The scaled dimensions of a kitchen with dimensions 6.3m by 4.8m, if the kitchen plan is drawn to a scale of 1:500, are given as follows:
1.26 cm and 0.96 cm.
How to obtain the scaled dimensions?The scaled dimensions are obtained applying the proportions in the context of the problem.
The scale is of 1:500, meaning that each dimension is divided by 500, as follows:
6.3 m: 6.3/500 = 0.0126 m = 1.26 cm.4.8 m: 4.8/500 = 0.0096 m = 0.96 cm.More can be learned about proportions at https://brainly.com/question/24372153
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"The scores X on a pretest for a college statistics course and the course grade Y were recorded for 10 students. The results are as follows: X ---- 75,81, 57, 79, 68, 93, 96, 84, 41, 89 Y ----- 2, 3, 1, 2, 1, 4, 4, 3, 1, 3 What might you conclude?"
A. There is absolutely no correlation between the scores and grades
given.
B. There is a very weak correlation between the scores and grades given.
C. There is a moderate correlation between the scores and grades.
D. There is a strong correlation between the scores and grades.
Answer:
Step-by-step explanation:
C. There is a moderate correlation between the scores and grades.
Based on the scatter plot and the calculated correlation coefficient, we can conclude that there is a moderate positive correlation between the pretest scores and the course grades. This means that as the pretest scores increase, the course grades tend to increase as well. However, the correlation is not extremely strong, so other factors may be affecting the course grades besides the pretest scores.
The correlation between two variables describes the relationship between them. The strength of the correlation can be classified into four categories: no correlation, weak correlation, moderate correlation, and strong correlation.
In this case, since the values of X and Y appear to have a moderate association, it might be concluded that there is a moderate correlation between the scores on the pretest and the course grade.
However, correlation does not imply causality, meaning that even if there is a correlation between two variables, it does not mean that one variable causes the other. Further analysis, such as regression analysis, is needed to determine the strength and direction of the relationship and to determine if there is a causal relationship.
Find the x - and y -components of the vector a⃗ = (11 m/s2 , 36 ∘ left of −y -axis).
Express your answer in meters per second squared. Enter the x and y components of the vector separated by a comma.
The x- and y-components of the vector [tex]\mathbf{\hat a}}[/tex] are 8.9 m/s² and -6.4 m/s², respectively.
What is components?In mathematics, components are the parts or elements that make up a larger structure or object. In the context of vectors, components refer to the parts of a vector that describe its direction and magnitude in a particular coordinate system.
To find the x-components and y-components of the vector [tex]\mathbf{\hat a}}[/tex] = (11 m/s², 36 degrees left of -y-axis), we need to determine the direction of the vector. The notation "left of -y-axis" means that the vector makes an angle of 36 degrees with the negative y-axis, as measured counterclockwise from the negative y-axis.
The magnitude (or length) of the vector is given by the first component, which is 11 m/s².
The x-component of the vector can be found by multiplying the magnitude by the cosine of the angle:
x-component = magnitude x cos(angle) = 11 m/s² x cos(36°) = 8.9 m/s²
The y-component of the vector can be found by multiplying the magnitude by the sine of the angle:
y-component = magnitude x sin(angle) = 11 m/s² x sin(36°) = -6.4 m/s²
The negative sign indicates that the y-component is in the opposite direction of the negative y-axis.
Therefore, the x- and y-components of the vector [tex]\mathbf{\hat a}}[/tex] are 8.9 m/s² and -6.4 m/s², respectively.
Expressed as an ordered pair, the components are (8.9 m/s², -6.4 m/s²).
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I will give brainliest and ratings if you get this correct
The derivative formula for the division of two functions is equal to d [θ(x)] / dx = [g(x) · f'(x) - f(x) · g'(x)] / [g(x)]², where θ(x) = f(x) / g(x).
How to proof the derivative of the division of two function
In this problem we need to derive the formula for the derivative of the division of two functions, that is, the expression θ(x) = f(x) / g(x). First, we write the definition of the derivative for the given expression:
[tex]\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{\theta(x + h) - \theta (x)}{h}[/tex]
Second, substitute and expand the expression by algebra properties:
[tex]\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{\frac{f(x + h)}{g(x + h)} - \frac{f(x)}{g(x)} }{h}[/tex]
[tex]\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} \frac{f(x + h) \cdot g(x) - f(x) \cdot g(x + h)}{h\cdot g(x + h)\cdot g(x)}[/tex]
Third, expand and simplify the expression one more time by algebra properties and limit properties:
[tex]\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{f(x + h) \cdot g(x) - f(x) \cdot g(x) + g(x) \cdot f(x) -f(x) \cdot g(x + h)}{h \cdot g(x + h) \cdot g(x)}[/tex]
[tex]\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} g(x) \cdot \frac{f(x + h) - f(x)}{h\cdot g(x+h)\cdot g(x)} - \lim_{h \to 0} f(x) \cdot \frac{g(x + h) - g(x)}{h\cdot g(x+h)\cdot g(x)}[/tex]
[tex]\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} \frac{g(x)}{g(x + h) \cdot g(x)} \cdot \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} - \lim_{h \to 0} \frac{f(x)}{g(x+ h) \cdot g(x)} \cdot \lim_{h \to 0} \cdot \frac{g(x + h) - g(x)}{h}[/tex]
Fourth, simplify the resulting expression by evaluating the limits:
d [θ(x)] / dx = [g(x) / [g(x)]²] · f'(x) - [f(x) / [g(x)]²] · g'(x)
d [θ(x)] / dx = [g(x) · f'(x) - f(x) · g'(x)] / [g(x)]²
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Suppose that the world's current oil reserves is R = 2090 billion barrels. If, on average, the total reserves is decreasing by 18 billion barrels of oil each year, answer the following: A.) Give a linear equation for the total remaining oil reserves, R , in terms of t , the number of years since now. (Be sure to use the correct variable and Preview before you submit.) R = B.) 15 years from now, the total oil reserves will be billions of barrels. C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all used up) approximately years from now. (Round your answer to two decimal places.)
a) A linear equation for the total remaining oil reserves, R, in terms of t, the number of years since the current year, is 2,090 - 18t.
b) Based on the above linear equation, 15 years from now, the total oil reserves will be 1,820 billion barrels.
c) Using division operation, the world's oil reserves will be completely depleted approximately 116 years from now.
What is a linear equation?A linear equation is a mathematical or algebraic equation written in the form of y = mx + b.
A linear equation consists of a constant and a first-order term, where m is the slope, and variable b, the y-intercept.
The current total world oil reserves, R = 2,090 billion barrels
Average decrease per year = 18 billion barrels
a) Linear equation for R is 2,090 - 18t
b) In 15 years, the total oil reserves = 2,090 - 18(15)
= 2,090 - 270
= 1,820
c) The constant rate of decrease = 18 billion barrels per year
The world's oil reserves will be completely depleted approximately 116 years from now (2,090/18).
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A school newspaper reporter decides to randomly survey 13 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 23% of students attend Tet festivities. We are interested in the number of students who will attend the festivities. Part (a) Part (b) List the values that X may take on. O X =0, 1, 2..... 23 x = 1, 2, 3....23 x = 1, 2, 3....13 OX0.1.2..... 13 OO Part (c) Give the distribution of X. X-OX (0:0) Part (d) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.) student(s) O Part (e) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.) Part (0) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)
The probability that more than 2 students will attend is 0.9179.
Part (a) List the values that X may take on.
X may take on the values 0, 1, 2, 3, ..., 13.
Part (b) Give the distribution of X.
The distribution of X can be represented as follows: X-0:0, 1:0.23, 2:0.23, 3:0.23, 4:0.23, 5:0.23, 6:0.23, 7:0.23, 8:0.23, 9:0.23, 10:0.23, 11:0.23, 12:0.23, 13:0.23
Part (c) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)
We can expect 3 students to attend the festivities.
Part (d) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)
The probability that at most 3 students will attend is 0.6923.
Part (e) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)
The probability that more than 2 students will attend is 0.9179.
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Using The Distance Formula: What is the length of AB
With A(3,4) and B(-4,6)
A'B' = D2/3 (AB)
Wilson Montgomery was curious about the difference between a simple discount note and a simple interest note. He is considering taking out one or the other. Let him know which one he should take out based on proceeds and effective rate. Both have the same terms: $5,500 at 6% for 18 months. Round to the nearest tenth.
What is the answer to this question?
