To determine the original price of Janelle's sneakers, we calculate the inverse of the 15% discount that left her with a final price of $75.65, revealing the original price to be $89.00.
To find the original price of the sneakers that Janelle bought with a 15% discount, we need to understand that the final price after the discount represents 85% of the original price. This is because a 15% discount reduces the original price by 15%, leaving us with 100% - 15% = 85% of the original price. Janelle's sneakers cost her $75.65 after the discount.
Let's denote the original price by x. Therefore, 85% of x is equal to $75.65. We can set up an equation to represent this relationship:
0.85x = $75.65
To find x, we divide both sides of the equation by 0.85:
X = $75.65 / 0.85
x = $89.00
Thus, the original price of the sneakers was $89.00 before the 15% discount.
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:
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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what is the solution to this equation?
ds/dt=cost + sint where s(\pi)=1
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.
A particular restaurant can legally have only 150 people in it at one time. The tables in the restaurant can seat 4 people at a time. The number of tables, t, in the restaurant can be represented by the inequality 4t < 150. What is the maximum number of tables the restaurant can have?
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.
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
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 ?
41 divided by 278.8=
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?
Pamela's age is two times Jiri's age. The sum of their ages is 63 . What is Jiri's age?
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.
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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a car is purchased for 26,000 after each year the resale decrease by 35% what will the resale value be
I need to find the length x, to the nearest whole number
In the following distribution of the variable semesters completed, which is the mode: 4, 3, 1, 0, 3, 3, 4, 0, 3, 2?
The weight of water is 62 1/2 lb per cubic foot. What is the weight of 1 1/9 cubic feet of water?
Final answer:
To determine the weight of 1 1/9 cubic feet of water, convert the mixed number to an improper fraction and multiply by the weight per cubic foot, resulting in approximately 77.16 pounds.
Explanation:
The student is asking to calculate the weight of 1 1/9 cubic feet of water given that the weight of water is 62 1/2 lb per cubic foot. To find the weight of the water, we multiply the volume by the weight per unit volume:
Convert 1 1/9 to an improper fraction: 1 1/9 = 10/9.
Multiply 10/9 cubic feet by 62.5 lb/ft³ (weight of water per cubic foot).
Calculate: (10/9) × 62.5 = 694.44/9 ≈ 77.16 lb.
Hence, the weight of 1 1/9 cubic feet of water is approximately 77.16 pounds.
What is the next number 3 4 6 9 13 18 24
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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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 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
Solve for B
6=10B+12C
Ron Co. sold sweatshirts ($20) and baseball caps ($10). If total sales were $2,860 and people bought 6 times as many sweatshirts as caps, how many of each were sold?
To find the number of baseball caps and sweatshirts sold, we can set up an equation using the given information and solve for the variables. The solution shows that 22 baseball caps and 132 sweatshirts were sold.
Explanation:Let's solve this problem step by step:
Let x represent the number of baseball caps sold.Since people bought 6 times as many sweatshirts as caps, the number of sweatshirts sold would be 6x.The total sales revenue can be calculated by multiplying the price of each item by the number of items sold. So, the equation becomes: 10x + 20(6x) = 2860.Simplifying the equation gives us 10x + 120x = 2860.Combining like terms, we get 130x = 2860.Dividing both sides of the equation by 130, we find that x = 22. So, 22 baseball caps were sold.Since people bought 6 times as many sweatshirts as caps, the number of sweatshirts sold would be 6 * 22 = 132.Therefore, 22 baseball caps and 132 sweatshirts were sold.
The problem is solved by setting up equations based on the given information. Ron Co. sold 132 sweatshirts at $20 each and 22 baseball caps at $10 each to make a total of $2,860 in sales.
Explanation:To solve the problem, let's define the variables representing the number of sweatshirts and caps sold. Let's say 's' equals the number of sweatshirts and 'c' equals the number of baseball caps.
We are given two pieces of information:
The price of a sweatshirt is $20, and the price of a cap is $10. The total sales can be expressed as the sum of the sales from sweatshirts and caps, which gives us the equation 20s + 10c = 2860.
Using the information that s = 6c, we can substitute 6c for s in the total sales equation to get 20(6c) + 10c = 2860. Simplifying this equation, we get 120c + 10c = 2860, which leads to 130c = 2860. Dividing both sides by 130 gives us c = 22.
Now, we can find the number of sweatshirts sold by substituting c into the equation s = 6c. So, s = 6(22) = 132.
Therefore, Ron Co. sold 132 sweatshirts and 22 baseball caps.
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)?
One integer is 6 less than another . the sum of their squares is 50 . find the integers
How many times do you need to multiply by ten to get from 0.3637 to 363.7
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:
How many solutions exist for the given equation? 12x+1=3(4x+1)-2
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?