Answers
The value of c is 5/2 that satisfy the conclusions of the mean value theorem.
Given Function:
f(x) = x^2-3x+3 on interval [1,4].
The Mean Value Theorem states that for a continuous and differentiable function f(x)=x^2-3x+3 on the interval [1,4] there exists such number c from the interval [1,4] that [tex]f'(c)=\frac{f(4)-f(1)}{4-1}[/tex].
f(4) = 4^2-3*4+3
= 16-12+3
= 4+3
= 7
f(1)=1^2-3*1+3
= 1-3+3
= 1
f'(c) = 2c -3
2c-3 = 7 - 1 / 4 - 1
2c - 3 = 6/3
2c -3 = 2
2c = 5
c = 5/2
Therefore the value of c = 5/2 that satisfy the conclusions of the mean value theorem.
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Related Questions
Lucy sold some items at a garage sale. She spent 7/12 of her earnings on a new bike. She uses 3/5 of the remainder to purchase a gift for her mom. What traction of her total earnings was spent on her mom's gift?
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First we have to find the fraction that represents the remainder after buying the bike, subtracting 7/12 from the total, represented by 12/12
The result is 5/12
Then we have to multiply 5/12 by 3/5 to find our final answer
[tex]\begin{gathered} \frac{5}{12}\cdot\frac{3}{5}=\frac{15}{60} \\ \frac{15}{60}=\frac{5}{20}=\frac{1}{4}\text{ Simplifying our fraction} \end{gathered}[/tex]The fraction of her total earnings spent on her mom's gift was 1/4
Geometric Probability: I don’t know how to do this please help quickly
Answers
Solution
From the question,
If buses arrive every 19 mins and each waited 3 mins before departing
Then we can say that each bus departed (19 + 3) = 22 mins.
if you arrived at the moment the bus left, you would need to wait for the next bus
The probability is
[tex]\frac{9}{22}=0.409[/tex]What is the probability of flipping a coin 11 times and getting heads 5 times?Round your answer to the nearest tenth of a percent.O A. 16.1%B. 8.1%O C. 22.6%O D. 0.5%SUBMIT
Answers
If you flip a coint there are two possible outcomes, "head"
Listed below are amounts (in millions of dollars) collected from parking meters by a security service company and other companies during similar time periods. Do the limited data listed here show evidence of stealing by the security service company's employees?The coefficient of variation for the amount collected by the security service company is __%.The coefficient of variation for the amount collected by other companies is __%.
Answers
The coefficient of variation of a dataset is given by the ratio between the standard deviation to the mean.
[tex]CV=\frac{\sigma}{\mu}[/tex]The mean and the standard deviation of a dataset with N elements are given by the following formulas:
[tex]\begin{gathered} \mu=\frac{\sum_i^Nx_i}{N} \\ \\ \sigma=\sqrt{\frac{1}{N-1}\sum_{n\mathop{=}0}^{\infty}(x_i-\mu)^2} \end{gathered}[/tex]Then, using those formula for the security service company, we have the following coefficient of variation:
[tex]\begin{gathered} \mu=1.53 \\ \sigma=0.15670212364724... \\ CV=0.102419689...\approx10.2\% \end{gathered}[/tex]Then, using those formula for the other companies, we have the following coefficient of variation:
[tex]\begin{gathered} \mu=1.72 \\ \sigma=0.11352924243951... \\ CV=0.0660053735...\approx6.6\% \end{gathered}[/tex]What is the first quartile of the data displayed in this box-and-whisker plot?O 49O 41O 37O 353436403844424648T54 56525058
Answers
1) In any box and whiskers plot we can tell the following about how to read it:
3) So, reading that box and whiskers plot, we can tell the first quartile is:
[tex]Q_1=37[/tex]When 9 and 2/3 is written in simplest radical form, which value remains under the radical?36927
Answers
Given
[tex]9^{\frac{2}{3}}[/tex]To write it in the simplest form and to find which value remains under the radical.
Explanation:
It is given that,
[tex]9^{\frac{2}{3}}[/tex]It is known that,
[tex]x^{\frac{m}{n}}=\sqrt[n]{x^m}[/tex]That implies,
[tex]\begin{gathered} 9^{\frac{2}{3}}=\sqrt[3]{9^2} \\ =\sqrt[3]{3\times3\times3\times3} \\ =3\sqrt[3]{3} \end{gathered}[/tex]Therefore, the simplest form of the expression is,
[tex]3\sqrt[3]{3}[/tex]and the value that remains under the radical is 3.
Use the spinner to find the theoretical probability of the event 6 2 The theoretical probability of spinning a multiple of 2 is
Answers
The spinner has six possible outcomes, 3 of them are multiples of 2 (2, 4 and 6). Then the probability is:
[tex]P=\frac{3}{6}=\frac{1}{2}[/tex]Therefore the probability is 1/2.
write a multiplication equation for the area of the square with side lengths of 1 meter
Answers
Area of a square is expressed using the formula;
A = L^2
L is the side length of the square
From the question, we are given;
L = 1 meter
The multiplication equation for the area of the square will be;
A = 1 meter * 1 meter
A = 1m^2
can someone help me set it up im very confused.
Answers
let h be the height of the television set
4: 3 = 46 : h
[tex]\frac{4}{3}=\frac{46}{h}[/tex]cross multiply
4h = 138
Divide both-side of the equation by 4
h = 34.8 inches
1.Given triangle ABC shown, graph its image after a dilation centered at the origin with a scale factor of two. Give the coordinates of the images of the vertices below.2. List all pairs of parallel line segments from problem 1.
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for the question 1: the image of the vertices will be A'=2(-4,4)=(-8,8); B'=2(-4,-3)=(-8,-6); C'=2(4,-3)=(8,-6)
for the question 2: there will be no pairs of parallel lines in the triangle
What is 7×312 using mental math
Answers
Step-by-step explanation:
2184 simple ..... .............
Answer:
Its 2184
Step-by-step Explained
Part A Estimate 10/12 - 3/8 using benchmark values. Your equation must show the estimate for each fraction and the final estimate for the expression.Part BSolve 10/12 - 3/8Part Ccalculate the difference between your stimate in Part A and the actual value calculated in Part B.Show the solution as an equation Based on the results was your estimate in Part A reasonable?
Answers
Answer:
[tex]\begin{gathered} A\text{. 1/2} \\ B\text{. 11/24} \\ C\text{. }\frac{1}{24} \\ \end{gathered}[/tex]Yes, the calculations in A were reasonable because the difference is pretty close to 0.
Step-by-step explanation:
For part A,
-estimate the fraction 10/12 using 1/2 as our benchmark
The lower range is 1/2 and the upper range is 1
The halfway point is:
[tex]\begin{gathered} \frac{1}{2}\cdot\frac{(1+2)}{2} \\ \frac{1}{2}\cdot\frac{3}{2}=\frac{3}{4} \end{gathered}[/tex]Therefore, our range is 1/2 < 3/4 < 1
10/12 ≥ 3/4, we round up to 1
-estimate the fraction 3/8 using the 1/2 as our benchmark:
The lower range is 0 and the upper range is 1/2
The halfway point is:
[tex]\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]Therefore, our range is 0 < 1/4 < 1/2
3/8 ≥ 1/4, we round up to 1/2
[tex]\frac{2}{2}-\frac{1}{2}=\frac{1}{2}[/tex]For part B, the denominators are 12 and 8, so the LCM would be;
[tex]\text{LCM}=24[/tex]Then, we make a common denominator and subtract the numerators
[tex]\begin{gathered} \frac{10}{12}-\frac{3}{8}=\frac{20}{24}-\frac{9}{24} \\ \frac{10}{12}-\frac{3}{8}=\frac{11}{24} \end{gathered}[/tex]For part C, compute the difference between the two results from parts A and B:
[tex]\frac{1}{2}-\frac{11}{24}=\frac{1}{24}[/tex]Yes, the calculations in A were reasonable because the difference is pretty close to 0.
