Chris must work at least 36 hours to earn a minimum of $300, assuming she sells 15 books and earns the $2 bonus for each book sold.
The inequality that represents the situation is: 7.50h + 2(15) ≥ 300 where "h" represents the number of hours Chris works, and "2(15)" represents the bonus earned for selling 15 books.
The left-hand side of the inequality calculates Chris's total earnings, which is the product of her hourly wage of $7.50 and the number of hours worked, plus the bonus earned for selling 15 books.
The inequality states that the total earnings must be greater than or equal to $300, which is the minimum amount Chris wants to earn. To solve the inequality, we can simplify it by first multiplying 2 and 15 to get 30: 7.50h + 30 ≥ 300
We can isolate "h" by subtracting 30 from both sides: 7.50h ≥ 270. we can solve for "h" by dividing both sides by 7.50: h ≥ 36.
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Steve bought 10 gallons of gas at the gas station with the highest price. how much more than cole did he pay for gas?
please help, thank you.
Steve paid $10 more than Cole for gas, regardless of the actual prices of gas at the two gas stations.
To answer this question, we need to know the prices of gas at both gas stations. Let's assume that Cole bought 10 gallons of gas at the gas station with the lowest price, and that the price difference between the two gas stations is $x per gallon.
If we denote the price per gallon of gas at the gas station where Cole bought gas as "c", then the total amount Cole paid for gas is:
10c
If we denote the price per gallon of gas at the gas station where Steve bought gas as "s", then the total amount Steve paid for gas is:
10s
The difference between the two amounts is:
10s - 10c
But we know that Steve bought gas at the gas station with the highest price, so we can assume that s = c + x.
Substituting this expression for s into the equation above, we get:
10s - 10c = 10(c + x) - 10c = 10x
So Steve paid $10 more than Cole for gas, regardless of the actual prices of gas at the two gas stations.
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Solve the system of linear equations by elimination
4x+6y=48
3x + 7y=51
To solve the system of linear equations by elimination, we need to eliminate one of the variables by multiplying one or both equations by a constant so that the coefficients of one of the variables are equal in both equations. Then, we can subtract one equation from the other to eliminate that variable and solve for the remaining variable.
In this case, we can eliminate y by multiplying the first equation by -7 and the second equation by 6, so that the coefficients of y are equal in both equations:
-28x - 42y = -336
18x + 42y = 306
Adding these two equations together, we get:
-10x = -30
Dividing both sides by -10, we get:
x = 3
Now that we have solved for x, we can substitute this value into one of the original equations to solve for y. Using the first equation, we get:
4x + 6y = 48
4(3) + 6y = 48
12 + 6y = 48
Subtracting 12 from both sides, we get:
6y = 36
Dividing both sides by 6, we get:
y = 6
Therefore, the solution to the system of linear equations is x = 3 and y = 6.
You are told that you can expect to see 6 characters during your times there! You really want to fill out your autograph book which holds 48 signatures.
The percentage of your book that can be filled during your reservation at Goofy's kitchen would be 12. 5%
How to find the percentage ?If there are 6 characters and each one signs your book once, then the total number of signatures you would be able to get are 6 signatures in total.
The calculation to determine the percentage of your book occupied involves dividing the number of signatures by its overall capacity and then multiplying that value by 100.
The percentage that would be covered is:
= 6 signatures / 48 total capacity x 100
= 12.5 %
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You decide to work fewer hours per week, which results in an 8% decrease in your pay. what percentage increase in pay would you have to receive in order to gain your original salary again?
You would have to receive an approximately 8.696% increase in pay to regain your original salary after an 8% decrease.
To find the percentage increase in pay needed to regain your original salary after an 8% decrease, follow these steps:
1. Assume your original salary is 100%. After an 8% decrease, your salary becomes 100% - 8% = 92%.
2. Calculate the difference between your original salary (100%) and your current salary (92%). The difference is 100% - 92% = 8%.
