Answer:
x = 9.6
Step-by-step explanation:
Given that x varies directly as y then the equation relating them is
x = ky ← k is the constant of variation
To find k use the condition x = 4 when y = 15
k = [tex]\frac{x}{y}[/tex] = [tex]\frac{4}{15}[/tex]
x = [tex]\frac{4}{15}[/tex] y ← equation of variation
When y = 36, then
x = [tex]\frac{4}{15}[/tex] × 36 = [tex]\frac{144}{15}[/tex] = 9.6
The problem is related to direct variation and can be solved using the formula x=ky which expresses the direct proportionality of x and y. The constant of variation k is found using the values of x and y given and is applied to find the new x value when y=36.
Explanation:The problem discussed here is related to the concept of direct variation or direct proportionality. When we say that 'x varies directly as y', it means that x is proportionally related to y, and that relationship can be expressed by the equation x = ky, where k is the constant of variation.
In this case, you are given that x = 4 when y = 15. So, you can find the constant of variation 'k' by dividing x by y. Hence, k = x/y = 4/15.
Now, you are asked to find the value of x when y = 36. Given that x = ky, simply substitute k = 4/15 and y=36 into this equation. Therefore, x = (4/15)*36 which will yield the value of x.
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Mei has 8 jars of soup. Each jar obtains 300 milliliters of sup. What is the smallest pot Mei can use to heat all the soup?
Answer:
2400 milliliters of soup
Step-by-step explanation:
8*300=2400
what is 3.1 ÷ 17.36
Answer:0.17857
Step-by-step explanation:
Step 1 :
434
Simplify ———
25
Equation at the end of step 1 :
31 434
—— ÷ ———
10 25
Step 2 :
31
Simplify ——
10
Equation at the end of step 2 :
31 434
—— ÷ ———
10 25
Step 3 :
31 434
Divide —— by ———
10 25
3.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
31 434 31 25
—— ÷ ——— = —— • ———
10 25 10 434
Final result :
5
—— = 0.17857
28
Answer:
5 = 0.17857
28
Step-by-step explanation:
Change the decimals into fractions.
31 ÷ 434
10 25
*They were simplified from their natural fractions.
To divide fractions, write the division as multiplication by the reciprocal of the divisor.
31 × 25
10 434
Simplify by the greatest common factor.
775 ÷ 155 = 5
4340 ÷ 155 28
Don’t understand #3 please help quickly
Answer:
the answer is b
Step-by-step explanation:
Create a 3rd degree
polynomial and divide it by x-2. Show all steps. WILL MARK BRAINLEST!
Step-by-step explanation:
Monomial = x^2, 1 term
Binomial = x^2 + x, 2 terms
Trinomial = x^2 + x + 3, three terms
Binomial is more than 3 terms
Let's do a 3rd degree polynomial like:
[tex] {x}^{3} + 2x^{2} + 4x + 8[/tex]
Now let's put parenthesis around (x^3 + 2x^2) and (4x + 8)Let's treat both of these as seperate for now. In the first part, you can see an x^2 can be factored out of itFor example:[tex] {x}^{2} (x + 2)[/tex]
As you can see, if you do the distributive property, it equals the original.Now let's factor the second part, the 4x + 8. This can be factored by a 4.
[tex]4(x + 2)[/tex]
Your new equation is:
[tex] \frac{( {x}^{2} + 4)(x + 2)}{x - 2} [/tex]
x^2 + 4 can be factored again down to (x + 2)(x + 2)
YOUR FINAL EQUATION IS:
[tex] \frac{(x + 2)(x + 2)(x + 2)}{x - 2} [/tex]
If it takes Trixie 8 minutes to run a mile, then 8m represents her total time where m is the number of miles she has run. List the ordered pairs (number of miles, total time) for 0, 1, 2, and 3 miles.
Answer: (1,8) (2,16) (3,24)
Step-by-step explanation:
Because if it takes Trixie 8 minutes per mile then the ratio would be 1:8 and that means every mile you add 8 minutes.
Are all right triangles similar?Are all equilateral triangles similar?
Answer:
Yes to both.
Step-by-step explanation:
Similar means the same shape but the sizes may be different.
Right angles are similar and so are equilateral triangle.
Right triangles are not necessarily similar unless they have the same hypotenuse and an acute angle. All equilateral triangles are similar because they have equal angles and sides. This discussion relates to the nature of mathematical truths, which are absolute in their systems, compared to observational truths that rely on variable sensory evidence.
Not all right triangles are similar because they can have different ratios between their sides despite having a right angle. However, if two right triangles have the same length of their hypotenuse and an acute angle correspondingly, they are indeed similar according to a mathematical corollary.
In contrast, all equilateral triangles are similar because they all have equal angles (60 degrees each) and their side lengths are also in the same ratio, which is 1:1:1, making them the same shape, although they can be different sizes.
This connects to the larger questions about mathematical truths. For instance, the statement that the three interior angles of a triangle are equivalent to two right angles is a mathematical truth that is similar to definitional truths, such as 'green is a color,' since both are based on definitions and logical deductions in their respective systems.
However, mathematical truths differ from observational truths like 'there is beer in the refrigerator' because observational truths are subject to sensory evidence which can change, whereas mathematical truths are absolute within the context of their axiomatic systems.
When considering questions that lead to insights into forms, mathematical questions are often better suited over observational ones as they transcend physical reality and provoke a more abstract level of reasoning.
Julie has 42 sheets of paper. She gives 17 sheets of paper to karo. How many sheets of paper does julie have now explained please help me
Answer:
25
Step-by-step explanation:
Subtract 17 from 42.
Answer:
42-17=25
Step-by-step explanation:
just subtract 17 from 42
Which is the simplified version of 7x+12+3x=-6(x-7)+9x ?
Answer:
x=30/7
Step-by-step explanation:
7x+12+3x=-6(x-7)+9x
10x+12=-6x+42+9x
10x+12=3x+42
10x-3x+12=42
7x+12=42
7x=42-12
7x=30
x=30/7
A restaurant bill comes to $28.35 find the total coast if the tax is 6.25% and 20% tip is left on the amount before tax
Answer:
The total cost of the bill = $36.146
Step-by-step explanation:
Here, the total amount of the bill = $28.35
Now, the amount of tip = 20%
So, calculating 20% on the bill amount, we get
[tex]\frac{20}{100} \times 28.35 = 5.67[/tex]
or, the amount of 20% tip = $5.67
So, the total bill amount after 20% tip = Bill Amount + Tip
= $28.35 + $5.67 = $34.02
Now, the tax is calculated on the amount of bill $34.02.
[tex]\frac{6.25}{100} \times 34.02 = 2.126[/tex]
or, the amount of tax on the bill = $2.126
So, the total bill amount after 6.25% tax = Bill Amount + Tax
= $34.02 + $2.126 = $36.146
Hence, the total cost of the bill = $36.146.
General Motors stock fell from 32$ per share in 2006 to 20$ per share during 2008. A) If you bought and then sold 300 shares all these prices what was your loss B) Exress your loss as a percent of the purchase price
Answer:
Step-by-step explanation:
total purchase price = 32*300 = 9600
total selling price = 20*300 = 6000
Net capital loss =total purchase price- total selling price =9600-6000 = 3600. Purchase price of one share is 32
Selling price of one share is 20
Number of shares bought are 300 Net % loss = (3600*100)/9600=37.5%
Final answer:
The total loss from buying and then selling 300 shares of General Motors stock, which fell from $32 to $20 per share, is $3600. Expressed as a percent of the purchase price, the loss is 37.5%.
Explanation:
To calculate the loss when buying and selling shares, we first find the loss per share and then multiply by the total number of shares. For General Motors, the price fell from $32 per share to $20 per share. This results in a loss of $12 per share. If you bought and sold 300 shares at these prices, your total loss would be:
Loss per share = $32 - $20 = $12
Total loss = $12 × 300 shares = $3600.
To express this loss as a percent of the purchase price:
Loss Percentage = (Loss per share / Purchase price per share) × 100
Loss Percentage = ($12 / $32) × 100 = 37.5%.
James wants to set aside money each month to save for a down payment on a new home. How much will James need to save each month if he wants to have $30,000 in three years and can earn a 6% interest rate that compounds monthly
Answer:3.80000000000
Step-by-step explanation:
Answer:
$763
Step-by-step explanation:
i got it right on my test
Of the total number of spectators at a circus show, 1/4 are men. 2/5 of the remaining number of spectators are women. There are 132 women at the circus show. How many children are at the circus show?
Answer: There are [tex]198[/tex] children at the circus show.
Step-by-step explanation:
Let be "x" the total number of spectators at the circus show and "c" the number of children at the circus show.
