By using a rule of 3, we will see that:
The second number is 33.33% larger than the first one.The first number is 25% smaller than the second one.How to find the percentages?
In the first case, we want to know by what percent of the first number is the second larger.
Then the 100% will be taken as the first number, so we have the relation:
100% = 15
And the other number will represent a percentage X, so we write:
X = 20
By taking the quotient of these two equations, we get:
X/(100%) = 20/15
Solving this for X, we get:
X = (20/15)*100% = 133.33%
We can conclude that the second number is 33.33% larger than the first number.
For the second part, we take 20 as our 100%, and we do the same thing:
X = (15/20)*100% = 75%
Then 15 is (100% - 75% = 25%) 25% smaller than 20.
As you can see the percentages are different. Why does this happen? because in each case the 100% represents a different number.
Finally, we can conclude that:
The second number is 33.33% larger than the first one.The first number is 25% smaller than the second one.If you want to learn more about percentages, you can read:
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Two spherical balloons are filled with water. The first balloon has a radius of 3cm, and the second has a radius of 6cm.
How much greater is the volume of water in the larger balloon than in the smaller balloon?
Use 3.14 to approximate pi. Round to the nearest hundredth if necessary.
what is the slope of the line through point (2/3, 4/7) and (2/3, 11/7)
a. 0
b. 1
c. 2/3
d. undefined
A simple random sample of 50 adults was surveyed, and it was found that the mean amount of time that they spend surfing the Internet per day is 54.2 minutes, with a standard deviation of 14.0 minutes. What is the 99% confidence interval (z-score = 2.58) for the number of minutes that an adult spends surfing the Internet per day?
Answer:
The correct answer is 49.1 minutes to 59.3 minutes
Step-by-step explanation:
The 99% confidence interval for the number of minutes that an adult spends surfing the Internet per day is [49.091, 59.308].
What is confidence interval?A confidence interval (CI) is a range of estimates for an unknown parameter.
The formula for confidence interval is mean ± (standard normal variate at α level of significance)*(standard deviation)/ (√sample size)
CI = 54.2 ± 2.58 * 14/√50
CI = 54.2 ± 5.1081
CI = [49.091, 59.308]
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How do you solve
6(3b + 5) = 2(6b - 21) and
10y - 4 = 2(5y - 2)?
Find the area of a trapezoid if the altitude is 6 inches and the median is 8 inches. (Hint: Recall that the median of a trapezoid is equal to half the sum of the bases.)
Answer:
48 sq. in.
Step-by-step explanation:
Formula for finding trapezoid area: A = 1/2(h)(b1 + b2)
They said the median of a trapezoid is equal to half the sum of the bases, so multiply the median by 2 to get the sum of the bases.
Sum of the bases = 8(2) = 16
Now plug what you have into the equation to find the area: A = 1/2(6)(16)
Simplify to get: 48
Hope this helps!
24 red marbles is 40% of how many marbles
Answer:
60 marbles
Step-by-step explanation:
Given: 24 red marbles is 40% of how many marbles
Let number of marbles be x
"24 red marbles is 40% of how many marbles"
24 = 40% of x
solve for x
First change % to decimal
24 = 0.40x
Division property of equality, divide by 0.04 both sides
x = 24÷0.40
x = 60
Hence, 40% of 60 is 24
In a study of 100 new cars, 29 are white. find and , where is the proportion of new cars that are white
You are planning to take a group of friends to the movies for your birthday. The local movie theater charges $12.99 per person. When you check the company's website, you find that they also offer a special group rate. The group rate is only $8.99 per person but also includes a $20 reservation fee in addition to the cost per person
Answer: Hello mate!
lets suppose you have (x -1) friends (then when you count yourself, there are x persons in the group) where x is a natural number.
you have two possible prices at the movie theater:
1) the $12.99 per person, then if you have x persons in the group, the total charge is $12.99*x
2) with the promotion they pay $8.99 per person and includes a $20 reservation, then the total charge is $8.99*x + $20
now, let's find the number x is where the second option is cheaper than the first.
in order to do this, we can regulate both equations in order to determine in which x₀ the costs are the same, then if x< x₀, the first option is cheaper and if x>x₀ the second option is cheaper.
$12.99*x₀ = $20 + $8.99x₀
$12.99x₀ - $8.99x₀ = $20
$4x₀ = $20
x₀ = 20/4 = 5
Then if in your group are less than 5 persons, took option 1.
if there are more than 5 persons, took the option 2
if there are exactly 5 persons, both options cost the same.
Akule borrowed $1500 at an annual simple interest rate of 12%. He paid $270 in interest. For what period of time did Akule borrow money
Using the simple interest formula I = PRT, it is calculated that Akule borrowed $1500 at an annual interest rate of 12% for 1.5 years to pay $270 in interest.
Explanation:The subject of this question is Mathematics, specifically focusing on simple interest calculation. To find out the period of time Akule borrowed money for, we can use the simple interest formula I = PRT, where I is the interest paid, P is the principal amount borrowed, R is the annual interest rate, and T is the time in years. Akule paid $270 in interest on a $1500 loan at 12% annual simple interest. Using the formula, we solve for T as follows:
T = I / (P × R)
T = $270 / ($1500 × 0.12)
T = $270 / $180
T = 1.5 years
Therefore, Akule borrowed the money for 1.5 years.
Akule borrowed the money for 0.18 years.
Explanation:To find the period of time Akule borrowed the money, we can use the formula:
Interest = Principal × Rate × Time
Given that Akule paid $270 in interest and borrowed $1500 at an annual simple interest rate of 12%, we can plug in these values into the formula:
270 = 1500 × 0.12 × Time
Simplifying the equation, we get:
0.12 × Time = 270 / 1500
Time = (270 / 1500) / 0.12
Time = 0.18 years
Hence, Akule borrowed the money for 0.18 years.
On a fraction line 6 friends want to equally share 3 yards of yarn how much yarn does each friend get
A deck of cards has 3 blue, 4 black, and 6 purple cards. Draw 2 cards without replacing any cards. What is the probability of both cards being blue?
(1 pt) find the coordinates of the point (x, y, z) on the plane z = 3 x + 4 y + 4 which is closest to the origin.
The solution to the problem involves setting up and solving a system of equations derived from the distance function in 3D. The minimum point of the distance function corresponds to the point in the plane that's closest to the origin.
Explanation:
To find the coordinates of the point (x, y, z) on the plane z = 3x + 4y + 4 which is closest to the origin, we need to find the minimum distance from origin (0,0,0) to any point on the plane. The distance equation is given by √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²]. This is simply Euclidean distance in 3D.
In this case, we can define the distance function d = √(x² + y²+ (3x + 4y + 4)²). To find the minimum distance, we take the derivative of this distance function with respect to both x and y, set them to 0, and solve the resulting equations. The solutions to these equations yield x and y. We substitute x and y into z = 3x + 4y + 4 to get z.
Finally, solving these equations we obtain the coordinates of the point (x, y, z) on the plane that is closest to the origin.
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Answer:
(-6/13, -8/13, 2/13)
Step-by-step explanation:
You want the point on the plane z = 3x +4y +4 that is closest to the origin.
Normal vectorWhen the plane equation is written in standard form, the variable coefficients comprise a vector that is normal to the plane. The line normal to the plane and passing through the origin can be written in terms of this vector. Solving for the variable in that equation lets us find the point on the plane where the line intersects.
The standard form equation for the plane is ...
3x +4y -z = -4 . . . . . . . subtract 4+z from the given equation
Then the normal to the plane is ...
N = (3, 4, -1)
and the vector equation of the line through the origin is ...
L = (0, 0, 0) +tN = (3t, 4t, -t)
Point of intersectionThe value of t that makes a point on the line satisfy the plane equation is ...
3(3t) +4(4t) -(-t) = -4
26t = -4
t = -4/26 = -2/13
Then the point tN is ...
(-2/13)(3, 4, -1) = (-6/13, -8/13, 2/13)
The point on the plane closest to the origin is (-6/13, -8/13, 2/13).
Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 8y = sin(x).
mike gioulis would like to have $25,000 in 4 years to pay off a balloon payment on his business mortgage. His money market account is paying 1.825% compounded daily Disregarding leap years, how much money must Mike put in his account now to achieve his goal? round to the nearest whole dollar
Mike need to deposit approximately $22,815 in his money market account now, which has a 1.825% interest rate compounded daily, to have $25,000 in 4 years.
Explanation:To find out how much Mike should invest now, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the amount of money accumulated after n years, including interest.
P = principal amount (the initial amount of money)
r = annual interest rate (in decimal)
n = number of times interest applied per time period
t = time the money is invested for in years
In this case, Mike wants to have A = $25,000 in t = 4 years. The interest rate r is 1.825% or 1.825/100 = .01825 in decimal form, and since it is compounded daily, n = 365. So, we can plug into the formula and solve for P:
$25,000 = P(1 + .01825/365)^(365*4)
By performing the calculation, we find that P is approximately $22,815. Mike will therefore need to invest this amount in his money market account now to achieve his goal.
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Evaluate bh for for b = 5 and h = 10. Type a numerical answer in the space provided. If necessary, use the / key to represent a fraction bar. Do not type spaces in your answer.
Answer:
[tex]bh=50[/tex] for b=5 and h=10.
Step-by-step explanation:
Given : The value of b=5 and h=10.
To find : Evaluate bh ?
Solution :
As we have given bh i.e. b and h are multiplied together,
So, [tex]bh=b\times h[/tex]
Substitute, b=5 and h=10
[tex]bh=5\times 10[/tex]
[tex]bh=50[/tex]
Therefore, [tex]bh=50[/tex] for b=5 and h=10.
Zhi bought 18 tickets for games at a fair. Each game requires 3 tickets. Zhi wrote the expression 18 – 3g to find the number of tickets she has left after playing g games. Diego correctly wrote another expression, 3(6 – g), that will also find the number of tickets Zhi has left after playing g games. Use the drop-down menus to explain what each part of Zhi's and Diego's expressions mean.
Answer: In the picture below.
Step-by-step explanation:
The provided mathematical expressions represent the process of calculating Zhi's remaining tickets after playing 'g' games at a fair. '18 - 3g' symbolizes subtracting three times the number of games played from the initial total (18) tickets. '3(6 – g)', on the other hand, corresponds to multiplying the number of tickets per game (3) by the subtraction of already played games from total possible games (6).
Explanation:The subject of this question is based on mathematical expressions and variables. In the case of Zhi's expression, 18 represents the total number of tickets she bought. 'g' corresponds to the number of games played, and 3 is the number of tickets required for each game. Therefore, '18 – 3g' means subtracting three times the number of games played (3g) from the total quantity of tickets (18), which would give us the number of tickets left.
Diego's expression, however, expresses the same idea differently. '6 – g' symbolises the number of games Zhi could play before she runs out of tickets (since 18 tickets divided by 3 tickets per game equals 6 games). The '3' outside the bracket is again the number of tickets each game requires. As such, '3(6 – g)' expresses the multiplication of the tickets needed per game (3) by the difference between the total games possible and the games already played (6-g). This, therefore, provides the same result—Zhi's remaining tickets after g games.
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does anyone know how to answer this question? it's number four on limits.
how many frogs in the population do not have spots on their back
HURRY!!! PLEASE HELP WITH QUESTIONS!!!! WILL MAKE BRAINIEST ANSWER!!!!
THESE ARE ALL THE ONES I GOT WRONG/W WRONG ANSWER!!!
1.Lauren has gross pay of $765 and federal tax withholdings of $68. Determine Lauren's net pay if she has the additional items withheld: Social Security tax that is 6.2% of her gross pay Medicare tax that is 1.45% of her gross pay State tax that is 22% of her federal tax
A.$691.52
B.$666.21
C.636.98-NOT THE ANSWER
D.$623.52
2.Trevor’s total employment compensation is $33,500. If Trevor has no job expenses and his gross pay is $28,600, then his total employee benefits are _____% of his gross pay.
A.4.9
B.8.5
C.14.6-NOT THE ANSWER
D.17.1
3.Which of the following items may be a good consideration in selecting a bank?
I. The bank sends a representative to the local mall to promote new applications.
II. Number of ATMs or bank branches near where you live, shop, work, or travel.
III. Knowledge of personal usage habits and needs.
A.I and II
B.II and III
C.I and III
D.I, II and III- NOT THE ANSWER
4.When choosing a bank, why might ATM availability be valuable to someone who values convenience over cost?
A.ATM's allow you to conduct bank transactions without going to the bank, so a bank without ATM's will require you to come in to the main office for everything.-NOT THE ANSWER
B.Checks are deposited in ATM's, so some retailers will not accept checks from a bank without ATM service.
C.A greater availability of ATM's may make it easier to do bank transactions. Someone may choose this availability over a higher savings interest rate.
D.ATM cards double as debit cards, so a bank without ATM service cannot issue debit cards.
5.Assume that you are going to open a checking account. You are examining different banks and banking accounts to choose a bank account for your needs. Which of the following statements should not be one of your reasons for examining different banks?
A.Being more informed leads to being better prepared to make financial decisions.-NOT THE ANSWER
B.Bank E offers you a chocolate bar for filling out an application for checking and credit at the same time.
C.Banks could have charges that you do not know about until reading carefully.
D.You will become more aware of how well the banks meet your particular needs.
6. Which of the following is not something that you could do with a normal checking account?
A.Deposit cash into your account.
B.Demand in writing that money be paid to another person from your account.-NOT THE ANSWER
C.Give permission to a merchant to demand money from your account.
D.Make purchases or get cash now, and pay back the bank in monthly payments.
7.A point of sale transaction occurs when an ATM withdrawal is made.
Please select the best answer from the choices provided
T-THIS IS THE CORRECT ANSWER ON E2020
F
8.Elizabeth has $252.00 in her account on Sunday. Over the next week, she makes the following changes to her balance via deposits and purchases:
Day
Debit ($)
Credit ($)
Monday
114.60
150.00
Tuesday
79.68
Wednesday
161.39
Thursday
57.40
Friday
22.85
75.00
Saturday
140.55
On what day does Elizabeth first get charged an overdraft fee?
A.Wednesday
B.Thursday
C.Friday-NOT THE ANSWER
D.Saturday
9.Consider the following incomplete deposit ticket:
What was Art’s total deposit? 1st deposit picture
A.$1,701.23
B.$1,545.83
C.$1,856.63- NOT THE ANSWER
D.$1516.35
10.
1. Given gross salary is = $768
Federal tax withholding = $68
Social security = 6.2% or 0.062*765 = $47.43
Medicare tax = 1.45% or 0.0145*765 = $11.09
State tax = 22% or 0.22*68 = $14.96
Now net salary = gross salary - tax deductions
[tex]765-(68+47.43+11.09+14.96)[/tex] = $623.52 (option D)
2. [tex]\frac{33500-28600}{28600}*100[/tex] = 17.13% (option D)
3. Option B.II and III
4. B.Checks are deposited in ATM's, so some retailers will not accept checks from a bank without ATM service.
5. B.Bank E offers you a chocolate bar for filling out an application for checking and credit at the same time.
6. D.Make purchases or get cash now, and pay back the bank in monthly payments.
7. A point of sale transaction occurs when an ATM withdrawal is made- yes this is right.
8. The answer is Thursday.
9. No picture given.
what is the slope of the line that goes through (0,0) (5,1)
Let
[tex]A(0,0)\\B(5,1)[/tex]
we know that
the formula to calculate the slope between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
Substitute the values in the formula
[tex]m=\frac{(1-0)}{(5-0)}[/tex]
[tex]m=\frac{1}{5}[/tex]
therefore
the answer is the option b
the slope is equal to [tex]\frac{1}{5}[/tex]
You have a bag of 42 candies you want to give to your 6 friends. the company that makes the candies guarantees that exactly 6 of the candies in the bag are red, the most delicious color. anyone who doesn't get a red candy will be so upset that they will stop being your friend! but the candies are in identical wrappings, so you are forced to give each friend 7 candies and hope for the best. what's the probability you lose one or more friends?
Final answer:
To calculate the probability of losing one or more friends, we need to calculate the probability that a friend does not get a red candy and multiply it by the number of friends. The probability is 0.458.
Explanation:
To answer this question, we need to calculate the probability that at least one friend will not get a red candy.
First, let's calculate the probability that a friend does not get a red candy. There are 42 candies in the bag and 6 of them are red. So, the probability that a friend does not get a red candy is (42-6)/42 = 36/42 = 6/7.
Since each friend gets 7 candies, the probability that one friend does not get a red candy is (6/7)^7, because each candy is independent. Finally, since there are 6 friends, we multiply the probability by 6 to get the probability that at least one friend does not get a red candy: 6 * (6/7)^7 = 0.458 (rounded to 3 decimal places).
What is 235◦, expressed in radian measure?
plzz help me out, what is -4a +9>9
Solve.
[tex]2\pi \sqrt{ \frac{ \frac{9}{2} }{32} } [/tex]
If n is a term of the sequence 2, 5, 8, 11, ..., which expression would give the value of n?
what are possible solutions to a system of linear equations and what do they represent graphically?
Final answer:
Solutions to a system of linear equations are represented graphically as the intersections of lines on a graph and can be unique, infinitely many, or none. Graphical representations are essential in various applications, like economic models, and software like R facilitates solving these systems.
Explanation:
Possible solutions to a system of linear equations can be one of three types: a unique solution, infinitely many solutions, or no solution. Graphically, these solutions are represented by the intersections of lines on a graph. In the case of a unique solution, the lines intersect at exactly one point.
For example, consider two linear equations of the form y = mx + b. Graphically, each equation is represented by a straight line. Where these lines cross is the solution to the system. If both equations produce the same line, they have infinitely many solutions since every point on the line satisfies both equations.
A line with a slope of 2 passes through (3,9) Which choice is an equation of this line?
The equation of the line with a slope of 2 passing through the point (3, 9) is y = 2x + 3.
The equation of a line with slope (m) passing through a point (x₁, y₁) is given by the point-slope form:
y - y₁ = m(x - x₁)
The slope (m) is 2, and the point (x₁, y₁) is (3, 9). Plug these values into the equation:
y - 9 = 2(x - 3)
Now, you can simplify this equation:
y - 9 = 2x - 6
To isolate y, add 9 to both sides:
y = 2x - 6 + 9
y = 2x + 3
Therefore, the equation of the line with a slope of 2 passing through the point (3, 9) is y = 2x + 3.
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Given the area of a triangle is 14x^2 +15x+4 and the base is 4x+2,write the algebraic expression for the height
A mutual fund has total assets of 2.4 million dollars and 300,000 shares. What is the net asset value of one share of the fund? a. $0.08 b. $0.80 c. $8.00 d. $80.00
Answer:
Net assest value of one share is $8 .
Option (c) is correct .
Step-by-step explanation:
As given
A mutual fund has total assets of 2.4 million dollars and 300,000 shares.
As 1 million = 1000000
Total assest value = $2.4 × 1000000
Thus
[tex]Net\ asset\ value\ of\ one\ share = \frac{2.4\times 1000000}{300000}[/tex]
Put all the values in the above
[tex]Net\ asset\ value\ of\ one\ share = \frac{24\times 1000000}{300000\times 10}[/tex]
[tex]Net\ asset\ value\ of\ one\ share = \frac{24}{3}[/tex]
Net asset value of one share = $8 .
Therefore net assest value of one share is $8 .
Option (c) is correct .
the answer to this math question
The drawing shows the friends ended up with 1/2 the pie.