Based on the proceeds and effective rate, Wilson should take out the simple discount note, which has a higher proceeds of $5,005 and a higher effective rate of 9.9% compared to the simple interest note's proceeds of $5,995 and effective rate of 9.0%.
How to take out based on proceeds and effective rate?To compare the simple discount note and the simple interest note, we can calculate the proceeds and effective rates for each.
For the simple discount note, the interest is deducted upfront and the borrower receives the difference, or the proceeds. The interest on a $5,500 note at 6% for 18 months can be calculated as:
Interest = Principal × Rate × Time
Interest = $5,500 × 6% × 1.5 years
Interest = $495
The proceeds for the simple discount note can be calculated as:
Proceeds = Principal - Interest
Proceeds = $5,500 - $495
Proceeds = $5,005
The effective rate for the simple discount note can be calculated using the formula:
Effective Rate = Interest / Proceeds × 100%
Effective Rate = $495 / $5,005 × 100%
Effective Rate = 9.9%
For the simple interest note, the interest is calculated on the principal amount and added to the principal at the end of the term. The interest on a $5,500 note at 6% for 18 months can be calculated as:
Interest = Principal × Rate × Time
Interest = $5,500 × 6% × 1.5 years
Interest = $495
The total amount due at the end of the term for the simple interest note can be calculated as:
Total Due = Principal + Interest
Total Due = $5,500 + $495
Total Due = $5,995
The effective rate for the simple interest note can be calculated using the formula:
Effective Rate = Interest / Principal × 100%
Effective Rate = $495 / $5,500 × 100%
Effective Rate = 9.0%
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Please help me with this question :(
1. The amount of pizzas which the pizzeria must sell for employees to receive the bonus is 78.
2. The new number of pizzas sold is considered as percent increase of 20%.
How many pizzas must the pizzeria sell for employees to receive the bonus?The pizzeria sold 65 pizzas yesterday and the owner offers bonus if the number sold increases by 20% today. The number that must be sold, to receive a bonus is computed as follows:
= 65 pizza * (65 pizza * 20%)
= 65 pizza * 13 pizza
= 78 pizza.
Is the number of pizzas sold as a percent increase or decrease?It is a percent increase which is computed as follows. The formula for percentage increase is: ((Final value - Initial value)/Initial value * 100).
The Percent increase:
= (78 pizza - 65 pizza) / 65 pizza.
= 13 pizza / 65 pizza
= 0.2
= 20%
Full question "A local pizzeria sold 65 pizzas yesterday. (step 1) The owner offers the employees a bonus if the number of pizzas sold increases by 20% today. How many pizzas must the pizzeria sell for employees to receive the bonus? Explain your reasoning. (Part 2) Suppose the actual number of pizzas sold today was 60. Describe the number of pizzas sold as a percent increase or decrease, rounded to the nearest hundredth. Show your work. Answer:"
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Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where
P(-3, 3, 2), Q(-1, 6, 5), R(-4, 2, 1), S(3, 1, 4).
The volume of the parallelopiped is 4
How to solve for the volumeWe have to solve this with the use of matrix system in math
PQ, PR, PS where
P(-3, 3, 2), Q(-1, 6, 5), R(-4, 2, 1), S(3, 1, 4)
we have to find
Q - P
(-1, 6, 5) - (-3, 3, 2)
= (2, 3, 3)
R - P
R(-4, 2, 1) - (-3, 3, 2)
= ( -1 , -1, -1)
S - P
S(3, 1, 4) - (-3, 3, 2)
= (6 , -2, 2)
we would have [tex]\left[\begin{array}{ccc}2&3&3\\-1&-1&-1\\6&-2&2\end{array}\right][/tex]
the determinant of the matrix is the volume
2[(-1 * 2) - 3[(-1x2)-(6x-1)] + 3[(-1x-2) -(6 x -1)]
= -8 - 12 + 24
= 4
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Augustus is generally selfish and somewhat unpopular at school. He decides that
he could improve his image by sharing his candy with everyone at school. When he
has a pile of 100,000 candies, he generously plans to give away 60% of the candies
that are in the pile each day. Although Augustus may be earning more candies for
doing his homework, he is only giving away candies from the pile that started
100,000 (He's not that generous!)
Graph
The number of pieces of candy that will be left on day 4 would be 2, 560 candies .
