Evaluate 3^2+(6-2)•4-6/3
Answer:
23
Step-by-step explanation:
3^2+(6-2)•4-6/3
Order of operations:
= 9 + (4)•4 - 6/3
= 9 + 16 - 2
= 25 -2
= 23
32+(6−2)(4)− 6/3
your answer is =23
32+(6−2)(4)− 6/3
=9+(6−2)(4)− 6/3
=9+(4)(4)− 6/3
=9+16− 6/3
=25− 6/3
=25−2
=23
a 34 gram sample of a substance that's used to treat thyroid disorders has a k-value of 0.137. find the substance's half-life, in days. round to the nearest tenths.
Answer:
5.1 days
Step-by-step explanation:
Given in the question,
initial amount of substance = 34 grams
k-value = 0.137
To find the half life of this substance we will use following formula
[tex]N(0)/2 = N(0)e^{-kt}[/tex]
here N(0) is initial amount of substance
t is time in days
Plug values in the formula
[tex]34 /2 = 34e^{-0.137t}[/tex]
1/2 = e^{-0.137t}
Take logarithm on both sides
ln(1/2) = ln( e^{-0.137t})
ln(1/2) = -0.137t
t = ln(1/2) / -0.137
t = 5.059
t ≈ 5.1 days (nearest to tenths)
Which polynomial function has a leading coefficient of 1, roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2?
f(x) = 2(x + 7)(x + 5)(x – 2)
f(x) = 2(x – 7)(x – 5)(x + 2)
f(x) = (x + 7)(x + 5)(x + 5)(x – 2)
f(x) = (x – 7)(x – 5)(x – 5)(x + 2)
ANSWER
[tex]f(x) = (x -7)(x - 5) {(x - 5)}(x + 2)[/tex]
EXPLANATION
If the polynomial has a root -2, with multiplicity 1, then (x+2) is a factor.
If the polynomial has root, 7 with multiplicity 1, then (x-7) is a factor.
If the polynomial has root 5, with multiplicity 2, then (x-5)² is a factor of the polynomial.
The fully factored form of the polynomial is
[tex]f(x) =a (x + 2)(x - 7) {(x - 5)}^{2} [/tex]
It was given that the polynomial has a leading coefficient of 1.
Hence a=1.
This implies that,
[tex]f(x) =(x + 2)(x - 7) {(x - 5)}^{2}[/tex]
Or
[tex]f(x) = (x -7)(x - 5) {(x - 5)}(x + 2)[/tex]
Answer:
f(x) = (x -7)(x - 5) {(x - 5)}(x + 2) the answer is D
Step-by-step explanation:
A recipe calls for 4 cups of strawberries for every 6 cups of whipped topping. If gary uses 54 cups of whipped topping how many cups of strawberries does he need?
Answer:
36 cups
Step-by-step explanation:
If you notice, 6 times 9 is 54. So, 4 times 9 is 36. You need 36 cups of strawberries!
the area of the top face of a cube is 9 square meters. what is the volume of the cube
for a cube v=a^3, so 9^3= 729
As an estimation we are told ?3 is €4. Convert €83.60 to pounds. Give your answer rounded to 2 DP.
Answer:
€83.60 = £62.70
Step-by-step explanation:
£3/€4 = £x/€ 83.60
¾ = x/83.60
Multiply each side by the lowest common denominator (4 × 83.60)
3 × 83.60 = 4x
Divide each side by 4
x = (3 × 83.60)/4 = £62.70
∴ €83.60 = £62.70
(The conversion factor is out of date. The current conversion factor is closer to £6 = €7.)
Using the given exchange rate, we set up a conversion equation and solve for the unknown variable. We find that €83.60 is roughly equivalent to 62.86 pounds.
Explanation:Based on the given exchange rate, 1 pound (£) is equivalent to 1.33 Euros (€). Therefore, to convert €83.60 to pounds, we should do the following:
Set up the conversion ratio: 1.33 €/£ = 83.60 €/x £To solve for x (the value in pounds), cross-multiply: 1.33x = 83.60Divide both sides by 1.33: x = 83.60/1.33Rounding off to two decimal places, x = 62.86 £Therefore, €83.60 is approximately equivalent to 62.86 pounds.
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-2(bx-5) = 16 the value of x in terms of b is the value of x when b is 3 is ????
Answer:
x = -3/bx = -1 when b=3Step-by-step explanation:
Eliminating parentheses, you get ...