3. To find the percentage increase needed to regain your original salary, divide the difference (8%) by your current salary (92%): 8% / 92% = 0.08696.
4. Multiply the result by 100 to convert it to a percentage: 0.08696 (100) = 8.696%.
So, you would have to receive an approximately 8.696% increase in pay to regain your original salary after an 8% decrease.
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Robert, by 3/4 pound of Grace, and divided into six equal portions. What is the way of each portion
Each portion of Grace weighs 1/8 pound.
What is weight?It gauges how much gravity is pulling on a body.
If Robert has 3/4 pound of Grace and he wants to divide it into six equal portions, we can find the weight of each portion by dividing 3/4 by 6:
(3/4) / 6 = (3/4) * (1/6) = 1/8
So each portion of Grace weighs 1/8 pound.
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Town officials want to estimate the number of households that own a dog. Answer the following.
There are 300 households in the town.
Estimate how many households that own a dog
__ households
The estimated number of households that own a dog in the town is 120 households.
To estimate the number of households that own a dog in the town with 300 households, you will need to follow these steps:
1. Collect a random sample of households from the town. The sample size should be large enough to be representative of the entire population.
2. Determine the proportion of sampled households that own a dog.
3. Multiply the proportion of dog-owning households in the sample by the total number of households in the town (300).
For example, let's say you collected data from 50 households and found that 20 of them owned a dog. The proportion of dog-owning households would be 20/50 = 0.4 (40%).
To estimate the total number of households that own a dog in the town, multiply 0.4 by 300:
0.4 * 300 = 120 households
So, the estimated number of households that own a dog in the town is 120 households.
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The five smith children run to the ice cream truck. In how many orders can they be served one at a time?
Please answer the other questions if possible
There are 120 possible orders in which the five Smith children can be served one at a time.
How to calculate the number of ordersIf we assume that each child is served one at a time, then the first child can be served in 5 ways, the second child can be served in 4 ways (since one child has already been served), the third child can be served in 3 ways, the fourth child can be served in 2 ways, and the fifth child can be served in 1 way.
Therefore, the total number of orders in which the children can be served one at a time is:
5 x 4 x 3 x 2 x 1 = 120
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Cecilia found a house she likes. She needs to borrow $95,000 to buy the house. What annual income does Cecilia need to afford to borrow the money?
Required annual income does Cecilia need to afford to borrow the money is $221,395.
To determine the annual income that Cecilia needs to afford borrowing $95,000 for the house she likes, we need to consider her debt-to-income ratio (DTI).
Normally, lenders require a DTI ratio of 43% or lower which means that the total amount of debt Cecilia has (including the mortgage payment) should not exceed 43% of her gross income.
Let a DTI ratio of 43%, Cecilia's annual income should be at least $221,395 to afford borrowing $95,000 for the house.
We can calculate it by multiplying the amount of the loan by 100 and dividing by the DTI ratio: $95,000 x 100 / 43 = $221,395
Hence, required annual income does Cecilia need to afford to borrow the money is $221,395.
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With all the responses in, Jayda found the Mean Absolute Deviation (MAD), rounded to the nearest tenth. Select the correct Mean Absolute Deviation and what it tells you about the data set.
The numbers 0, 1, 3, 10, 12, 12, 15, 17, 18, 22, 66
From the given data set, the mean absolute deviation is 10.72
What is the mean absolute deviationTo determine the mean absolute deviation of the data set, we need to find the mean first.
