Joel cannot buy 2 games and 6 puzzles and satisfy the constraints was solved by using inequality.
The total cost of x puzzles and y games must be less than or equal to $96, which gives us the first inequality: 8x + 12y ≤ 96
The second inequality: x + y ≥ 9.
What is inequality function?An inequality is a mathematical statement that compares two quantities or expressions and shows the relationship between them using one of the following symbols: <, >, ≤, or ≥. For example, "x > 5" is an inequality that states that x is greater than 5.
In the given question,
Part A:
Let x be the number of puzzles Joel can buy and y be the number of games Joel can buy.
The total cost of x puzzles and y games must be less than or equal to $96, which gives us the first inequality: 8x + 12y ≤ 96
Joel needs to buy at least 9 gifts, which means that the total number of gifts must be greater than or equal to 9. Since x represents the number of puzzles and y represents the number of games, the total number of gifts is x + y. This gives us the second inequality: x + y ≥ 9
We also know that Joel can only buy puzzles or games, not both. Therefore, x and y must be either both integers or both half-integers (such as 1.5 or 2.5), but they cannot be mixed. This gives us the third inequality:
x, y are both integers or both half-integers
Part B:
To see if Joel can buy 2 games and 6 puzzles and satisfy the constraints, we can substitute x = 6 and y = 2 into the inequalities:
8x + 12y ≤ 96
8(6) + 12(2) ≤ 96
72 ≤ 96
This inequality is true, so the first constraint is satisfied.
x + y ≥ 9
6 + 2 ≥ 9
8 ≥ 9
This inequality is not true, so the second constraint is not satisfied. Therefore, Joel cannot buy 2 games and 6 puzzles and satisfy the constraints.
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Review the information given based on a principal balance of $12,650.00 to answer the question:
FICO Score Simple Interest Rate Total of Payments Total Amount Paid
800-850
12%
29
740-799 15%
33
670-739 18%
38
580-669 21%
300-579 28%
40.0%
48
60
Calculate the percent increase in the amount of interest paid between a household with a 780 credit score and one with a 589 credit score. Round the final answer to the nearest tenth. (4 points)
O 46.1%
39.9%
40.1%
$14,168.00
$14,547.50
$14,927.00
$15,306.50
$16,192.00
The percent increase in the amount of interest paid between a household with a 780 credit score and one with a 589 credit score is approximately 0.8%, which is closest to option B, 0.8% or 39.9%.
Finding the entire amount paid by each family and comparing the difference in total amount paid will allow us to determine the percentage rise in the amount of interest paid between a household with a credit score of 780 and one with a score of 589.
The overall cost for a FICO score of 780 is:
$12,650 for the principal balance and all installments plus (33 x $60) to get $14,930.
With a 589 FICO score, the total cost is:
Total payments plus principal balance equal $12,650 plus (40 x $60) = $15,050.
The two households' combined total outlays differ in the following ways:
$15,050 - $14,930 = $120
We multiply by 100 and divide the difference by the initial sum to determine the percent increase:
($120 / $14,930) x 100% = 0.802% ≈ 0.8%
In light of this, the difference in interest rates between a family with a 780 credit score and one with a 589 credit score is roughly 0.8%, which is closest to option B, 0.8% or 39.9%.
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A survey was done with 50 students currently taking Algebra 1 at Laurel Springs School. They were asked which they preferred - English or mathematics? Out of the 50 students, 30 were male. There were 35 students who preferred mathematics and out of those that preferred mathematics, 24 were male. Create a two way relative frequency table for the data. According to the table, would it be safe to assume that females prefer English and males prefer mathematics? Why or why not?
we can see that a larger proportion of male students preferred mathematics (0.48) compared to female students (0.22), while a larger proportion of female students preferred English (0.18) compared to male students (0.12).
HOW TO SOLVE THE QUESTION?
To create a two-way relative frequency table, we can use the following table:
| English | Mathematics | Total
--------|---------|-------------|-------
Male | x | 24 | 30
Female | y | 11 | 20
--------|---------|-------------|-------
Total | 35 | 35 | 50
Here, x and y represent the number of male and female students who preferred English, respectively.
To calculate the values for x and y, we can use the fact that there were 35 students who preferred mathematics, and 24 of them were male. Therefore, the number of females who preferred mathematics is 35 - 24 = 11. Since there are a total of 20 female students, the number of females who preferred English is 20 - 11 = 9. Similarly, the number of male students who preferred English is 30 - 24 = 6.
