of wire: 51 cents ÷ 17 inches = 3 cents per inch.
Next, we multiply the cost per inch by the desired length of wire to find the total cost: 3 cents/inch × 33 inches = 99 cents.
Therefore, 33 inches of wire will cost 99 cents at the same rate.
6 - x = -12 A) -18 B) -6 C) 0 D) 18
Answer:
D
Step-by-step explanation:
6 - x = -12
subtract 6 from each side
6 - 6 - x = -12 - 6
-x = -18
divide each side by -1
-x / -1 = -18 / -1
x = 18
Answer:
The answer is D.) 18
Step-by-step explanation:
Subtract 6 from both sides. Divide both sides by −1. The answer is 18.
Three consecutive even integers have the property that when the difference between the first and twice the second is found, the result is eight more than the third. Find the three consecutive even integers
Consecutive even integers are -8, -6 and -4
Step-by-step explanation:
Let be the first even integer then the next two integers will be: x+2 and x+6
According to given property, we get
[tex]x - 2(x+2) = (x+4)+8\\x-2x-4 = x+4+8\\-x-4 = x+12\\-x-x = 12+4\\-2x = 16[/tex]
Dividing both sides by -2
[tex]\frac{-2x}{-2} = \frac{16}{-2}\\x = -8[/tex]
The two next integers are:
x+2 = -8+2 = -6
x+4 = -8+4 = -4
Verification:
[tex]-8-2(-6) = -4+8\\-8+12 = +4\\4 = 4[/tex]
Hence, Consecutive even integers are -8, -6 and -4
Keywords: Linear equation, Variables
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how do u slove for 3x-6=15
Add 6 on both sides, canceling out that -6
3x = 21
Divide both sides by 3 to isolate that variable and get your answer
x = 7.
Answer:
x=7
Step-by-step explanation:
3x-6+6=15+6
3x=21
3x/3=21/3
x=7
Mark and Mike are brothers. The sum of their ages is eleven. Mike's age is ten
less than two times Mark's age. How old is each brother?
X =
Write the system:
Solution:
Answer:mark is 7. Mike is 4
Step-by-step explanation:x+y=11. Y=2x-10 thus substituting for y in equation1 we have x+2x-10=11. 3x-10=11. 3x=11+10. 3x=21. X=21/3. X=7. Mike =(2×7)-10=14-10=4
Step-by-step explanation:
Mark's age is x
so Mike's age is
[tex]2x - 10[/tex]
and we know that the sum of their ages is eleven so:
2x+x- 10 = 11
3x-10=11/+10
3x=21/÷3
x=7
Mark is 7 years old and
Mike is 4 years old.
Is 3 a solution to the equation 6x – 7 = 11?
Answer:
Step-by-step explanation:
Yes
First you add 7 to both sides b/c the 7 would be negative. Then your left with 6x=18. Then you divide both sides by 6 and get 3
Answer:
Yes 3 is a solution.
Step-by-step explanation:
6(3) - 7 = 11 6 times three equals 18 so then 18 minus 7 equals 11 so yes.
A rectangular parking lot has an area of 15,000 feet squared, the length is 20 feet more than the width. Find the dimensions
Dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet
Solution:Given that
Area of rectangular parking lot = 15000 square feet
Length is 20 feet more than the width.
Need to find the dimensions of rectangular parking lot.
