Answer:
To calculate the monthly payment for each option, we can use the loan formula:
Payment = (P * r) / (1 - (1 + r)^(-n))
where P is the principal amount, r is the monthly interest rate, and n is the total number of payments.
For Option A, the principal amount is $60,000, the interest rate is 4% per year, and the loan term is 10 years. We first need to convert the annual interest rate to a monthly interest rate:
r = 4% / 12 = 0.00333333 (rounded to 8 decimal places)
n = 10 years * 12 months/year = 120 months
Using the loan formula, we get:
Payment = (60000 * 0.00333333) / (1 - (1 + 0.00333333)^(-120)) = $630.55
Therefore, the monthly payment for Option A is $630.55.
For Option B, the principal amount is also $60,000, the interest rate is 3% per year, and the loan term is 20 years. We convert the annual interest rate to a monthly interest rate:
r = 3% / 12 = 0.0025 (rounded to 4 decimal places)
n = 20 years * 12 months/year = 240 months
Using the loan formula, we get:
Payment = (60000 * 0.0025) / (1 - (1 + 0.0025)^(-240)) = $342.61
Therefore, the monthly payment for Option B is $342.61.
To calculate the total amount paid over the life of the loan for each option, we simply multiply the monthly payment by the total number of payments:
For Option A, the total amount paid = $630.55 * 120 months = $75,665.92
For Option B, the total amount paid = $342.61 * 240 months = $82,226.40
To calculate the total interest paid over the life of the loan for each option, we subtract the principal amount from the total amount paid:
For Option A, the total interest paid = $75,665.92 - $60,000 = $15,665.92
For Option B, the total interest paid = $82,226.40 - $60,000 = $22,226.40
Therefore, Option A has a lower monthly payment and total amount paid over the life of the loan, but Option B has a longer loan term and a lower interest rate, resulting in a higher total interest paid over the life of the loan
A cash prize of $3800 is to be awarded at a fundraiser. If 1900 tickets are sold at $4 each, find the expected value. Round your answer to the nearest cent
The expected value is dollars.
Answer:
The total amount of money collected from selling tickets is: 1900 tickets × $4/ticket = $7,600 Since the cash prize is $3,800, the expected value can be calculated as follows: Expected value = (Probability of winning) × (Cash prize) + (Probability of losing) × (Cost of ticket) The probability of winning is 1 out of 1900 tickets sold, or 1/1900. The probability of losing is 1899/1900. So, the expected value is: (1/1900) × $3,800 + (1899/1900) × $4 = $1.999 Rounding to the nearest cent, the expected value is $2.00.
(p^2n^1/2)^0
√ p^5n^4 equivalent to p^18n^6 √p?
The two expressions are not equivalent.
To simplify the expression (p^2n^1/2)^0 √ p^5n^4, we first need to understand the properties of exponents and radicals.
Recall that any number raised to the power of zero is equal to 1, so (p^2n^1/2)^0 = 1.
Next, we can simplify the radical term by multiplying the exponents inside and outside the radical:
√ p^5n^4 =
(p^5n^4)^(1/2)
= p^(5/2)n^(4/2)
= p^(5/2)n^2
Combining this result with the previous step, we have:
(p^2n^1/2)^0 √ p^5n^4
= 1 * p^(5/2)n^2
= p^(5/2)n^2
This is not equivalent to p^18n^6 √p. In fact, p^(5/2)n^2 cannot be simplified any further without additional information about the expression. ,
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15. For the following testing problems, H_0: mu=10, H_a: mu not equal 10. n=25, sigma-3, sample mean xbar =11. The Z-value is: 3.41 1.67 0.105 1.15
H_0: mu=10, H_a: mu not equal 10. n=25, sigma-3, sample mean xbar =11. The Z-value is 1.67. Option B
How to calculate the Z-valueTo calculate the Z-value, we can use the formula:
Z = (xbar - mu) / (sigma / sqrt(n))
Where xbar is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.
Given:
H_0: mu = 10
H_a: mu ≠ 10
n = 25
sigma = 3
xbar = 11
We can plug in the values and get:
Z = (11 - 10) / (3 / sqrt(25))
Z = 5/3
Therefore, the Z-value is 1.67.
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I am lost this question. Please help!
Answer:
3p^3
pq
There is probably more
Step-by-step explanation:
question in picture thank you
The correct equation is: 5/6 - 1/6 = 4/6
What you mean by term Number line ?A number line is a visual representation of numbers, ordered from left to right, where each point on the line corresponds to a number. The number line can be used to represent a wide range of numbers, including integers, fractions, decimals, and even negative numbers.
On a basic number line, 0 is located in the center, with positive numbers to the right and negative numbers to the left. The numbers are usually evenly spaced, with tick marks or dots indicating each value. The distance between any two points on the number line represents the difference between the corresponding numbers.
According to question Option D is correct
This is because starting at 5/6 and ending at 1/6 involves moving in the negative direction on the number line. To find the distance between these two points, we need to subtract the smaller number (1/6) from the larger number (5/6).
So, 5/6 - 1/6 = 4/6, which simplifies to 2/3. This means that the distance between 5/6 and 1/6 on the number line is 2/3.
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Topic: Break even (1)
Crystal Clear is concerned about the recent rise in the price of aluminium - the metal from
which the business make the frames for its greenhouses. This price rise has meant that the
firm's variable costs have risen from £60 to £100 per small greenhouse. Fixed costs and the
selling price per unit however, have remained unchanged.
Q3
Activity: Calculate:
a) the percentage change in the firm's variable costs (give your answer to two decimal places)
b) the new number of Crystal Clear's smallest greenhouses that would need to be sold per
month for the business to break even
our workings:
Answer:
a) the percentage change in the firm's variable costs is 66.67%.
b) Crystal Clear would need to sell 200 of its smallest greenhouses per month to break even.
Step-by-step explanation:
a) The percentage change in variable costs can be calculated using the formula:
((New Value - Old Value) / Old Value) * 100%
Substituting the values, we get:
((£100 - £60) / £60) * 100% = 66.67%
Therefore, the percentage change in the firm's variable costs is 66.67%.
b) The break-even point is the point at which the total revenue equals total costs. The total cost is the sum of fixed costs and variable costs.
Let's assume that the fixed costs for Crystal Clear are £10,000 per month. Then, the total cost can be calculated as:
Total Cost = Fixed Cost + (Variable Cost per unit * Number of units)
We can rearrange this formula to find the number of units:
Number of units = (Fixed Cost + Total Cost) / Variable Cost per unit
At the break-even point, the total revenue equals the total cost. Let's assume that the selling price per unit is £150. Then, the break-even point can be calculated as:
Total Revenue = Total Cost
Number of units * Selling Price per unit = Fixed Cost + (Variable Cost per unit * Number of units)
Number of units * £150 = £10,000 + (£100 * Number of units)
Number of units * (£150 - £100) = £10,000
Number of units = £10,000 / £50
Number of units = 200
Therefore, Crystal Clear would need to sell 200 of its smallest greenhouses per month to break even.
7. Manoj and his younger sister Sandhya had their birthday yesterday i.e. Saturday, 15 th February, 2003. They were both born on Saturday. The sum of their ages is 23. Find their dates of birth.
Answer:
to find the date of birth from the age, you need to subtract the number of years and days from the current date. In this case, the current date is 15 February 2003. The sum of their ages is 23, which means that Manoj and Sandhya have a difference of 23 years between their dates of birth. Since they were both born on Saturday, their dates of birth must be on the same day of the month. Therefore, we can assume that Manoj was born on 15 February 1980 and Sandhya was born on 15 February 2003. This is one possible solution, but there may be other solutions depending on the leap years and calendar changes.
Answer:
The dates of birth of Manoj and Sandhya are February 15th, 1981 and February 15th, 1979 respectively.
Step-by-step explanation:
Let's use a system of equations to solve the problem.
Let M be Manoj's age and S be Sandhya's age. We know that their ages sum up to 23, so:
M + S = 23
We also know that they were both born on a Saturday, which means their birthdays fall on the same day of the week. In 2003, February 15th was a Saturday, so we can assume that they were born on February 15th in different years. Let's represent the year of Manoj's birth as M_year and the year of Sandhya's birth as S_year.
Since they were both born on a Saturday, we know that the year of Manoj's birth plus his age (M_year + M) must have the same remainder when divided by 7 as the year of Sandhya's birth plus her age (S_year + S). In other words:
(M_year + M) mod 7 = (S_year + S) mod 7
We can simplify this equation by subtracting M from both sides and then substituting 23 - S for M:
(M_year + (23 - S)) mod 7 = (S_year + S) mod 7
Now we have two equations with two unknowns. We can solve for M_year and S_year by guessing values for S and then checking if there are integers M and S_year that satisfy both equations. We know that M and S must be positive integers and that their sum is 23. Here are a few guesses:
If S = 1, then M = 22 and the equation becomes:
(M_year + 22) mod 7 = (S_year + 1) mod 7
This simplifies to:
M_year mod 7 = (S_year + 6) mod 7
There are no integers M_year and S_year that satisfy this equation, since the two sides always have different remainders when divided by 7.
If S = 2, then M = 21 and the equation becomes:
(M_year + 21) mod 7 = (S_year + 2) mod 7
This simplifies to:
M_year mod 7 = (S_year + 5) mod 7
The only pair of integers that satisfies this equation is M_year = 2 and S_year = 4.
Therefore, Manoj was born on February 15th, 1981 and Sandhya was born on February 15th, 1979.
So the dates of birth of Manoj and Sandhya are February 15th, 1981 and February 15th, 1979 respectively.
which one of the equations below could be used as a line of best fit to approximate the data in the scatter plot?
There are many tools available to calculate the line of best fit, including Excel, R, and Python. These tools provide the best equation that approximates the data
To determine which equation could be used as a line of best fit to approximate the data in a scatter plot, we need to look for the equation that closely follows the general trend of the data. The line of best fit is the straight line that best represents the data on the graph.
One common method for finding the line of best fit is through linear regression analysis. This involves calculating the slope and intercept of the line that best fits the data. The equation for a line is y = mx + b, where m is the slope and b is the y-intercept.
In general, the equation that could be used as a line of best fit depends on the data on the scatter plot. However, we can determine the best equation by looking at the trend of the data. If the data shows a positive trend, we need to choose an equation with a positive slope. If the data shows a negative trend, we need to choose an equation with a negative slope.
To determine the equation of the line of best fit for a specific scatter plot, we need to use regression analysis. and allows us to make predictions based on the data.
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A survey showed that 75% of adults need correction for their eyesight. If 12 adults are randomly selected find the probability that no more than one of them need correction of her eyesight is 18 significantly low number of adult record I said correction.
The probability that no more than one of them need correction of her eyesight is 5.960.
What is probability?
Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
Here using formula , Binomial distribution: P(X) = [tex]nC_x \times p^x\times q^{n-x}[/tex]
=> P(an adult need correction), p = 0.75
=>q = 1 - p = 0.25
Sample size, n = 12
P(no more than 1 of them need correction for their eyesight) = P(none of them need correction) + P(only 1 need correction)
=> [tex]0.25^{12}[/tex] + [tex]12\times0.75\times0.25^{11}[/tex]
=> 5.960
If the probability of an event is less than 0.05, it can be considered significantly low
Therefore, 1 is a significantly low number of adults requiring eyesight correction.
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Pls help me
If ABCD is a parallelogram, what is the length of BD?
The value of length BD in the given parallelogram is 10 units.
What is parallelogram?A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In other words, opposing sides and angles are congruent and parallel. There are numerous crucial characteristics of parallelograms, including:
A parallelogram's opposing sides are congruent.
A parallelogram's opposing angles are congruent.
The parallelogram's subsequent angles are additional (add up to 180 degrees).
A parallelogram's diagonals cut each other in half (i.e. they intersect at their midpoints).
According to the properties of parallelogram the diagonals of a parallelogram bisect each other.
Thus, BE = ED
Given BE = 5
Thus, ED = 5.
Now, the value of BD = BE + ED = 5 + 5 = 10
Hence, the value of BD in the given parallelogram is 10 units.
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Assume a company is preparing a budget for its first two months of operations. During the first and second months it
expects credit sales of $40,000 and $77,000, respectively. The company expects to collect 30% of its credit sales in
the month of the sale and the remaining 70% in the following month. What amount of cash collections from credit
sales would the company include in its cash budget for the second month?
Multiple Choice
$23,100
$51,100
$53,900
$35,100
Number of rational zeros? g(x)=x^4-12x^3+2x-14
Answer:
1
Step-by-step explanation:
Lucie a effectue le calcul : 235×27=6 345
Donner le résulta des produit suivants.
a.23.5 ×27 b.23.5×2.7 c.2.35×0.27
Step-by-step explanation:
a. 23.5 × 27 = 634.5
b. 23.5 × 2.7 = 63.45
c. 2.35 × 0.27 = 0.6345
Learning Task 3 : Solve the problem. Provide an illustration if necessary. ( 3 points each)
1.The length of o a rectangle is 12 cm and its width is 2 cm less than ¾ of its length. Find the
area of a rectangle .
2.A circular clock with a circumference of 88 cm, is mounted on the wall. How much area of
the wall did it occupy ( Use : π = 22/7 ).
3. The length of a rectangle is 52 cm and its perimeter is 200 cm . What is the area of the rectangle?
Step-by-step explanation:
1. 84 cm^2
2. 616 cm^2
3. 2496 cm^2
Given:
A triangle
l (length) = 12 cm
w (width) is 2 cm less than 3/4 of its length
Find: A (area) - ?
First, let's find the width of the rectangle according to the given information:
[tex]w = (\frac{3}{4} \times 12) - 2 = 9 - 2 = 7 \: cm[/tex]
Now, we can find the area:
[tex]a = w \times l[/tex]
.
2. Given:
A circular clock
C (circumference) = 88 cm
π = 22/7
Find: A (area) - ?
[tex]c = 2\pi \times r[/tex]
First, let's find the radius of the clock:
[tex]2 \times \frac{22}{7} \times r = 88[/tex]
[tex] \frac{44}{7} \times r = 88[/tex]
Multiply both sides of the equation by 7 to eliminate the fraction:
[tex]44r =616[/tex]
Divide both parts of the equation by 44 to make r the subject:
[tex]r = 14[/tex]
Now, we can find the area:
[tex]a = \pi {r}^{2} [/tex]
[tex]a = \frac{22}{7} \times {14}^{2} = 616 \: {cm}^{2} [/tex]
.
3. Given:
A rectangle
l (length) = 52 cm
P = 200 cm
Find: A (area) - ?
First, let's find the width of the rectangle (the perimeter is equal to the sum of all side lengths):
P = 2l + 2w
2w = P - 2l
2w = 200 - 2 × 52
2w = 96 / : 2
w = 48 cm
Now, we can find the area:
A = w × l
A = 48 × 52 = 2496 cm^2
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped with a mean of 59 ounces and a standard deviation of 6 ounces. Using the Empirical Rule, answer the following questions. Suggestion: Sketch the distribution. a) 95% of the widget weights lie between and b) What percentage of the widget weights lie between 53 and 71 ounces? % c) What percentage of the widget weights lie above 41? %
The proportion of company breadth between the widget's weight of [tex]0.13[/tex]and its weight of [tex]71[/tex]ounce is [tex]81.53[/tex].
What does the term "company" mean?Meaning of the word "company" A company is a collective of individuals. The word "company" is frequent and has several distinct meanings, but they are all related to gatherings or interactions of people. The most frequent usage of the term "company" is to describe a firm.
a) Using the Empirical Rule, we know that for a bell-shaped distribution, approximately [tex]68[/tex]% of the data falls within one standard deviation of the mean, [tex]95[/tex]% falls within two standard deviations of the mean, and [tex]99.7[/tex]% falls within three standard deviations of the mean. Therefore, for this problem, we can say:
[tex]95[/tex]% of the widget weights lie between [tex](59-2(6)) = 47[/tex] and [tex](59+2(6)) = 71[/tex] ounces.
b) To find the percentage of widget weights that lie between 53 and 71 ounces, we need to find the z-scores for each value and use a standard normal distribution table to find the areas under the curve.
The z-score for [tex]53[/tex] ounces is: [tex](53-59)/6 = -1.00[/tex]
The z-score for [tex]71[/tex] ounces is: [tex](71-59)/6 = 2.00[/tex]
Using a standard normal distribution table, we can find the area to the left of each z-score:
The area to the left of [tex]z = -1.00[/tex] is 0.1587
The area to the left of [tex]z = 2.00[/tex] is 0.9772
To find the percentage of widget weights between [tex]53[/tex] and [tex]71[/tex] ounces, we can subtract the area to the left of [tex]z = -1.00[/tex] from the area to the left of [tex]z = 2.00[/tex] and multiply by [tex]100[/tex]:
Percentage [tex]= (0.9772 - 0.1587) * 100 = 81.85[/tex]%
Therefore, approximately [tex]81.85[/tex]% of the widget weights lie between 53 and [tex]71[/tex] ounces.
c) To find the percentage of widget weights that lie above [tex]41[/tex] ounces, we need to find the z-score for [tex]41[/tex] and use a standard normal distribution table to find the area to the right of the z-score.
The z-score for 41 ounces is: [tex](41-59)/6 = -3.00[/tex]
Using a standard normal distribution table, we can find the area to the right of [tex]z = -3.00[/tex]:
The area to the right of [tex]z = -3.00[/tex] is [tex]0.0013[/tex]
To find the percentage of widget weights above [tex]41[/tex]ounces, we can multiply the area to the right of [tex]z = -3.00[/tex] by [tex]100[/tex]:
Percentage [tex]= 0.0013 * 100 = 0.13[/tex]%
Therefore, approximately [tex]0.13[/tex] % of the widget weights lie above [tex]41[/tex]ounces.
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Between the widget's weight of 0.13 and its weight in ounces, there is an 68 % company breadth.
What do you mean by the term percentage?Percentage is a way of expressing a quantity or value as a fraction of 100. It is denoted by the symbol %, which means "per cent" or "out of 100"
a) Using the Empirical Rule, we know that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of mean, and approximately 99.7% of the data falls within three standard deviations of mean.
Since the mean weight of the widgets is 59 ounces and the standard deviation is 6 ounces, we can use the Empirical Rule to determine that:
Approximately 68% of the widget weights lie between 53 and 65 ounces (one standard deviation below and above the mean).
Approximately 95% of widget weights lie between 47 and 71 ounces.
Approximately 99.7% of widget weights lie between 41 and 77 ounces.
b) To find the percentage of widget weights that lie between 53 and 71 ounces, we can use the Empirical Rule and subtract the percentage of widget weights that lie outside of this range from 100%.
we can estimate that approximately 68% of the widget weights lie between 53 and 71 ounces.
Therefore, the percentage of widget weights that lie between 53 and 71 ounces is approximately 68%.
c) To find the percentage of widget weights that lie above 41 ounces, we can use the Empirical Rule and subtract the percentage of widget weights that lie within three standard deviations below the mean from 100%.
Therefore, the percentage of widget weights that lie above 41 ounces is approximately:
100% - 99.7% = 0.3%
So, approximately 0.3% of the widget weights lie above 41 ounces.
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A 25% orange juice drink is mixed with a 100% orange juice drink. The function f(x) = (4)(1.0)+z(0.25)
models the
4+z
concentration of orange juice in the drink after a gallons of the 25% drink are added to 4 gallons of pure juice.
What will be the concentration of orange juice in the drink if 2 gallons of 25% drink are added? Give the answer as a percent
but do not include the percent sign (%).
To solve the problem, we need to use the given function f(x) = 4 + z(0.25) where x is the amount of 25% orange juice drink added and z is the amount of 100% orange juice drink added.
We know that initially 4 gallons of pure juice are present. So, the total amount of juice in the mixture is 4 + x gallons.
When we add 2 gallons of 25% orange juice drink, x = 2 and z = 0. So, using the function f(x), we get:
f(2) = 4 + z(0.25)
= 4 + 0(0.25)
= 4
Therefore, the concentration of orange juice in the drink after adding 2 gallons of 25% orange juice drink is 4%, expressed as a percent but without the percent sign.
Answer: 4
I need help with this question
Answer:
5/7
Step-by-step explanation:
ratio of boys to girls---> 2:5
ratio sum: 2+5=7
girls ratio =5/7
OR
total of people in 7th grade choir=28
hence, no of girls in 7th grade choir=5/7 × 28
=20
proportion of girls in choir= 20/28 = 5/7
Given ∆ABC below where AC = 26 and m∠C = 52°, determine the value of x.
Enter your answer as a decimal rounded to the nearest tenth (one decimal place)
x represents a length, we can discard the negative sοlutiοn and cοnclude that x ≈ 15.7.
What is triangle?A triangle is a three-sided pοlygοn with three angles. It is a fundamental geοmetric shape and is οften used in geοmetry and trigοnοmetry.
Using the Law οf Cοsines:
c² = a² + b² - 2ab cοs(C)
where c is the side οppοsite angle C, a and b are the οther twο sides, and C is the angle between sides a and b.
Substituting the knοwn values:
26² = x² + (x+7)² - 2x(x+7) cοs(52°)
Simplifying and sοlving fοr x:
676 = x² + x² + 14x + 49 - 2x² cοs(52°) - 14x cοs(52°)
676 = 2x² - 14x cοs(52°) + 49
2x² - 14x cοs(52°) - 627 = 0
Using the quadratic fοrmula:
[tex]x = [14 cos(52^\circ) \± \sqrt{((14 cos(52^\circ))}^2 - 4(2)(-627))] / (2(2))[/tex]
x ≈ 15.7 οr x ≈ -21.6
Since x represents a length, we can discard the negative sοlutiοn and cοnclude that x ≈ 15.7.
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Suppose that diastolic blood pressure readings of adult males have a bell-shaped distribution with a mean of 80 mmHg and a standard deviation of 9 mmHg. Using the empirical rule, what percentage of adult males have diastolic blood pressure readings that are less than 62 mmHg? Please do not round your answer.
95% of adult males have diastolic blood pressure readings that are at least 62 mmHg
The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule is further illustrated below
68% of data falls within the first standard deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.
From the information given, the mean is 80 mmHg and the standard deviation is 9 mmHg.
95% fall within two standard deviations.
2*9=`18
80 - 18 = 62 mmHg
Therefore, 95% of adult males have diastolic blood pressure readings that are at least 62 mmHg.
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(−20,F1) , (−10,F2) Step 1 of 2 : Compute the missing y values so that each ordered pair will satisfy the given equatio
[tex](-20, -4)[/tex] and are all of the ordered pairings that fulfil this equation [tex]F = 9/5C + 32. (-10, 14)[/tex].
What exactly are equation, and what varieties exist?Lines come in two varieties: identities and dependent equations. All possible values of the parameters result in an identity. Only certain combinations of the variables' values render a conditional equation true. Two expressions joined by the equals symbol ("=") form an equations.
What basic equation structure is used?Ax+By=C is the classic pattern for two-variable linear equations. A typical form linear equation is, for instance, 2x+3y=5. Finding all intercepts of a solution in this format is not too difficult. The approach additionally proves useful when trying to solve solutions combining two linear systems.
To find the missing y values, we need to substitute the given [tex]x[/tex] values into the equation [tex]F = 9/5C + 32[/tex] and solve for [tex]F[/tex].
For the first ordered pair (-20, F1):
[tex]F1 = 9/5(-20) + 32[/tex]
[tex]F1 = -36 + 32[/tex]
[tex]F1 = -4[/tex]
So the missing y value is [tex]-4[/tex], and the complete ordered pair is [tex](-20, -4)[/tex].
For the second ordered pair (-10, F2):
[tex]F2 = 9/5(-10) + 32[/tex]
[tex]F2 = -18 + 32[/tex]
[tex]F2 = 14[/tex]
So the missing y value is [tex]14[/tex], and the complete ordered pair is [tex](-10, 14)[/tex].
Therefore, the complete set of ordered pairs that satisfy the equation [tex]F = 9/5C + 32[/tex] is:
[tex](-20, -4)[/tex] and [tex](-10, 14)[/tex].
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The complete question is:
Given the equation
F=9,5
C+32
F=95C+32
where C is the temperature in degrees Celsius and F is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:
(−20,F1)
(−20,F1),(−10,F2)(−10,F2)
Step 1 of 2 : Compute the missing y values so that each ordered pair will satisfy the given equation.
I would really need help with this asap!! Thank you!!!
The value of the functions are;
1. (f+g(x)) = -x² -x + 1, (f-g(x)) = -5x²+ 5x - 7
2. (f+g(x)) = 6x² - 4x + 6, (f-g(x)) = 2x² - 6x + 10
3. (f+g(x)) = 3√m . √4, (f-g(x)) = √m· √4
4. (f+g(x)) = 7x² - 3x - 5, (f-g(x)) = x² + 3x + 5
How to determine the functionsIt is important to note that functions are described as an equation or expression showing the relationship between two variables.
From the information given, we have the functions
1.
f(x) = -3x² + 2x - 3
g(x) = 2x² - 3x + 4
To add the functions, we have;
(f+g(x)) = -3x² + 2x - 3 + 2x² - 3x + 4
collect the like terms and add
(f+g(x)) = -x² -x + 1
(f-g(x)) = -3x² + 2x - 3 - 2x² +3x - 4
collect the like terms and subtract
(f-g(x)) = -5x²+ 5x - 7
2. f(x) = 4x² - 5x + 8
g(x) = 2x² + x - 2
(f+g(x)) = 4x² - 5x + 8 + 2x² + x - 2
(f+g(x)) = 6x² - 4x + 6
(f-g(x)) =4x² - 5x + 8 - 2x² - x +2
subtract the values
(f-g(x)) = 2x² - 6x + 10
3. f(x) = 2√m
g(x) = 3√4m
(f+g(x)) = 2√m + √m. √4
(f+g(x)) = 3√m . √4
(f-g(x)) = 2√m -√m. √4
(f-g(x)) = √m· √4
4. f(x) = √16x^4
g(x) = 3x² - 3x - 5
(f+g(x)) = √16x^4 + 3x² - 3x - 5
find the square root
(f+g(x)) = 7x² - 3x - 5
(f-g(x)) =√16x^4 - 3x² + 3x +5
(f-g(x)) = x² + 3x + 5
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Suppose the weights of sumo wrestlers are normally distributed with a mean of 330lbs and a standard deviation of 15lbs. An up and coming competitor wants to defeat wrestlers whose weights are in the top 10%. What is the minimum weight of the sumo wrestlers at the highest weight of the league? Round your answer to the nearest whole number, if necessary.
Answer: To find the weight of the sumo wrestlers at the highest 10%, we need to find the z-score that corresponds to the top 10% of the distribution.
Using a standard normal table or a calculator, we can find that the z-score that corresponds to the top 10% is approximately 1.28.
Next, we can use the formula for a z-score to find the weight that corresponds to this z-score:
z = (x - mu) / sigma
where z is the z-score, x is the weight we want to find, mu is the mean weight, and sigma is the standard deviation.
Substituting in the values we know, we get:
1.28 = (x - 330) / 15
Solving for x, we get:
x = 1.28(15) + 330 = 349.2
Rounding to the nearest whole number, the minimum weight of the sumo wrestlers at the highest weight of the league is 349 lbs.
Step-by-step explanation:
Determine the least possible degree on the graph
Answer:
The least possible degree is 3.
5/8 of the students at Hawthorne are only Los Angeles Lakers fans. Of those who do not like the Lakers, 3/4 like only the Los Angeles Clippers. a. What fraction of the entire school does not like the Lakers? b. What fraction of the entire school likes the Clippers? c. What fraction of the entire school does not like the Clippers? d. What fraction of the entire school does not like either the Lakers or the Clippers?
Part A: Fraction of all students who does not like Lakers = 3/8.
Part B: Fraction of all student who likes the Clippers = 9/32
Part C: Fraction of all student who does not likes the Clippers = 23/32.
Part D: Fraction of all student who does not likes either the Clippers or Lakers : 35/32
Define about the fraction:The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.
Given data:
Students who likes only Los Angeles Lakers = 5/8
Students who does not likes only Los Angeles Lakers: 1 - 5/8 = 3/8
From 3/8, only 3/4 like the Los Angeles Clippers.
= 3/8 * 3/4
= 9/32
Now,
Students who does not like the Los Angeles Clippers: 1 - 9/32 = 23/32.
Part A: Fraction of all students who does not like Lakers = 3/8
Part B: Fraction of all student who likes the Clippers = 9/32
Part C: Fraction of all student who does not likes the Clippers = 23/32.
Part D: Fraction of all student who does not likes either the Clippers or Lakers :
= 3/8 + 23/32
= 35/32
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5. Kelly's dad is working with her to create a
budget for her part-time job. He would like her
to follow the percentages below. Complete the
table to determine how much money Kelly will
be able to give, save, and spend if she makes
$800 per month.
Answer:
he get 100$ in day time u can understand
Answer:
You can save money by putting aside part of your income on a regular basis or by putting aside extra income, or by reducing your expenses.
Step-by-step explanation:
Kelly spending per month on different working fields are shown in attachment!
lolita started eating at 6:35 am and he finished at 7:03
Answer:
He took 28min eat.
Step-by-step explanation:
A line has a slope of 1 and passes through the point (
–
2,5). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = x + 7
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. We are given that the slope of the line is 1, so we can substitute m = 1 into the equation:
y = 1x + bWe also know that the line passes through the point (-2, 5), so we can substitute x = -2 and y = 5 into the equation and solve for b:
5 = 1(-2) + b5 = -2 + bb = 7Therefore, the equation of the line in slope-intercept form is:
y = x + 7
This is the final answer, written in slope-intercept form using integers.Answer:
The Equation of the Line is : y = x + 7
Step-by-step explanation:
Equation of the Line in Slope-Intercept Form is y = mx + b
where m is the Slope and b is the y-intercept
since the slope (m) = 1 , Substitute by m = 1 in the above equation
Then the Equation will be y = x + b
Since the line passes through point ( -2 , 5 ) , Then y = 5 when x = - 2
Substitute , Then 5 = -2 + b
Then b = 5 + 2 =7
So the Equation will be y = x + 7
Hope this is Helpful
Find the equation in standard form for the circle whose diameter has an endpoint at (-3, -4) and the origin.
4 x 2 + 4 y 2 - 12 x + 16 y = 0
4 x 2 + 4 y 2 + 12 x - 16 y = 0
4 x 2 + 4 y 2 - 12 x - 16 y = 0
4 x 2 + 4 y 2 + 12 x + 16 y = 0
[tex]4 x 2 + 4 y 2 - 12 x + 16 y = 0[/tex]
Find the length of line AB.
Answer:
21
Step-by-step explanation:
You want the length of segment AB, given similar triangles AEB and ADC with AE=14, ED=12, and BC=18.
Similar trianglesCorresponding sides (or segments) of similar triangles are proportional:
AB/AE = BC/ED
AB = AE·BC/ED = 14·18/12 = 14·3/2
AB = 21
What is the volume of the triangular prism 2 Cm 3 cm 5 cm
Answer:
10cm
Step-by-step explanation:
V = (1/3)Length x width x height
V = (1/3)(2)(3)(5)
V = 10