The image of the point (-2,2) under a translation is (-3,5). Find the coordinatesof the image of the point (-3,1) under the same translation.Submit Answer
Answers
We have an inital coordinate given (-2,2) and after a translation we got a new coordinate called (-3,5)
We can find the transformation like this:
-3= -2-1
5= 2+3
So then the transformation is given by:
[tex]T\rightarrow(x-1,y+3)[/tex]If we apply this transformation to the (-3,1) coordinate we got:
[tex](-3-1=-4,1+3=4)[/tex]So then the final answer would be (-4,4)
A rectangular field is 300 meters long and 150 meters wide.What is the area of the field in square kilometers? Do notround your answer.km²XG?Conversion facts for length1000 millimeters (mm) = 1 meter (m)100 centimeters (cm) = 1 meter (m)10 decimeters (dm) = 1 meter (m)1 decameter (dam) = 10 meters (m)1 hectometer (hm)100 meters (m)1 kilometer (km)1000 meters (m)I need help with this math problem.
Answers
Given:
A rectangular field is 300 meters long and 150 meters wide.
Required:
Find the area of the field in square kilometer.
Explanation:
The area of the rectangle is given by the formula:
[tex]\begin{gathered} A=length\times width \\ A=300\times150 \\ A=45000\text{ m}^2 \end{gathered}[/tex][tex]1m=\frac{1}{1000}km[/tex][tex]\begin{gathered} A=45000\times\frac{1}{1000000} \\ A=0.045\text{ km}^2 \end{gathered}[/tex]Final Answer:
The area of the
Diego's goal is to walk more than 70,000 steps this week. The mean number of steps that Diego walked during the first 4 days of the week is 8,019.If the mean number of steps Diego walks during the last 3 days of the week is 12, 642, will Diego reach his goal of walking more than 70,000 steps this week? Explain your reasoning.
Answers
Solution
Diego goal was walk more than 70000 steoes
And in average in the first 4 days he walks 8019 steps
The expected mean number of steps for the next 3 days is 12642 then we can do this:
8019*4 + 12642*3= 32076 +37926 = 70002
then since 70002 > 70000
We can conclude that Diego can reach the goal for this case
Jeremy says this dilation can be represented by (X+3\4,Y+3\4)Julie says this dilation can be represented by (3\4X, 3\4Y)whoo is correct and why
Answers
The scale factor for dilation is 3/4. Therefore, the dilation can be represented below
[tex](\frac{3}{4}x,\frac{3}{4}y)[/tex]This means Julie is correct.
what is the inequality of 7x ≤14 on a numberline
Answers
To find the inequality on a number line, we need to solve the inequality for x:
[tex]7x\leq14[/tex]Divide both sides by 7 to isolate the x variable:
[tex]\frac{7x}{7}\leq\frac{14}{7}[/tex][tex]x\leq\frac{14}{7}[/tex]Then:
[tex]x\leq2[/tex]Therefore, the inequality represents that x can be equal to or less than 2
Can someone Help me with Trigonometry, will mark Brainliest if correct ;) show your work and draw a diagram of the answer pls
Answers
So we will use trigonometry to solve this because it is a right triangle. The hypotenuse is the ladder (h) and the two smallest sides are the floor and the vertical wall (w).
That angular ladder does with the ground= A
sin A = opposite / hypotenuse
[tex]\begin{gathered} \sin \text{ A = }\frac{14.8}{15}=0.986 \\ A=\sin ^{-1}(0.986)=80.4\text{degrees} \end{gathered}[/tex]No, the ladder will not be safe
Now let's make it safe:
The lenght of the ladder (w) is constant, so it remains 15
So now let's ask in an inequality what height will be safe (70degrees or less)
[tex]\begin{gathered} A=\sin ^{-1}(\frac{w}{15})\leq70 \\ \sin (\sin ^{-1}(\frac{w}{15}))\leq\sin (70) \\ \frac{w}{15}\leq0.9396 \\ (15)\frac{w}{15}\leq0.9396(15) \\ w\leq14.09 \end{gathered}[/tex]What does that mean? As long as you position the ladder against the wall so that the height from the ground to the top of the ladder is <14.09 ft
what is 9×9 can you pls tell me
Answers
ANSWER
9X9 is a product of two integers numbers.
