A. True.
In a two-column proof, the left column consists of statements, which are the facts or assumptions that lead to the proof of the theorem, while the right column consists of the reasons or justifications that explain how each statement logically follows from the previous one. Therefore, the left column states your reasons is a true statement.
The answer to the student's question is True. In a two-column proof, the left column contains the statements (steps) and the right column contains the corresponding reasons (justifications).
Explanation:The answer to the question, 'True or false? In a two-column proof, the left column states your reasons', is A. True.
A two-column proof is organized into two columns. The left column contains the 'Statements' and the right column contains the corresponding 'Reasons'. The 'Statements' are the steps that lead to the conclusion of the proof, while the 'Reasons' justify each of those steps according to rules or laws of mathematics.
For example, if we want to prove that the opposite angles of a parallelogram are equal. The left column (Statements) could contain the first step 'ABCD is a parallelogram' and the right column (Reasons) would give the explanation 'Given'. Therefore, in a two-column proof, the left column does represent statements, not reasons.
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Suppose there are approximately 310 million people in the U.S. If the world population is 7.2 billion people, what percent of the world population is in the U.S.?
Round your answer to the nearest tenth of a percent.
The percentage of the world population that is in the U.S. is approximately 4.3%.
To find the percentage of the world population that is in the U.S., we need to divide the population of the U.S. by the world population and then multiply the result by 100.
Let's calculate the percentage:
Percentage = (U.S. population / World population) * 100
Given that the U.S. population is approximately 310 million and the world population is approximately 7.2 billion, we can substitute these values into the equation:
Percentage = (310 million / 7.2 billion) * 100
To perform the calculation, we need to convert the populations to the same units. Let's convert 310 million to billion:
310 million = 310 / 1000 billion
= 0.31 billion
Now, let's substitute the converted values:
Percentage = (0.31 billion / 7.2 billion) * 100
Simplifying the equation:
Percentage = 0.04305555556 * 100
= 4.305555556
Rounding the result to the nearest tenth of a percent, the percentage of the world population that is in the U.S. is approximately 4.3%.
Therefore, approximately 4.3% of the world population is in the U.S.
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I NEED HELP BY TMRW WILL GIVE THE BRAINLIEST TITLE
The mid points of the four sides of square ABCD are joined to form square WXYZ as shown. The area of square WXYZ is 16. The area of triangle YCX is….
F. 4
G. 2
H. 1.5
J. 1
K. None of these
The area of triangle YCX is given as follows:
G. 2 units squared.
How to obtain the area of the triangle?The area of square WXYZ is 16, hence the side length is given as follows:
s² = 16
s = 4.
Considering the midpoints, we have that the sides of the right triangle are given as follows:
YC = CX = 4/2 = 2
Hence the area of the triangle is given as follows:
0.5 x 2 x 2 = 2 units squared.
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Two added to the square root of the sum of a number and five is equal to seven. Find the number.
Answer:
Step-by-step explanation:
PLEASE HELP AS SOON AS POSSIBLE
A) The interval where the graph is increasing is: (0,0) to (40, 4)
The interval where the graph remains constant is from: (120, 3) to (140, 3).
The interval where the graph is decreasing in depth is from: (140, 3) to (180, 0).
B) The domain is from 0 to 180 minutes.
The range of the graph is from 0 to 4 feet.
C) Yes, the graph represents a function
D) The graph depicts the filling of the pool from 0 to 4 feet, followed by a period of constant depth, and finally, the draining of the pool back to 0 feet.
How to find the range and domain of the graph?Part A:
- Increasing interval:
The interval where the graph is increasing is from the starting point coordinate (0,0) to the coordinate (40, 4)
- Constant interval:
The interval where the graph remains constant at a depth of 4 feet which is from (40, 4) to (80, 4) and then from where the depth is 3 feet which is from the coordinates (120, 3) to (140, 3).
- Decreasing interval:
The interval where the graph is decreasing in depth is from the coordinates (140, 3) to (180, 0).
