Answer:
[tex]c= \dfrac{9}{4}[/tex]
Step-by-step explanation:
For a function f(x) to satisfy the Mean Value Theorem, it must satisfy the following conditions:
Be defined and continuous on the interval [a,b]Be differentiable on (a,b)There is at least one number c in the interval (a,b) (that is a < c < b) such that [tex]f'(c)=\dfrac{f(b)-f(a)}{b-a}[/tex]Given [tex]f(x)=\sqrt{x}$ in [0,9][/tex]
1. f(x) is defined and continuous on [0,9] since a polynomial function is continuous everywhere.
2. f(x) is differentiable in the interval (0,9) since a polynomial function is differentiable everywhere.
[tex]f(9)=\sqrt{9}=3\\f(0)=\sqrt{0}=0\\f'(x)=\dfrac{1}{2\sqrt{x} }[/tex]
3.By the mean value theorem:
[tex]f'(c) = \displaystyle\frac{f(b)-f(a)}{b-a}\\\\\frac{1}{2\sqrt{c}} = \frac{f(9) - f(0)}{9-0} = \frac{3}{9}\\\\\frac{1}{2\sqrt{c}} = \frac{1}{3}\\\\$Cross multiply$\\\\2\sqrt{c}=3\\\\$Square both sides$\\\\(2\sqrt{c})^2=3^2\\\\4c=9\\\\c= \dfrac{9}{4}[/tex]
Mrs. Nestler enjoys listening to classical music. She has the following audio CDs by her favorite composers in her collection: 4 by Bach, 6 by Beethoven, 3 by Brahms, and 2 by Handel. If she selects 4 CDs randomly from her collection without replacing them, what is the probability that she will choose one by each composer.
Answer:
10.55% probability
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the CDs are chosen is not important. So we use the combinations formula to solve this question.
1 Bach CD, from a set of 4.
1 Beethoven CD, from a set of 6.
1 Brahms CD, from a set of 3.
1 Handel CD, from a set of 2.
So, D=144
4 CDs from a set of 4+6+3+2 = 15.
So, T= 1365
p= D/T= 144/1365 = 0.1055
10.55% probability that she will choose one by each composer
Xavier and Yifei have been married for exactly 37 years.Yifei is four years older than Xavier. Now the sum of their ages is 124. How old was Yifei when theywere married?a) Set up and write an equation that represents
Answer:
Xavier's age = 23
Yifei's age = 27
Step-by-step explanation:
Represent Yifei's age with Y and Xavier's age with X;
Given that the sum of their ages is 124;
X + Y = 124
Also, given that Yifei is 4 years older
Y = X + 4
Required
Find their age when they got married
From the parameters above, we've been able to form a simultaneous equation
[tex]X + Y = 124[/tex]
[tex]Y = X + 4[/tex]
Substitute X + 4 for Y in the first equation
[tex]X + X + 4 = 124[/tex]
[tex]2X + 4=124[/tex]
Subtract 4 from both sides
[tex]2X + 4 - 4 = 124 - 4[/tex]
[tex]2X = 120[/tex]
Divide both sides by 2
[tex]\frac{2X}{2} = \frac{120}{2}[/tex]
[tex]X = 60[/tex]
Substitute 60 for X in the second equation
[tex]Y = X + 4[/tex] becomes
[tex]Y = 60 +4[/tex]
[tex]Y = 64[/tex]
To get their ages when they got married; we simply subtract 37 from their current ages
Xavier's age = 60 - 37
Xavier's age = 23
Yifei's age = 64 - 37
Yifei's age = 27
Circle P has a circumference of approximately 75 inches. Circle P with radius r is shown. What is the approximate length of the radius, r? Use 3.14 for . Round to the nearest inch.