It's equal to 81.
Kapp and Stark go for a cross country run along a mountain trail. This graph models the elevation over time for their runwhich statement accurately describes Kapp and Starks run shown in the graph?
Answers
Hi! Let's analyze the sentences attached in the image:
a. They spent more minutes maintaining a constant elevation than decreasing.False. They just maintain a constant elevation at 11100feet (15min) and at 2800feet (15min), while they spent 90 minutes decreasing.
b. They spent more minutes maintaining a constant elevation than increasing.False. They just maintain a constant elevation at 11100feet (15min) and at 2800feet (15min), while they spent 60 minutes increasing.
c. They spent more time decreasing the elevation than increasing.True. They spent 90 minutes decreasing and 60 minutes increasing. So, 90>60.
d. They spent more time increasing the elevation than decreasing.False. They spent 60 minutes increasing and 90 minutes decreasing, so 60<90.
How do you perform the indicated operation?(4y + 11)(3y² -2y -7)
Answers
we use distributive property
[tex](4y\times3y^2)+(4y\times-2y)+(4y\times-7)+(11\times3y^2)+(11\times-2y)+(11\times-7)[/tex][tex]\begin{gathered} (12y^3)+(-8y^2)+(-28y)+(33y^2)+(-22y)+(-77) \\ 12y^3-8y^2+33y^2-28y-22y-77 \\ 12y^3+25y^2-50y-77 \end{gathered}[/tex]Find the point-slope equation of the line using the point (7, 4) and slope of2Use the slash key (/) to indicate a fraction.
Answers
The general equation of a line is given as:
y = mx + c where
m = slope
c = intercept on y axis.
We are given a point (x,y) so we use the relation below to develop the equation.
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=slope \\ \text{where:} \\ y_1=\text{ 4} \\ x_1=7 \end{gathered}[/tex][tex]\frac{y-4}{x-7}=2[/tex]Crossmultiplying, we have:
2x - 14 = y - 4
Adding 4 to both sides,
y = 2x - 14 + 4
y = 2x - 10
1. A company supplies pins to a customer. It uses an automatic lathe to produce the pins. Due to factors such as vibration, temperature and wear and tear, the lengths of the pins and normally distributed with a mean of 25.30 mm and a standard deviation of 0.45 mm. The customer will only buy pins with lengths in the interval 25.00 ± 0.50 mm.
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The percentage of the pins that will be acceptable to the customer is 63.16%.
What will the percentage be?Based on the information, the probabilty that the pin lies is between 24.5 and 25.5. This will be illustrated as P(24.5 <x < 25.5).
So convert this into Z score, will be:
P(24.5 <x < 25.5):
= P((24.5-25.3)/0.45 <Z < (25.5-25.3)/0.45)
Solving this, we will get
P(-16/9<Z < 4/9) = P(-1.77 <Z < 0.44),
By looking at the z table and solving for Z by using P (Z<0.44)-P(Z>-1.77) will be:
= 0.67 -(1-0.9616)
= 0.6316
= 63.16%
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Complete question
A company supplies pins to a customer. It uses an automatic lathe to produce the pins. Due to factors such as vibration, temperature and wear and tear, the lengths of the pins and normally distributed with a mean of 25.30 mm and a standard deviation of 0.45 mm. The customer will only buy pins with lengths in the interval 25.00 ± 0.50 mm. What percentage of the pins will be acceptable to the customer?
marh questions i need to solve and i have problems with it
Answers
7.
Given the side ratio as:
[tex]5:13[/tex]The area ratio is the second power of the above, which is:
[tex]\begin{gathered} 5^2:13^2 \\ =25:169 \end{gathered}[/tex]Given the area ratio of:
[tex]36:49[/tex]The perimeter ratio is:
[tex]\begin{gathered} \sqrt{36}:\sqrt{49} \\ \\ =6:7 \end{gathered}[/tex]Study Surface Area and Volume of Pyramid and Cone1. How to find lateral area and total surface area of pyramid?
Answers
Explanation:
Lateral area of pyramid
Lateral area of squared pyramid is the sum of areas of its side faces.
[tex]\begin{gathered} L=2al \\ \text{a is base length} \\ l\text{ is slant height and it is given as,} \\ l=\sqrt[]{\frac{a^2}{4}+h^2} \\ \text{Here, h is height of pyramid.} \end{gathered}[/tex]Total surface area of pyramid
It is sum of the areas of its lateral faces and its base.
[tex]\begin{gathered} \text{Total surface area=}\frac{1}{2}pl+B \\ p\text{ is perimeter of base} \\ l\text{ is slant height} \\ B\text{ is base area} \end{gathered}[/tex]how do I solve an angle in right triangles. what is angle B?AB=7BC=3
Answers
To find the value of the b angle.
First, label the sides of the right angle
The biggest side is always the hypotenuse
The side between the right angle and angle A is the adjacent side.
and the other side it's my opposite side.
Let's use the trigonometric function to find the value of b
I have the value of the hypotenuse
h = 7
and the value of my opposite side
opp = 3
So we need a trigonometric function that involves my hypotenuse and the opp
sin = opp/ hyp
Replace the values
sin b = 3/7
Solve the equation for b
b = arcsin (3/7)
b = 25.376
Rounded to hundredths
b = 25.37
Rewrite 9/11 and 6/7 so that they have a common denominator.Then use <, =, or > to order 9/11 and 6/7
Answers
Answer:
• 9/11=63/77
,• 6/7=66/77
,• 9/11<6/7
Explanation:
Given the fractions: 9/11 and 6/7
First determine the lowest common multiple of the denominators: 11 and 7
L.C.M of 11 and 7 = 77
Next, make this the common denominator as follows:
[tex]\begin{gathered} \frac{9}{11}=\frac{9}{11}\times\frac{7}{7}=\frac{63}{77} \\ \frac{6}{7}=\frac{6}{7}\times\frac{11}{11}=\frac{66}{77} \end{gathered}[/tex]Comparing the numerators, since 63<66:
[tex]\implies\frac{9}{11}<\frac{6}{7}[/tex]Find the area the sector.arc circle 7A. 1083π4 in²B. 1083π8 in²C. 57π4 in²D. 38π in²
Answers
Solution:
Given:
A circle with the sector details;
[tex]\begin{gathered} r=19\text{ }in \\ \theta=135^0 \end{gathered}[/tex]The area of a sector is given by;
[tex]\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\ A=\frac{135}{360}\times\pi\times19^2 \\ A=\frac{1083\pi}{8}\text{ }in^2 \end{gathered}[/tex]Therefore, the area of the sector is;
[tex]\frac{1083\pi}{8}\text{ }in^2[/tex]NEED HELP!! Graph each function.Find the asymptote. Tell how the graph is transformedfrom the graph of its parentfunction.2. f(x)=3log4 (x + 6)1.f(x)= log₂x +43.f(x)=log (x+5)5.f(x)=2.5log2 (x+7)-34. f(x) = 3 + ln x6. f(x)=-0.8 In (x-1.5) +2
Answers
1)
The given function is expressed as
f(x) = log2x + 4
where
2 is the base of the logarithm
The graph is shown below
If a function, f(x) is translated d units upwards, it becomes f(x) + d
For the given function, the parent function is f(x) = log2x where 2 is the base.
f(x) = log2x + 4 means that the parent function was translated or shifted by 4 units upwards
On the left, the graph gets close to x = 0 but it doesn't touch it. Thus,
Vertical asymptote is x = 0
On Monday, Freda spent $20 to buy 3 burgers and 4 orders of fries for her friends to share for lunch. Let r represent the cost of a burger and y represent the cost of an order of fries. What linear equation would model this?
Answers
Let:
r = Cost of a burger
y = Cost of an order of fries
Freda spent $20 to buy 3 burgers and 4 orders of fries for her friends to share for lunch, therefore:
[tex]3r+4y=20[/tex]