The number of pieces of candy left on day 8 would be 66 candies .
How to find the number or candy left ?To find the number of candy left on the fourth day, given that Augustus only gives candies after the pile of 100, 000 candies is reached, the formula is:
= Number of starting candy x ( 1 - Percent given away ) ^ number of days
= 100, 000 x ( 1 - 60 % ) ⁴
= 100, 000 x 40 % ⁴
= 2, 560 candies
On Day 8, this would be:
= 100, 000 x ( 1 - 60 % ) ⁸
= 66 candies
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The question is:
How many pieces of candy will be left on day 4? On day 8?
In a survey, 32 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $45 and standard deviation of $19. Construct a confidence interval at a 80% confidence level.
Give your answers to one decimal place.
Answer:
{40.7,49.3}
Step-by-step explanation:
[tex]\displaystyle CI=\bar{x}\pm z\frac{s}{\sqrt{n}}\\\\CI_{80\%}=45\pm1.282\biggr(\frac{19}{\sqrt{32}}\biggr)\\ \\CI_{80\%}\approx45\pm 4.3\\\\CI_{80\%}=\{40.7,49.3\}[/tex]
Thus, we are 80% confident that the true sample mean amount spent is between $40.70 and $49.30
3. What is the volume of this complex figure?
3 m
4 m
6m
4 m
7m
Answer:
27,64,216,64,243
Step-by-step explanation:
Any number raise to power 3
Find EF, please!!!!!!!!!!
Answer:
EF = 7
Step-by-step explanation:
You want to know the length of midsegment EF in the triangle with it labeled 43-4x and the parallel base segment labeled 32-2x.
MidsegmentThe midsegment is half the length of the base segment, so we have ...
(43 -4x) = 1/2(32 -2x)
43 -4x = 16 -x . . . . . simplify
27 = 3x . . . . . . . . add 4x-16
9 = x . . . . . . . . divide by 3
EF = 43 -4x = 43 -4(9) = 43 -36
EF = 7
Question 4 of 8
Solve the inequality and enter your solution as an inequality comparing the
variable to a number.
X+4> 11
Answer here
Answer:
[tex]x > 7[/tex]
Step-by-step explanation:
Given the inequality
[tex]x+4 > 11[/tex]
Lets solve the inequality for [tex]x[/tex].
Subtract [tex]4[/tex] from both sides of the inequality.
[tex]x > 11-4[/tex]
Evaluate [tex]11-4[/tex].
[tex]x > 7[/tex]
[tex]x[/tex] is greater than 7
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The circumference of a circle is 81.64 feet. What is the radius of the garden? Use 3.14 for π and do not round your answer
Answer:13
Step-by-step explanation:
r = circumference/2pi
81.64/6.28 = 13
The radius of the garden is 13 units.
One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 2.2 cubic feet of water weigh in pounds?
In tons?
To find the weight of 2.2 cubic feet of water in pounds, we can use the following formula:
Weight in pounds = Volume in cubic feet x Density of water in pounds per cubic foot
The density of water is 62.4 pounds per cubic foot, so we can substitute the values into the formula:
Weight in pounds = 2.2 x 62.4 = 138.08
So, 2.2 cubic feet of water weighs 138.08 pounds.
To convert this weight to tons, we can divide by 2000, as there are 2000 pounds in a ton:
Weight in tons = 138.08 / 2000 = 0.06904 tons
So, 2.2 cubic feet of water weighs 0.06904 tons.
Answer:
0.0680 tonsStep-by-step explanation:
First, we need to find how many gallons of water 2.2 cubic feet hold:
2.2 cubic feet * 7.48 gallons per cubic foot = 16.456 gallons
Next, we'll find the weight of the water in pounds:
16.456 gallons * 8.33 pounds per gallon = 136.08 pounds
Finally, we'll convert the weight to tons:
136.08 pounds / 2000 pounds per ton = 0.0680 tons
So 2.2 cubic feet of water weigh 136.08 pounds and 0.0680 tons.
Hope it helps! : )This is the continuation of the question I have asked previously:
d. find the logarithmic model. Use one of these equations as your base: y1~alog(x1)+k or y1~aln(x1)+k. Then write down the best fit curve for the data.