mean = (0 + 1 + 3 + 10 + 12 + 12 + 15 + 17 + 18 + 22 + 66) / 11
mean = 16
Now, let's calculate the mean absolute deviation
|0 - 16| = 16
|1 - 16| = 15
|3 - 16| = 13
|10 - 16| = 6
|12 - 16| = 4
|12 - 16| = 4
|15 - 16| = 1
|17 - 16| = 1
|18 - 16| = 2
|22 - 16| = 6
|66 - 16| = 50
MAD = (16 + 15 + 13 + 6 + 4 + 4 + 1 + 1 + 2 + 6 + 50) / 11
MAD = 10.72
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Jones Corporation has the following budgeted sales for the selected four-month period: Month Unit Sales July 20,000 August 35,000 September 25,000 October 30,000 Sales price per unit is $180 Plans are to have an inventory of finished product equal to 20 percent of the unit sales for the next month. There were 4,000 units in beginning inventory on July 1. Three pounds of materials are required for each unit produced. Each pound of material costs $20. Inventory levels for materials equal 30 percent of the needs for the next month. Desired ending inventory for September is 25,200 pounds of material. Beginning inventory for July was 20,700 pounds of material. Each unit requires 0. 6 hours of direct labor and the average wage rate is $16 per hour. Variable overhead rate is $3. 50 per direct labor hour. There is also fixed overhead of $22,000 per month. The company pays a 3% commission on sales. The Company has fixed selling and administrative expenses as follows: Rent $6,000/month Utilities $1,200/month Advertising $400/month Office Salaries $35,000/month Required: If required, round your answers to two decimal places. A. Prepare a sales budget for July, August, and September and in total for the quarter. Jones Corporation Sales Budget July August September Total Units to be sold fill in the blank 6165fff8cfc9fd8_1 fill in the blank 6165fff8cfc9fd8_2 fill in the blank 6165fff8cfc9fd8_3 fill in the blank 6165fff8cfc9fd8_4 Sales price $fill in the blank 6165fff8cfc9fd8_5 $fill in the blank 6165fff8cfc9fd8_6 $fill in the blank 6165fff8cfc9fd8_7 $fill in the blank 6165fff8cfc9fd8_8 Total sales dollars $fill in the blank 6165fff8cfc9fd8_9 $fill in the blank 6165fff8cfc9fd8_10 $fill in the blank 6165fff8cfc9fd8_11 $fill in the blank 6165fff8cfc9fd8_12 B. Prepare a production budget for July, August, and September and in total for the quarter. Jones Corporation Production Budget July August September Total Sales fill in the blank e6b46cf35019f97_1 fill in the blank e6b46cf35019f97_2 fill in the blank e6b46cf35019f97
Answer:
Step-by-step explanation:
A. Sales Budget:
To prepare the sales budget, we need to multiply the unit sales by the sales price per unit for each month. The sales budget for July, August, September, and the total quarter is as follows:
Jones Corporation Sales Budget
Month Unit Sales Sales price Total sales dollars
July 20,000 $180 $3,600,000
August 35,000 $180 $6,300,000
Sept 25,000 $180 $4,500,000
Total 80,000 $180 $14,400,000
B. Production Budget:
To prepare the production budget, we need to calculate the number of units to be produced each month to meet the sales demand and maintain the desired ending inventory level. The production budget for July, August, September, and the total quarter is as follows:
Jones Corporation Production Budget
Month Unit Sales Add: Desired Ending Inventory Total Units Needed Less: Beginning Inventory Units to be Produced
July 20,000 4,000 24,000 - 24,000
August 35,000 5,000 40,250 20,000 20,250
Sept 25,000 7,000 28,750 15,250 13,500
Total 80,000 16,000 93,000 35,250 57,750
Note: The desired ending inventory for finished goods for each month is calculated as 20% of the unit sales for the next month. For materials, the desired ending inventory for September is given as 25,200 pounds.
Therefore, we can calculate the total materials needed for September and subtract the desired ending inventory to find the materials to be purchased for September.
The production budget takes into account the inventory levels for both finished goods and materials.
We can now calculate the total direct materials needed, direct labor hours needed, and total manufacturing overhead costs for the quarter.
C. Direct Materials Budget:
To prepare the direct materials budget, we need to calculate the total materials needed for production and deduct the beginning inventory and desired ending inventory levels to determine the materials to be purchased each month.
