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If f(x)=x^3+x-7 and g(x)=-5x, find (fog)(x) and (gof)(x)
(fog)(x)=?
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store is giving away $10 coupon to every 7th person and $25 coupon to every 18th person. Which person will be the first for both coupons?
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In a bag, a child has 325 coins worth $19.50. There were three types of coins: pennies, nickels, and dimes. If the bag
contained the same number of nickels as dimes, how many of each type of coin was in the bag?
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The number of pennies, nickels, and dimes will be 227, 49, and 49, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
In a pack, a kid has 325 coins worth $19.50. There were three kinds of coins: pennies, nickels, and dimes. In the event that the pack contained a similar number of nickels as dimes.
Let 'x' be the number of dimes and nickels and 'y' be the number of pennies. Then the equations are given as,
x + x + y = 325
2x + y = 325 ....1
0.1x + 0.25x + 0.01y = 19.50
0.35x + 0.01y = 19.50 ...2
From equations 1 and 2, then we have
0.35x + 0.01(325 - 2x) = 19.50
0.35x + 3.25 - 0.02x = 19.50
0.33x = 16.25
x = 49
Then the value of 'y' will be given as,
2(49.24) + y = 325
y = 227
The number of pennies, nickels, and dimes will be 227, 49, and 49, respectively.
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A flagpole is 25 feet tall. A rope is tied to the top of the flagpole and secured to the ground 16 feet from the base of the flagpole. Draw the situation and then use the Pythagorean theorem to estimate the length of the rope to the nearest integer value
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P. theorem -- a^2 + b^2 = c^2
a = 25
b = 16
so 25^2 + 16^2 = c^2
c^2 = 881
c = sqrt881
The price of a notebook was
$3.35
yesterday. Today, the price fell to
$3.10
. Find the percentage decrease. Round your answer to the nearest tenth of a percent.
Answers
.25/3.35 = .0746
.0746*100 = 7.46 or 7.5 rounded
Joe Jay purchased a new colonial home for $260,000, putting down 20%. He decided to use Loyal Bank for his mortgage. They were offering a 6½% for a 25-year mortgage. The principal after the first payment had a balance outstanding of:
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Final answer:
The outstanding balance on Joe Jay's mortgage after the first payment cannot be determined without the monthly payment amount. Typically the initial payments are mainly applied to interest, so the principal would remain close to the financed amount of $208,000.
Explanation:
Joe Jay made a 20% down payment on a $260,000 home, which equals $52,000 ($260,000 * 0.20). The remaining balance he would need to finance through a mortgage would be $260,000 - $52,000 = $208,000. To find out the balance outstanding after the first payment, we would typically use an amortization formula or a financial calculator, considering the 6.5% annual interest rate and the 25-year term of the mortgage. Unfortunately, without additional information such as the monthly payment amount, we cannot calculate the exact principal balance outstanding after the first payment. Generally, the first few payments in an amortization schedule primarily cover interest, so the principal would not change much from the initial $208,000.
Final answer:
The principal after the first payment has an outstanding balance of $206,830.79.
Explanation:
To find the principal after the first payment, we need to calculate the amount of the loan that remains after the down payment and the first payment.
Step 1: Calculate the down payment amount by multiplying the purchase price by the down payment percentage: $260,000 * 0.20 = $52,000.
Step 2: Calculate the loan amount by subtracting the down payment from the purchase price: $260,000 - $52,000 = $208,000.
Step 3: Calculate the monthly interest rate by dividing the annual interest rate by 12: 6.5% / 12 = 0.00542.
Step 4: Calculate the principal after the first payment by subtracting the monthly payment from the remaining loan balance: $208,000 - $1,169.21 = $206,830.79.
Therefore, the outstanding balance after the first payment is $206,830.79.
The pair of points is on the graph of an inverse variation. Find the missing value.
(5, 4) and (x, 7)
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Answer:
The missing value of [tex]x =\frac{20}{7} =2 \frac{6}{7}[/tex]
Step-by-step explanation:
The inverse variation is given by: [tex]x \propto \frac{1}{y}[/tex]
Now convert this into an equation we must multiply the constant variation k we get,
[tex]x =\frac{k}{y}[/tex]
To find the value of k;
use the coordinates (5,4) , where x =5 and y =4
then,
[tex]5=\frac{k}{4}[/tex] or
[tex]k =5 \times 4[/tex]
On Simplify, we get:
k = 20
the equation become: [tex]x=\frac{20}{y}[/tex]
When y =7 we have;
[tex]x= \frac{20}{7}[/tex]
(x ,7) = [tex](\frac{20}{7} , 7)[/tex]
therefore, the missing value x is, [tex]x =\frac{20}{7} =2 \frac{6}{7}[/tex]
Answer:
2 6/7
Step-by-step explanation:
cos(2θ) + 7 cos(θ) = 8
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Jason scored 14,568 points playing a video game. The all-time high score is 22,401 points. How much greater is the all-time high score than Jason's score?
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22,401-14,568=7,833
Which of these numbers is composite? 29, 41, 47, 82, 89
Answers
82 is a composite number.
2cos^2x+cosx-1=0
Find the degree solutions
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cos x=t
2t²+t-1=0
t=[-1⁺₋√(-1+8)]/2=(-1⁺₋3)/4
We have two possible set solutions:
First set solutions.
t₁=(-1-3)/2=-4/4=-1
cos x=-1 ⇒x=cos⁻¹ (-1)=π +2kπ or 180º+360ºk (k=(...-2,-1,0,1,2...)
Second set solutions:
t₂=(-1+3)/4=2/4=1/2
cos x=1/2 ⇒ x=cos⁻¹ 1/2=π/3+2kπ U 5π/3+ 2kπ or
60º+360ºK U 300º+360ºK (k=...-2,-1,0,1,2,...)
solutions: first set solutions U second set solutions:
Answer in radians : π +2kπ U π/3+2kπ U 5π/3+ 2kπ (k=...-1,0,1,...)
Answer is degrees: 180º+360ºk U 60º+360ºK U 300º+360ºK (k=...-2,-1,0,1,2,...)
The primary solutions in degrees are x = 60°, 180°, and 300°.
We need to solve the equation 2cos²(x) + cos(x) - 1 = 0 and find the degree solutions.
Let's solve this step-by-step:
First, let u = cos(x). The equation becomes 2u² + u - 1 = 0.This is a quadratic equation in u. Solve it using the quadratic formula: u = [tex]\frac{-b \pm \sqrt{b^2 - 4ac}}{ 2a}[/tex]Here, a = 2, b = 1, and c = -1. Substitute these values into the quadratic formula:[tex]u = \frac{-1 \pm \sqrt{1^2 - 4(2)(-1)}}{ (2 * 2)}[/tex]
u = [-1 ± √(1 + 8)] / 4
u = [-1 ± √9] / 4
u = [-1 ± 3] / 4This gives us two solutions: u = 1/2 and u = -1.Recall u = cos(x):
cos(x) = 1/2 leads to x = 60° and x = 300°
cos(x) = -1 leads to x = 180°Thus, the solutions to the equation 2cos²(x) + cos(x) - 1 = 0 in degrees are x = 60°, 180°, and 300°.
The price of a notebook was
$3.90
yesterday. Today, the price fell to
$3.40
. Find the percentage decrease. Round your answer to the nearest tenth of a percent.
Answers
Final answer:
The percentage decrease in the price of the notebook from $3.90 to $3.40 is 12.8% when rounded to the nearest tenth of a percent.
Explanation:
To find the percentage decrease in the price of a notebook from $3.90 to $3.40, we use the formula for percentage change:
Percentage Change = [(Old Price - New Price) / Old Price] × 100%
Plugging in our values we get:
Percentage Decrease = [($3.90 - $3.40) / $3.90] × 100%
Percentage Decrease = [$0.50 / $3.90] × 100%
Percentage Decrease = 0.1282 × 100%
Percentage Decrease = 12.82%
When rounded to the nearest tenth, the percentage decrease is 12.8%.
Given the following sets.
A=(0,1,2,3)
B=(a,b,c,d)
C=(0,a,2,b)
Find A n C.
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Answer:
A ∩ C = {0, 2}
Step-by-step explanation:
The elements that sets A and C have in common are {0, 2}.
The male Cuban tree frog is about 2/5 the size of the female Cuban tree frog. The average size of the female Cuban tree frog is 6 inches. what is he size of the male cuban tree frog?
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The size of the male Cuban tree frog is 2 2/5 inches.
Given that, the male Cuban tree frog is about 2/5 the size of the female Cuban tree frog. The average size of the female Cuban tree frog is 6 inches.
We need to find the size of the male Cuban tree frog.
How to multiply fractions with whole numbers?Multiplying fractions with whole numbers is an easy concept. We just need to convert the whole number into a fraction by writing 1 as the denominator and writing the whole number as the numerator. Then it is multiplied by the given fraction. After multiplying these, the final result should be in the form of a proper fraction or a mixed fraction.
Now, 2/5 × 6
=12/5
=2 2/5
Therefore, the size of the male Cuban tree frog is 2 2/5 inches.
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Furry Pets pet store has 20 animals and 2/5 of them are puppies. Pets Galore pet store has 12 animals and 3/4 of them are puppies. Which store has more puppies?
Furry Pets
Pets Galore
Each store has the same number of puppies
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20 x 2/5
40/5
8
Furry Pets has 8 puppies.
Pets Galore has 12 animals and 3/4 puppies.
12 x 3/4
36/4
9
Pets Galore has 9 puppies.
8 is less than 9, so Pets Galore has more puppies.
1. An average of 50,000 people visit Riverside Park each day in the
summer. The park charges $21.00 for admission. Consultants predict
that for each $1.00 increase in the entrance price, the park would lose
an average of 3,500 customers per day.
(a) Express the daily revenue from ticket sales, R as a function of
the number of $1.00 price increases, x.
(b) What ticket price(rounded to nearest cent) maximizes the revenue
from ticket sales?
(c) What ticket price will lead to no revenue?
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Determine the ticket price that leads to zero revenue by setting the equation equal to zero and solving for the variable which is $17.50
Explanation:To solve this problem, we first need to express the revenue from ticket sales as a function of the number of $1.00 price increases. We can use the formula R = (50,000 - 3,500x) * (21 + x), where R represents the daily revenue and x represents the number of price increases.
N= Number of visitors and $P = price $R = Revenue
N = 50,000 - (P-15)*2500
R = N*P = 50,000P -2,500P^2 + 15*2500P
R = 87,500P -2,500P^2
dR/dP = 87,500 - 5000P = 0 for max
P = $17.50 for max revenue
Next, we can find the ticket price that maximizes the revenue by finding the vertex of the quadratic equation. The ticket price that leads to no revenue can be found by setting the daily revenue equal to zero and solving for x.
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A guy walks into the store and steals $100 bill from the register without the owner’s knowledge. He comes back 5 minutes later and buys $70 worth of goods with the $100 bill. The owner gives him back $30 in change. How much money did the owner lose?
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first the guy steals $100 from the owner. Therefore that $100 is a direct loss for the owner.
the same guy comes and pays $100 for goods worth $70. and the balance is paid back to the guy.
So the owner gets 100 and pays back 30 and gives goods worth 70. Therefore that transaction is cancelled as the amounts have been paid and no net effect with that transaction . the owner gets 70 for the goods he sold so that transaction wont lose his money. the fact that the guy paid for the bill with the money he stole isn't relevant here as the transaction has been completed
so the only loss for the owner is the $100 the guy stole at first
answer is $100
Answer:
The money that owner loses is:
$ 100
Step-by-step explanation:
Since, the guy walks into the store and steals $100 bill from the register without the owner’s knowledge.
Again he comes back with the bill and buys $70 worth of goods with the $100 bill. The owner gives him back $30 in change.
This means that the loss that the owner gets at the starting is recovered as the bill is returned back to the owner and the only loss that is remaining is the cost of the goods that he buy (i.e. $ 70 ) and cost that owner returned him (i.e. $ 30)
Hence, the total loss of the owner is:
$ 70+$ 30=$ 100
I need to find the length x, to the nearest whole number
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One integer is 6 less than another . the sum of their squares is 50 . find the integers
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1^2 = 1
7^2 = 49
49+1 = 50
A guy walks into a store and steals $100 from register, comes back and buys $70 worth of merchandise, pys for it with same $100 and gets $30 cash back. how much did store lose?
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Given that the store already lose $100 stolen by the guy, this guy also bought a merchandise worth 70$, and gets a change of $30. The merchandise was paid, but still, the store lost $100, and then an additional $30, for giving it back to the guy. So the total lost of the store would be $130. Hope this answer helps.
What is the next number 3 4 6 9 13 18 24
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How many solutions exist for the given equation? 12x+1=3(4x+1)-2
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12x=3(4x+1)-3
12x=12x+3-3
12x=12x
there are infinite solutions in that no matter what x is equal to, the equation will always be true (at least I think that's the answer...)
A telemarketer will make 25 calls in one hour. the probability of making a sale on any given call is .09. what is the probability that he will make at least one sale during the hour?
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The probability that he will make at least one sale during the hour will be 0.766.
What is binomial distribution?Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as
[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]
A telemarketer will make 25 calls in one hour. the probability of making a sale on any given call is .09.
Then the probability that he will make at least one sale during the hour will be given as,
P(x ≥ 1) = 1 - P(x = 1)
P(x ≥ 1) = 1 - ²⁵C₁ (0.09)¹ (1 - 0.09)²⁴
P(x ≥ 1) = 1 - 25 x 0.09 x 0.10399
P(x ≥ 1) = 1 - 0.233978
P(x ≥ 1) = 0.766
The probability that he will make at least one sale during the hour will be 0.766.
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It is observed that 55.50 mL of water at 20°C completely fills a container to the brim. When the container and the water are heated to 60°C, 0.35 g of water is lost. (a) What is the coefficient of volume expansion of the container? (b) What is the most likely material of the container? Density of water at 60°C is 0.98324 g/mL.
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The coefficient of volume expansion of the container is approximately 0.000161/°C. Based on this, the container is most likely made from a material with similar coefficient value, such as Pyrex glass.
Explanation:The first thing to note is that the change in volume of the water is equal to the volume of the water that was lost through evaporation when the water and its container were heated. This volume can be found by dividing the amount of water lost (0.35g) by its density at 60° C (0.98324 g/mL), giving a volume loss of about 0.356 mL.
The coefficient of volume expansion of the container can be calculated using the formula ΔV/V0 = β ΔT, where ΔV is the change in volume, V0 is the initial volume, β is the coefficient of volume expansion, and ΔT is the change in temperature. Solving for β gives, β = ΔV / (V0 * ΔT) = 0.356 mL / (55.50 mL * 40C) gives approximately 0.000161/°C.
Material of the container can then be inferred based on its coefficient of volume expansion. The value of β is in the order of 10^-5/°C which indicates that the most likely material options are glass or metal, as these materials have coefficients of volume expansion in that range. Of these, Pyrex glass has a value that is closest to the calculated coefficient of volume expansion, around 0.000032/°C.
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x:2,4,5,7,8 y:4,8,10,14,16 does this table represent a non or linear function?
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In a zoo the ratio of adults to children is 13 to 11. If there are 96 people in the zoo how many children are there?
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13/24(96) = 1248/24 = 52 <== adults
11/24(96) = 1056/24 = 44 <== children
Erin is buying floor tile to put in a room that is 10 ft. by 15 ft. She has chosen tiles that are 18 in by 18 in. Assuming that she needs to buy 10% extra to be safe, how many tiles will she need to buy?
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so lets see what area we need. 10 ft by 15 ft = 150 ft^2
now out tile area is 1.5ft by 1.5 ft = 2.25 ft^2
150/2.25 =200/3=66+2/3, we need atleast 66 and 2/3rd of a tile, we must by atleast 10% to be extra safe so
10% of 66+2/3 is 6.6 + 2/30, so we will by 66+2/3 + 6.6+2/30 =73.3333333333, so we will by a total of 73 tiles.
Erin should buy 74 tiles to be safe.
Since Erin is buying floor tile to put in a room that is 10 ft. by 15 ft., and she has chosen tiles that are 18 in by 18 in., assuming that she needs to buy 10% extra to be safe, to determine how many tiles will she need to buy the following calculation must be performed:
The equality between feet and inches must be established, then the area of the room must be calculated, and then the area of each tile. Then, the area of the room must be divided by the area of the tile to know how many should be used.
1 foot = 12 inches 1.1 x ((10 x 12) x (15 x 12)) / (18 x 18) = X 1.1 x (120 x 180) / 324 = X 1.1 x 21,600 / 324 = X 23,760 / 324 = X 73.33 = X
Therefore, Erin should buy 74 tiles to be safe.
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Ten randomly selected automobiles were stopped, and tread depth of the right front tire was measured. The mean was 0.32 inch, and the standard deviation was 0.08 inch. Find the margin of error for the confidence level of 95%.
If you increase the confidence level will the confidence interval estimate be wider or narrower?
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Solve for x
4ln(4x)=-4
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㏑(4x) = -1
e⁽ⁿ⁽⁴ˣ = e⁻¹
4x = e⁻¹
x = ¹/₄e⁻¹
Height
Salary
64
91
65
94
66
88
67
103
69
77
70
96
72
105
72
88
74
The following data set presents the heights of 12 male law school classmates whose law school examination scores were roughly equal. It also gives their annual salaries 5 years after graduation. Each of them went into corporate law. The height is in inches and the salary in units of $1,000.
Height
Salary
64
91
65
94
66
88
67
103
69
77
70
96
72
105
72
88
74
122
74
102
75
90
76
114
(a) Do the above data establish the hypothesis that a lawyer’s salary is related to his height? Use the 5 percent level of significance.
(b) What was the null hypothesis in part (a)?
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The analysis aims to see if there's a correlation between lawyers' height and salary, using statistical tests to determine if the null hypothesis—which states there is no relationship—should be rejected at a 5% significance level.
Explanation:The purpose of this analysis is to discover whether there is a statistical relationship between the height of male lawyers and their salary five years after graduating from law school. To determine this, we can utilize statistical methods such as correlation and regression analysis. However, it should be noted that merely finding a correlation does not establish causation, and any findings would require a more robust analysis to conclude that height is a determinant factor in salary.
In part (a), if we were to perform the statistical test, we would calculate the correlation coefficient to establish the strength and direction of the relationship between height and salary. If the p-value from this test is less than the level of significance (5%), the null hypothesis would be rejected, suggesting that there is a relationship between height and salary.
The null hypothesis in part (a) states there is no relationship between the height of lawyers and their salary. Specifically, it asserts that any observed association in the sample data results from random variation and does not reflect the population of corporate lawyers.
someone came into my shop and stole $100.00 from the register without my knowledge. The person came back in with the same $100.00 five minutes later and he bought $70.00 worth of items and gave him back $30.00 in change. How much money did I lose?