For the given mathematical statements:
For L: n represents jerry's run time.
For M: n represents the age of his father.
For N: n represents amount her sister has.
For O: n represents age of his younger brother.
To write the variables n represents each expression,
Take the following steps:
→ Identify the variable in each expression.
→ Determine what the variable represents by looking at the context of the problem and the information provided in the expression.
→ Write down the meaning of the variable for each expression.
Therefore,
L. Lisa can run the 100-yard dash 5 seconds faster than Jerry. Lisa's time is n-5 seconds.
Here,
n represents jerry's run time.
M: Pedro is 3 times younger than his father. Pedro is n + 3 years old.
Here,
n represents the age of his father,
N: Lucia has $10.00 less than her sister. Lucia has n-10 dollars.
Here,
n represents amount her sister has.
O: Jack is 2 times taller than his younger brother. Jack is 2 x n inches tall.
Here,
n represents age of his younger brother.
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3. A website is offering a promotion, during which customers can buy up to 100 photos for a flat fee. The
cost per photo varies inversely with the number of photos a customer buys, as shown in the table below.
What function models the data?
To determine the function that models the data, we need to analyze the relationship between the cost per photo and the number of photos a customer buys. From the given information, we can observe that the cost per photo varies inversely with the number of photos. This implies that as the number of photos increases, the cost per photo decreases, and vice versa.
To model this relationship, we can use the inverse variation equation, which can be expressed as:
y = k/x
Here, y represents the cost per photo, x represents the number of photos, and k is the constant of variation.
Let's examine the data given in the table to find the value of k:
Number of Photos (x) Cost per Photo (y)
10 10
25 4
50 2
100 1
We can see that as the number of photos increases, the cost per photo decreases. We can use any pair of values from the table to solve for k. Let's choose the pair (50, 2):
2 = k/50
Solving for k:
k = 2 * 50 = 100
Now that we have the value of k, we can write the function that models the data:
y = 100/x
Therefore, the function that models the data is y = 100/x, where y represents the cost per photo and x represents the number of photos a customer buys.
If lines 1, m, and n are parallel,
AB= 8, BC = 5, and DE = 10,
what is the length of EF ?
B
C
A
D
E
LL
·1
m
n
The value of length of EF is,
⇒ EF = 6.25
We have to given that,
Here, lines 1, m, and n are parallel,
And, AB = 8, BC = 5, and DE = 10,
Now, By using proportionality theorem we get;
⇒ AB / AC = DE / DF
Substitute all the values, we get;
⇒ 8 / (8 + 5) = 10 / (10 +EF)
⇒ 8 / 13 = 10 / (10 + EF)
⇒ 8 (10 + EF) = 10 × 13
⇒ 80 + 8EF = 130
⇒ 8 EF = 130 - 80
⇒ 8 EF = 50
⇒ EF = 50 / 8
⇒ EF = 6.25
Therefore, The value of length of EF is,
⇒ EF = 6.25
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write equation in slope intercept form
In slope intercept form, the line's equation is y = 2x + 1. We must apply the formula y = mx + b to formulate an equation in slope intercept form. The slope of the line is represented by m, while the y-intercept is represented by b.
We need two locations on the line to find the slope. Assume we have points (2,5) and (4,9). We may calculate the slope using the following formula:
m = (9 - 5) / (4 - 2) m = (9 - 5) / (4 - 2)
m = 2
As a result, the slope of the line is 2.
We must now identify the y-intercept, which is the point at where the line crosses the y-axis.
We can utilise one of the points we already have to discover this. Let's start with (2,5).
y = mx + b
5 = 2(2) + b
5 = 4 + b
b = 1
As a result, the y-intercept is 1.
Now we can enter the numbers we discovered for m and b into the formula:
y = mx + b
y = 2x + 1
As a result, the slope intercept form equation of the line is y = 2x + 1.
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Find sin ø
Triangle side=16 side =20 base =12
Answer:
C. 16/20
Step-by-step explanation:
Given:
Perpendicular = 16 Hypotenuse = 20Base = 12To find:
Sine Theta
Sine of Theta is defined as the ratio of the perpendicular to the hypotenuse.
In this case, the perpendicular is 16 and the hypotenuse is 20.
Sin theta : Perpendicular/Hypotenuse
Therefore, Sin Theta = 16/20
Select the correct answer. Over which interval of the domain is function m negative? A linear function of a solid diagonal line intercepts y-axis at (0, 4) and x-axis at (6, 0) A. B. C. D.
In interval notation, this can be written as (0, 6), which corresponds to option A.
To determine over which interval of the domain the function is negative, we need to examine the behavior of the linear function between the x-axis intercept and the y-axis intercept.
Given that the linear function intersects the y-axis at (0, 4) and the x-axis at (6, 0), we can calculate the slope of the line using the formula:Slope = (change in y) / (change in x) = (0 - 4) / (6 - 0) = -4 / 6 = -2/3
Since the slope of the line is negative, we know that the function is decreasing as x increases. Therefore, the function is negative over the interval of the domain where x is greater than 0 and less than 6, excluding the endpoints.O
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x = 12 log 8x ( Find the value of x.?
The value of x that satisfies the equation x = 12 log₆ (8x) is x = 0.
We have,
To find the value of x in equation x = 12 log₆ (8x), we can solve it algebraically.
Here's how:
Start by isolating the logarithm term by dividing both sides of the equation by 12:
x/12 = log₆ (8x)
Now, rewrite the logarithmic equation in exponential form:
6^(x/12) = 8x
Apply the properties of exponents to simplify the equation further:
(2^3)^(x/12) = (2^3)^x
2^(3x/12) = 2^(3x)
Since the bases are equal, we can equate the exponents:
3x/12 = 3x
Next, cross-multiply to get rid of the fraction:
3x = 12 * 3x
Simplify:
3x = 36x
Subtract 36x from both sides:
3x - 36x = 0
Simplify:
-33x = 0
Divide both sides by -33:
x = 0
Therefore,
The value of x that satisfies the equation x = 12 log₆ (8x) is x = 0.
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division of a whole number by zero is ____
Answer: not defined/undefined
Step-by-step explanation:
a whole number cannot be divided by zero, thus the answer will always be undefined
A computer costs £968. A tax of 16.5% is then added to the cost of the computer. Work out the amount of tax that is added to the cost of the computer.
The amount of tax that is added to the cost of the computer is 159.72
How to determine the amount of tax that is added to the cost of the computer.From the question, we have the following parameters that can be used in our computation:
Computer cost = 968
Tax percentage = 16.5%
Using the above as a guide, we have the following:
Tax amount = Computer cost * Tax percentage
substitute the known values in the above equation, so, we have the following representation
Tax amount = 968 * 16.5%
Evaluate
Tax amount = 159.72
Hence, the amount of tax that is added to the cost of the computer is 159.72
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In ΔVWX, w = 680 cm, ∠X=80° and ∠V=32°. Find the area of ΔVWX, to the nearest 10th of a square centimeter.
Write the comparison using <, >, or =.
Z 3 pounds
32 ounces
14 pounds
40 ounces
1,000 pounds
1 ton
4,000 pounds
1 pound and 5 ounces
1.5 pounds
2 tons
28 ounces
25 ounces
3 pounds 32 ounces < 14 pounds 40 ounces
1,000 pounds = 1 ton
1 pound and 5 ounces < 1.5 pounds
2 tons = 4,000 pounds
28 ounces > 25 ounces
What are the values in the compared weights?The comparison of the values of the given weights is as follows:
3 pounds 32 ounces < 14 pounds 40 ounces
This is because there are fewer pounds and ounces in 3 pounds 32 ounces compared to 14 pounds 40 ounces.
1,000 pounds = 1 ton
This is because 1,000 pounds is equal to 1 ton.
1 pound and 5 ounces < 1.5 pounds
This is because 1 pound and 5 ounces is less than 1.5 pounds.
2 tons = 4,000 pounds
This is because 2 tons is equal to 4,000 pounds.
28 ounces > 25 ounces
This is because 28 ounces is greater than 25 ounces.
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Complete question:
Write the comparison using <, >, or =.
3 pounds 32 ounces vs 14 pounds 40 ounces
1,000 pounds vs 1 ton
1 pound and 5 ounces vs 1.5 pounds
2 tons vs 4,000 pounds
28 ounces vs 25 ounces
If you can afford to pay back $250 each month for 20 years at 7½%, how much could you afford to borrow?
One could afford to borrow $34,892.
How much could be afford to borrow?To calculate the loan amount one could afford, we will use formula for the present value of an annuity. The formula is [tex]PV = PMT * [(1 - (1 + r)^{-n}) / r][/tex]
Plugging values:
PV = $250 × [(1 - (1 + 0.625%)^(-240)) / 0.625%]
PV ≈ $250 × [1 - (1 + 0.00625)^(-240)] / 0.00625]
PV ≈ $250 × [1 - 0.1277] / 0.00625]
PV ≈ $250 × 0.8723 / 0.00625]
PV ≈ $34,892.
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invests $8,505 in a retirement
account with a fixed annual interest rate of
8% compounded continuously. How long
will it take for the account balance to
reach $42,125.54?
The time it will take for the account balance to reach $42,125.54 is 20 years.
What is the time taken to reach the sum?The time it will take for the account balance to reach $42,125.54 is calculated by applying the following formula.
[tex]A = Pe^{rt}[/tex]
where;
A is the final account balance = $42,125.54P is the initial investment = $8,505r is the annual interest rate = 8% = 0.08t is the time in yearsThe time it will take for the account balance to reach $42,125.54 is calculated as;
42,125.54 = 8,505 e^(0.08t)
42,125.54 / 8,505 = e^(0.08t)
4.953 = e^(0.08t)
Take ln of both sides;
ln(4.953) = 0.08t
1.6 = 0.08t
t = 1.6 / 0.08
t = 20 years
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find domain and range?Type in the answer in interval notation. Example: [2,5)
Use U for union to combine intervals. Example: (-oo,2] U [4,oo)Enter DNE for an empty set. For the infinity symbol
, type oo (two lowercase o's)
The domain and range of the given function are Domain: (−∞,∞),{x|x∈R} and Range: [−2,∞),{y|y≥−2}.
A polynomial function of the form f(x) = ax² + bx + c is called a quadratic function. We already know that the x-intercepts of a quadratic function are given by the quadratic formula (or can be found by factoring). In this worksheet we learn that the graph of any quadratic function is a parabola.
From the given graph, the vertex is (0, -2).
So, the quadratic equation is f(x)=x²-2.
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (−∞,∞),{x|x∈R}
Range: [−2,∞),{y|y≥−2}
Therefore, the domain and range of the given function are Domain: (−∞,∞),{x|x∈R} and Range: [−2,∞),{y|y≥−2}.
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A lottery game contains 29 balls numbered 1 through 29. What is the probability of choosing a ball numbered 30?
The probability of choosing a ball numbered 30 is determined as 0.
What is probability?The probability of an event is a number that indicates how likely the event is to occur.
Also we can defined probability as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Mathematically, the formula for probability is given as;
Probability = number of favorable outcomes / total number of outcomes of an event.
In the given question;
the desired outcome = 30the total possible outcome = 1 to 29There are zero 30 between 1 to 29.
Probability = 0 / 29
Probability = 0
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1. Discuss ONE current issue which relates to Malaysian Public Sector Accounting. Your issues should be registered in MMLS and should be different from others. Your answer should include the detail of issue and recommendation to the issue highlighted.
One current issue which relates to Malaysian Public Sector accounting is Political support and willingness of the key stakeholders to initiate and carry out the reform.
What is public sector accounting?Public sector accounting is a process used by government agencies and municipalities to record financial transactions. It focuses on tracking funds generated from tax revenues and expenditures related to projects or appropriations.
The issue is Political support and willingness of the key stakeholders to initiate and carry out the reform.
This, in some cases, might imply the support from the highest level of authorities, such as a President or a Prime Minister. In most of the cases, the Ministry of Finance (MoF) assumes the leading role in PSA reform implementation. Other key players, including the Treasury, Supreme Audit Institutions, and Professional Accounting Organizations (PAO), need to be also identified and involved to ensure the success of the reform process.
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Mr Anil bought some American dollars for Rs 540000 at the exchange rate of 1$=Rs 120 to visit USA. Unfortunately, because of his Visa Problem, he cancelled his trip. Within a week Nepali rupee is devaluated by 5%.He again exchanged his dollars to Nepali rupee after a week. a) How many dollars did he get with Rs 540000? b) What is the new exchange rate after devaluation in Nepali rupee? c) How much did he gain or lose? d) After devaluation of Nepali rupee, if the bank took 2% commission, how many rupee would he gain or lose?
Answer: a) To find out how many dollars Mr Anil got with Rs 540,000, we'll divide the amount in Nepali rupees by the exchange rate.
Exchange rate: 1$ = Rs 120Amount in Nepali rupees: Rs 540,000Number of dollars = Amount in Nepali rupees / Exchange rateNumber of dollars = 540,000 / 120Number of dollars = 4,500Therefore, Mr Anil got 4,500 dollars with Rs 540,000.
b) After the devaluation of the Nepali rupee by 5%, the new exchange rate would be 5% less than the previous rate.
New exchange rate = Previous exchange rate - (Previous exchange rate * 5%)
New exchange rate = 120 - (120 * 0.05)New exchange rate = 120 - 6New exchange rate = 114The new exchange rate after the devaluation is 1$ = Rs 114.
c) To calculate how much Mr Anil gained or lost, we need to compare the initial exchange rate with the new exchange rate.
Initial exchange rate: 1$ = Rs 120New exchange rate: 1$ = Rs 114Gained or lost = Number of dollars * (New exchange rate - Initial exchange rate)
Gained or lost = 4,500 * (114 - 120)Gained or lost = 4,500 * (-6)Gained or lost = -27,000Mr Anil lost 27,000 rupees due to the devaluation of the Nepali rupee.
d) If the bank took a 2% commission on the transaction, we need to calculate the commission amount and adjust the gain or loss accordingly.
Commission amount = Number of dollars * (Commission rate)Commission amount = 4,500 * (0.02)Commission amount = 90Adjusted gain or loss = Gained or lost - Commission amountAdjusted gain or loss = -27,000 - 90Adjusted gain or loss = -27,090
After the devaluation of the Nepali rupee and considering the 2% commission, Mr Anil would lose 27,090 rupees.
Two coins are tossed. What is the probability of both coins landing on heads?
The probability of both coins landing on heads when two coins are tossed is 1/4, or 0.25, or 25%.
When two coins are tossed, there are four possible outcomes: both coins can land on heads (HH), both coins can land on tails (TT), the first coin can land on heads and the second coin on tails (HT), or the first coin can land on tails and the second coin on heads (TH).
Since we are interested in the probability of both coins landing on heads, we need to determine the number of favorable outcomes (HH) out of the total number of possible outcomes.
Out of the four possible outcomes, only one outcome is favorable (HH). Therefore, the probability of both coins landing on heads is 1 out of 4.
In fraction form, this can be written as 1/4. The probability can also be expressed as a decimal, which is 0.25, or as a percentage, which is 25%.
It's important to note that in this case, we assume that the coins are fair and unbiased, meaning that the probability of landing on heads is equal to the probability of landing on tails, which is 1/2 or 0.5 for each coin individually.
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Kenneth walks 2 miles in 40 minutes. What is his speed?
Kenneth's speed given that he was able to walk 2 miles in 40 minutes was 0. 05 miles per minute.
How to find the speed ?To calculate Kenneth's speed, there is a need to divide the distance he walked by the time it took. This would show how fast he was walking such that he could cover the distance in that time.
Kenneth walked 2 miles in 40 minutes.
His speed was therefore:
Speed = Distance / Time
Speed = 2 miles / 40 minutes
Speed = 0. 05 miles per minute
In conclusion, Kenneth's speed is 0. 05 miles per minute.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
A and C. Hope this helps!
Please answer the problem in the picture below.
Answer:
C) 6 cm.
Step-by-step explanation:
Let's define some variables.
Let AH = h, MH = x.
The attached file is a drawing of the givens.
A triangle's area is found using the formula [tex]A = \frac{b \times h}2[/tex], where:
A = The area of the triangle
b = The base of the triangle
h = The height of the triangle (In our case, AH)
We'll use the given lengths and area of triangle TAH to find the height:
[tex]12 = \frac{8 \times h}2\\12 = 4h\\h = 3[/tex]
We will now do the same but with triangle MAH to find MH:
[tex]9 = \frac{3 \times x}2\\18 = 3x\\x = 6[/tex]
The length of MH is 6 cm.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
C
Step-by-step explanation:
I hope this helps!
Answer:
C.) a great circle
Step-by-step explanation:
100 Points! Algebra question. Photo attached. Thank you!
The population mean weight of the packages is 6.74 pounds and the population proportion of packages that weigh less than 5 pounds is approximately 0.301.
To calculate the population mean, we need to multiply each weight value by its corresponding frequency (number of packages), sum up these products, and divide by the total number of packages.
Population mean = Sum of (Weight × Packages) / Total number of packages
Population mean = 1967.5 / 292
Population mean = 6.74 pounds
To find the population proportion of packages that weigh less than 5 pounds, we need to sum up the frequencies (packages) of weights less than 5 pounds and divide it by the total number of packages.
Packages with weight less than 5 pounds: 5 + 16 + 28 + 22 + 17 = 88
Population proportion = Packages with weight less than 5 pounds / Total number of packages
Population proportion = 88 / 292
Population proportion = 0.301
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Neighbor Jim will give her a board that he says is 8 and 1/2 feet long. Neighbor Malia will give her two boards that she says are each 126 inches long. What is the total combined length of lumber Jenna has received?
The Jenna has entered a total concerted length of timber that measures 354inches.
To calculate the total concerted length of timber Jenna has entered, we need to convert all the measures to a harmonious unit.
Let's convert the measures to elevation for easier computation. Neighbor Jim's board is 8 and1/2 bases long, which is equal to8.5 bases. Since there are 12 elevation in a bottom, the length of Jim's board in elevation is8.5 * 12 = 102 elevation.
Neighbor Malia has two boards, each measuring 126 elevation. Now we can add up the lengths of all the boards to find the total concerted length.
Total combined length = Jim's board length Malia's board length Malia's board length = 102 elevation 126 elevation 126 elevation = 354 elevation.
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please answer in steps
Answer:
(2x + 21)/24
Step-by-step explanation:
To add or subtract functions, a common denominator must be achieved. We can do this by multiplying the numerator and denominator of the first term by 2 and the numerator/denominator of the second term by 3 so the denominator for both terms is 24.
(4x + 3)2/24 - (2x + 5)3/24
Now, simplify the expression
(8x + 6 - 6x + 15)/24
(2x + 21)/24
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
Los Angeles, 479,689.21, 46.9
Step-by-step explanation:
A: 1,356,000/372.4 v.s. 3,884,000/503 = Los Angeles
B: 479,689.21 or 4,729.1 * 100.1
C: 837,442/17,855=46.9
what number represents the same amount as 2 hundreds + 12 tens + 6 ones ?
Answer:
326
Step-by-step explanation:
The value of the given expression is 326.
Given:
The given expression 2 hundreds + 12 tens + 6 ones.
To find:
The value of the given expression.
Explanation:
The numeric form of given expression is:
2 hundreds + 12 tens + 6 ones
2 hundreds + 12 tens + 6 ones
2 hundreds + 12 tens + 6 ones
Therefore, the value of the given expression is 326.
a) Share £5 in the ratio 2 : 3
b) Share £50 in the ratio 2:3
c) Share £500 in the ratio 2 : 3
Which of the following is a solution to the equation x2=−144
?
Answer:
There is no real solution
Step-by-step explanation:
Square numbers are never negative
Answer:
D. This equation has no real solution
Step-by-step explanation:
Because a squared number can not be negative
If it were x^2=144 the answer could be 12 or-12
Which equation is represented by the graph?
A:
y= (£-1)+3
B:
4=(¢- 32+1
C:
9=-¢+32_1
D:
4=-¢- 32+1
Answer:
C: y = -(x +3)² -1
Step-by-step explanation:
You want the vertex-form equation of the parabola with vertex (-3, -1) and opening downward.
Vertex formFor vertex (h, k), the vertex form equation of a parabola is ...
y = a(x -h)² +k
Given that (h, k) = (-3, -1), the equation will have the form ...
y = a(x -(-3))² + (-1)
y = a(x +3)² -1 . . . . . . . . . . matches choice C
The value of 'a' will be negative when the parabola opens downward. Here, its value is -1.
y = -(x +3)² -1
__
Additional comment
Once you identify the left-shift of 3 units as resulting in an equation with (x +3)² as a component, you can make the appropriate answer choice without considering anything else. Of course, the fact that the curve opens downward immediately eliminates choices A and B.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
D. 9 in
Step-by-step explanation:
The volume of a sphere is given by the formula[tex]\bold{ V = \frac{4}{3} \pi r^3}[/tex] where r is the radius of the sphere.
In this case, we know that the volume is[tex] 972\pi[/tex] cubic inches.
Substituting this into the formula, we get:
[tex]972\pi = \frac{4}{3} \pi r^3[/tex]
Dividing both sides by π, we get:
[tex]972 = \frac{4}{3} r^3[/tex]
Multiplying both sides by [tex]\frac{3}{4}[/tex], we get:
[tex]729 = r^3[/tex]
Taking the cube root of both sides, we get:
r = 9
Therefore, the radius of the sphere is 9 inches.