4. a. Where on your radio dial would you find a station with a frequency of 93.3? Show work to justify your answer.
b. If you turned the radio dial to be 4 centimeters from the left end of the radio, what radio station would you pick up? Show work to justify your answer.
d. The logarithmic model can be expressed as y1~alog(x1)+k or y1~aln(x1)+k.
The best fit curve for the given data would be: y1 = 0.2 * log(x1) + k or y1 = 0.2 * ln(x1) + k
a. If you wanted to find a station with a frequency of 93.3 on your radio dial, you would need to use the formula Frequency = 88 + 0.2 * (Channel Number). Using this formula, we can calculate that the channel number for a frequency of 93.3 is:
Channel Number = (Frequency - 88) / 0.2
Channel Number = (93.3 - 88) / 0.2
Channel Number = 5.3
Therefore, a station with a frequency of 93.3 can be found on channel 5.3 on your radio dial.
b. If you turned the radio dial to be 4 centimeters from the left end of the radio, the channel number would be:
Channel Number = 4 / 0.2
Channel Number = 20
Using the formula Frequency = 88 + 0.2 * (Channel Number), we can calculate that the frequency for channel 20 is:
Frequency = 88 + 0.2 * (Channel Number)
Frequency = 88 + 0.2 * (20)
Frequency = 96.0
Therefore, turning the radio dial to be 4 centimeters from the left end of the radio, you will pick up a station with a frequency of 96.0.
A school is having a movie day. They are selling popcorn at the school for $0.50 per bag. If a student purchases popcorn with $5, how much popcorn would the student receive?
This student would receive 10 bag of popcorns.
How to determine the quantity of popcorn?Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.
In order to determine the quantity of popcorn, we would make use of the information provided about the unit price for one bag of popcorn by using the following mathematical expression;
Number of bag of popcorns = Cost of one bag of popcorn/Unit price
Substituting the given parameters into the mathematical expression above, we have the following;
Number of bag of popcorns = 5/0.50
Number of bag of popcorns = 10 bag of popcorns.
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) Joe bought six bunches of seedless black
grapes for $15. How many bunches can
Anjali buy if she has $7.50?
Answer:
Step-by-step explanation:
Since Joe bought six bunches of seedless black grapes for $15, the cost per bunch of grapes is $15 / 6 = $2.50.
Since Anjali has $7.50, she can buy $7.50 / $2.50 = 3 bunches of seedless black grapes.
The depth of a certain part of the Earth's seabed is 36,078 feet. How deep is it in (a) fathoms ? (b) leagues (marine)?
Step-by-step explanation:
(a) To convert feet to fathoms, we can use the conversion factor 1 fathom = 6 feet. Hence, we can divide the depth in feet by 6 to find the depth in fathoms:
36,078 feet / 6 feet/fathom = 6,013 fathoms
So the depth of the seabed is 6,013 fathoms.
(b) To convert feet to leagues (marine), we can use the conversion factor 1 league (marine) = 5,556 feet. Hence, we can divide the depth in feet by 5,556 to find the depth in leagues (marine):
36,078 feet / 5,556 feet/league (marine) = 6.52 leagues (marine)
So the depth of the seabed is approximately 6.52 leagues (marine).
please help me out ty!
1. Rectangle reports operating cash flows of $3.59 billion, investing cash flows of $0.59 billion, and financing cash flows of -$4.18
billion.
2. Circle reports operating cash flows of $1.39 billion, investing cash flows of -$0.29 billion, and financing cash flows of -$1.38 billion.
The beginning cash amount is $0.69 billion.
3. Pentagon reports operating cash flows of $0.08 billion, investing cash flows of $0.62 billion, and a change in total cash of $0.05
billion.
4. Square reports operating cash flows of $0.59 billion, financing cash flows of $0.41 billion, and a change in total cash of $0.01 billion.
5. Hexagon reports investing cash flows of -$1.40 billion, financing cash flows of $1.02 billion, and a change in total cash of $0.01
billion.
(Net cash outflows should be indicated with a minus sign. Enter your answers in billions rounded to 2 decimal places.)