Answer:
12 inches, I hope this is right! :)
Step-by-step explanation:
circumference = 75 inches
75 / 2 = 35.7
37.5 / π = 11.9366207
Rounded to the nearest inch:
12 inches
Answer:
12 inches
Step-by-step explanation:
The circumference of a circle can be found using the following formula.
c= 2πr
We know that the circumference is 75 inches and we are using 3.14 for pi. Therefore, we can substitute 75 in for c and 3.14 for pi.
75= (2*3.14) r
Multiply 2 and 3.14
75= 6.28* r
We want to find r, or the radius. Therefore, we must get r by itself.
r is being multiplied by 6.28. The inverse of multiplication is division. Divide both sides by 6.28.
75/6.28= 6.28*r/6.28
75/6.28=r
11.9426752=r
Round to the nearest inch. The 9 in the tenth place tells us to round 11 up to a 12.
12= r
r= 12 inches
The approximate length of the radius is 12 inches.
The pront for a company this year was $100,000. Each year the profit increases at a rate
of 1.2% per year. Which function shows the company's profit as a function of time in
years?
Answer:
f(t) = 100,000 ⋅ 0.012 t
Step-by-step explanation:
Store pays $56 for a GPS navigation system the markup is 25% what price will the store sell it for
[tex]\text{We need to find how much the store will sell a GPS navigation system}\\\\\text{We know that the store paid \$56 for it}\\\\\text{We also know that they will mark up the price by 25\%}\\\\\text{We can find 25\% of 56}\\\\56\cdot0.25=14\\\\\text{We can now add that to the original price to get the price the store}\\\text{will sell it for}\\\\56+14=70\\\\\boxed{\$70}[/tex]
expand the linear expression 4(10x -4)
Answer:
40x - 16
Step-by-step explanation:
(see attached for reference)
By utilizing the distributive property:
4(10x -4)
= (10x)(4) -4 (4)
= 40x - 16
Answer:
4x10x= 40x -4x4=-16 40xtimes-4<-----------thats your answer
Step-by-step explanation:
<1 and <3 are complementary and <1= <2 Which one of these statements will always be true?
A. M<2 = m<3
B. <2 and <3 are complementary
C. M<1= m<3
D. <2 and <3 are supplementary
Answer:
B. ∠2 and ∠3 are complementary
Step-by-step explanation:
The substitution property of equality lets you put ∠2 in place of ∠1 in the statement ...
∠1 and ∠3 are complementary.
∠2 and ∠3 are complementary . . . . using ∠2 for equal ∠1 in the above
Answer: ∠2 and ∠3 are complementary
Step-by-step explanation:
Please tell me the answer to c ignore the question b thank you
Answer:
c).[tex] {1000}^{m} \div {100}^{n} \\ \\ {10}^{3m} \div {10}^{2n} [/tex]
Since they have the same base and are dividing we subtract the exponents
That's
[tex] {10}^{3m - 2n} [/tex]
So
z = 3m - 2nHope this helps you
Answer:
[tex]\boxed{ z = 3m-2n}[/tex]
Step-by-step explanation:
=> [tex]1000^m / 100^n[/tex]
=> [tex](10)^{3m} / (10)^{2n}[/tex]
Using rule of exponents [tex]a^m/a^n = a^{m-n}[/tex]
=> [tex]10 ^{3m-2n}[/tex]
Comparing it with [tex]10^z[/tex], we get
=> z = 3m-2n
A student is filling out a college application that requires she supply either her math SAT score or her math ACT score. She scored 610 on the math SAT and 27 on the math ACT. Which should she report given that the mean SAT math score was 515 with a standard deviation of 114, and the mean ACT math score was 21.0 with a standard deviation of 5.1
Answer:
Due to the higher z-score, she should report her ACT grade.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Which should she report
The grade with the higher z-score.
SAT:
Scored 610, mean 515, standard deviation 114. So [tex]X = 610, \mu = 515, \sigma = 114[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{610 - 515}{114}[/tex]
[tex]Z = 0.83[/tex]
ACT:
Scored 27, mean 21, standard deviation 5.1. So [tex]X = 27, \mu = 21, \sigma = 5.1[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{27 - 21}{5.1}[/tex]
[tex]Z = 1.18[/tex]
Due to the higher z-score, she should report her ACT grade.
Answer:
ACT
Step-by-step explanation:
Please please please please help me. i will do anything, anything!! please
Answer:
[tex]d \approx 2.2[/tex]
Step-by-step explanation:
It is the same process as in previous problems.
Once the origin is the point (0, 0):
[tex]d=\sqrt{(x_{1}-x_{2})^2 + (y_{1}-y_{2})^2}[/tex]
[tex]d=\sqrt{(2-0)^2 + (-1-0)^2}[/tex]
[tex]d=\sqrt{2^2 + (-1)^2}[/tex]
[tex]d=\sqrt{5}[/tex]
[tex]d \approx 2.2[/tex]
Answer:
2.2
Step-by-step explanation:
The distance formula
[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex] with
[tex]x_1=0\\y_1=0\\x_2=2\\y_2=-1[/tex]
[tex]\sqrt{(0-2)^2+(0-(-1))^2}=\sqrt{2^2+1^2}=\sqrt{5}[/tex]
[tex]\sqrt{5} =2.2360...=2.2[/tex]
The lengths of adult males' hands are normally distributed with mean 190 mm and standard deviation is 7.4 mm. Suppose that 45 individuals are randomly chosen. Round all answers to 4 where possible.
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For the group of 45, find the probability that the average hand length is less than 189.
Find the third quartile for the average adult male hand length for this sample size.
For part b), is the assumption that the distribution is normal necessary?
Answer:
a. The distribution of the sample means is normal with mean 190 mm and standard deviation 1.1031 mm.
b. The probability that the average hand length is less than 189 is P(M<189)=0.1823.
c. The third quartile for the average adult male hand length for this sample size is M_75=190.7440.
d. The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
Step-by-step explanation:
We have a normal distribution, with mean 190 and standard deviation 7.4.
We take samples of size n=45 from this population.
Then, the sample means will have a distribution with the following parameters:
[tex]\mu_s=\mu=190\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{7.4}{\sqrt{45}}=\dfrac{7.4}{6.7082}=1.1031[/tex]
The probability that the sample mean is less than 189 can be calculated as:
[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{189-190}{7.4/\sqrt{45}}=\dfrac{-1}{1.1031}=-0.9065\\\\\\P(M<189)=P(z<-0.9065)=0.1823[/tex]
The third quartile represents the value of the sample where 75% of the data is to the left of this value. It means that:
[tex]P(M<M^*)=0.75[/tex]
The third quartile corresponds to a z-value of z*=0.6745.
[tex]P(z<z^*)=0.75[/tex]
Then, we can calculate the sample mean for the third quartile as:
[tex]M=\mu_s+z^*\sigma_s=190+0.6745\cdot 1.1031=190+0.7440=190.7440[/tex]
The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Which correctly compares the ranges of the data?
The range in shelter A is 11, and the range in shelter B is 4.
The range in shelter A is 20, and the range in shelter B is 10.
The range in shelter A is 13, and the range in shelter B is 8.
The range in shelter A is 22, and the range in shelter B is 18.
Answer:
The range in shelter A is 22, and the range in shelter B is 18.
Step-by-step explanation:
Okay so basically, the range is the difference between the smallest number and the greatest number.
The smallest weight for shelter a is 8. The largest weight is 30.
30-8= 22.
Same thing for the other shelter. The smallest weight is 10, and the largest weight is 28. 28-10= 18.
Answer:
D; The range in shelter A is 22, and the range in shelter B is 18.
Step-by-step explanation:
edg2020
Shelter A: 30-8= 22
Shleter B: 28-10= 18
The range is max minus min. Therefore D is correct. Pretty simply stuff yall
A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Five marbles are drawn
from the bag.
What is the approximate probability that exactly two of the five are blue?
