Answers
The derivative of the function f(x) = Sin⁻¹(3x) is f'(x) = 3/√(1-9x²) , the correct option is (c) .
In the question ,
a function is given as
f(x) = Sin⁻¹(3x) , we need to find the derivative .
we know that the derivative of Sin⁻¹(x) is equal to 1/√(1 - x²) .
So , on differentiating both sides with respect to "x" .
we get
f'(x) = d/dx (Sin⁻¹(3x))
= 1/√1-(3x)² × d/dx (3x)
= 1/√(1 - 9x²) × 3
On simplifying further ,
we get
= 3/√(1 - 9x²)
Therefore ,the derivative of the function is 3/√(1-9x²) , the correct option is (c) .
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Related Questions
12 + -3/2 z =- 14
Solve the missing variable, Z
Answers
Answer:
z=-52/3
Step-by-step explanation:
1) 12 + -3/2 z= -14
2) -3/2 z = -26
3) z=-26(-2/3)
4) z= 52/3
-1/4-a-4=7/4a-3
solving equations with one unlike equations
Answers
Answer:
a = -5/11
Step-by-step explanation:
You want to solve the equation -1/4-a-4=7/4a-3.
SolutionThe first step in solving this 3-step equation can be to add the opposite of (-a) so that the variable 'a' appears only on one side of the equation:
-1/4 -a -4 +a = 7/4a -3 +a
-17/4 = 11/4a -3 . . . . . . . . . . . simplify
The second step is to add the opposite of the constant (-3) so that the constant is on one side of the equation, and the variable is on the other side.
-17/4 +3 = 11/4a -3 +3
-5/4 = 11/4a . . . . . . . . . . simplify
The third step is to multiply by the inverse of the coefficient of the variable:
(4/11)(-5/4) = (4/11)(11/4a)
-5/11 = a . . . . . . . . . . . . . . . simplify
Check-1/4 -(-5/11) -4 = (7/4)(-5/11) -3
-17/4 +5/11 = -35/44 -3
(-187 +20)/44 = (-132 -35)/44
-167/44 = -167/44 . . . . . . answer checks OK
David and his children went into a grocery store and he bought $7.50 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.50. He bought 5 more bananas than apples. By following the steps below, determine the number of apples, x, and the number of bananas, y, that David bought.
DETERMINE THREE WAYS TO HAVE 5 MORE BANANAS THAN APPLES
Answers
Answer:
Let the number of apples and bananas bought be x and y respectively.
x + 5 = y ------ equation (1)
0.75x + 0.50y = 7.50 ------ equation (2)
Substitute equation (1) into equation (2):
0.75x + 0.50(x+5) = 7.50
0.75x + 0.50x + 2.50 = 7.50
1.25x = 5
∴x = 4
Substitute x = 4 into equation (1):
∴y = 4+5
= 9
∴David bought a total of 4 apples and 9 bananas.
3. A company’s penetration rate is the percent of the market that uses its product. A market research firm is testing the
penetration rate for ACME widgets. In a random sample of 425 widget consumers, 185 purchased the ACME brand.
(a) Do these data provide good evidence that ACME’s penetration rate for widgets is greater than 40%? Test at the
2.5% level of significance.
(b) Explain the meaning of the P-value in the context of the data.
Answers
No, the data provided does not give good evidence that ACME’s penetration rate for widgets is greater than 40%, Test at the
2.5% level of significance
P-value in the data is 40% and this refers to the probability that the assumed penetration rate is greater tan 40 %
How to get the p value penetration rateThe central limit theorem is frequently employed in situations when it is necessary to identify the features of the population but it is challenging to analyze the entire population.
The central limit theorem gives the formula
Z = (X - μ) / σ
Definition of variables
sample mean, X = 185
population mean, μ = ?
standard deviation, σ = ?
sample size, n = 185
significance level = 2.5% = 0.025
confidence level = 1 - significance level = 1 - 0.025 = 0.975 = 97.5%
z score, z
Z score for 97.5% confidence level = 1.96
substituting into the formula
Z = (X - μ) / σ
The given variables are not enough for the calculation
population mean, μ = ?
standard deviation, σ = ?
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ned)
Sam went to eat at Texas Roadhouse. His bill was $45. In addition, he left a 15% tip
for the waitress. He also needed to pay 5% sales tax. How much did Sam spend at
Texas Roadhouse?
Answers
The total amount of money Sam paid for his food, tip for the waitress and sales tax at the Texas Roadhouse is $54
What is the total amount Sam spent at Texas Roadhouse?Sam's bill at the Texas Roadhouse = $45Percentage tip for the waitress = 15%Percentage sales tax = 5%Amount of tip = 15% × $45
= 0.15 × 45
= $6.75
Amount of sales tax = 5% × $45
= 0.05 × 45
= $2.25
Total amount Sam spent at the Texas Roadhouse = Sam's bill at the Texas Roadhouse + Amount of tip for the waitress + Amount of sales tax
= $45 + $6.75 + $2.25
= $54
In conclusion, the total amount of money Sam paid at the Texas Roadhouse is $54
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help me pleasseeee please help please help urgent
Answers
Answer: number 3
explanation: I took the
Fasting blood glucose levels are normally distributed with mean u = 117
mg/dL and standard deviation o = 15.2 mg/dL. Compute the upper 40.
percent Round answers to 1 decimal place.
Answers
the upper 40 percent round answers to 1 decimal place is 113.1
mean( [tex]\mu\\[/tex]) = 117 mg/dL
S.D.(σ) = 15.2 mg/dL
The r code which is used to get 40th percentile in qnorm(0.4,117, 15.2 ) = 113.1
What is mean?
Mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations), the geometric mean, and the harmonic mean.
What do you mean by geometric mean?
Geometric Mean (GM) is the average value or mean which signifies the central tendency of the set of numbers by finding the product of their values.
What do you mean by arithmetic mean?
The quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables.
What do you mean byharmonic mean?
The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals.
What do you mean by Standard Deviation?
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
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the table shows the number of pounds that 10 students in gary langs weight training class could bench press and squat. make a scatterplot to display the relationship between the bench press and squat weights for this sample. (use squat as the explanatory variable). describe the relationship shown in the scatterplot
Answers
The scatter plot that displays the relationship between the bench press and squat weights for this sample is given by the second image at the end of the answer.
From the scatter plot, it can be taken that the relationship is that the variables have a positive association, as when the bench press weight increases, so does the squat weight. The relationship, however, is not strong, as the scatter plot is not 100% increasing.
How to built the scatter plot?The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:
(bench press weight, squat weight).
From the table given by the first image at the end of the answer, the points are listed as follows:
(95, 141), (111, 208), (113, 100), (125, 218), (135, 284), (145, 275), (165, 338), (180, 338), (140, 420), (196, 420), (95, 141), (111, 208).
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Please help me solve this equation
Answers
[tex]39 + \frac{1}{7}r[/tex] when r = -1/2
[tex]39 + \frac{1}{7}*\frac{-1}{2} \\\\39 + \frac{-1}{14}\\\\[/tex]
= 38.92857 (in decimal form)
= 545/14 (in fractional form)
The assets and liabilities of a landscaping business are listed below.
Owned Inventory
$30,500
Cash
$75,420
Building Mortgage
$154,265
Savings Account
$28,000
Owned Equipment
$15,670
Small Business Loan
$25,652
Credit Cards
$11,450
Accounts Receivable
$11,560
Investments
$178,925
Which balance sheet correctly shows the assets, liabilities, and net worth of the landscaping business?
Answers
The total value of the ice cream shop owner's business assets would be; $286,898.
What are business assets?Business assets are the value of the assets of the Ice Cream Shop. The business assets consist of liabilities (amounts owed outsiders) and equity (the difference between assets and liabilities).
Business Assets:
Owned Inventory $30,500
Cash $75,420
Savings Account $28,000
Owned Equipment $15,670
Accounts Receivable $11,560
Property Value $125,768
Total assets = $286,898
Business Liabilities:
Small Business Loan $25,652
Other Debt $1,235
Building Mortgage $154,265
Total liabilities = $171,152
Equity = $115,746 ($286,898 - $171,152)
The total value of the ice cream shop owner's business assets would be; $286,898.
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Answer:
The net worth of the landscaping business is $148,708.
Step-by-step explanation:
Assets:
(Owned Inventory) $30,500
(Cash) $75,420
(Savings Account) $28,000
(Owned Equipment) $15,670
(Accounts Receivable) $11,560
(Investments) $178,925
30500+75420+28000+15670+11560+178925 = 340075
Liabilities:
(Building Mortgage) $154,265
(Small Business Loan) $25,652
(Credit Cards) $11,450
154265+25652+11450= 191367
Assets - liabilities = net worth
340075 - 191367 = 148708
So, the net worth of the landscaping business is $148,708.
A pentagon is transformed according to the rule R0, 180°. Which is another way to state the transformation?
Answers
Answer:
Using transformation rules, the transformation can also be stated by option A, that is (x, y) → (–x, –y).
------------------------------------
The first option, of (x, y) → (–x, –y), is a rotation of 180º degrees around the origin, which is the transformation made on the pentagon.
As for the other transformations:
The second option, (x, y) → (–y –x), is a reflection around the line y = -x.
The third option, of (x, y) → (x, –y), is a reflection across the x-axis.
The fourth option, of (x, y) → (–x, y), is a reflection across the y-axis.
Step-by-step explanation:
What is the equation of this graphed line
Answers
Answer: y = -9/8 + 7
Step-by-step explanation:
point a = (0,7), point b = (8,-2)
y = mx + b
b = 7
y = mx + 7
-2 = 8m + 7
-9 = 8m
m = -9/8
y = -9/8 + 7
Answer:
y= -9/8x+7
Step-by-step explanation:
find the slope
y2-y1/x2-x1
-2-7/8-0
-9/8
y=mx+b
m=slope
b=y intercept
y= - 9/8x + b
y= -9/8x+7
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Solve for a.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
4x +49x+8
Answers
Explanation:
Collect like terms by adding their coefficients (4+49)x +8
Add the numbers 53x+8
Hope this helps:)
-268=-6(-6-6k)+2k
k= ???
Answers
Answer:
k = - 8
Step-by-step explanation:
- 268 = - 6(- 6 - 6k) + 2k ← distribute parenthesis by - 6
- 268 = 36 + 36 k + 2k ( subtract 36 from both sides )
- 304 = 38k ( divide both sides by 38 )
- 8 = k
What's the area of a rectangle with side lengths of 6/8 metter and 4/10 metter?
Answers
Answer:
3/10 meters^2
Step-by-step explanation:
we multiply length by width to get are
6/8x4/10
6*4/8*10
24/80
3/10
Hopes this helps please mark brainliest
Answer: Hi the answer to that would be 3/10.
Step-by-step explanation: The first one explains the formula and the second one shows my work. I hope this helps!!!
Classify the following number: 4. Choose all that apply.
Answers
Answer: real number, integer, whole number, rational #
Step-by-step explanation:
Look at a chart about rational numbers vs irrational numbers.
A train goes at a constant speed. It can travel 159 miles in 2 1/2 hours. What distance would it travel in 2 hours
Answers
Answer:
127.2 miles
Step-by-step explanation:
using the relationships
speed = [tex]\frac{distance}{time}[/tex] ( time in hours ) = [tex]\frac{159}{2.5}[/tex] = 63.6 mph
constant speed is 63.6 mph
then
distance = speed × time = 63.6 × 2 = 127.2 miles
one half of 5 times y plus the quantity of y and 7
Answers
The simplified expression for the given word problem is 3y + 7/2.
What are algebraic expressions?When addition, subtraction, multiplication, division, and other mathematical operations are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.
An algebraic expression is composed of various parts. To better comprehend the idea of Variables, Constants, Terms, and Coefficients of any algebraic equation.
According to the given word problem
5 times y = 5y
5 times y plus the quantity of y and 7 = 5y + y + 7
one-half of 5 times y plus the quantity of y and 7 = 1/2(5y + y + 7)
So, simplify the expression now, we get
1/2( 5y + y + 7) = 1/2(6y +7)
= 1/2 × 6y + 1/2 × 7
= 3y + 7/2
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Which of the following is a good point estimator for the population variance?
Answers
A good point estimator for the population variance is: s².
What is a two-tailed test?A two-tailed test can be defined as a type of hypothesis test in which a rejection of the null hypothesis occurs for values of the point estimator in either tail of the sampling distribution.
In Statistics, the basis of an inference about the population is usually used to determine statistical inference based on all of the statistics that are calculated from samples.
This ultimately implies that, the sample mean should be close to the population mean, the sample proportion should be close to the population proportion, and the sample standard deviation should be close to the population standard deviation.
In this context, we can logically deduce that standard deviation (s²) is considered as a good point estimator for the population variance.
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Find the Smallest number which
being added 28 to
exactly divisable by 32, 36, 48
and 96
Answers
Answer:
265 is the snakiest number
Step-by-step explanation:
36 = 3 x 12 and 96 = 8 x 12 so LCM is 3 x 8 x 12 = 288
288 = 32x9 = 36x8 = 48x6 = 96x3
288 - 28 = 260
So 260 is the smallest number that meets the requirements
A shoe store is offering a series of markdowns for its customers due to its need for quick cash. The shoe store is offering the markdowns in the following order: 35%, 20%, and 10%. What would be the sale price of a pair of boots, if it originally costs $165.00?
Answers
The final price of the shoes after successive discounts is $77.22.
What is a discount?
A discount is a reduction in the regular selling price of a good or service, either in terms of money or as a percentage.
Main Body:
Sale price = Original price - discount
The formula for successive discount is given by=
Cost price*(1 - discount₁/100)*(1 - discount₂/100)*(1 - discount₃/100)
Now calculating:
According to the question , Cost price = $165
sale price = 165*(1-0.35)*(1-0.20)*(1-0.10)
= 165*0.65*0.8*0.9
= $77.22
Hence the answer to sale price of the shoe would be $77.22
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A sample of size 39 will be drawn from a population with mean 23 and standard
deviation 10. Find the probability that will be greater than 25.
Answers
The probability that X will be greater than 25 is 0.42
Given,
The sample size, n = 39
The mean of the population, μ = 23
The standard deviation of the population, σ = 10
We have to find the probability for X > 25.
Here,
Z score = (X - μ) / σ
Z score = (X - 23) / 10
Now,
We have to find P(X > 25)
Then,
P(X > 25) = P(z > (25 - 23) / 10)
P(X > 25) = P(z > 2/10)
That is,
P(X > 25) = P(z > 0.2)
Here,
0.5 - P(0 ≤ z ≤ 0.2)
= (0.5 - 0.0792)
= 0.42
Therefore,
The probability that X will be greater than 25 is 0.42
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If four people equally share a 1/2 page to 3/4page.what fraction of the page in the photograph
Answers
The fraction of page in the photograph is 3/32.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.Proper fractions are those in which the numerator value is less than the denominator value. as in 7/9 and 8/10. Improper Fraction - A fraction is deemed improper if the numerator value exceeds the denominator value. Example: 6/5 and 11/10.So, the fraction of the page in the photograph:
We know that,
The fraction of the page is 1/2.4 people share as 3/4.Now, calculate as follows:
(1/2 ÷ 4) × 3/41/2 × 1/4 × 3/41/8 × 3/43/32Therefore, the fraction of page in the photograph is 3/32.
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Answer:
=3/32
Step-by-step explanation:
(1/2÷4)*3/4
1/2*1/4*3/4
1/8*3/4
There-For The Answer Is:
=3/32
MARK AS BRAINLIEST ANSWER
Given g(x) = −2x^2 + 3x + 20, find g(0), g(−2.5), g(4), g(0.75), g(20)
Answers
The functions g(0) = 20, g(−2.5) = 0, g(4) = 0, g(0.75) = 21.125, g(20) = -720 as a result of the mapping with the function g(x) = −2x² + 3x + 20
What is a function?A function is a mapping whose codomain is the set of real numbers. It can also be defined as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
From the function g given as g(x) = −2x² + 3x + 20, by careful mapping we have the following;
put 0 for values of x
g(0) = -2(0)² + 3(0) + 20
g(0) = 20.
put -25 for values of x
g(-25) = -2(-25)² + 3(-25) + 20
g(-25) = -12.5 - 7.5 + 20
g(-25) = 0
put 4 for values of x
g(4) = -2(4)² + 3(4) + 20
g(4) = -32 + 12 + 20
g(4) = 0
put 0.75 for values of x
g(0.75) = -2(0.75)² + 3(0.75) + 20
g(0.75) = -1.25 + 2.25 + 20
g(0.75) = 21.125
put 20 for values of x
g(20) = -2(20)² + 3(20) + 20
g(20) = -800 + 60 + 20
g(20) = -720
Therefore, by proper mapping of the function g(x) = −2x² + 3x + 20, we derived g(0) = 20, g(−2.5) = 0, g(4) = 0, g(0.75) = 21.125, and g(20) = -720.
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Answer:
g(0) = 20
g(-2.5) = 0
g(4) = 0
g(0.75) = 21.125
g(20) = -720
Step-by-step explanation:
Hello!
We can evaluate each value by plugging the value inside the parenthesis into x in the equation [tex]-2x^2 + 3x + 20[/tex].
Evaluateg(0)g(0) = -2(0)² + 3(0) + 20g(0) = -2(0) + 0 + 20g(0) = 0 + 0 + 20g(0) = 20g(-2.5)g(-2.5) = -2(-2.5)² + 3(-2.5) + 20g(-2.5) = -2(6.25) - 7.5 + 20g(-2.5) = -12.5 - 7.5 + 20g(-2.5) = -20 + 20g(-2.5) = 0g(4)g(4) = -2(4)² + 3(4) + 20g(4) = -2(16) + 12 + 20g(4) = -32 + 12 + 20g(4) = -20 + 20g(4) = 0g(0.75)g(0.75) = -2(0.75)² + 3(0.75) + 20g(0.75) = -2(0.5625) + 3(0.75) + 20g(0.75) = -1.125 + 2.25 + 20g(0.75) = 1.125 + 20g(0.75) = 21.125g(20) g(20) = -2(20)² + 3(20) + 20g(20) = -2(400) + 60 + 20g(20) = -800 + 60 + 20g(20) = -740 + 20g(20) = -720The values are, in order, 20, 0, 0, 21.125, and -720.
Im giving 20 points for this
Answers
Answer:
(B)={8,10,15,18,20}
Step-by-step explanation:
Write the linear equation when given the following information.
m = -2 and b = -5
Answers
Answer:
y=-2x-5
Step-by-step explanation:
m =-2 and b=-5 so when substituted it will get you y=-2x-5
Who wants brainliest? First right answer first serve
Answers
Step-by-step explanation:
i marked where to put them
Z-Grand Shipping Company manufactures boxes in the shape of a cube.
The formula for the surface area of a cube is 6s, where s is the length of one side.
Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is
square feet
The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is
square feet
The surface area of the large box is times larger than the small box.
Please Help?
Answers
Answer:
Z-Grand Shipping Company manufactures boxes in the shape of a cube.
The formula for the surface area of a cube is 6s, where s is the length of one side.
Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is 216
square feet
The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is 54
square feet
The surface area of the large box is 4 times larger than the small box.
{So for the first line which is The surface area of each large box is
square feet.}
Ans;216
{The second line which is The surface area of each small box is
square feet.]
Ans;54
{The Third line which is The surface area of the large box is times larger than the small box.}
Ans;4
Thank you So much Hope this helps you! Please Mark Brainleast looking forward to help everyone ty!
Answer:
Z-Grand Shipping Company manufactures boxes in the shape of a cube.
The formula for the surface area of a cube is 6s, where s is the length of one side.
Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is 216
square feet
The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is 54
square feet
The surface area of the large box is 4 times larger than the small box.
{So for the first line which is The surface area of each large box is
square feet.}
Ans;216
{The second line which is The surface area of each small box is
square feet.]
Ans;54
{The Third line which is The surface area of the large box is times larger than the small box.}
Ans;4
Ken spends $344.76 before tax at a hardware store. If the sales tax rate in his city is 7.5%, what is the total cost of his purchase? Round to the nearest cent if necessary.
Answers
Answer:
$318.90
Step-by-step explanation:
Turn the percent into a decimal and multipy it by 344.76
0.075 × 344.76 = 25.857
after you get your answer you subtract 344.76 and 25.857
$344.76 - 25.857 = $318.903
round you answer to the nearest cent
= $318.90
(2,y) and (x,−3).
4x+2y=14
Answers
Minus 4x from both sides than you have to put the X first because y=mx+b. See how the X is first? So anytime you do an equation like that make sure to put the X first.