The direct materials budget for July, August, September, and the total quarter is as follows:
Jones Corporation Direct Materials Budget
Month Units to be Produced Materials required per unit Total Materials Needed Add: Desired Ending Inventory Total Materials Required Less: Beginning Inventory Materials to be Purchased
July 24,000 3 72,000 - 72,000 20,700 51,300
August 20,250 3 60,750 7,500 68,250 51,300 16,950
Sept 13,500 3 40,500 25,200 65,700 36,300 29,400
Total
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he figure below is a net for a rectangular prism. Side a = 62 centimeters, side b = 21 centimeters, and side c = 16 centimeters. What is the surface area of this figure?
The surface area of the rectangular prism is 4960 cm².
The rectangular prism can be divided into six rectangular faces, with opposite faces having the same area. To find the surface area, we need to calculate the area of each face and add them up.
The net shows three rectangles with dimensions of 62 cm x 21 cm, 62 cm x 16 cm, and 21 cm x 16 cm.
Therefore, the surface area of the rectangular prism is:
Area of the first rectangle = 62 cm x 21 cm = 1302 cm²
Area of the second rectangle = 62 cm x 16 cm = 992 cm²
Area of the third rectangle = 21 cm x 16 cm = 336 cm²
Total surface area = 2(Area of first rectangle) + 2(Area of second rectangle) + 2(Area of third rectangle)
= 2(1302) + 2(992) + 2(336)
= 2604 + 1984 + 672
= 4960 cm²
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Select all the expressions that are equivalent to –25 (fraction 2 over 5)
(15 – 20d).
The equivalent expressions are,
A. [tex]-30 + 40d - 10c[/tex],
B. [tex]-6 + 8d - 2c[/tex]
D. [tex]6 - 8d + 2c[/tex].
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, [tex]2x+3[/tex]
The given expression.
[tex]\implies -25(15 - 20d + 5c)[/tex]
[tex]\implies -125(3 - 4d + c)[/tex]
So, the given expression can be converted into
[tex]k(3 - 4d + c)[/tex]
The equivalent expressions are:
A. [tex]-30 + 40d - 10c[/tex],
B. [tex]-6 + 8d - 2c[/tex]
D. [tex]6 - 8d + 2c[/tex].
A. [tex]-30 + 40d - 10c[/tex]
[tex]\implies -30 + 40d - 10c[/tex]
[tex]\implies -10(3 - 4d + c)[/tex]
B. [tex]-6 + 8d - 2c[/tex]
[tex]\implies -6 + 8d - 2c[/tex]
[tex]\implies -2(3 - 4d + c)[/tex]
D. [tex]6 - 8d + 2c[/tex]
[tex]\implies6 - 8d + 2c[/tex]
[tex]\implies2(3 - 4d + c)[/tex]
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Tina collects cans to recycle at the supermarket. Last week, on
Wednesday and Thursday, she collected 37 cans each day. On Tuesday, Friday,
Saturday, and Sunday, she collected 43 cans each day. Tina gets 5 cents for every can
she recycles.
а
How much money did Tina get for her cans last week?
Tina received $12.30 for recycling her cans last week.
How to calculate the money Tina get ?To find how much money Tina got for her cans last week, we need to find the total number of cans she collected and then multiply that by 0.05 (since she gets 5 cents per can).
On Wednesday and Thursday, Tina collected 37 cans each day, for a total of 2 x 37 = 74 cans.
On Tuesday, Friday, Saturday, and Sunday, she collected 43 cans each day, for a total of 4 x 43 = 172 cans.
The total number of cans collected is 74 + 172 = 246 cans.
To find the total amount of money Tina received, we multiply 246 by 0.05, which gives us:
246 x 0.05 = $12.30
Therefore, Tina received $12.30 for recycling her cans last week.
