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.
Why do you round 117290 up to 120000
will mark brainliest!!
solve this system of linear equations. separate the x- and y- values with a coma. 9x=27-9y
20x=71-9y
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.
Tickets for rides at the fair cost $0.75 each you can also buy a roll of 25 tickets for $15 what is the cost of each ticket if you buy a roll of tickets
Final answer:
The cost per ticket when buying a roll of 25 tickets for $15 at the fair is $0.60, which is less than the single ticket price of $0.75.
Explanation:
The student has asked about the cost of each ticket if bought in a roll at a fair. To find the cost per ticket when purchasing a roll of 25 tickets for $15, you simply divide the total cost of the roll by the number of tickets in the roll.
Cost per ticket = Total cost of the roll / Number of tickets in the roll
Cost per ticket = $15 / 25
Cost per ticket = $0.60
Therefore, when buying a roll of tickets, the cost of each ticket is $0.60, which offers a saving compared to the single ticket price of $0.75.
Write an equation of the line in the figure.
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.
The three tools the Federal Reserve uses to enact monetary policy are:
Hey there! Hope this helps!
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
Find the specified element in the inverse of the given matrix
Find the probability that in a family of 4 children there will be
a.at least 1 boy
b.at least 1 boy and at least 1 girl
c.out of 2000 families with 4 children each how many would you expect to have 1 or 2 girls. assume that the probability of a male birth is 1/2.
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
Its number 15. Thank you
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.
To get more about the percentage visit:
https://brainly.com/question/24304697
Present 5 mixed numbers that add up to the whole number 10.
Please help badly I cannot answer
what is 5.62 rounded to?
use all place values.
Evaluate the line integral c y3 ds,
c.x = t3, y = t, 0 ≤ t ≤ 3
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)
which algebraic expression represents the "phrase the quotient of -8 and the sum of a number and three"
A -8/g+3
B 8/g+3
C -8+g/3
D -8/g +3
The algebraic expression represents the given phrase is -8/(g+3). Therefore, option A is the correct answer.
The given phrase is "the quotient of -8 and the sum of a number and three".
We need to identify which algebraic expression represents the given phrase.
What is an algebraic expression?Algebraic expressions are the mathematical statement that we get when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.
Let the unknown number be g.
Now, the quotient of -8 and the sum of a number and three=-8/(g+3)
The algebraic expression represents the given phrase is -8/(g+3). Therefore, option A is the correct answer.
To learn more about an expression visit:
brainly.com/question/16804733.
#SPJ2
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
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.
What is the mean of the high temperatures, in degrees Fahrenheit, for the week? Show your work.
The sutton police department must write, on average, 6 tickets a day to keep department revenues at budgeted levels. suppose the number of tickets written per day follows a poisson distribution with a mean of 6.5 tickets per day. interpret the value of the mean.
can someone please help with transformations of parent functions
How many real solutions does the system have Y=-3x-3 Y=x^2-3x+5
A backpack that normally sells for 39 is on sale for 34% off. Find the amount of the discount and the sale price.
An omelet station uses 3 eggs to make each omelet. What is the cost for the total number of eggs in a single omelet if a case of 30 dozen eggs has an as-purchase cost of 32.40?