Answer:
y = 2x - 12
Step-by-step explanation:
(y-4)/(-4-4) = (x-8)/(4-8)
(y-4)/-8 = (x-8)/-4
y-4 = 2x - 16
y = 2x - 16 + 4
y = 2x - 12
A storage shed is to be built in the shape of a box with a square base. It is to have a volume of cubic feet. The concrete for the base costs $ per square foot, the material for the roof costs $ per square foot, and the material for the sides costs $ per square foot. Find the dimensions of the most economical shed.
A storage shed is to be built in the shape of a box with a square base. It is to have a volume of cubic feet.
The dimensions of the most economical shed are height = 10 ft and side 5 ft
Taken data
volume = 250 cubic feet
base costs = $4 per square foot
material for the roof costs = $6 per square foot
material for the sides costs = $2.50 per square foot
to find out the dimensions of the most economical shed solution
let us consider length of side x and height is h
so we can say x²h = 250
and h = 250 / x²
now cost of material = cost of base + cost top + cost 4 side
cost = x²(4) + x²(6) + 4xh (2.5)
cost = 10 x² + 10xh
put here h = 250 / x²
cost = 10 x² + 10x (250/ x² )
cost = 10 x² + (2500/ x )
if we differentiate and we get
c' = 20 x - 2500 / x²
put c' = 0 solve x
20 x - 2500 / x² = 0
x = 5
so we say one side is 5 ft base
and height is h = 250 / x²
h = 250 / 5²
height = 10 ft
Hence the answer is, the dimensions of the most economical shed are height = 10 ft and side 5 ft
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I need help with this as soon as possible
Answer: 763*42 = 32,046
32,046/82 = 390.8048
Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 109.6°. 250.4° 63.2° 70.4° 19.6°
Answer:
70.4*
Step-by-step explanation:
Supplementary angles add up to 180*. This means that we must take 109.6 and try to find a number to add up to 180. We do the equation
180-109.6=70.4 therefore, the answer is 70.4*
Answer: 70.4
Step-by-step explanation: i took the test and got it right
Jada was helping her cousin with his math homework. He was supposed to solve the equation 8 + x = 5. He said, "If I subtract
8 from both sides, I get x = 5-8. This doesn't make sense. You can't subtract a bigger number from a smaller number. If I have
5 grapes, I can't eat 8 of them!"
What do you think Jada could say to her cousin to help him understand why 5-8 actually does make sense?
Jada could say to her cousin that we get a negative value which we is needed to make solution complete.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Jada was helping her cousin with his math homework.
He was supposed to solve the equation 8 + x = 5.
He said, "If I subtract 8 from both sides, I get x = 5-8.
5 grapes, I can't eat 8 of them!" Jada said.
Actually we can subtract 8 from five but we get a negative value.
5-8=-3
It means we should three more apples to eat.
Hence we can subtract 8 from five which makes sense.
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jules burns 100 kcalories during her morning walk. how many additional kcalories is she likely to burn in the post-exercise period?
15 additional kcalories is she likely to burn in the post-exercise period .
What do food calories mean?
When your body digests and absorbs food, calories are the amount of energy that is released. Foods that have more calories might give your body extra energy. Your body stores extra calories as body fat when you consume more calories than you need. Foods might contain a lot of calories even if they are fat-free.Since 1925, this calorie's definition has been based on the joule, and as of 1948, one calorie is roughly equal to 4.2 joules.jules burns 100 kcalories during her morning walk.
15 additional kcalories is she likely to burn in the post-exercise period .
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what is the simplified fraction form of 75 over 100
Answer:
75/100
3/4
there it is
50 students were randomly sampled and asked questions about their exercise habits. one of the questions they were asked concerned the frequency of exercise, defined to be the number of times they exercised in a week. this variable would be characterized as which type of random variable?
The random variable used in this situation is discrete random variable.
What is a random variable?
Suppose there is an event and the outcome of an event has to be represented by a variable. That variable is called random variable.
50 students were randomly sampled and asked questions about their exercise habits. one of the questions they were asked concerned the frequency of exercise, defined to be the number of times they exercised in a week
Since there is a notation about frequency in this question, it cannot be continuous. So it is a discrete random variable.
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can someone help me really quick
(Please Explain how you know this is correct.)
The rate of calories burned by bike riding is 4 calories per minute
First we have to choose points from the graph
The coordinates of the first point = (10, 40)
The coordinates of the second point = (20, 80)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line = (80-40) / (20-10)
= 40/10
= 4 calories per minute
Hence, the rate of calories burned by bike riding is 4 calories per minute
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PLSSS HELPP MEEE I RLLY NEED ITTT ASAP
(Factoring Algebraic Expressions MC) (Also If I use ^ that means its the power of a number)
Rewrite x^4y^2 − 2x^3y^3 using a common factor.
