The equation of the line in point-slope form is y - 2 = -3(x + 9), and in slope-intercept form is y = -3x - 25.
To find the equation of the line passing through(- 9,2) and parallel to the line y = – 3x 3, we need to use the fact that resemblant lines have the same pitch.
The pitch of the given line y = – 3x 3 is-3,
so the pitch of the resemblant line we want to find is also-3. Point- pitch form Using the point- pitch form, the equation of the line is given by
y- y1 = m( x- x1),
where( x1, y1) is the given point and
m is the pitch.
Substituting the given values,
we get y- 2 = -3( x-(- 9))
y- 2 = -3( x 9)
y- 2 = -3 x- 27
y = -3 x- 25
Hence in slope-intercept form is y = -3x - 25.
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Marcos harvests a lot of cherry tomatoes in his garden this year. each day, he keeps one-third and brings the rest into the office to give away. by the time the tomatoes start to get a little mushy, marcos has less than
one eighty first of the original harvest left. how many days after marcos harvested the tomatoes do they start to get a little mushy?
The tomatoes start to get mushy after more than 6 days.
Note: The calculation assumes that the number of tomatoes harvested is large enough for the continuous division process to approach zero.
Let's assume that Marcos initially harvested X cherry tomatoes.
According to the given information, each day Marcos keeps one-third of the tomatoes and brings the remaining amount into the office. This means that after the first day, Marcos would have 2/3 (or 2/3X) of the original harvest left.
On the second day, he would keep one-third of the remaining tomatoes and bring 2/3 × 1/3 (or 2/9) of the original harvest into the office. This would leave him with 2/3 × 2/3 (or 4/9) of the original harvest.
In general, after N days, the amount of tomatoes left can be calculated using the following formula:
Amount of tomatoes left = (2/3)^N × X
The question states that Marcos has less than one eighty-first of the original harvest left when the tomatoes start to get mushy. In other words, when the amount of tomatoes left is less than 1/81 of the original harvest, we can write the following inequality:
[tex](2/3)^N × X < 1/81[/tex]
To find the number of days (N) when the tomatoes start to get mushy, we need to solve for N in the inequality above.
Taking the logarithm (base 2/3) of both sides of the inequality:
[tex]N > log2/3(1/81) / log2/3(2/3)[/tex]
N > 4 / (2/3)
N > 4 × 3/2
N > 12/2
N > 6
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geometry geometry geometry
We can solve this problem by using some properties of centroids of the triangle and the fact that the centroid divides each median in a 2:1 ratio.
What is a centroid of a triangle?The centroid of a triangle is the point intersection of the three medians of the triangle.
First find the value of MR. The centroid divides each median in a 2:1 ratio, so we have:
MR = 2/3 * R + 1/3 * M
R is the centroid, so R = (P + V + M)/3.
Substituting, we get: MR = 2/3 * [(P + V + M)/3] + 1/3 * M
= 2/9 * P + 2/9 * V + 5/9 * M
Now, substitute the given values of PV and M to find MR:
MR = 2/9 * (3w+7) + 2/9 * (12y-9) + 5/9 * (5x-9) = (2w/3 + 8y/9 + 25x/9) - 1
Simplifying the expression: MR = (2w + 24y + 25x - 27)/9
Next, let's find the value of RP using the centroid. Since R is the midpoint of PV:
RP = 2/3 * R + 1/3 * P
Substituting the values of R and P:
RP = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * (3w+7)
= (2w/9 + 8y/9 + 5x/3 + 7/3) + (w+7)/3
= (5w/3 + 8y/9 + 5x/3 + 10)/3
Simplifying this:
RP = (5w + 8y + 5x + 30)/9
Next, find the value of RV using the centroid. R is the midpoint of PV:
So, RV = 2/3 * R + 1/3 * V
Substituting R and V values:
RV = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * (12y-9) = (2w/9 + 8y/9 + 5x/3 + 7/3) + 4y/3 - 3
Simplifying: RV = (5w + 20y + 5x - 18)/9
Find the value of RW using the centroid. R is the midpoint of VW, so: RW = 2/3 * R + 1/3 * W
Substituting the values of R and W:
RW = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * 1.75x = (2w/9 + 8y
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The regular polygon has the following measures.
a = 2√3 yd
s = 4 yd
Segment a is drawn from the center of the polygon
perpendicular to one of its sides.