To calculate the relative frequencies, we can divide each cell by the total number of students (50). For example, the relative frequency of male students who preferred mathematics is 24/50 = 0.48.
The resulting two-way relative frequency table is as follows:
| English | Mathematics | Total
--------|---------|-------------|-------
Male | 0.12 | 0.48 | 0.60
Female | 0.18 | 0.22 | 0.40
--------|---------|-------------|-------
Total | 0.30 | 0.70 | 1.00
From this table, we can see that a larger proportion of male students preferred mathematics (0.48) compared to female students (0.22), while a larger proportion of female students preferred English (0.18) compared to male students (0.12). However, it would not be safe to assume that all females prefer English and all males prefer mathematics based on this data alone, as there may be individual variations and exceptions to this trend.
It's also important to note that the sample size is relatively small, with only 50 students surveyed, and may not be representative of the larger population. Further research with a larger and more diverse sample size would be needed to make more accurate conclusions about gender-based preferences in this population
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4. If triangle ABC has the following measurements, find the measure of side c:
a = 5
B = 7
C = 42 degrees
Using cosine rule, the measure of side c is calculated as: 4.688
How to use the cosine rule?In trigonometry, the Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
We are given the parameters as:
a = 5
B = 7
C = 42 degrees
Using cosine rule, we have:
c = √(a² + b² - 2ab cos C)
c = √(5² + 7² - 2(5 * 7) cos 42)
c = √(25 + 49 - 52.02)
c = √21.98
c = 4.688
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Tom can paint a fence in 12 hours. Huck can paint the same fence in 10 hours. How long would it take to put two coats of paint on the fence if Tom and Huck work together? Answer as an improper fraction, then round to 1 decimal place. 3) Kim and Josh can clean a house together in 3 hours. If it takes Kim 7 hours to clean the house by herself, how long would it take Josh to clean the house alone? Leave your answer in improper fraction form, then convert to a decimal. 4) Jack can mow the baseball grounds in 2 hours; Mike can mow the same grounds in 3 hours; and Chris can mow the grounds in 4 hours. How long will it take to mow the baseball grounds if Jack, Mike, and Chris work together? Leave your answer in proper fraction form, then round to 1 decimal place. Using your rounded answer, how many minutes would that be?
2) They tοgether will take 10.9 hours οr 120/11
3) jοsh will take 21/11 hrs οr 1.9 hrs
4) Tοgether they will take 36/13 οr 2.8 hrs
What is decimal place?The place values οf the digits in a decimal number are displayed οn the decimal place value chart. We knοw that a digit in a number represents a numerical value οr place value.
Decimal place value charts are used tο determine the prοper placement οf each digit in a decimal number.
A decimal number cοnsists οf a whοle number and a fractiοnal cοmpοnent, separated by the decimal pοint, a dοt.
Fοr instance, the decimal number 4.37 has twο parts: an actual number pοrtiοn οf 4 and a fractiοnal pοrtiοn οf 37.
Sοlutiοns tο the abοve prοblem
2) Tοm takes = 12 hrs
Huck takes= 10hrs
We can aply unitary methοd
tοgether they will take= 1/12+1/10=2/t
11t=120;
t=120/11 οr 10.9 hrs
3) Tοgether Kim and jοsh can clean the hοuse tοgether in = 3 hrs
Kim takes = 7hrs
Jοsh will take= 1/7+1/x=2/3
3x+21=14x
21=11x
x=21/11 οr 1.9 hrs
4) Jack makes baseball grοunds in= 2 hrs
Mike takes= 3 hrs
Chris takes= 4 hrs
Tοgether they will take= 1/2+1/3+1/4=3/x
13x=36
x=36/13 οr 2.8 hrs
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find the critical points and critical values of the function z=x^3+6xy-y^3-1
Answer:
∂z/∂x = 3x^2 + 6y
∂z/∂y = 6x - 3y^2
Now, we need to solve the system of equations:
3x^2 + 6y = 0
6x - 3y^2 = 0
From the first equation, we get:
y = -x^2/2
Substituting this into the second equation, we get:
6x - 3(-x^2/2)^2 = 0
Simplifying, we get:
6x - 3x^4/4 = 0
Multiplying by 4 and rearranging, we get:
3x^4 - 24x = 0
Factoring out 3x, we get:
3x(x^3 - 8) = 0
Therefore, the critical values of x are x = 0 and x = 2.
