The maximum height of Marsha's math book is 36 feet.
To find the maximum height of Marsha's math book, we need to find the vertex of the parabolic equation h = [tex]-16x^2 + 24x + 30[/tex]. The vertex of a parabola is the highest or lowest point on the curve, depending on whether the parabola opens upward or downward.
To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c[/tex]. In this case, a = -16 and b = 24, so we have:
x = -b/2a = -24/(2*(-16)) = 0.75
To find the y-coordinate of the vertex, we can substitute x = 0.75 into the equation h = [tex]-16x^2 + 24x + 30[/tex], which gives us:
h = [tex]-16(0.75)^2 + 24(0.75) + 30 = 36[/tex]
Therefore, the maximum height of Marsha's math book is 36 feet.
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Besides the 3 discontinuities (infinite, removable and jump) name 3 scenarios in which the derivative does not exist. Draw a sketch of the situation.
The function may still be continuous.
The lack of differentiability only implies that the function is not smooth at that point.
How to find that either the derivative exists or not?Here are three scenarios in which the derivative of a function may not exist, along with a sketch of each situation:
Corner: A function may not be differentiable at a corner, where the graph abruptly changes direction.
At a corner, the left and right-hand limits of the derivative do not match. Here is a sketch of the situation:
/
/
/
/
/
---------------/----------------
Cusp: A function may not be differentiable at a cusp, where the graph has a sharp point.
At a cusp, the left and right-hand limits of the derivative approach different values. Here is a sketch of the situation:
/
/
/
/
/
------/--------
\
\
\
\
\
Vertical tangent: A function may not be differentiable at a vertical tangent, where the graph has a vertical line tangent to the curve.
At a vertical tangent, the derivative is either infinite or undefined. Here is a sketch of the situation:
|
|
------|-------
|
|
Note that in all three of these situations, the function may still be continuous.
The lack of differentiability only implies that the function is not smooth at that point.
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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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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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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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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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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
The two-way frequency table shows the results of a survey of middle school students.
Find the probability that a randomly chosen student is a male who enjoys reading. Round
to the nearest thousandth.
Totals
Enjoys Reading
Female
Male
Enjoyment of Reading
Yes
No
40
30
15
30
55
60
70
45
Totals
115
The probability that a randomly chosen student is a male who enjoys reading P(male and enjoys reading) ≈ 0.261
To calculate the probability that a randomly chosen student is a male who enjoys reading, you need the number of males who enjoy reading divided by the total number of students.
The probability that a randomly chosen student is a male who enjoys reading can be found by dividing the number of males who enjoy reading by the total number of students.
From the table, we see that there are 30 males who enjoy reading and a total of 115 students. Therefore, the probability is:
P(male and enjoys reading) = 30/115
Rounding to the nearest thousandth, we get:
Therefore, The probability that a randomly chosen student is a male who enjoys reading P(male and enjoys reading) ≈ 0.261
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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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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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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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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
Edwin fills 15 test tubes with a solution. each test tube contains 150 milliliters of solution.
how many liters of solution in all is there in the test tubes?
2.25 l
22.5 l
225 l
2,250 l
2.25 liters of solution in all is there in the test tubes. So, the correct option is 2.25 l.
The total volume of solution in the 15 test tubes can be calculated by multiplying the volume of one test tube by the number of test tubes:
Total volume = 15 test tubes × 150 milliliters/test tube
Total volume = 2,250 milliliters
However, the question asks for the answer in liters, so we need to convert milliliters to liters by dividing by 1,000:
Total volume = 2,250 milliliters ÷ 1,000
Total volume = 2.25 liters
Therefore, there are 2.25 liters of solution in all the test tubes.
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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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Find the volume of the cone with a height and radius both of 7.
The volume of the cone with a height and radius both of 7 units is 359.24 cubic units.
How to calculate the volume of a cone?In Mathematics and Geometry, the volume of a cone can be determined by using this formula:
V = 1/3 × πr²h
Where:
V represent the volume of a cone.h represents the height.r represents the radius.By substituting the given parameters into the formula for the volume of a cone, we have the following;
Volume of cone, V = 1/3 × 3.142 × 7² × 7
Volume of cone, V = 1/3 × 3.142 × 49 × 7
Volume of cone, V = 359.24 cubic units.
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Answer:
343/3
Proof of answer is in the image, please give brainliest
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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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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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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hem t
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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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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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 arc length of CD
Answer: 15 feet
Step-by-step explanation:
Sandra Waterman purchased a 52-week, $2,800 T-bill issued by the U.S. Treasury. The purchase price was $2,791.
a. What is the amount of the discount?
b. What is the amount Ms. Waterman will receive when the T-bill matures?
c. What is the current yield for the 52-week T-bill at the time of purchase?
Note: Enter your answer as a percent rounded to 2 decimal places.
(a) Discount amount is $6. (b) Maturity value is $2,200. (c) Current yield is 0.27%.
Here, we have,
A discount is a reduction in the regular selling price of a good or service, either in terms of money or as a percentage.
A product may, for instance, be discounted by $10 from its list price or by 10% from its list price. A sales discount is a lower price that a company offers on a good or service.
Find out how to add discounts to invoices. A sales discount, usually referred to simply as a "discount," offers clients of a business a lower price on one or more of the goods or services being provided.
(a) Discount amount
= Maturity (face) value - Purchase price
=$2,200 - $2,194
=$6
(b) Maturity value
=Face value
=$2,200
(c) Current yield
=Discount amount / Purchase price
=$6 / $2,194
=0.0027, or 0.27%
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Suppose you want to represent a triangle with sides of 12 feet, 15 feet, and 18 feet on a drawing where 1 Inch - 3 feet How long should the sides of the triangle be in inches? 12 feet should be inches. 15 feet should be 18 feet should be inches.
In linear equation, The sides of the triangle on the drawing should be 6 inches, 8 inches, and 9 inches.
What in mathematics is a linear equation?
An algebraic equation B. y=mx+b (where m is the slope and b is the y-intercept) containing simple constants and first-order (linear) components, such as the following, is called a linear equation.
The above is sometimes called a "linear equation in two variables" where x and y are variables. Equations in which the variable is power 1 are called linear equations. axe+b = 0 is a one-variable example where a and b are real numbers and x is a variable.
A triangle with sides 12 feet, 16 feet, and 18 feet on a drawing where 1 inch = 2 feet.
Then, 1 feet of original triangle = 1/2 inch on drawing.
Now, the sides of the triangle on the drawing are
12 feet = 1/2 * 12 = 6 in
12 feet = 1/2 * 16 = 8 in
12 feet = 1/2 * 18 = 9 in
Hence, the sides of the triangle on the drawing should be 6 inches, 8 inches, and 9 inches..
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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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NEED ASAP
At a large university, 20% of a random sample of male students have an overall grade point
average (GPA) of 3. 5 or higher. A random sample of female student records found that
25% had a GPA of 3. 5 or higher. The president of the university wants to determine
whether there is evidence of a difference in grades between males and females. What
would she write as the null and alternative hypotheses for this situation?
The null hypothesis (H0) for this situation would be that there is no difference in the proportion of male and female students with an overall GPA of 3.5 or higher.
The alternative hypothesis (Ha) would be that there is a difference in the proportion of male and female students with an overall GPA of 3.5 or higher.
Formally, we can write the hypotheses as:
H0: p_male = p_female (where p_male represents the proportion of male students with an overall GPA of 3.5 or higher, and p_female represents the proportion of female students with an overall GPA of 3.5 or higher)
Ha: p_male ≠ p_female
The president of the university can test these hypotheses using a hypothesis test for the difference in proportions. She can calculate the test statistic using the sample proportions and sample sizes for male and female students, and then compare it to the appropriate critical value or p-value based on the desired level of significance.
If the test results provide strong evidence against the null hypothesis, she can reject it and conclude that there is a statistically significant difference in the proportion of male and female students with an overall GPA of 3.5 or higher. If the test results do not provide enough evidence to reject the null hypothesis, she can fail to reject it and conclude that there is not enough evidence to suggest a difference in grades between males and females.
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The mass of a tumor grows at a rate proportional to its size. The first measurement of its size was 4. 0 grams. Four months later its mass was 6. 76 grams. How large was the tumor six months before the first measurement? If the instrument can detect tumors of mass 1 gram or greater, would the tumor have been detected at that time?
The tumor was approximately 1.47 grams six months before the first measurement. It would not have been detected by the instrument at that time.
Let M(t) be the mass of the tumor at time t (in months) since the first measurement. Since the rate of growth is proportional to the size of the tumor, we have the differential equation dM/dt = kM, where k is the proportionality constant. The general solution to this differential equation is M(t) = Me^(kt), where M is the initial mass of the tumor.
Using the given data, we have M(0) = 4.0 and M(4) = 6.76. Substituting these values into the equation M(t) = Me^(kt), we get the system of equations M = 4.0 and 6.76 = Me^(4k). Solving for M and k, we get M = 4.0 and k = ln(6.76/4.0)/4 ≈ 0.153. Thus, the equation for the mass of the tumor is M(t) = 4.0e^(0.153t).
To find the mass of the tumor six months before the first measurement (i.e., when t = -6), we plug in t = -6 into the equation M(t) = 4.0e^(0.153t) to get M(-6) ≈ 1.47 grams.
Finally, we check whether the tumor would have been detected at that time. Since the mass of the tumor was less than 1 gram at that time, the instrument would not have detected it.
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The table shows the length, in inches, of fish in a pond.
11 19 9 15
7 13 15 28
Determine if the data contains any outliers. If so, list the outliers.
There is an outlier at 28.
There is an outlier at 7.
There are outliers at 7 and 28.
There are no outliers.
Answer:
There is an outlier at 28.
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.
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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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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