The team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.
Understanding Word Problem in Solving MathsWe can derive an inequality from the problem statement which is:
8X + 12Y >= 1000
This inequality represents the amount of money the basketball team needs to raise by selling donuts.
X is the number of half dozen boxes sold
Y is the number of full dozen boxes sold.
To find a solution in terms of the given context, we can plug in different values for X and Y that satisfy the inequality. For example:
If the team sells 50 half dozen boxes and 50 full dozen boxes, they will make:
8(50) + 12(50) = $400 + $600 = $1000
So this is a valid solution that meets the fundraising goal.
If the team sells 100 half dozen boxes and 0 full dozen boxes, they will make:
8(100) + 12(0) = $800
This is not enough to meet the fundraising goal, so it is not a valid solution.
If the team sells 0 half dozen boxes and 100 full dozen boxes, they will make:
8(0) + 12(100) = $1200
This is more than the fundraising goal, so it is a valid solution, but the team may not want to sell so many full dozen boxes.
Therefore, one solution in terms of the given context is that the team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.
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A landscaper worded 8-1/2 hours on Monday, 3-1/3 hours on Tuesday and 6-1/4 hours on Wednesday. How many total hours did she work?
If landscaper worked 8-1/2 hours on Monday, 3-1/3 hours on Tuesday and 6-1/4 hours on Wednesday then total of 18.08 hours worked.
To find the total number of hours worked, we need to add up the hours worked on each day.
On Monday, the landscaper worked for 8-1/2 hours, which is the same as 8.5 hours.
On Tuesday, the landscaper worked for 3-1/3 hours, which is the same as 3.33 hours
On Wednesday, the landscaper worked for 6-1/4 hours, which is the same as 6.25 hours.
To find the total hours worked, we add the hours worked on each day:
Total hours worked = 8.5 + 3.33 + 6.25
Total hours worked = 18.08
Therefore, the landscaper worked a total of 18.08 hours.
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Below is a model of the athletic field at IDEA Brentwood what is the area in square yards
The area in square yards of the athletic field at IDEA Brentwood would be 170. 24 yards ²
How to find the area ?The shape of the athletic field at IDEA Brentwood is shown to be a rectangle with two semi - circles attached.
The area of the athletic field at IDEA Brentwood is the sum of the areas of these shapes.
Area of rectangle :
= 15 x 8
= 120 yards ²
The area of the two semi - circles would be:
= π x radius x radius
= π x ( 8 / 2 ) x ( 8 / 2 )
= 50. 24 yards ²
The area of the athletic field at IDEA Brentwood is :
= 50. 24 + 120
= 170. 24 yards ²
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A cylinder with a radius of 8 inches is cut from the prisim. What is the volume of the new object
The volume of the new object is approximately 439.3 cubic inches
What is the volume of the new object?To find the volume of the new object, we need to first know the volume of the prism before the cylinder is removed hence we do this:
The volume of a cylinder: = πr²h
where:
r = radius
h = height
Note that the volume of a rectangular prism is : = lwh
l = length
w = width
h = height
Assumption: In the above case, we will assume that the dimensions of the rectangular prism because the cylinder can be cut out from the center of one of the faces.
Hence the length and width of the prism will be taken to be twice the radius of the cylinder, that is 16 inches, and the height will be taken to be same as the radius of the cylinder, that ia 8 inches.
So V_prism = lwh
= 16 × 16 × 8
= 2048 cubic inches
V_cylinder = πr²h
= π × 8² × 8
= 512 π cubic inches
Hence To get the volume of the new object, we need to subtract the volume of the cylinder from the volume of the prism:
V_new = V_prism - V_cylinder
= 2048 - 512π
= 2048 - 1608.70
= 439.3 cubic inches
Hence, the volume of the new object is about 439.3 cubic inches
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cost function definition
If it takes 15 minutes for water in a pot to boil, the expression 20x+ 15 can be used to find the total time needed to cook x batches of boiled cornbread. Which expression can also be used to determine the total time needed to cook x batches of boiled cornbread? PLS ANSWER ASAPP I REALLY NEED TO ANSWER THIS QUESTION
A 18x + 4x + 6 + 7
B 10x + 10x + 20 - 5
C 6(5x + 5) - 10x + 15
D 3(x + x + x + 3)+ 2x + 15
the correct expression which can also be used to determine the total time needed to cook x batches of boiled cornbread is,
B) 10x + 10x + 20 - 5.
Given that;
The expression 20x + 15 represents the total time needed to cook x batches of boiled cornbread.
We can simplify this expression by factoring out the common factor of 5: = 20x + 15
= 5(4x + 3)
Therefore, the expression that can also be used to determine the total time needed to cook x batches of boiled cornbread must have a factor of 5 in it.
Option A:
18x + 4x + 6 + 7 does not have a factor of 5,
so it cannot be the correct answer.
Option B:
10x + 10x + 20 - 5
= 20x + 15,
which is the same as the original expression.
Therefore, Option B is equivalent to the original expression and can also be used to determine the total time needed to cook x batches of boiled cornbread.
Option C:
6(5x + 5) - 10x + 15 = 30x + 15 - 10x + 15 = 20x + 30,
which does not have a factor of 5.
Therefore, Option C is not correct.
Option D:
3(x + x + x + 3) + 2x + 15 = 9x + 6 + 2x + 15 = 11x + 21,
which does not have a factor of 5.
Therefore, Option D is not correct.
Therefore, the correct answer is,
B) 10x + 10x + 20 - 5.
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y + 6 < 10 or 2y - 3> 9
Answer:
2y - 3> 9 it is not y + 6< 10
(x+3) (x-2) =2x
find the valűe of x
Step-by-step explanation:
[tex](x + 3)(x - 2) = 2x\\ {x}^{2} + x - 6= 2x \\ {x}^{2} - x - 6 = 0 \\ (x - 3)(x + 2) = 0 \\ x = 3 \: or \: x = - 2[/tex]
I need done asap I have 1 min
Question 10 of 10
A minor arc will have a measure that is
O A. less than 180°
B. equal to 180°
OC. more than 180°
Answer:
Less than 180
Step-by-step explanation:
Minor: Less than 180
Major: More than 180
Trapezoid WXYZ is rotated 90 degrees clockwise around point A to create trapezoid WXYZ what must be true A angle W is half the measure of angle W B Wx is equal to WX
C WX is perpendicular to YZ D WZ is equal to WX
Answer:
B) Wx is equal to WX.
When a shape is rotated 90 degrees, the length of its sides and angles do not change. Therefore, the length of Wx in the original trapezoid will be the same as the length of WX in the rotated trapezoid.
I-Ready
What is the distance between point P and point Q?
I need help please
here is the picture is about Row Ops
The given operation of the matrix is expressed as: -9y + 2z = 12
How to use Matrix to solve simultaneous Equations?Matrices can be used to solve simultaneous linear equations, by first writing them in matrix form and then pre-multiplying by the inverse. Note firstly that these simultaneous equations can be written as the following matrix equation. If you need convincing, multiply out the matrices.
The simultaneous equations formed by the matrix are:
x + 2y + z = -5
4y - 2 = 3
4x - y + 6 = -8
We are told to Multiply row 1 by -4 and this gives us:
-4x - 8y - 4z = 20
Adding it to row 3 gives us:
-9y + 2z = 12
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The number of meters a student swam this week are listed.
200, 450, 600, 650, 700, 800
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability and equals 600.
The IQR is the best measure of variability and equals 250.
The mean is the best measure of variability and equals about 567.
The median is the best measure of variability and equals 625.
The appropriate measure of variability for the data shown and its value is A. The range is the best measure of variability and equals 600.
What is the range?The range is one of the three measures of variability.
The range shows the difference between the highest value and the lowest value in a data set.
The other measures of variability are the IQR (Interquartile Range) and the the Standard Deviation.
Range:Highest value = 800 m
Lowest value = 200 m
The range = 600 m (800 - 200)
IQR = 400 (600 - 200)
Mean = 567 (3,400 ÷ 6)
Median = 625 [(650 + 600) ÷ 2]
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Denise is designing the seating arrangement for a concert at an outdoor theater. To give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats. Explain to Denise how to create an equation to predict the number of seats in any row. Then using your equation. show your work to determine the number of seats in row 18.
