Answer:
118 miles
Step-by-step explanation:
Assuming that a month has 4 weeks
Each week has 5 weekdays.
The number of weekdays in a month is the number of weeks times 5.
4 X 5 = 20
Multiply the number of weekdays in a month by 5.9 miles.
20 X 5.9 miles = 118 miles
Therefore he runs 118 miles every months.
Plz answer the attachment as soon as possible in under 3 minutes for brainliest and 40 points! math
Answer:
Table #4
Step-by-step explanation:
because for every one x added, 2 y are added( if that makes any sense)
Answer:
Second from the top
The answer you have selected:
40:8 , 50:10, 60:14, 90:18
Proportions can be viewed as fractions:
40/8, 50/10, 60/14, 90/18
Now we have to simplify these fractions
5 , 5 , 4.3, 5
Unfortunately, they do not all come out to the same number, so this answer is incorrect
The second answer from the top:
4/2 , 7/3.5, 8/4, 10/5
These all equal 2 when simplified
2, 2, 2, 2
This shows a proportional relationship between x and y. If you would like to continue to make sure the bottom two are incorrect, you can use the steps that I have used for the first two. Hope this helps :)
nate runs 8 miles each week write an expression for the number of miles he runs in ‘n’ weeks find the number of miles neutrons in five weeks
Answer:
0ne week= 8 miles
W=5n
Solve the inequality for u
-5u+27 [less than or equal to] 2
Answer:
5≤u
Step-by-step explanation:
Put the words and numbers into an equation:
-5u+27≤2
Put all like terms on one side:
27-2≤5u ---> Do you see what I did there? Now you don't have to work with negatives. :)
Simplify:
25≤5u
Solve:
5≤u
:)
what two digit number is a multiple of 5 and has 3 less tens than ones
Answer:
25
Step-by-step explanation:
If a two digit number is a multiple of 5, then it ends with 0 or with 5.
If a two digit number ends with 0, then the number of ones is 0 and the number of tens must be 3 less that is impossible.
Hence, this two digit number must end with 5. If it ends with 5, then the number of ones is 5 and number of tens must be 5 - 3 = 2.
Therefore, the number is 25.
The question is about two-digit numbers that are multiples of 5 and have fewer tens than ones. Numbers such as 15, 25, 35, 45, 50, 65, 75, 85, and 95 satisfy these conditions.
Explanation:The subject of this question is a mathematical problem solving task regarding two-digit numbers and their properties. The most important criteria are that the number is a multiple of 5 and has less tens than ones. First, multiples of 5 are numbers that end in 0 or 5. Secondly, having less tens than ones implies that the digit in the ones place must be greater than the digit in the tens place.
An example of a number that fulfills these conditions would be 15. Here, the digit in the ones place (5) is greater than the digit in the tens place (1). Also, 15 is a multiple of 5 because it can be divided by 5 without leaving a remainder.
However, 15 is just one of many possible answers. Other numbers that satisfy these conditions are: 25, 35, 45, 50, 65, 75, 85, and 95.
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How many solutions dose the equation have 2(x+3)=12
[tex]
2(x+3)=12 \\
x+3=6 \\
x=3
[/tex]
Hope this helps.
Answer:
The answer is 1 solution.
Step-by-step explanation:
2(x+3)=12
First, do the multiplication by multiplying two times everything in the parentheses
2x+6=12
Then, subtract six from twelve.
2x+6=12
-6 -6
--------------------
2x=6
Finally, divide everything by two.
x=3
It has one solution, and the solution is x=3!
How many square centimeters are in a rectangle that measures 1 meter by 3 meters
Answer:
30,000 cm^2.
Step-by-step explanation:
The area = 3*1 = 3 square meters.
There are 100^2 = 10,000 cm^2 in a square meter
So the area in square centimeters is 3 * 10,000 = 30,000.
One side of a rectangle is 3 feet shorter than twice the other side find the sides if the area is 209 ft.²
The one side of rectangle is 11 feet and other side is 19 feet.
Step-by-step explanation:
Given,
Area of rectangle = 209 square feet
Let one side of rectangle = w
other side of rectangle = 2w-3
Area of rectangle = One side * other side
[tex]209=w*(2w-3)\\209=2w^2-3w[/tex]
[tex]0=2w^2-3w-209\\2w^2-3w-209=0[/tex]
[tex]2w^2+19w-22w-209=0\\w(2w+19)-11(2w+19)=0\\(2w+19)(w-11)=0[/tex]
Either;
2w+19=0 =>2w=-19
Or,
w-11=0 => w=11
As length cannot be negative, therefore,
One side of rectangle = 11 feet
Other side of rectangle = 2w-3 = 2(11)-3 = 22-3 = 19 feet
The one side of rectangle is 11 feet and other side is 19 feet.
Keywords: rectangle, area
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Which function has a range of vy s 5)?
of(x) = (x - 4)2 + 5
O (x) = -(x - 4)2 + 5
o f(x) = (x - 5)2 + 4
Of(x) = -(x - 5)2 + 4
Answer:
see the explanation
Step-by-step explanation:
Verify the range of each quadratic function
case 1) we have
[tex]f(x)=(x-4)^2+5[/tex]
This is a vertical parabola open upward (the leading coefficient is positive)
The function is written in vertex form
The vertex represent a minimum
The vertex is the point (4,5)
The range is the interval [5,∞)
[tex]y\geq 5[/tex]
case 2) we have
[tex]f(x)=-(x-4)^2+5[/tex]
This is a vertical parabola open downward (the leading coefficient is negative)
The function is written in vertex form
The vertex represent a maximum
The vertex is the point (4,5)
The range is the interval (-∞,5]
[tex]y\leq 5[/tex]
case 3) we have
[tex]f(x)=(x-5)^2+4[/tex]
This is a vertical parabola open upward (the leading coefficient is positive)
The function is written in vertex form
The vertex represent a minimum
The vertex is the point (5,4)
The range is the interval [4,∞)
[tex]y\geq 4[/tex]
case 4) we have
[tex]f(x)=-(x-5)^2+4[/tex]
This is a vertical parabola open downward (the leading coefficient is negative)
The function is written in vertex form
The vertex represent a maximum
The vertex is the point (5,4)
The range is the interval (-∞,4]
[tex]y\leq 4[/tex]
A cell phone plan cost $200 to start. Then there is a $50 charge each month.
1. what is the total cost (start up fee and monthly charge) to use the cell phone plan for 1 month?
2. what is the total cost for x months?
Answer:
1) $250
2) $200 + $50x
Step-by-step explanation:
1)
$200 (start up fee) + $50 * ( 1 month ) = $200 + $50 = $250
2)
$200 (start up fee) + $50 * ( x months ) = $200 + $50x
Hope this helps :)
10.31988 to the nearest hundredth
Answer:
10.32
Step-by-step explanation:
10.31988
the 9 makes the 1 to a 2 so...
10.32
Whats the analysis of yieldsof 2x square+9x+10
Answer:
The roots of the equation are -2.5 and -2
Step-by-step explanation:
We are given a quadratic equation and we are supposed to find the roots of the equation.
y = [tex]2x^{2}+9x+10[/tex]
To find the roots put y= 0.
We can factorize the given equation to get the roots.
[tex]2x^{2}+ 4x + 5x + 10[/tex] = 0
2x ( x + 2 ) + 5 ( x + 2 ) = 0
( 2x + 5 )( x + 2 ) = 0
x = -[tex]\frac{5}{2}[/tex] and x = -2
Hence the roots of the quadratic equation are -2.5 and -2.
How many terms are in the algebraic expression 14m-8.8n+5p-1
Answer:
4 terms
Step-by-step explanation:
Terms are separated by adding or subtracting.
The terms are:
14m
-8.8n
5p
-1
The variables are not separate terms because they are multiplying with the coefficient, not adding or subtracting.
Please help me! I’m desperate
Answer:
(a) d = 0.012v^2
(b) 4.8 m
(c) 25 m/s
Step-by-step explanation:
(a) Writing an equation to fit a bunch of data is often a matter of trial and error. You can often get an idea of the sort of function that is involved by graphing the data points.*
When we do that, we see the relationship is non-linear with an upward curvature. It might be described by a polynomial or exponential function.
When we try a quadratic equation, we find the fit is really quite good. The graphing calculator that does this quadratic regression analysis tells us the equation is essentially ...
d = 0.012·v^2
__
(b) The equation predicts a depth of 4.8 m.
d = 0.012·20^2 = 4.8
__
(c) Solving for speed, we get a speed of 25 m/s.
7.5 = 0.012v^2
625 = v^2 . . . . . . divide by .012
25 = v . . . . . . . . . take the square root
_____
* The energy of a falling object is proportional to the square of its speed. If we assume that the depth of penetration into the clay is proportional to the energy absorbed, then it is not surprising to see a quadratic relationship between speed and distance. What is surprising is that this relationship would show up in middle school math problem, not a high-school physics problem.
Essentially, you have to assume the form of the equation, then find the coefficients that make it so. Working with the evenly spaced table values of 5, 10, 15 m/s can simplify the effort.
A graphing calculator or spreadsheet can do the bulk of the work once the data is entered.
jada 2 miles in 12 minutes jadas cousin swims 1 mile in 24 minutes who is moving faster how much faster
Final answer:
Jada's speed (⅔ mile per minute) is three times faster than her cousin's speed (⅔ mile per minute); thus, Jada is moving faster.
Explanation:
To determine who is moving faster between Jada and her cousin, we need to calculate their swimming speeds and compare them. Speed can be calculated by dividing the distance by the time it takes to cover that distance.
Jada's Speed:
Jada swims 2 miles in 12 minutes. To find her speed, we use the formula:
Speed = Distance ÷ Time
Speed = 2 miles ÷ 12 minutes = ⅔ mile per minute
Jada's Cousin's Speed:
Jada's cousin swims 1 mile in 24 minutes. Using the same formula:
Speed = 1 mile ÷ 24 minutes = ⅔ mile per minute
Comparison and Result:
Jada's speed is ⅔ mile per minute, whereas her cousin's speed is ⅔ mile per minute. Jada is swimming at a higher speed because she covers more distance in less time compared to her cousin. Specifically, she swims three times faster, evidenced by comparing their speeds:
Jada's speed ÷ Cousin's speed = ⅔ mile per minute ÷ ⅔ mile per minute = 3
Therefore, Jada is moving three times faster than her cousin.
16. A farmer plants 0.4 of a field with wheat.
The field is 2.3 acres.
Part A
Shade the grids to model the multiplication. How do i shade the grid
Step-by-step explanation:
the farmer plants 0.4 of the total field which is 2.3 acres
⇒0.4×2.3= 0.92 acres
now draw a grid of area 2.3 acres and in that area shade 0.92 acres.Use a proper scale to draw the grid. It will a be pictorial representation of the proper and its solution.
You decide to begin selling glow sticks at the local star wars convention. Your cost for each glow stick is $2.02 plus you have to pay a fixed weekly fee of $190 for the booth. Your plan is to sell each glow stick for $3.60.
You would have to sell approximately 52 bracelets per week in order to pay your fee.
190 ÷ 3.60 = 52.7
This is your net profit after covering both the cost of the glow sticks and the booth fee. The actual profit you make will depend on how many glow sticks you manage to sell at the convention.
To determine the profit you make from selling glow sticks at the Star Wars convention, you can calculate the profit per unit and the total profit considering the costs and selling price.
Here are the key values:
Cost per glow stick: $2.02
Fixed weekly fee for the booth: $190
Selling price per glow stick: $3.60
Now, let's calculate the profit per unit:
Profit per unit = Selling price per unit - Cost per unit
Profit per unit = $3.60 - $2.02 = $1.58
This means you make a profit of $1.58 for each glow stick you sell.
To find the total profit, you need to consider how many glow sticks you sell. Let's assume you sell 'x' glow sticks. Your total profit can be calculated as:
Total Profit = Profit per unit × Number of Units Sold
Total Profit = $1.58x
Now, you need to take into account the fixed weekly booth fee of $190. So, your total profit after deducting the booth fee will be:
Total Profit - Booth Fee = $1.58x - $190
This is your net profit after covering both the cost of the glow sticks and the booth fee. The actual profit you make will depend on how many glow sticks you manage to sell at the convention.
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One yard of a ribbon costs 3 1/2 dollars. How much should one pay for: 5/8 yards?
The one should pay [tex]2\frac{3}{16}[/tex] dollars
Step-by-step explanation:
Let us revise how to multiply a mixed number by a proper fraction
Change the mixed number to improper fraction by multiplying the whole number by the denominator and ad the the product to the numerator and put the sum over the denominator ( [tex]a\frac{b}{c}=\frac{ac+b}{c}[/tex] )Multiply the two numerators and multiply the two denominators∵ One yard of a ribbon costs [tex]3\frac{1}{2}[/tex] dollars
∵ We need to find the cost of [tex]\frac{5}{8}[/tex] yards
- Multiply the cost of 1 yard by [tex]\frac{5}{8}[/tex]
∵ [tex]3\frac{1}{2}[/tex] = [tex]\frac{3(2)+1}{2}[/tex] = [tex]\frac{6+1}{2}[/tex]
∴ [tex]3\frac{1}{2}[/tex] = [tex]\frac{7}{2}[/tex]
∵ The cost = [tex]\frac{7}{2}[/tex] × [tex]\frac{5}{8}[/tex]
∴ The cost = [tex]\frac{7(5)}{2(8)}[/tex]
∴ The cost = [tex]\frac{35}{16}[/tex]
Change the improper fraction to a mixed number
∵ 35 ÷ 16 = 2 and remainder 3 ⇒ (16 × 2 = 32)
∴ [tex]\frac{35}{16}[/tex] = [tex]2\frac{3}{16}[/tex]
∴ The cost = [tex]2\frac{3}{16}[/tex] dollars
The one should pay [tex]2\frac{3}{16}[/tex] dollars
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Answer:
2.1875
Step-by-step explanation:
please help me with this question.
Answer:
b. Shift left 3 units
Step-by-step explanation:
You're given
y = √(x + 3)
y = √(x - (-3))
y = √(x - amount_shifted)
amount shifted = -3
so shifted 3 units and the negative means it's shifted to the left
what isthe turning point of the parabola equation isY=(x+2)(x-8)
Answer:
(3, - 25 )
Step-by-step explanation:
Given a quadratic in standard form : y = ax² + bx + c : a ≠ 0
The the x- coordinate of the turning point is
x = - [tex]\frac{b}{2a}[/tex]
Given
y = (x + 2)(x - 8) ← expand factors using FOIL
= x² - 6x - 16 ← in standard form
with a = 1 and b = - 6, thus
x = - [tex]\frac{-6}{2}[/tex] = 3
Substitute x = 3 into the equation for corresponding value of y
y = (3 + 2)(3 - 8) = 5(- 5) = - 25
turning point at (3, - 25 )
scientific notation
how do I do this?
Answer:
Post the questions and I'll do my best to help
Step-by-step explanation:
TIMEDDDDD PLEASE ANSWER 15 POINTS
Jolianne worked half as many hours as Andrew. Jolianne makes $10 per hour and has saved $27. Andrew makes $8 per hour and has no money saved. After getting paid, they have the same amount of money.
Andrew claims that only his table and equation are correct, but Jolianne claims that both tables and equations are valid. Which statement regarding their claims is true?
Andrew is correct because t cannot be used to represent the number of hours Jolianne worked.
Andrew is correct because Jolianne worked half as many hours as he did and he did not work twice as many hours as she did.
Jolianne is correct because if one lets t = hours Andrew worked, then his equation is valid. If one lets t = hours Jolianne worked, then Andrew worked twice as many so her equation is valid, too.
Jolianne is correct because when solving t in her equation, t = hours Jolianne worked, and when solving for t in Andrew’s equation, t = hours Jolianne worked so they are equal.
Answer:
Andrew is correct because Jolianne worked half as many hours as he did and he did not work twice as many hours as she did
Step-by-step explanation:
Let
x ----> number of hours worked by Jolianne
t ----> number of hours worked by Andrew
we know that
The number of hours worked by Jolianne multiplied by $10 per hour plus $27 saved must be equal to the number of hours worked by Andrew multiplied by $8
The linear equation that represent this situation is
[tex]10x+27=8t[/tex] ----> equation A
[tex]x=\frac{t}{2}[/tex] -----> equation B
substitute equation B in equation A
[tex]10(\frac{t}{2})+27=8t[/tex]
so
Andrew's table and equation is correct
Jolianne's table and equation are not correct, because Andrew did not work twice as many hours as she did
Answer:
the answer is B :)
Step-by-step explanation:
4y+3y=21 simplify as much as possible
Answer:
y=3
Step-by-step explanation:
Add the y and divide
7y=21
21/7=3
y=3
The sum of 3 consecutive even numbers is 408. What is the largest of the numbers
Answer:135,136,137
Step-by-step explanation:
408 divided by 3=136
136-1=135
136+1=137
135,136,137
The largest number of the three consecutive even numbers that sum to 408 is 138.
Explanation:The problem is a classic arithmetic sequence problem in mathematics, where a common difference exists between each number. For consecutive even numbers, this difference is 2. If the sum of three consecutive even numbers is 408, we can form the equation 3n+6=408 (since the first number is 'n', the next is 'n+2', and the following is 'n+4'). Solving this equation gives us n=134, hence the sequence of numbers is 134, 136 and 138. The largest number in this sequence is 138.
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please help me I can fail math
in 1982, a belt sold for $11.50 ten years later, the price of the belt increased by 80%. How much more did it sell for in 1992? How much would the belt cost in 1992?
Answer:
It sold for $9.20 more in 1992 than in 1982.
It sold for $20.70 in 1992.
Step-by-step explanation:
The price in 1982 was $11.50.
The price increased by 80% of $11.50.
We need to find 80% of $11.50.
To find a percent of a number, multiply the percent by the number.
80% of $11.50 =
= 80% * $11.50
= 0.8 * $11.50
= $9.20
It sold for $9.20 more in 1992.
The price in 1992 is the original price of the belt plus the amount of increase.
$11.50 + $9.20 = $20.70
It sold for $20.70 in 1992 than in 1982.
The garden view hotel is seventeen less than twice the height of the plaza hotel. If their combined height is 361 feet, how tall is the gardenview hotel?
The garden view hotel is 235 feet tall
Step-by-step explanation:
The given is:
The garden view hotel is seventeen less than twice the height of the plaza hotelTheir combined height is 361 feetWe need to find the height of the garden view hotel
Assume that the height of garden view hotel is x feet and the height of the plaza hotel is y feet
∵ The height of the garden view hotel = x feet
∵ The height of the plaza hotel = y feet
∵ The height of the garden view hotel is 17 less than twice the
height of the plaza hotel
- That means x is less than 2 × y by 17, equate x by the difference
of 2 × y and 17
∴ x = 2y - 17 ⇒ (1)
∵ Their combined height = 361 feet
∴ x + y = 361
- Find y in terms of x by subtraction x from both sides
∴ y = 361 - x ⇒ (2)
Substitute y in equation (1) by equation (2)
∵ x = 2(361 - x) - 17
- Simplify the right hand side
∴ x = 722 - 2x - 17
- Add like terms
∴ x = 705 - 2x
- Add 2x to both sides
∴ 3x = 705
- Divide both sides by 3
∴ x = 235
The garden view hotel is 235 feet tall
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The height of the Gardenview Hotel is 235 feet, which we found by first creating a system of equations using the information given and then solving by substitution.
To find the height of the Gardenview Hotel, let's create a system of equations based on the information given. Let G be the height of the Gardenview Hotel and P be the height of the Plaza Hotel. We are told that the Gardenview Hotel is seventeen less than twice the height of the Plaza Hotel, which we can express as G = 2P - 17. Additionally, we know their combined height is 361 feet, so G + P = 361.
Now we can solve the system of equations step by step:
Substitute the expression for G from the first equation into the second equation: (2P - 17) + P = 361.
Combine like terms: 3P - 17 = 361.
Add 17 to both sides of the equation: 3P = 378.
Divide both sides of the equation by 3 to find the height of the Plaza Hotel: P = 126.
Now use the value of P to solve for G using the first equation: G = 2(126) - 17.
Simplify to find the height of the Gardenview Hotel: G = 252 - 17.
Thus, the height of the Gardenview Hotel is 235 feet.
A music player was marked down by 1/4 of the original price.
a. If the sales price is $128, what is the original price?
b. If the music player was marked up by 1/2 before it was placed on the sales floor, what was the price that the store paid for the player?
c. What is the difference between the discount price and the price that the store paid for the music player?
pleaseee anyone :( it is due tmm 100 points
PLEASE SHOW ALL OF YOUR WORK! I NEED THIS ASAP! I WILL GIVE YOU BRAINLIEST! IF YOU SEND ME NONSENSE OR ANSWERS WITH NO WORK, I WILL REPORT YOU!!!! HAPPY NEW YEAR!!!!!!!!!
Answer:
Part A) 170.66$ would be the original price.
Part B) 256$ would be the price that the store paid for the music player.
Part B) What you need to balance is your markup, meaning how much to raise your price, and your markdown or discount, meaning, how to much to decrease prices.
Step-by-step explanation:
Part A) Determining the Original Price
Note: when a shopkeeper devalues of a certain product or commodity as he/she is being unable to sold the product or commodity at the original selling price that was planned, it normally means the product or commodity is being markdown due to certain issues.
So, a music player was marked down by 1/4 of the original price, and we have to calculate the original price if the sales price is $128.
Let 'p' be the original price
As a music player was marked down by 1/4 of the original price
So, Markdown = 1/4p
As the sales price is $128
As the Sale price = [tex]p - \frac{p}{4}[/tex] ⇒ [tex]\frac{3p}{4}[/tex]
[tex]128 = \frac{3p}{4}[/tex]
[tex]552 =3p[/tex]
[tex]p =170.66[/tex]
Hence, 170.66$ would the original price.
Part B) Determining the Price that the store paid for the music player
When an amount is added to the cost price of a product or commodity in order to determine the selling price, it means the the product or commodity is being marked up.
So, as the music player was marked up by 1/2 before it was placed on the sales floor and we have to determine the price that store paid for the player.
So, dividing the original price by 2 and adding the result to the original price would give us the price that store had to pay for the music player.
As the original price is 170.66.
So, the price that the store paid for the music player can be calculated as:
price = 170.66 + 170.66/2
price = 170.66 + 85.33
price = 255.99$ ≈ 256$
Therefore, 256$ was the price that the store paid for the music player.
Part C) Determining the difference between the discount price and the price that the store paid for the music
For example, let suppose you are a shopkeeper and have a jeans fabric business. You want to make money from it. But, in order to earn money from selling jeans fabric, you have to make sure that your price must be at the right value price both in terms of generating money and also giving your customer a great value for the money to given them a decent deal.
What you need to balance is your markup, meaning how much to raise your price, and your markdown, meaning, how to much to decrease prices.
In business, the conditions may never always remain favorable due to certain circumstance, hence bad days. Sometimes, the conditions get ideal for business, hence good days.
As I earlier sated that when a shopkeeper devalues of a certain product or commodity as he/she is being unable to sold the product or commodity at the original selling price that was planned, it normally means the product or commodity is being markdown due to certain issues.
For example, the cost price of 1 Jeans fabric is 10$, and you want to earn profit. So, you mark up your fabric to 30$. As $30 is $20 more than $10. So, markup value will be 2. In terms of percentage, it means you have a markup of 200%.
But, due to certain issues, your sales are being effected due to certain condition. In order to not affect the sales, you want to markdown the price - a kind of discount. Your starting price was $30 and want to decrease the price to $20. It means the difference is $10. So, you have made a markup or given a discount of $30/$10 = 0.33. In terms of percentage, it is around 33%. So, you have given the discount of 33% to hope for the great sales.
So, in the question, when the music player was marked down by 1/4 of the original price, it means the discount of 1/4 of the original price was provided. As the sale price was $128, and original price was $170.66. So, discount of 1/4 or 25% was offered.
As the original price was $170, and it was marked up by 1/2 by the owner or creator of music player before it was placed on the sales floor. So, 256$ was the price that the store paid for the music player.
Keywords: markdown, markup, discount, price
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Can someone plzzz help me with numbers 8 and 9 plzzz show work plzzz
Answer:
For question 9: Angle 1= 20, angle 2= 70, angle 3= 70, angle 4= 20, angle 5= 20, angle 6= 70, and angle 7= 70.
Step-by-step explanation:
8 4583/5000 simplified
Answer:
it's already simplified :) your welcome
Sam & Avery are making small and large birdhouses for a craft show. Small houses sell for $10 and large houses sell for $15. It takes Sam 3 hours to build small houses and 5 hours to build large houses. He only has 24 hours of building time. Avery only has time to decorate 12 houses of either size. How many small & large houses should be made to make the most money?
If Sam had 30 days instead of only 24 hours and Avery had time to decorate 100 birdhouses instead of only 12, discuss solution methods you used and why.
Answer:
8 small houses; 0 large houses80 small houses; 0 large housesStep-by-step explanation:
a) The maximum number of houses Sam can build in 24 hours is 8, so the constraint is in construction, not decoration. For each small house Sam constructs, he makes $10/3 = $3.33 per hour of work. For each large house Sam constructs, he makes $15/5 = $3.00 per hour. The most money is to be made by building only small houses.
Sam should make 8 small houses and 0 large houses in 24 hours.
__
b) If Sam works 8-hour days, then he can complete at most 80 small houses. The constraint remains in construction, so the answer is the same: build only small houses.
_____
If Sam works more than 16 2/3 hours per day, he can build 100 large houses or more, so the constraint moves to decoration. The decorator makes more money by decorating large houses, so all the effort should go to construction of large houses.
If Sam works between 10 and 16 2/3 hours per day, the best revenue will come from some mix. The problem statement is unclear as to how many hours Sam works in 30 days.