Knowing that [tex]\frac{1}{4}[/tex] of the spectators are men, we can find the remaining:
[tex]x-\frac{1}{4}x=\frac{3}{4}x[/tex]
Since [tex]\frac{2}{5}[/tex] of the remaining number of spectaros are women and there are a total of 132 women, we can write the following equation:
[tex](\frac{2}{5})(\frac{3}{4}x)=132[/tex]
Solving for "x", we get:
[tex]x=(132)(\frac{20}{6})\\\\x=440[/tex]
Therefore, we get that "c" is:
[tex]c=440-\frac{1}{4}(440)-132\\\\c=198[/tex]
Duke went to the convenience store to buy a frozen pizza and some
toothpaste, and while he was in the checkout line, he also threw a ballpoint
pen and a banana into his shopping basket. Which two products were
impulse purchases?
A. The frozen pizza and the banana
O
O
B. The ballpoint pen and the toothpaste
C. The ballpoint pen and the banana
O
O
D. The frozen pizza and the toothpaste
Answer:
ballpoint pen and banana
Step-by-step explanation:
What is y - 2 = -3(x – 7) written in standard form?
Choose 1 answer:
A-y - 2 = -3x + 21
B-y=-3x + 23
C-3x + y - 23 = 0
D-3x + y = 23
Answer:
It's D
Step-by-step explanation:
-3+y=23
To write the equation in standard form, distribute and rearrange the terms. The equation is 3x + y = 23.
Explanation:To write the equation y - 2 = -3(x - 7) in standard form, we need to expand the expression and rearrange the terms. Starting with the given equation, we can distribute the -3 to the terms inside the parentheses: y - 2 = -3x + 21. Next, we can move the -3x term to the left side of the equation by adding 3x to both sides: 3x + y - 2 = 21. Finally, we can move the constant term (-2) to the right side of the equation by adding 2 to both sides: 3x + y = 23. Therefore, the equation in standard form is 3x + y = 23 (Option D).
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A freight train travels 1445 miles in 25 hours. What is the train's average rate of speed?
Final answer:
The average speed of the freight train is found by dividing the distance traveled, 1445 miles, by the time taken, 25 hours, resulting in an average speed of 57.8 mph.
Explanation:
To calculate the average speed of the freight train, we divide the total distance traveled by the time it took to cover that distance. The train travels 1445 miles in 25 hours.
The formula for average speed is:
average speed = total distance / total time
Therefore, the average speed of the train is:
average speed = 1445 miles / 25 hours = 57.8 miles per hour (mph)
How many like terms are in 3x–2y+7?
Answer:
None.
Step-by-step explanation: 3x does not have the same coefficient as 2y or 7
at a store 20 feet of fencing cost $36 at the rate how much will 15 feet of fencing cost
Answer:
15 feet of fencing costs $27
Step-by-step explanation:
We know 15/20 = 3/4 so...
36 x 3/4 = 27
Another way:
36 divided by 20 = 1.8
1.8 x 15 = 27
answer:
$24
Step-by-step explanation:
36 divided by 15 equals 2.4 then 2.4x5 secne 15 is 5 away from 20 equals 12 then 36 - 12 = 24
Find the sum of the first 50 terms in this geometric series 1+10/11+100/121
Answer:
10.91
Step-by-step explanation:
The sum of the first 50 terms in this geometric series is 11.00.
What is a geometric series?When all the terms of a geometric sequence are added, then that expression is called geometric series.
Lets suppose its initial term is f=a , multiplication factor is r
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
We are given that;
n=50
Series= 1+10/11+100/121
Now,
To find the sum of the first 50 terms in this geometric series, we need to use the formula:
Sum = [tex]a1(1 - r^n) / (1 - r)[/tex]
where a1 is the first term, r is the common ratio, and n is the number of terms. We can identify that the first term is 1, the common ratio is 10/11, and the number of terms is 50. Plugging these values into the formula, we get:
Sum = 1(1 - (10/11)^50) / (1 - 10/11) Sum = (1 - 0.000000000000000000000000000000000000000000000001) / (1/11) Sum = (0.9999999999999999999999) / (0.09090909) Sum = 10.99998
Rounding this result to two decimal places, we get:
Sum = 11.00
Therefore, by the given geometric sequence the answer will be 11.00.
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Beatriz is in charge of setting up a banquet hall. She has five tables that will seat six people each. If nor more than 62 people will attend, how many tables seating four people each will she need?
Answer:16
I think this is the answer
Justin began his walk at 3:05 p.m. He arrived at his destination at 4:32 p.m. How long did Justin walk? Show your work and explain how you found your answer.
PLZZZ HELP!!! 16 POINTS!!!!
Answer:
The answer to this question is it took him an hour and 27 minute
Two customers went to a post office to buy postcards and large envelopes. Each postcard
costs the same amount, and each large envelope costs the same amount.
The first customer paid $12 for 14 postcards and 5 large envelopes.
The second customer paid $24.80 for 10 postcards and 15 large envelopes.
•
What was the cost in dollars of each large envelope?
A $1.42 c $1.15
B $0.35 D $0.63
The right answer is Option A.
Step-by-step explanation:
Let,
x be the postcards
y be the large envelops
According to given statement;
14x+5y=12 Eqn 1
10x+15y=24.80 Eqn 2
Multiplying Eqn 1 by 3;
[tex]3(14x+5y=12)\\42x+15y=36\ \ \ Eqn \ 3[/tex]
Subtracting Eqn 2 from Eqn 3;
[tex](42x+15y)-(10x+15y)=36-24.80\\42x+15y-10x-15y=11.20\\32x=11.20\\[/tex]
Dividing both sides by 32
[tex]\frac{32x}{32}=\frac{11.20}{32}\\x=0.35[/tex]
Putting x=0.35 in Eqn 1;
[tex]14(0.35)+5y=12\\4.90+5y=12\\5y=12-4.90\\5y=7.10[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{7.10}{5}\\y=1.42[/tex]
Therefore, one large envelope costs $1.42
The right answer is Option A.
Keywords: linear equations, subtraction
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Answer: A. $1.42
Step-by-step explanation: I did it on the test and got it right!
Algebraic Woru
An algebraic word problem can be presented in either a real-life or
require you to set up and solve an equation or inequality to arrive at the
require you to translate words into an expression, equation, or inequate
1. Kyle has three times as much money in his savings account as
Hayden. Hayden has twice as much money in his savings account
as Jeremy. Combined Kyle, Hayden, and Jeremy have a total of
$612. How much money does Kyle have in his account?
(A) $68 Khles Hot money = 3
(B) $136
(C) $204
(D) $306
(E) $408
The right answer is Option D.
Step-by-step explanation:
Let,
Kyle's money = x
Hayden's money = y
Jeremy's money = z
According to statements;
Kyle has three times as much money in his savings account as Hayden.
x = 3y Eqn 1
Hayden has twice as much money in his savings account as Jeremy.
z = 2y Eqn 2
Combined Kyle, Hayden, and Jeremy have a total of $612.
x+y+z=612 Eqn 3
Putting value of x and z from Eqn 1 and 2 in Eqn 3
[tex]3y+y+2y=612\\6y=612[/tex]
Dividing both sides by 6
[tex]\frac{6y}{6}=\frac{612}{6}\\y=102[/tex]
Putting in Eqn 1;
[tex]x=3(102)\\x=306[/tex]
Kyle has $306 in his account.
The right answer is Option D.
Keywords: Linear equations, division
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1/2 / 3 equals x / 4
Answer:
x=2/3
Step-by-step explanation:
(1/2)/3=x/4
(1/2)(1/3)=x/4
1/6=x/4
cross product,
6*x=1*4
6x=4
x=4/6=2/3
x=2/3
Of all the students who participate in the school music programs in the district, 394 students play a wind instrument. If 2/5 of the students play a wind instrument, how many students in the district participate in the school music program
Answer:
985 students in the district participate in the school music program.
Step-by-step explanation:
2/5=0.4
394/0.4=985
paul has a total of 15 markers and pencil. Each pencil cost $0.30 and each marker costs $1.25 how many pencils does paul have
Answer:
1
Step-by-step explanation:
At the local bakery, 3 boxes of cookies cost $12.00. How much does each box of cookies cost, in dollars?
Answer:
If 3 boxes equals $12.00 then 1 box equals $4.00
Step-by-step explanation:
You divide 3 boxes by 3 and 12 dollars by 3 to get 1 box equals 4 dollars
Answer:You have 3 boxes that all cost $12.00. So to find the total of each box you divide $12 by 3 boxes of cookies 12/3=$4.00 each
Step-by-step explanation:
A rectangle has 3 square feet and width 1/2 foot. What is the length of the rectangle
Answer:
We Know, Area = Length * Width
Here, A = 3
W = 1/2
Substitute it into the expression,
3 = L * 1/2
L = 3/ 1/2
L = 3/2 ft²
So, the length of the rectangle would be 3/2 ft²
Hope this helps! :)
The length of the rectangle is found to be 6 feet by using the formula for the area of a rectangle and solving for length.