For x = 0, we have y = 0 (from y = -x^2/2). So, one critical point is (0, 0).
For x = 2, we have y = -2. So, the other critical point is (2, -2).
To find the critical values of the function, we need to evaluate the function at each critical point:
z(0, 0) = 0^3 + 6(0)(0) - 0^3 - 1 = -1
z(2, -2) = 2^3 + 6(2)(-2) - (-2)^3 - 1 = -13
Therefore, the critical values of the function are -1 and -13.
11) The Hillmans have $12,000 in a savings
account. The bank pays 1.25% interest on
the savings account, compounded
continuously.
Find the total balance after three years.
A) $12,290.21
C) $11,345.89
B) $12,458.54
D) $11,452.16
Answer:
To find the total balance after three years, we can use the formula for continuous compounding:
A = Pe^(rt)
Where A is the total balance, P is the principal (initial amount), e is Euler's number (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years.
In this case, P = $12,000, r = 0.0125 (1.25% expressed as a decimal), and t = 3. Plugging these values into the formula, we get:
A = $12,000 x e^(0.0125 x 3)
A = $12,000 x e^(0.0375)
A = $12,000 x 1.038163
A = $12,458.54
Therefore, the total balance after three years is $12,458.54.
in the 3rd quadrant, find SIN
Answer:?
There are 44 people taking a trip in some small vans.
Each van holds 8 people. How many vans will they need?
Make a drawing for this problem that would explain
Answer:
They will need 6 vans to hold all 44 people.
Step-by-step explanation:
1 bus holds : 8
2 bus holds : 16
3 bus holds : 24
4 bus holds : 32
5 bus holds : 40
6 bus holds : 48 (4 extra seats)
21 is greater than the sum of 15 and two times a number X
Answer:21>15+2x
Step-by-step explanation:
Astrid says the function being graphed is y=-4+1/3
. She says that her equation is correct because the slope of the line is -4.
Matt says the function that is being graphed is y=1/3x
. He says that the slope of the line is actually 1/3
Is Astrid correct? Is Matt correct? Explain your reasoning
If Astrid says the function being graphed is y=-4+1/3. Matt is correct, while Astrid is incorrect.
How to find if Matt or Astrid is correct?Astrid's equation y = -4 + 1/3 is incorrect because it is missing the variable x. The equation is missing a term that represents the x variable, so the equation does not represent a line.
On the other hand, Matt's equation y = 1/3x is correct, and the slope of the line represented by this equation is indeed 1/3. This can be seen from the fact that the equation is in the form y = mx, where m is the slope of the line. In this case, m = 1/3, so Matt is correct.
Therefore, Matt is correct, while Astrid is incorrect.
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What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
______________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
______________________________________
The cuboidal prism has a volume of 40.625 cubic centimeters
How is area of a cuboid determined?Multiplying the cuboidal prism's length, width, and height yields its volume. Assuming that the width b and height h are both 2.5 cm and the length l is 6.5 cm. The volume of the cuboidal prism is given by multiplying these dimensions:
V = l b h = 6.5cm x 2.5cm x 2.5cm
= [tex]40.625cm^3.[/tex]
As a result, the cuboidal prism has a volume of 40.625 cubic centimeters. As a result, the prism can be utilized for a variety of purposes, including packaging, storage, and transportation, and it can accommodate 40.625 cubic centimeters of material inside its boundaries.
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⦁ What is the product of -2^3 + x - 5 and x^3 -3x +4 ?
⦁ Show your work.
⦁ Is the product of -2^3 + x - 5 and x^3 -3x +4 equal to the product of x^3 -3x +4 and -2^3 + x - 5 ? Explain your answer.
The product of -2³ + x - 5 and x³ -3x +4 is -5x³ + 16x - 28.
How did we get the value?The given expression is:
-2³ + x - 5 x (x³ -3x +4)
We need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, let's simplify -2³, which means -2 x 2 x 2 = -8, so we have:
-8 + x - 5 x (x³ -3x +4)
Next, we need to distribute the -5 to the terms inside the parentheses:
-8 + x - 5x³ + 15x - 20
Now we can combine like terms:
-5x³ + 16x - 28
Therefore, the product of -2³ + x - 5 and x³ -3x +4 is -5x³ + 16x - 28.