Answer:113
Step-by-step Explanation:
To create an equation to predict the number of seats in any row, we need to start by defining a few variables:
Let's call the number of seats in the first row "a".
Let's call the number of additional seats in each row after the first row "d".
Since we know that each row has 6 more seats than the previous row, we can set d equal to 6:
d = 6
We also know that the first row has 11 seats, so we can set a equal to 11:
a = 11
To find the number of seats in any row, we can use the following formula:
number of seats in a given row = a + (n - 1) * d
Where "n" is the number of the row we are interested in.
Using this formula, we can find the number of seats in row 18:
number of seats in row 18 = 11 + (18 - 1) * 6
= 11 + 102
= 113
Therefore, there are 113 seats in row 18.
Guadalupe's credit card has an APR of 23%, calculated on the previous monthly balance, and a minimum payment of 2%, starting the month after the first purchase. Her credit card record for the last 7 months is shown in the table below. End of month 2 3 5 6 7 Previous balance $0.00 $900.00 $899.25 $898.50 $897.75 $897.00 $896 26 New charges $900.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 Payment Finance Principal received charges paid $0.00 $0.00 $0.00 $18.00 $17.99 $17.97 $17.96 $17.94 $17.93 How is the new balance calculated? $17.25 $17.24 $17.22 $17.21 $17.19 $17.18 $0.75 $0.75 $0.75 $0.75 $0.75 $0.75 New balance $900.00 $899.25 $898.50 $897.75 $897.00 $896.26 $895.51
Answer:$909.03
Step-by-step explanation:he new balance on Guadalupe's credit card is calculated as follows:
First, we calculate the interest charged on the previous balance. Since the APR is 23%, the monthly interest rate is 23%/12 = 1.92%. So the interest charged on the previous balance for the month is:
Interest = Previous balance x Monthly interest rate
= $900.00 x 1.92%
= $17.28
Next, we add the finance charge, which is calculated as 1% of the previous balance plus any new charges. So the finance charge for the month is:
Finance charge = 1% x (Previous balance + New charges)
= 1% x ($900.00 + $0.00)
= $9.00
The total amount due is the sum of the previous balance, the interest charged, and the finance charge:
Total amount due = Previous balance + Interest + Finance charge
= $900.00 + $17.28 + $9.00
= $926.28
The minimum payment due is 2% of the total amount due, which is:
Minimum payment = 2% x Total amount due
= 2% x $926.28
= $18.53
If the minimum payment is less than $25, the minimum payment due is $25. So in this case, the minimum payment due is $25.
Guadalupe made a payment of $18.00, which is less than the minimum payment due, so she will be charged a late fee in addition to the interest on the unpaid balance.
The principal paid is the difference between the payment made and the interest charged, which is:
Principal paid = Payment - Interest
= $18.00 - $17.28
= $0.72
The new balance is the sum of the previous balance, any new charges, and the interest charged, minus the payment made, plus any finance charge and late fee:
New balance = Previous balance + New charges + Interest - Payment + Finance charge + Late fee
= $900.00 + $0.00 + $17.28 - $18.00 + $9.00 + $0.75
Solve 4x-8 + 4 = 16.
The solutions are x =
and x =
BEYHODNA
MIGRANTA
www
www
wer
Answer:
x = 5
Step-by-step explanation:
To solve the equation 4x-8 + 4 = 16, we first combine the constants on the left-hand side:
4x-8+4 = 16
4x-4 = 16
Next, we add 4 to both sides to isolate the variable on one side:
4x-4+4 = 16+4
4x = 20
Finally, we divide both sides by 4 to solve for x:
4x/4 = 20/4
x = 5
Therefore, the solution to the equation 4x-8 + 4 = 16 is x = 5.
A store manager kept track of the number of newspaper sold each week over a seven week period.the result were as fellows 71,81,202,113,269,248,242
The median number of newspapers sold is 202 newspaper. So, correct option is C.
To find the median, we need to arrange the given data in ascending or descending order.
The given data in ascending order: 71, 81, 113, 202, 242, 248, 269
Since there are 7 data points, the median will be the fourth value in the sorted list. Therefore, the median number of newspapers sold is 202.
Hence, the correct answer is option C, which states that the median number of newspapers sold is 202.
The median is the middle value of a dataset when arranged in order, and it's a measure of central tendency that is less affected by outliers than the mean. In this case, the median value represents the value at which half the data points are below it and half are above it.
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Complete question is:
A store manager kept track of the number of newspaper sold each week over a seven week period. the result were as fellows 71,81,202,113,269,248,242
Find the median number of newspapers sold.
A. 175 newspapers
B. 113 newspapers
C. 202 newspapers
D. 242 newspapers
What is the length of the side labeled x cm?
10.8
13.7
9.9
20.8
Answer:
B
Step-by-step explanation:
the answer is B because I know it
Element X is a radi
an experiment starts out with 490 grams of Element X, write a function to represent
the mass of the sample after t years, where the monthly rate of change can be found
from a constant in the function. Round all coefficients in the function to four decimal
places. Also, determine the percentage rate of change per month, to the nearest
hundredth of a percent.
15 POINTS!! ASAP TYYY
Answer:
A
Step-by-step explanation:
She earns $15 per poinsettia.
Solve the following logarthlic equations : 3ln(2x) =12
Step-by-step explanation:
[tex]3 ln(2x) = 12[/tex]
[tex] ln(2x) = 4[/tex]
Let both sides be a power of a base e.
[tex]e {}^{ln(2x)} = e {}^{4} [/tex]
The e and ln would just cancel out so
[tex]2x = e {}^{4} [/tex]
[tex]x = \frac{ {e}^{4} }{2} [/tex]
You deposit $3000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 30 years?
The amount you will have in the account in 30 years is $22836.77
How much will you have in the account in 30 years?From the question, we have the following parameters that can be used in our computation:
You deposit $3000 each year 7% interest compounded annually.Using the above as a guide, we have the following:
Amount = P * (1 + r)^t
Where
P = Principal = 3000
r = Rate = 7%
t = time = 30
Substitute the known values in the above equation, so, we have the following representation
Amount = 3000 * (1 + 7%)^30
Evaluate
Amount = 22836.77
Hence, the amount is 22836.77
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HELPPPPPPPPP GNG IM STURGGLING 100 POINTS
Find f(-1).
Provide your answer below:
f(t)=-3t²-2t+1
Answer:
f(-1)=0
Step-by-step explanation:
To evaluate the function f(t) = -3t² - 2t + 1, we will start by plugging in -1 everywhere t occurs in the function :
[tex]\star \phantom{t-u} f(-1)=-3(-1)^2-2(-1)+1\\\\\\\star\phantom{t-u} f(-1)=-3*1+2+1\\\\\star\phantom{t-u} f(-1)=-3+3\\\\\underline{\star\phantom{t-u}f(-1)=0}[/tex]
[tex]\bigstar[/tex] Therefore the answer is f(-1) = 0
Can someone please answer these 2 questions asap and please show me the breakdown of it so I learn a better way of doing it.
Answer:
x = 5√2, x = 3√2
Step-by-step explanation:
Question 1:
Using the 30-60-90 triangle properties, YX = WX /√3.
YX = 5√3 /√3 = 5.
Using the 45-45-90 triangle properties, x = YX *√2.
x = 5 *√2 = 5√2.
Question 2:
Using the 45-45-90 triangle properties, BC = AB *√2.
BC = 6 *√2 = 6√2.
Using the 30-60-90 triangle properties, x = BC / 2.
x = 6√2 / 2 = 3√2.
Use synthetic division to rewrite the following fraction in the form q(x)+r(x)d(x)
, where d(x) is the denominator of the original fraction, q(x)is the quotient, and r(x) is the remainder.
The result of the synthetic division is:4x⁵+17x⁴+14x³-3x²+2 = (4x⁴ + 5x³ - x²) (x + 3) + 56
what is synthetic division ?
Synthetic division is a simplified method of dividing a polynomial by a linear factor. It is commonly used in algebra to find the quotient and remainder when dividing a polynomial by a linear factor of the form (x-a).
In the given question,
To use synthetic division to rewrite the fraction, we first set up the problem like this:
-3 | 4 17 14 -3 0 2
| -12 -15 3 0
+----------------------------------
4 5 -1 0 0 2
The coefficients of the polynomial are written in descending order of powers of x, with any missing terms replaced by zeros. The divisor, x + 3, is written on the left, and the first coefficient of the polynomial is written on the top of the vertical line.
We then proceed to perform synthetic division as follows:
Bring down the first coefficient, which is 4, and write it under the horizontal line.
Multiply the divisor, -3, by the number we just brought down, which gives -12. Write this number under the next coefficient, 17.
Add the two numbers, 17 and -12, to get 5. Write this number under the next coefficient, 14.
Multiply the divisor, -3, by 5, which gives -15. Write this number under the next coefficient, -3.
Add the two numbers, -3 and -15, to get -18. Write this number under the next coefficient, 0.
Multiply the divisor, -3, by -18, which gives 54. Write this number under the next coefficient, 2.
Add the two numbers, 2 and 54, to get 56. This is the remainder, which we write above the divisor.
The result of the synthetic division is:
4x⁵+17x⁴+14x³-3x²+2 = (4x^4 + 5x³ - x²) (x + 3) + 56
Therefore, we have rewritten the fraction in the desired form:
4x⁵+17x⁴+14x³-3x²+2
---------------------- = 4x⁴ + 5x³ - x² + 56/(x+3)
x+3
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14. Jill tossed a coin three times. Draw a tree diagram to represent the sample space.
Here is a tree diagram to represent the sample space of Jill tossing a coin three times:
H T
/ \ / \
H T H T
/ \ / \ / \ / \
H T H T H T H T
What is sample space?The concept of the sample space is fundamental to the calculation of probabilities because it defines the set of all possible outcomes that we are interested in measuring the likelihood of. By specifying the sample space, we can define events (subsets of the sample space) and assign probabilities to those events.
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which value of x is in the solution set of -4/3x+5<17
A. -8
B. -9
C. -12
D. -16
Please help!
Answer:
-9
Step-by-step explanation: Definitely correct
Amelia has a music box that is shaped like a right rectangular
prism. She wants to pack the music box into a container,
with 1 in. of packing material between each face of the
music box and the container. A bag contains 200 in.3 of
packing material. How many bags of packing material will
Amelia need? Show your work.
The number of packing materials the Amelia will need = 2.4
How to calculate the quantity of packing materials Amelia will need?From the diagram given above, the formula for the volume of a right rectangular prism = Length×width ×height.
Where;
Length = 10in
Width = 6 in
Height = 8 in
The volume = 10×6×8 = 480 in³
But one bag = 200in³
The amount of bag that the music box can contain = 480/200 = 2.4
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Question 6(Multiple Choice Worth 1 points)
(06.01 MC)
P
The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 5 units, and the right cylinder has a height of 5 units. Which
conclusion can be made from the given information?
O The volume of the prism is half the volume of the cylinder.
O The volume of the prism is twice the volume of the cylinder.
The volume of the prism is equal to the volume of the cylinder.
O The volume of the prism is not equal to the volume of the cylinder.
N
we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder.
How to solve the problem ?
The given information states that the cross-sectional areas of a triangular prism and a right cylinder are congruent, and both have a height of 5 units. Based on this information, we can conclude that the volumes of the two shapes may be equal, but we cannot conclude that the volume of the prism is half or twice the volume of the cylinder.
To determine the volumes of the two shapes, we need to know their respective formulas. The volume of a triangular prism is given by V = (1/2)bh, where b is the length of the base of the triangular cross-section and h is the height of the prism. The volume of a right cylinder is given by V = πr²h, where r is the radius of the circular cross-section and h is the height of the cylinder.
Since the cross-sectional areas of the two shapes are congruent, we can assume that their bases are similar. Therefore, the base of the triangular prism must be a triangle with the same area as the circular base of the cylinder. However, without further information about the shape and size of the cross-section, we cannot determine the values of b and r.
Therefore, we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder. The only conclusion that can be made is that the volume of the prism is equal to the volume of the cylinder, assuming that the cross-sectional areas are congruent.
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