The true balance of the Ledger Control Account for January 2019 is $3,447,600 (debit).
To correct the Ledger Control Account for the month of January 2019, we need to analyze the given entries and make appropriate adjustments to arrive at the true balance.
Step 1: Analyzing the given entries
From the information provided, we can identify the following entries in the Ledger Control Account:
- Opening Balance (bf): $318,000 (debit)
- Purchases: $1,364,300 (debit)
- Cheques paid to creditors: $41,200 (credit)
- Purchases Returns: $31,000 (debit)
- Transfer from Sales Ledger: $31,000 (credit)
- Discount Received: $31,000 (credit)
- Closing Balance (c/d): $1,724,100 (debit)
Step 2: Adjusting the entries
To arrive at the true balance, we need to make adjustments for any errors or omissions in the given entries. Let's correct each entry:
- Opening Balance (bf) remains unchanged.
- Purchases: No adjustment needed.
- Cheques paid to creditors should be debited instead of credited. Adjust the entry to $41,200 (debit).
- Purchases Returns should be credited instead of debited. Adjust the entry to $31,000 (credit).
- Transfer from Sales Ledger should be debited instead of credited. Adjust the entry to $31,000 (debit).
- Discount Received should be debited instead of credited. Adjust the entry to $31,000 (debit).
- Closing Balance (c/d) remains unchanged.
Adjusted entries:
- Opening Balance (bf): $318,000 (debit)
- Purchases: $1,364,300 (debit)
- Cheques paid to creditors: $41,200 (debit)
- Purchases Returns: $31,000 (credit)
- Transfer from Sales Ledger: $31,000 (debit)
- Discount Received: $31,000 (debit)
- Closing Balance (c/d): $1,724,100 (debit)
Step 3: Calculating the true balance
To calculate the true balance, we need to sum up the debit and credit entries separately and find the difference:
Debit total: $318,000 + $1,364,300 + $41,200 + $31,000 + $31,000 + $1,724,100 = $3,509,600
Credit total: $31,000 + $31,000 = $62,000
True balance: Debit total - Credit total = $3,509,600 - $62,000 = $3,447,600 (debit)
Therefore, the true balance of the Ledger Control Account for January 2019 is $3,447,600 (debit).
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Find m of angle ZLK if m of angle ZLK= x+86, m of angle MLK =130 degrees, and m of angle MLZ = x+ 66
We know that the sum of the angles in triangle MLK is 180 degrees. Therefore, we can find the measure of angle KLM as follows:
m∠MLK + m∠KLM + m∠LMK = 180
130 + m∠KLM + m∠LMZ = 180
We also know that angles ZLK and MLZ are vertical angles, so they are congruent. Therefore:
m∠ZLK = m∠MLZ
x + 86 = x + 66
86 = 66
This is a contradiction, so there is no value of x that satisfies the given conditions. Therefore, we cannot find the measure of angle ZLK.
The median cost of a home in 2014 is $___
The median cost of a home in 2014 is $480
How to determine the medianFirst, we need to know that the median of a given set of data is expressed as the middle number determined with the data set is arranged in an order from least to greatest or in an ascending order.
Also, note that the median is one of the measures of central tendency.
From the information given, we have that;
The median cost of a home in 2014 traced from the point year to the cost on the graph is;
$480
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Consider the expressions below. A. 11 x 2 + 6 x − 6 B. 7 x 2 + 16 x + 25 C. 11 x 2 − 5 x + 13 D. 7 x 2 − 3 x + 8 For each expression below, select the letter that corresponds to the equivalent expression given above. ( x 2 + 15 x + 65 ) + ( 2 x − 5 ) ( 3 x + 8 ) is equivalent to expression . ( 4 x + 1 ) ( 3 x − 4 ) − ( 5 x 2 − 10 x − 12 ) is equivalent to expression . ( 8 x 2 + 19 x + 4 ) + ( 3 x + 2 ) ( x − 5 ) is equivalent to expression . ( 6 x + 1 ) ( 3 x − 7 ) − ( 7 x 2 − 34 x − 20 ) is equivalent to expression .
Answer: the correct answer would option (C).
Step-by-step explanation:7x²+16x+25 is corresponds to the equivalent expression of (x²+15x+65) + (2x - 5) (3x +8).
7x²-3x+8 is corresponds to the equivalent expression of (4x + 1)(3x - 4) - (5x²-10x-12)
11x²+6x-6 is corresponds to the equivalent expression of (8x²+19x+4) + (3x + 2)(x - 5).
11x²-5x+13 is corresponds to the equivalent expression of (6x + 1)(3x - 7) - (7x²-34x-20)
What is expression?
Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Given expression no. 1 as :
⇒ (x²+15x+65) + (2x - 5) (3x +8).
⇒ x²+15x+65 + 6x²-15x+16x-40
⇒ 7x²+16x+25
Hence, the correct answer would be option (B).
Given expression no. 2 as :
⇒ (4x + 1)(3x - 4) - (5x²-10x-12)
⇒ 12x²+3x-16x-4 - 5x²+10x+12
⇒ 12x²-13x-4 - 5x²+10x+12
⇒ 7x²-3x+8
Hence, the correct answer would be option (D).
Given expression no. 3 as :
⇒ (8x²+19x+4) + (3x + 2)(x - 5).
⇒ (8x²+19x+4) + 3x²+2x-15x-10
⇒ 8x²+19x+4 + 3x²-13x-10
⇒ 11x²+6x-6
Hence, the correct answer would be option (A).
Given expression no. 4 as :
⇒ (6x + 1)(3x - 7) - (7x²-34x-20)
⇒ 18x²+3x-42x-7- 7x²+34x+20)
⇒ 11x²-5x+13
Hence, the correct answer would be option (C).
Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k. Two lines labeled f of x and g of x. Line f of x passes through points negative 4, 0 and negative 3, 1. Line g of x passes through points negative 4, 0 and negative 3, negative 2. Question 6Select one: a. −2 b. negative one half c. one half d. 2
As we can see, this is the equation of line `g(x)` that passes through the points `(-4,0)` and `(-3,-2)`. Therefore, the value of `k` is `2`.
The correct answer to the given question is option d.
We have the function `g(x) = k⋅f(x)`. The values of `f(x)` and `g(x)` are given as follows:
Line `f(x)` passes through points `(-4,0)` and `(-3,1)`.
Line `g(x)` passes through points `(-4,0)` and `(-3,-2)`.
Now, we have to determine the value of `k`.
Formula to find slope of a line is given by:(y2 - y1)/(x2 - x1)
Here, (x1, y1) = (-4, 0) and (x2, y2) = (-3, 1) for line f(x).
So, slope of line `f(x)` is given by:(1 - 0)/(-3 - (-4)) = 1
So, equation of line `f(x)` is given by:
y - y1 = m(x - x1) ⇒ y - 0 = 1(x - (-4)) ⇒ y = x + 4
Also, (x1, y1) = (-4, 0) and (x2, y2) = (-3, -2) for line g(x).
So, slope of line `g(x)` is given by:(-2 - 0)/(-3 - (-4)) = 2
So, equation of line `g(x)` is given by: y - y1 = m(x - x1) ⇒ y - 0 = 2(x - (-4)) ⇒ y = 2x + 8
Now, we can substitute the value of `k` and the equation of line `f(x)` to find the equation of line `g(x)`.
Let `k = 2`.
Then, `g(x) = k⋅f(x) = 2(x + 4) = 2x + 8`.
As we can see, this is the equation of line `g(x)` that passes through the points `(-4,0)` and `(-3,-2)`.
Therefore, the value of `k` is `2`. Hence, option (d) is the correct answer: `2`.
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Factor the quadratic equation
x^2-5x-25
Answer:
x^2-5x-25 doesnt factorise im very sorry, maybe check ur question
I’m giving 15 points for this one pls help
Answer:
A:(-1,0)
B:(0,5)
C:(2,9)
D:(5,0)
Step-by-step explanation:
count the x axis to get x and y axis to get y
(x,y)
Answer:
See below
Step-by-step explanation:
A is located at (-1,0) which is an x-intercept
B is located at (0,5) which is the y-intercept
C is located at (2,9) which is the vertex
D is located at (5,0) which is an x-intercept
Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found
he differences in the y-values as 7-1=6, 17-7= 10, and 31-17 = 14. Then he concluded that since the
Eifferences of 6, 10, and 14 are increasing by 4 each time, the function has a constant rate of change and is
near. What was Willis's mistake?
X
1
2
3
4
y
1
7
17
31
O He found the differences in the y-values as 7-1=6, 17-7= 10, and 31-17 = 14.
He determined that the differences of 6, 10, and 14 are increasing by 4 each time.
O He concluded that the function has a constant rate of change.
O He reasoned that a function that has a constant rate of change
Willis's mistake is assuming that a constant difference in the y-values implies a constant rate of change, which is not necessarily true for non-linear functions.
While it is true that a linear function will always have a constant rate of change, the converse is not true. A non-linear function can also have a constant difference in the y-values over a certain interval, but the rate of change is not constant. This is because the rate of change of a non-linear function varies at different points along the curve.
In this case, Willis did not consider the possibility of a non-linear function with a constant difference in the y-values. Therefore, his conclusion that the function is linear based on the constant differences in the y-values is not necessarily correct. To determine whether the function is linear or non-linear, Willis should have examined the differences in the x-values as well, or plotted the points on a graph to see if they lie on a straight line.
he yearly cost in dollars, y, at a video game arcade based on total game tokens purchased, x, is y = y equals StartFraction 1 Over 10 EndFraction x plus 60.x + 60 for a member and y = y equals StartFraction 1 Over 5 EndFraction x. x for a nonmember. Explain how the graph of a nonmember’s yearly cost will differ from the graph of a member’s yearly cost.
The key differences between the graphs of a nonmember's and a member's yearly cost lie in the slope, y-intercept, and the overall rate of increase in cost as the number of game tokens purchased increases.
The given equations represent the yearly cost in dollars for a member and a nonmember at a video game arcade based on the total game tokens purchased.
For a member:
y = (1/10)x + 60x + 60
For a nonmember:
y = (1/5)x
To understand how the graph of a nonmember's yearly cost differs from a member's yearly cost, let's analyze the equations and their characteristics.
Slopes:
The slope of the member's equation is (1/10), indicating that for every unit increase in the number of game tokens purchased (x), the yearly cost (y) for a member increases by 1/10 of a dollar. This means that the member's yearly cost increases at a slower rate compared to the nonmember's yearly cost.
The slope of the nonmember's equation is (1/5), which means that for every unit increase in the number of game tokens purchased, the yearly cost for a nonmember increases by 1/5 of a dollar. Therefore, the nonmember's yearly cost increases at a faster rate compared to the member's yearly cost.
y-intercepts:
For the member's equation, the y-intercept is 60, which represents the fixed cost component for being a member of the arcade. This means that even without purchasing any game tokens (x = 0), a member incurs a yearly cost of $60.
For the nonmember's equation, there is no additional fixed cost component. The y-intercept is 0, indicating that a nonmember has zero yearly cost if no game tokens are purchased (x = 0).
Overall cost:
The member's equation includes both a fixed cost component and a variable cost component, whereas the nonmember's equation only includes the variable cost component. This means that for any given number of game tokens purchased, the member's yearly cost will be higher than the nonmember's yearly cost.
Graphically, the member's equation will result in a line with a positive slope that intersects the y-axis at 60. The nonmember's equation will yield a line with a steeper positive slope that intersects the origin (0,0). The graph of the nonmember's yearly cost will rise more quickly than the graph of the member's yearly cost.
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find the coordinates of the points of intersection of the graph y=13-x with the axes. Find the area of the right triangle formed by this line and the coordinate axis
Answer:
Y(0,13)
X(13,0)
Half the members of a fishing tribe catch fish per day and half catch fish per day. A group of 10 members could build a boat for another tribe in 1 day and receive a payment of 45 fish for the boat. Part 2 a. Suppose the boat builders are drawn at random from the tribe. From the tribe's perspective, what is the expected cost of building the boat? enter your response here fish. (Enter your response as an integer.) Part 3 b. Now supposing that members are selected based on opportunity cost, the minimum cost that the boat could be built for is enter your response here fish. (Enter your response as an integer.)
a. From the tribe's perspective, the expected cost of building the boat when the boat builders are drawn at random from the tribe is 975 fish.
The number of members who catch fish per day is equal to the number of members who catch fish per day, which means that half of the tribe has a higher opportunity cost than the other half.
The expected cost can be calculated by multiplying the number of workers who catch fish per day by the daily cost of their fishing and adding this to the number of workers who catch fish per day multiplied by their daily cost of fishing.
b. When members are selected based on opportunity cost, the minimum cost that the boat could be built for is 450 fish. The cost of building the boat is equal to the opportunity cost of the members who build it, which is the value of their next best alternative.
