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.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?
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.
Evaluate the expression 3c – d for the given variable. d = -c + 7
Today only, a table is being sold for $333 . This is 74% of its regular price. What was the price yesterday?
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.
How many integers between 100 and 300 inclusive,are divisible by 10?
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:
boiling point of water is 212 Fahrenheit Paul wants to boil water to make pasta right now he only has ice which is at a temperature of -4 degrees how many degrees must Paul change the temperature of the water for it to become boiling water
Paul must increase the temperature by 216 degrees Fahrenheit to boil his ice and be able to cook his pasta.
Explanation:Paul needs to raise the temperature of the ice he has from -4 degrees Fahrenheit to the boiling point of water, which is 212 degrees Fahrenheit. To determine how many degrees Paul needs to change the temperature, we subtract the current temperature of the ice from the desired temperature to boil water. Here is the step-by-step calculation: Subtract -4 from 212. The result is that Paul needs to increase the temperature by 216 degrees Fahrenheit for the ice to reach the boiling point and cook his pasta.
Learn more about Temperature Change here:https://brainly.com/question/32089365
#SPJ2
what are characteristics of complex numbers
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%.
A baseball manager has 12 players of the same ability how many nine player starting lineup starting create
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:
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
2. Wandabaked168cookies,packagedtheminboxesof12,andsoldeachboxfor $1.20. How many boxes of 12 can be packaged if there are 168 cookies? What was the total amount of money that Wanda made for all of the boxes sold?
------------------------------------------------------
This question is solved using proportions.
In each box, there are 12 cookies.She baked 168 cookies.Thus, to find the number of boxes, we use a rule of three.
1 box - 12 cookies.
x boxes - 168 cookies.
Applying cross multiplication:
[tex]12x = 168[/tex]
[tex]x = \frac{168}{12}[/tex]
[tex]x = 14[/tex]
Thus, 14 boxes can be packaged.
------------------------------------------------------
Now, we find the amount of money she made.
She sold 14 boxes.Each box for $1.20.Thus:
[tex]T = 14 \times 1.2 = 16.8[/tex]
She made $16.8.
A similar question is found at https://brainly.com/question/21369672
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.
To know more about B.C. and A.D.
https://brainly.com/question/12154202
#SPJ5
Use the percent of change to find the new amount 120 pounds decreased by 30%
You put $100 in an account. The account earns $2 simple interest in 6 months. What is the annual interest rate?
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.
Three tables are placed side by side. One table is 2 feet 9 inches wide, another is 4
feet 8 inches wide, and the third is 6 feet 11 inches wide. How wide are they combined?
Write your answer in feet and inches. Use a number less than 12 for inches
Final answer:
The combined width of the three tables is 14 feet 4 inches, calculated by first converting each table's width to inches, adding them together, and then converting the total back to feet and inches.
Explanation:
To find the combined width of the three tables placed side by side, you need to add the widths together. First, convert all measurements to inches, add them, and then convert back to feet and inches.
Table 1: 2 feet 9 inches = (2 × 12) + 9 = 24 + 9 = 33 inches
Table 2: 4 feet 8 inches = (4 × 12) + 8 = 48 + 8 = 56 inches
Table 3: 6 feet 11 inches = (6 × 12) + 11 = 72 + 11 = 83 inches
Now, add the inches: 33 + 56 + 83 = 172 inches.
To convert 172 inches back to feet and inches, divide by 12 (since there are 12 inches in a foot): 172 ÷ 12 = 14 feet 4 inches (since 172 divided by 12 is 14 with a remainder of 4).
Therefore, the combined width of the tables is 14 feet 4 inches.
It takes 23 minutes for 6 people to paint 6 walls. How many minutes does it take 9 people to paint 7 walls?
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
Learn more about Probability here:https://brainly.com/question/22962752
#SPJ6
A square has an area that is less than 100m^2. What is a reasonable range for the graph of the squares side
How many numbers are between 0 and 1/10
what is the value of -2 x^2 +4y if x = -2 and y =3
Simplify 2 square root of 10 times 3 square root of 12
answers
A.6squar rootof120
B.12squar rootof60
C.12squar rootof30
D.5squar rootof120
The simplified form of the expression [tex]2\sqrt{10} \times 3\sqrt{12}[/tex] is [tex]6\sqrt{120}[/tex] which corresponds to answer choice A.
Given: [tex]2\sqrt{10} \times 3\sqrt{12}[/tex]
To find: simplify
We can break down the expression [tex]2\sqrt{10} \times 3\sqrt{12}[/tex] and multiply the roots and whole numbers as follows:
[tex]\text{product is} = 2\sqrt{10} \times 3\sqrt{12} \\\text{product is} = 2 \times 3 \times \sqrt{10} \times \sqrt{12}\\\text{product is} = 6 \times \sqrt{120}\\\text{product is} = 6\sqrt{120}[/tex]
The simplified form of the given expression is 6√120, which corresponds to answer choice A.
Which lines are Parallel? Justify your answer
Answer:
Lines e and f are parallel since their alternate exterior angles 75 ad 75 are congruent.
Step-by-step explanation:
Parallel lines mean that angle relationships exits where specific angles are congruent to each other. 75 and 75 are in the position of alternate exterior angles for lines e and f. Since they are congruent, these lines must be parallel. However, a and b have same side exterior angles which must add to 180. 75 + 115 does not equal 180. It equals 190. Therefore a and b cannot be parallel.
Answer:
E and F on edgenuidy
Step-by-step explanation:
did it rn
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.
Learn more here: https://brainly.com/question/15703332
A 250 ml glass of orange juice contains 22 grams of sugar. how much sugar is in a two-liter (2,000 ml) bottle of orange juice?
Orange juice contains some amount of sugar in it. There is 176 g of sugar present in a 2000 ml bottle of orange juice.
Given:
A 250 ml glass of orange juice contains 22 grams of sugar.
It is required to calculate the amount of sugar present in the 2000 ml bottle of juice.
Now, the amount of sugar present in 1 ml of juice will be,
[tex]\dfrac{22}{250}=\dfrac{11}{125}\rm \; g[/tex]
So, the amount of sugar in 2000 ml of juice will be,
[tex]\dfrac{11}{125}\times 2000=11\times 16\\=176\rm \; g[/tex]
Therefore, there is 176 g of sugar present in a 2000 ml bottle of orange juice.
For more details, refer to the link:
https://brainly.com/question/20414391