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2. 7.G.1.2 Can a quadrilateral be drawn that meets the conditions described below? Select Yes or No by placing a check or X in the appropriate box. Conditions Two pairs of parallel sides and at least two right angles One pair of parallel sides and no right angles One pair of parallel sides and three right angles No parallel sides and four right angles Yes No
The complete conditions are
Two pairs of parallel sides and at least two right angles : YesOne pair of parallel sides and no right angles :YesOthers are NoChecking if a quadrilateral can be drawn from the conditionsBy definition a quadrilateral is a shape that has four sides and four angles
Next, we test the conditions
Two pairs of parallel sides and at least two right angles
This is true because quadrilaterals like rectangles and squares have two pair of parallel sides and right angles
One pair of parallel sides and no right angles
This is also true because quadrilaterals like trapezoid have one pair of parallel sides and may or may not have right angle
One pair of parallel sides and three right angles
This is false because a quadrilateral cannot be drawn with this condition
No parallel sides and four right angles
This is false because a quadrilateral cannot be drawn with this condition
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Mike is shopping for new clothes. He has a coupon for 20% off of his total purchase. His purchase price before the discount is $68. Let T represent the total cost after the discount. Which equation can be written to model this scenario? Select ALL that apply. 68 – 0. 2(68) = T
A 68 – 0. 2 = T
B 68 – 20 = T
C 0. 2(68) = T
D 0. 8(68) = T
68 – 0. 2 = T and 0. 2(68) = T equation can be written to model this scenario. The correct options are A and C.
The equation 68 – 0.2(68) = T is correct since it represents the total cost after the 20% discount is applied.
The equation 68 – 0.2 = T is not correct since it does not correctly calculate the total cost after the discount.
The equation 68 – 20 = T is not correct since it subtracts the discount amount from the original price, which would give the discounted price before the discount, not the total cost after the discount.
The equation 0.8(68) = T is not correct since it calculates the discounted price, not the total cost after the discount.
Therefore the correct options are a and c.
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What is the distance between (-9, -6)(−9,−6)left parenthesis, minus, 9, comma, minus, 6, right parenthesis and (-2, -2)(−2,−2)left parenthesis, minus, 2, comma, minus, 2, right parenthesis
Answer: The answer to your question is the square root of 65
Sonia has a hat collection. The ratio of white hats to
blue hats in her hat collection is 10:9. Which ratio is
equivalent to 10:97
The equivalent ratio is 10:107.78
To solve this problem, we need to find a ratio that is equivalent to 10:9 but has a denominator of 97.
First, we can set up a proportion:
10/9 = x/97
To solve for x, we can cross-multiply:
10 * 97 = 9 * x
970 = 9x
To find the value of x, you divided both sides of the equation by 9, resulting in:
x = 107.78 (rounded to two decimal places)
So the equivalent ratio is 10:107.78, but since we can't have a fractional hat, we can round up to 108. Therefore, the answer is 10:108.
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I. Suppose you a business owner and sell clothing. The following represents the number of items sold and the cost for each item: Use matrix operations to determine the total revenue over the two days:
Monday: 3 T-shirts at GH¢10 each, 4 hats at GH¢15 each, and 1 pair of shorts at GH¢20.
Tuesday: 4 T-shirts at GH¢10 each, 2 hats at GH¢15 each, and 3 pairs of shorts at GH¢20.
The total revenue over the two days is GH¢305.
We can represent the number of items sold and the cost for each item in matrices as follows:
[tex]\begin{equation}A = \begin{bmatrix} 3 & 4 & 1 \ 4 & 2 & 3 \end{bmatrix}, \quad B = \begin{bmatrix} 10 \ 15 \ 20 \end{bmatrix}\end{equation}[/tex]
Here, matrix A represents the number of items sold on each day, and matrix B represents the cost per item. To find the total revenue, we need to multiply the two matrices and then take the sum of all the elements in the resulting matrix:
[tex]\begin{equation}A \cdot B = \begin{bmatrix} 3 & 4 & 1 \ 4 & 2 & 3 \end{bmatrix} \cdot \begin{bmatrix} 10 \ 15 \ 20 \end{bmatrix} = \begin{bmatrix} 95 \ 140 \end{bmatrix}\end{equation}[/tex]
Therefore, the total revenue over the two days is GH¢(95 + 140) = GH¢305.
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Find the surface area of this cone please help
The calculated value of the surface area of the cone is 36π
From the question, we have the following parameters that can be used in our computation:
Radius, r = 4 meters
Slant height, l = 5 meters
using the above as a guide, we have the following:
SA = πr(r + l)
Substitute the known values in the above equation, so, we have the following representation
SA = π * 4 * (4 + 5)
Evaluate
SA = 36π
Hence, the surface area of the cone is 36π
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consider the following 8 numbers, where one labelled x is unknown. 26 , 7 , 17 , x , 21 , 6 , 34 , 27 given that the range of the numbers is 63, work out 2 values of x .
The two possible values of x are -29 and 69.
To find two possible values for x, we need to use the fact that the range of
the numbers is 63.
The range is defined as the difference between the largest and smallest
numbers in the set.
First, we can find the largest and smallest numbers in the set:
Smallest number = 6
Largest number = 34
Next, we can set up two equations to represent the range of the numbers,
using the two possible scenarios for x:
Scenario 1:
If x is the smallest number in the set, then the range is equal to [tex]34 - x.[/tex]
Scenario 2: If x is the largest number in the set, then the range is equal to
[tex]x - 6[/tex].
We can then set up two equations and solve for x in each scenario:
Scenario 1:
[tex]34 - x = 63x = 34 - 63x = -29[/tex]
Scenario 2:
[tex]x - 6 = 63x = 63 + 6x = 69[/tex]
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(2) 44% of the students in Prof. Young's class are Liberal Arts major, 64% major in Business Administration, and 39% major in both. Compute the probability that a student selected at random in Prof. Young's class major in Liberal Arts or Business Administration.
The probability that a student selected at random from the class majors in Liberal Arts or Business Administration is 0.69 or 69%.
Let us say that the event that a student is a Liberal Arts major is 'LA' and the event that a student is a Business Administration major is 'BA'.
Now according to the question, we know that 44% of students are Liberal Arts majors, 64% of students are Business Administration majors,
and 39% of students are majoring in both.
With this information, we can say that:
P(LA) = 44% = 0.44
P(BA) = 64% = 0.64
• P(LAN BA) = 39% = 0.39
Now in order to find the probability that a student
is selected at random majors in either Liberal Arts
or Business Administration, we need to compute the value of P(LA U BA), which is the probability of either of the event happening.
The formula for the probability of the union of two events can be used to find the union that is: PILA U BA) = P(LA)+P(BA)-PILAN BA)
Now by substituting the values in the above equation, we get:
P(LA U BA) = 0.44 + 0.64 -0.39
P(LA U BA) = 0.69
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The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.
The unique equation of the given parabola in the form of f(x) = (x - a)(x - b) is given by, f(x) = x(x + 6).
The y intercept of the parabola is at (0,0).
Zeros of the parabola are at x = 0, -6.
Given the model equation for the parabola is f(x) = (x - a)(x - b)
It is the standard equation of a parabola with zeros x = a, b.
Here from the graph we can see that at x = -6, 0 the value of y reaches 0 that is the parabola has zeros at x = 0, -6.
So, a = 0 and b = -6
So, f(x) = (x - 0)(x - (-6))
f(x) = x(x + 6)
From the graph we can also see that the parabola is downward negative Y axis.
At y intercepts x = 0
So, the equation becomes in that case,
f(x) = 0.
So (0, 0) is the only y intercept of the parabola.
Hence, the equation of the unique parabola is, f(x) = x(x + 6) and Y intercept is at (0, 0) and zeros are at x = 0, -6.
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The question is incomplete. The complete question will be -
"The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros."
Which type of bankruptcy will affect a person's credit score for seven years?
chapter 7
chapter 9
chapter 11
chapter 9
The type of bankruptcy that typically affects a person's credit score for seven years is Chapter 7 bankruptcy.
Chapter 7 bankruptcy involves the liquidation of assets to pay off debts, and it remains on a person's credit report for up to seven years from the filing date. This can have a significant negative impact on a person's credit score and their ability to obtain credit in the future.
Chapter 9 bankruptcy is specifically designed for municipalities such as cities, towns, and counties, and it does not apply to individuals or affect personal credit scores.
Chapter 11 bankruptcy is primarily used by businesses to reorganize their debts and continue operating. While it can affect a business owner's personal credit if they have personal liability for the business debts, it does not have a specific time frame for how long it remains on a credit report. The impact on an individual's credit score can vary depending on the circumstances and how the bankruptcy is structured.
Hence the answer is Chapter 7.
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Answer:
Chapter 13
Step-by-step explanation:
it’s not on there but that’s the answer
8-70. Assume Figure A and Figure B, at right, are similar. Homework Help
a. If the ratio of similarity is (3)/(4), then what is the ratio of the perimeters of Figures A and B ?
b. If the perimeter of Figure A is p and the linear scale factor is r, what is the perimeter of Figure B?
c. If the area of Figure A is a and the linear scale factor is r, what is the area of Figure B?
a. The ratio of the perimeters of Figures A and B will also be (3)÷(4).
b. This is because the corresponding sides of Figure B are (3÷4) is smaller than those of Figure A, and the perimeter is the sum of all the sides.
c. The area of Figure B will be (9÷16)a.
What is perimeter ?Perimeter refers to the total length of the boundary or the outer edge of a two-dimensional closed shape. It is the sum of the lengths of all sides of the shape.
a. Since the ratio of similarity is (3)÷(4), this means that the corresponding sides of Figure A and Figure B are in the ratio of (3)÷(4). Therefore, the ratio of the perimeters of Figures A and B will also be (3)÷(4).
b. If the perimeter of Figure A is p and the linear scale factor is r, then the perimeter of Figure B will be (3÷4)p. This is because the corresponding sides of Figure B are (3÷4) is smaller than those of Figure A, and the perimeter is the sum of all the sides.
c. If the area of Figure A is a and the linear scale factor is r, then the area of Figure B will be (3÷4) square times smaller than that of Figure A. This is because the area of a similar figure proportional to the square of the linear scale factor.
Therefore, the area of Figure B will be (9÷16)a.
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Use the box method to distribute and simplify (-2x-6)(-4x - 1). Drag and
drop the terms to the correct locations of the table.
(-2x-6) (-4x-1)
Answer:69x-44
Step-by-step explanation:
69-44=67
Rectangle abcd was dilated to create rectangle a’b’c’d’. the area of rectangle abcd is 16in^2 and the area of the rectangle a’b’c’d’ is 64in^2. which scale factor was used to dilate the rectangle?
help asap please!!!!!
If the area of rectangle abcd is 16in² and the area of the rectangle a’b’c’d’ is 64in², the scale factor used to dilate the rectangle was 2.
When a rectangle is dilated, its dimensions are multiplied by a common factor known as the scale factor. The scale factor is the ratio of the corresponding sides of the original rectangle and the dilated rectangle.
Let the scale factor be represented by k. The area of the original rectangle is 16 in², so we can write:
length x width = 16
Let L and W represent the length and width of the original rectangle, respectively. Therefore, we have:
LW = 16
After dilation, the area of the new rectangle is 64 in². The length and width of the new rectangle are kL and kW, respectively. Therefore, we can write:
(kL)(kW) = 64
Simplifying the above equation, we get:
k²LW = 64
Substituting the value of LW from the first equation, we get:
k²(16) = 64
Solving for k, we get:
k = √4 = 2
This means that the length and width of the new rectangle are twice the length and width of the original rectangle.
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Find the distance in between the point P( - 4, 2, 1) and the point Q(-1,2,0).
The distance between the points P(-4, 2, 1) and Q(-1, 2, 0) is [tex]\sqrt{(10)}[/tex] units.
The distance formula is derived from the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs (the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
In three-dimensional space, we have to use a variation of the Pythagorean theorem that involves finding the distance between the two points in each of the three dimensions (x, y, and z) and then adding up the squares of those distances, before taking the square root of the sum.
To find the distance between two points P(x1, y1, z1) and Q(x2, y2, z2) in three-dimensional space, we use the distance formula:
d = [tex]\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2)}[/tex]
Using the given points P(-4, 2, 1) and Q(-1, 2, 0), we have:
d = [tex]\sqrt{((-1 - (-4))^2 + (2 - 2)^2 + (0 - 1)^2)}[/tex]
= [tex]\sqrt{(3^2 + 0^2 + (-1)^2)}[/tex]
= [tex]\sqrt{(10)}[/tex]
Therefore, the distance between the points P(-4, 2, 1) and Q(-1, 2, 0) is sqrt(10) units.
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Q4.
Mr Jones has two sizes of square paving stones.
He uses them to make a path.
3.72m
large
1.55m
small
ASKED
The path measures 1.55 metres by 3.72 metres.
Calculate the width of a small paving stone.
The width of a small paving stone is 0.62 m or 62 cm
Length of path = 4 sides of a large paving stone = 3.72 m
Width of large paving stone: 3.72 m ÷ 4 = 0.93 m
Width of small paving stone: 1.55 m − 0.93 m = 0.62 m
or: Length of path = 6 sides of a small paving stone = 3.72 m
Width of small paving stone: 3.72 m ÷ 6 = 0.62 m
or: Let the width of the small paving stone be x and the width
of the large paving stone be y.
Then in cm: x + y = 155 cm,
and 2x + 3y = 372 cm
We can see from the diagram that y = 372 cm – 2 × (x + y)
so y = 372 cm − 2 × 155 cm = 372 cm – 310 cm = 62 cm
Therefore, the width of a small paving stone is 0.62 m or 62 cm.
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Use the given terms to generate a recursive rule. Sequence:13,15,23,55,183
To generate a recursive rule for the sequence 13, 15, 23, 55, 183, we need to identify the pattern in the sequence.
Looking at the differences between each term, we can see that:
15 - 13 = 2
23 - 15 = 8
55 - 23 = 32
183 - 55 = 128
So the differences are increasing by a factor of 4 each time.
Using this pattern, we can create a recursive rule:
a(1) = 13
a(n) = a(n-1) + 4^(n-2)
So for example,
a(2) = a(1) + 4^(2-2) = 13 + 1 = 14
a(3) = a(2) + 4^(3-2) = 14 + 4 = 18
a(4) = a(3) + 4^(4-2) = 18 + 16 = 34
a(5) = a(4) + 4^(5-2) = 34 + 64 = 98
a(6) = a(5) + 4^(6-2) = 98 + 256 = 354
And so on.
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Cameron and Lindsey need to make 160 cookies for the bake sale. Cameron made 2/5 of the cookies Lindsey made 16 cookies What fraction of the cookies do they still need to make?
The fraction of the cookies do they still need to made after Cameron and Lindsey made 80 cookies is 1/2.
Fractions are referred to as the components of a whole in mathematics. A single thing or a collection of objects might be the entire. When we cut a slice of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Roman. "Fractus" means "broken" in Latin.
The fraction was expressed verbally in earlier times. It was afterwards presented in numerical form. A piece or sector of any quantity is another name for the fraction.
Total cookies to be made is 160
Out of which Cameron made 2/5 of the cookies so,
2/5 x 160 = 64 cookies are made by Cameron
Lindsey made 16 cookies
So total cookies that still need to be made is,
= 160 - (64 + 16) = 80
The fraction of cookies still need to made is 80/160 = 1/2 .
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