-2bx +10 = 16
Subtract 10 and divide by -2b:
x = 6/(-2b)
x = -3/b
__
When b=3, you have ...
x = -3/3
x = -1
Tell which statement is the best estimate for the division problem 185 divide 61
Answer:
whichever is closest to 3.032787
It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking. Among mildly obese people, the mean number of minutes of daily activity (standing or walking) is approximately Normally distributed with mean 371 minutes and standard deviation 65 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with mean 528 minutes and standard deviation 108 minutes. A researcher records the minutes of activity for an SRS of 6 mildly obese people and an SRS of 6 lean people.Use z-scores rounded to two decimal places to answer the following:What is the probability (Image for It appears that people who are mildly obese are less active than leaner people. One study looked at the averag0.0001) that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes? What is the probability (Image for It appears that people who are mildly obese are less active than leaner people. One study looked at the averag0.0001) that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?
Answer:
0.0322; 0.9929
Step-by-step explanation:
Since the data is normally distributed, we use z scores for these probabilities.
The formula for a z score of a sample mean is
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
For the sample of mildly obese people, the mean, μ, is 371; the standard deviation, σ, is 65; and the sample size, n, is 6.
Using 420 for X,
z = (420-371)/(65÷√6) = 49/(65÷2.4495) = 49/26.5360 ≈ 1.85
Using a z table, we see that the area under the curve to the left of this is 0.9678. However, we want the area to the right, so we subtract from 1:
1-0.9678 = 0.0322
For the sample of lean people, the mean, μ, is 528; the standard deviation, σ, is 108; the sample size, n, is 6.
Using 420 for X, we have
z = (420-528)/(108÷√6) = -108/(108÷2.4495) = -108/44.0906 ≈ -2.45
Using a z table, we see that the area under the curve to the left of this is 0.0071. We want the area under the curve to the right, so we subtract from 1:
1-0.0071 = 0.9929
The probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes is about 3.2%. For the 6 lean people, this probability is approximately 0.7%.
Explanation:For this type of problems, we use the concept of z-scores in statistics. The z-score is a measure of how many standard deviations a data point is from the mean. In this case, we will first calculate the standard error by dividing the standard deviation by the square root of sample size and then find the z-score by dividing the value of interest (420 minutes) minus mean by the standard error.
For mildly obese people, mean = 371 min, standard deviation = 65 min, sample size = 6. So, standard error = 65/sqrt(6) ≈26.51. The z-score for 420 min = (420-371)/ 26.51 ≈1.85. This indicates 420 minutes is 1.85 standard deviations above the mean. The probability that z-score exceeds 1.85 (assuming a one-tailed test since we are looking for the mean to be more than 420 minutes) is 0.032 (approximately). Hence, the probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes is about 0.032 or 3.2%.
For lean people, mean = 528 min, standard deviation = 108 min, sample size = 6. Using the same approach, standard error = 44.11. The z-score for 420 min = (420-528)/44.11 ≈-2.45. This indicates 420 minutes is 2.45 standard deviations below the mean. The probability that z-score is less than -2.45 (assuming a one-tailed test for under 420 minutes) will be more than 99%. The probability that z-score exceeds -2.45 (420 min or more time) is about 1 - 0.993 = 0.007. Hence, the probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes is about 0.007 or 0.7%.
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Given a spherical weather balloon with a volume of 36π cubic feet. What is the diameter, in feet, of the weather balloon?
A) 3
B) 6
C) 9
D) 12
Answer:
option B [tex]D=6\ ft[/tex]
Step-by-step explanation:
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
In this problem we have
[tex]V=36\pi\ ft^{3}[/tex]
substitute and solve for r
[tex]36\pi=\frac{4}{3}\pi r^{3}[/tex]
simplify
[tex]27=r^{3}[/tex]
[tex]r=3\ ft[/tex]
Find the diameter
[tex]D=2r=2(3)=6\ ft[/tex]
Answer:
b)6
Step-by-step explanation:
Please answer this question, will give brainliest!
See the attached picture:
Solve for y.
xy + p = 5
The value of y for the equation [tex]xy + p = 5[/tex].
What is equation?An equation is a statement of equality between two mathematical expressions containing one or more variables.
According to the given question.