Part B:
- Domain: The domain of the relation is the set of time values represented on the x-axis. The domain here is from 0 to 180 minutes.
- Range: The range of the relation is the set of depth values represented on the y-axis. The range of the graph is from 0 to 4 feet.
Part C:
Yes, the graph represents a function. This is because, each input (x-value) is associated with a unique output (y-value).
Part D:
The graph represents the depth of water in a kids' swimming pool over a certain amount of time between 0 and 180 minutes.
At the beginning, the pool is empty, and then the depth slowly increases with time. From 0 to 40 minutes, the depth increases at a constant rate until it reaches 4 feet. Thereafter, it remains constant at that depth for the next 40 minutes, indicating the pool is full. Afterward, there is a gradual decrease in depth over time. From 140 to 180 minutes, the water is drained from the pool, and the depth eventually reaches 0 feet.
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The population of the bacteria is initially 20. At the end of Week 1, the population of the bacteria is 30. The population grows by 50% each week. What is the bacteria population at the end of Week 12? Round the answer to the nearest whole number. Enter your answer in the box.
Answer:
The population of the bacteria at the end of Week 12 is approximately 1,148
Step-by-step explanation:
The equation of a parabola is (x−3)2=16(y+7) . What are the coordinates of the vertex and focus of the parabola? What is the equation of the directrix?
The coordinates of the vertex of the parabola are (3, -7). The focus of the parabola is located at (3, -3). The equation of the directrix is y = -11.
The given equation of the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus/directrix.
Comparing the given equation with the standard form, we can see that the vertex is at (3, -7).
The coefficient 4p in this case is 16, so p = 4. Since the parabola opens upward, the focus will be p units above the vertex. Therefore, the focus is located at (3, -7 + 4) = (3, -3).
To find the directrix, we need to consider the distance p below the vertex. Since the parabola opens upward, the directrix will be p units below the vertex. Hence, the equation of the directrix is y = -7 - 4 = -11.
In summary, the coordinates of the vertex are (3, -7), the focus is located at (3, -3), and the equation of the directrix is y = -11.
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Choose the correct graph of the function
The graph of the function [tex]y = \sqrt{x} - 3[/tex] is given by the image presented at the end of the answer.
How to obtain the graph of the function?The function for this problem is defined as follows:
[tex]y = \sqrt{x} - 3[/tex]
The parent function is defined as follows:
[tex]y = \sqrt{x}[/tex]
The subtraction by 3 means that the function was translated 3 units down.
Missing InformationThe function is [tex]y = \sqrt{x} - 3[/tex]
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Which graph represents the solution of y ≤ x^2 – 1 and x > y^2 – 3?
A On a coordinate plane, a parabola opens to the right and goes through (6, 3), has vertex (negative 3, 0), and goes through (6, negative 3). Another parabola opens down and goes through (2, negative 5), has vertex (0, negative 1), and goes through (2, negative 5). Everything inside of the first parabola and outside of the second parabola is shaded.
B On a coordinate plane, a parabola opens to the right and goes through (6, 3), has vertex (negative 3, 0), and goes through (6, negative 3). Another parabola opens down and goes through (2, negative 5), has vertex (0, negative 1), and goes through (2, negative 5). Everything inside of the first parabola and second parabola is shaded.
C On a coordinate plane, a parabola opens to the right and goes through (6, 3), has vertex (negative 3, 0), and goes through (6, negative 3). Another parabola opens up and goes through (negative 2, 3), has vertex (0, negative 1), and goes through (2, 3). Everything inside of the first parabola and second parabola is shaded.
D On a coordinate plane, a parabola opens to the right and goes through (6, 3), has vertex (negative 3, 0), and goes through (6, negative 3). Another parabola opens up and goes through (negative 2, 3), has vertex (0, negative 1), and goes through (2, 3). Everything inside of the first parabola and outside of the second parabola is shaded.
The graph that represents the solution of y ≤ x² - 1 and x > y² - 3 is option D.The graph that represents the solution of y ≤ x^2 – 1 and x > y^2 – 3 is D.