Required:
1. What is the amount of the change in total cash of Rectangle?
2. What is the ending cash amount of Circle?
3. What is the amount of cash flows from financing activities of Pentagon?
4. What is the amount of cash flows from investing activities of Square?
5. What is the amount of cash flows from operating activities of Hexagon?
1. Change in total cash
2. Ending cash amount
3. Amount of outflows
4. Amount of outflows
5. Amount of inflows
To get the cash flows from operating activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.39 billion. Rounding to two decimal places, we get -$1.01 billion).
What is algebraic expression ?
An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.
The change in total cash of Rectangle is $0.02 billion (3.59 - 0.59 - 4.18 = -0.98, which is rounded to -$1.00 billion, and then added to the beginning cash amount of $0.69 billion to get $0.69 - $1.00 = -$0.31 billion or -$0.31/100 = -$0.02 billion).
The ending cash amount of Circle is $0.72 billion (1.39 - 0.29 - 1.38 = -0.28, which is added to the beginning cash amount of $0.69 billion to get $0.41 billion or $0.41/100 = $0.72 billion).
The amount of cash flows from financing activities of Pentagon is -$0.55 billion (the change in total cash of $0.05 billion is the sum of the operating cash flows and investing cash flows, which is $0.08 billion + $0.62 billion = $0.70 billion. To get the cash flows from financing activities, we subtract this from the change in total cash, which is $0.05 billion, to get -$0.65 billion. Rounding to two decimal places, we get -$0.55 billion).
The amount of cash flows from investing activities of Square is -$0.40 billion (the change in total cash of $0.01 billion is the sum of the operating cash flows and financing cash flows, which is $0.59 billion + $0.41 billion = $1.00 billion. To get the cash flows from investing activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.99 billion. Rounding to two decimal places, we get -$0.40 billion).
The amount of cash flows from operating activities of Hexagon is -$1.01 billion (the change in total cash of $0.01 billion is the sum of the investing cash flows and financing cash flows, which is -$1.40 billion + $1.02 billion = -$0.38 billion.
Therefore, To get the cash flows from operating activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.39 billion. Rounding to two decimal places, we get -$1.01 billion).
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Which composition of similarity transformations maps polygon ABCD to polygon A'B'C'D'?
The correct transformation is, a dilation with a scale factor less than 1 and then a reflection.
What is transformations?A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.
Given that, a transformation that maps polygon ABCD to polygon A'B'C'D',
We are asked to select the correct composition of similarity transformations,
According to the graph, there is a scale factor of 1/2 which is smaller than 1,
Also, the polygon is dilating and then reflected.
Hence, the correct transformation is, a dilation with a scale factor less than 1 and then a reflection.
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Aida is 15 years old. Brice is five years younger than Aida. Henry is three years younger than Aida. How old is Brice?
Answer:
Bryce is 10 years old
Step-by-step explanation:
The age of Brice is given by B = 10 years old
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as B
Now , the value of B is
Substituting the values in the equation , we get
The age of Aida = 15 years
The age of Brice = 5 years younger than Aida
On simplifying the equation , we get
So , age of Brice = 15 - 5 = 10 years
The age of Henry = three years younger than Aida
So , the age of Henry = 15 - 3 = 12 years
Hence , the age of Brice is 10 years old
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Prove that the surds in this expression cannot be added or subtracted showing step by step solutions. Thanks!
2√200+ 3√300
A bag contains 4 white marbles, 3 red marbles, and 5 blue marbles. Miko takes one marble from the bag, replaces it, and then takes another. Find P(red, then white).
Answer:
To find the probability of Miko taking a red marble first, then a white marble, we can use the formula for joint probability:
P(red, then white) = P(red) * P(white | red)
Where P(red) is the probability of Miko taking a red marble first and P(white | red) is the probability of Miko taking a white marble second, given that he took a red marble first.
P(red) = 3/12 = 1/4
P(white | red) = 4/12 = 1/3
So,
P(red, then white) = 1/4 * 1/3 = 1/12
Therefore, the probability of Miko taking a red marble first, then a white marble is 1/12.
Convert the complex number 2√2(cos 135° + i sin 135°) into rectangular
(standard) form. Express your answer in simplest radical form.
The solution to the complex number in rectangular form is; -2 + 2i
How to express complex number in rectangular form?The complex number is given as;
2√2(cos 135° + i sin 135°)
The standard form is a + bi.
The value of cos 135° is; -(√2)/2
The value of sin 135° is; (√2)/2
Plugging these values into the given equation is;
2√2(-(√2)/2 + ((√2)/2)i)
Expanding the bracket gives;
-2 + 2i
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a.find the profit function
B.find the marginal profit function
C.find marginal average profit function
D. use marginal analysis to estimate the profit from the sale of 201st doll
a. The profit function is given by P(x) = R(x) - C(x). Substituting the expressions for R(x) and C(x), we have P(x) = 12x + 300√x - 2500.
b. The marginal profit function is the derivative of the profit function with respect to x. To find the marginal profit function, we will differentiate P(x) is dP/dx = 12 + 300/2√x.
c. The marginal average profit function is the derivative of the profit function divided by the number of units sold is dP/dx ÷ x = (12 + 300/2√x) ÷ x.
d. To estimate the profit from the sale of the 201st doll, we will evaluate the profit function at x = 201 is $16.62.
What do you mean by profit function?
A profit function is a mathematical model that represents the profit made from selling a certain product or service as a function of the number of units sold. The profit function is calculated as the difference between the total revenue and the total cost of producing and selling the product.
Mathematically, if R(x) represents the total revenue from selling x units of a product and C(x) represents the total cost of producing and selling x units of the product, then the profit function can be represented as P(x) = R(x) - C(x).
a. The profit function is given by P(x) = R(x) - C(x). Substituting the expressions for R(x) and C(x), we have:
P(x) = 14x - (2x - 300√x + 2500)
P(x) = 12x + 300√x - 2500
b. The marginal profit function is the derivative of the profit function with respect to x. To find the marginal profit function, we will differentiate P(x):
dP/dx = 12 + 300/2√x
c. The marginal average profit function is the derivative of the profit function divided by the number of units sold.
dP/dx ÷ x = (12 + 300/2√x) ÷ x
d. To estimate the profit from the sale of the 201st doll, we will evaluate the profit function at x = 201:
P(201) = 12 * 201 + 300 * √201 - 2500 = $3347.09
Since we want the profit from the sale of one unit, we divide the profit by 201:
P(201) ÷ 201 = $16.62
So, the estimated profit from the sale of the 201st doll is $16.62.
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The 147 heights of males from a data set of body measurements vary from a low of 152.0 cm to a high of 192.5 cm. Use the range rule of thumb to estimate the standard deviations and compare
the result to the standard deviation of 12.22 cm calculated using the 147 heights. What does the result suggest about the accuracy of estimates of s found using the range rule of thumb? Assume the
estimate is accurate if it is within 1.7 cm.
Answer:The range rule of thumb states that the standard deviation (s) is approximately equal to the range (R) divided by 4, where the range is the difference between the maximum and minimum values of a data set.
Using this formula, we can estimate the standard deviation of the heights as:
s = R / 4 = (192.5 - 152.0) / 4 = 20.625 / 4 = 5.156 cm
Comparing this estimate to the actual standard deviation of 12.22 cm, we see that the estimate is off by a factor of approximately 2.37.
Since the estimate is not within 1.7 cm of the actual standard deviation, it suggests that the range rule of thumb is not a very accurate way to estimate the standard deviation of this data set. The standard deviation calculated using the full set of data is much larger than the estimate, which means that the spread of the data is greater than what would be expected based on the range rule of thumb.
a positive angle less than 360 degrees that is coterminal with -305 is
The positive angle which is less than 360 degrees and is co-terminal with -305 as required is; 55°.
What is the positive angle co-terminal with -305°?It follows from the task content that the position angle which is co-terminal with -305° as required is to be determined.
Let the positive angle in discuss be; x.
Therefore, the angle x = 360 + (-305)
Consequently, it can be calculated as follows;
x = 360 - 305.
x = 55°
Hence, the required value of the positive co-terminal angle is; 55°.
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Help me with this question…..
Answer:
A.
Step-by-step explanation:
Since [tex]5[/tex] can rewritten as [tex]\sqrt{25}[/tex] and [tex]6[/tex] rewritten as [tex]\sqrt{36},[/tex] we can see which options go between [tex]\sqrt{25}[/tex] and [tex]\sqrt{36}.[/tex] The only square root that goes between is [tex]\sqrt{29}.[/tex] Therefore the answer is [tex]\boxed{A.}[/tex] (or [tex]\sqrt{29}.[/tex])
