Answer:
$300
Step-by-step explanation:
Let x represent the side length of the square base in feet. Then the height of each side is ...
... h = (50 ft³)/(x ft)² = (50/x²) ft
The cost of the sides of the box is then ...
... (4 sides) × (x ft)(50/x² ft)/side × $2/ft² = $400/x
The cost of the bottom is ...
... (x ft)² × $25/ft² = $25x²
So, the total dollar cost is
... C = 400/x + 25x²
This will be a minimum where its derivative with respect to x is zero.
... 0 = -400/x² +50x
... 400/50 = 8 = x³ . . . . . add 400/x²; multiply by x²/50
... x = ∛8 = 2
For this value of x, the minimum cost is ...
... C = 400/2 + 25·2² = 300
The minimum possible cost is $300.
_____
Comments on the problem
1) Cardboard boxes are usually made of cardboard. They are rarely made of wood and alumninum.
2) The cost of the bottom is half the cost of the sides. When the dimensions are unconstrained, you will find (as here) the cost is shared equally between the bottom and pairs of opposite sides—each being 1/3 the total cost.
Six friends go out to lunch and decide to split the bill evenly. The bill comes to $61.56. How much does each person owe?
Answer:
each person owe $10.26
Step-by-step explanation:
Six friends go out to lunch and decide to split the bill evenly. The bill comes to $61.56.
Total bill for 6 friends = $61.56
To find bill cost for 1 person we divide the total cost by 6
Bill for each person = [tex]\frac{61.56}{6}= $10.26[/tex]
So each person owe $10.26
If (x-y)^2=100 and xy=20. what's the value of x^2+y^2?
Answer: The value of [tex]x^2+y^2[/tex] is 140
Step-by-step explanation:
We are given an expression:
[tex](x-y)^2=100[/tex]
And,
xy = 20
Using the identity:
[tex](a-b)^2=a^2+b^2-2ab[/tex]
Solving the expression:
[tex]x^2+y^2-2xy=100[/tex]
Putting the value of 'xy' in above equation, we get:
[tex]x^2+y^2-2(20)=100\\\\x^2+y^2=100+40\\\\x^2+y^2=140[/tex]
Hence, the value of [tex]x^2+y^2[/tex] is 140
In the △PQR, PQ = 39 in, PR = 17 in, and the altitude PN = 15 in. Find QR.
Final answer:
To find the length of QR, we used the Pythagorean theorem on triangle PNQ to find NQ, then added it to PR, resulting in QR measuring 53 inches.
Explanation:
To find the length of side QR in △PQR, we can apply the Pythagorean theorem to one of the right triangles formed by the altitude PN. The triangle we'll use is △PNQ, where NQ is part of QR, and PN is given as 15 in.
Firstly, we can calculate NQ using the Pythagorean theorem:
PN² + NQ² = PQ²
15² + NQ² = 39²
NQ² = 39² - 15²
NQ² = 1521 - 225
NQ² = 1296
NQ = √1296
NQ = 36 in
Since PR = 17 in, we can conclude that NR is the difference between PR and NQ:
NR = PR - NQ
NR = 17 - 36
NR = -19 in
The negative value indicates a mistake since lengths cannot be negative. Therefore, we should use the entire length of PQ instead:
QR = NQ + NR
QR = 36 + 17
QR = 53 in
Thus, side QR measures 53 inches.
Observe the two functions on the graph.
Match each function with a type of function.
f(x):
g(x):
exponential
quadratic
cubic
linear
The graph of [tex] f(x) [/tex] is a straight line, so it is a linear function.
The graph of [tex] g(x) [/tex] has the same shape of the graph of [tex] y=e^x [/tex] (for example), so it is an exponential function.
Answer:
f(x) is linear
g(x) is exponential
Step-by-step explanation:
exponential -> It is a graph of half curve
quadratic -> it is a graph of a U shaped curve
cubic -> it is a graph of a full curve that goes top and bottom
linear -> It is a graph of a line
In the give graph f(x) is a line graph , so it is Linear
The graph g(x) is a curve that goes at the top not at the bottom. Its like a half curve. so it is an exponential
What is the maximum Number of different sizes of faces that a rectangular Prism can have.
Answer:
3
Step-by-step explanation:
For a rectangular prism of dimensions L × W × H, pairs of opposite faces will have dimensions ...
L × WW × HH × LThese will be three different sets of dimensions if L, W, and H are all different lengths.
Tanya's science class had a quiz on 13 of the first 40 days of class. Which is this ratio as a decimal?
