A box without a top is to be made from a 30 cm by 30 cm rectangular piece of cardboard by cutting out square corners with a side length of x and then folding up and taping the sides.
What is the maximum possible volume of the box?
What value of x maximizes the volume of the box?
Answers
V = x(30 -2x)²
A graphing calculator can show the local maximum of this function.
a) The maximum possible volume is 2000 cm³.
b) The value of x that maximizes the volume of the box is 5 cm.
Related Questions
Use a calculator to find the r-value of these data. Round the value to three decimal places.
Answers
It's calculated as
r = -108.2 / √((132.8)(90.8)) = -0.9853
Set your calculator to REG then LIN. Input the data as 5,19 then press M+. Continue doing this until the last data. To find r, press SHIFT then number 2 and look for r value. You can only follow this procedure if we have the same calculator. You can use an online calculator also in finding r. in socscistatistics (dot) com. Refer to the attached picture for the graph, values, and computation.
Answer:
i believe the answer is a.
Step-by-step explanation:
Use the graph below to answer the question that follows: cosine graph with points at 0, 3 and pi, negative 5 and 2 pi, 3 What are the amplitude, period, and midline of the function?
Amplitude: 4; period: 2π; midline: y = −1
Amplitude: 8; period: 2π; midline: y = 1
Amplitude: 8; period: π; midline: y = −1
Amplitude: 4; period: π; midline: y = 1
Answers
A = (l-5l + 3) / 2
A = 8/2
A = 4
The middle line is given by:
y = -1
The period of the function is given by:
T = l x2 - x1 l
T = l 0 - 2pi l
T = l - 2pi l
T = 2pi
Answer:
Amplitude: 4; period: 2π; midline: y = -1
Final answer:
The amplitude of the cosine function is 4, the period is 2π, and the midline is y = -1.
Explanation:
The question asks to determine the amplitude, period, and midline of a cosine function based on its graph. The amplitude is the maximum distance from the midline to the peak of the wave, which from the given points (0, 3) and (π, -5) is |-5 - 3| / 2 = 4. The period is the length of one complete cycle of the wave, which appears to be 2π since it starts repeating after (0, 3) to (2π, 3). The midline is the horizontal line that bisects the wave into two equal parts, which from the given points is at y = -1 since it's the average of the maximum and minimum values. The correct answer is: Amplitude: 4; period: 2π; midline: y = − 1.
A circle has a radius of 2 yards and a central angle aob that measures 145°. what is the area of sector aob? use 3.14 for pi and round your answer to the nearest tenth.
Answers
A = (S '/ S) * (pi) * (r ^ 2)
Where,
S '/ S = relation of arcs
r: radius of the circle
Substituting values we have:
A = (145/360) * (3.14) * (2 ^ 2)
A = 5.058888889
Rounding off we have:
A = 5.1 yd ^ 2
Answer:
the area of sector "aob" is:
A = 5.1 yd ^ 2
The area of a trapezoid is 144 square inches. if the height is 12 inches, find the length of the median.
Answers
Answer: 12 inches
Step-by-step explanation: In this problem, since we're asked to find the length of the median, let's use our formula for the area of a trapezoid that involves the median which is shown below.
Area = median · height
We know that the area is 144 and the height is 9 so we can set up the equation 144 = M · 12. Now to solve for m, we divide both sides of the equation by 12 and we find that 12 = M.
So the length of the median of the trapezoid is 12 inches.
Given an area of 144 square inches and a height of 12 inches, the median is found to be 24 inches.
To find the length of the median of a trapezoid, we can use the formula for the area of a trapezoid, which is:
Area = 0.5 × (Base1 + Base2) × Height
We are given that the area is 144 square inches and the height is 12 inches. The formula can be rearranged to solve for the average of the two bases or the median (M):
144 = 0.5 × M × 12
Simplifying this equation, we get:
M = (144 × 2) / 12
M = 288 / 12
M = 24 inches
Thus, the length of the median is 24 inches.
a membership at a gym cost 15 dollars a person without a membership must pay 1.75 each time they go to the gym how many time will a person have to go to make the membership a better deal
Answers
What is the greatest common factor of 73, 47, 74, and 79?
Answers
A rectangular prism has a volume of 150 cm3. if the height measures 3 cm and the width measures 2 cm, what must the length be to achieve the given volume?
Answers
3 x 2 x 25 = 150
Confused, thanks.
Can you use a right triangle to represent the distance the distance between any two points on the coordinate plane? Explain.
Answers
Final answer:
A right triangle can represent the distance between two points on the coordinate plane using the Pythagorean theorem.
Explanation:
Yes, a right triangle can be used to represent the distance between any two points on the coordinate plane. By connecting the two points with a straight line, the path forms the hypotenuse of a right triangle, and the legs represent the distance along the x and y axes. Using the Pythagorean theorem, a² + b² = c², we can calculate the straight-line distance between the two points.
EXTRA POINTS
Find an equation, in slope-intercept form, that passes through point (1, 5) with slope 1.
Select one:
a. y = -x + 1
b. y = x + 4
c. y = -x + 4
d. y = x + 1
Answers
The given point is (x,y) = (1,5) which means x = 1 and y = 5 pair up together.
Plug the three pieces of info (m = 1, x = 1, y = 5) into the y = mx+b equation. Then solve for b
y = mx+b
y = 1*x + b ... replaced m with 1
5 = 1*1 + b .... replaced x with 1, replaced y with 5
5 = 1+b
1+b = 5
b+1 = 5
b+1-1 = 5-1
b = 4
Since m = 1 and b = 4, we know that y = mx+b turns into y = 1x+4 which simplifies to y = x+4
-----------------------------------------------------------------------------------
Answer: y = x+4
Jacqueline is deciding between two mortgages for her new home. The first mortgage is an 80/20 mortgage with interest rates of 4.75 and 7.525%, respectively. The second mortgage is a 30-year mortgage with a 5.25% and a $58.30 monthly PMI. If the house price is $145,000, which mortgage payment will be lower initially, and by how much?
Answers
Final answer:
The initial payment for the first mortgage will be lower by $409.07.
Explanation:
To determine which mortgage payment will be lower initially and by how much, let's calculate the monthly payments for each option.
First Mortgage: 80/20 Mortgage
The first mortgage has two parts, with interest rates of 4.75% and 7.525% respectively. Assuming a house price of $145,000, the loan amount for the first part is 80% of $145,000 = $116,000, and the loan amount for the second part is 20% of $145,000 = $29,000.
Monthly payment for the first part: Principal * Monthly interest rate = $116,000 * (4.75% / 12) = $463.33
Monthly payment for the second part: Principal * Monthly interest rate = $29,000 * (7.525% / 12) = $183.23
Total monthly payment for the first mortgage: $463.33 + $183.23 = $646.56
Second Mortgage: 30-Year Mortgage with PMI
The second mortgage is a 30-year mortgage with an interest rate of 5.25% and a $58.30 monthly PMI.
Loan amount for the second mortgage: $145,000
Monthly payment for the second mortgage: Principal * Monthly interest rate + PMI = $145,000 * (5.25% / 12) + $58.30 = $1,055.63
Therefore, the initial payment for the first mortgage will be lower by $1,055.63 - $646.56 = $409.07.
Jacqueline's first mortgage option has a lower initial monthly payment of $808.04 compared to the second option's $859.69, making it $51.65 cheaper monthly.
Jacqueline is choosing between two mortgage options for a $145,000 house. Let's compare the monthly payments for each mortgage.
Option 1: 80/20 Mortgage
This option involves two loans: the first for 80% of the house price ($116,000) at 4.75%, and the second for 20% ($29,000) at 7.525%.
First loan monthly payment: Use the formula for the monthly payment on a mortgage:M = P[r[tex](1+r)^{n}[/tex]] / [[tex](1+r)^{n-1}[/tex]]
Where P is the loan amount, r is the monthly interest rate, and n is the number of payments.
P = $116,000, r = 4.75%/12 = 0.003958, n = 30*12 = 360First loan monthly payment: $606.69Second loan monthly payment: P = $29,000, r = 7.525%/12 = 0.006271, n = 30*12 = 360Second loan monthly payment: $201.35Total first option monthly payment: $606.69 + $201.35 = $808.04
Option 2: 30-year Mortgage
Total loan amount: $145,000, PMI = $58.30Calculate mortgage payment using the same formula: P = $145,000, r = 5.25%/12 = 0.004375, n = 30*12 = 360Monthly payment before PMI: $801.39Total second option monthly payment: $801.39 + $58.30 = $859.69Now, comparing the two, the first option has an initial monthly payment of $808.04, while the second option has an initial monthly payment of $859.69. So, the first mortgage payment is lower by $51.65.
write “10 times the value of y” three different ways using symbols
Answers
10y
y*10
y(10)
NEED HELP ASAP I will give you Brainly
Can someone please help me with this??
(PLEASE USE THE PICTURES ABOVE)
And please do what it says.
Thanks soo much
thanks
Answers
For ax +by = c, you can solve for y to put the equation into slope-intercept form.
by = -ax +c . . . . . . subtract the x-term
y = (-a/b)x +c/b . .. divide by the coefficient of x
The slope is the x-coefficient, -a/b; the y-intercept is c/b. The function is an odd-degree polynomial function, so its domain and range are both "all real numbers."
2x+3y=18
Slope-intercept form: y = (-2/3)x +6
Domain: all real numbers
Range: all real numbers
Slope: -2/3
Y-intercept: 6
3x-4y > 16
Slope-intercept form: y < (3/4)x -4
Domain: all real numbers
Range: all real numbers
Slope: 3/4
Y-intercept: -4
_____
You will note that the inequality symbol in y < (3/4)x -4 is reversed from that in 3x -4y > 16. That is because in solving for y, we divided by -4. When you multiply or divide an inequality by a negative number, you must reverse the sense of the inequality.
Maci has a family photograph with a width of 4 in and a height of 6 in. She wants to enlarge the photograph so that its width is 10 in. What will the height of the enlarged photograph be?
A. 13 in
B. 14 in
C. 12 in
D. 15 in
Answers
Laney is 4 ft 8 in tall there are 2.54 centimeters in one inch what is Laney's height in centimeters
Answers
[tex]56 \times 2.54 = 142.24[/tex]
Laney's height is about 142 cm
find the surface area of each figure. Round your answers to the nearest tenth, if necessary
Answers
h₁=8.4 cm
h₂=7.8 cm
b= 9 cm
A= 3(1/2bh₁)+1/2 bh₂
A=3(1/2(9)(8.4))+1/2 (9)(7.8)
A= 148.5 cm³
What is the transformation that occurs to the equation y = 2^x if it changes to y = 2^(x - 8)?
The graph moves 8 units to the right.
The graph moves 8 units to the left.
The graph moves 8 units up.
The graph moves 8 units down.
Answers
HELP! - Chloe must pick a 6-digit personal identification number for her bank card. Each digit must be between 0 and 9. Which expression represents the number of different combinations of 6-digit numbers she can create?
|
A: 6+10
B: 6x10
C: 10x10x10x10x10x10
D: 6x6x6x6x6x6x6x6x6x6
Answers
to find the number of combinations you would multiply the number pf digits to choose from (10) by the number of digits required (6)
so you would have 10 x 10 x 10 x 10 x 10 x 10
the answer would be C.
Answer: c
C: 10x10x10x10x10x10
A residual plot is shown.
Which statements are true about the residual plot and the equation for the line of best fit for the data? Check all that apply.
1) The equation for the line of best fit is not a good approximation for the data because the points have a curved pattern.
2) The equation for the line of best fit is a good approximation for the data because the points are random, having no pattern.
3) The residual plot has a linear pattern.
4) The points of the residual plot are spread evenly above and below the x-axis.
5) The residual plot has the pattern of a curve.
6) The equation for the line of best fit is not a good approximation for the data because the points have a linear pattern.
Answers
The second one is not true because the point do not look random. they look like they might be a parabola
The third one is not a choice because plot does not have a linear (straight line) pattern. Linear means straight line.
The fourth one is not true. There is only 1 point below the x axis. The rest are above the x axis.
The 5th one is true.
The 6th one is not true. Those points do not have a straight line pattern.
Answer:
I didn't have that sixth option, but the correct answers are
1. (A.) The equation for the line of best fit is not a good approximation for the data because the points have a curved pattern.
and
5. (E.) The residual plot has the pattern of a curve.
the statement cot theta=12/5 sec theta= -13/5 and the terminal point determined by theta is in quadrant 4
Answers
What’s the point-slope form of a line with slope 2/5 that contains the point (-3,6)
Answers
Answer:
The equation of this line is y - 6 = 2/5(x + 3)
Step-by-step explanation:
To find this, start with the base form of point-slope form.
y - y1 = m(x - x1)
Now put the slope in for m and the two coordinates in for (x1, y1).
y - 6 = 2/5(x + 3)
Can someone help me with these four questions? They're the pictures (including possible answers)
Answers
Start by drawing a dot on each y-coordinate of every given x value in the interval table (-13, -10, -5, -2, and 0). Then, for each interval, draw a straight line between the two y-coordinates of the two x-values given in the interval. So, for interval A, you would draw a straight line from f(-13) to f(-10). This line would have a steep downward slope; this means that the average rate of change over this interval is negative, or less than zero. A satisfies the question.
Interval B has a positive slope between the two y-coordinates, so it doesn’t satisfy the question. Interval C has a line with a slope of 0, but does satisfy the question because it’s asking for average changes less than or equal to zero.
The answer for this problem would be intervals A and C, the answer that is selected.
Write p(x) = 21 + 24x + 6x2 in vertex form.
Answers
p(x) = 21 + 24x + 6x2 => p(x) = 6x2 + 24x + 21
Rewrite the first 2 terms as
6(x^2 + 4x)
then you have p(x) = 6(x2 + 4x ) + 21
Now complete the square of x^2 + 4x:
p(x) = 6(x^2 + 4x + 4 - 4) + 21
= 6(x+2)^2 - 24 + 21
p(x) = 6(x+2)^2 - 3 this is in vertex form now.
We can read off the coordinates of the vertex from this: (-2, -3)
Answer:
p(x) = 6(x+2)^2 - 3
Step-by-step explanation:
A triangular building is bounded by three streets. The building measures approximately 83 feet on the first street, 189 feet on the second street, and 178 feet on the third street. Approximate the ground area K covered by the building.
Answers
We have then:
A = root ((s) * (s-a) * (s-b) * (s-c))
Where,
s = (a + b + c) / 2
Substituting values:
s = (83 + 189 + 178) / 2
s = 225 feet
A = root ((225) * (225-83) * (225-189) * (225-178))
A = 7352.509776 feet ^ 2
Rounding off we have:
A = 7353 feet ^ 2
Answer:
The ground area K covered by the building is:
K = 7353 feet ^ 2
To approximate the ground area covered by the triangular building, we can use Heron's formula. The area ≈ 5884.88 square feet.
Explanation:To approximate the ground area covered by the triangular building, we can use Heron's formula. Heron's formula states that the area of a triangle can be calculated using the lengths of its three sides. The formula is:
Area = sqrt(s(s-a)(s-b)(s-c)), where s is the semiperimeter of the triangle and a, b, and c are the lengths of the sides.
First, we need to calculate the semiperimeter, which is half the sum of the lengths of the three sides:
s = (83 + 189 + 178) / 2 = 225
Using the given lengths of the sides, we can now calculate the area:
Area = sqrt(225(225-83)(225-189)(225-178))
Area ≈ 5884.88 square feet
4(3x-12)=5 (2x+6)
Break down how to solve this
Answers
9514 1404 393
Answer:
x = 39
Step-by-step explanation:
The usual approach is ...
12x -48 = 10x +30 . . . . use the distributive property to eliminate parentheses
2x -48 = 30 . . . . . . . . . subtract 10x from both sides [1]
2x = 78 . . . . . . . . . . . . add 48 to both sides [2]
x = 39 . . . . . . . . . . . . divide both sides by the coefficient of x
The solution is x = 39.
__
Check
4(3x -12) = 5(2x +6) . . . . given
4(3·39 -12 = 5(2·39 +6) . . . . substitute for x
4(117 -12) = 5(78 +6) . . . . . . . multiply
4(105) = 5(84) . . . . . . . . . . . . add
420 = 420 . . . . . . . . . . . . . . multiply
The found value of x makes the equation true, so is the solution.
_____
Additional Notes
[1] The point of the solution process is to put the variable on one side of the equal sign and a constant on the other side. To that end, we subtract the smallest variable term from both sides of the equation. The net result is a variable term on one side of the equal sign that has a positive coefficient.
We could have subtracted either of the constant terms first, and subtracted the variable term second. In this latter approach, the variable term subtracted is the one on the same side of the equation as the remaining constant term. Unless care is taken to select the constant on the side of the largest variable term (for subtraction), the net result may be a negative variable term. Technically, that works just as well, but can tend to increase the probability of an error being made.
__
[2] We notice that all of the terms in the equation after the last step have the x-coefficient as a common factor. This gives us the opportunity to divide by that coefficient at this stage. Doing this would give x-24=15. Then adding 24 would give the same final solution. Sometimes I like to work equations this way so the variable is "bare" (has a coefficient of 1) sooner, and the numbers are smaller.
__
In this discussion, when we talk about subtracting or dividing, we mean the entire equation is involved. The properties of equality tell us the equal sign remains valid if the same operation is performed on both sides of the equation. Our discussion here takes for granted that understanding. We have occasionally said "[do such and such] to both sides". Even where it isn't stated, the "to both sides" always applies.
One competitor in a 100-mile bicycle race took a total of 5 hours to complete the course. his average speed in the morning was 23 miles per hour. his average speed in the afternoon was 13 miles per hour. how many hours did he ride in the morning, and how many hours did he ride in the afternoon?
Answers
We set up two different equations to represent the given info in the description. The first one is morning time + afternoon time = total time to complete the course. So it's x + y = 5. Next, we do morning average multiplied by morning ride time + afternoon average multiplied by afternoon ride time = total distance. So it's 23x + 13y = 100. Then, set up a system of equations:
x + y = 5
23x + 13y = 100
Now, we must pick which variable we want to solve for first. This way we can plug the number we solve for back into one of the original equations to find the other missing variable. I'm going to solve for x first so we multiply by the first equation by - 13. You'll see why in a bit.
- 13(x + y = 5) >> - 13x - 13y = - 65
Your new system of equations is:
- 13x - 13y = - 65
23x + 13y = 100
Now we combine like terms amongst the two equations. Notice the y-variables will cancel each other out, leaving us with just the x to solve for like I want.
10x = 35
Divide by 10 on both sides to isolate variable x
x = 35/10 or 3.5
Now that we have x, we solve for y. Plug your x-value back into either equation; I choose the first because it's easiest.
3.5 + y = 5
Subtract 3.5 from both sides to isolate variable y.
3.5 + y - 3.5 = 5 - 3.5
y + 0 = 1.5
y = 1.5
So the competitor rode 3.5 hours in the morning and 1.5 hours in the afternoon.
OR
The competitor rode 3 hours, 30 minutes in the morning and 1 hour, 30 minutes in the afternoon.
Which products are greater than 2 5/6?
A.
1/8 × 2 5/6
B.
2 5/6 × 2 5/6
C.
2 5/6 × 1 5/8
D.
5/6 × 2 5/6
E.
6/5 × 2 5/6
Answers
After converting mixed numbers to improper fractions and completing the multiplication, options B, C, and E yield products that are greater than 2 5/6. Options A and D are less than 2 5/6.
Explanation:The question asks to evaluate which of the given products are greater than 2 5/6.
We will convert the mixed numbers to improper fractions to make the multiplication easier and then compare the products with 2 5/6 (= 17/6).
For option A (1/8 × 2 5/6), multiplying by 1/8 will clearly result in a product smaller than 2 5/6.For option B (2 5/6 × 2 5/6), squaring 2 5/6 will definitely give a product larger than 2 5/6 itself.For option C (2 5/6 × 1 5/8), since both numbers are greater than 1, their product will be greater than either of the numbers.For option D (5/6 × 2 5/6), 5/6 is less than 1, so the product will be less than 2 5/6.For option E (6/5 × 2 5/6), 6/5 is a reciprocal of 5/6 and is greater than 1, hence their product will be greater than 2 5/6.Therefore, the correct answers are options B, C, and E.
Can someone help meh with this math question? I will award brainliest. For a standard-position angle determined by the point (x,y). what are the values of the trigonometric functions. For the point (6,8), find csc theta and sec theta?
Answers
sin θ = opposite leg/hypotenuse, so
csc θ= hypotenuse/opposite leg
hypotenuse =√((leg1)² +(leg2)²) =√(6²+8²)=√(36+64)=√100=10
csc θ = 10/8=5/4
cscθ =5/4
sec θ is inverse of cos θ , cos θ =adjacent leg/hypotenuse, so
sec θ =hypotenuse/ adjacent leg =10/6=5/3
sec θ =5/3
The value of -4^2 is _____?
16
-16
8
-8
Answers
multiplying to negative numbers will make a positive number
How much 30% paint thinner solution should be added to a gallon of 10% paint thinner solution to make a solution that is 20% paint thinner
Answers
Explanation:
You can set an equation in this way:
1) Number of gallons of 30% thinner solution to be added: x gallons
2) Amount of thineer in the x gallons: 0.30x
3) Amount of thineer in the 1 gallon solution of 10% thinner: 0.10 (1) = 0.10
4) Number of gallons of the final solution, which is 20%: 1 + x
5) Amount of thineer in the final 20% solution: 0.2 (1 + x)
6) Equality:
Amount of thinner in the 30% solution + amount of thinner in the 10% solution = amount of thinner in the 20% solution
0.30x + 0.1 = 0.2 (1 + x)
7) Solve
0.3x - 0.2x = 0.2 - 0.1
0.1x = 0.1
x = 1
That is 1 gallon of 30% thinner solution should be added.
A car rental agency advertised renting a car for $ 26.95 per day and $ 0.28 per mile. if brad rents this car for 4 days, how many whole miles can he drive on a $ 250 budget?
Answers
250 = 26.95(4) + 0.28m
Now we just solve for m
250 = 107.80 + 0.28m
142.20 = 0.28m
m ≈ 507.857 miles
We are looking for WHOLE miles though and if he goes even a decimal point over that many miles (and change), he will be over budget. Thus, we must round down to the whole integer.
Brad can drive 507 miles on a $250 budget for a 4-day rental.
All you would do is multiply 26.95 by 4 to find the cost of the rental for four days which is 107.8. Then you would subtract that number from the total he has to spend which would give you 142.2. The divide 142.2 by 0.28 and that gives you 507.857142. But you would round to the nearest whole number and that would give you 507 miles