In order to solve the given inequality y ≤ x² - 1 and x > y² - 3, we need to follow these steps:Firstly, we will rewrite the given inequality in standard form as y² - x + 3 ≤ 0 and x² - y - 1 ≥ 0.Then we need to find the solutions of the above two inequalities. By solving these two inequalities we get the region which is common to both the inequalities and we can plot it on the graph paper.In the first inequality y² - x + 3 ≤ 0, the coefficient of x is negative which means the parabola will be open downwards.
On plotting the parabola we can observe that it passes through (0, -3) and (-2, -1). Also, we can see that it intersects the x-axis at x = 3. Therefore, the solution to the inequality y² - x + 3 ≤ 0 is the region below the parabola including the boundary.In the second inequality x² - y - 1 ≥ 0, the coefficient of y is negative which means the parabola will be open downwards. On plotting the parabola we can observe that it passes through (0, -1) and (-2, 1). Also, we can see that it intersects the y-axis at y = -1.
Therefore, the solution to the inequality x² - y - 1 ≥ 0 is the region above the parabola including the boundary.Now, we need to find the common region between the two solutions obtained above. The common region will be the solution to the inequality y ≤ x² - 1 and x > y² - 3. By observing the graphs we can see that the common region is the shaded region inside the first parabola and outside the second parabola.The correct option is D.
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balance at the beginning of the month
R15000
sales R25000
rent income 5000
total income?
The total income for the month, considering the beginning balance of R15,000, sales of R25,000, and rent income of R5,000, amounts to R45,000.
To calculate the total income for the month, we need to consider the beginning balance, sales, and rent income.
Beginning balance: R15,000
Sales: R25,000
Rent income: R5,000
To find the total income, we sum up the beginning balance, sales, and rent income:
Total income = Beginning balance + Sales + Rent income
Total income = R15,000 + R25,000 + R5,000
Total income = R45,000
Therefore, the total income for the month is R45,000.
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The July bank statement sent by the bank to ABC company shows a balance of cash on deposit at July 31 of Br.4,964.47 Assume that on July 31, assume the on July 31, ABCs ledger shows a bank balance of Br. 4 173. 83. 1. A deposit of Br 410. 90 made after banking hours and doesnt appear in the bank statement2. A check drawn for Br. 79 had been erroneously charged by the bank Br.973. For checks issued in July have not yet been paid by the bank (outstanding checks). : Theses checks are;- Check No date amount 801 June 15 ---Br.100,00 888 July 24 ----Br. 10.25 890 July 27--- Br. 294.50 891 July 30 ---Br. 205.004. A check written for birr 210 had been incorrectly charged by the bank as birr 120 5. Proceeds from collection of a interest bearing note receivable from David. ABC Company had left this note with the banks collection department. The face amount of the note was birr 500 6. Br. 24.75 interest earned on average account balance during July7. A check for Br. 10 returned with the statement had been recorded in the check register as Br. 100. The check was for the payment of an obligation to Davis Equipment Company for the purchase of office supplies on account 8. Br. 5,00 fee charged by bank for handling collection of note receivable 9. Br. 50.25 check from customer John deposited by ABC company charged bank as Non sufficient fund (NSF) 10. Br. 12.70 service charged by bank for the month of July. 11. Check number 875 was issued July 20 in the amount of Br 85 but was erroneously recorded in the cash payment Journal as Br 58 for payment of telephone expense
After making all the necessary adjustments, the reconciled bank balance for ABC Company's ledger at the end of July is Br. 4,164.42.
To reconcile the bank statement balance with the company's ledger balance for ABC Company, we need to go through the provided information step by step and make the necessary adjustments. Let's calculate the adjusted bank balance:
Starting with the bank statement balance: Br. 4,964.47
Add the deposit made after banking hours: + Br. 410.90
New bank balance: Br. 5,375.37
Now let's make adjustments for the outstanding checks and other transactions:
Deduct the erroneously charged check: - Br. 973
New bank balance: Br. 4,402.37
Deduct the outstanding checks:
Check No. 801: Br. 100.00
Check No. 888: Br. 10.25
Check No. 890: Br. 294.50
Check No. 891: Br. 205.00
Total deduction: Br. 609.75
New bank balance: Br. 3,792.62
Correct the incorrectly charged check: + Br. 90
New bank balance: Br. 3,882.62
Add the proceeds from the collection of the interest-bearing note: + Br. 500.00
New bank balance: Br. 4,382.62
Add the interest earned on the average account balance: + Br. 24.75
New bank balance: Br. 4,407.37
Deduct the incorrectly recorded check: - Br. 90
New bank balance: Br. 4,317.37
Deduct the fee charged for handling the collection of the note: - Br. 5.00
New bank balance: Br. 4,312.37
Deduct the check returned due to insufficient funds: - Br. 50.25
New bank balance: Br. 4,262.12
Deduct the service charge for the month of July: - Br. 12.70
New bank balance: Br. 4,249.42
Deduct the erroneously recorded check: - Br. 85.00
New bank balance: Br. 4,164.42
Now, we compare the adjusted bank balance (Br. 4,164.42) with the ledger balance provided (Br. 4,173.83).
Adjusted bank balance: Br. 4,164.42
Ledger balance: Br. 4,173.83
The difference between the adjusted bank balance and the ledger balance is Br. 9.41. This difference is likely due to some unrecorded transactions or errors in recording. To reconcile the balances fully, further investigation is required to identify the specific cause of the discrepancy and make the necessary adjustments in the company's ledger.
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Please need answer thanks
Answer:
Area of the shaded region= 4 units
Step-by-step explanation:
width (x-axis)= 3-1 = 2
length (y-axis) = 2-0 = 2
Area of rectangle= Length × Width
= 2 × 2 = 4
I NEED HELP!! I'll give you brainliest!! A high school wants to expand its P.E. schedule. To better understand the needs of the students, the principal looked at which forms of exercise are preferred by the 18 students in the sample group.The Venn Diagram shows this information be gathered.a. How many students preferred swimming over running or walking?b. How many students choose running or walking?c. Which students preferred swimming and walking, but not running
Answer:
a. Three students preferred swimming over running and walking.
b. Fourteen students chose running or walking.
c. Alex and Jose preferred swimming and walking, but not running.
Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form.
If you are using a screen-reader, please consult your instructor for assistance.
x=
y=
Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer
In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.
Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.
Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.
Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$
Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.
Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$
Therefore, $x=y=12\sqrt{3}$, which is our answer.
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Graph the polar equation and determine about which axis it is symmetric r=2 sin 3 theta
A graph of the polar equation r = 2sin3(θ) is shown below.
The polar equation r = 2sinθ is symmetric with respect to the polar axis.
How to graph a polar equation?In Mathematics and Geometry, the relationship between a polar coordinate (r, θ) and a rectangular coordinate (x, y) based on the conversion rules is given by the following polar equations:
a = rcos(θ) ....equation 1.
b = rsin(θ) ....equation 2.
Where:
θ is the angle.r is the radius of a circle.Based on the information provided above, we can logically deduce the following polar equation r = 2sin3(θ), which would be plotted on a coordinate axis by using an online graphing tool.
By critically observing the graph of this polar equation r = 2sin3(θ), we can logically conclude that it is symmetric with respect to the polar axis;
-r = -2sin3(π - θ)
-r = -2sin(3π - 3θ)
-r = 2sin(-3θ)
-r = -2sin(3θ)
r = 2sin3(θ)
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Answer: pretty sure it's C but im not sure
Step-by-step explanation:
exam review on ed 2023
Find the quotient of 10^-4/10^2
The quotient of 10⁻⁴/10² is 10⁻⁶
How to Find the quotient of 10⁻⁴/10²?Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.
For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.
Division law states that:
10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ
In this case have:
10⁻⁴/10² = 10⁻⁴⁻² (Division law)
10⁻⁴/10² = 10⁻⁶
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(1+y)^2-y^2=-11x+10 write in standard form
Answer:
[tex]2y+11x=9[/tex]
Step-by-step explanation:
[tex](1+y)^2-y^2=-11x+10\\1+2y+y^2-y^2=-11x+10\\1+2y=-11x+10\\2y=-11x+9\\2y+11x=9[/tex]
Recall the standard form of a linear equation is [tex]Ax+By=C[/tex].
QUESTION:↓
A and B working together can do a work in 6 days. If A takes 5 days less than B to finish the work, in how many days B alone can do it alone.
B alone can finish the work in 15 days.
How to determine 5 days less than B to finish the work, in how many days B alone can do it alone.Let's assume that B takes x days to finish the work alone.
If A takes 5 days less than B to finish the work, then A takes (x - 5) days to finish the work alone.
We are given that A and B working together can finish the work in 6 days.
Using the concept of work rates, we can set up the following equation:
1/(x - 5) + 1/x = 1/6
To solve this equation, we can find a common denominator:
(x + x - 5)/(x(x - 5)) = 1/6
Simplifying the equation:
[tex](2x - 5)/(x^2 - 5x) = 1/6[/tex]
Cross-multiplying:
[tex]6(2x - 5) = x^2 - 5x[/tex]
[tex]12x - 30 = x^2 - 5x[/tex]
Rearranging the equation:
[tex]x^2 - 17x + 30 = 0[/tex]
Factoring the quadratic equation:
(x - 2)(x - 15) = 0
Setting each factor equal to zero:
x - 2 = 0 or x - 15 = 0
Solving for x:
x = 2 or x = 15
We discard the solution x = 2 since it suggests that B can complete the work in two days, which contradicts the fact that A takes five days fewer than B.
Therefore, B alone can finish the work in 15 days.
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A ratio of two angles is 5 to 3 and their sum is 180 degrees. Find the measure of each angle. The find their complements. Make a sketch, set up the corresponding equation and solve it.
Answer:
112.5
67.5
Step-by-step explanation:
We know the ratio is:
5:3
So, we can write it as:
5x+3x=180, with 5x being one angle, and 3x being the other
combine like terms
8x=180
divide both sides by 8
x=22.5
5(22.5)=112.5
3(22.5)=67.5
So, one angle is 112.5 and the other is 67.5.
Hope this helps!
Analyzing a Solution
Mark used a number line to model dividing by 3. He
3
divided the number line from 0 to 1 in 3 equal sections,
and then divided each of those sections into 2 equal
1
parts. Mark says+3 is 3.
Is his answer correct? Explain why or why not.
No, his answer is not correct because each of the smaller divisions represents 1/6, not 3.
Mark's answer is not correct.
When dividing a number line into equal sections, the value of each section represents a fraction of the whole.
In this case, Mark divided the number line from 0 to 1 into 3 equal sections and then divided each of those sections into 2 equal parts.
Initially, the whole number line from 0 to 1 represents the number 1. When Mark divided it into 3 equal sections, each section represents 1/3 (one-third) of the whole.
So far, this is correct.
However, when Mark further divided each of the 1/3 sections into 2 equal parts, each part represents 1/2 (one-half) of the 1/3 section.
So, each of these smaller divisions represents 1/2 [tex]\times[/tex] 1/3 = 1/6 (one-sixth) of the whole.
Therefore, the correct representation of each of the smaller divisions is 1/6, not 3.
Mark made an error by mistakenly assuming that each smaller division represents the number 3.
In summary, Mark's answer of 3 is incorrect because each of the smaller divisions represents 1/6, not 3.
The correct representation for dividing the number line as described is 1/6.
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What does the y-intercept of the line tell you about the situation?
Please answer this quickly it’s due in 10min
The y-intercept of the linear function means that her initial distance from the finish line is of 10 kilometers.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the y-intercept.The graph crosses the y-axis at y = 10, hence the intercept b is given as follows:
b = 10.
The y-values represent the distance in the context of this problem, hence the initial distance is of 10 km.
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what is the horizontal asymptote ?
In mathematics, a horizontal asymptote is a horizontal line that a function approaches as the input values (usually x) approach positive or negative infinity. It describes the behavior of a function as its input values become extremely large or small.
For a rational function, which is a function expressed as the ratio of two polynomials, the degree of the numerator and denominator determines the existence and location of horizontal asymptotes. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is the x-axis (y = 0).
If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients of the numerator and denominator. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.
For example, consider the function [tex]f(x) = (3x^2 + 2x + 1) / (2x^2 + 5)[/tex]. In this case, both the numerator and denominator have a degree of 2. Therefore, the horizontal asymptote is the ratio of the leading coefficients: y = 3/2.
Horizontal asymptotes help understand the long-term behavior of functions and are useful for graphing and analyzing mathematical models in various fields, including economics, physics, and engineering.
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TREVISION AVAILABLE
In a shopping survey of 225 people, 60% said they preferred to shop online. How many people
said they shop online?
135
20% of those people who shop online said they always get their order delivered. How many
people have shopping delivered?
27
Of the 40% of people in the survey who said they went in store to shop, only 60% of them said
they had loyalty cards. How many people had the cards?
Out of the 225 people surveyed, 135 said they shop online, 27 said they always get their order delivered, and 54 said they had loyalty cards.
To calculate the number of people who said they shop online, we can use the percentage given. If 60% of the 225 people surveyed said they prefer to shop online, we can find the number by multiplying the total number of people surveyed by the percentage:
Number of people who shop online = 225 * 0.60
Number of people who shop online = 135
Therefore, 135 people said they shop online.
To find the number of people who have shopping delivered, we need to calculate 20% of the number of people who shop online:
Number of people with shopping delivered = 135 * 0.20
Number of people with shopping delivered = 27
Hence, 27 people said they always get their order delivered.
Now let's calculate the number of people who had loyalty cards. First, we need to find the number of people who said they go in-store to shop. This is 40% of the total surveyed:
Number of people who go in-store to shop = 225 * 0.40
Number of people who go in-store to shop = 90
Out of these 90 people, only 60% said they had loyalty cards:
Number of people with loyalty cards = 90 * 0.60
Number of people with loyalty cards = 54
Therefore, 54 people said they had loyalty cards.
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OTHER ONE FROM THE QUESTION PLEASE.
Answer:
Step-by-step explanation:
Rotation symmetry can be also defined as radial symmetry. This is because no matter how many degrees you turn a figure or shape, it will still be the same figure/shape.
See attachment for an example.
Hope this helps! :)
simplify 7 1/2 - ( 3 + 7 1/3 )
Answer:
7 1/2-(3+7 1/3)= -17/6=-2 5/6 ≅ -2.8333333
Step-by-step explanation:
Given a circle of radius 1 centered at the origin, suppose the point (1,0) on the circle is rotated about the origin by an angle of θ.
a) For what values of θ will the x coordinate of the rotated point be positive? For what values will it be negative?
b) Describe the relationship between the x-coordinate of the rotated point and the values of cos(θ).
c) Compute cos(90°), cos(180°), and cos(270°) using the relationship you described in part b).
pls help they taught me nothing
Answer:
See below
Step-by-step explanation:
When [tex]-\frac{\pi}{2} < \theta < \frac{\pi}{2}[/tex], the x-coordinate of the rotated point will be positive since they cover Quadrants I and IV, both of which have positive x-values.
When [tex]\frac{\pi}{2} > \theta > \frac{3\pi}{2}[/tex], the x-coordinate of the rotated point will be negative since they cover Quadrants II and III, both of which have negative x-values.
The x-coordinate of the rotated point will be equal to cosθ since both of these values depend on the angle of θ.
cos(90°) = 0, cos(180°) = -1, and cos(270°) = 0
This is why referring to a unit circle is crucial in understanding this material.
Question Find the patient's ratio of total cholesterol to HDL cholesterol using the given information. Total cholesterol is 185 mg/dl, and HDL cholesterol is 40 mg/ /dl. Enter your answer as a fraction. Simplify your answer. Provide your answer below:
The ratio of total cholesterol to HDL cholesterol can be found by dividing the total cholesterol by the HDL cholesterol. So, the patient's ratio of total cholesterol to HDL cholesterol is:185 mg/dl ÷ 40 mg/dl = 4.625 mg/dl (dividing both numerator and denominator by 5)⇒ 37/8 (after simplification).
Thus, the patient's ratio of total cholesterol to HDL cholesterol is 37/8
What the meaning of statement this?
For the ordinal number, this statement means;
1. "α < β if an only if α ∈ β": This is saying that an ordinal number α is less than an ordinal number β if and only if α is a member of β and α is a subset of β.
2. "α = {β : β < α}" can be interpreted as: "α is the set of all ordinals β such that β is less than α".
What more should you know about the ordinal number?1. "α < β if an only if α ∈ β": This is saying that an ordinal number α is less than an ordinal number β if and only if α is a member of β.
In other words, α is less than β if and only if α is contained within β and every element of α is less than or equal to every element of β.
This is a fundamental property of ordinal numbers and is based on the von Neumann definition of ordinals where each ordinal is the well-ordered set of all smaller ordinals.
For an example of how this definition can be used. Let α = 1 and β = 2. Then, α is a member of β because 1 is a natural number and 2 is a natural number.
Additionally, α is a subset of β because every element of α, which is just 1, is less than or equal to every element of β, which is just 2. Therefore, α < β according to the definition.
2. "α = (β : β < α)" is a definition of ordinal numbers in set theory. It says that an ordinal number α is the set of all ordinal numbers that are less than α. In other words, α is the set of all ordinal numbers that are smaller than α.
For example, when we use the von Neumann definition, the ordinal number 3 would be represented as the set {0, 1, 2} because 0, 1, and 2 are the ordinal numbers less than 3.
Find more exercises on Ordinal numbers;
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Si a/7=b/5=c/8 y además a+b+c= 80 hallar c-b
Step-by-step explanation:
Podemos escribir las relaciones como:
a = 7x
b = 5x
c = 8x
Sustituyendo las expresiones anteriores en la ecuación a+b+c=80, obtenemos:
7x + 5x + 8x = 80
20x = 80
x = 4
Sustituyendo el valor de x en las expresiones de a, b y c:
a = 7(4) = 28
b = 5(4) = 20
c = 8(4) = 32
Por lo tanto, c - b = 32 - 20 = 12
Melissa's uncle from Japan promised to give her 21g of gold. The local jewelry exchange will buy gold for $1152 per ounce. How much money can Melissa get for selling the gold?
Use 1oz=28g and do not round any computations.
Answer:
Step-by-step explanation:
1 oz = $1152
1 oz = 28 grams
0.1 oz = 2.8 grams
21/2.8 = 7.5
0.1 x 7.5 oz = (2.8 x 7.5)grams
0.75 oz = 21 grams
75% of 1152 is 864
So,
0.75 oz = $864
a car travels 52/2 kilometers in 23/4 minutes.what is the unit rate in kilometers per minute
Step-by-step explanation:
To find the unit rate in kilometers per minute, we need to divide the distance traveled (52/2 kilometers) by the time taken (23/4 minutes).
52/2 kilometers = 26 kilometers
23/4 minutes = 5.75 minutes
So, the unit rate in kilometers per minute is:
26 kilometers / 5.75 minutes = 4.52 kilometers per minute (rounded to two decimal places)
The unit rate of the car that travels 5 2/5 km in 2 3/4 mins is 1.96 km/min.
Distance travelled by a car = 5 2/5 km = 5.4 km
Time travelled = 2 3/4 mins = 2.75 mins
The unit rate in km/min = 5.4/2.75
The unit rate in km/min = 1.96 km/min.
Happy to help, have a great day! :)