Answer:
.325
Step-by-step explanation:
If she had a quiz on 13 of the 40 days , the fraction is 13/40
13/40 = .325
Answer: The fraction of the days on which the quiz has been held expressed as a decimal is 0.325
Step-by-step explanation:
Decimal numbers are not considered as integers. They are rounded off to write an integer.
Fraction is present in the form of [tex]\frac{p}{q}[/tex] where [tex]q\neq 0[/tex]
We are given:
Number of days, the class had quiz = 13
Total number of days = 40
The fraction becomes: [tex]\frac{13}{40}[/tex]
Expression this as a decimal = 0.325
Hence, the fraction of the days on which the quiz has been held expressed as a decimal is 0.325
Help please #10 if you can
Answer:
200,000 m
Step-by-step explanation:
We will multiply the length of the ant by the number of ants to find out how long the line is.
10 million is 10 with 6 zeros
20 * 10 ^-3 move the decimal 3 places to the left
20. * 10 ^-3 = .02
.02 * 10000000
200000
Which graph represents f(x)=1/2x^2 ?
Answer:
See below.
Step-by-step explanation:
The one that looks like the attachment.
It is vertically shortened from f(x) = x^2, so appears wider than f(x) = x^2 does. The vertex is still at (0, 0), it still opens upward, and it remains symmetrical about the y-axis.
[tex]f(x)=\dfrac{1}{2}x^2\\\\for\ x=0\to f(0)=\dfrac{1}{2}(0)=0\to(0,\ 0)\\\\for\ x=\pm1\to f(\pm1)=\dfrac{1}{2}(\pm1)^2=\dfrac{1}{2}(1)=\dfrac{1}{2}\to\left(-1,\ \dfrac{1}{2}\right);\ \left(1;\ \dfrac{1}{2}\right)\\\\for\ x=\pm2\to f(\pm2)=\dfrac{1}{2}(\pm2)^2=\dfrac{1}{2}(4)=2\to(-2,\ 2);\ (2,\ 2)\\\\for\ x=\pm4\to f(\pm4)=\dfrac{1}{2}(\pm4)=\dfraC{1}{2}(16)=8\to(-4,\ 8);\ (4,\ 8)[/tex]
These prisms are similar. Find the volume of the larger prism in decimal form. Ratio 5:7. Volume of smaller Prism is 50 m3
Answer:
137.2 m³
Step-by-step explanation:
The ratio of volumes is the cube of the ratio of linear dimensions. The larger volume is ...
... V = (7/5)³ × 50 m³ = 2.744 × 50 m³
... V = 137.2 m³
Conner bought some pears.He used 2/6 of the pears to make dessert.He gave 1/4 remainder to his neighbor.What fraction of the pears did he give to his neighbor
First, let's subtract 1 (100%) by 2/6:
1 - 2/6 = 4/6
Knowing that Conner gave his neighbor 1/4 of the remainder, we simply have to multiply 4/6 by 1/4:
4/6 * 1/4 = 4/24 = 1/6
Conner gave 1/6 of his pears to his neighbor.
pls help!!!
in which line is a mistake first made when solving the following system of equations by substitution? 2x - y =-4 3x + y = -9
line 1: 2x -y = -4
y= 3x-9
line 2: 2x-(3x-9)=-4
line 3: 2x-3x+9=-4
line 4: -1x + 9 = -4
line 5: -1x = -13
line 6: x = 13
Answer:
The very first line has an error.
Step-by-step explanation:
When you are solving the second system of equations for y, you need to subtract 3x from both sides and therefore it should be negative.
3x + y = -9
y = -3x - 9
Since the 3x isn't negative in the first line, there is an error.
you pay $2.76 for 6 bagels. what is the unit price?
a) $0.46 per bagel
b)$0.48 per bagel
c)$0.52 per bagel
d)$0.44 per bagel
Answer:
a) $0.46 per bagel
Step-by-step explanation:
When you are looking for a unit price, you have to divide the price in this instance by the amount of items that you have. For example, here you just have to divide $2.76 by 6 to get $0.46.
Hope I could help! :)
Permutations and Combinations!
how many 5 digit numbers can be formed that do not contain the digits 0 or 8?
Answer:
9×9×8×7×6= 27,216
Step-by-step explanation:
Your answer is :- 9×9×8×7×6= 27,216
Why did i multiply 9×9×8×7×6 ⤵️
Because we can fill each place of a five digit number with ten digits (0,1,2,3,4,5,6,7,8,9).