We have a equation
[tex]xy + p = 5[/tex]
Solve the above the equation for y
[tex]xy +p - p = 5 -p[/tex] ( subtracting p both the sides)
[tex]\implies xy = 5-p[/tex]
[tex]\implies \frac{xy}{x} = \frac{5-p}{x}[/tex] (dividing both the sides by x)
[tex]\implies y = \frac{5-p}{x}[/tex]
Therefore, the value of y for the equation [tex]xy + p = 5[/tex].
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Please help, thanks a lot! :)
Match the stem and leaf plot to the correct set of data.
A.) 17, 17, 13, 28, 28, 26, 37, 35
B.) 7, 7, 3, 8, 8, 6, 7, 5
C.) 1.3, 1.7, 1.7, 2.6, 2.8, 2.8, 3.5, 3.7
D.) 1.3, 1.7, 1.7, 2.6, 2.8, 2.8, 3.5, 3.7, 3.7
Answer:
I believe the answer is A. 17, 17, 13, 28, 28, 26, 37, 35
The answer is C.
The stem, shows the number before the decimal point. The higher the number, the longer the stem goes down.
The leaf, shows the number after the decimal point. Each leaf is added to a row to match the stem of the original number.
1.3, 1.7, 1.7 all have a "1" before the decimal so they all go in the same row like this:
1 | 3 7 7
If we keep doing this, we see that C is the correct answer.
Best of Luck!
A number from 8 to 15 is drawn at random. What is the probability that the number is an even number?
Answer:
The probability that the answer is an even number is 50%.
Step-by-step explanation:
There are 8 terms: 8, 9, 10, 11, 12, 13, 14, 15. Even numbers: 8, 10, 12, 14. So, 4 out of the 8 terms are even, which is equivalent to 50%.
The probability that the number is an even number is 1/2.
What is the probability?The probability is defined as the ratio of number of favourable outcomes and the the total number of possible outcome.
A number from 8 to 15 is drawn at random.
The number between 8 to 15 are 8, 9, 10, 11, 12, 13, 14, 15 = 8
Total even number = 8, 10, 12, 14 = 4
The probability that the number is an even number is;
[tex]\rm Probability =\dfrac{Total \ even \ number}{Total \ number}\\\\Probability =\dfrac{4}{8}\\\\Probability =\dfrac{1}{2}[/tex]
Hence, the probability that the number is an even number is 1/2.
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Estimate the circumference of the circle with the given radius or diameter. Use 3.14 for ?. Round to the nearest unit. (Half. 24in written inside the circle) 1. 27in. 2. 79in. 3. 1,809in. 4. 152in. Mathematics, Connexus. Rectangular prisms and volume Part 1, Math 6B, Unit 3: Geometry and Measurement.
Answer:
The perimeter of a circle can be found by using the followinfg expression
P = 2*π*r
where
π = 3.14
r = radius of the circle = half the diameter of the circle
In this case, if we are given the radius, we use
P = 2*π*r
If we are given the diameter, we use
P = 2*π*(D/2) = π*D
1) 27in
radius = 27in
P = 2*(3.14)*(27 in) = 169.56 in
diameter = 27 in
P = (3.14)*(27 in) = 84.78 in
2) 79 in
radius = 79 in
P = 2*(3.14)*(79 in) = 496.12 in
diameter = 79 in
P = (3.14)*(79 in) = 248.06 in
3) 1809 in
radius = 1809 in
P = 2*(3.14)*(1809 in) = 11360.52 in
diameter = 1809 in
P = (3.14)*(1809 in) = 5680.26 in
4) 152 in
radius = 152 in
P = 2*(3.14)*(152 in) = 954.56 in
diameter = 152 in
P = (3.14)*(152 in) = 477.28 in
Answer:
no
Step-by-step explanation:
The Garcia family started the day with 2 gallons of milk. They drank 1 quart of milk for breakfast and 3 pints for lunch.How many pints of milk did the Garcia family have left after lunch.
Answer:
11 pt
Step-by-step explanation:
Convert all volumes to pints
Starting volume
2 gal × 4 qt/1 gal = 8 qt
8 qt × 2 pt/1 qt = 16 pt
Breakfast
1 qt × 2 pt/1 qt = 2 pt
Stating volume = 16 pt
Less breakfast = -2 pt
Less lunch = -3 pt
After lunch = 11 pt
The Garcia family had 11 pt of milk left after lunch.
I need help with this problem
Answer:
h = 15Step-by-step explanation:
The formula of an area of a parallelogram:
[tex]A=bh[/tex]
b - side
h - height
We have b₁ = 18 and h₁ 10 and b₂ = 12.