Let assume width of the rectangular parking lot in feet be represented by variable "x"
As Length is 20 feet more than the width,
so length of rectangular parking plot = 20 + width of the rectangular parking plot
=> length of rectangular parking plot = 20 + x = x + 20
The area of rectangle is given as:
[tex]\text {Area of rectangle }=length \times width[/tex]
Area of rectangular parking lot = length of rectangular parking plot [tex]\times[/tex] width of the rectangular parking
[tex]\begin{array}{l}{=(x+20) \times (x)} \\\\ {\Rightarrow \text { Area of rectangular parking lot }=x^{2}+20 x}\end{array}[/tex]
But it is given that Area of rectangular parking lot = 15000 square feet
[tex]\begin{array}{l}{=>x^{2}+20 x=15000} \\\\ {=>x^{2}+20 x-15000=0}\end{array}[/tex]
Solving the above quadratic equation using quadratic formula
General form of quadratic equation is
[tex]{ax^{2}+\mathrm{b} x+\mathrm{c}=0[/tex]
And quadratic formula for getting roots of quadratic equation is
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
In our case b = 20, a = 1 and c = -15000
Calculating roots of the equation we get
[tex]\begin{array}{l}{x=\frac{-(20) \pm \sqrt{(20)^{2}-4(1)(-15000)}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{400+60000}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{60400}}{2}} \\\\ {x=\frac{-(20) \pm 245.764}{2 \times 1}}\end{array}[/tex]
[tex]\begin{array}{l}{=>x=\frac{-(20)+245.764}{2 \times 1} \text { or } x=\frac{-(20)-245.764}{2 \times 1}} \\\\ {=>x=\frac{225.764}{2} \text { or } x=\frac{-265.764}{2}} \\\\ {=>x=112.882 \text { or } x=-132.882}\end{array}[/tex]
As variable x represents width of the rectangular parking lot, it cannot be negative.
=> Width of the rectangular parking lot "x" = 112.882 feet
=> Length of the rectangular parking lot = x + 20 = 112.882 + 20 = 132.882
Hence can conclude that dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet.
A backpack is normally $64.99,but sale,it is marked down to $45.49.what percent off is the sale price?
Answer:
30%
Step-by-step explanation:
Here we want to setup the equation
[tex]y = a - (a\times x)[/tex]
where y is the discounted price, a is the normal price and x is the percent off. so now we wanna plug in known values and solve for percent off.
[tex]45.49 = 64.99 - (64.99x)[/tex]
through algebra,
[tex] - 19.5 = - (64.99x)[/tex]
[tex] \frac{ - 19.5}{ - 64.99} = x[/tex]
[tex]x = .3000...[/tex]
so in percentage that is 30%
8 people eat at Charlie Brown's for Thanksgiving. How many different seating
arrangements can be formed around the ping pong table?
Answer: 40,320
Step-by-step explanation: Let's say that there is person A,B,C,D,E,F,G,H. and 8 chairs. For the first chair, 8 different people could potentially sit in it, making 8 different possibilities. No matter who sits there, the logic follows the next table. However, since one person is sitting in the first chair, there are 7 different possibilities about who would be sitting in the second chair. If you multiply the two together, there are 56 different possibilities just for the first and second chair. For the third chair, there are 6 different possibilities about whom could sit. Multiply 56*6 and you get 336 possibilities. Keep multiplying out and you get a grand total of 40,320 different arrangements!
Answer:
5040
Step-by-step explanation:
The answer is (8 - 1)!
The reason is that the first person is fixed. Any place is the same as any other place. After that there are 7! choices for the next position.
Answer: 5040
The board of directors of a corporation must select a president a secretary and a treasurer in how many possible ways can this be accomplished if there are 22 members on the board of directors
There are 9240 possible ways in which a president, a secretary and a treasurer can be selected from the 22 members on the board of directors.
Solution:Give that the board of directors of a corporation must select a president a secretary and a treasurer.
Need to calculate in how many possible ways this can be accomplished if there are 22 members on the board of directors
Here we are assuming that one person can hold only one position means one if get selected for president he is out of the race for remaining positions that are secretary and treasure
Lets for sake of understanding, we simplify our question.
Lets say there are 3 members A , B and C . In how many ways two positions of Secretary and treasurer can be filled .
So for selecting secretary we have three option that are A , B or C.
And once secretary is selected , number of option for selecting treasure is two.
So it is found that number of selecting 2 positions for 3 members is product of option available for selecting first position that is secretary multiplied by option available for selecting second position that is treasurer = 3 x 2 = 6
So now applying same logic for selecting members for 3 positions from 22 menbers we get
For selecting president members available = 22
Once president is selected, then option available for selecting a Secretary = 21
And one secretary is also selected, then option available for selecting a treasure = 20
So number of ways in which three positions can be filled by 22 member = 22 x 21 x 20 = 9240
Hence there are 9240 possible ways in which a president , a secretary and a treasurer can be selected from the 22 members on the board of directors.
Show the steps on how to follow 3x - 7 =1/2x +6
Answer:
x=26/5
Step-by-step explanation:
first you would multiply both sides by 2
then you woud end up with 6x- 14 = x+12
then combine like terms subtract x on both sides
5x=26 then divide both sides by 5
x=26/5
Scott buys candy that costs $8 per pound. He will buy at least 5 pounds of candy. What are the possible amounts he will spend on candy?
Use c for the amount (in dollars) Scott will spend on candy.
Write your answer as an inequality solved for c .
Answer: 8*5≥c
sorry if wrong! Not my strong suit !
Final answer:
Scott spends at least $40 on candy if buying a minimum of 5 pounds at $8 per pound.
Explanation:
Scott buys candy at $8 per pound and will buy at least 5 pounds. Let's use c for the amount he will spend on candy. The possible amounts he will spend on candy can be expressed as:
5 pounds x $8/pound ≤ c would mean $40 ≤ c
Therefore, the inequality solved for c is $40 ≤ c.
David is shoveling driveways to raise money for his Spring
Break trip. Each driveway he shovels, he earns $15. After shoveling 12 driveways, David has $243 saved for his trip.
Write an equation to represent the amount David has saved as a function of the number of driveways he has shoveled.
Answer:
Total savings = $63 + 12 ( m)
: m = number of driveways shoveled
Step-by-step explanation:
Here, the money earned for each road David shovels = $15
The number of driveway shoveled by David = 12
The total money saved David has after he is done with his work = $243
Now, The number of money saved by shoving 12 driveways
= 12 x ( Money earned by shoveling 1 driveway)
= 12 x ( $15) = $ 180
Total savings = His previous savings + Money earned from Shovel work
⇒ $243 = His previous savings + $ 180
⇒ His previous savings = $243 - $180 = $63
Now, we can write his total savings as:
Total savings = $63 + 12 ( m)
: m = number of driveways shoveled
GETS BRAINILST!!!!The table below shows a correct representation that 12 pounds (lb) of sugar cost $4: lb lb lb lb lb lb lb lb lb lb lb lb $1 $1 $1 True False
Answer:
I believe the answer is false because there is no facts that say true.
Answer:
believe the answer is false because there is no facts that say true.
Step-by-step explanation:
A company has two manufacturing plants with daily production levels of 7 x + 19 items and 2 x - 7 items, respectively. The first plant produces how many more items daily than the second plant?
The first plant produces 5x + 26 more items daily than the second plant
Solution:Given that , A company has two manufacturing plants
The daily production levels of one company is 7x + 19 items
And daily production levels of another company is 2 x - 7 items
To find the number of items first plant produce more than the second plant, wed need to subtract the number of items produced by second plant from the the number of items produced by first plant.
Extra items produced by 1st plant = daily production of 1st plant - daily production of 2nd plant
Extra items produced count = 7x + 19 – (2x – 7)
= 7x + 19 – 2x + 7
= 7x – 2x + 19 + 7 = 5x + 26
Hence, the 1st plant produces 5x + 26 items more than 2nd plant
Jack used 1 2 of a bag of okra to make 1 4 of a gallon of jambalaya. If Jack's recipe is for 1 gallon of jambalaya, how much okra will he need to make double the recipe? A) 1 bag of okra B) 2 bags of okra C) 3 bags of okra D) 4 bags of okra
Answer:
4 bags of okra
Step-by-step explanation:
To find the unit rate: multiply the numerator by the reciprocal of the denominator.
unit rate =
1/2 divided by 1/4
= 1/2× 4/1
=4/2
= 2 bags per gallon
Therefore, double the recipe: 2 × 2 = 4 bags of okra
Section 5.4 Exercise 16
The mean household income in a country in a recent year was about $69,953 and the standard deviation was about $90,000. (The median income was $55,517)
a) If a Normal model was used for these incomes, what would be the household income of the top 4%?
b) How confident should one be in the answer in part a?
c) Why might the Normal model not be a good one for incomes?
a) The income would be s
(Round to the nearest dollar as needed)
Answer:
Step-by-step explanation:
a) To find the household income of the top 4%, we can use the standard Normal distribution table or calculator to find the Z-score associated with the 96th percentile.
The Z-score corresponding to the 96th percentile is approximately 1.75. We can then use the Z-score formula to find the income value:
Z = (x - mean) / standard deviation
1.75 = (x - 69953) / 90000
x - 69953 = 1.75 * 90000
x - 69953 = 157500
x = 227453
Therefore, the household income of the top 4% is about $227,453.
b) The answer in part a should be taken with some caution as the Normal model assumes that the incomes follow a bell-shaped distribution, which may not be the case for all income distributions.
c) The Normal model may not be a good one for incomes because incomes often have a skewed distribution with a long tail to the right, meaning there are a small number of individuals with very high incomes that can greatly affect the mean and standard deviation. In addition, incomes may have outliers or gaps that are not well captured by a Normal distribution.
what is -87 = 1 + 8x?
Answer:
-87= 1 + 8x
-88= 8x
x= -11
Basically bring over the one to the other side of the equation and solve for x by dividing.
Use the compound interest formulas A=P(1+r/n)^nt and A=Pe^rt to solve the problem given. Round answers to the nearest cent.
Find the accumulated value of an investment of $15,000 for 6 years at an interest rate of 4% if the money is a. compounded
semiannually; b. compounded quarterly: c. compounded monthly d. compounded continuously.
Answer:
a) $19,023.63
b) $19,046.02
c) $19,061.13
d) $19,068.74
Step-by-step explanation:
P = 15000
t = 6
r = 0.04
a) Compounded semiannually means 2 times per year, so n = 2.
A = 15000 (1 + 0.04/2)^(2×6)
A = 19023.63
b) Compounded quarterly means 4 times per year, so n = 4.
A = 15000 (1 + 0.04/4)^(4×6)
A = 19046.02
c) Compounded monthly means 12 times per year, so n = 12.
A = 15000 (1 + 0.04/12)^(12×6)
A = 19061.13
d) Compounded continuously means we use the continuous equation:
A = 15000 e^(0.04×6)
A = 19068.74
HELPPPPPP The scatter plot shows a regression line of advertising dollars spent and sales. If the company were to spend $350,000 on advertising, what would be the predicted sales? A) $105 million B) $110 million C) $115 million D) $120 million
Answer:
120 i think i don't know
Step-by-step explanation:
Answer:
D) $120 millionStep-by-step explanation:
The scatter plot is attached. There you can match the value assigned to $350,000.
Using a red line, we find that the answer is between 115 and 125, closer 125 than 115.
So, if you look all choices, there are two possibilities, C and D. However, $115 million can't be the right answer because our graphic approximation is closer to 125.
Therefore, the right answer is D) $120 million.
If the company were to spend $350,000 on advertising, the predicted sales would be $120 million.
4x+(x-y/8)=17 and 2y+x-(5y+2/4)=2 by using elimination method
Answer:
x=811/238, y=36/119. (811/238, 36/119).
Step-by-step explanation:
4x+(x-y/8)=17
2y+x-(5y+2/4)=2
-----------------------
4x+x-y/8=17
5x-y/8=17
40x-y=136
y=40x-136
------------------
2y+x-5y-2/4=2
2y-5y+x-1/2=2
-3y+x=2+1/2
-3y+x=4/2+1/2
-3y+x=5/2
-3(40x-136)+x=5/2
-120x+408+x=5/2
-119x=5/2-408
-119x=5/2-816/2
-119x=-811/2
119x=811/2
x=(811/2)/119
x=(811/2)(1/119)=811/238
y=40(811/238)-136
y=16220/119-136
y=36/119
x=811/238, y=36/119.
Which unit rate is higher 24 for 5 or 5 for 24
Answer:
24 for 5 is higher because you have to divide 24 by 5 and if you do that it gives you $4.8, while 5 for 24 gives you a unit rate of $0.20.
6. Find the selling price of each of the following:
(i) a television set marked €800 + VAT at 20%
Answer:
€960
Step-by-step explanation:
€800 + VAT at 20%
€800 + 20% of €800 =
= €800 + 20% * €800
= €800 + 0.2 * €800
= €800 + €160
= €960
At a track meet, Tim ran at a constant speed of 300 meters per minute.
After 8 minutes, he still had 600 meters left to run.
The distance Tim ran was three times as long as the distance Eric ran.
What was the distance that Eric ran?
Tim ran a total of 3000 meters, which is three times the distance that Eric ran. By dividing Tim's distance by three, we find that Eric ran 1000 meters.
Explanation:To solve for the distance Eric ran, we need to first determine the total distance Tim ran and then divide that by three as Tim's distance is three times longer than Eric's.
Tim's speed is 300 meters per minute, and he ran for 8 minutes before having 600 meters left to run. To calculate the distance Tim ran:
Multiply Tim's speed by the time he ran: 300 meters/minute * 8 minutes = 2400 meters.Add the remaining distance to determine Tim's total distance: 2400 meters + 600 meters = 3000 meters.Since Tim's distance is three times Eric's distance, divide Tim's total distance by three to find Eric's distance: 3000 meters / 3 = 1000 meters.Therefore, the distance that Eric ran was 1000 meters.
Mr. Smith had 33 dozen cans. He sold 340 of them at 15$ each. He sold the remaining cans at a discount of 20% each. How much money did he collect from selling the cans.
he collected a total of $5,772 from selling all the cans.
Mr. Smith collected $5,772 from selling all the cans.
He sold 340 cans at full price for a total of $5,100.
He sold the remaining 39 cans at a discount of 20% each, for a total of $672.
Therefore, he collected a total of $5,772 from selling all the cans.
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Weat is the
The point slope form of the equation of the line that passes through (-9, -2) and (1, 3) is
slope-intercept form of the equation for this line?
o y = 2 x + 2
0 y = 2 x 4
o y = x + 2
O y = x - 2
Save and Exit
Submit
e
.
o
Answer:
The slope intercept of the given line equation AB is [tex]y = \frac{1}{2} ( x)- \frac{5}{2}[/tex]
Step-by-step explanation:
Here,the two given point s are A ( -9,-2) and B (1,3).
Now, the slope m of the line AB = [tex]= \frac{y_2 - y_1}{x_2 -x_1}[/tex]
[tex]\implies m = \frac{3 - (-2)}{1 - (-9)} = \frac{3+2}{1+9} = \frac{5}{10} = \frac{1}{2}[/tex]
or, the slope of line AB = 1/2
Now, the POINT SLOPE FORM of any equation with point (x0,y0) and slope m is given as :
y - y0 = m (x -x0)
So, the line equation of AB is given as :
[tex]y - 3 = \frac{1}{2} ( x-1)\\\implies y =3 + \frac{1}{2} ( x-1)\\or, y = \frac{1}{2} ( x)- \frac{5}{2}[/tex]
SLOPE INTERCEPT form is y = mx + c
Hence, the slope intercept of the given line equation AB is [tex]y = \frac{1}{2} ( x)- \frac{5}{2}[/tex]
578 business and personal emails there are 30 fewer personal emails so how many personal emails
Answer:
Personal emails = 274 emails.
Step-by-step explanation:
Given,
Business and personal emails = 578
Therefore, there are two types of emails. Again, there are 30 fewer emails in personal emails.
The total number of emails after deducting the fewer personal emails = (578 - 30) = 548 emails.
Therefore, each type of email, according to the question = (548/2) = 274 emails
So, personal emails are 274. Business emails = (274 + 30) = 304 emails.
The problem involves setting up and solving an equation based on the information given: that the number of personal emails is 30 fewer than the number of business emails, and the total is 578. By doing this, we deduce that there are 274 personal emails.
Explanation:The problem tells us that there is a total of 578 emails, both business and personal combined. Furthermore, we know that there are 30 fewer personal emails than business emails. We can use this information to create an equation and solve for the number of personal emails.
First, we can represent the number of business emails as 'x'. So, the number of personal emails would be 'x - 30'. The sum of the business and personal emails is 578, so our equation is x + (x - 30) = 578.
Solving this equation gives us: 2x - 30 = 578, 2x = 608 and finally x = 304. This is the number of business emails. To get the number of personal emails, you subtract 30 from the total business emails (as the question states). So, there are 304 - 30 = 274 personal emails.
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A recipe requires 1/3 cup of milk for each 1/4 cup of water. How many cups of water are needed for each cup of milk?
Answer:
3/4
Step-by-step explanation:
1 / (1/3) = 3
1/4 * 3 = 3/4
Live Fund are selling their holding at $5,000 per share. How much would Live Fun receive if they sold half thier holding in Marks Brothers?
Live Fund receive [tex]\bold{\$2500 N}[/tex] it they sold half thier holding in Marks Brothers.
Solution:
Given: Sale price of Live Fund holding is 5000 dollar
To find: Amount that Live Fund will get if they sell half of their holding in Marks Brothers.
Assume the total holdings held by Live Fund in Marks Brothers as N
Therfore, half the number of shares or (half the holdings) of Live Fund will be [tex]\frac{N}{2}[/tex].
Thus, if each share is valued at [tex]\$5000[/tex], then the total value of the number of shares sold will be as follows,
[tex]\Rightarrow5000\times\frac{N}{2}\text{ dollars }\rightarrow\frac{5000\times N}{2}\text{ dollars }[/tex]
[tex]\Rightarrow2500 N\text{ dollars }[/tex]
Hence, Live Fund will receive [tex]\$2500 N[/tex]
A sports statistician determined that the probability of a certain rugby team winning its next match is 3/8 . Find the odds against the team winning its next match.
Answer:
Odds in against the team winning is 5 : 3
Step-by-step explanation:
Consider the provided information.
The odds against is the ratio of how many ways an outcome can't take place compared to how many ways it can take place.
Here the probability of winning its next match is 3/8.
That means total number of outcomes are 8.
Favorable outcomes are 3.
Therefore, the unfavorable outcomes are 8-3=5.
We need to find the odds against the team winning its next match.
Therefore, odds in against the team winning is 5 : 3
The probability of odds against the team winning is [tex]\frac{5}{8}[/tex]
To find the odds against the rugby team winning, subtract the probability of winning from 1 to get the probability of not winning and form a ratio of these probabilities, resulting in odds of 5:3 against the team winning.
Explanation:The student is asking about the calculation of odds against a rugby team winning its next match given a certain probability of winning. First, we need to understand the probability of the team not winning (losing or drawing) because the odds against the team winning would be the ratio of it losing to it winning. Since the probability of winning is given as 3/8, the probability of not winning is 1 - 3/8 = 5/8. The odds against the team winning are therefore expressed as the ratio of the probability of not winning to the probability of winning, which is 5/8 to 3/8, or simply 5:3 when converted into odds format.
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what is the slope and y intercept of the function k(x)=7/9x-2
Answer:
For the given function, Slope is [tex]\frac{7}{9}[/tex] and y-intercept is -2.
Step-by-step explanation:
The given function in x is :
[tex]k(x)=\frac{7}{9}x-2[/tex] .....1
Since, we know that the general form of equation of a line is :
[tex]y=mx+c[/tex] .....2
where, y is the dependent variable, x is independent variable, m is the slope and c is the y intercept of the line.
On comparing equation 1 and 2, we get :
[tex]k(x) = y[/tex];
[tex]m = \frac{7}{9}[/tex]; and
[tex]c=-2[/tex];
Thus, we can conclude that
slope of function is [tex]\frac{7}{9}[/tex] and y-intercept is -2.