196
496
36%
O 40%
Answer:
34.56%
Approximately 35%
Step-by-step explanation:
Total number of marbles present= 10 red+ 15 yellow+5 green+20 blue
Total= 50 marbles
Probability of picking a blue ball = 20/50
Probability of a blue = 0.4= p
Probability of no blue = 1-0.4 = 0.6= q
If five balls are selected, probability of
exactly 2 to be blue is
Probability= 5C2(0.4)²(0.6)³
probability= 5!/(2!3!)(0.4)²(0.6)³
probability= 10*0.16*0.216
Probability= 0.3456
Then to percentage
0.3456 to percentage= 0.3456*100
0.3456 to percentage= 34.56%
Approximately 35%
Answer:
C: 36%
Step-by-step explanation:
Correct on Edge
Solve this rational equation:
Х
1
x – 4
+
=
2
x2 - 6x + 8
x – 2
Hey there! :)
Answer:
x = -1.
Step-by-step explanation:
[tex]\frac{1}{x-4}+ \frac{x}{x-2}= \frac{2}{x^{2}-6x+8 }[/tex]
Make each fraction have a common denominator:
[tex]\frac{1(x-2)}{x^{2}-6x+8}+ \frac{x(x-4)}{x^{2}-6x+8}= \frac{2}{x^{2}-6x+8 }[/tex]
Simplify:
[tex]\frac{x-2}{x^{2}-6x+8}+ \frac{x^{2}-4x }{x^{2}-6x+8}= \frac{2}{x^{2}-6x+8 }[/tex]
Disregard the denominator and solve the numerators:
x - 2 + x² - 4x = 2
Combine like terms:
x² - 3x - 2 = 2
x² - 3x - 4 = 0
Factor:
(x - 4)(x + 1)
***Only one of these solutions works because if x = 4, the denominator of the first fraction would be 0, which is undefined. Therefore, the only possible solution is x = -1.
Evaluate: 26.45 + 4.79 + 120.02 - 3.20 =
Answer:
Hello There!
`~~~~~~~~~~~~~~~~~~`
26.45 + 4.79 + 120.02 - 3.20 =
148.06
Step-by-step explanation: Simplify the expression.
Hope this helped you. Brainliet would be nice!
Answer:
Step-by-step explanation:
BODMAS
Align the decimals properly
26.45 + 4.79 + 120.02 = 150.26
26.45
+ 4.79
120.02
______
151.26
______
151.26 - 3.20 = 148.06
At the Arctic weather station, a warning light turns on if the outside temperature is below -25 degrees Fahrenheit. Which inequality models this situation?
Answer:
T < -25
Step-by-step explanation:
Was correct on TTM
Given a triangle with: a =
150, A = 75°, and C = 30°
Using the law of sines gives: c = 0
Answer:
[tex] c = 77.6 [/tex]
Step-by-step explanation:
You may have entered the measure of a side as the measure of an angle.
[tex] \dfrac{\sin A}{a} = \dfrac{\sin C}{c} [/tex]
[tex] \dfrac{\sin 75^\circ}{150} = \dfrac{\sin 30^\circ}{c} [/tex]
[tex] c\sin 75^\circ = 150 \sin 30^\circ [/tex]
[tex] c = \dfrac{150 \sin 30^\circ}{\sin 75^\circ} [/tex]
[tex] c = 77.6 [/tex]
You are correct. Good job!
Select the two values of x that are roots of this equation.
x2 + 2x- 6 = 0
A. X= -1 - 7
B. x= -1+ 7
C. x = -1 - 2-17
2
D. x = -1 + 2-17
Answer:
x = 2, -3
Step-by-step explanation:
[tex]x^2 + 2x- 6 = 0\\=>x^2 +3x - 2x- 6 = 0\\=>x(x+3) - 2(x +3) = 0\\=> (x-2)(x+3) = 0\\\\[/tex]
(x-2) = 0 or (x+3) = 0
x = 2 or x = -3
Thus, two values of x are x = 2, -3
Note: The options given are incorrect.
Answer:
a and b.
Step-by-step explanation:
i’m assuming that the 7 is square root of seven.
ap3x verified
Jarrods filing status on last years tax return was single, while paige’s was head of household. If both had taxable incomes of 80,456, how did the amounts of taxes they paid compare according to the table below
Answer:
C. Jarrod paid $1335 more than Paige in taxes
Step-by-step explanation:
just took the test
Please help ill mark you the brainlist The scale on a map indicates that 1 cm represents 50 km. If two cities are 400 km apart, then how far apart would the cities be on this map?
Answer:
8 cm
Step-by-step explanation:
divide 400 by 50 which is 8.
Need help with assignment
Answer:
1. r = 5 cm; area = 78.5 sq. cm.
2. diameter, d = 17'; area = 226.98 sq. ft.
3. diameter, d = 11"; area = 95.0 sq. in
4. radius, r = 2.4 m; area = 18.1 sq. m
5. radius, r = 30'; area = 2827.4 sq. m
Step-by-step explanation:
Area = pi * r^2
pi = 3.1416
1. radius, r = 5 cm
area = pi*5^2 = 78.5 sq. cm.
2. diameter, d = 17'
radius, r = d/2 = 8.5'
area = pi * 8.5^2 = 226.98 sq. ft.
3. diameter, d = 11"
radius, r = 11/2 = 5.5"
area = pi * 5.5^2 = 95.0 sq. in
4. radius, r = 2.4 m
area = pi * 2.4^2
= 18.1 sq. m
5. radius, r = 30'
area = pi 30^2
= 2827.4 sq. m
A survey was taken of students in math classes to find
out how many hours per day students spend on social
media. The survey results for the first-, second-, and
third-period classes are as follows:
First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9, 2, 4, 3,0
Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1, 3
Which is the best measure of center for second period
and why?
Bryan works at the ballpark selling bottled water. She sells 19 bottles in One shift. The large bottles sell for $8 each and the small bottles sell for $3 each. At the end of One game, she has taken in $102. How many large and small bottles did Bryan sell?
Answer:
9 large and 10 small
Step-by-step explanation: The combination to get 19 and start from the middle which is 10 and 9 and interchange them until you get 102 which should be 8x + 3y x is the number of large bottles and y the number of small bottles. Another way to do it is 8x + 3y = 102 and plugin into the calculator both sides on different equations and get the interception
Answer:
9 large bottles
10 small bottles
Step-by-step explanation:
You have to create a system of equations.
Bryan sells a total number of 19 bottles.
x + y = 19
The large bottles sell for $8, and the small bottles sell for $3. She made $102.
8x + 3y = 102
You can solve this system of equations using substitution. Rearrange the first equation so that it is equal to y. Then, plug the y into the second equation.
x + y = 19
y = 19 - x
8x + 3(19 - x) = 102
8x + 57 - 3x = 102
5x = 45
x = 9
Now that you have found the x-value, solve for y.
x + y = 19
9 + y = 19
y = 10
There were 8 large bottles sold and 10 small bottles sold.
A circle is represented by the equation x2+y2=445. a) State the radius. b) Find y if point A(-9,y) is on this circle.
Answer:
R= sqrt 445
Y = 19
Step-by-step explanation:
Radius is the square root of 445
Find y
So, First step is to substitute what you have
-9^2 + y^2 = 445
81 + y^2 = 445
-81 -81
y^2 =364
Y is about 19
Let me know if I'm incorrect
Hope this helps :)
Mike tabulated the following values for heights in inches of seven of his friends: 65, 71, 74, 61, 66, 70, and 72. Mike wishes to construct a 95% confidence interval. What value of t* should Mike use to construct the confidence interval? Answer choices are rounded to the hundredths place.
Answer:
a) 95% confidence intervals are
(64.188, 72.652)
b) Mike use
(t₀.₀₂₅ , ₆)= 2.4469
Step-by-step explanation:
Step(i):-
Given data
x : 65 71 74 61 66 70 72
Mean of 'x'
x⁻ = ∑ x / n
[tex]x^{-} = \frac{65+71+74+61+66+70+72}{7} = 68.42[/tex]
x : 65 71 74 61 66 70 72
x - x⁻ : -3.42 2.58 5.58 -7.42 -2.42 1.58 3.58
(x-x⁻)² : 11.69 6.65 31.13 55.05 5.85 2.49 12.81
∑((x-x⁻)²) = 125.67
Variance
S² = ∑((x-x⁻)²) / n-1 = [tex]\frac{125.67}{6} = 20.945[/tex]
Standard deviation S = √20.945 =4.576
Step(ii):-
95% confidence intervals are determined by
[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } , x^{-} +t_{\alpha } \frac{S}{\sqrt{n} })[/tex]
Degrees of freedom
ν =n-1 = 7-1 =6
[tex]t_{\frac{\alpha }{2} , n-1 } = t_{(\frac{0.05}{2} , 6)}[/tex] = (t₀.₀₂₅ , ₆)= 2.4469
[tex](68.42 - 2.4469 \frac{4.576}{\sqrt{7} } , 68.42 +2.4469\frac{4.576}{\sqrt{7} })[/tex]
( 68.42 - 4.232, 68.42 + 4.232)
(64.188, 72.652)
Conclusion:-
95% confidence intervals are
(64.188, 72.652)
Answer:
64.19 to 72.67
Step-by-step explanation:
A baseball player has a batting average of 0.25. What is the probability that he has exactly 2 hits in his next 7 at bats
Answer:
The probability that he has exactly 2 hits in his next 7 at-bats is 0.3115.
Step-by-step explanation:
We are given that a baseball player has a batting average of 0.25 and we have to find the probability that he has exactly 2 hits in his next 7 at-bats.
Let X = Number of hits made by a baseball player
The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]
where, n = number of trials (samples) taken = 7 at-bats
r = number of success = exactly 2 hits
p = probability of success which in our question is batting average
of a baseball player, i.e; p = 0.25
SO, X ~ Binom(n = 7, p = 0.25)
Now, the probability that he has exactly 2 hits in his next 7 at-bats is given by = P(X = 2)
P(X = 2) = [tex]\binom{7}{2}\times 0.25^{2} \times (1-0.25)^{7-2}[/tex]
= [tex]21 \times 0.25^{2} \times 0.75^{5}[/tex]
= 0.3115
What is the perimeter of the equilateral triangle if one side is 6 feet?
Answer:
18 feet
Step-by-step explanation:
Equilateral triangles have 3 equal sides.
If one side is 6 feet, the other two are also 6 feet.
Perimeter is all the sides added.
6 + 6 + 6
= 18
How many multiples of 4, that are smaller than 1,000, do not contain any of the digits 6, 7, 8, 9 or 0?
Answer:
44
Step-by-step explanation:
11×4
hope it helped!
An airline allows passenger 33 kg of luggage cost to lower the weight of a suitcase by 25% to stay within the limit how much does suitcase originally way
Answer:
The suitcase originally weighed 44kg.
Step-by-step explanation:
1- 0.25= 0.75 (multiplier)
33÷0.75=44
The suitcase originally weighed 44kg
Square ABCD is shown below with line EF and passing through the center:
Answer: B) contain the points E and F
Step-by-step explanation:
Dilation of 2 means to multiply both the x- and y-coordinates by 2
see image below
The only option that is true that E'F' contains points E and F
Answer:
contains the points E and F
Step-by-step explanation:
The center of dilation is an invariant point. It doesn't move, regardless of the dilation factor.
Likewise, any line through the center of dilation will not move. It is not rotated or translated by dilation--it simply is stretched (or compressed) along its length. It is still an infinite line, and it still goes through all of the points it went through before dilation.
The line through the center of dilation that contains points E and F, after dilation, ...
contains the points E and F.