[tex]b_1h_1=b_2h[/tex]
Substitute:
[tex]12h=(18)(10)[/tex]
[tex]12h=180[/tex] divide both sides by 12
[tex]h=15[/tex]
Determine whether or not the given procedure results in a binomial distribution. if not, identify which condition is not met. spinning an american roulette wheel 74 times and recording the number the ball lands on.
Answer:
This procedure does not result in a Binomial distribution.
Step-by-step explanation:
In a Binomial distribution there are only 2 outcomes in each trial.. In the roulette experiment there are more than 2 possible outcomes for each trial so this condition is not met.
The spinning of an American roulette wheel 74 times doesn't result in a binomial distribution because there are more than two possible outcomes and thus the second condition - only two possible outcomes for each trial - for a binomial experiment is not met.
Explanation:The procedure of spinning an American roulette wheel 74 times and recording the number the ball lands on does not result in a binomial distribution. This is because it does not meet all the conditions necessary for a statistical experiment to be classified as a binomial experiment.
For an experiment to be classified as a binomial experiment, it must meet the following conditions:
There must be a fixed number of trials.There are only two possible outcomes for each trial, termed as success and failure.The trials are independent and must be repeated under identical conditions.Although the procedure meets the condition of having a fixed number of trials, it fails on the second and third conditions. On a roulette wheel, there are 38 possible outcomes, not two, so it fails the condition of only having two outcomes (success or failure). Moreover, the outcome of each spin is independent but the conditions are not identical, as the chance of landing on any particular number is not the same for every spin (if we consider landing on a specific number as 'success').
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In the figure below, △ABC ~ △PQR. If the Area of △ABC is 40 cm2, what is the area of △PQR? show your work.
Answer:
90 square cm.
Step-by-step explanation:
For similar figures, the length of corresponding sides are proportional.
So we can write 4k = 6 where k is the proportionality constant.
Note: In terms of area, the scale factor would be k^2 and in terms of volume, it would be k^3y
Solving 4k = 6, we see that k = 6/4 or 3/2
We need area, so we multiply area of ABC by k^2 to get area of PQR.
[tex]40(\frac{3}{2})^2\\=40(\frac{9}{4})\\=90[/tex]
Area of PQR = 90 cm^2
Answer:
The area of △PQR is [tex]90\ cm^{2}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
so
Let
z-----> the scale factor
x---> the corresponding side triangle PQR
y---> the corresponding side triangle ABC
[tex]z=\frac{x}{y}[/tex]
substitute the values
[tex]z=\frac{6}{4}=1.5[/tex]
step 2
Find the area of triangle PQR
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
so
Let
z-----> the scale factor
x---> the area of triangle PQR
y---> the area of triangle ABC
[tex]z^{2} =\frac{x}{y}[/tex]
we have
[tex]z=1.5[/tex]
[tex]y=40\ cm^{2}[/tex]
substitute the values
[tex]1.5^{2} =\frac{x}{40}[/tex]
[tex]x=40(1.5^{2})=90\ cm^{2}[/tex]
Kendra's credit card is stolen. She calls the credit card company to report it and the company says there are three large purchases on her card. She tells the company she did not make those purchases. Why does the credit card company tell her she is only responsible for $50.00 of those charges?
A. Federal law regulates a consumer's liability for fraudulent charges.
B. Credit card companies do not penalize consumers in cases of fraud.
C. Credit card companies know when charges are not made by the consumer.
D. Federal law states that credit card companies must collect that amount from consumers.
Answer:
A
Step-by-step explanation:
Federal law regulates a consumer's liability for fraudulent charges. Is what I got.
Answer:
A. Federal law regulates a consumer's liability for fraudulent charges.
Step-by-step explanation:
Under FCBA rules if a client reports about the lost cred card befor eit is used by someone else then the owner of the card is not responsible for any charges. As per the rule Card holders liability for unauthorised use of their credit card ends at $50. FCBA is a federal law that was framed in 1974 and allows us to dispute charges and temporarily withhold payment without affecting credit score. It is because of FCBA that she would not be charges more than fifty dollars.
While flying an aircraft, a pilot looks out to the horizon. The altitude of the plane is 9.4 km. Earth has an average radius of about 6378 km. How far away is the horizon to the nearest tenth of a kilometer?