A: x^2y(xy − 2xy^2)
B: x^2y^2(x^2 − 2xy)
C: 2xy^2(x^2 − x^2y)
D: 2xy(x^3y − x^2y)
Rewritten equation using a common factor is (B) [tex]x^{2} y^{2}(x^{2} -2xy)[/tex].
Given equation,
[tex]x^{4}y^{2}-2x^{3}y^{3}[/tex]
Taking [tex]x^{2} y^{2}[/tex] common,
[tex]x^{2} y^{2}(x^{2} -2xy)[/tex]
Hence, the equation.
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A recipe says it produces the best summer drink. The recipe calls for 12 cup of lemonade for every 112 cups of iced tea. If 16 cups of the summer drink are made, how many of those are cups of lemonade? use the table to help you find your answer.
A recipe says it produces the best summer drink. The recipe calls for 12 cup of lemonade for every 112 cups of iced tea. If 16 cups of the summer drink are made
then 8 cups of lemonade are needed.
What is unitary method?
It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams.
5 ice-creams cost is $125.
Step 1: Let's find the cost of 1 ice cream.
In order to do that, divide the total cost of ice-creams by the total number of ice-creams.
The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-
creams = 125/5 = 25.
Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams.
The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75.
Finally, we have the cost of 3 ice-creams i.e. $75.
lemonade: tea : total
1 1 1+1=2
We need a total of 16 and divide it
= 16/2 = 8
Then the composition will be
lemonade: tea: total
1*8 = 8 1*8 = 8 2*8 = 16
Hence, 8 cups of lemonade are needed.
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Joann and Phyllis each improved their flower gardens by
planting daisies and carnations. Joann bought 10 daisies and 4
carnations and paid $52.66. Phyllis bought 3 daisies and 6
carnations and paid $43.11. How much is each daisy? How
much is each carnation?
2.99 for each daisy and 5.69 for each carnation.
What is carnation?
carnation is a flowering devotion.
Sol- Let x represent the cost of each daisy.
Let y represent the cost of each carnation.
Given that as per question,
Joann brought 3 Daisy and 4 carnation and paid $52.66.-------eq(1)
10x+4y =52.66
Phyllis bought 3 daisies and 6 carnation and paid $043.11---------eq(2)
Multiplying the EQ 1 by 3
30x +12y= 157.98------eq (3)
Multiplying the equation (2) by -2
-6x -12y= -86.22-------eq(4)
On equation (3) and (4)
X=2.99
Substitute the value of x into the equation 2 we get
Y= 5.69
Thus each daisy costs
2.99 and each carnation cost 5.69.
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the slope of the curve y= 3x²-8/5-2x at the point (2,4).
pls answer this
Answer: y=3x2
Step-by-step explanation:
Johnson electronics sells electrical and electronic components through catalogs. Catalogs are updated and printed every year. The variable production cost is $5 per catalog. Data indicate that, on average, each printed catalog generates a profit of $35 from sales (i. E. , $40 revenue). What is the optimal service level for the catalogs printing decision?.
Johnson electronics sells electrical and electronic components through catalogs. Catalogs are updated and printed every year. The variable production cost is $5 per catalog. Data indicate that, on average, each printed catalog generates a profit of $35 from sales.
The optimal order quantity will be 11450.
Let’s use the news vendor model here.
The profit means that if we print less we will incur a certain opportunity loss. This is also known as cost of understocking (Cu) = 35
The production cost is $5 and if the product is not sold, we will incur a cost of (Co) = 5. The fixed cost is incurred either way in a year. As a result we need to consider the critical fractile value
C.F. = Cu/(Cu + Co) = 35/(40) = 0.875
The value of z at 0.875 is 1.15. This means that the optimal order/production will be 8000 + 1.15*3000 = 11450
Hence the answer is, the optimal order quantity will be 11450.
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Stanley deposits $1,000 into a savings account that pays 1% interest per year. At the end of the first year, he's earned $10 in interest and there is $1,010 in the account. If the account has simple interest, the 1% interest for year two would be based off ____________. If the account has compounding interest, the 1% interest for year two would be based off ________________. (note: the first choice goes in the first blank, the second choice goes in the second blank).
If the account has simple interest, the 1% interest for year two would be based off simple interest. If the account has compounding interest, the 1% interest for year two would be based off Compound interest.
Interest on Interest
In performing a straightforward interest calculation, $1,000 that earned 1% interest in one year would yield $1,010 (or .01 x 1,000) at the end of the year. However, that calculation is based on simple interest, paid only on the principal or the deposited funds.
In savings accounts, interest can be compounded, either daily, monthly, or quarterly, and you earn interest on the interest earned up to that point.
The more frequently interest is added to your balance, the faster your savings will grow. Using our $1,000 example earlier and applying daily compounding every day, the amount that earns interest grows by another 1/365th of 1%. At the end of the year, the deposit has grown to $1,010.05 versus $1,010 via simple interest.
Hence the answer is If the account has simple interest, the 1% interest for year two would be based off simple interest. If the account has compounding interest, the 1% interest for year two would be based off Compound interest.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
a. In 2001, it has been calculated that the number of enrolled students that the school would have is given as 150.
b. In the academic year 2018, 468 thousand students are anticipated to enroll at the institution abroad.
How to find the population's sizeThe equation that would be used to get the value of the population has been given to us as follows,
y = 123.1(1.069)^x
We are to find x and use it to solve the equation.
X would be used to tell us the number of years that have passed or what lies as the difference.
in which x is the number of years that have changed.
x = 2001 - 1998 = 3
We have to input the value of x to get the value of y
y = 123.1(1.069)³
This gives us y = 150.4
Hence 150 students would be enrolled.
b. We have to solve for the year 2018
Similarly, the difference between these years is given as:
x = 2018 - 1998 = 20
Put the value in the equation
y = 123.1 * (1.069)²⁰
Y is therefore 467.5
y ~ 468 thousand
Hence 468 are enrolled in this year.
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to what is 9% increased to get 79.57
Please help :(
Answer:
Step-by-step explanation:
6.57
pls send the correct answer
Answer:
z=53 y=37 and x=90
Step-by-step explanation:
Since there's a transversal, x is 90 because of alternate angles. Also alternate exterior angles are z so z=53 degrees. 180-(90+53)=37 degrees is y.
a random sample of 25 was drawn from a normal distribution with a standard deviation of 5. the sample mean is 80. determine the 95% confidence interval estimate of the population mean.
Answer:
For A, the confidence interval formula above cannot be applied because n is less than 30, so we use the t-score confidence interval value
C.I = Mean ± t score × Standard deviation/√n
Mean = 80
Standard deviation = 5
n = 25
Degree of freedom = 25 - 1 = 24
Hence, 95% confidence interval degree of freedom t score = 2.064
Hence, Confidence Interval =
80 ± 2.064 × 5/√25
80 ± 2.064 × 1
80 ± 2.064
Confidence Interval =
80 - 2.064
= 77.936
80 + 2.064
= 82.064
Confidence Interval: (77.936, 82.064)
What is the solution to |x-9| -3 < 1
PLEASE PLEASE PLEASE
Answer:
[tex]\textsf{Solution}: \quad 5 < x < 13[/tex]
[tex]\textsf{Interval Notation}: (5, 13)[/tex]
Step-by-step explanation:
Given inequality:
[tex]|x-9|-3 < 1[/tex]
To solve an inequality containing an absolute value, isolate the absolute value on one side of the inequality:
[tex]\implies |x-9|-3 +3 < 1+3[/tex]
[tex]\implies |x-9| < 4[/tex]
Apply the absolute rule:
[tex]\textsf{If $|u| < a$\; and\; $a > 0$, \;then \; $-a < u < a$}.[/tex]
[tex]\implies -4 < x-9 < 4[/tex]
[tex]\implies -4 < x-9 \;\; \textsf{and}\;\;x-9 < 4[/tex]
Solve case 1:
[tex]\implies -4 < x-9[/tex]
[tex]\implies x-9 > -4[/tex]
[tex]\implies x-9 +9 > -4+9[/tex]
[tex]\implies x > 5[/tex]
Solve case 2:
[tex]\implies x-9 < 4[/tex]
[tex]\implies x-9+9 < 4+9[/tex]
[tex]\implies x < 13[/tex]
Therefore, x is greater than 5 and smaller than 13.
Merge the overlapping intervals to obtain the solution:
[tex]\boxed{5 < x < 13}[/tex]
a rectangular storage container without a lid is to have a volume of 10 m3. the length of its base is twice the width. material for the base costs $20 per square meter. material for the sides costs $12 per square meter. find the cost (in dollars) of materials for the least expensive such container. (round your answer to the nearest cent.)
245.31 (dollars) is the cost (in dollars) of materials for the least expensive such container.
What is maxima and minima ?Calculus maxima and minima are found using the concept of derivatives. Knowing that the derivative concept gives information about the slope/slope of a function, we find the point where the slope is zero. These points are called inflection points/stationary points. These are the points associated with the maximum or minimum (local) values of the function.
Knowledge of maxima and minima is essential for our everyday problems. In addition, this article also explains how to find the absolute maximum and minimum values.
Solvable maximum and minimum arithmetic problems are discussed in this article.
CalculationSuppose the width is x (m), length of the base is 2x (m), the base area is 2x^2 (m^2).
Since the volume is 10 (m^3), the height has to be 10/2x^2 (m) = 5/x^2.