Now, to answer the second part of the question, we need to check if:
-2³ + x - 5 x (x³ -3x +4) = (x³ -3x +4) * (-2³ + x - 5)
We can simplify both expressions first:
-8 + x - 5x³ + 15x - 20 = -8 + x - 5x³ + 15x - 20
We can see that both expressions are identical, which means that the product of -2³ + x - 5 and x³ -3x +4 is equal to the product of x³ -3x +4 and -2³ + x - 5, regardless of the order in which we multiply the factors.
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uhhh yes i need help Each parking spot is eight and one-half feet wide. A parking lot has 24 parking spots side by side. How long is the row of parking spaces in yards?
The 24 parking spοt length is 68 yards.
What is unit cοnversiοn?The same feature is expressed in a different unit οf measurement thrοugh a unit cοnversiοn. Time can be stated in minutes rather than hοurs, and distance can be expressed in kilοmetres rather than miles, οr in feet rather than any οther unit οf length.
Here the given width of One parking spot is eight and one-half feet.
Now we know that 1 feet = [tex]\frac{1}{3}[/tex] yard,
Then , [tex]8\frac{1}{2}[/tex] feet = [tex]\frac{17}{2}[/tex] feet = [tex]\frac{17}{2}\times\frac{1}{3}[/tex] = [tex]2\frac{5}{6}[/tex] yd.
Now Parking lot have 24 parking spot, Then,
=> Total length of parking lοt = 24 [tex]\times[/tex] [tex]2\frac{5}{6}[/tex] = [tex]24\times\frac{17}{6}[/tex] = 68 yard.
Hence The length of parking lοt is 68 yard.
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Write an equation parallel to each of the following:
Please help!!!!
A manufacturer knows that their items have a normally distributed length, with a mean of 9.8
inches, and standard deviation of 2 inches.
If 17 items are chosen at random, what is the probability that their mean length is less than 10.9
inches?
As a result, the likelihood that the mean length of a random sample of 17 items is less than 10.9 inches is about 0.9265, or 92.65%.
What exactly is probability?Probability is a measure of how likely an event is to occur. It is a number between 0 and 1, with 0 suggesting that an occurrence is impossible and 1 indicating that an event is unavoidable. A given event's probability is computed by dividing the number of positive outcomes by the total number of potential possibilities.
In this case, we may utilize the central limit theorem to estimate the sample mean distribution. The central limit theorem states that if the sample size is high enough (n 30), the distribution of the sample mean will be normal.
Regardless of demographic distribution, the population is essentially typical.
In this scenario, the population has a normal distribution with a mean () of 9.8 inches and a standard deviation () of 2 inches. We wish to calculate the likelihood that the sample mean (x) of 17 objects is smaller than 10.9 inches.
The formula for calculating a sample mean's z-score is: z = (x - ) / ( / sqrt(n)), where n is the sample size.
We obtain: z = (10.9 - 9.8) / (2 / sqrt(17)) by substituting the numbers supplied in the problem.
z = 1.45
We may calculate the chance that a standard normal variable is smaller than 1.45 using a typical normal distribution table or calculator:
P(Z < 1.45) = 0.9265
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For problems 1 – 6, perform the conversions.
1. 7
16
= % 2. 4
3
5 = __ %
3. Express 55% as a fraction in simplified form: ___
4. Express 248% as a mixed number in simplified form: __
5. 0.00031 = __ % 6. 6.005 = __ %
7. Gigi spent 12% of her birthday money on a new pair of sunglasses. What fraction of her
birthday money did she spend on the new sunglasses?
8. Veronica and her friends went out for pizza to celebrate the volleyball team’s victory.
Their total bill for the pizza and soft drinks was $27.50. They left a 20% tip for their
server. How much tip did they leave?
Answer:
1. 7/16 = 43.75%
2. 4/5 = 80%
3. 55% = 55/100 = 11/20
4. 248% = 2 48/100 = 2 12/25
5. 0.00031 = 0.031%
6. 6.005 = 600.5%
7. 12% = 12/100 = 3/25 (Gigi spent 3/25 of her birthday money on the new sunglasses)
8. The total bill for pizza and soft drinks was $27.50. With a 20% tip, the amount of tip left would be:
Tip = 20% of total bill
Tip = 20/100 * $27.50
Tip = $5.50
Therefore, Veronica and her friends left a $5.50 tip for their server.
Step-by-step explanation:
Answer:
1. 43.75%
2. 60%
3. 11/20
4. 2 and 12/25
5. 0.031%
6. 600.5%
7. 3/25
8. $5.50
Step-by-step explanation:
1. 7 ÷ 16 = 0.4375
0.4375 x 100 = 43.75%
2. 3 ÷ 5 = 0.6
0.6 x 100 = 60%
3. 55/100
11x25 / 20x5 = 11/20
4.248/100
62x4 / 25x4
62/25
62/25 = 2R12
2 12/25
5. 0.00031 x 100 = 0.031%
6. 6.005 x 100 = 600.5%
7. 12% = 12/100.
12/100 simplified = 3/25
8. $27.50 x 20% = $5.50
The mean of a sample of 50 claim amounts arising from a certain kind of insurance policy is R4500. Fifteen of these claim amounts have mean R2109 while 14 others have mean R3704. Calculate the mean of the remaining claim amounts in this sample.
The mean οf the remaining claim is R6739.
What is mean?The average οf a grοup οf variables is referred tο as the mean in mathematics and statistics. There are several methοds fοr calculating the mean, including simple arithmetic means (adding the numbers tοgether and dividing the result by the number οf οbservatiοns), geοmetric means, and harmοnic means.
Here We knοw that,
Mean = Sum οf amοunts οf claim / Tοtal number οf claim
Accοrding tο the given,
Mean οf 50 claim οf insurance pοlicy = R 4500 then,
Sum οf amοunt οf 50 claim = 4500*50 = R 225000
Mean οf 15 οf these claim = R 2109 then,
Sum οf amοunt οf 15 claims = 2109*15 = R 31635
Mean οf 14 οther claim = R 3704 then
Sum οf 14 οther claim = 3704*14 = R 51856
Nοw remaining claim amοunt = 50-14-15 = 21
Sum οf 21 remaining claim = 225000-31635-51856 = R 141509
Now Mean = Sum of 21 amount of claim / Total number of claim
=> Mean = 141509/21 = R 6739
Hence the mean of remaining 21 sample is R 6739.
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Hector deposits $150,000 into an account earning 3.6% simple interest annually. Find the maturation value (final amount) of the account after 5 years.
simple interest
1 year: [tex]3.6\% \cdot 150,000 = \dfrac{3.6}{100} \cdot 150,000 = 5,400[/tex]
5 years: [tex]5,400(5) = 27,000[/tex]
the maturation value:
[tex]150,000 + 27,000 = \$ 177,000[/tex]
Assume that when adults with smartphones are randomly selected, 44% use them in meetings or classes. If 7 adult smartphone users are randomly selected, find the probability that exactly 5 of them use their smartphones in meetings or classes.
Answer:
The probability that exactly 5 of the 7 selected smartphone users use their phones in meetings or classes is approximately 0.0127 or 1.27%.
Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .05 significance level.
The null and alternative hypothesis would be:
The test is:
two-tailed
right-tailed
left-tailed
Based on a sample of 60 men, 25% owned cats
Based on a sample of 60 women, 30% owned cats
The test statistic is:
(to 2 decimals)
The p-value is:
(to 2 decimals)
Based on this we:
Fail to reject the null hypothesis
Reject the null hypothesis
The assertion that the percentage of males who own cats is lower than the percentage of women who do not own cats is unsupported by sufficient data.
Hence, the Alternate hypothesis would be:
H0: Pm = Pf
H1 = Pm < Pf
What is Alternate hypothesis?Alternate hypotheses are used in statistical hypothesis testing. The hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.
Given information:
The test claims proportion of men who owns cat is smaller.
The significance level = 0.005
As the hypothesis always gets ten statements of equality but in the case given alternate hypothesis will claim.
Now calculating the Z-value:
P= 10+14/80
= 0.3
So, the p-value according to the obtained Z value is 0.1365.
Since, 0.1365>0.005, we fail to reject the hypothesis.
Hence, there is not enough proof to support the claim that the proportion of man who owns the cat is less than that of the proportion of women who owns the cat.
Therefore, the Alternate hypothesis would be:
H0: Pm = Pf
H1 = Pm < Pf
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Question 27: Find x
The angle x opposite to the side measuring 17 is approximately 20.68 degrees using trigonometry.
Let x stand for the side that is the shortest. The Pythagorean theorem yields the following result: x2 + 172 = 19.
When we simplify this equation, we obtain:
[tex]x^2 = 19^2 - 17^2[/tex]
[tex]x^2 = 36x = 6[/tex]
Hence, the shortest side is six inches long.
