Answer:
\(\frac{dy}{dx}\) = - 21\(x^{6}\) + 6x² + 1
Step-by-step explanation:
Differentiate each term using the power rule
\(\frac{d}{dx}\) (a\(x^{n}\) ) = na\(x^{n-1}\)
Given
y = - 3\(x^{7}\) + 2x³ + x , then
\(\frac{dy}{dx}\) = (7 × - 3 )\(x^{6}\) + (3 × 2)x² + (1 × 1 )\(x^{0}\)
= - 21\(x^{6}\) + 6x² + 1
If a ball is thrown upward at 112 feet per second from the top of a building that is 120 feet high, the
height of the ball can be modeled by s = 120 + 112t - 16t^2where t is the number of seconds after the ball
is thrown. How long after it is thrown is the height 120 feet?
Answer: 7 seconds
Step-by-step explanation:
Obtain the time after the ball is thrown at the height of 120 feet.
Substitute s = 120 in s = -16t^2 + 112t + 120 and solve for t as follows:
\(\begin{aligned}&120=-16 t^{2}+112t+120 \\&-16 t^{2}+112 t+120-120=0 \\&-16 t^{2}+112t=0 \\&16 t^{2}-112t=0 \\&16 t(t-7)=0 \\&12 t=0, t-7=0 \\&\Rightarrow t=0, t=7\end{aligned}\)
Note that, time cannot be negative or 0. So, ignore t = 0
Therefore, after 7 seconds the ball will reach at a height of 120 feet.
The length of a rectangle is three times its width.
If the perimeter of the rectangle is 48 cm, find its area.
The area of the rectangle is 108cm²
What is area of a rectangle?The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units.
So, the area of a rectangle is the number of unit squares within the boundary of the rectangle or the space occupied within the perimeter of this shape is called the area of the rectangle.
The area of a rectangle is Length ×width
perimeter of a rectangle = 2(l+w)
l= 3w
therefore P= 2(3w+w)
P= 2(4w)
p= 8w
p=48cm
48= 8w
divide both sides by 8
w= 6cm
from l= 3w
l= 3×6= 18cm
therefore the area of the rectangle is 18×6= 108cm²
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A candy company produces packets of candy every day. Each packet they produce has a slightly unique weight. The mean of the weights is 72g, and the variance of the weights is 16g.
What is the minimum weight of a packet of candy with a z-score of -0.6? (round to the nearest tenth as needed)
To determine the minimum weight of a packet of candy with a z-score of -0.6, we need to use the formula:
z = (x - μ) / σ
where:
z = -0.6 (given)
μ = 72g (given)
σ = sqrt(16g) = 4g (since variance = standard deviation squared)
Substituting the values in the formula, we get:
-0.6 = (x - 72) / 4
Multiplying both sides by 4, we get:
-2.4 = x - 72
Adding 72 to both sides, we get:
x = 69.6g
Therefore, the minimum weight of a packet of candy with a z-score of -0.6 is approximately 69.6g (rounded to the nearest tenth).
An item is priced at $14.29. If the sales tax is 5%, what does the item cost including sales tax?
Answer:3-5=787879. youu
Step-by-step explanation:
Use the two given functions to write y as a function of x.
y = -3a + 3, a = -5x + 1
Answer:
Step-by-step explanation:
To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.
Given:
y = -3a + 3
a = -5x + 1
Substituting the value of "a" in the first equation:
y = -3(-5x + 1) + 3
Now, let's simplify this expression:
y = 15x - 3 + 3
y = 15x
Therefore, y can be expressed as a function of x as:
y = 15x
Which of these is not a possible r-value?
ОА. 1.2
Ов. 0.5
Ос. -0.75
OD. -0.1
Answer:
Step-by-step explanation:
A
find the area of the triangle
9514 1404 393
Answer:
108 cm²
Step-by-step explanation:
The area of a triangle is given by the formula ...
A = 1/2bh
where b represents the base length, and h represents the height--the perpendicular distance from the base to the opposite vertex. The area of this triangle is ...
A = 1/2(12 cm)(18 cm) = 108 cm²
A bucket contains six white balls and five red balls. A sample of four balls is selected
at random from the bucket, without replacement. What is the probability that the
sample contains...
Exactly two white balls and two red balls?
At least two white balls?
To solve this problem, we can use the formula for probability:
P(event) = number of favorable outcomes / total number of outcomes
First, let's find the total number of outcomes. We are selecting 4 balls from 11 without replacement, so the total number of outcomes is:
11C4 = (11!)/(4!(11-4)!) = 330
where nCr is the number of combinations of n things taken r at a time.
Now let's find the number of favorable outcomes for each part of the problem.
Part 1: Exactly two white balls and two red balls
To find the number of favorable outcomes for this part, we need to select 2 white balls out of 6 and 2 red balls out of 5. The number of ways to do this is:
6C2 * 5C2 = (6!)/(2!(6-2)!) * (5!)/(2!(5-2)!) = 15 * 10 = 150
So the probability of selecting exactly two white balls and two red balls is:
P(2W2R) = 150/330 = 0.45 (rounded to two decimal places)
Part 2: At least two white balls
To find the number of favorable outcomes for this part, we need to consider two cases: selecting 2 white balls and 2 red balls, or selecting 3 white balls and 1 red ball.
The number of ways to select 2 white balls and 2 red balls is the same as the number of favorable outcomes for Part 1, which is 150.
To find the number of ways to select 3 white balls and 1 red ball, we need to select 3 white balls out of 6 and 1 red ball out of 5. The number of ways to do this is:
6C3 * 5C1 = (6!)/(3!(6-3)!) * (5!)/(1!(5-1)!) = 20 * 5 = 100
So the total number of favorable outcomes for selecting at least two white balls is:
150 + 100 = 250
And the probability of selecting at least two white balls is:
P(at least 2W) = 250/330 = 0.76 (rounded to two decimal places)
2x-y≤-3
graph the inequality
Therefore , the solution of the given problem of inequality graph comes out to be the graph of the inequality 2x - y ≤ -3 is a line that cuts through the x-y plane
What do you mean by inequality graph?An inequality graph is a graph that represents the solution set of an inequality, showing the values of the independent variable (usually represented on the x-axis) for which the inequality is true.
Here,
An inequality can be represented graphically by shading the region on a coordinate plane that satisfies the inequality. The direction of shading (above or below the line) depends on the inequality symbol.
The graph of the inequality 2x - y ≤ -3 in the x-y plane can be plotted by finding the boundary line for the inequality and shading the region that satisfies the inequality. To do this, we can start by setting the equation 2x - y = -3 and finding the x- and y-coordinates of the points on the line. Then we can plot these points and draw the line that connects them.
Next, we will determine which side of the line represents the solution set. To do this, we can pick a point that is not on the line and substitute its x- and y-coordinates into the inequality. If the inequality is true for the point, we shade the region that contains the point. If the inequality is false, we shade the region that does not contain the point.
So the graph of the inequality 2x - y ≤ -3 is a line that cuts through the x-y plane and is shaded on one side. The shaded region represents all the x- and y-coordinates that satisfy the inequality.
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witch of the following best described perpendicular lines?
Answer: I have to make one up In geometry, a branch of mathematics, perpendicular lines are defined as two lines that meet or intersect each other at right angles (90°).
Step-by-step explanation:
Find the exact length of each line segment.
Then estimate the length of each line segment to the
nearest tenth of a unit.
Use the sketch tool if it helps you with your thinking.
The actual and estimated distances are
AB = √17 = 4.1
GH = √32 = 5.7
Calculating the distance of the pointsFrom the question, we have the following parameters that can be used in our computation:
A = (0, 4) and B = (1, 0)
The distance is then calculated as
AB = √[(4 - 0)² + (1 - 0)²]
Evaluate
AB = √17
When estimated, we have
AB = 4.1
Also, we have
G = (0, 0) and H = (4, -4)
So, we have
GH = √[(4 - 0)² + (4 - 0)²]
Evaluate
GH = √32
When estimated, we have
GH = 5.7
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A cylinder has a volume of 659.4 cubic centimeters. The diameter of the cylinder is 10 cm. What is the height of the cylinder?
(Assume = 3.14)
A.
42 cm
B.
2.1 cm
C.
8.4 cm
D.
21 cm
The height is 8.4.
Calculated with H = V / πr^2, with H for height, V for volume, and r for radius (the diameter divided by 2).
The average snail can move 1.81 X 10³ mi in 5 hours. What is its rate of speed in miles per hour?
Answer:
Step-by-step explanation:
How Far Can A Snail Travel In One Hour
If a snail can travel over half an inch per minute, that means in one hour a snail can travel up to 40 inches. If you want to think about how far this is in feet, it means that snails move up to 3.5 feet per hour.
Consider the fact that the average human being can walk about a mile, or 5280 feet, in one hour.
This means that snails can take up to 1,500 days, or over 4 years, to travel just one mile.
A baker makes 60 muffins. He sells 24 of the muffins.
He put the rest of the muffins in boxes. Each box can hold 4 muffins.
Which equation can be used to find b, the number of boxes the baker will need?
OA.
B.
OC.
OD. (60
60+ 24 ÷ 4 = b
60 24 ÷ 4 = b
-
(60+24) ÷ 4 = b
24) = 4 = b
-
Answer:c
Step-by-step explanation:
c
Answer:b
Step-by-step explanation:
What is the distance between Point A and Point C?
A: 27−−√ units
B: 41−−√ units
C: 34−−√ units
D: 130−−−√ units
Maria, Ahmad, and Bob sent a total of 52 text messages during the weekend. Maria sent fewer messages than Bob. Ahmad sent times as many messages as Bob. How many messages did they each send?
Answer:
Maria sent 7 messages
Bob sent 5 messages
Ahmad sent 45 messages
Step-by-step explanation:
Given that Maria, Ahmad, and Bob sent a total of 52 text messages during the weekend.
If Maria sent fewer messages than Bob, and Ahmad sent times as many messages as Bob
Since the exact figures were not given, then let make an assumption that Ahmad sent 9 times as many messages as Bob.
If Bob sent 5 messages, then, Ahmad will send 5 × 9 = 45 messages
Also, it is given that Maria sent fewer messages than Bob. Take 45 away from 52. That is,
52 - 45 = 7
Therefore,
Maria sent 7 messages
Bob sent 5 messages
Ahmad sent 45 messages
true or false HELP me
Answer:
True
Step-by-step explanation:
Write an expression for 3 more than twice the number n.
Please answer my question
Answer:
2n+3
Step-by-step explanation:
please help!! find the reciprocal of these numbers.
6.2
-2.3
0.9
-22.7
Answer:
They have its own reciprocal
Estimate 32.79 dived by 8.1
What is the slope of the line that goes through the points -4–2 and 8–5
Answer:
-7/12
Step-by-step explanation:
-5-2 = -7 y
and
8- (-4)=12 x
Answer:
slope = -1/4
Step-by-step explanation:
m = (y2-y1)/(x2-x1)
m = (-5-(-2))/(8-(-4)
m = -3/12
m = -1/4
Hope this helps! :3
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What is the equation in point-slope form of the line that passes through the point (−1,−4) and has a slope of –3? Drag and drop the appropriate number, symbol, or variable to each box.
Answer:
y+4=-3(x+1)
Step-by-step explanation:
Hope this helps may all your sweet dreams come true!
Answer:
y+4=-3(x+1)
Step-by-step explanation:
this is right im in the test
27 points! please help me if you can <3 and yes I have been working on this for almost 4 hours
Answer:
330 milkshakes
Step-by-step explanation:
240 divided by 8 = 90
90 = number of large milkshakes
240 + 90 = 330
Write a story that could represent this math problem. (2 points)
If John has 3 of 4 slices of pie, and Tom has 2 of 6 slices of pie, how many do they have all together?
I believe that is what type of story you needed, if wrong let me know.
Answer: Suppose Rita is trying to find the area of the carpet of 3/4 and 2/6 for a room of 4/4 sq to 6/6 sq with balcony of 1/4 and 4/6
Explanation: In the given rectangle fig. length is given 3/4 and breadth is given 2/6 for the whole rectangle is 4/4 to 6/6.
for each block length is given 1/4 and breadth is given 1/6. The darker shaded area represents the carpet of the above story.
The answer after multiplying it is 6/24 or 1/4.
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Simplify 6x^2y^3(2x^2y)^3
Answer: 6x2y3(2x2y)3
=48x^8 y^6
write an equation in slope - intercept form for the line that passes through the given point and has the given slope.
The equation of slope is y = mx + (y1 - mx1)
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept.
To write an equation in slope-intercept form for the line that passes through a given point and has a given slope, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the given slope.
We can then simplify the equation to get it into slope-intercept form:
y - y1 = m(x - x1)
y = mx - mx1 + y1
By rearranging the terms, we can see that the y-intercept is y1 - mx1. Thus, the final equation in slope-intercept form is:
y = mx + (y1 - mx1)
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Note: The full question is
write an equation in slope - intercept form for the line that passes through the given point and has the given slope m.
Which is the simplified form of the expression three 7/5 X +4-232 -5/4 X
The simplified form of the expression is 123/20 x - 228
How to determine the simplified form of the expression?From the question, we have the following parameters that can be used in our computation:
three 7/5 X +4-232 -5/4 X
Rewrite the above expression properly
So, we have the following representation
37/5 x + 4 - 232 - 5/4 x
Collect the like terms in the above expression
So, we have the following representation
37/5 x - 5/4 x + 4 - 232
Evaluate the like terms in the above expression
So, we have the following representation
123/20 x + 4 - 232
Solving further, we have
123/20 x - 228
Hence, the solution is 123/20 x - 228
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At the start of track camp, Mary-Margaret could do 30 squats. Mary-Margaret performed 36 more squats every week while participating in the
track camp. The total number of squats is modeled by 36w + 30, where w is the number of weeks participating in the camp.
Which of the following expressions is equivalent to 36w +30 ?
A
6w+5
B
66
6 (6w +5
D
66w
Answer:
C) 6 (6w +5)
Step-by-step explanation:
6w+5 ≠ 36w +30
66 ≠ 36w +30
6 (6w +5) -> 36w + 30 = 36w +30
66w ≠ 36w +30
This leaves us with the option of 6 (6w +5)
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
0=x^2-10x+30 by completing the square
Answer:
15 and -5
Step-by-step explanation:
D=(-10)^2-4*30*1=100-120=-20
x1=(10+20):2=15
x2=(10-20):2=-5
Section 1
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A box of blocks contains 35 red, 40 blue, and 50 green blocks. If the box only contains red, blue, and green blocks, and a child randomly
selects a block, what is the probability the block is red?
Answer:
\(P(Red) = \frac{7}{25}\)
Step-by-step explanation:
Given
\(Red = 35\)
\(Blue = 40\)
\(Green = 50\)
Required
Determine the probability of red
\(P(Red) = \frac{n(Red)}{Total}\)
Substitute value for n(Red) and calculate Total
\(P(Red) = \frac{35}{35 + 40 + 50}\)
\(P(Red) = \frac{35}{125}\)
Divide numerator and denominator by 5
\(P(Red) = \frac{7}{25}\)