Now, let us assume the five digit number is abcde, where each alphabet represent a digit.
so according to our question a cannot be equal to 0 ( a≠0), because if a will be equal to zero then our number will be a four digit number. So a can be equal to 9 digits.
b digit can also be equal to 9 numbers. why??because we can place zero on the position of b and only one number will not be repeated which is a.
Now for c, d, e :- accordingly no number will be repeated so on the place of c, there can be 8 digits. On the place of d, there can be 7 digits. And on the place of e there can be 6 digits.
Therefore,
a×b×c×d×e=9×9×8×7×6=27,216
Can you please help me solve 18 and 21 please?
18. x = y = -3
21. y was substituted into the wrong equation. The solution is (x, y) = (2, 1).
Step-by-step explanation:18. Adding y to the first equation transforms it to ...
... x = y
Then you can substitute for either variable in the second equation.
... 2y -5y = 9 . . . . . substitute for x
... -3y = 9 . . . . . . . . simplify
... y = -3 . . . . . . . . . divide by the coefficient of y
.. x = -3 . . . . . . . . . x and y have the same value
___
21. The first equation is being used to find an expression for y in terms of x. If you substitute that expression back into the same equation, it will tell you nothing you didn't already know. (Here, it is telling you 5 = 5.) The expression is only useful if you substitute it into a different equation. Here, it needs to be substituted into the second equation:
... Step 2: 3x -2(-2x+5) = 4 ⇒ 7x -10 = 4 . . . . . substitute for y in the second eqn
... Step 3: 7x = 14 . . . . . add 10
... Step 4: x = 2 . . . . . . . divide by 7
... Step 5: y = -2·2 +5 = 1 . . . . . find the value of y from x using the expression from step 1. Now, you know the solution is (x, y) = (2, 1).
_____
The attached graph shows the solution to the problem of 21.
Re-arrange the BMI formula for h, height.
Answer:
[tex]Height=\sqrt{\frac{weight}{\text{body mass index}}}[/tex]
Step-by-step explanation:
We have BMI formula that is body mass index formula which is:
[tex]\text{Body mass index}=\frac{weight}{height^2}[/tex]
Now, we have to arrange the formula for height:
we will rearrange the terms and derive the formula for height in terms of weight and height.
[tex]Height^2=\frac{weight}{\text{body mass index}}[/tex]
Hence, the required result is:
[tex]Height=\sqrt{\frac{weight}{\text{body mass index}}}[/tex]
Sophia puts $250 in the bank with a 2.5% annual interest rate compounded monthly. If Sophia does not touch his money, how much money will she have after four years? A) $260.00 B) $275.00 C) $275.95 D) $276.26
Answer:
D) $276.26Step-by-step explanation:
Deposited amount initially (P) = $250.
Rate of interest(r) = 2.5% compounded monthly = 0.025
Number of years (t) = 4.
Number of months in an year (n) = 12.
Formula for compound interest:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex].
Plugging values in formula, we get
[tex]A= 250(1+\frac{0.025}{12})^{12\times 4}[/tex]
[tex]A= 250(1.00208)^{48}[/tex]
[tex]A= 250\times \:1.10506[/tex]
A=276.26.
Therefore, correct option is D) $276.26.A bridge over a gorge is supported by an arch in the shape of a semi-ellipse. The length of the bridge is 400 ft. and the maximum height is 100 ft. Draw a picture of the problem and label it with numeric values. Find the height of the arch 50 ft. from the center. Round to the nearest foot.
Final answer:
To find the height of the arch 50 ft. from the center, we can use the equation of a semi-ellipse. The height of the arch is approximately 31 ft. when rounded to the nearest foot.
Explanation:
To find the height of the arch 50 ft. from the center, we can use the equation of a semi-ellipse. The equation of a semi-ellipse with a length of a and a maximum height of b is given by: ((x^2)/(a^2))+((y^2)/(b^2)) = 1. In this case, the length of the bridge is 400 ft. and the maximum height is 100 ft., so we have: ((x^2)/(200^2))+((y^2)/(100^2)) = 1. To find the height when x = 50 ft., we substitute x = 50 into the equation and solve for y. Plugging in the values, we get: ((50^2)/(200^2))+((y^2)/(100^2)) = 1. Simplifying, we have: (2500/40000)+((y^2)/(100^2)) = 1.
Multiplying both sides by 40000 to get rid of the denominators, we have: 2500 + 400((y^2)/10000) = 40000. Simplifying further, we get: 2500 + 40(y^2) = 40000. Subtracting 2500 from both sides, we have: 40(y^2) = 37500. Dividing both sides by 40, we have: (y^2) = 937.5. Taking the square root of both sides, we have: y = 30.62. So, the height of the arch 50 ft. from the center is approximately 31 ft. when rounded to the nearest foot.
Which situation can be modeled by the inequality 48−10x≥8?
A. You have $48 to spend on socks, but you need to save at least $8 to pay for the bus trip home. You plan to spend the rest on socks at $10 each (including tax).
B. You loaned $48 to your older brother. He pays you $8 a week and needs to pay you back within 10 weeks.
C. You can buy socks in packages of 10 pairs. You have $48 to spend but want to have at least $8 left.
D. You owe your parents $48 and plan to pay them $10 a week until you owe them less than $8.
Answer:
A. You have $48 to spend on socks, but you need to save at least $8 to pay for the bus trip home. You plan to spend the rest on socks at $10 each (including tax).
Step-by-step explanation:
cause it's A
Answer:
A. You have $48.00 to spend on socks, but you need to save at least $8.00 to pay for the bus trip home. You plan to spend the rest on socks at $10.00 each (including tax).
Step-by-step explanation:
Proportional Relationships Please help :3
Worth 25 per answer (i think cause i put 50 points)
Answer:
6
Step-by-step explanation:
Since the relationship is proportional, when y is increased by a factor of 3 from 7 to 21, so is x—from 2 to 2×3 = 6.
There are 12 apples in a basket. 5 of these apples are green. The rest of them are red. (a) What is the ratio of red apples to all apples in the basket? (b) What is the ratio of red apples to green apples?
For someone who is clinically underweight and has been encouraged by their doctor to gain a few pounds, how many calories per day should someone consume to gain 2 pounds in two weeks assuming they burn 2000 calories per day?
Answer:
2500 total calories per day.
Step-by-step explanation:
Assuming that 3500 excess calories produces 1 pound gain, 7000 excess calories required for 2 pound gain
to be accomplished in 14 days
7000/14 = 500 excess calories per day
2000 required calories per day
2500 total calories per day.
3. A family is tracking its spending habits. Over the past year, the grocery bill has ranged from $110 to $170. Suppose you were going to plot these points on a coordinate grid. (a) What is a good scale to use for the y-axis? Explain your reasoning. (b) What is a good interval to use for the y-axis? Explain your reasoning. Answer:
The best way to plot them is by month.
170 - 110 = $60.
We are supposed to plot in months and the above calculation is in year, convert it into months
60/5 = $5 each month
So, the coordinates would be 0, 110 1, 115 2, 120 3, 125
The month will be in the x axis and your money will be the Y axis
A suitable y-axis scale to plot spending habits ranging from $110 to $170 would start at $100 and go up to $180, while a good interval for the y-axis would be $10 to allow for clear plotting of values in whole dollars.
To answer the student's question about how to plot spending habits on a coordinate grid:
A good scale for the y-axis when plotting the family's grocery bills that range from $110 to $170 would be one that fits the entire range of values without being too cramped or too spread out. For instance, a scale that starts at $100 and goes up to $180 would allow all points to be plotted clearly. Since these are monetary values, maintaining a scale that reflects currency would be logical.A good interval for the y-axis could be multiples of $10 since this allows for clear and precise plotting of bills that are likely to be in whole dollars, making the graph easier to read while still being detailed enough to discern differences of $10.Zoomfast Tire & Battery stores are selling new steel-belted radial tires. They promise that when these tires are used your car will get 10% better gasoline mileage. If Gloria's red convertible now goes 420 miles on a tank of gasoline, how far could she drive on a tank if she switched to the new tires?
Answer:
462 mi
Step-by-step explanation:
Gloria gets 420 mi/tank.
10 % of 420 is
420 × 0.10 = 42 mi
She will be able to drive an extra 42 mi.
420 + 42 = 462 mi
With her new tires, a tank of gas will take her 462 mi.
Answer:
462
Step-by-step explanation:
to find 10% of 420 you take
420 x .10 = 42
then add 42 to 420
420+42=462
The cost of a laptop computer in 2007 was $1,250. In 2009, the price decreased to $1,100.
A.) Find the percent decrease in the price of the laptop from 2007 to 2009.
B.) Find the percent decrease in the price of the laptop from 2009 to 2010 if the price decreased by $165 in 2010.
Given : The Cost of Laptop in 2007 is $1250
Given : The Cost of Laptop in 2009 is $1100
Decrease in Price of Laptop from 2007 to 2009 : (1250 - 1100) = $150
A) Percent Decrease in the Price of the Laptop from 2007 to 2009 is :
[tex]\mathsf{\implies \frac{Decrease\;in\;Price\;of\;Laptop\;from\;2007\;to\;2009}{Price\;of\;Laptop\;in\;2007} \times 100}[/tex]
[tex]\mathsf{\implies \frac{150}{1250} \times 100}[/tex]
[tex]\mathsf{\implies 12\%}[/tex]
Given : Decrease in Price of Laptop from 2009 to 2010 = $165
B) Percent Decrease in the Price of the Laptop from 2009 to 2010 is :
[tex]\mathsf{\implies \frac{Decrease\;in\;Price\;of\;Laptop\;from\;2009\;to\;2010}{Price\;of\;Laptop\;in\;2009} \times 100}[/tex]
[tex]\mathsf{\implies \frac{165}{1100} \times 100}[/tex]
[tex]\mathsf{\implies 15\%}[/tex]
The percent decrease in laptop prices, use the formula ((Original Price - New Price) / Original Price) x 100%. The percent decrease from 2007 to 2009 is 12%, and from 2009 to 2010 is 15% with a $165 decrease.
The cost of a laptop computer in 2007 was $1,250. In 2009, the price decreased to $1,100.
A.) To find the percent decrease from 2007 to 2009, you use the formula: Percent decrease = ((Original Price - New Price) / Original Price) x 100%
Substitute the values: ((1250 - 1100) / 1250) x 100% = 12%
Therefore, the percent decrease in the price of the laptop from 2007 to 2009 is 12%.
B.) To find the percent decrease from 2009 to 2010 with a $165 decrease, you apply the same formula: Percent decrease = ((Price in 2009 - Price in 2010) / Price in 2009) x 100%.
Substitute the values: ((1100 - (1100 - 165)) / 1100) x 100% = 15%
Therefore, the percent decrease in the price of the laptop from 2009 to 2010 is 15%.
help please? i would really appreciate it.
Answer:
The answer is option C i.e; y=0.9x-45
Step-by-step explanation:
When you substitute the values of x you have to get same values as given in the table
For example: substitute x=50 in the equation y=0.9x-45
Y= 0.9(50)-45
Y= 45-45
Y=0
What numbers are on the nnumber line starting with the number 1 then it has 10 spaces then 1.01 then 10 spaces then 1.02 then 10 spaces then 1.03 then 10 spaces then 1.04.
You are referring to the thousandths spot.
1.00(0)000001
So, between any given number n to n.01 there are 10 numbers.
n.001, n.002, n.003, ..., n.01
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x − 5
y ≥ −x − 4
A. (−5, 2)
B. (5, −2)
C. (−5, −2)
D. (5, 2)
Answer:
B. (5,-2)
Step-by-step explanation:
Plug in X and Y, verify accuracy
The graph of the function, f(x) = 3x^2 + x + 2, opens down/up and has a maximum/minimum value.
If the function has a ∪ shape (opens up), then it only goes so low—has a minimum value.
Any even-degree function with a positive leading coefficient will open up, so have a minimum. Your function is degree 2 (even) and has a leading coefficient of 3 (positive).
_____
Comment on other polynomial functions
If the leading coefficient of an even-degree function is negative, it will have an inverted-U shape (∩), so will have a maximum.
Any odd-degree function will have a generally rising (/) or generally falling (\) shape, depending on the sign of its leading coefficient. If positive, then rising; if negative, then falling.
The graph shows how far a snail traveled over time. What information can you draw from the point (3,18) on the graph?
The point (3, 18) on the graph means the snail's position when the time is 3 units of time from the time reference is 18 units of distance from the the reference point for distance.
_____
We cannot conclude anything else. We don't know if the snail is moving (or has moved), or if there are any other points on the graph.
Answer: B) The snail traveled 18 ft in 3 h.
Step-by-step explanation: If you look at the graph they graphed (3, 18) the left side says distance (ft) and the dot is to the right of the 18 so it traveled 18 feet. At the bottom it says time (h) and the dot above the 3 so it took to travel 8 feet.
Hope This Helped ^_^
The table shows the total distance (d), in kilometers, a bicycle traveled after t hours.
Time in hours (t) Distance in kilometers (d)
(t) (d)
0 0
1 8
2 16
Which equation shows the relationship between d and t?
d=8t
d=16t
d=t+8
d=t+16
Answer:
d = 8t
Step-by-step explanation:
To find a correlation, you need to find what numbers correlate and how.
Lets try multiplying the t value by 8 to get the value ( as one value is 1 and the other is 8 so it would seem suitable)
1 * 8 = 8
2 * 8 = 16
Both values match up which means that to get d, you multiply t by 8.
This means that your answer is d = 8t.