Answer:
6387 km
Step-by-step explanation:
6378 km -9.4 km =
6386.6 km
Round to the nearest tenth: 63787 km
Hope I helped, sorry if not tho
plz help me
The table shows the change in the annual sales turnover of a company in millions of dollars, S(x), where x represents the years since the company was founded.
x S(x)
1 $495
3 $598.95
5 $724.73
7 $876.92
9 $1,061.08
What is the predicted average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11]?
A.
$184.15 per year
B.
$111.42 per year
C.
$222.83 per year
D.
$92.08 per year
Answer:
its going to be d
Step-by-step explanation:
Answer:
The correct option is B.
Step-by-step explanation:
The general exponential regression model is
[tex]y=ab^x[/tex]
Using regression tool the exponential regression model for the given data is
[tex]S(x)=449.9999(1.09999)^x[/tex]
[tex]S(x)=450(1.1)^x[/tex]
The value of function at x=9 is
[tex]S(9)=450(1.1)^9=1061.07646[/tex]
The value of function at x=11 is
[tex]S(11)=450(1.1)^{11}=1283.90252[/tex]
The average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is
[tex]m=\frac{S(11)-S(9)}{11-9}[/tex]
[tex]m=\frac{1283.90252-1061.07646-}{2}=111.413\approx 11.42[/tex]
The average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is 11.42. Therefore the correct option is B.
1. Collin noticed that various combinations of nickels and dimes could add up to $0.65.
Let x equal the number of nickels
Let y equal the number of dimes
What is the domain where y is a function of x and the total value is $0.65?
A. (0,1,2,3,4,5,6,7,8,9,10,11,12,13)
B. (1,2,3,4,5,6,7,8,9,10,11,12,13)
C. (0,1,3,5,7,9,11,13)
D. (1,3,5,7,9,11,13)
Answer:
Step-by-step explanation:
dimes only cannot give total ending in 5 cents
so theres at least 1 nickel
n by the same reason, no.of nickels must be odd no.
most nickels is 0.65/0.05=13
combining the above, ans is D. (1,3,5,7,9,11,13)
Answer:
The Answer Is D (1,3,5,7,9,11,13)
Step-by-step explanation:
How do you do this problem? Simple and concise explanation please! TOP ANSWERERS!!!!
Answer:
Just B and C
Step-by-step explanation:
Reduce this to the lowest amount possible.
log(3abc/6a^2b) = 2
=================
log(c/2a) = 2
c/2a = 10^2
c = 2a * 100
c = 200a
This one is also correct.
=================
The rest are just incorrect.
There is only 1 answer that works and that is B.
C is close, but it is not correct.
D is backwards. B is the right way and D is the upside down of B.
E and F are just not the way to handle logs. Subtracting logs means division, not multiplication and not 1 log.
=================
A shampoo company begins selling a new bottle of shampoo that is advertised as 25% more shampoo than the old bottle. If the new bottle holds 15 ounces of shampoo, how much did the old bottle hold?
15 - 25% = 14.47 ounces of shampoo
The original shampoo bottle held 12 ounces before the 25% increase to 15 ounces. For the tile cleanser, the percent by mass of HCl is calculated to be 14.84%. Discussions of consumer product concentrations, like laundry detergent costs per ounce, often involve linear relationships and predictive models.
The question requires understanding percent increase and how to calculate the original amount given the increased quantity. To find the original volume of the shampoo bottle before the 25% increase, we set up the equation where the original volume (V) times 1.25 (to represent the 25% increase) equals the new volume of 15 ounces:
V x 1.25 = 15 ounces
To solve for V, we divide both sides of the equation by 1.25:
V = 15 ounces / 1.25
V = 12 ounces
Therefore, the old bottle held 12 ounces of shampoo.
To address another concept related to consumer products, the question on mass percentage, namely the percent by mass of HCl in a tile cleanser, also represents a common mathematical calculation in consumer product information. The calculation is as follows:
Percent by mass = (mass of solute / total mass of solution) x 100%
Percent by mass of HCl = (135 g / (135 g + 775 g)) x 100%
Percent by mass of HCl = (135 g / 910 g) x 100%
Percent by mass of HCl = 14.84%
Thus, the bottle of tile cleanser has 14.84% by mass of HCl.
When discussing the cost per ounce of laundry detergent in different sizes, such as a 40 oz. size or a 90 oz. size, the concept of linear relationships may be explored, as well as the possibility of identifying outliers or considering the validity of predictive models like the least-squares line.
