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?
2.8 repeating as a fraction
Two algebraic expressions separated by an equal symbol in between them and with the same value are called equations.
Example = 2 x +4 = 12
here, 4 and 12 are constants and x is variable
A collection of constants, variables connected using one or more arithmetic operator is called an expression
Example = 4 y, 3 x+4.
Consider an equation to prove 2.8 as a repeating fraction.
Let x = 2.8 repeating
Multiply both sides of the equation by 10 to get a whole number.
10 x = 28.8 repeating
Next, we subtract the original equation from the multiplied equation to eliminate the repeating part:
10 x - x = 28.8 repeating - 2.8 repeating
9 x = 26
Now, we can solve for x by dividing both sides of the equation by 9
x = [tex]\dfrac{26}{9}[/tex]
Therefore, the decimal number 2.8 repeating can be expressed as the fraction [tex]\dfrac{26}{9}[/tex].
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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?
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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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?
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)?
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.
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?
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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Brandy wants to buy a digital camera that costs $300. Suppose she saves $15 each week. In how many weeks will she have enough money for the camera?
It will take Brandy 20 weeks to save enough money to buy the digital camera.
To find out how many weeks it will take for Brandy to save enough money for the camera, we can set up an equation:
Let x be the number of weeks it will take for Brandy to save enough money.
$15 * x = $300
Solving for x:
x = $300 / $15
x = 20
Therefore, it will take Brandy 20 weeks to save enough money to buy the digital camera.
Given the following sets.
A=(0,1,2,3)
B=(a,b,c,d)
C=(0,a,2,b)
Find A n C.
Answer:
A ∩ C = {0, 2}
Step-by-step explanation:
The elements that sets A and C have in common are {0, 2}.
what is the solution to this equation?
ds/dt=cost + sint where s(\pi)=1
In the following distribution of the variable semesters completed, which is the mode: 4, 3, 1, 0, 3, 3, 4, 0, 3, 2?
If net income is $115,000 and interest expense is $30,000 for 2012 what is the rate earned on total assets for 2012 (round percent to one decimal point)?
How many solutions exist for the given equation? 12x+1=3(4x+1)-2
A retiree invests $5,000 in savings plan that pays 4% per year. What will the account balance be at the end of the first year ?
How many times do you need to multiply by ten to get from 0.3637 to 363.7
What is the next number 3 4 6 9 13 18 24
Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume that [tex] \frac{ \sqrt{x^2-36} }{x} [/tex] 0 ≤ θ < π/2.
x=6secФ
41 divided by 278.8=
Determine an equation for a function that has a slope of -5 and crosses the x-axis at (3,0)
To find the equation of the line with a slope of -5 that crosses the x-axis at (3,0), use point-slope form to get y = -5x + 15, which is the required equation.
Explanation:To determine an equation for a function that has a slope of -5 and crosses the x-axis at (3,0), you can use the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Here, the slope m is -5 and the point on the line is (3,0). Plugging these values into the point-slope form, we get:
y - 0 = -5(x - 3)
This simplifies to:
y = -5x + 15
This equation represents a line with a slope of -5 that crosses the x-axis at the point (3,0), meeting all the conditions given in the question.
Solve for x
4ln(4x)=-4
Pamela's age is two times Jiri's age. The sum of their ages is 63 . What is Jiri's age?
Solve for B
6=10B+12C
One integer is 6 less than another . the sum of their squares is 50 . find the integers
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.
Aurelio can choose between 3 pairs of pants and 4 shirts .How many different outcomes are in the sample space
Answer:
12
Step-by-step explanation:
a car is purchased for 26,000 after each year the resale decrease by 35% what will the resale value be
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
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?
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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I need to find the length x, to the nearest whole number
The pair of points is on the graph of an inverse variation. Find the missing value.
(5, 4) and (x, 7)
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:
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:
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.