The cost of making such container is
cost of base: 2x^2*15 = 30x^2
cost of sides: (2*2x*5/x^2 + 2*x*5/x^2)*9 = 270/x
The overall cost is hence the sum of the base and the sides: f(x) = 30x^2 + 270/x
The get the minimum,
df(x)/dx = 30*(2x - 9/x^2) = 0
so x = (9/2)^(1/3) = 1.651 (m)
f(x) = 245.31 (dollars)
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Fiona is x years old.
Thomas is 3 years older than Fiona.
Cara is twice as old as Fiona.
Solve the equation and work out Fiona`s,Thoma`s and Cara`sage
Fiona's age will be 'x' years, age of the Thomas is 'x+3' years whereas Cara is '2x' years old.
What is a system of linear equations in three variables?
A three-variable system of three equations can be solved using a series of steps that force one variable to be eliminated. The steps include rearranging equations, multiplying both sides of an equation by a nonzero constant, and adding a nonzero multiple of one equation to another.
If age of Fiona is 'x', the age of Thomas is 'y' and the age of Cara is 'z' years old.
Then by the given conditions, we can write
y = x + 3
z = 2x
Hence, if Fiona's age will be 'x' years, age of the Thomas is 'x+3' years whereas Cara is '2x' years old.
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exercise statement: the initial pressures for bicycle tires when first filled are normally distributed, with a mean of 70 pounds per square inch (psi) and a standard deviation of 1.2 psi. a random sample of 15 tires is drawn from this population. what is the probability that the mean tire pressure of the sample is less than 69 psi? use minitab how-to
Answer:
Below
Step-by-step explanation:
70 - 69 = 1
1/1.2 is .83 S.D. below the mean for a z-score = -.83
from a z-score table this corresponds to .2033 or 20.33%
If a car rental company charges $7 a day and 9 a mile to rent one of its cars, then the cost z, in dollars, to rent a
car for 2 days and drive y miles can be found from the equation
z = 7x + 0.09y
a. How much does it cost to rent a car for 4 days and drive it for 280 miles under these conditions? It costs $__
b. A second company charges $10 a day and 7¢ a mile for the same car. Write an equation that gives the cost z,
in dollars, to rent a car from this company for a days and drive it y miles.
Z=___
c. A car is rented from each of the companies for 2 days. To find the mileage at which the cost of renting the
cars from each of the two companies will be equal, solve the following system for y:
z= 7x + 0.09y
Z= 102 +0.07y
H= 2
y=____ miles
Answers for a) $53.2, b) z = 10x+0.07y and c) y =300
What is an equation?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, a car rental company charges $7 a day and 9 a mile to rent one of its cars, then the cost z, in dollars, to rent a car for 2 days and drive y miles can be found from the equation
z = 7x + 0.09y
a) x = 4, y = 280
z = 7*4 + 280*0.09
z = 53.2
Therefore, the cost to rent a car for 4 days and drive it for 280 miles is $53.2
b) The equation that gives the cost z
z = 10x+0.07y
c) When the costs are equal, then,
10*2+0.07y = 7*2+0.09y
20+0.07y = 14+0.09y
0.02y = 6
y = 300
Therefore, the cost of renting the cars from each of the two companies will be equal when y = 300 miles.
Hence, Answers for a) $53.2, b) z = 10x+0.07y and c) y =300
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16 students want lemonade and 32 students want iced tea. What is the ratio of the number of students who want lemonade to the total number of students?
Answer:
16:48 or 16 to 48 or 16 / 48
Step-by-step explanation:
figure out how many students want lemonade Figure out what the total number of students there are Use a colon the word to or make it a fractionAnswer:
16:48
Step-by-step explanation:
16 is the total amount of students who want lemonade.
You add 16 with 32 to get 48 students in total.
So the ratio is 16:48.
Verify that each equation is an identity.
tan+1/sec = sin+ cos
[tex]\cfrac{tan(\theta )+1}{sec(\theta )}~~ = ~~sin(\theta )+cos(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{tan(\theta )+1}{sec(\theta )}\implies \cfrac{~~ \frac{ sin(\theta )}{cos(\theta ) } +1~~}{\frac{1}{cos(\theta )}}\implies \cfrac{~~ \frac{ sin(\theta )+cos(\theta )}{cos(\theta ) } ~~}{\frac{1}{cos(\theta )}}[/tex]
[tex]\cfrac{ sin(\theta )+cos(\theta )}{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ } \cdot \cfrac{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1}\implies sin(\theta )+cos(\theta )[/tex]
solve by completing the square 3x^2+4x-6=0
Answer:
36.5x-53=543
Step-by-step explanation:
find the value of the expression of -1/3 - (-5/12)
Answer:
to subtract fractions, find the LCD and then combined
The answer is 1/12.
Divide £24 in the ratio 3:2
Answer:16
Step-by-step explanation:
help pls if ur good with money
Answer:Top right answer (You had extra money at the end of the month
Step-by-step explanation:
