The total amount of candy left after adding the candy received from the grandmother and the sister, and subtracting the candy eaten by the friend, is approximately 0.63 pounds.
Explanation:First, we add up the amounts of candy you received. You started with 1/3 pound from your grandmother and received an additional 1/2 pound from your sister, for a total of 5/6 pound of candy. However, because your friend ate some, we subtract 1/5 pound from this total. To do this, we need to convert all fractions to have a common denominator, which is 30 in this case. Therefore, 5/6 becomes 25/30, and 1/5 becomes 6/30. Subtraction gives us (25-6)/30 = 19/30 or approximately 0.63 pounds of candy left.
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The sum of 5 consecutive even number is 100 the middle number is
100/5 =20
16 + 18 +20 +22 +24 = 100
middle number is 20
When a measurement in inches is converted to centimeters,will the number of centimeters be greater or less than the number of inches
What is the ratio of 400 to 400 in fraction form
Answer: 400/400 which reduces to 1/1
Step-by-step explanation:
On Monday, a local hamburger shop sold a combined total of 556 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Monday?
To solve problems about spans of time that include B.C. and A.D. dates, you would need to use which numbers?
The correct numbers to use in solving problems about spans of time like B.C. and A.D. should be “integers”.
Integers are whole numbers (not a fractional number or not a decimal number) which can take a value of negative, zero, or positive number. Example of integers would be -1, 0 and 1.
In calculations, the time period would be on the x-axis. Since B.C. and A.D. are two different spans of time, therefore in the calculations, the date of BC should be negative (negative x-axis) while the date of AD should be positive (positive x-axis). This would place the origin as the common reference.
To solve problems about spans of time that include B.C. and A.D. dates, Integers will be used .
What is B.C. and A.D. ?
The terms A.C. and B.C. stands for anno Domini and before Christ
These are used to label years in the Gregorian calendars.
For solving a Problem that involve B.C and A.D. , Integers will be used
As the time span are neither in fraction or decimal
It can be negative , 0 and positive
B.C will be on the negative side of the x axis and A.D. will be equal to the positive side of the x axis.
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Hans's vegetable garden has an area of 400 ft2. It is the shape of a rectangle with a length of 40 ft and a width of 10 ft. He has decided to expand the garden to make room for several new varieties of lettuce. The new garden will be a larger rectangle. He plans on making the new length 3 times the current length and the new width 3 times the current width.
To calculate the new area of Hans's expanded garden, multiply the new length by the new width. The new garden will have an area of 3600 ft^2.
The original garden area is 400 ft2, with a length of 40 ft and a width of 10 ft.
To find the new garden's area after expansion:
Calculate the new length: 40 ft * 3 = 120 ft.Calculate the new width: 10 ft * 3 = 30 ft.Multiply the new length by the new width: 120 ft * 30 ft = 3600 ft2.Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
a.Divide all terms in the equation by a.
b.Subtract the constant (the term without an x) from both sides.
c.Add a constant (in terms of a and b) that will complete the square.
d.Take the square root of both sides of the equation.
e.Solve for x.
Answer:
See below.
Step-by-step explanation:
We are going to take the quadratic formula ax²+bx+c=0
a.Divide all terms in the equation by a.
[tex]\frac{ax^{2} }{a} +\frac{b}{a}x+\frac{c}{a}=0\\\\x^{2} +\frac{b}{a}x+\frac{c}{a} =0[/tex]
b.Subtract the constant (the term without an x) from both sides.
[tex]x^{2} +\frac{b}{a}x+\frac{c}{a} -\frac{c}{a} =\frac{-c}{a} \\\\x^{2} +\frac{b}{a}x=-\frac{c}{a}[/tex]
c.Add a constant (in terms of a and b) that will complete the square.
[tex]x^{2} +\frac{b}{a}x=-\frac{c}{a}\\\\[tex]x^{2} +\frac{b}{a}x+\frac{b^{2} }{4a^{2} } =-\frac{c}{a} +\frac{b^{2} }{4a^{2}}\\\\(x+\frac{b}{2a}) ^{2} =\frac{-4ac+b^{2} }{4a^{2} }[/tex]
d.Take the square root of both sides of the equation.
[tex]x+\frac{b}{2a} =[tex]\\x+\frac{b}{2a} =\frac{\sqrt{-4ac+b^{2} } }{2a}\\x=\frac{\sqrt{-4ac+b^{2} } }{2a}-\frac{b}{2a} [/tex]
e.Solve for x.
[tex]x=-b+\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]
Susan invests
3
times as much money at
11
%
as she does at
7%
. If her total interest after
1
year is
$2000
, how much does she have invested at each rate?
When a crew rows with the current, it travels 18 miles in 3 hours. Against the current, the crew rows 6 miles in 3 hours. Let x=the crew's rowing rate in still water and let y = the rate of the current. Find the rate of rowing in still water and the rate of the current.
The speed of the boat in still water is 4mph and the speed of the current is 2mph.
Using the distance formula expressed as:
Distance = speed * time
d = st
Let x be the crew's rowing rate in still water and;
let y be the rate of the current
If a crew rows with the current and it travels 18 miles in 3 hours, the
3(x+y)=18
If they row against the current, the crew rows 6 miles in 3 hours then;
3(x-y)=6
The equations becomes
x + y = 6
x - y = 2
Add both equations
2x = 6 + 2
2x = 8
x = 4
Recall that x + y = 6
4 + y = 6
y = 2
Hence the speed of the boat in still water is 4mph and the speed of the current is 2mph.
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find the poin on the graph 0f f(x)=1-x^2 that are closest to0(0,0)
Help with this math question
How many numbers are between 0 and 1/10
Use the percent of change to find the new amount 120 pounds decreased by 30%
You buy a pair of jeans at a department store. Jeans 39.99 Discount -10.00 Subtotal 29.99 Sales tax 1.95 Total 31.94 a. What is the percent of discount to the nearest percent? The percent of discount is ___%. b. What is the percent of sales tax to the nearest tenth of a percent? The percent of sales tax is ___% c. The price of the jeans includes a 60% markup. After the discount, what is the percent of markup to the nearest percent? The percent of markup is ___%
The discount offered on the jeans is 25 percent. The sales tax charged on the jeans is 6.5 percent. Markup on the jeans after allowing discount is 60 percent.
a. To find the percent of discount, we need to calculate the actual discount and divide it by the original price, then multiply by 100. From the given information, the original price of the jeans is $39.99 and the discount is $10.00. Therefore, the actual discount is $10.00 and the original price is $39.99. The percent of discount to the nearest percent is:
Percent of discount = (actual discount / original price) x 100
Percent of discount = (10.00 / 39.99) x 100
Percent of discount = 25%
Therefore, the percent of discount to the nearest percent is 25%.
b. To find the percent of sales tax, we need to divide the sales tax by the subtotal, then multiply by 100. From the given information, the subtotal is $29.99 and the sales tax is $1.95. Therefore, the percent of sales tax to the nearest tenth of a percent is:
Percent of sales tax = (sales tax / subtotal) x 100
Percent of sales tax = (1.95 / 29.99) x 100
Percent of sales tax = 6.5%
Therefore, the percent of sales tax to the nearest tenth of a percent is 6.5%.
c. The price of the jeans includes a 60% markup, which means that the selling price is 160% of the cost price. Let x be the cost price of the jeans. Then, the selling price of the jeans is 1.6x. After the discount of $10.00, the selling price becomes 1.6x - 10.00. The percent of markup after the discount to the nearest percent is:
Percent of markup = ((selling price - cost price) / cost price) x 100
Percent of markup = (((1.6x - 10.00) - x) / x) x 100
Percent of markup = (0.6x - 10.00) / x x 100
Percent of markup = 60 - (1000 / x)
Percent of markup = 60%.
So, the percent of markup after the discount is approximately 60%.
Trapezoid ABCD is similar to rectangle EFGH. Side CD is proportional to side ___.
You put $100 in an account. The account earns $2 simple interest in 6 months. What is the annual interest rate?
Evaluate the expression 3c – d for the given variable. d = -c + 7
A standard deck of cards contains 52 cards. one card is selected from the deck. ?(a) compute the probability of randomly selecting aa heartheart or spadespade. ?(b) compute the probability of randomly selecting aa heartheart or spadespade or clubclub. ?(c) compute the probability of randomly selecting aa twotwo or diamonddiamond.
The probability of randomly selecting a heart or a spade is 1/2. The probability of randomly selecting a heart or a spade or a club is 3/4. The probability of randomly selecting a two or a diamond is 17/52.
Explanation:(a) There are 13 hearts and 13 spades in a standard deck of cards. The probability of randomly selecting a heart or a spade can be calculated as:
P(Heart or Spade) = P(Heart) + P(Spade) = 13/52 + 13/52 = 26/52 = 1/2
(b) To find the probability of randomly selecting a heart or a spade or a club, we add the probability of selecting a club to the previous result:
P(Heart or Spade or Club) = P(Heart or Spade) + P(Club) = 1/2 + 13/52 = 39/52 = 3/4
(c) There are 4 twos and 13 diamonds in a standard deck of cards. The probability of randomly selecting a two or a diamond can be calculated as:
P(Two or Diamond) = P(Two) + P(Diamond) = 4/52 + 13/52 = 17/52
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In 2006,111.7 million household owned at least
In 2006, 112.8 million households owned at least one TV set. About 5.8 million households owned 3 or more TV sets in 2006. What percentage of those owning atleast one TV set was this? Round to the nearest integer
5.8 / 112.8 = 0.051418 which is 5.1418 percent, rounds down to 5%.
What is the solution set of x 2 + 5x - 5 = 0?
Answer:
a=1 b=5 c=-5
We solve by using the quadratic formula.
x = -5 +- sq root (5² - 4*1*-5) / (2 * 1)
x = [-5 +- sq root (25 + 20)]/ 2
Step-by-step explanation:
what is 8m-3-7m???????
Answer:
i personally think it's 4
Step-by-step explanation:
even tho this was 4 years ago ehhhhhhh
what are characteristics of complex numbers
Allen's monthly take-home pay is $3000, and his monthly rent is $750. If both his monthly take-home pay and his rent increase by $200, what percentage of Allen's take-home pay will be used to pay rent?
Answer:
29.68%
Step-by-step explanation:
Allen's monthly take-home pay is $3000
His monthly rent is $750
Now both his monthly take-home pay and his rent increase by $200
So, After increase Allen's monthly take-home pay =$3000+$200= $3200
After increase His monthly rent = $750+200=$950
Now we are supposed to find what percentage of Allen's take-home pay will be used to pay rent
So, percentage = [tex]\frac{\text{Rent after increase}}{\text {Take- home pay after increase}} \times 100[/tex]
= [tex]\frac{950}{3200}\times 100[/tex]
= [tex]\frac{950}{32}[/tex]
= [tex]29.68\%[/tex]
Hence 29.68% of Allen's take-home pay will be used to pay rent.
Solve the equation for a. 55a – 44a = 11
One 16-ounce bottle of an energy drink has an average of 500 mg of caffeine with a standard deviation of 25 mg. In a carton containing 30 bottles, what is the standard deviation of the average amount of caffeine?
Final answer:
The standard deviation of the average amount of caffeine in a carton containing 30 bottles of an energy drink is approximately 4.564 mg.
Explanation:
To calculate the standard deviation of the average amount of caffeine in a carton containing 30 bottles of an energy drink, we can use the concept of the sampling distribution of the sample mean.
When independent random samples of a fixed size are taken from a population, the standard deviation of the sample means (σx-bar) is equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is also known as the standard error of the mean.
The formula to find the standard deviation of the sample means is:
σx-bar = σ / √n
In this case, the population standard deviation is given as 25 mg of caffeine, and the sample size is 30 bottles.
So, we calculate the standard deviation of the average amount of caffeine as follows:
σx-bar = 25 mg / √30
σx-bar ≈ 25 mg / 5.477
σx-bar ≈ 4.564 mg (rounded to three decimal places)
Thus, the standard deviation of the average amount of caffeine in a carton containing 30 bottles is approximately 4.564 mg.
Lowell bought 4 1/4 pounds of apples and 3 3/5 pounds of oranges. How many pounds of fruit did lo buy?
Answer:
7.85 pounds (or 7 17/20 pounds)
Step-by-step explanation:
In decimal, the total is ...
4.25 + 3.60 = 7.85 . . . pounds
As mixed numbers, the total is ...
(4 +1/4) + (3 +3/5) = (4 +3) + (1/4 +3/5) = 7 +(5/20 +12/20) = 7 17/20 . . . pounds
Lowell bought 7 17/20 pounds of fruit.
_____
Comment on the math
Any calculator can add these numbers for you. You may have to enter them as (4+1/4) and (3+3/5) if your calculator does not support mixed number entry. Depending on the calculator, you may be able to get it to show you the mixed number result. If you want a mixed number and you get a decimal number, you may have to reduce the fraction yourself:
7 85/100 = 7 17/20 . . . . . . a factor of 5/5 can be removed from the fraction
___
Any two fractions can always be added using the formula ...
a/b + c/d = (ad +bc)/(bd)
Here, that means the sum of 1/4 and 3/5 is ...
1/4 + 3/5 = (1·5 +4·3)/(4·5) = (5+12)/20 = 17/20 . . . . . the result above
In some cases, you may have to reduce the resulting fraction.
Lowell bought [tex]4 \frac{1}{4}[/tex] pounds of fruit.
Explanation:To find the total weight of fruit Lowell bought, we need to add the weights of the apples and oranges together.
Lowell bought [tex]4 \frac{1}{4}[/tex] pounds of apples and [tex]3 \frac{3}{}[/tex] pounds of oranges. To add these fractions, we need to find a common denominator, which in this case is 20.
Converting both fractions to twentieths, we have [tex]\frac{17}{20}[/tex] pounds of apples and [tex]\frac{68}{20}[/tex] pounds of oranges. Adding these together, we get a total of [tex]\frac{85}{20}[/tex] pounds. Simplifying the fraction, we find that Lowell bought [tex]4 \frac{1}{4}[/tex] pounds of fruit.
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what is the relationship between the 3s in 9338
Answer:
The 3 in the hundreds place has 10 times the value of the 3 in the tens place.
Step-by-step explanation:
In a base-10 place-value number system such as the one we customarily use, the value of a given digit is multiplied by 10 when it is placed one position farther to the left of the decimal point.
The threes in this number are in adjacent positions—one is in the tens place, and the one to its left is in the hundreds place. The digit in the hundreds place has a value of 300, which is 10 times the value of 30 that the digit in the tens place has.
If you are given a circle with center c, how do you locate the vertices of a square inscribed in circle c?
Answer:
The square is inscribed in a circle that means the square is drawn inside a circle such that it's vertices lie on the circle.
You need to remember that the vertices of the square lie on the circumference of circle and the center of circle is also the midpoint of diagonals of the square i.e. Diagonal of the square is equal to diameter of the circle.
We could also see the image of such figure.
To locate the vertices of a square inscribed in a circle, follow these steps: draw the circle, choose a point on the circumference, create a radius, find the midpoint, and connect the points to form a square.
Explanation:To locate the vertices of a square inscribed in a circle, you can follow these steps:
Draw the circle with center C.Choose any point on the circumference of the circle and label it A.Draw a line segment from C to A, creating a radius.Construct a perpendicular bisector of the radius to find the midpoint, which we'll call M.Draw a line segment from M to the circumference of the circle, which intersects at two points. Label them B and D.Connect points ABCD to form a square.Now you have located the vertices of a square inscribed in circle C.
what is the value of -2 x^2 +4y if x = -2 and y =3
The best leaper in the animal kingdom is the puma, which can jump to a height of 12 ft when leaving the ground at an angle of 45 degrees. with what speed in si units, must the animal leave the ground to reach that height?