A square pyramid and a cone have the same base area. The volume of the cone is 100cm^3 , and the height of the cone is 15 cm. The height of the square pyramid is 24 cm. Find the volume of the square pyramid to the nearest whole unit.
Answer:
160 cm³
Step-by-step explanation:
1. Calculate the base area of the cone
The volume for the volume (V) of a cone is
V = ⅓Ah
Data:
V = 100 cm³
h = 15 cm
Calculation:
100 = ⅓ A× 15
100 = 5A
A = 100/5 = 20 cm²
2. Volume of Pyramid.
The volume for the volume (V) of a square pyramid is
V = ⅓Ah
Data:
A = 20 cm²
h = 24 cm
Calculation:
V = ⅓× 20× 24 = 160 cm³
The volume of the square pyramid is 160 cm³.
A betting company wishes to sell 5000 tickets 50 of which will win prizes. I.) A students decided to buy 200 tickets. Let X be the number of tickets that win a prize. Write the probability distribution of X and give its mean. Ii.) Using a Poisson approximation for the distribution of X find the probability of at least three tickets winning a prize. Iii.) Calculate the number of tickets that should be bought so as the probability of at least one winning a prize is 90%
Answer:45000,000,000,000
Step-by-step explanation:you just have to times it
the graph shows that lisa's earnings are proportional to the number of hours that she works.This relationship can be represented by an equation in the form y = kx. what is the value of k in the equation?
c. 25 because she gets $25 per hour
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 3x2 − 4x + 1, [0, 2] Yes, it does not matter if f is continuous or differentiable, every function satifies the Mean Value Theorem. Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on double-struck R. No, f is not continuous on [0, 2]. No, f is continuous on [0, 2] but not differentiable on (0, 2). There is not enough information to verify if this function satifies the Mean Value Theorem. If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisify the hypotheses, enter DNE). c =
[tex]f(x)=3x^2-4x+1[/tex] is a polynomial and thus continuous everywhere and differentiable on any open interval. (second option)
The MVT then guarantees the existence of [tex]c\in(0,2)[/tex] such that
[tex]f'(c)=\dfrac{f(2)-f(0)}{2-0}=\dfrac{5-1}2=2[/tex]
We have
[tex]f'(x)=6x-4[/tex]
so
[tex]6c-4=2\implies6c=6\implies c=1[/tex]
The true statement is: (b) Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable
Mean value theorem states that:
If [tex]\mathbf{f(x)\ is\ continuous}[/tex] [a,b] and
[tex]\mathbf{f(x)\ is\ differentiable}[/tex] on (a,b),
Then there is a point c in (a,b), such that: [tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]
The function is given as:
[tex]\mathbf{f(x) = 3x^2 - 4x + 1}[/tex]
And the interval is: [tex]\mathbf{[0,2]}[/tex]
We have
[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]
This becomes
[tex]\mathbf{f'(c) = \frac{f(2) - f(0)}{2 - 0}}[/tex]
[tex]\mathbf{f'(c) = \frac{f(2) - f(0)}{2}}[/tex]
Calculate f(2) and f(0)
[tex]\mathbf{f(2) = 3\times 2^2 - 4\times 2 + 1 = 5}[/tex]
[tex]\mathbf{f(0) = 3\times 0^2 - 4\times 0 + 1 = 1}[/tex]
So, we have:
[tex]\mathbf{f'(c) = \frac{5-1}{2}}[/tex]
[tex]\mathbf{f'(c) = \frac{4}{2}}[/tex]
[tex]\mathbf{f'(c) = 2}[/tex]
Recall that:
[tex]\mathbf{f(x) = 3x^2 - 4x + 1}[/tex]
Differentiate
[tex]\mathbf{f'(x)= 6x - 4}[/tex]
Substitute c for x
[tex]\mathbf{f'(c)= 6c - 4}[/tex]
Substitute 2 for f'(c)
[tex]\mathbf{ 6c - 4 = 2}[/tex]
Collect like terms
[tex]\mathbf{ 6c = 4 + 2}[/tex]
[tex]\mathbf{ 6c = 6}[/tex]
Divide both sides by 6
[tex]\mathbf{c = 1}[/tex]
The interval is given as: [0,2]
The value of c is true for interval (0,2).
Hence, the true statement is:
(b) Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable
Read more about mean value theorems at:
https://brainly.com/question/3957181
Hank and Debra each one two milking cows. One day, they Milked their cows and compared the amount of milk the cows produced in that day
Answer:
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Step-by-step explanation: