Answers
Answer:
f(x)=-18x^2
Step-by-step explanation:
Given:
1+Integral(f(t)/t^6, t=a..x)=6x^-3
Let's get rid of integral by differentiating both sides.
Using fundamental of calculus and power rule(integration):
0+f(x)/x^6=-18x^-4
Additive Identity property applied:
f(x)/x^6=-18x^-4
Multiply both sides by x^6:
f(x)=-18x^-4×x^6
Power rule (exponents) applied"
f(x)=-18x^2
Check:
1+Integral(-18t^2/t^6, t=a..x)=6x^-3
1+Integral(-18t^-4, t=a..x)=6x^-3
1+(-18t^-3/-3, t=a..x)=6x^-3
1+(6t^-3, t=a..x)=6x^-3
That looks great since those powers are the same on both side after integration.
Plug in limits:
1+(6x^-3-6a^-3)=6x^-3
We need 1-6a^-3=0 so that the equation holds true for all x.
Subtract 1 on both sides:
-6a^-3=-1
Divide both sides by-6:
a^-3=1/6
Raise both sides to -1/3 power:
a=(1/6)^(-1/3)
Negative exponent just refers to reciprocal of our base:
a=6^(1/3)
Related Questions
Use the percent formula, A = PB, where A is P percent of B, to answer the following question. What is 24% of 60?
Answers
It should be noted that 24 percent of 60 is 14.4.
How to calculate the percentage?The question is to calculate 24% of 60.
This will go thus:
= 24% × 60
= 24/100 × 60
= 0.24 × 60
= 14.4
Therefore, 24% of 60 is 14.4.
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27. What is the reflection image of (5, –3) across the y-axis? (–5, 3) (–5, –3) (–3, 5) (5, 3)
Answers
The search results are unrelated to the question of finding the reflection image of (5, -3) across the y-axis. To find the reflection image of a point across the y-axis, we need to change the sign of the x-coordinate of the point. Therefore, the reflection image of (5, -3) across the y-axis is (-5, -3).
The Ozzie Chocolate Company is preparing to offer a new product in its candy offerings, the Minty Dark Chocolate Bite bar. Material costs per new candy bar are
$0.25 for chocolate, $0.02 for sugar, and $0.03 for mint flavoring. Labor costs of the new product are approximately $0.15 per bar. Adding a production line devoted to the new candy will cost $250,000 per year.
(a) If the sales price is $1.40 per candy bar, how many must the company make per year in order to break even? Assume that each bar made is sold at full price.
(b) What is the company's profit or loss if they make and sell 270,000 candy bars at the $1.40 price in the first year?
(c) About 20% of the food consumed in the U.S. is imported. Production in many industries has been offshored. What ethical issues do companies face when presented with the decision to move operations?
Answers
Answer:
a) 263,158
b) $164,500
c) Ethical issues companies face when deciding to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...
Step-by-step explanation:
a)
Total cost = (0.25 + 0.02 + 0.03 + 0.15) x + 250,000
Total revenue = 1.40x
Setting the two equations equal to each other and solving for x, we get:
(0.45)x + 250,000 = 1.40x
0.95x = 250,000
x ≈ 263,158
b)
If the company sells 270,000 candy bars at $1.40 each, the total revenue generated is:
270,000 * $1.40 = $378,000
The total cost of producing 270,000 candy bars is:
(0.25 + 0.02 + 0.03 + 0.15) * 270,000 + $250,000 = $213,500
Therefore, the company's profit is:
$378,000 - $213,500 = $164,500
c)
Ethical issues companies face when presented with the decision to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...
You are installing a rectangular pool in your backyard. The pool measures 24 feet by 16 feet. You also would like to build a concrete walkway around the pool. You have allocated 560 ft? of your backyard for both the pool and the walkway around it. How wide should you make the walkway?
Answers
Answer:
The walkway should be 2ft wide.
Step-by-step explanation:
Let x be the width of the walkway surrounding the pool.
The area including the pool is 560ft².
Let's solve for the value of x.
The length plus twice the width of the pool is multiplied by the width plus twice the width of the pool. This makes up the whole area.
A = lw
560 = (24 + 2x)(16 + 2x)
560 = 384 + 48x + 32x + 4x²
4x² + 80x + 384 - 560 = 0
4x² + 80x - 176 = 0
Divide the whole equation by 4
x² + 20x - 44 = 0
(x + 22)(x -2) = 0
x = -22; x = 2
Since we are dealing with dimensions, take the one with the positive value.
x = 2ft
Let's check
560ft² = (24ft + 2x)(16ft + 2x)
560ft² = (24ft + 2(2ft)) (16ft + 2(2ft))
560ft² = (24ft + 4ft)(16ft + 4ft)
560ft² = (28ft)(20ft)
560ft² = 560ft² ✔
if you answer this question you will get 30 points
Answers
Answer:
2 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
Step-by-step explanation:
1+1 is 2
I believe the theorem is the Intermediate Value Theorem.
Answers
Yes you have the correct theorem.
The idea is to get everything to one side so we can form a function
\(\sin\left(e^{2x}\right) = 2x-1\\\\\sin\left(e^{2x}\right)-2x+1 = 0\\\\f(x) = \sin\left(e^{2x}\right)-2x+1\\\\\)
Afterward, we plug in x = 0 to find that
\(f(x) = \sin\left(e^{2x}\right)-2x+1\\\\f(0) = \sin\left(e^{2*0}\right)-2*0+1\\\\f(0) = \sin\left(1\right)+1\\\\f(0) \approx 1.84147\\\\\)
I set my calculator to radian mode, which is fairly common in many calculus courses.
Repeat for x = 1
\(f(x) = \sin\left(e^{2x}\right)-2x+1\\\\f(1) = \sin\left(e^{2*1}\right)-2*1+1\\\\f(1) \approx -0.10615\\\\\)
We see that f(x) changes in sign from positive to negative, when going from x = 0 to x = 1. Because f(x) is continuous, there must be at least one point in the road where it cuts through the x axis when f(x) = 0. This is the place where the intermediate value theorem kicks in.
Therefore, f(x) has at least one root on the interval 0 < x < 1. We don't know what the solutions are, or how many. We only know that at least one exists on this interval.
All of those ideas then extend back to the original equation. Since f(x) has at least one root, this must mean the original equation has at least one solution.
the ratio of peanuts to raisins in a snack mix is 5:4. A bag of the snack mix contains 200 peanuts. How many raisins are in the bag?
Answers
Number of raisins in the bag is 160 raisins
Given that;
Ratio of peanuts to raisins = 5:4
Bag of the snack mix contains = 200 peanuts
Find:
Number of raisins in the bag
Computation:
Number of raisins in the bag = 4[200/5]
Number of raisins in the bag = 4[40]
Number of raisins in the bag = 160 raisins
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When subtracting 1.578 from 127.3, the result on the calculator is 125.722. Round the answer to the appropriate precision based on the precision of the numbers in the subtraction column
Answers
Answer:
\(127.3 - 1.578 \approx 125.7\)
Step-by-step explanation:
Given
\(127.3 - 1.578 = 125.722\)
Required
Round to the precision of the 1.578
The number in the subtraction column is 1.578; so, the question implies that we round up 125.722 to the precision of 1.578
The precision of 1.578 is 4 (i.e. it has 4 digits). Hence, 125.722 will be approximated to 4 significant digits.
So, we have:
\(125.722 \approx = 125.7\)
or
\(127.3 - 1.578 \approx 125.7\)
Suppose that, based on a sample, the 95% confidence interval for the mean
of a population is (27, 43). What was the mean of the sample?
A. 35
B. 31
C. 33
D. 37
Answers
Answer:
A would be the correct answer
Step-by-step explanation:
28.
Car A and car B are 120 km apart. If they move towards each other, they will meet in 1 hour. If they
move in the same direction, car A will catch up with car B in 5 hours. Find the speed of car A and
the speed of car B. (Assume that the speeds of the cars are constant.)
Answers
Towards each other effective speed = x+y
t= d/r
120/(x+y) = 1
x+y=120..........................(1)
in the same direction effective speed = x-y
120/(x-y) =5
x-y = 24...................(2)
solve (1) & (2)
add
2x=144
x=72
you find out y
pls help I have headache i try everything
Answers
Answer:
210 students
Step-by-step explanation:
30%=63
10%=63÷3
=21
100%=21×10
=210
Please help me with this question
Answers
Answer:
Can you take a better picture
Step-by-step explanation:
what is 5 x 2/9 as a fraction.
Answers
Answer:
10/9
Step-by-step explanation:
So first you have to convert 5 to a fraction. 5/1 is equal to 5 so that means that 5/1 can work. 5/1x2/9=10/9 because all you have to do is multiply the numerator with the numerator and the denominator with the denominator.
Hope this helps
Answer:
10/9 (1 1/9
Step-by-step explanation:
That’s the fraction way, so all you simply do is multiply 5 by the numerator (2) then you would put it over the 9, which would make it 10/9. Also if you would like to simplify it but still it be a fraction, it would be 1 1/9.
I hope this helps!
(pwease give brainliest)
Leah works at an appliance store. She recorded her recent sales.
washing machines 3
dishwashers 1
ovens 6
clothes dryers 5
What is the experimental probability that the next appliance Leah sells will be an oven?
Answers
6/15
you add everything she sells together. ( 3+1+6+5=15) Then you put the amount of ovens she sells above taht number, making it a fraction.
Suppose that $17,699 is invested at an interest rate of 6.6% per year, compounded continuously
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
Answers
\(s(t) = 17699(1 .066) {}^{t} \)
b)\(s(1) = 17699(1.066) = 18867.13 \\ s(2) = 17699(1.066) {}^{2} = 20112.36 \\ s(5) = 17699(1.066) {}^{5} = 24363.22 \\ s(10) = 17699(1.066) {}^{10} = 33536.73\)
c)\(s(t) = 2 \times initial \: capital \: \\ s(t) = 2 \times 17699\)
\(17699(1.066) {}^{t} = 2 (17699) \\ 1.066 {}^{t} = 2 \\ t = log¹°⁰⁶⁶(2) = 10.84511 \: years\)
Solve the equation for m. 7(m+5)=21 m = -2 m = 2 = m= 9
Answers
Answer:
I'm thinking it's 9
Step-by-step explanation:
Function or Not a Function
Label:
Explanation:
Help plz
Answers
Answer: Hi hope this helps!
Step-by-step explanation:
Label: Not a function
Explanation: if you look at the x column, I there are two 1s with each one having a different Number in the F(x) column. Also there are two gives each one having a different Number in the F(x) column. Since these numbers aren't the same they are NOT functions.
Answer: Not a function
Step-by-step explanation:
Factor the Expression. If the expression cannot be factored, say so. 10.) c^2 - 9c - 18
Answers
we can match 0 and find the roots
\(C^2-9C-18=0\)ussing...
\(C=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)where a=1, b=-9 and c=-18
so replacing
\(\begin{gathered} C=\frac{-(-9)\pm\sqrt[]{(-9)^2-4(1)(-18)}}{2(1)} \\ \\ C=\frac{9\pm\sqrt[]{81+72}}{2} \\ \\ C=\frac{9\pm3\sqrt[]{17}}{2} \end{gathered}\)we have 2 roots
\(\begin{gathered} C_1=\frac{9+3\sqrt[]{17}}{2} \\ \\ C_2=\frac{9-3\sqrt[]{17}}{2} \end{gathered}\)now the factoring is
\((C-\frac{9-3\sqrt[]{17}}{2})(C-\frac{9+3\sqrt[]{17}}{2})=0\)\(n^{5} = 1254\)
How am i supposed to solve this?
Answers
Answer:
Step-by-step explanation:
\(n^{5}= 1254\\n^{5} = 2.3.11.19\)
Therefore it is not possible that n is a perfect power of 5
it is approximately 4.16
Answer:
n ≈ 4.165
Step-by-step explanation:
To solve this, you need to take the 5th root of both sides:
\(n^5=1,254\)
\(\sf{\sqrt[5]{n^5} =\sqrt[5]{1254}}\)
On the lhs we're only left with n as n^5 and the 5th root cancel each other out.
On the right-hand side we need to calculate:
\(n\approx4.165\)
5. Determine the value of t4 in an arithmetic sequence given that t₁ = 11 and S9 = 243.
Answers
The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).
We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.
From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:
243 = (9/2)(2(11) + (9-1)d)
243 = 9(22 + 8d)
243 = 198 + 72d
45 = 72d
d = 45/72 = 5/8
Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:
tₙ = a + (n-1)d
t₄ = 11 + (4-1)(5/8)
t₄ = 11 + 3(5/8)
t₄ = 11 + 15/8
t₄ = 88/8 + 15/8
t₄ = 103/8
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Rafael bought a bag of candy that contains 50 pieces. 30 of those pieces are chocolate and 5 are caramel. Write a ratio that compares the number of chocolate pieces to the number of pieces that are not either chocolate or caramel.
Answers
Answer:
so 50:30
=50-30=20
chocolate and 5are caramel
20:5
5can go into 20 =4
20:5
=4:1
Step-by-step explanation:
bag of candy is 50pieces 30piecesare chocolate and 5arecaramel
step 2 . you will subtract 50from30=20
step 3. 5can go into 20=4times
20:5 is equal to 4:1
5.(x+3) = 2x-3 Help pls
Answers
Answer:
x= -6
Step-by-step explanation:
5.(x+3) = 2x-3
5x+15=2x-3
5x-2x+15=-3
5x-2x=-3-15
3x=-3-15
3x=-18
x=-6
Step-by-step explanation:
5(X+3) =2X_3
Expand the brackets
5X + 15 = 2X _ 3
CLT(Collect like terms)
5X_2X= _3 _ 15
3X = _ 18
DBS( Divide both sides) by 3
3X/ 3 = _18 / 3
X = _9
is the product of 18 negative numbers and 20 positive numbers a positive number or negative
Answers
Answer:
positive
Step-by-step explanation:
even negatives = positive
whatever positives = positive
positive*positive = positive
Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations.
(a) The process standard deviation is 0.15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects. If required, round your answer to four decimal places.
(b) Through process design improvements, the process standard deviation can be reduced to 0.05. Assume that the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects. If required, round your answer to four decimal places.
(c) What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?
Answers
Answer:
\(\mathbf{P(X < 9.85 \ or \ X> 10.15) \approx 0.3171}\) to four decimal places.
\(\mathbf{P(X < 9.85 \ or \ X> 10.15) =0.0027}\) to four decimal places.
Step-by-step explanation:
a)
Assuming X to be the random variable which replace the amount of defectives and follows standard normal distribution whose mean (μ) is 10 ounces and standard deviation (σ) is 0.15
The values of the random variable differ from mean by ± 1 \such that the values are either greater than (10+ 0.15) or less than (10-0.15)
= 10.15 or 9.85.
The probability that the amount of defectives which are either greater than 10.15 or less than 9.85 can be calculated as follows:
\(P(X < 9.85 \ or \ X> 10.15) = 1-P ( \dfrac{9.85-10}{0.15}< \dfrac{X-10}{0.15}< \dfrac{10.15-10}{0.15})\)
\(P(X < 9.85 \ or \ X> 10.15) = 1- \phi (1) - \phi (-1)\)
Using the Excel Formula ( = NORMDIST (1) ) to calculate for the value of z =1 and -1 ;we have: 0.841345 and 0.158655 respectively
\(P(X < 9.85 \ or \ X> 10.15) = 1- (0.841345-0.158655)\)
\(P(X < 9.85 \ or \ X> 10.15) =0.31731\)
\(\mathbf{P(X < 9.85 \ or \ X> 10.15) \approx 0.3171}\) to four decimal places.
b) Through process design improvements, the process standard deviation can be reduced to 0.05.
The probability that the amount of defectives which are either greater than 10.15 or less than 9.85 can be calculated as follows:
\(P(X < 9.85 \ or \ X> 10.15) = 1-P ( \dfrac{9.85-10}{0.05}< \dfrac{X-10}{0.05}< \dfrac{10.15-10}{0.05})\)
\(P(X < 9.85 \ or \ X> 10.15) = 1- \phi (3) - \phi (-3)\)
Using the Excel Formula ( = NORMDIST (3) ) to calculate for the value of z =3 and -3 ;we have: 0.99865 and 0.00135 respectively
\(P(X < 9.85 \ or \ X> 10.15) = 1- (0.99865-0.00135)\)
\(\mathbf{P(X < 9.85 \ or \ X> 10.15) =0.0027}\) to four decimal places.
(c) What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?
The main advantage of reducing the process variation is that the chance of getting the defecting item will be reduced as we can see from the reduction which takes place from a to b from above.
Can someone help me with 5, 6, and 7 I’ll mark as brainliest. You don’t have to explain if you don’t want to. Just answer is fine
Answers
5. Area = 63.75 square units
Perimeter = 34 units
Sum of interior angles = 30 degrees
6. Area = 61. 40 square units
7. Length = 58. 2 units
How to simply the expressionWe need to know that formula for calculating the area of a trapezoid is expressed as;
5. Area = a + b/2(h)
Substitute the values, we have;
Area = 6.5 + 10.5/2(7.5)
Add the values
Area = 63.75 square units
Perimeter = a + b+ c + d
Perimeter = 8.5 +6.5 + 10. 5 + 8.5
Add the values
= 34 units
6. Area of a sector is = (θ/360º) × πr²
= 110/360 × 3.14 × 8²
Find the square and multiply
= 61. 40 square units
7. Length of an Arc = θ × (π/180) × r
Length = 210 × 3.14/180 × 16
Multiply the values
Length = 58. 2 units
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HELP PLEASE! E lies in the interior of
m
m
m
Show Your Work
Answers
Which is a better estimate for the weight of a double-decker bus
Answers
Step-by-step explanation:
Coaches are typically sized to a height of 4.38 meters, whereas 'high-bridge' vehicles are usually around 20 centimeters higher. At an average height of 18.65 metres, integrated double-deckers are often permitted .
10. A company manufactures photo cells. It uses the expression
(2x3,3 millimeters per second to calculate the maximum capacity
of a photo cell with area x3 square millimeters. Use a property
of exponents to simplify this expression.
Answers
the expression \((2x^3)^3\) millimeters per second , after simplification we get \(8x^9\)
Given
The company uses the expression \((2x^3)^3\) millimeters per second to calculate the maximum capacity with area \(x^3\)
Lets apply the property of exponents to simplify the expression \((2x^3)^3\)
We apply power property of exponents.
If we have exponent inside and outside the parenthesis then we multiply it
we distribute outside exponent inside the parenthesis
\((a^nb^m)^k=a^{nk}b^{mk}\)
In the given expression , 2 has exponent 1
\((2x^3)^3\\(2^1x^3)^3\\2^{1\cdot 3}x^{3 \cdot 3}\\2^3x^9\\8x^9\)
The simplified expression after applying the property is \(8x^9\)
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Answer:
8x^9
Step-by-step explanation:
(2x^3)(2x^3)(2x^3)
8x^9
Question 5
Provide an appropriate response.
For the stem-and-leaf plot below, what are the maximum and minimum entries?
Stem
ES
1
ions
2
Leaf
77889
011234456677788999
01123445566 678 899
58
3
4
om
max: 47 min: 18
max:45min 17
35
max 38min: 7
max 48. min 17
Answers
Answer:
max 48, min 17
Step-by-step explanation:
Apparently, your plot is supposed to be ...
1 | 77889
2 | 011234456677788999
3 | 01123445566678899
4 | 58
The smallest stem is 1, and its smallest leaf is 7, representing a value of 17.
The largest stem is 4, and its largest leaf is 8, representing a value of 48.
The extremes represented by this plot are: max 48, min 17.
Shamin Jewelers sells diamond necklaces for $442 less 10%. Jewelers offers the same necklace for $527 less 34%, 14% What additional rate of discount must offer to meet the competitor's price
Answers
Answer:
The selling price of the diamond necklace at Shamin Jewelers after 10% discount is:
$442 * 0.9 = $397.80
The selling price of the same necklace at the competitor's store after 34% and 14% discount is:
$527 * 0.66 * 0.86 = $247.08
So, Shamin Jewelers needs to offer an additional discount to meet the competitor's price:
$397.80 - $247.08 = $150.72
To calculate the additional rate of discount, we divide the difference by the original selling price at Shamin Jewelers and multiply by 100:
($150.72 / $442) * 100 = 34.11%
Therefore, Shamin Jewelers must offer an additional 34.11% discount to meet the competitor's price.
Step-by-step explanation: