The sale price of an item is $45 after a 40% discount is applied. What is the original price of the item?
The original price of the item is $75.
Suppose the original price of the item =x
Discount =40%
What is the percentage?The percentage is the value per hundred.
Given discounted price or sale price of the item =$45
This means [tex]x-\frac{x*40}{100} =45[/tex]
[tex]\frac{60x}{100} =45[/tex]
[tex]\frac{3x}{5} =45[/tex]
[tex]x=75[/tex]
So, the original price of the item =$75
Hence, the original price of the item is $75.
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The temperature in Fairbanks, Alaska, fell 10 degrees in 2 hours.
Explain why the average temperature change was –5ºF per hour.
The temperature fall can be represented by −10. To find the average change per hour, divide −10 by 2. −10 divided by 2 is −5.
Sally's soccer team won 68% of the games they played.if they won 17 games, how many did they play?
Answer: The total number of games played are 25
Step-by-step explanation:
Let the total number of games played be 'x'
We are given:
Number of games won = 17
Percentage of games won = 68 %
Calculating the total number of games:
[tex]68\% \text{ of x}=17[/tex]
So,
[tex]\frac{68}{100}\times x=17\\\\x=\frac{17\times 100}{68}=25[/tex]
Hence, the total number of games played are 25
In a 4 x 3 factorial design, there are how many levels of the first grouping factor?
James covers a distance of 8 meters in the first second of a 100 meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started? a. 11 c. 28 b. 20 d. 80
Answer:
Option b. 20 meters
Step-by-step explanation:
James covers a distance of 8 meters in the first second of 100 meter race.
Then, he sprints at a speed of 9 meters per second.
We have to find how far is James from the finish line 9 seconds after the start of the race.
James covers distance in first second = 8 meters.
Time remaining in 9 seconds after running 8 meter = 9 - 1 = 8 seconds.
In another 8 seconds James covers the distance = speed × time
= 9 × 8 = 72 meters
Total distance covered in 9 seconds = 8 + 72 = 80 meters
Distance remaining in 100 meter race after 9 seconds = 100 - 80 = 20 meters.
James is 20 meters far from the finish line 9 seconds after the race has started.
Option b. 20 meters is the answer.
Determine whether each of these sets is the power set of a set, where a and b are distinct elements.
a.∅
c.{∅,{a},{∅,a}}
Mary invests £12000 in a saving account. The account pays 1.5% compound interest per year. Work out the value of her investment after 2 years.
To find the value of Mary's investment after 2 years in a saving account with compound interest, we can use the compound interest formula. Substituting the given values into the formula gives us £12363.61.
Explanation:To calculate the value of Mary's investment after 2 years, we can use the compound interest formula: A = P(1 + r/n)^(nt), where:
A is the final amountP is the principal amount (initial investment)r is the annual interest rate (as a decimal)n is the number of times the interest is compounded per yeart is the number of yearsIn this case, the principal amount is £12000, the annual interest rate is 1.5% (0.015 as a decimal), and the number of times the interest is compounded per year is 1. Plugging these values into the formula, we get:
A = 12000(1 + 0.015/1)^(1*2)
Simplifying this, we get:
A = 12000(1.015)^2
Calculating further, we get:
A ≈ 12000(1.030225) ≈ £12363.61
Therefore, the value of Mary's investment after 2 years is approximately £12363.61.
The diagram shows a square of side 7 cm with two quadrants drawn inside. Find the area of the shaded region. (take pi= 22/7)
Its number 15. Thank you
If one score is randomly selected from a normal distribution with m = 100 and s = 20, the probability of obtaining a score between x = 90 and x = 100 is p = 0.3085.
a. True
b. False
Please help badly I cannot answer
Bryson hopes to win a three-day vacation in a drawing that is being held at his office. He purchased 40 raffle tickets. There were 500 raffle tickets sold. What is the theoretical probability of Bryson winning the trip?
A-2/25
B-1/5
C-4/5
D-500/40
Lenny uses two pieces of yarn for a craft project. The first piece is 5.89 meters long. The second piece is 2.147 meters long. What is the total length of the two pieces of yarn? Enter your answer in the box. M__
Answer: 8.04 meters
Step-by-step explanation:
length of first piece of yarn = 5.89 meters
length of second piece of yarn = 2.147 meters
Total length of of the two pieces of yarn = length of first piece of yarn + length of second piece of yarn = 5.89 meters + 2.147 meters = 8.037 meters
The rule apply for the addition and subtraction is :
The least precise number present after the decimal point determines the number of significant figures in the answer.
Thus the answer will be 8.04 meters as least precise number 5.89 contains two decimal places.
5x-3 (2x-4)=7x+16. solve for x
Which pair of measurements is not equivalent?
24 feet, 8 yards
24 inches, 2 feet
10 feet, 120 inches
3 miles, 15,480 feet
The pair of measurements that is not equivalent is 3 miles and 15,480 feet. All other pairs are equivalent when converted to the same units. This determines which measurements do not match in the same units.
To determine which pair of measurements is not equivalent, we need to convert them into the same units and compare them:
24 feet, 8 yards: 1 yard = 3 feet, so 8 yards = 8 * 3 = 24 feet. Therefore, 24 feet is equivalent to 8 yards.24 inches, 2 feet: 1 foot = 12 inches, so 2 feet = 2 * 12 = 24 inches. Therefore, 24 inches is equivalent to 2 feet.10 feet, 120 inches: 1 foot = 12 inches, so 120 inches = 120 / 12 = 10 feet. Therefore, 10 feet is equivalent to 120 inches.3 miles, 15,480 feet: 1 mile = 5280 feet, so 3 miles = 3 * 5280 = 15,840 feet. Therefore, 3 miles is not equivalent to 15,480 feet.Thus, the pair of measurements that is not equivalent is 3 miles, 15,480 feet.
Write an equation of the line in the figure.
For the box shown, the total area is 94 cm2. determine the value of x
Part a determine the correct sketches for v=100cos(ωt+ϕ) versus ωt for ϕ=90∘, 45∘, 0∘, −45∘, and −90∘.
Consider the equation y = 14 – 2x. with y on the vertical axis and x on the horizontal axis, the horizontal intercept of this line is
Explain how to solve 2x + 7 = 15
The formula f=5280m can be used to convert a measurement of f feet to an equivalent measurement m miles. If an airplane flies at 21,120 feet above the ground, how much is that in miles?
A. 4 miles
B. 5.3 miles
C. 111, 513, 600 miles
D. 132, 620, 600 miles
A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]\frac{y}{x}=k[/tex] or [tex]y=kx[/tex]
In this problem we have
Points [tex](2,14)[/tex] and [tex](4,28)[/tex]
so
Find the value of k
First point
[tex]\frac{14}{2}=k[/tex]
[tex]k=7[/tex]
Second point
[tex]\frac{28}{4}=k[/tex]
[tex]k=7[/tex]
the function is
[tex]y=kx[/tex] --------> substitute the value of k
[tex]y=7x[/tex]
therefore
the answer is
[tex]y=7x[/tex]
In this problem with a single point was sufficient to calculate the equation, since in a direct variation the line passes through the origin, it is not necessary to use the formula of the slope
I an a factor of 28. the other factor is 4. what number am i
What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?
It can be convenient to subtract the right side of the inequality from both sides.
... 2(3x -1) -(4x -6) ≥ 0
... 2x +4 ≥ 0 . . . . . . . . . collect terms
... x +2 ≥ 0 . . . . . . . . . . divide by the coefficient of x
... x ≥ -2 . . . . . . . . . . . . add the opposite of the constant
Any value of x that is at least -2 will be in the solution set.
A backpack that normally sells for 39 is on sale for 34% off. Find the amount of the discount and the sale price.
What is the mean of the high temperatures, in degrees Fahrenheit, for the week? Show your work.
Find the specified element in the inverse of the given matrix
Why do you round 117290 up to 120000
The three tools the Federal Reserve uses to enact monetary policy are:
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Unfortunately, arsenic occurs naturally in some ground water†. a mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. a well in texas is used to water cotton crops. this well is tested on a regular basis for arsenic. a random sample of 36 tests gave a sample mean of x = 6.8 ppb arsenic, with s = 2.9 ppb. does this information indicate that the mean level of arsenic in this well is less than 8 ppb? use α = 0.01. (a) what is the level of significance? 0.01 state the null and alternate hypotheses. h0: μ = 8 ppb; h1: μ > 8 ppb h0: μ = 8 ppb; h1: μ < 8 ppb h0: μ > 8 ppb; h1: μ = 8 ppb h0: μ < 8 ppb; h1: μ = 8 ppb h0: μ = 8 ppb; h1: μ ≠ 8 ppb (b) what sampling distribution will you use? explain the rationale for your choice of sampling distribution. the standard normal, since the sample size is large and σ is known. the student's t, since the sample size is large and σ is unknown. the student's t, since the sample size is large and σ is known. the standard normal, since the sample size is large and σ is unknown. what is the value of the sample test statistic? (round your answer to three decimal places.) -2.483 (c) estimate the p-value. p-value > 0.250 0.125 < p-value < 0.250 0.050 < p-value < 0.125 0.025 < p-value < 0.050 0.005 < p-value < 0.025 p-value < 0.005 sketch the sampling distribution and show the area corresponding to the p-value. webassign plot webassign plot webassign plot webassign plot (d) based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? are the data statistically significant at level α? at the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. at the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. at the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. at the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) interpret your conclusion in the context of the application. there is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb. there is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.