(−3x)(y3)+7xy3+(−x)(y3)+(−3x)(y3) = 0
The simplest cost function is the linear cost function C(x)=mx+b, where the y-intercept b represents the fixed cost of operating a business and the slope m represents the variable costs. Suppose that a small bicycle manufacturer has daily fixed costs of $1900 and each bicycle costs $40 to manufacture.a. Write a linear function that expresses the cost of manu. x bicycles in a day.C(x)=b. Graph the linear function.
Answer: C(x) = 40X + 1900
Step-by-step explanation: given from the question,
daily fixed costs = $1900 and
daily variable costs = $40
the linear cost function C(x)=mx+b, where the y-intercept b represents the fixed cost of operating a business and the slope m represents the variable costs
The cost of manufacturing x bicycle per day will be
C(x) = 40X + 1900
What is the rate of change of the function shown in the table below
Answer: -3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
What is the slope of the line shown
Answer: The Option is A, slope is -1/3
Step-by-step explanation:
find the surface area of the rectangular prism
Answer:
23 units²
Step-by-step explanation:
height = 2
length = 4
width = 2.5
Formula = 2(wl + lh + hw) ⇒ 2 [(2.5 × 4) + (4 × 2) + (2 ×2.5)] = 23 units²
Hope this helps.
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The volume inside a rectangular storage room is 2,106 cubic feet. The room is 9 feet high. Find the area of the floor.
Answer:
Area of the floor is 234 feet²
Step-by-step explanation:
To find the area of the floor of a rectangular storage room that is 2,106 cubic feet and has a height of 9 feet , we will follow the steps below;
First, write down the formula for calculating its volume
volume = l×b×h
but area=l×b
volume = area × h
From the question given volume = 2106 cubic feet
height h = 9 feet
volume = area × h
2106 = area × 9
Divide both-side of the equation by 9
2106/9 = area × 9/9
234 = area
area = 234 feet²
Area of the floor is 234 feet²
Divide 45 in the ratio 7:8
Answer:
0.0195?
Step-by-step explanation:
Answer:
21 : 24
Step-by-step explanation:
Sum the parts of the ratio, 7 + 8 = 15 parts
divide 45 by 15 to find one part of the ratio
45 ÷ 15 = 3 ← value of 1 part of ratio, thus
7 parts = 7 × 3 = 21
8 parts = 8 × 3 = 24
45 divided in the ratio 7 : 8 is 21 : 24
The heights (in cm) and arm spans (in cm) of 31 students were measured. The association between (height) and (arm span) is shown in the scatterplot below. The equation of the line of best fit modeling this relationship is given:
y=4.5+0.977x
Mike is 172 cm tall and George is 165 cm tall. Using the model, how many centimeters longer would we expect Mike's arm span to be than George's? Round your answer to the thousandths place.
Answer: Mike's arm span is 7.165 cm longer than the George's one.
Step-by-step explanation:
We have that the association between height and arm span is modeled by the equation
y = 4.5 + 0.977*x
where y is height and x is arm span.
Mike is 172 cm tall, so his arm span is:
172cm = 4.5 + 0.977*x
x = (172 - 4.5)/0.977 = 171.443 cm
and George is 165 cm tall, so his arm span is:
x = (165 - 4.5)/0.977 = 164.278 cm
Then the difference between their arm span is:
171.443cm - 164.278cm = 7.165 cm
So Mike's arm span is 7.165 cm longer than the George's one.
What is the volume of the rectangular prism?
Answer:210
Step-by-step explanation:
deon buys candy that cost $6 per pound. he will buy at most 7 pounds.
Answer:
He will spend 42 dollars
Step-by-step explanation:
7 times $6
= $42
(If that's what you're asking)
Answer:
7 × $ 6 = $42 so it all equals to 42 dollars
Would you rather read 12 pages every night in a chapter book with 144 pages or read 50 pages 3 times a week in a chapter book with 132 pages? Choose an option you would rather have and provide a mathematical justification as to why you made that choice.
Answer:
Read 12 pages every night in a chapter book with 144 pages.
Thus the first option is the best because you will use fewer number of days to complete the reading.
Step-by-step explanation:
For the first option;
Read 12 pages every night in a chapter book with 144 pages, the number of days taken to complete the book will be;
144/12= 12 days
For the second option
50 pages = 3 times
132 pages = ? ------perform cross product
(132*3)/ 50 =7.92 ≈ 8 times
3 times = 1 week
8 times = ?
(8*1)/3 = 2.64 weeks
1 week =7 days
2.64 weeks=?
2.64*7 = 18.5 days
Thus the first option is the best because you will use fewer number of days to complete the reading.
Eight pounds of peanuts cost $24.00. Six pounds of walnuts cost half as much.
Which is more expensive and by how much?
Answer:
peanuts are more expensive by $1.00.
Step-by-step explanation:
∵ The cost of eight pounds of peanuts = $24.00
∴ The cost of one pound of peanuts = [tex]\frac{24}{8}[/tex]
= $3.00 per pound
∵ The cost of six pounds of walnuts half as much = [tex]\frac{1}{2} \times 24[/tex]
= $12.00
∴ the cost of one pound of walnuts = [tex]\frac{12}{6}[/tex]
= $2.00 per pound
Difference in the cost per pound = $3.00 - $2.00 = $1.00
Therefore, peanuts are more expensive by $1.00.
A botanist is working with a sample of algae cells in a petri dish. The change in the population of algae cells can be modeled by this function, where I represents the time in minutes
f(t) = 0.89€
Which statement describes the population of algae cells in the sample?
The population is decaying at a rate of 89% per minute,
The population is decaying at a rate of 11% per minute.
The population is growing at a rate of 89% per minute.
The population is growing at a rate of 11% per minute.
Answer:
The population is decaying at a rate of 11% per minute.
Step-by-step explanation:
We have that € is the inicial sample of algae cells, and f(t) shows the sample after t minutes.
As € is multiplied by a number between 0 and 1, that means the sample will decrease it's size as the time passes.
The inicial sample is €, and after 1 minute the sample will be 0.89€, that is, it will decrease by 0.11€ or 11% of the previous sample.
So the correct option is:
The population is decaying at a rate of 11% per minute.
Answer:
The correct answer is b) The population is decaying at a rate of 11% per minute.
Step-by-step explanation:
Given the function
f(t) = 0.89€
We can see that every time the variable v grows 1, the population grows only 0.89. So the population is decreasing. And the percentage of decreasing we get it by discounting 1 -0.89= 11%
A tank that is 25 cm long, 10 cm wide, and 8 cm deep can hold how many liters of water?
Answer:
volume of tank = 2000 cm³
Step-by-step explanation:
given data
tank long = 25 cm
tank wide = 10 cm
tank deep = 8 cm
to find out
how many liters of water
solution
we get here volume of this tank that is express as
volume of tank = tank long × wide × deep .......................1
put here value and we will get
volume of tank = 25 × 10 × 8
volume of tank = 2000 cm³
Is 17,22,29 a right triangle
Answer:
No!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
formula:
a^2+b^2=c^2
Answer:
No
Step-by-step explanation:
The only way that those side lengths formed a right triangle is if they formed a pythagorean triple. [tex]\sqrt{17^2+22^2}=\sqrt{773}\neq 29[/tex]. Therefore, that is not a right triangle. Hope this helps!
Help pleas this late
Answer:
V = 282.10 cm³
Step-by-step explanation:
[tex]V= \pi r^2\frac{h}{3}[/tex] Use this equation to find the volume of the cone
[tex]V=3.14(3.5)^{2} \frac{22}{3}[/tex] Simplify the (3.5)²
V = 3.14(12.25)(22/3) Multiply
V = 282.10 cm³
If this answer is correct, please make me Brainliest!
Is 28,45,53 a right triangle
Answer:
yes
Step-by-step explanation:
The numbers satisfy the Pythagorean theorem:
53^2 = 28^2 +45^2
2809 = 784 +2025
(28, 45, 53) is a Pythagorean triple. These lengths will make a right triangle.
Talulah is an ecologist who studies the change in the penguin population of Antarctica over time. She observed that the population decays by a factor of 8/9 every 4 months. The population of penguins can be modeled by a function, P, which depends on the amount of time, t (in months). When Talulah began the study, she observed that there were 27,000 penguins in Antarctica. Write a function that models the population of the penguins t months since the beginning of Talulah's study. P(t) =
Answer:
P(t) = 27000 * (8/9)^(t/4)
Step-by-step explanation:
The population of penguins in Antarctica decays by 8/9 every 4 months, starting from an initial count of 27,000. The function for the penguin population P(t) after t months is P(t) = 27,000 × (8/9)^(t/4).
Explanation:Talulah, an ecologist, has observed that the population of penguins in Antarctica decays by a factor of 8/9 every 4 months. To model this decay, we can use an exponential decay function. Given that the initial population (P0) is 27,000 penguins, the function P(t) that models the population at time t (in months) since the beginning of Talulah's study is:
P(t) = P0 × (decay factor)(t/rate period)
Where P0 is the initial population, the decay factor is 8/9, and the rate period is 4 months. Plugging in these values gives us:
P(t) = 27,000 × (8/9)(t/4)
This function allows researchers to predict the penguin population at any given time t months after Talulah's initial observation.
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1. Krista is taller than Jan. Jan is shorter than Len, but taller than
Mick. Len is shorter than Krista. Who is the tallest?
After comparing the height of each person, we can confidently say that Krista is the tallest from all the given individuals.
Explanation:Krista is taller than Jan. Jan is shorter than Len, but taller than Mick. Len is shorter than Krist. The question provides information that allows us to compare the height of each individual. Based on given information we were provided, Krista is taller than Jan, Len is shorter than Krista but taller than Mick, and Jan is shorter than Len but taller than Mick. This means that Krista is taller than Len, Jan, and Mick, making Krista the tallest.
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what is the equation of a line that has a slope of -4 and goes through (-1,6)
Answer:
Step-by-step explanation:
Given
slope(m) = - 4
Points ( x1 , y1) = ( - 1 , 6)
Now
The equation of a line is given by
y - y1 = m( x - x1)
y - 6 = - 4 ( x + 1)
y - 6 = -4x - 4
4x + y - 6 + 4 = 0
4x + y - 2 = 0
Hope it helps:)
The equation of the line with a slope of -4 and passing through the point (-1, 6) is y = -4x + 2.
Given that the slope (m) is -4 and the point it passes through is (-1, 6), we can substitute these values into the point-slope form:
y - 6 = -4(x - (-1))
y - 6 = -4(x + 1)
Now, we can distribute the -4 to the terms inside the parentheses:
y - 6 = -4x - 4
Next, we can move the -6 to the other side of the equation by adding 6 to both sides:
y = -4x - 4 + 6
y = -4x + 2
Therefore, the equation of the line is y = -4x + 2.
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The speed of a ship is given by , where d is the distance the ship travels in 3 hours. If the ship travels 48 miles in 3 hours, what is the speed of the ship? A. 12 miles per hour B. 16 miles per hour C. 45 miles per hour D. 51 miles per hour
Answer:
the answer is 16mph
Step-by-step explanation:
Answer:
16 miles per hour
Step-by-step explanation:
Suppose a city with population 200,000 has been grown a rate of 4%.If the rate continues,find the population of this city in 19 years?
The scale factor of triangle ABC to triangle DEF is 6. Which description is correct?
Answer:
None are correct
Step-by-step explanation:
Because triangle ABC is the original as it says in the problem"Triangle ABC TO Triangle DEF" which means the answer should be Triangle DEF is 6 times larger than triangle ABC.
As an estimation we are told £3 is €4.
Convert €91.30 to pounds.
Give your answer rounded to 2 DP.
Answer:
68.48 pounds
Step-by-step explanation:
€91.30 to pounds
€91.30 * (3 pounds/ 4€) = 68.475 pounds about 68.48 pounds
What is the y-intercept in the equation y=4x-3?
Answer:
-3
Step-by-step explanation:
The equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 4x-3
4 is the slope and -3 is the y intercept
What would be the coordinates at 315° if the coordinates at 135° are at (-square root 2/2, square root 2/2)?
Answer:
We choose C
Step-by-step explanation:
the coordinates at 135° are at ([tex]\frac{-\sqrt{2} }{2}[/tex], [tex]\frac{\sqrt{2} }{2}[/tex] )
As we can see, the x coordinate of the point is negative and the y coordinate of it is positive.
So this point is located at the quadrant ii
From 135 ° to 315°, it is rotated 180°
=> Each coordinate (x,y) is changed to (-x,-y)
= ([tex]\frac{\sqrt{2} }{2}[/tex], [tex]-\frac{\sqrt{2} }{2}[/tex] ) the new coordinate is located in quadrant iii
We choose C
Find the volume to the nearest hundredth using 3.14 instead of pi.
Answer:
48π ≈ 150.72
Step-by-step explanation:
The volume formula is V = 1/3Bh
The base area formula would be πr²
Since 8 is the diameter, 4 would be the radius
Now plug that in, π (4²) = 16π
Now multiply that by the height, 9, and get 144π
Multiply again by 1/3 and you'll get 48π
Answer:
150.72 ft^3
Step-by-step explanation:
The volume of a cone is
V = 1/3 pi r^2 h
We need to get the radius
r = d/2 = 8/2 =4
V = 1/3 (3.14) (4)^2 *9
V = 1/3 (3.14) 16 *9
V =150.72
Rounding to the nearest hundredth
V = 150.72
A bakery sold 340 mocha cupcakes in a day, which was 85% of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
400
Step-by-step explanation:
Given:
Number of mocha cupcakes in a day = 340
Total number of cupcakes sold that day = [tex]85\%[/tex]
To find:
Total number of cupcakes sold by the bakery
Solution:
Let x denotes total number of cupcakes sold by the bakery.
According to question,
[tex]\frac{85}{100}x=340\\x=\frac{340}{85}\times 100=400[/tex]
So,
Total number of cupcakes sold by the bakery = 400
Ryan is building a ramp so he can easily move things in and out of an overhead storage area in his garage. The storage area is 8 feet off the ground, and Ryan has 15 feet of space along the ground to build the ramp.
A triangle with side lengths 15 feet, 8 feet, and an unlabeled hypotenuse.
What is the length of the ramp Ryan will build?
7 feet
10 feet
17 feet
23 feet
Answer:
17 feet
Step-by-step explanation:
c=the length of the ramp
a=8 ft
b=15 ft
Pythagorean Theorem
c²=a²+b²
c²=8²+15²
c²=64+225
c²=289
c=√289
c=17 ft
The length of the ramp of the triangular path is AC = 17 feet
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the base of the ramp is BC = 15 feet
The height of the ramp is AB = 8 feet
So , length of the ramp Ryan needs to build is AC is
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
AC = √ ( AB )² + ( BC )²
AC = √ ( 8 )² + ( 15 )²
AC = √ ( 64 + 225 )
AC = √289
AC = 17 feet
Therefore , the value of AC is 17 feet
Hence , the length of the ramp is 17 feet
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A truangular bandana has an area of 42 square inches. The height of the triangle is 5 1/4 inches. Enter and solve an equation ti find the length of the base of the triangle.
Answer: The length of the base of the triangle is 16 inches.
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula
Area of a triangle (A) = base x height x 1/2
Replacing with the values given:
42 = b (5 1/4) 1/2
Solving for b (lenght of the base)
42 / (5 1/4) 1/2 = b
16 in = b
The length of the base of the triangle is 16 inches.
Feel free to ask for more if needed or if you did not understand something.
Final answer:
The length of the base of the triangle is 16 inches, calculated by using the area formula for a triangle and the given height.
Explanation:
To find the length of the base of the triangle, we use the formula for the area of a triangle, A = (b * h) / 2, where A is the area, b is the base, and h is the height. We know the area (A) is 42 square inches and the height (h) is 5 1/4 inches. Plugging these values into the formula gives us:
42 = (b*5.25) / 2
Multiplying both sides by 2 to isolate the term with b gives us:
84 = b* 5.25
Dividing both sides by 5.25 yields:
b = 84 / 5.25
Calculating this division, we get the length of the base (b):
b = 16 inches
lena's coffee shop makes a blend that us a mixture of two types of coffee. Type A coffee costs Lena $5.70 per pound, and type B coffee costs $4.25 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $885.30. how many pounds of type A coffee were used?
Answer: 39 pounds of type A coffee were used.
Step-by-step explanation:
Let x represent the number of pounds of type A coffee that were used in the blend.
Let y represent the number of pounds of type B coffee that were used in the blend.
Type A coffee costs Lena $5.70 per pound, and type B coffee costs $4.25 per pound. The total cost of the mixture is $885.30. It means that
5.7x + 4.25y = 885.3- - - - - - - - - -1
This month's blend used four times as many pounds of type B coffee as type A. It means that
y = 4x
Substituting y = 4x into equation 1, it becomes
5.7x + 4.25 × 4x = 885.3
5.7x + 17x = 885.3
22.7x = 885.3
x = 885.3/22.7
x = 39
y = 4x = 4 × 39
y = 156
The weight of Type A coffee used was approximately 39 pounds. This is determined by setting up and solving an equation based on the provided costs per pound of the coffees and the total cost.
Explanation:In this problem, we need to solve for the amount of Type A coffee. Let's represent the weight of Type A coffee as x and the weight of Type B coffee as 4x, as it's mentioned the weight of Type B is four times Type A. We know that the combination of Type A and B coffee costs $885.30, so we can set up the equation using the costs per pound for each type: (5.70*x) + (4.25*4x) = 885.30.
Solving this equation, we have 5.70x + 17x = 885.30, or 22.7x = 885.3. Dividing both sides by 22.7, we get x = 38.97 pounds. So, approximately 39 pounds of Type A coffee were used.
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