Since the boat builders are drawn from the tribe with half the members catching fish per day and the other half catching fish per day, the minimum cost would be equal to the opportunity cost of the members who catch fish per day since their cost is higher than the other half of the tribe who catch fish per day. Therefore, the minimum cost would be 450 fish.
Half of the members catch fish per day, and half of the members catch fish per day. Hence the total cost of building the boat would be the summation of the costs of the members in the group.
For instance, the expected cost of building the boat can be calculated by multiplying the number of workers who catch fish per day by the daily cost of their fishing and adding this to the number of workers who catch fish per day multiplied by their daily cost of fishing.
In this case, the expected cost would be the cost of ten members who build the boat. Since each member is expected to contribute to the building of the boat, the total cost will be calculated as the summation of the cost of the members, which equals 975 fish.
Therefore, from the tribe's perspective, the expected cost of building the boat when the boat builders are drawn at random from the tribe is 975 fish.
The opportunity cost of building the boat is the value of the next best alternative.
When members are selected based on opportunity cost, the minimum cost that the boat could be built for is the opportunity cost of the members who build it. In this case, the members are drawn based on their fishing cost, meaning members with the lowest opportunity cost would be selected to build the boat.
Therefore, the minimum cost would be equal to the opportunity cost of the members who catch fish per day since their cost is higher than the other half of the tribe who catch fish per day. Hence the minimum cost of building the boat would be 450 fish.
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Imogen has 2 toy elephants and 7 toy bears in a box. She picks a toy at random and does not replace it. She then picks a second toy at random. Draw a tree diagram to work out the probability that the second toy she chooses will be a different type of animal to the first toy. Give your answer as a fraction in its simplest form.
The probability of choosing a different type of animal as the second toy is $\frac{7}{18}.
The problem is to draw a tree diagram to determine the probability of choosing a different type of toy animal when two toys are randomly selected. Imogen has two toy elephants and seven toy bears in a box.
It should be noted that a tree diagram is a visual tool that can be used to show the possible outcomes of a particular event. Each branch represents a possible outcome and the probabilities associated with each branch are assigned in the diagram. The steps involved in solving the problem are:
Step 1: Construct the tree diagram.
Step 2: Calculate the probability of choosing a different type of animal as the second toy. Step 3: Simplify the fraction. Solution:
Step 1: Construct the tree diagram. The tree diagram for the given problem is shown below. [asy] size(200); defaultpen(linewidth(0.7)); draw((0,0)--(2,-2),MidArcArrow(size=10)); draw((0,0)--(2,2),MidArcArrow(size=10)); draw((2,2)--(4,2),MidArcArrow(size=10)); draw((2,-2)--(4,-2),MidArcArrow(size=10)); draw((2,2)--(4,0),MidArcArrow(size=10)); draw((2,-2)--(4,0),MidArcArrow(size=10)); draw((4,2)--(6,2),MidArcArrow(size=10)); draw((4,0)--(6,0),MidArcArrow(size=10)); draw((4,-2)--(6,-2),MidArcArrow(size=10)); label("Elephant",(-1,0)); label("Bear",(-1,2)); label("Bear",(3,2)); label("Bear",(3,0)); label("Bear",(3,-2)); label("Elephant",(3,0)); label("Bear",(5,2)); label("Elephant",(5,0)); label("Bear",(5,-2)); [/asy] Step 2: Calculate the probability of choosing a different type of animal as the second toy. The total number of outcomes is 9, as there are 2 elephants and 7 bears. There are four possible ways in which Imogen can pick two different types of animal:
Elephant followed by bear, Bear followed by elephant, Elephant followed by elephant, and Bear followed by bear. The probability of choosing a different type of animal as the second toy is the sum of the probabilities of the first two outcomes, which is: $P(\text{different animal}) = \frac{2}{9}\times\frac{7}{8}+\frac{7}{9}\times\frac{2}{8}$ $=\frac{14}{72}+\frac{14}{72}$ $=\frac{28}{72}$
Step 3: Simplify the fraction. The fraction can be simplified by dividing the numerator and denominator by the highest common factor. The highest common factor of 28 and 72 is 4. Hence, $\frac{28}{72} = \frac{7}{18}$
Therefore, the probability of choosing a different type of animal as the second toy is $\frac{7}{18}$.
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The probability that the second toy Imogen chooses will be a different type of animal to the first toy is 7/18. This is calculated by determining the probability of picking an elephant then a bear, and the probability of picking a bear then an elephant, and adding these two probabilities.