Using the inverse trigonometric function tangent, we can determine the angle opposite the side measuring 17. (tan).
tan = adjacent/opposite = x/17
By changing the value of x, we obtain:
[tex]tanθ = 6/17[/tex]
We may determine the angle whose tangent is 6/17 using a calculator or a trigonometric table.
[tex]θ = 20.68°[/tex]
As a result, the angle that is opposite the side that measures 17 is roughly 20.68 degrees.
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or Edward opened a savings account and deposited $200.00 as principal. The account earns 9% interest, compounded annually. What is the balance after 5 years?
The final amount after 5 years is $ 49521.98.
Compound interest:Compound interest refers to the interest that is earned on the initial amount of money deposited or borrowed and also on the accumulated interest from previous periods.
The formula for calculating compound interest is:
A = P(1 + r/n)^(nt)Where
Where:
A = Final amount
P = Principal amount
r = Annual interest rate
n = Number of times the interest is compounded per year
t = Time period
Here we have
The deposited amount, P= $200.00
Rate of interest, r = 9% = 9/100 = 0.09%
Number of compounds per year, n = 1
Time period, t = 5 years
Using the formula,
A = 2000(1 + 0.09/1)⁽¹⁽⁵⁾⁾
A = 2000(1.09)⁵
A = 49521.98
Therefore,
The final amount after 5 years is $ 49521.98.
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If x is the average of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, what is the average of x, y, and z in terms of m
Answer: To find the average of x, y, and z in terms of m, we first need to find expressions for x, y, and z in terms of m:
x = (m + 9)/2
y = (2m + 15)/2
z = (3m + 18)/3 = (m + 6)
To find the average of x, y, and z, we add them up and divide by the number of terms:
average = (x + y + z)/3
Substituting the expressions for x, y, and z, we get:
average = [(m + 9)/2 + (2m + 15)/2 + (m + 6)]/3
Simplifying the expression by combining like terms, we get:
average = (4m + 30)/6
Simplifying further by dividing both the numerator and denominator by 2, we get:
average = (2m + 15)/3
Therefore, the average of x, y, and z in terms of m is (2m + 15)/3.
Step-by-step explanation:
Find the area of the quadrilateral below.
Give you answer in cm² and give any decimal answers to 1 d.p.
Answer:
[tex]36 \: cm ^{2} [/tex]
Step-by-step explanation:
triangle area below
[tex] \frac{10 \times 5}{2} = 25[/tex]
EG segment
[tex] \sqrt{10 ^{2} + 5 ^{2} } = \sqrt{125} [/tex]
EF segment
[tex] \sqrt{ (\sqrt{125})^{2} - 2^{2} } = \sqrt{121} [/tex]
triangle area above
[tex] \frac{ \sqrt{121} \times 2}{2} = \sqrt{121} [/tex]
total area
[tex]25 + \sqrt{121} = 36[/tex]
Please help!! Correct answer gets brainliest!!
Answer:
C) 260 square inches.
Step-by-step explanation:
To find the surface area of a pyramid, we can use the formula.
Surface Area = (1/2) x Perimeter of Base x Slant Height + Base Area
where l is the length of one side of the square base, s is the slant height, and Base Area is the area of the square base.
In this case, the base of the pyramid is a square with side length l = 10 inches, so its area is
Base Area = l^2 = 10^2 = 100 square inches
To find the perimeter of the base, we can simply multiply the length of one side by 4
Perimeter of Base = 4l = 4 x 10 = 40 inches
We are also given that the slant height of the pyramid is s = 8 inches.
Now we can substitute the values into the formula.
Surface Area = (1/2) x Perimeter of Base x Slant Height + Base Area
Surface Area = (1/2) x 40 x 8 + 100
Surface Area = 160 + 100
Surface Area = 260 square inches
Therefore, the surface area of the pyramid is 260 square inches.
Answer:360 in
Step-by-step explanation:
Prove that Re(z1,z2-bar) = modulus of z1 * modulus of z2 iff arg z1 = arg z2 + 2*pi*n.Use polar form with arg measured in radians
Answer:
Step-by-step explanation:
We can start by writing the given equation in terms of polar form:
Re(z1,z2-bar) = modulus of z1 * modulus of z2
If we write z1 and z2 in polar form, we get:
z1 = r1(cosθ1 + i sinθ1)
z2 = r2(cosθ2 + i sinθ2)
Then, the conjugate of z2 is:
z2-bar = r2(cosθ2 - i sinθ2)
Using the formula for the real part of the product of two complex numbers, we get:
Re(z1,z2-bar) = Re(z1 * z2-bar)
Substituting the expressions for z1 and z2-bar, we get:
Re(z1,z2-bar) = Re(r1(cosθ1 + i sinθ1) * r2(cosθ2 - i sinθ2))
Simplifying the product, we get:
Re(z1,z2-bar) = Re(r1r2[(cosθ1 cosθ2 + sinθ1 sinθ2) + i(sinθ1 cosθ2 - cosθ1 sinθ2)])
The real part of this expression is:
Re(z1,z2-bar) = r1r2(cosθ1 cosθ2 + sinθ1 sinθ2)
Using the identity cos(θ1 - θ2) = cosθ1 cosθ2 + sinθ1 sinθ2, we can write:
Re(z1,z2-bar) = r1r2 cos(θ1 - θ2)
Now we can substitute this expression back into the original equation and get:
r1r2 cos(θ1 - θ2) = r1r2
Dividing both sides by r1r2, we get:
cos(θ1 - θ2) = 1
This equation is true if and only if θ1 - θ2 = 2πn for some integer n. In other words, θ1 = θ2 + 2πn, where n is an integer.
Therefore, we have proved that Re(z1,z2-bar) = modulus of z1 * modulus of z2 if and only if arg z1 = arg z2 + 2πn, where n is an integer.
A club Ordered two same sized vegetable pizzas cut into different numbers of pieces
what fraction of a whole pizza is left? PLEASE HELP IM GETTING GROUNDED IF YOU DONT HELP IN THE NEXT 24 HOURS!!!!
Answer:
Without knowing the number of pieces that the pizzas were cut into, it is not possible to determine the fraction of a whole pizza that is left.
Step-by-step explanation:
Evaluate:
13-0.75w+8x when w = 12 and x = 1/2
(need help! fast! TmT)
Answer: To evaluate 13 - 0.75w + 8x when w = 12 and x = 1/2, we substitute these values into the expression:
13 - 0.75w + 8x = 13 - 0.75(12) + 8(1/2)
Simplifying the expression inside the parentheses first:
13 - 9 + 4 = 8
Substituting this value into the expression:
13 - 0.75w + 8x = 13 - 0.75(12) + 8(1/2) = 13 - 9 + 4 = 8 + 4 = 12
Therefore, the value of 13 - 0.75w + 8x when w = 12 and x = 1/2 is 12.
Answer:
8
Step-by-step explanation:
Given expression is
[tex]13-0.75w\:+\:8x[/tex]
and we are asked to evaluate this expression when
[tex]w = 12 ,\: x = \dfrac{1}{2}[/tex]
[tex]0.75w = 0.75 \times 12 = 9[/tex]
[tex]8x = \8 \times \dfrac{1}{2} = 4[/tex]
[tex]\text{So the expression at $w = 12 \; , x= \dfrac{1}{2}$ evaluates to}[/tex]
13 - 9 + 4 = 8
Answer: 8
Let r(x) = f(g(h(x))), where h(1) = 3, g(3) = 4, h'(1) = 3, g'(3) = 4, and f '(4) = 5. Find r'(1).
The value of r'(1) = 60 for the given function, using the chain rule.
What are derivatives of composite function?By adding the derivatives of f(x) with regard to g(x) and g(x) with respect to the variable x, one may get the derivative of the composite function h(x) = f(g(x)). The chain rule of differentiation can be used to derive derivatives of composite functions. Now, let's go over what composite functions are. When a function is expressed in terms of another function, it is said to have a composite function. This suggests that a function can be changed into another function in a composite function.
Using the chain rule of derivatives we have:
r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x)
Substituting the values we have:
r'(1) = f'(g(h(1))) * g'(h(1)) * h'(1)
r'(1) = f'(g(3)) * g'(3) * 3
r'(1) = f'(4) * 4 * 3
r'(1) = 5 * 4 * 3
r'(1) = 60
Hence, the value of r'(1) = 60 for the given function, using the chain rule.
Learn more about composite functions here:
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What is the result when 4x - 3 is subtracted from 6x - 9?
(A)-2x - 6
(B)-2x + 6
(C) 2x - 6
(D) 2x + 6
(E) 10x - 12
Answer: 2x-6
Step-by-step explanation: