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Nancy builds a hollow wooden ramp for an obstacle course as part of an athletic event. The ramp and the net of the ramp are shown below. Units are in feet. The surface area of the ramp is square feet. Nancy wants to sell the wooden ramp at a price based on the surface area. If each square foot of wood of the ramp is sold for $3, the ramp would sell for $.
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Nancy can sell the wooden ramp for $486 based on the surface area.
What is Area of Rectangle?The area of Rectangle is length times of width.
The area of each rectangular face is length times width, so the top and bottom faces have an area of:
2 x (8 feet x 3 feet) = 48 square feet
The side faces also have an area of:
2 x (8 feet x 6 feet) = 96 square feet
The area of each triangular face is one-half the product of the base and the height, so the front and back faces have an area of:
2 x (0.5 x 3 feet x 6 feet) = 18 square feet
The total surface area of the ramp is the sum of the areas of all the faces:
48 + 96 + 18 = 162 square feet
If each square foot of wood of the ramp is sold for $3, then the ramp would sell for:
162 square feet x $3/square foot = $486
Therefore, Nancy can sell the wooden ramp for $486 based on the surface area.
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What is one way to determine if a quadrilateral has parallel sides
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Maya's penny bank is 3/10
full. After she adds 520
pennies, it is
4/5 full. How many pennies can Maya's bank hold?
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Maya's bank can hold 1733 pennies.
Explanation:To find out how many pennies Maya's bank can hold, we can set up an equation using the given information. Let's start with the fact that Maya's bank is 3/10 full before adding 520 pennies. This means that 3/10 of the bank's capacity is equal to 520 pennies. We can use this information to find the total capacity of the bank.
Since 3/10 of the bank's capacity is equal to 520 pennies, we can set up the equation (3/10)x = 520, where x represents the total capacity of the bank in pennies.
To solve for x, we can multiply both sides of the equation by 10/3 to cancel out the fraction. This gives us x = (10/3) * 520 = 1733.33. Since we cannot have a fraction of a penny, we round down to the nearest whole number. Therefore, Maya's bank can hold 1733 pennies.
what is the equivalent fraction of each one. 3/4 and 9/15 and24/40 and 5/7
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9/15 = 3/5
24/40 = 3/ 5
5/7 = 10/14
How many MP3 players in the shipment would you predict to be damaged if 6 MP3s in the sample had been damaged
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Substitute known values. Let x be the number of defective MP3 players in the population.
6 / 50 = x / 3500
50 x 70 = 3500, so multiply the numerator and denominator of the fraction 6/50 by 70.
(6x70) / (50x70) = x / 3500
420 / 3500 = x / 3500
420 = x
Based on the sample, we can predict that 420 MP3 players in the shipment would be defective.
Jalla's hourly wage is $11.791. Round her salary to the nearest cent
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Jalla's hourly wage, when rounded to the nearest cent, is $11.79.
Explanation:To round Jalla's wage to the nearest cent, we must look at the numbers following the decimal. In this case, Jalla's hourly wage is $11.791. Decimal rounding rules tell us that if the number following the decimal is equal to 5 or more, round up; otherwise, round down. In this case, the number after the decimal is 9, more than 5, so we round the second decimal place up. Therefore, rounding to the nearest cent, Jalla earns $11.79 per hour, her rounded wage.
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Help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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https://brainly.com/question/9281713
One side of a regular hexagon is 4 cm. What is the length of one other side?
a. 4 cm
b. 5 cm
c. 6 cm
d. can't be determined.
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the answer is a, 4 cm
Answer:
Your Answer is 4 CM
Step-by-step explanation:
Julia has to measure an object. She does not have a ruler. Tell what Julia could do to solve her problem.
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so... say you can use a tie or something with length, and use that to measure whatever object you need it for.
for example, I can just grab a string, cut it, and measure something, and the measurement may just be that the object is my string 6 times, so I know the length of the object is 6 times the length of the string I cut.
it doesn't quite matter how long the string cut was, all that matters is that is relable or referenciable for reuse. Later on I could always just get the string measure and convert it to metric, once I found a ruler or imperial units.
but in the short run, it doesn't really matter the length of the string cut, all that matters is that is referenciable, the object will be 6 times my string cut, here, in France, in Pluto, in Andromeda, anywhere.
bear in mind that the measure units we use today, are only usable because they're referenciable, so if I tell you 15 inches of something, you know how much 15 inches is, so that's all that matters.
Brian is playing a video game. He earns the same number of points for each star he picks up. He earns 2400 points for 6 stars, 4000 points for 10 stars, and 5,200 points for 13 stars. What is the independent and dependent value?
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A stadium has a total of 18000 seats. Of these 7500 are field seats and the rest are grandstand seats. Write an equation that can be used to find the number of standsteats s
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Write an absolute value equation that has the solutions x=23
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Quick help!! If you not sure of the answer PLEASE DON'T COMMENT
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Answer is B
check all that apply
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You need to do the same steps I used for the other one.
x² < 81
Find the critical points of the inequality
x² = 81
Then take square root
x = [tex]\pm \sqrt{81} [/tex]
x = 9 or x = -9
Thus,
The answer is option B 9
The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side than from the larger side of the rectangle. The perimeter of the rectangle is equal to 56 cm. Find the lengths of the sides of the rectangle.
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If you draw a diagram, and draw perpendiculars from the intersection to the sides of the rectangle, you will see they are the mid point of each side.
see the attached figure
If the mid point of the smaller side is ---------> x.
The mid point of the larger side will be -----------> (x + 4)
The full length if the smaller side will be 2x and the length of the larger side will be 2(x + 4) = 2x + 8
The perimeter = 2 times the length + 2 times the width.
2(2x + 8) + 4x = 56
4x + 16 + 4x = 56
8x = 40
x = 5
Therefore
length = 2x + 8 = 18cm
width = 2x = 10cm
the answer is
the lengths of the sides of the rectangle are
length = 18cm
width = 10cm
Answer:
length is 18 and width is 10
The equation of the circle whose center is at (3, 7) and whose radius is 6 is a. (x + 3)² + (y + 7)² = 6 b. (x + 3)² + (y + 7)² = 36 c. (x - 3)² + (y - 7)² = 36
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Gaff has used 331/3 of his monthly minutes on his cell phone plan. If he already used 200 mintues, how many does he have left this month?
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The first step to solve this problem is to compute for the total minutes allowable in his cell phone plan. To compute for this, you have to divide the number of minutes consumed by the fraction of the time consumed.
200 minutes / 33 1/3% = 600 minutes
To compute for the remaining minutes left for this month, you have to deduct the consumed minutes to the total allowable minutes in his plan.
600 minutes – 200 minutes = 400 minutes left
Write the first four terms in the multiplication pattern given by the formula 10*5n
(The n is exponent)
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10*5^1, 10*5^2 , 10*5^3, 10*5^4
= 50, 250, 1250 and 6250 answer
please help please ..
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Divide by the coefficient of P to find the value of P.
14,400/2.4 = P = 6000
A line has the following vector equation.
[x, y] = [2, -3] + t[5, 1]
a) State the coordinates of three other points on the line. Can you show your work please.
b) Write another vector equation of this line.
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.. [x, y] = [2, -3] +5[5, 1] = [27, 2]
.. [x, y] = [2, -3] +10[5, 1] = [52, 7]
.. [x, y] = [2, -3] +20[5, 1] = [102, 17]
b) You can replace t with any function of whatever parametric variable you want to use. For example, t = -3s+2.
.. [x, y] = [2, -3] +(-3s +2)[5, 1]
.. = [2 -15s +10, -3 -3s +2]
.. [x, y] = [12, -1] +s[-15, -3]
_____
The graph uses "t" instead of "s" for the parameter of the second version of the line. This is a Desmos thing: it likes "t" for parametric equations. The second equation is shown as dotted, so you can see it is the same line as the first equation (solid red).
the length of a rectanglr exceeds its width by 5 inches, and the area is 84 square inches. what are the length and width of a a rectangle
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The area is the product of length and width, which is to say that the length and width are factors of the area.
Assuming the dimensions are integers, you want factors of 84 that differ by 5.
... 84 = 1×84 = 2×42 = 3×28 = 4×21 = 6×14 = 7×12
The last of these pairs differ by 5, so ...
the length is 12 inchesthe width is 7 inches.Answer:
The answer is l=12, w=7
Step-by-step explanation:
Find the value of each expression. Show your work.
18.) ₉P₃
Answers
The formula of permutations is:
[tex]nPr = \frac{n!}{(n-r)!} [/tex]
In the given case n=9 and r=3. Using these values, we get:
[tex]9P3= \frac{9!}{(9-3)!} \\ \\ = \frac{9!}{6!} \\ \\ = \frac{9*8*7*6!}{6!} \\ \\ =9*8*7 \\ \\ =504 [/tex]
Thus 9P3 is equal to 504.
9! is expanded above using the following factorial formula:
n! = n(n-1)(n-2)(n-3)....3.2.1
Answer:
The value of the expression is 504.
Step-by-step explanation:
We are given the expression [tex]9P3[/tex].
Now, [tex]9P3[/tex] represents the permutations of 9 objects which are taken 3 at a time.
Also, its value is given by,
[tex]9P3=\dfrac{9!}{(9-3)!}\\\\9P3=\dfrac{9!}{6!}[/tex],
where ! represents the factorial given by,
[tex]n!=n(n-1)(n-2)...3.2.1[/tex]
Thus, evaluating the expression, we get,
[tex]9P3=\dfrac{9!}{6!}\\\\9P3=\dfrac{9\times 8\times 7\times 6!}{6!}\\\\9P3=9\times 8\times 7\\\\9P3=504[/tex]
Thus, the value of the expression is 504.A spinner has three sections. The table shows the results of spinning the arrow on the spinner 80 times.
What is the experimental probability of the arrow stopping over Section 1?
Section 1 Section 2 Section 3
28 36 16
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Answer: [tex]\frac{7}{20}[/tex]
Step-by-step explanation:
From the given table, The number of times arrow comes results in section 1= 28
The total number of times spinner spins =80
Now, the experimental probability of the arrow stopping over Section 1 is given by:-
[tex]\text{P(Section 1)}=\frac{28}{80}=\frac{7}{20}[/tex]
Hence, the experimental probability of the arrow stopping over Section 1 is [tex]\frac{7}{20}[/tex]
divide 56 in the ratio 5 3
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But,
5 + 3 = 8
56/8 = 7
7*5 = 35
7*3 = 21
Hope this helps !
Photon
The given value is 56
We need to divide in the ratio 5 : 3
We can do it this way:
5x + 3x = 56
8x = 56
[tex] \frac{8x}{8} = \frac{56}{8} [/tex]
8 and 8 cancels out
x = 7
5(7) : 3(7)
35 : 21
Helene bought 6 bottles of juice. The bottles were on sale at 10 bottles for $12. Which explanation correctly tells how to calculate the cost of 6 bottles? A. Step 1 Multiply $12 by 10 to figure out the cost of 1 bottle. Step 2 Divide that cost by 6. B. Step 1 Divide $12 by 10 to find out the cost of 1 bottle. Step 2 Multiply that cost by 6. C. Step 1 Multiply $12 by 10 to find out the cost of 1 bottle. Step 2 Multiply that cost by 6. D. Step 1 Divide $12 by 10 to find out the cost of 1 bottle. Step 2 Divide that cost by 6.
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the cost of 10 bottles was $12.
therefore we need to find the cost of one bottle and then find the cost for 6 bottles.
if 10 bottles cost - $ 12
then 1 bottle costs - $ 12 / 10 bottles
here we divided 12 by 10 , cost of 1 bottle is 12/10 to find the cost of 6 bottles we have to multiply by 6 .12 / 10 x 6
correct answer is therefore B. divide 12 by 10 and then mulitply by 6
Option: B is the correct answer.
B. Step 1: Divide $12 by 10 to find out the cost of 1 bottle.
Step 2 : Multiply that cost by 6.
Step-by-step explanation:The cost of 10 bottles is: $ 12.
This means that the cost of 1 bottle is:$ (12/10)=$ 1.2
( Since the cost of 1 bottle will be less and hence the total cost must be divided by the number of items in order to obtain the cost of 1 item)
and similarly in order to find the cost of 6 items we need to multiply the cost of 1 item by 6.Hence, cost of 6 bottles of juice is: $ (1.2×6)=$ 7.2
Hence, the correct answer is:
B. Step 1: Divide $12 by 10 to find out the cost of 1 bottle.
Step 2: Multiply that cost by 6.
What does the expression 12f + 24 represent?
Answers:
Answers
Answer:
Option 1 : twenty four more than twelve times a number
Step-by-step explanation:
Given : 12f+24
To Find : What does the expression 12f+24 represents?
Solution:
The given expression : 12f+24
Option 1 : twenty four more than twelve times a number
The given expression 12f+24
This expression means 24 more than twelve times f
f is any number
So, we can say twenty four more than twelve times a number .
Thus Option 1 is correct
Option 2 :twenty four more than twelve plus a number
Let f be a number
So, (12+f)+24 is the obttained expression from option 2
Option 3 :twelve times the difference of number and twenty four.
Let f be a number
So, 12(24-f) is the obttained expression from option 3
Option 4 : twelve times the sum of a number plus twenty four
Let f be a number
So, 12(24+f) is the obttained expression from option 4
Thus option 1 represent the given expression 12f+24
In in a random survey, 8 out of every 13 students were taking Pre-Algebra, how many students out of the larger population of 8,000 students would be taking Pre-Algebra?
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An open rectangular box having a volume of 108 in.3 is to be constructed from a tin sheet. find the dimensions of such a box if the amount of material used in its construction is to be minimal. hint: let the dimensions of the box be x in. by y in. by z in. then, xyz = 108 and the amount of material used is given by
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That being the case, the height of the box is half the base edge length and the dimensions are
.. x = y = 6 in
.. z = 3 in
_____
If x and y are the base dimensions, the volume is
.. xyz = 108
and we want to minimize the area
.. area = xy +2(x+y)z
These equations are symmetrical in x and y, so the solution will require x=y. Making that substitution, we have
.. x^2*z = 108
.. x^2 +4xz = area = x^2 +4x(108/x^2)
That is, we want to minimize x^2 +432/x. A graphing calculator finds the minimum at x=y=6, (and z = 108/x^2 = 3).
Given that the volume of a rectangular box is a product of its length, breadth, and height, we define our problem using the given volume of 108 cubic inches and the formula for the surface area of an open box. To find the dimensions that will use minimal material requires the application of calculus and optimization techniques.
Explanation:In this problem, we know that the volume of the open rectangular box is 108 cubic inches. The volume of a rectangular box can be calculated with the formula V = xyz where x, y, and z are the length, width, and height. If we let the dimensions of the box be x, y, and z inches respectively, it means that the volume V = 108 = x*y*z.
The amount of material used or the surface area S of an open box (a rectangular box without a top) is given by the formula S = xy + 2xz + 2yz. Here, our task is to minimize this surface area.
To minimize the surface area, we need to employ calculus, specifically the concept of optimal control. However to apply calculus, we need to express S in terms of one variable. We can get this by expressing y in terms of x and z using the volume formula. This leads to a complex optimization problem that involves calculus.
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Mario was given some birthday money. He puts the money in an account. Every month after that, he deposits the same amount of money.The equation that models this situation is y = 75x + 50, where y is the amount of money in the account and x is the number of deposits.What does the y-intercept mean in this situation? A. He puts $75 in the account each month. B. He puts $50 in the account each month. C. He was given $75 for his birthday. D. He was given $50 for his birthday.
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The y intercept in the equation y=75x+50 shows that he was given $50 for his birthday which is option D.
What is equation?Equation is like a relationship between two variables in equal to form which is simplified in order to get the value of both variables.
How to evaluate an equation?The given equation is y=75x+50 where y is the amount of money in the account and x is the number of deposits. Put the value of x=0 and we get y=50 means when deposit is 0 means no deposits then the amount of money in account is equal to 50 which concludes that Mario was given 50 on his birthday.
Hence y intercept in the equation y=75x+50 shows that he was given $50 for his birthday.
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Which of the following is a solution to 3tan^3x=tanx?
PLEASE HELP
Answers
0, π, 2π, π/6, 5π/6, 7π/6 and 11π/6
Explanation:
3 tan³x = tan x
3 tan³x - tan x = 0
tan x (3 tan²x - 1) = 0
either tan x = 0
This means that:
x = 0 , π or 2π ...........> I
or 3 tan²x - 1 = 0
This means that:
3 tan²x = 1
tan²x = [tex] \frac{1}{3} [/tex]
tan x = ± [tex] \frac{1}{ \sqrt{3}} [/tex]
at tan x = [tex] \frac{1}{ \sqrt{3}} [/tex]
x = π/6 or 7π/6 ...................> II
at tan x = - [tex] \frac{1}{ \sqrt{3}} [/tex]
x = 5π/6 or 11π/6 ..............> III
From I, II and III, the solutions for x would be:
0, π, 2π, π/6, 5π/6, 7π/6 and 11π/6
Hope this helps :)
Answer:
its 150 degrees i think
Step-by-step explanation:
i could be wrong though but i'm like 80% sure im right