Explanation:Firstly, let's define the event: Picking an elephant (E) and picking a bear (B). At the beginning, Imogen has 2 elephants and 7 bears in the box, making a total of 9 toys.
When Imogen picks the first toy, the probabilities are: P(E) = 2/9 and P(B) = 7/9. Then, Imogen picks the second toy, not replacing the first one.
So, we have two scenarios for the second pick: Given that the first pick was an elephant, the probabilities for the second pick are: P(E) = 1/8 (because one elephant left) and P(B) = 7/8 (there are still 7 bears). If the first pick was a bear, the probabilities for the second pick are: P(E) = 2/8 (still 2 elephants) and P(B) = 6/8 (one bear left).
Now, we're interested in the probability of picking two different types of animal toys. That will be the sum of the probabilities of picking an elephant then a bear, and the probability of picking a bear then an elephant. So it's (P(E) * P(B|E)) + (P(B) * P(E|B)) = (2/9 * 7/8) + (7/9 * 2/8) = 14/72 + 14/72 = 28/72 which reduces to 7/18.
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Selena and Drake are evaluating the expression (StartFraction r s Superscript negative 2 Baseline Over r squared s Superscript negative 3 Baseline EndFraction) Superscript negative 1, when r = negative 1 and s = negative 2.
Selena’s Work
Drake’s Work
(StartFraction r s Superscript negative 2 Baseline Over r squared s Superscript negative 3 Baseline EndFraction) Superscript negative 1 Baseline = (r Superscript negative 1 Baseline s) Superscript negative 1 Baseline = StartFraction r Over s EndFraction = StartFraction negative 1 Over negative 2 EndFraction = one-half
(StartFraction (negative 1) (negative 2) Superscript negative 2 Baseline Over (negative 1) squared (negative 2) Superscript negative 3 EndFraction) Superscript negative 1 = (StartFraction (negative 1) (negative 2) cubed Over (negative 1) squared (negative 2) squared EndFraction) Superscript negative 1 = (StartFraction negative 8 Over 4 Endfraction) Superscript negative 1 Baseline = StartFraction 4 Over negative 8 EndFraction = negative one-half
Who is correct and why?
Selena is incorrect because she should have substituted the values for the variables first, and then simplifed.
Selena is correct because she simplified correctly and then evaluated correctly after substituting the values for the variables.
Drake is incorrect because he should have simplified first, before substituting the values for the variables.
Drake is correct because he substituted the values for the variables first, and simplified correctly.
The correct option is that B. Selena is correct because she simplified correctly and then evaluated correctly after substituting the values for the variables.
How to explain the informationSelena is correct. She simplified correctly and then evaluated correctly after substituting the values for the variables. Drake is incorrect because he should have simplified first, before substituting the values for the variables.
When Drake substituted the values for the variables first, he ended up with the expression (StartFraction negative 8 Over 4 Endfraction) Superscript negative 1. This is incorrect because he did not simplify the expression first. If he had simplified first, he would have gotten the expression (StartFraction negative 2 Over 1 Endfraction) Superscript negative 1, which is equal to one-half.
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f(x) = =
Answer
x + 2
4
-x-2
Step 1 of 3: Evaluate this function at x = 3. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate
"Undefined".
if x < 3
if x ≥ 3
f(3) =
Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used.
Evaluating this function at f(3) = 5.
How to determine the If the function is undefined at the given valueTo evaluate the function f(x) = (x + 2)/(4 - x) at x = 3, we substitute x = 3 into the function:
f(3) = (3 + 2)/(4 - 3)
= 5/1
= 5
Therefore, f(3) = 5.
Evaluating this function at f(3) = 5.
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Trey made20000 in taxable income last year. suppose the income tax rate is 10% for the first $9500 plus 14% for the amount over $9500. How much must trey pay in income tax for last year?
Trey must pay $2420 in income tax for last year.
To solve this problemBased on the tax rates, we'll divide his taxable income into two halves.
The first portion is the minimal amount of Trey's taxable income between $9500 and $20,000 that is subject to a 10% tax rate. Consequently, the first component is $9500.
The second portion is the amount over $9500, which is $20,000 - $9500 = $10,500.
Now, let's calculate the tax for each portion:
Tax on the first portion (10% rate) = $9500 * 0.10 = $950.
Tax on the second portion (14% rate) = $10,500 * 0.14 = $1470.
We sum up the taxes on both portions to find Trey's total income tax:
Total income tax = Tax on the first portion + Tax on the second portion = $950 + $1470 = $2420.
So, Trey must pay $2420 in income tax for last year.
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Cómo se hace y cómo es el proceso ayuda porfaaaaa
Answer:
30: 100
31: -13
32: -45
33: 14
34: -32
35: -22
36: 17
scientific notation of 5,8×10⁴ +2,3 ×10⁵
The sum in scientific notation is 2.88 × 10⁰
To add numbers in scientific notation, we need to make sure the exponents are the same. Let's add 5.8 × 10⁴ and 2.3 × 10⁵.
First, we need to adjust the numbers so that they have the same exponent. We can do this by moving the decimal point.
5.8 × 10⁴ can be written as 0.58 × 10⁵ (moving the decimal point one place to the right).
Now, we have 0.58 × 10⁵ + 2.3 × 10⁵. Since the exponents are the same, we can add the coefficients:
0.58 + 2.3 = 2.88
The sum of the coefficients is 2.88. To express this in scientific notation, we need to adjust the decimal point and exponent.
Since we moved the decimal point one place to the right in 0.58 × 10⁵, we need to move it one place to the left in 2.88.
2.88 can be written as 0.288 × 10¹.
Therefore, the sum of 5.8 × 10⁴ and 2.3 × 10⁵ is 0.288 × 10¹.
In scientific notation, this can also be expressed as 2.88 × 10⁰ or simply 2.88.
So, the sum of 5.8 × 10⁴ and 2.3 × 10⁵ is 2.88.
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Question 7 of 40
What is the solution to the equation below?
-3+√√2x-1=8
OA. 36
OB.
B. J
C. 9
OD. 13
The solution to the equation is x = 61
What is the solution to the equation?From the question, we have the following parameters that can be used in our computation:
-3 + √(2x - 1) = 8
Add 3 to both sides of the equation
So, we have
√(2x - 1) = 11
Take the square of both sides
2x - 1 = 121
So, we have
2x = 122
Divide through by 3
x = 61
Hence, the solution is x = 61
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A news reporter wants to assess the top 30 college quarterbacks. The reporter recorded the number of plays and the number of passes a quarterback completed in one season.
This sample data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.
The correlation coefficient (r) between the number of plays and the number of passes completed by the top 30 college quarterbacks, using Excel, the correlation coefficient is approximately 0.83.
To calculate the correlation coefficient (r) between the number of plays and the number of passes completed by the top 30 college quarterbacks, you can use Excel. Here's a step-by-step guide:
Open Excel and enter the data for the number of plays in one column and the number of passes completed in another column. Ensure that the data is entered consistently, with the same row representing the same quarterback's data in both columns.
Select an empty cell where you want to display the correlation coefficient.
Use the CORREL function in Excel to calculate the correlation coefficient. The syntax for the CORREL function is: =CORREL(array1, array2). In this case, array1 represents the range of cells containing the number of plays, and array2 represents the range of cells containing the number of passes completed. For example, if the number of plays is in column A (A2:A31) and the number of passes completed is in column B (B2:B31), the formula would be: =CORREL(A2:A31, B2:B31).
Press Enter to calculate the correlation coefficient. The result will be displayed in the cell you selected.
Round the correlation coefficient to two decimal places using the ROUND function. The syntax for the ROUND function is: =ROUND(number, num_digits). In this case, number represents the correlation coefficient, and num_digits represents the number of decimal places to round to. For example, if the correlation coefficient is in cell C1, the formula would be: =ROUND(C1, 2).
By following these steps, you can use Excel to calculate the correlation coefficient (r) between the two data sets for the top 30 college quarterbacks.
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how do i do this I’ve been struggling for 45 minutes and i can’t seem to solve it…
Answer:
(a) start value = $45,000
(b) 4.6875 months exactly
======================================================
Explanation
Part (a)
I'll use x in place of t, and y in place of 'a'. The reason for this will be mentioned in part (b)
x = t = number of monthsy = a = account value in thousands of dollarsThe equation [tex]a = 45+75t-4t^2[/tex] turns into [tex]y = 45 + 75x - 4x^2[/tex] which rearranges to [tex]y = -4x^2+75x+45[/tex]
Let's plug in x = 0 so we can find the account value (variable y) at the very start.
[tex]y = -4x^2+75x+45\\\\y = -4*0^2+75*0+45\\\\y = 45\\\\[/tex]
The nice thing is any term involving x will go to zero, which leaves behind 45 at the end.
The initial value is $45,000. Recall that y is the value in thousands of dollars.
Think of it like saying 45*1000 = 45,000.
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Part (b)
The template for a general quadratic is [tex]y = ax^2+bx+c[/tex] which involves 'a', so that's why I swapped to x,y to avoid confusion.
That template is used to help complete the square to get a quadratic into vertex form.
Compare [tex]y = ax^2+bx+c[/tex] with [tex]y = -4x^2+75x+45[/tex] to find these values
a = -4b = 75c = 45Plug the first two items into the formula below
h = -b/(2a)
h = -75/(2*(-8))
h = 4.6875
This is the x coordinate of the vertex (h,k). It's the number of months it takes to reach the peak value.
-------------------
Extra info: If you plug x = 4.6875 back into the function, then you'll get y = 308.671875 which represents an account value of $308,671.88 (after rounding to the nearest penny). This is the investment's maximum value.
Solve for the value of c.
(2c-3)°
97°
Answer:
the value of c is 50°.
Step-by-step explanation:
To solve for the value of c in the equation (2c - 3)° = 97°, we can start by isolating the term with c.
First, we add 3 to both sides of the equation to get rid of the -3:
(2c - 3)° + 3 = 97° + 3
Simplifying the equation, we have:
2c° = 100°
Next, we divide both sides of the equation by 2 to solve for c:
(2c°)/2 = (100°)/2
Simplifying further, we have:
c° = 50°
which is equal to (sinx+cosx)^2+(sinx-cosx)^2 using identities?
The expression (sinx + cosx)^2 + (sinx - cosx)^2 simplifies to
4 + 2sinxcosx.How to simplify the identityTo simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 using trigonometric identities, we can expand and simplify the expression.
Expanding the squared terms
(sin^2x + 2sinxcosx + cos^2x) + (sin^2x - 2sinxcosx + cos^2x)
Using the trigonometric identity sin^2x + cos^2x = 1, we can simplify further:
(1 + 2sinxcosx + 1) + (1 - 2sinxcosx + 1)
Simplifying the expression, we have:
2 + 2sinxcosx + 2
Combining like terms, we get:
4 + 2sinxcosx
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What’s the answer for this one please show work!
Answer:
∠ MON = 51°
Step-by-step explanation:
∠ LON is composed of the 2 angles LOM and MON , that is
∠ LOM + ∠ MON = ∠ LON
42° + ∠ MON = 93° ( subtract 42° from both sides )
∠ MON = 51°
Answer:
<MON= 51°
Step-by-step explanation:
Look at the diagram and locate LON. You can see that LON is the angle of the complete line. Now LOM is given which is the angle of a part of the lines. So that means that to find MON we can minus LON with LOM.
<MON= <LON - <LOM
= 93-42
<MON= 51°
Feel free to ask any doubt you have!
find the 9th term of the geometric sequence. 12,36,108,...
The 9th term of the given sequence is 78732.
The given sequence is 12, 36, 108... is a geometric sequence with a common ratio of 3.To find the 9th term of the given sequence, we will use the formula for the nth term of a geometric sequence, which is given by:
aₙ = a₁rⁿ⁻¹
Here, a₁ = 12 and r = 3.
Therefore, the formula for the nth term becomes:
aₙ = 12(3)ⁿ⁻¹
Now, we need to find the 9th term of the sequence. Hence, n = 9. Substituting the values of a₁ and r, and n in the formula, we get:
a₉ = 12(3)⁹⁻¹= 12(3)⁸= 12(6561)= 78732
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Solve the inequality |4x + 5|-7> 12.
Select the graph of the solution set.
←
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2
+0+
-8 -7 -6 -5 -4 -3 -2 -1
H
O+
5
0 8 7 5 4 3 2 1 0 1 2 3 4
-8 -7
09
-5 -4
3
9
0 1 2 3
4
2
-3 -2 -1 01
5678
6.
7 8
5 6 7 8
+0+
3 4 5 6 7 8
Answer:
Bottom graph
Step-by-step explanation:
[tex]|4x+5|-7 > 12\\|4x+5| > 19\\\\4x+5 > 19\\4x > 14\\x > \frac{7}{2}\\\\4x+5 < -19\\4x < -24\\x < -6[/tex]
Therefore, the last graph is the correct answer
See attached for the math problem
The equations are R + P + D = 800, 3.5R + 4.25P + 4D = 2910 and R = P + D + 440
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let R represent the number of Regular gallons, P represent that of Premium and D represent that of Diesel.
A total of 800 gallons was sold, hence:
R + P + D = 800 (1)
Also:
$2910 was sold combined, therefore:
3.5R + 4.25P + 4D = 2910 (2)
440 more gallons of regular was sold, hence:
R = P + D + 440 (3)
The equations are R + P + D = 800, 3.5R + 4.25P + 4D = 2910 and R = P + D + 440
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What is the probability that both events B and C will occur?
The probability that both events B and C will occur is:
P(B and C) = 9/20
What is the probability that both events B and C will occur?Probability is the likelihood of an event to occur. It is expressed as a number in the range from 0 to 1.
The probability of an impossible event is 0, that of an event that is certain to occur is 1.
We have:
The probability that event B will occur, P(B) = 3/4
The probability that event C will occur, P(C) = 3/5
The probability that both events B and C will occur is:
P(B and C) = P(B) × P(C)
P(B and C) = 3/4 × 3/5
P(B and C) = 9/20
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Which order pair is not a solution to
The ordered pair which is not a solution to the inequality y - 3x < 10 is (-6,0).
Which ordered pair is not a solution to the inequality?Given the inequality in the question:
y - 3x < 10
Given the ordered pairs: (0,-4), (0,-1), and (-6,0). To determine which ordered pair is not a solution, we need to plug the values into the inequality and check.
For (0,-4):
y - 3x < 10
Plug in x = 0 and y = -4
-4 - 3(0) < 10
-4 < 10
True: -4 is less than 10.
For (0,-1):
y - 3x < 10
Plug in x = 0 and y = -1
-1 - 3(0) < 10
-1 < 10
True: -1 is less than 10.
For (-6,0):
y - 3x < 10
Plug in x = -6 and y = 0
0 - 3(-6) < 10
18 < 10
False: 18 is Not less than 10.
Therefore, (-6,0) is not a solution to the inequality.
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Nigerian coffee costs $4.25 per 8 ounces at The Daily Grind while Bolivian coffee costs $4.50 per 8 ounces. A 50-pound mixture of these two coffees will cost $8.75 per pound. How many pounds of each kind of coffee is needed for the coffee.
Let [tex]x[/tex] be the number of pounds of Nigerian coffee and [tex]y[/tex] be the number of pounds of Bolivian coffee.
We can set up a system of equations to represent the given information:
The cost of x pounds of Nigerian coffee is [tex]\$4.25/8\: \text{oz} \times 16\: \text{oz/lb} \times x\: \text{lb} = \$17x[/tex].The cost of y pounds of Bolivian coffee is [tex]\$4.50/8\: \text{oz} \times 16\: \text{oz/lb} \times y\: \text{lb} = \$18y[/tex].The cost of the 50-pound mixture is [tex]\$8.75/\text{lb} \times 50\: \text{lb} = \$437.50[/tex].The total weight of the mixture is [tex]x + y = 50\:\text{ lb}[/tex].So we have the following system of equations:
[tex]\qquad\quad\begin{aligned} 17x + 18y &= 437.50 \\ x + y &= 50 \end{aligned}[/tex]
Solving this system of equations, we get:
[tex]\qquad\qquad\quad\begin{aligned} x &= 12.5 \\ y &= 37.5 \end{aligned}[/tex]
[tex]\therefore[/tex] We need 12.5 pounds of Nigerian coffee and 37.5 pounds of Bolivian coffee for the mixture.
[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]
(ノ^_^)ノ [tex]\large\qquad\qquad\qquad\rm 06/21/2023[/tex]
True/False: 0.5% = 5/100
Reason:
0.5% = 0.5/100 = 5/1000
or you could say
5/100 = 0.05 = 5%
Discuss whether f(x)=x^2 increases or decreases when x>1
We can conclude that the function f(x) = x² is increasing when x > 1.The given function is f(x) = x². You need to determine whether this function is increasing or decreasing when x > 1.
To do this, we can find the derivative of the function and evaluate it for x > 1.If the derivative is positive, then the function is increasing, and if it is negative, then the function is decreasing.
The derivative of the function f(x) = x² is given by:f '(x) = 2x
We can see that the derivative is always positive when x > 1, as 2x is always positive for x > 0.Therefore, we can conclude that the function f(x) = x² is increasing when x > 1.
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