A carpenter is building a rectangular shed with a fixed perimeter of 68 ft. What are the dimensions of the largest shed that can be built? What is its area?
The dimensions of the largest shed are _____ by _____.
The area of the largest shed is _____.
Answer:
The dimensions of the largest shed are 17 ft by 17 ft.
The area of the largest shed is 289 sq ft.
Step-by-step explanation:
Given that:
Fixed perimeter of the rectangular shed = 68 ft
To find:
The dimensions of the largest shed that can be built = ?
And
Area of the largest shed that can be built = ?
Solution:
First of all, let us have a look at the formula for perimeter of a rectangular shape shed:
Perimeter of a rectangle = 2 [tex]\times[/tex] (Length + Width)
68 = 2 [tex]\times[/tex] (Length + Width)
Length + Width = 34
The largest possible values are only in the case when the rectangle is a square.
i.e. Length = Width
Therefore values of length and width are:
Length = Width = [tex]\frac{34}{2} = 17\ ft[/tex]
Area of a square is given by the formula:
[tex]A = Side \times Side[/tex]
[tex]A[/tex] = 17 [tex]\times[/tex] 17 = 289 sq ft
The answer is:
The dimensions of the largest shed are 17 ft by 17 ft.
The area of the largest shed is 289 sq ft.
Order the following numbers from least to greatest
-14/3
-5.1
-4
Answer:
-14/3 -5.1 -4
Step-by-step explanation:
Find the volume of the prism
Answer:
do you have an image for that?
Step-by-step explanation:
Let f(x) = 4x – 2 and g(x) = x + 1. Find the following function value.
(f - g)(-3)
Answer:
(f - g)(3) = 6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = 4x - 2
g(x) = x + 1
Step 2: Find
Find (f - g)(x)
Substitute: (f - g)(x) = 4x - 2 - (x + 1)Distribute -1: (f - g)(x) = 4x - 2 - x - 1Combine like terms: (f - g)(x) = 3x - 3Find (f - g)(3)
Substitute: (f - g)(3) = 3(3) - 3Multiply: (f - g)(3) = 9 - 3Subtract: (f - g)(3) = 6Find the solution of this system of equations
2x - 2y = -20
-2x + 4y = 14
How many five-symbol computer passwords can be formed using the letters A to J and the digits 3 to 6
Answer:
3354 ???
Step-by-step explanation:
i think thats right, have a good day! :)
plz give me brainliest if u can
At the end of a snow storm, Mia saw there was a lot of snow on her front lawn. The temperature increased and the snow began to melt at a steady rate. Let SS represent the depth of snow on Mia's lawn, in inches, tt hours after the snow stopped falling. The table below has select values showing the linear relationship between tt and S.S. Determine the rate at which the snow is melting per hour.
Answer:
the snow per hour is
Step-by-step explanation:
um wait what chart theres no info to awnser this sorry you may delete this awnser :( but im letting ya know
Answer:
1.5 is the answer.
Step-by-step explanation:
what is the value of b and c
Answer:
its 7
Step-by-step explanation:
Andre performs a 90-degree counterclockwise rotation of Polygon P and gets Polygon P', but he does not say what the center of the rotation is. Can you find the center? Explain how you know.
Answer:
eefhhdfbhvfhfajfdhjk,nm?sorry dont knwo
Step-by-step explanation:
find the slope of (6,3) and (5, -1)
Answer:
the slope is 4
Step-by-step explanation:
the slope is found by subtracting the y values for the numerator and then subtracting the x values for the denominator
y values -1-3=-4
x values 5-6=-1
slope=-4
slope=4
-1
Answer:
4
Step-by-step explanation:
Formula for solving for the slope of two points-
(y2-y1)/(x2-x1)
(-1-3)/(5-6)=
-4/-1=
4/1=
4
P÷7 when p=42..................
4x-3=2x+7 Someone Help Please
Answer:
x=5
Step-by-step explanation:
4x-3=2x+7
subtract 2x from both sides
2x-3=7
add 3 to both sides
2x=10
divide both sides by 2
x=5
Answer:
x = 5
Step-by-step explanation:
Original Equation:
4x - 3 = 2x + 7
Add 3 to both sides
4x = 2x + 10
Subtract 2x from both sides
2x = 10
Divide both sides by 2
x = 5
Hope this helps :)
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A grocery store recently changed their apple supplying vendor. The vendor told the store manager that the mean weight for each apple is bell-shaped with # mean of 7.5 ounces and a standard deviation of 1.33 ounce (a) One customer comes to this grocery store and randomly picks 25 apples. What is the mean and standard deviation of the distribution of the mean weight for 25 apples? (b) What is the probability that the mean weight of 25 apples exceeds 8.2 ounces? (c) Another customer randomly picks 10 apples. Will the probability of the mean weight that the 10 apples exceeds 8.2 ounces of this customer be higher than the last customer in part b? Explain it.
Answer:
b) 0.0042495
c) 0.048021
Hence, the probability of the mean weight that the 10 apples exceeds 8.2 ounces of this customer wil be higher than the last customer in part b because the number of random samples in part b is greater that that in part c
Step-by-step explanation:
mean of 7.5 ounces and a standard deviation of 1.33 ounce
When random number of samples are given, we solve using z score with the formula
= z = (x-μ)/σ/√n, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
n is the random number of samples
(a) One customer comes to this grocery store and randomly picks 25 apples. What is the mean and standard deviation of the distribution of the mean weight for 25 apples?
(b) What is the probability that the mean weight of 25 apples exceeds 8.2 ounces?
x > 8.2 ounces
= z = (x - μ)/σ/√n
z = (8.2 - 7.5)/1.33/√25
z = (8.2 - 7.5)/1.33/5
z = 2.63158
Probability value from Z-Table:
P(x<8.2) = 0.99575
P(x>8.2) = 1 - P(x<8.2) = 0.0042495
(c) Another customer randomly picks 10 apples. Will the probability of the mean weight that the 10 apples exceeds 8.2 ounces of this customer be higher than the last customer in part b?
For n= 10
x > 8.2 ounces
= z = (x - μ)/σ/√n
z = (8.2 - 7.5)/1.33/√10
z = 1.66436
Probability value from Z-Table:
P(x<8.2) = 0.95198
P(x>8.2) = 1 - P(x<8.2) = 0.048021
Hence, the probability of the mean weight that the 10 apples exceeds 8.2 ounces of this customer wil be higher than the last customer in part b because the number of random samples in part b is greater that that in part c
Parallel to the line y=-3x + 5 passes through (-4,5)
Answer:
The equation of line that is Parallel to the line y=-3x + 5 passes through (-4,5) is: y = -3x-7
Step-by-step explanation:
Given equation of line is:
[tex]y = -3x+5[/tex]
General form of slope-intercept equation of line is:
[tex]y=mx+b[/tex]
Comparing both we get
m = -3
The slope of two parallel line sis equal.
Let m1 be the slope of line parallel to given line, then
m1 = -3
Putting in general form
[tex]y = -3x+b[/tex]
Putting (-4,5) in equation
[tex]5 = -3(-4) +b\\5 = 12+b\\b = 5-12\\b = -7[/tex]
Putting in the general form, we get
[tex]y = -3x-7[/tex]
Hence,
The equation of line that is Parallel to the line y=-3x + 5 passes through (-4,5) is: y = -3x-7
A patient has been ordered Oxycodone 10mg Q6H PO for 5 days. How many 10mg tablets should be dispensed?
Answer:20 tablets
Step-by-step explanation:
Asked my MD father.
Write a division problem that has a quotient of 12.
At least one of the numbers you give must be a proper fraction. The other can be a proper fraction, whole number, or
improper fraction. Neither the dividend nor the divisor can be 12.
An island population of 20,000, grows by 5% each year, compounded continuously. How many inhabitants will the island have in 5 years according to the exponential growth function? Round your answer down to the nearest integer, and do not include the units in your answer.
Answer:
The answer is "25680.508"
Step-by-step explanation:
Use formula:
[tex]A=Pe^{rt}[/tex]
[tex]=20000 \times e^{((0.05) \times (5))}\\\\=20000 \times e^{(.25)}\\\\=25680.508[/tex]
There are 52 cards in a standard deck of cards, with four of each type of card: Ace ,2,3,4,5,6,7,8,9,10,Jack ,Queen ,King . Let event A be choosing a 7 out of a deck of cards. Identify the numbers of each of the following. Enter the probability as a fraction:
Answer:
The probabilitiy of pulling a seven is 1/13 or 7.69%
Step-by-step explanation:
Im not sure if you wanted just the probability of pulling a seven or if you wanted others as well but to find out the probability you take the total amount of cards, 52, then you take the total amount of 7's in the deck which is 4, one for each card type.
Therefore you get 4/52 or simplified to 1/13 by dividing by 4 on the numerator and the denominator.
The probability is defined as the ratio of favorable outcome to the total number of outcomes. The probability of getting a 7 out of deck of cards is 1 / 13.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
Given that,
The total number of cards = 52
The types of card present in a the deck = 4.
Suppose A be the event of selecting one 7 out of a deck of cards,
Then, the probability of event A can be given as,
P (A) = Number of 7's in the deck ÷ Total number of cards in the deck.
Since, there are four types of cards, the number of 7's in the card is 4.
Thus, P(A) = 4 / 52
=> P(A) = 1 / 13
Hence, the probability selecting one 7 out of a deck of cards is P(A) = 1 / 13.
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Carly purchased 9 1/2 pints of ice cream for a party. If each guest will be served exactly 3/5 pints of ice cream, what is the greatest number of guests that Carly can serve?
Answer:
he can only serve 2
Step-by-step explanation: since 3.5 plus 3.5 is 7.0 if you add one more it turns to 7.0 plus 3.5 10.5 so the greatest he can serve is two people
help pls !! what is the value of K ?
Directions; Write a system of equations for each of the descriptions below, and then solve the systems. Hint: you can graph the equations to find the solutions.
16. Three times one number is equal to two times the larger one and their difference is 1. What are the numbers?
17. Joseph has 30 coins and they are all either dimes or nickels. The total $2.15. How many dimes does he have?
18. A golfer completed 18 holes with a total of 79 strokes. On each hole he met par, which was either four or five each time. How many holes were played in four strokes?
19. There are two numbers. The difference between them equals six, and one of the numbers is three times the other number. There are two pairs of numbers that satisfy these descriptions, What are they?
20. There is a number that is three-fifths the total of the other number. When four is added to one of the numbers their sum will be equal to the other number. There are two pairs of numbers that satisfy these descriptions. What are they?
Answer: Here are the answers. I walked you through 16 in my answer.
16. 3x=2y
1 =y-x
x=2 and y=3
17. $2.15=.10d+.05n
d=30-n
There are 17 nickels and 13 dimes
18. 18=4x+5y (since that's the total amount of holes and each par is either 4 or 5 strokes each)
4x=79-5y (since there are 79 total strokes and each was either 4 or 5)
No solution
Step-by-step explanation: For each problem, you have to write down the information you know, then define variables for the unknown. For 16, for example, they tell you that one number, which I have chosen to call x, is equal to two times the larger number, which I have chosen to name y. So, you'd have an equation that equals x. It also tells you that you need three times x, and two times y, which can be rewritten as 3x and 2y. In other words, 3x=2y. That said, you can move on to the next equation. Since you know the difference is 1, in other words, y-x=1, or y=x+1 ( I isolated y by adding x to both sides), you can put that into your equation as well. From there, I used the substitution method to solve.
3x=2y
so 3x=2(x+1)
y=x+1
3x=2(x+1) --- orig equation
3x=2x+2 --- distributive property (Multiplied x+1 by 2)
x=2 ---- subtracted 2x from both sides
**Now, to find y, you can substitute x into either equation. Since I know y=x+1 where x=2, I know that y must be 3. To check this, you can graph on Desmos. The lines should intersect at (2,3).
For 18, the lines are parallel so they never intersect. There is no solution.
answer:
16. 3x = 2y, 1 = y - x → 2, 3
17. 2.15 = 0.10d + 0.05n, d = 30 - n → 13 dimes and 17 nickels
18. 18 = 4a + 5b = 79, b = 79 - 72 = 7 → 11 holes
19. 3x - x = 6, y = 3x → Pair 1: 3 and 9, Pair 2: 9 and 3
20. a = 3/5b, 2/5b = 4 → Pair 1: 6 and 10, Pair 2: 10 and 6
i hope this helps!! ♡
Factorise fully
15x-10
Answer:
15
x
+
10
y
Factor
5
out of
15
x
.
5
(
3
x
)
+
10
y
Factor
5
out of
10
y
.
5
(
3
x
)
+
5
(
2
y
)
Factor
5
out of
5
(
3
x
)
+
5
(
2
y
)
.
5
(
3
x
+
2
y
)
Step-by-step explanation:
Monica was baking A recipe for banana nut muffin with her mom the recipe calls for 3/4 cups of walnuts but they only have 1/4 cup measuring scoop how many 1/4 cup scores will Monica need in order to get the correct measurements of walnuts
Answer: She will need three cups scores.
Step-by-step explanation:
3/4 divided by 1/4 is three.
–3t — 6t =
syplified
Answer:
-9t
Step-by-step explanation:
-3t -6t
using multiplication of signs
-×-=+
so add the numbers because they have the same
coefficient
-3-6= -9
so
-3t-6t=9t
(a) Solve 5x - 2 = x + 8
Show clear algebraic working.
Answer:
Required Answer:-[tex]{:}\longrightarrow[/tex][tex]\sf 5x-2=x+8 [/tex]
interchange both sides[tex]{:}\longrightarrow[/tex][tex]\sf 5x-x=8+2 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 4x=10 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {10}{4}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {5}{2}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x=2.5 [/tex]
Anna is x years old and her sister, Jane is y years younger
What was the sum of their ages two years ago?
What will be the sum of their ages in 3 years?
How old was anna when Jane was born?
Answer:
Age of Anna = x years
Age of Jane i.e. Anna's sister = (x-y) years
a, What was the sum of their ages two years ago?
Solution,
Age of Anna two years ago = (x-2) years
Age of Jane two years ago = (x-y-2) years
Sum of their ages = x - 2 + x-y-2 = 2x - y -4
b. What will be the sum of their ages in 3 years?
Solution,
We have,
Present age of Anna = x years
Present age of Jane = (x-y) years
So,
Age of Anna after 3 years = (x+3) years
Age of Jane after 3 years = (x-y+3) years
Therefore,
Sum of their ages in 3 years = (x+3) +(x-y+3) = 2x - y+6
c. How old was Anna when Jane was born?
Solution,
Here,
According to question,
Jane is y years younger than Anna
So, Anna was y years when Jane was born.
[Suppose your age is 10 years and your brothers age is 14 years. You are 4 years younger than your brother. Also, his age was 4 years when you were born.]
Please help it would help alot
As I was sitting on a dock, I noticed that the wavelength of the waves were about 6 m long. The crest
of each wave would pass the front of the dock every 8 seconds. Find the frequency of the wave.
Answer:
IT IS C I BET YOU 6 AND 8
Step-by-step explanation:
The frequency of the wave is equal to: C. 0.125 Hertz
Given the following data:
Wavelength = 6 mTime period = 8 secondsTo determine the frequency of the wave:
A wave can be defined as a disturbance in a medium that progressively transports energy from a source location to another location without the transportation of matter.
Some of the characteristics associated with a wave are:
Speed.Amplitude.Wavelength.Time period.Frequency.Mathematically, the frequency of a wave is given by the formula:
[tex]Frequency = \frac{1}{Time\;period}[/tex]
Substituting the given parameters into the formula, we have;
[tex]Frequency = \frac{1}{8}[/tex]
Frequency = 0.125 Hertz
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Solve the quadratic equation numerically (using tables of x- and y- values). x(x + 3) = 0 a. x = -1 or x = 3 c. x = 0 or x = -3 b. x = 0 or x = -5 d. x =1 or x = -1
Answer:
Step-by-step explanation:
x = 0
x+3 = 0
x = -3
The answer is x could be 0 or -3
Answer:
c on edge
Step-by-step explanation:
Kaylie and Juan are in a Dance-a-thon. Contestants rest for the same amount of time every hour. Kaylie rests for 22 minutes in 4 hours. How long did they rest in 28 hours? Find the unit rate.
Answer:
154 mins or 2 hour and 34 mins
Step-by-step explanation:
Step 1:
22 : 4 Ratio
Step 2:
22 : 4 = x : 28 Equation
Step 3:
4x = 616 Multiply
Step 4:
x = 616 ÷ 4 Divide
Answer:
x = 154
Hope This Helps :)