Explanation:To compute the length of the rectangle, we need to use the formula for the area of a rectangle which is length times width. Given that the area is 3 square feet and the width is 1/2 foot, we can set up the equation length * 1/2 = 3 square feet. From here, solve for length by dividing both sides of the equation by 1/2.
Therefore, the length of the rectangle is 6 feet.
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Ohio is the home of two of the world’s largest aluminum smelters, in which metal is separated for recycling. Together, these two facilities process an average of 15 million pounds of aluminum each month. How many pounds of aluminum do the Ohio smelting plants average per week?
3.75 million pounds of aluminium
Step-by-step explanation:
The question requires you to perform division operation
Given that 15 million pounds is processed per month
A month has average 4 weeks.
The aluminium smelted per week will be;
15/4 = 3.75 million pounds of aluminium
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Keyword : pounds, average, month, week
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Goldberg's sleigh currently runs at 203mph, but he needs it to reach 400mph with all the packages he has to deliver.
If Goldberg is delivering presents at an altitude of 5,813.6ft, with the same drag and weight of a 2019 Challenger SRT® Hellcat Redeye, how much HP would he need to reach 400 mph?
Pro Tips:
100% driveline efficiency
P (air density) at 5813.6 ft = .0019 slug/ft^3
A (Area of Challenger front end) = 26.72 ft^2
C(d) (Coefficient of drag) = .398
Goldberg's sleigh required speed, 400 MPH = 587 ft/sec
F(drag) = 1/2 p x v^2 x C(d)A
P = F(drag) x V
Convert to Horsepower = P ( 1HP/550 ft lbf/sec)
Answer:
5,813 HP
Step-by-step explanation:
P=f*v
f=1/2*p*v^2*C*A
HP=(f*v)/550
Answer:
He needed 3747.61 HP to reach 400 mph.
Step-by-step explanation:
Given data :
P (air density) = 0.0019 slug/ft³
A (Area) = 26.72 ft²
C(d) = 0.398
crr = 0.015
V = 400 mph = 587 ft/sec = 178.92 m/sec
weight = 2019 lb = 8980.96 N [1 pound = 4.44822 N]
[tex]P=\frac{Force\times Displacement}{Time}[/tex]
P = Force × Velocity = FV
F = F(sum) = F(drag) + F(rolling resistance)
F(drag) = [tex]\frac{1}{2}P\times V^2\times C(d)A[/tex]
F(rolling resistance) = weight × crr
[tex]HP=\frac{P}{1hp}[/tex] 1hp = 745.7 watts
F(drag) = [tex]\frac{1}{2}P\times V^2\times C(d)A[/tex]
[tex]=\frac{1}{2}\times 0.0019\times 587^{2} \times 0.398\times 26.72[/tex]
= 3481.23 [tex]\frac{slug\times ft}{sec^2}[/tex]
convert [tex]\frac{slug\times ft}{sec^2}[/tex] to [tex]\frac{kg\times m}{s^2}[/tex]
1 slug = 14.5939 kg
1 ft = 0.3048 m
[tex]\frac{slug\times ft}{sec^2}[/tex] = 14.5939 × 0.3048 = 4.448 [tex]\frac{kg\times m}{s^2}[/tex] or newton
Since F(drag) = 3481.23 × 4.448 N
= 15484.51 N
P = F(drag) × V
= 15484.51 × 178.92 N m/s
= 2770488.529 watts
F rolling resistance = crr × w
= 0.015 × 8980.96 N
= 134.714 N
Power = (Fdrag + Frolling resistance) × V
= (15484.51 + 134.714) × 178.92
= 15619.224 × 178.92
= 279459.558 watts
Power in HP
[tex]HP=\frac{P}{hp}[/tex]
[tex]=\frac{279459.558}{745.7}[/tex]
= 3747.61 HP
He needed 3747.61 HP to reach 400 mph.
1. What is 15% of 60?
15%×60=
=15×60/100
=900/100
=9
Answer:
9
Step-by-step explanation:
15/100 = 60/x
Cross Multiply...
100x = 15*60
100x = 900
x = 900/100
x = 9