What is the vocabulary term for segment a?
What is the area of the polygon?
Round to the nearest tenth and include correct units.
Show all your work.
The vocabulary for the segment a is the apothem
The area of the polygon is about 41.6 yd²
What is the area of a regular figure?The area of a regular figure is the extent of the planer space the figure occupies.
The length of each side of the regular polygon, s = 4 yd
The length of the segment a = 2·√3
The vocabulary term for the segment a drawn from from the center of the polygon and perpendicular to one of its sides is the apothem
Therefore, the vocabulary term for segment a is the apothem
The polygon is a hexagon.
The area of a hexagon is; A = ((3·√3)/2) × s²
Therefore, the area of the polygon is; A = ((3·√3)/2) × (4)² = 24·√3 ≈ 41.6
The area of the polygon is about 41.6 yd²
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Which figure is a dilation of figure A?
The line passes through the same point on figure A and D.
From the figure, we have the original shape to be figure E
The center point of figure E is the origin
This means that a line drawn from the origin that passes through point A must pass through the same point on the shape
From the figure, the line passes through the same point on figure A and D.
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pyramid A and pyramid B are similar. find the surface area of pyramid B to the nearest hundredth.
The surface area of pyramid B to the nearest hundredth is 58.67 cm²
What are similar figures?Similar figures are two figures having the same shape. The ratio of the corresponding sides of similar shapes are equal.
The scale ratio of the height of the pyramid A to B is
9/6 = 3/2
Area factor = (3/2)² = 9/4
9/4 = 132/x
9x = 132×4
9x = 528
divide both sides by 9
x = 528/9
x = 58.67cm²
Therefore the surface area of pyramid B is 58.67cm².
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Solve problems 6,9, and 11 in the interval [0 pi, 2 pi]. Show all work, drawing diagrams as necessary.
The solutions to each trigonometric equation are:
Case 6: x = 50.768° (0.282π) or x = 129.232° (0.718π) or x = 230.768° (1.282π) or x = 309.232° (1.718π)
Case 9: x = 41.810° (0.232π) or x = 138.190° (0.768π) or x = 199.471° (1.108π) or x = 340.529° (1.892π)
Case 11: x = 208.164° (1.156π) or x = 331.836° (1.844π)
How to solve quadratic-like trigonometric equations
In this problem we find four cases of quadratic-like trigonometric equations, whose solutions must be found by means of algebra properties and trigonometric formulas. Now we proceed to solve for each case:
Case 6
cos² x + 3 / 5 = 1
cos² x = 2 / 5
cos x = ± √(2 / 5)
x = 50.768° (0.282π) or x = 129.232° (0.718π) or x = 230.768° (1.282π) or x = 309.232° (1.718π)
Case 9
9 · sin² x - 3 · sin x - 2 = 0
sin x = 2 / 3 or sin x = - 1 / 3
x = 41.810° (0.232π) or x = 138.190° (0.768π) or x = 199.471° (1.108π) or x = 340.529° (1.892π)
Case 11
sin² x - 8 · sin x - 4 = 0
sin x = - 0.472
x = 208.164° (1.156π) or x = 331.836° (1.844π)
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Debra has these snacks from a birthday party in a bag.
4 bags of chips
5 fruit snacks
6 chocolate bars
3 pieces of bubble gum
Debra will randomly choose one snack from the bag. Then she will put it back and randomly choose another snack. What is the probability that she will choose a chocolate bar and then a piece of gum?
A. 1/2
B. 1/3
C. 1/9
D. 1/18
Your answer is D. 1/18 is the probability that she will choose a chocolate bar and then a piece of gum
First, let's determine the total number of snacks in the bag:
4 bags of chips + 5 fruit snacks + 6 chocolate bars + 3 pieces of bubble gum = 18 snacks
Next, let's find the probability of choosing a chocolate bar:
There are 6 chocolate bars and 18 snacks total, so the probability is 6/18, which simplifies to 1/3.
Since she puts the chocolate bar back, the total number of snacks remains the same. Now, let's find the probability of choosing a piece of gum:
There are 3 pieces of gum and 18 snacks total, so the probability is 3/18, which simplifies to 1/6.
Finally, to find the probability of both events happening, multiply the probabilities together:
(1/3) * (1/6) = 1/18
So, the probability that Debra will choose a chocolate bar and then a piece of gum is 1/18. Your answer is D. 1/18.
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Evaluate the following indefinite ∫x tan^2 x dx
To evaluate the indefinite integral ∫x tan^2 x dx, we can use integration by parts.
Let u = x and dv = tan^2 x dx. Then, du/dx = 1 and v = ∫tan^2 x dx = tan x - x.
Using the formula for integration by parts, we have:
∫x tan^2 x dx = uv - ∫v du/dx dx
= x(tan x - x) - ∫(tan x - x) dx
= x(tan x - x) + ln|cos x| + C
Therefore, the indefinite integral of x tan^2 x dx is x(tan x - x) + ln|cos x| + C, where C is the constant of integration.
To evaluate the indefinite integral ∫x tan^2(x) dx, we can use integration by parts, which is defined as ∫udv = uv - ∫vdu.
First, let's choose our u and dv:
u = x, so du = dx
dv = tan^2(x) dx
To find v, we need to integrate dv. Since tan^2(x) = sec^2(x) - 1, we get:
v = ∫(sec^2(x) - 1) dx = tan(x) - x
Now, using integration by parts:
∫x tan^2(x) dx = x(tan(x) - x) - ∫(tan(x) - x) dx
Let's evaluate the remaining integral:
∫(tan(x) - x) dx = ∫tan(x) dx - ∫x dx
= ln|sec(x)| - (1/2)x^2 + C
So, the final answer is:
∫x tan^2(x) dx = x(tan(x) - x) - [ln|sec(x)| - (1/2)x^2] + C
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Let (6,t) = F(u(, t), (s, t)) where (1.0) - 6,0,(1,0) = -5,4 (1,0) = -7 (1,0) - 7,0,(1,0) - 9,(1,0) 5 F.(6, 7) = 4, F.(6, -7)=7 W,(1,0)= ______
It seems that the question provided is not clear and has some typos or formatting issues, making it difficult to understand the exact problem you need help with. Please rephrase or clarify the question, and I'll be more than happy to help you!
To find W,(1,0), we need to use the formula for the partial derivative of F with respect to u at (6,7) and (6,-7) and plug in the given values:
F_u(6,7) = 6,0(6,7) = -5
F_u(6,-7) = 6,0(6,-7) = -7
Now we can use these values to solve for W,(1,0) using the formula:
W,(1,0) = F(6,t) - F_u(6,7)(1-6) - F_u(6,-7)(1-6)
Plugging in the given values, we get:
W,(1,0) = F(6,t) - (-5)(-5) - (-7)(-5)
W,(1,0) = F(6,t) + 30
We still need to find F(6,t). To do this, we use the formula for the partial derivative of F with respect to s at (1,0) and plug in the given values:
F_s(1,0) = 1,0(6,0) - 7,0(1,0) - 9,0(1,0)
F_s(1,0) = -7
Now we can use F_u(6,7), F_u(6,-7), and F_s(1,0) to solve for F(6,t) using the formula:
F(6,t) = F_u(6,7)(6,t-7) + F_u(6,-7)(6,t+7) + F_s(1,0)(t)
Plugging in the given values, we get:
F(6,t) = (-5)(6,t-7) + (-7)(6,t+7) + (-7)(t)
F(6,t) = -77t - 188
Now we can substitute this value of F(6,t) into our formula for W,(1,0) to get the final answer:
W,(1,0) = -77t - 188 + 30
W,(1,0) = -77t - 158
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What is the measure of JG
measure of arc JG = 160 degrees
Step-by-step explanation:Main Concept: Intersecting chords
Chords are line segments with ends points that are both on the edge of the circle. Intersecting chords are a pair of chords on the same circle that intersect.
In an extreme example, the chords may intersect at one of the end points, making the intersecting chords an inscribed angle.
Because Intersecting chords intersect, if the line segments are extended into lines, the lines form two pairs of vertical angles. Vertical angles are congruent. Given one vertical angle pair, they will contain two arcs (in the extreme case, the arc will have a measure of zero).
The measure of each of the vertical angles is the average of the two contained arcs.
This problem
For this problem, FG and HJ are chords of the same circle, and they intersect.
If we call the intersection P, angle GPJ is given with a measure of 100 degrees.
Angle GPJ and Angle FPJ form a vertical angle pair, so they are congruent, because vertical angles are congruent.
The measure of each of the vertical angles is the average of the two contained arcs.
The two arcs that this vertical angle pair contain are the arc JG and arc FH.
The measure of arc FH is given as 40 degrees.
Substitute these known quantities into the equation describing the relationship between one of the vertical angles and the contained arcs.
[tex]m \angle GPJ=\frac{1}{2}(m ~\text{arc}JG + m ~\text{arc}FH)[/tex]
[tex](100^o)=\frac{1}{2}(m ~\text{arc}JG + (40^o))[/tex]
Multiply both sides by 2...
[tex]200^o=m ~\text{arc}JG + 40^o[/tex]
Subtract 40 degrees from both sides...
[tex]160^o=m ~\text{arc}JG[/tex]
How many more cubic inches of popcorn does the jumbo size hold compared to the regular size round to the nearest tenth
Cubic inches of popcorn does the jumbo size hold compared to the regular size round to the nearest tenth
To determine how many more cubic inches of popcorn the jumbo size holds compared to the regular size, you would need to:
1. Find the volume (in cubic inches) of both the jumbo and regular size popcorn containers.
2. Subtract the volume of the regular size container from the volume of the jumbo size container.
Unfortunately, without specific dimensions for the jumbo and regular size popcorn containers, I cannot provide a numerical answer. Please provide the dimensions, and I would be happy to help you with the calculations.
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Find the missing values assuming continuously compounded interest. (Round your answers to two decimal places.)
Initial Investment: $100
Annual % Rate: ?
Amount of time it takes to double: ?
Amount after 10 years: $1405
Answer:
Annual % Rate: 26.43%
Amount of time it takes to double: 2.62yr
Step-by-step explanation:
Solving for r(Annual%Rate)
A=P⋅e^(r⋅t)
1405=100⋅^(r⋅10)
1405=100⋅e(^10r)
1405/100=100/100⋅e^(10r)
14.05 = e^(10r)
log(14.05) = log(e^10r)
1.1476 = 10r⋅log(e)
1.1476/log(e) = 10r
1.1476/10⋅log(e) = r
r = 0.26426
=26.43%
Now we have r=26.43%. We can use this information to solve for t, the time period to double the initial investment:
2P = Pe^(rt)
2 = e^(0.2643t)
ln(2) = 0.2643t
t = ln(2)/0.2643
t = 2.62yr
Miles driven to see a space shuttle launch 19 27 14 28 30 51 28
For the given data set of miles driven to see a space shuttle launch, the mean is 28.14, the median is 28, and the mode is 28.
To analyze this data, let's find the mean (average), median, and mode.
1. Mean (average): Add all the miles together and divide by the total number of data points.
(19 + 27 + 14 + 28 + 30 + 51 + 28) / 7 = 197 / 7 = 28.14
The mean miles driven to see a space shuttle launch is 28.14.
2. Median: Arrange the data points in ascending order and find the middle value.
14, 19, 27, 28, 28, 30, 51
Since there are 7 data points, the median is the 4th value, which is 28.
The median miles driven to see a space shuttle launch is 28.
3. Mode: Identify the most frequently occurring value in the data set.
14, 19, 27, 28, 28, 30, 51
The number 28 appears twice, which is more than any other value.
The mode for miles driven to see a space shuttle launch is 28.
In summary, for the given data set of miles driven to see a space shuttle launch, the mean is 28.14, the median is 28, and the mode is 28.
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1 A) (In(x) +1) 2x In(2) Denivate h(x) = √xen(x) h( 1 B) In() + V2V C) V 2. In(x) + 2 D) In (30) + 2ln()
The derivatives of the given functions are:
A) h'(x) = (1/2)√xen(x)[2+In(x)]
B) h'(x) = (1/x) - V2V
C) h'(x) = (2/x) + 2
D) h'(x) = 0
A) To find the derivative of h(x) = √xen(x), we use the product rule of differentiation. Let u = √x and v = en(x).
Then, h(x) = uv, and h'(x) = u'v + uv'.
We have u' = (1/2)x^(-1/2) and v' = en(x)(1/x).
Substituting the values, we get h'(x) = (1/2)√xen(x)[2+In(x)].
B) To find the derivative of h(x) = In(x) + V2V, we use the sum rule of differentiation.
Using the properties of logarithms, we rewrite the function as h(x) = In(x) + (1/2)ln(x).
Taking the derivative, we get h'(x) = (1/x) - V2V.
C) To find the derivative of h(x) = V2 In(x) + 2, we use the sum rule of differentiation.
Taking the derivative, we get h'(x) = (2/x) + 2.
D) To find the derivative of h(x) = In(30) + 2ln(x), we use the sum rule of differentiation.
Taking the derivative, we get h'(x) = 0, since the derivative of a constant is always zero.
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Write an appropriate and interesting word for 15000 and 3000.solve it
An appropriate and interesting word for 15,000 is "fifteen thousand," while for 3,000, it is "three thousand."
To solve this question, we need to write the numbers 15,000 and 3,000 as words. To do this, first, we look at the place values of each digit. In 15,000, the "15" is in the thousands place, so we write it as "fifteen thousand." Similarly, in 3,000, the "3" is in the thousands place, so we write it as "three thousand."
By doing this, we have expressed the numbers using their word forms, which helps in understanding and communicating numerical values more effectively, especially in written or spoken contexts. Remember, when writing large numbers as words, we use the place values to guide us in expressing them accurately and understandably.
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The back of Tim's truck is 6. 5 feet long, 5 feet wide, and 7 feet tall. He has several boxes of collectables that he
needs to move. Each box of papers is shaped like a cube, measuring 2 feet on each side.
How many boxes of papers can Tim pack into the back of his truck? (Think logically to figure out how many will
fit. )
Tim can pack
boxes of papers into the back of his truck.
Tim's truck has a volume of (6.5 feet) x (5 feet) x (7 feet) = 227.5 cubic feet. Each box of papers has a volume of (2 feet) x (2 feet) x (2 feet) = 8 cubic feet. To determine how many boxes of papers Tim can pack into the truck, we need to divide the total volume of the truck by the volume of each box:
227.5 cubic feet ÷ 8 cubic feet per box = 28.44 boxes
Since we can't pack a fraction of a box, Tim can pack a maximum of 28 boxes of papers into his truck. However, this assumes that there is no wasted space due to irregular shapes of the boxes or other items in the truck.
In reality, Tim may be able to pack slightly fewer boxes depending on how he arranges them in the truck.
Hence, Tim's truck has a volume of 227.5 cubic feet. Each box of papers has a volume of 8 cubic feet.
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A survey of North middle school staff included staff members ages the ages were complied and displayed in a histogram which of the following statements best describes the data
The number of staff members under the age of 40 are 28 and the number of staff members 40 and older are 22.
From the given histogram,
A. Between the age 20-29 there are 10 members.
B. Under the age of 40 = 10+18
= 28
40 and older = 12+7+2+1
= 22
C) Total staff members = 28+22=50
D) Number of staff members are 50 years or older
= 7+2+1
= 10
Therefore, the number of staff members under the age of 40 are 28 and the number of staff members 40 and older are 22.
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what fraction is less greater than 1/2 and less than 4/5
A fraction that is greater than 1/2 and less than 4/5, we need to consider fractions between these two values. A fraction that is greater than 1/2 and less than 4/5 is 6/10.
Compare the two given fractions by finding a common denominator.
The lowest common denominator for 1/2 and 4/5 is 10.
Convert both fractions to equivalent fractions with a denominator of 10.
1/2 = 5/10
4/5 = 8/10
Identify a fraction between 5/10 and 8/10.
One possible fraction between these two is 6/10.
A fraction that is greater than 1/2 and less than 4/5 is 6/10.
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Find the average rate of change of g (x) = 2x² - 7x from x = 1 to x = 6.
Simplify your answer as much as possible.
The average rate of change of g(x) from x = 1 to x = 6 is 7
Finding the average rate of change of g(x)The average rate of change of a function over an interval is given by the difference in the values of the function at the endpoints of the interval, divided by the length of the interval.
In this case, we want to find the average rate of change of g(x) = 2x² - 7x from x = 1 to x = 6.
The value of g(x) at x = 1 is:
g(1) = 2(1)² - 7(1) = -5
The value of g(x) at x = 6 is:
g(6) = 2(6)² - 7(6) = 30
So the difference in the values of g(x) is:
g(6) - g(1) = 30 - (-5) = 35
The length of the interval is:
6 - 1 = 5
Therefore, the average rate of change of g(x) from x = 1 to x = 6 is:
Rate = 35/5
Evaluate
Rate = 7
So, the rate is 7
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The average rate of change is 7.
We know that,
The average rate of change = (final value - initial value)/change in the value of x.
Now,
The given function is,
g(x)=2x²-7x
The initial value of x is 1 (given)
∴ The initial value of the function g(x), at x=1,
g(1)=2(1)²-7(1)=2-7
or, g(1)= -5
Now, the final value of x is 6,
∴ Finding the final value of the function g(x) at x=6,
i.e, g(6)=2(6)²-7(6)
or, g(6)=72-42 = 30
∴ The change in the value of function g(x), from x= to x=6,
= g(6)-g(1)
= 30-(-5)
= 35
Now, change in the value of x = 6-1=5
∴ The average rate of change = 35/5 = 7
Hence the average rate of change is 7.
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(3x^3 y^2)^3 (2x^4 y^2)^2
Answer:
108y^10x^17
Step-by-step explanation:
Select the correct answer. What is the sum of the first five terms in this series? 3 + (-9) + 27 + (-81) + . . .
A. 243
B. -9
C. 61
D. 183
PLEASE HELPPP
MEEE LAST QUESTION FOR THE DAY!
Answer:
There are 16 unit squares on the geoboard. Each unit square represents 5 meters, so the total area is 16*5 = 80 square meters.
Here is a diagram of the geoboard with the unit squares labeled:
[Image of a geoboard with 16 unit squares labeled]
I hope this helps! Let me know if you have any other questions.
2 Tom Milk his cow and got 2 litres of Milk He gave Kevin 350 ml and Sold 500m to Bob. How much milk is left?
The amount of milk left is given by A = 1.150 Liters of milk = 1150 mL
Given data ,
Let the total amount of milk be = 2 Liters = 2000 mL
Now , Tom gave Kevin 350 ml and Sold 500mL to Bob
So , the remaining amount of milk is given by A
where A = total amount of milk - 350mL - 500mL
On simplifying the equation , we get
A = 2000 - 350 - 500
A = 1150 mL
Hence , the amount of milk left is 1150 mL
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Farmer jones raises only pigs and geese. he wants to raise at most 16 animals. he wants no more
than 12 geese. he spends $5 to raise a pig and $2 to raise a goose and has 550 available to spend. if he
makes a profit of s4 per pig and s8 per goose, how many of each does he need to raise in order to
maximize his profits?
write the objective function. let a represent the number of pigs and y represent the number of geese.
The profit per pig is $4 and the profit per goose is $8.
How can the farmer raise at most 16 animals in order to maximize his profits?Let's start by defining the variables:
a = number of pigs Farmer Jones raises
y = number of geese Farmer Jones raises
The problem tells us that he wants to raise at most 16 animals, so we can write:
a + y ≤ 16
It also tells us that he wants no more than 12 geese, so we can write:
y ≤ 12
We know that it costs $5 to raise a pig and $2 to raise a goose, and he has $550 available to spend. So the cost of raising the animals can be expressed as:
5a + 2y ≤ 550
Finally, we want to maximize his profits. The profit per pig is $4 and the profit per goose is $8. So the objective function for Farmer Jones' profits is:
Profit = 4a + 8y
To summarize, the linear programming model for this problem is:
Maximize: Profit = 4a + 8y
Subject to:
a + y ≤ 16
y ≤ 12
5a + 2y ≤ 550
where a and y are non-negative integers.
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100 points find the horizontal distance from the bottom of the ramp to the bottom of the platform. show your work, rounding to the nearest hundredth, if necessary.
The horizontal distance from the bottom of the ramp to the bottom of the platform is 57.74 feet.
What is the horizontal distance between the bottom of the ramp and the bottom of the platform?In order to find the horizontal distance between the bottom of the ramp and the bottom of the platform, we need to use the Pythagorean theorem. Let's call this distance "d". We know that the vertical distance from the bottom of the ramp to the bottom of the platform is 50 feet, and the length of the ramp is 70 feet.
Using the Pythagorean theorem, we can solve for the horizontal distance:
[tex]d^2 = 70^2 - 50^2[/tex]
[tex]d^2[/tex] = 4,900 - 2,500
[tex]d^2[/tex]= 2,400
d = √2,400
d = 48.99 (rounded to the nearest hundredth)
Therefore, the horizontal distance from the bottom of the ramp to the bottom of the platform is 48.99 feet (rounded to the nearest hundredth).
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Of 100 random students surveyed, 42 own a dog, 34 own a cat, 15 own a dog and a cat, and 9 own neither a dog nor a cat. Based upon the results, how many of the next 20 students surveyed would you expect to own a dog and a cat?
In the next 20 students surveyed, you would expect 5 to own a dog and a cat
How many of the next 20 students surveyed would you expect to own a dog and a cat?From the question, we have the following parameters that can be used in our computation:
Dog = 42
Cat = 34
Dog and cat = 15
Neither = 9
This means that
P(Dog and cat) = 15/100
When evaluated, we have
P(Dog and cat) = 5/20
So, when the next 20 students surveyed, we have
Dog and cat = 5/20 * 20
Evaluate
Dog and cat = 5
Hence, the number of dogs and cats is 5
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ANSWER THIS PLS BRAINLIEST IF CORRECT!!!!!!!!
x^5√x^9
Answer:
x^9√x
Step-by-step explanation:
In 2016, Dave bought a new car for $15,500. The current value of the car is $8,400. At what annual rate did the car depreciate in value? Express your answer as a percent (round to two digits between decimal and percent sign such as **. **%). Use the formula A(t)=P(1±r)t
The car depreciated at an annual rate of approximately 45.81%.
In 2016, Dave bought a new car for $15,500, and its current value is $8,400. To find the annual depreciation rate, we'll use the formula A(t) = P(1 ± r)t, where A(t) is the future value, P is the initial value, r is the annual rate, and t is the time in years.
Here, A(t) = $8,400, P = $15,500, and t = 1 (one year). We are solving for r, the annual depreciation rate.
$8,400 = $15,500(1 - r)¹
To isolate r, we'll first divide both sides by $15,500:
$8,400/$15,500 = (1 - r)
0.541935 = 1 - r
Now, subtract 1 from both sides:
-0.458065 = -r
Finally, multiply both sides by -1 to find r:
0.458065 = r
To express r as a percentage, multiply by 100:
0.458065 x 100 = 45.81%
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The car depreciated at an annual rate of 12.2%.
How to find depreciated value of car?The car depreciated in value over time, so we want to find the rate of decrease. We can use the formula:
A(t) = P(1 - r)t
where A(t) is the current value of the car, P is the original price of the car, r is the annual rate of depreciation, and t is the time elapsed in years.
We can plug in the given values and solve for r:
$8,400 = $15,500(1 - r)⁵
Dividing both sides by $15,500, we get:
0.54 = (1 - r)⁵
Taking the fifth root of both sides, we get:
(1 - r) = 0.878
Subtracting 1 from both sides, we get:
-r = -0.122
Dividing both sides by -1, we get:
r = 0.122
Multiplying by 100 to express as a percentage, we get:
r = 12.2%
Therefore, the car depreciated at an annual rate of 12.2%.
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The table shows the number of cups of flour, f, that a bakery needs for the number of pound cakes that they make, p.
Pound Cakes, p 3 6 9 14
Cups of Flour, f 8. 25 16. 5 24. 75 ?
Part A
Which equation relates the number of cups of flour to the number of pound cakes that the bakery makes?
f = 2. 75p
f = 0. 343p
f = 2. 75p + 8. 25
f = 0. 343p + 16. 5
Part B
How many cups of flour are needed for 14 cakes?
4. 802
21. 302
38. 5
46. 75
A) The equation relates the number of cups of flour to the number of pound cakes that the bakery makes is f = 2.75p
B) Cups of flour are needed for 14 cakes is 38.5
A) The number of cups of flour, f, that a bakery needs for the number of pound cakes that they make, p is directly proportional to each other which can be written in form ,
f/p = 8.25/3
f = (8.25/3)×p
f = 2.75 p
The equation forms is f = 2.75p
B) Cups of flour are needed for 14 cakes
Here p = 14
by putting the value in the equation we get ,
f = 2.75(14)
f = 38.5
hence , cups of flour are needed for 14 cakes is 38.5
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Gabby had 578 yards of fabric. she used 3215 yards of fabric. estimate the amount of fabric gabby has left. 1 yard 2 yards 3 yards 4 yards
Gabby does not have any fabric left, as she used more fabric than she had to start with.
How much fabric does Gabby have left after using 3215 yards, and what is the estimate?
Based on the information given, Gabby started with 578 yards of fabric and used 3215 yards of fabric. To estimate the amount of fabric Gabby has left, we need to subtract the amount of fabric used from the starting amount of fabric:
578 yards - 3215 yards = -2637 yards
Since the result is a negative number, it doesn't make sense in this context. It's possible that there was a mistake in the numbers given, or Gabby used more fabric than she had to start with.
Without further information or clarification, we cannot estimate the amount of fabric Gabby has left.
To estimate the amount of fabric Gabby has left, we can subtract the amount of fabric she used from the amount of fabric she had initially.
So, to find the estimate for the amount of fabric Gabby has left, we can perform the following calculation:
Estimate for the amount of fabric Gabby has left = 578 yards (initial amount) - 3215 yards (amount used)
Estimate for the amount of fabric Gabby has left = -2637 yards
However, the result is negative, which means that Gabby doesn't have any fabric left, and she needs to purchase an additional 2637 yards to make up for the shortfall.
Therefore, the estimate for the amount of fabric Gabby has left is 0 yards (she needs to purchase more fabric to continue her work).
