We can solve for the value of x using the formula:
V = l w h
where,
h = x the size of the cut since it would form the walls of the rectangle
w = 8.5 – 2x = it is subtracted by 2x since two sides will be cut
l = 11 – 2x
Substituting:
V = x (8.5 − 2x) (11 − 2x)
Expanding the expression:
V = 93.5 x – 39 x^2 + 4 x^3
To solve the maxima, we have to get the 1st derivative dV / dx then equate to 0. dV / dx = 0:
dV / dx = 93.5 – 78 x + 12 x^2
0 = 93.5 – 78 x + 12 x^2
We get:
x ≈ 1.585 in and x ≈ 4.915 in
Therefore Anya’s suggestion of 1.5 inches would create the larger volume since it is nearer to 1.585 inches.
There can be different volumes since volume refers to the amount of space inside the rectangle. They can only have similar perimeter and surface area, but not volume.
It is restricted to 0 in. < x < 4.25 in. because our w is 8.5 – 2x. Going beyond that value will give negative dimensions.
If n = 8 and 16 • 2m = 4n – 8, then m = ?
Final answer:
The value of m is 0.75 when n = 8 and the equation 16 • 2m = 4n – 8 is satisfied, by performing simple algebraic operations to isolate and solve for m.
Explanation:
To find the value of m when n = 8 and 16 • 2m = 4n – 8, we first replace n with 8 in the second equation:
16 • 2m = 4(8) – 8
16 • 2m = 32 – 8
16 • 2m = 24
Now we divide both sides of the equation by 16 to isolate 2m:
2m = 24 / 16
2m = 1.5
Finally, to find m, we divide both sides of the equation by 2:
m = 1.5 / 2
m = 0.75
So the value of m that satisfies the given conditions is 0.75.
If p-1 is a factor of p^4+p^2+p-k the value of k is
The value of k is 3 if p - 1 is a factor of [tex]p^4+p^2+p-k[/tex]
How to determine the value of k?The expression is given as:
[tex]p^4+p^2+p-k[/tex]
The factor is given as:
p - 1
Set the factor to 0
p - 1 = 0
Add to both sides
p = 1
Substitute 1 for p in the expression and equate it to 0
[tex]1^4+1^2+1-k = 0[/tex]
Evaluate the exponents
1+1+1-k = 0
Evaluate the sum
3-k = 0
Add k to both sides
k = 3
Hence, the value of k is 3 if p - 1 is a factor of [tex]p^4+p^2+p-k[/tex]
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what is the value of D to the nearest tenth ?
For the equation x^2+3x+j=0 , find all the values of j such that the equation has two real number solutions. Show your work.
The solution is j<2.25, meaning all values of j less than 2.25 will provide two real solutions.
For the equation [tex]x^2+3x+j=0,[/tex] to have two real number solutions, the discriminant must be greater than 0. The discriminant, D, of a quadratic equation [tex]ax^2+bx+c=0[/tex] is given by [tex]D=b^2-4ac[/tex].
In this case, a=1, b=3, and c=j. Applying the values, we get:
[tex]D=3^2-4(1)(j)[/tex]
D=9-4j
For two real solutions, D>0. Therefore:
9-4j>0
To find the values of j, solve the inequality:
9>4j
j<9/4
Thus, all the values of j that satisfy j<2.25 will ensure that the equation x^2+3x+j=0 has two real number solutions.
A restaurant did a survey among 100 customers to find their food preferences. The customers were asked about their preferences for beef or chicken. Out of the total 75 people who liked beef, 60 also liked chicken. There were 80 people who liked chicken.
Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)
Like beef Do not like beef Total
Like chicken A D G
Do not like chicken B E H
Total C F I
Part B: What percentage of the survey respondents did not like either beef or chicken? (3 points)
Part C: Do the survey results reveal a greater dislike for beef or chicken? Justify your answer. (2 points)
Answer:
A:
like beef do not like beef total
like chicken 60 20 80
do not like chicken 15 5 20
total 75 25 100
B: 5%
C: Beef. 20% of the people do not like chicken. 25% do not like beef ( 5% from each dislike both.)
Step-by-step explanation:
A city planner designs a park that is a quadrilateral with vertices at J(-3, 1), K(1, 3), L(5,-1), and M(-1,-3). There is an entrance to the park at the midpoint of each side of the park. A straight path connects each entrance to the entrance on the opposite side. Assuming each unit of the coordinate plane represents 10 m, what is the total length of the path to the nearest meter?
Arlene is comparing the prices of two truck rental companies. Company A charges $7 per hour and an additional $30 as service charges. Company B charges $8 per hour and an additional $40 as service charges.
Part A: Write an equation to represent each company's total charges for renting a truck for a certain number of hours. For both equations (one for Company A and one for Company B), define the variable used. (4 points)
Part B: Which company would charge less for renting a truck for 8 hours? Justify your answer. (3 points)
Part C: How much money is saved by using the services of Company A instead of Company B to rent a truck for 2 hours? (3 points)
Which of the following best describes the expression 6(y + 3)?
1.)The product of two constant factors six and three plus a variable
2.)The sum of two constant factors six and three plus a variable
3.)The product of a constant factor of six and a factor with the sum of two terms
4.)The sum of a constant factor of three and a factor with the product of two terms
Answer: Hence, option '3' is correct.
Step-by-step explanation:
Since we have given that
[tex]6(y+3)[/tex]
This expression can be written in statement.
Here, we can see that there are two terms:
1) A constant factor of 6
2) Sum of two terms
So, according to options it can be written as :
The product of constant factor of 6 and a factor with the sum of two terms i.e. y and 3.
Hence, option '3' is correct.
Help me plz so bad I don't want to get bad grade on this
Answer:
1. 16666666666667 2. .72727272727 3. .25
Step-by-step explanation:
all you do is divide the top number by the bottom number to get it in decimal form
Which graph represents the solution to the system of inequalities?
x + y ≤ 4
y – x ≥ 1
Nick has two more than twice as many quarters as dimes.. one fewer than three times as many nickels as dimes, and eight more pennies than dimes.. he has $7.37. How many of each coin does he have?
Thank you so much :)
An angle measures 20° more than the measure of a complementary angle. What is the measure of each angle?
An architectural drawing lists the scale as 1/4 = 1. If a bedroom measures 3 1/2 by 5 1/4 on the drawing, how large is the bedroom
Answer:
The measure of the bedroom is 14 by 21
Step-by-step explanation:
This scale represents the every measure in the drawing is a 1/4 of the original measure, so to find the original measure you must multiply the measure you find in the drawing by 4.
So for the beadroom (3 1/2, 5 1/4), you multiply each one by 4
The real measures of the beadroom are:
(3 1/2 * 4, 5 1/4 * 4)
(14,21)
The measure of the bedroom is 14 by 21
how to write unit form for (2 tens 1 one) x 10
If the APY of a savings account is 2.4% and if the principal in the savings account is $2200 for an entire year, what will be the balance of the savings account after all the interest is paid for the year? A. $2200 B. $2252.80 C. $2300 D. $2205.28
To solve this problem, we must recall that the formula for money with compound interest is calculated as:
Total = Principal × ( 1 + Rate ) ^ n
Total = $2,200 × ( 1 + 0.024 ) ^ 1
Total = $2,252.80
Therefore the answer is letter B.
Which factor does the width of the peak of a normal curve depend on?
Answer: The width of the peak depends on the Standard Deviation. The standard deviation is a measure used to quantify the variation or dispersion in the data set. If the standard deviation is low, this means that the set of data tends to be closer to the mean, then the width of the peak in the normal curve is small, for other part if the standard deviation is big, this means that the variation is big and the data set is more spread, this causes that the width of peak to be larger.
Which planet is 10 times as far as earth is from the Sun
HELPPPPPPPPPPPPPPPPPPPP
A triangle has squares on its three sides as shown below. What is the value of x?
FIRST ONE GETS BRAINLIEST AND 12 PTS!!
ANSWER BOTH QUESTIONS IF U CANT SEE THE CHOICES ITS FINE! ALL U NEED IS THE QUESTION
Answer:
12 and 13
Step-by-step explanation:
The restaurant bill you and your friend received was not itemized. You ordered 2 drink refills and the egg breakfast, for a total of $8.40. Your friend ordered 3 refills and the egg breakfast for $9.35.
(a) Write a system of equations for the situation. Use r for the amount charged for a refill and b for the amount charged for the egg breakfast.
(b) Graph the equations in the system.
(c) Use your graph to estimate how much each item cost.
Which is an obtuse angle?
∠CAB
∠BAC
∠BCA
∠ABC
K+3d=8c-8d
solve for d
A triangle has angles that measure 30, 60, 90. The hypotenuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle?
The net of a square pyramid is shown below: What is the surface area of the solid?What is the surface area of the solid?
32 square inches 14 square inches 20 square inches 24 square inches 32 square inches
A car dealer recently sold five cars for the following profits: $10,126, $9,999, $12,398, $12,007, and $4,567. What was the mean for the profits of the sales?
Answer:
$9819.4
Step-by-step explanation:
We have been given that a car dealer recently sold five cars for the following profits: $10,126, $9,999, $12,398, $12,007, and $4,567. We are asked to find the mean for the profits of the sales.
Since mean is the average of numbers. So let us add all the profits and divide the sum of profits by number of cars.
[tex]\text{Mean for the profits of the sales}=\frac{10126+9999+12398+12007+4567}{5}[/tex]
[tex]\text{Mean for the profits of the sales}=\frac{49097}{5}[/tex]
[tex]\text{Mean for the profits of the sales}=9819.4[/tex]
Therefore, the mean for the profits of sales is $9819.4.
Express without negative exponents
1/5^-1 = 5
.4^-2 = 6.25
so it would be 5 x 6.25
Write an equation ten times the sum of half a number and 6 is 8.
Haley and Samuel can each make one gift box in two hours. Rachael takes three hours to make the gift box alone. If Haley, Samuel, and Rachael work together, how long will it take them to make one gift box?
It will take 40 minutes for them to make one gift box.
Combined ratesGiven that Haley and Samuel can each make one gift box in two hours, while Rachael takes three hours to make the gift box alone, to determine, if Haley, Samuel, and Rachael work together, how long will it take them to make one gift box, the following calculation must be performed, using combined rates:
1/2 + 1/2 + 1/3 = X3/6 + 3/6 + 2/6 = X8/6 = X6/6 = 1 hour8/6 = 40 minutesTherefore, it will take 40 minutes for them to make one gift box.
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Answer:It will take 40 minutes for them to make one gift box
Step-by-step explanation:
A net can be folded to form a cube. The numbers on the three faces meeting at any vertex can be multiplied together. What is the smallest such product for the vertices of this cube