Answer:
a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.
Step-by-step explanation:
He appies the empirical 68-95-99.7 rule, where 68% of the data is expected to be within ne standard deviation from the mean, to the right and to the left.
Half of this (68%/2=34%) will be between the mean and one deviation standard to the right. This is between 10 hours and 10+2=12 hours.
The right answer is:
a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.
The function f(x) is given by the set of ordered pairs.
{(8,3), (0, 4), (1, 5), (2, -1), (-6, 10)}
Which is true regarding the function?
f(-3) = 8
f(3) = 5
f(8) = 0
f(-6) = 10
Answer: f(-6) = 10.
Step-by-step explanation: This above equation is the only one that contains both coordinates of one of the ordered pairs in the correct order, so it is the answer.
how to solve this? please help me
Answer:
tangent: y = 2x -2normal: y = -1/2x +3Step-by-step explanation:
Differentiating implicitly, you have ...
-y²·dx +(4-x)(2y)dy = 3x²·dx
So, the slope is ...
dy/dx = (3x² +y²)/(2y(4 -x))
At (x, y) = (2, 2), the slope of the curve is ...
dy/dx = (3·2² +2²)/(2·2(4 -2)) = 16/8 = 2
In point-slope form, the equation of the tangent line is then ...
y = m(x -h) +k
y = 2(x -2) +2
y = 2x -2 . . . . equation of tangent line
__
The normal to the curve is perpendicular to the tangent at the same point. The slope of the perpendicular line is the negative reciprocal of the tangent's slope, so is -1/2.
y = (-1/2)(x -2) +2
y = -1/2x +3 . . . equation of normal line
Suppose you want to have $0.5 million saved by the time you reach the age of 30 years and suppose that you are 20 years old now. If you can earn 5% on your funds, how much would you have to invest today to reach your goal?
Answer:
$306,956,6268
Step-by-step explanation:
Future value, FV = Present value PV [1 + rate]^t
PV = FV/[1 + rate]^t
PV = 500,000/[1.05]^10
PV = $306,956,6268
If a coin is tossed 4 times, and then a standard six-sided die is rolled 3 times, and finally a group of two cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?
Answer: 4,582,656
Step-by-step explanation:
A coin is tossed 4 times,
2^4 outcomes: 16
and then a standard six-sided die is rolled 3 times, 6^3
216 outcomes:
and finally, a group of two cards is drawn from a standard deck of 52 cards without replacements
It says a “group”, so, I guess the order doesn’t matter… So it is “52 choose 2”
52*51/ (2*1) = 26*51
how many different outcomes are possible?
16*216*26*51 = 4,582,656
The cost of unleaded gasoline in the Bay Area once followed a normal distribution with a mean of $4.74 and a standard deviation of $0.16. Sixteen gas stations from the Bay area are randomly chosen. We are interested in the average cost of gasoline for the 15 gas stations. What is the approximate probability that the average price for 15 gas stations is over $4.99?
Answer:
Approximately 0% probability that the average price for 15 gas stations is over $4.99.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 4.74, \sigma = 0.16, n = 16, s = \frac{0.16}{\sqrt{16}} = 0.04[/tex]
What is the approximate probability that the average price for 15 gas stations is over $4.99?
This is 1 subtracted by the pvalue of Z when X = 4.99. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4.99 - 4.74}{0.04}[/tex]
[tex]Z = 6.25[/tex]
[tex]Z = 6.25[/tex] has a pvalue very close to 1.
1 - 1 = 0
Approximately 0% probability that the average price for 15 gas stations is over $4.99.
Please answer this correctly
Answer:
50%
OR
1/2
Step-by-step explanation:
The box and whisker plot shows the time spent from 4 to 6 hours is Quartile 1 to 3 which makes it 50%.
A list of numbers begins iwth the number 6. Each number on the list is 10 more than -2 times the previous terms. what is the fourth number
Answer:
The fourth term is -18
Step-by-step explanation:
an = -2(an-1) +10
This is the recursive formula
a1 = 6
a2 = -2(a1) +10 = -2(6) +10 = -12+10 = -2
a3 = -2(a2) +10 = -2(-2) +10 = 4+10 = 14
a4 = -2(a3) +10 = -2(14) +10 = -28+10 = -18
problem decoded dude
follow meh
Carlos is almost old enough to go to school! Based on where he lives, there are 666 elementary schools, 333 middle schools, and 222 high schools that he has the option of attending.
Answer:
There are 36 education paths available to Carlos based on the schools around where he lives.
Step-by-step explanation:
Complete Question
Carlos is almost old enough to go to school. Based on where he lives, there are 6 elementary schools, 3 middle schools, and 2 high schools that he has the option of attending. How many different education paths are available to Carlos? Assume he will attend only one of each type of school.
Solution
We can use mathematics or manually writing out the possible combinations of elementary, middle and high school that Carlos can attend.
Using Mathematics
There are 6 elementary schools, meaning Carlos can make his choice in 6 ways.
There are 3 middle schools, meaning Carlos can make his choice in 3 ways.
Together with the elementary school choice, Carlos can make these two choices in 6 × 3 ways.
There are 2 high schools, Carlos can make his choice in 2 ways.
Combined with the elementary and middle school choices, Carlos can make his choices in 6×3×2 ways = 36 ways.
Manually
If we name the 6 elementary schools letters A, B, C, D, E and F.
Name the 3 middle schools letters a, b and c.
Name the 2 high schools numbers 1 and 2.
The different combinations of the 3 choices include
Aa1, Aa2, Ab1, Ab2, Ac1, Ac2
Ba1, Ba2, Bb1, Bb2, Bc1, Bc2
Ca1, Ca2, Cb1, Cb2, Cc1, Cc2
Da1, Da2, Db1, Db2, Dc1, Dc2
Ea1, Ea2, Eb1, Eb2, Ec1, Ec2
Fa1, Fa2, Fb1, Fb2, Fc1, Fc2
Evident now that there are 36 ways in which the 3 stages of schools can be combined. There are 36 education paths available to Carlos based on the schools around where he lives assuming that he will attend only one of each type of school.
Hope this Helps!!!
Answer:
36 education paths
Step-by-step explanation:
Hope this helps!
I need help pleaseee!
Step-by-step explanation:
we can use o as the center of the circle
OB=13
EB=12
OE=?
OE^2 +EB^2=OB^2
OE^2+12^2=13^2
OE^2=169-144
OE=
√25
OE=5
OC=OE+EC
EC =13-5
EC=8
Solve: x + 7 < 3 plsss help me
Answer:
The answer is -4.
Step-by-step explanation:
You should get this answer if you do 3 - 7.
3 squared times 3 squared simplified
Answer:
3^4
Step-by-step explanation:
3^2*3^2
3*3*3*3
3^4
The radius of a circle is 4 miles. What is the length of a 45° arc?
45°
r=4 mi
Give the exact answer in simplest form.
Answer:
2π miles
Step-by-step explanation:
2πr is the formula for the circumference of a circle.
Using that formula, the circumference for this circle is 8π.
Since the circle's full angle is 360°, we can use a ratio to find out how long the 45° arc is.
° : length
360 : 8π
9 : 0.4π
45 : 2π
The 45° is 2π mi long.
Show all work to identify the asymptotes and zero of the faction f(x) = 4x/x^2 - 16.
Answer:
asymptotes: x = -4, x = 4zeros: x = 0Step-by-step explanation:
The vertical asymptotes of the rational expression are the places where the denominator is zero:
x^2 -16 = 0
(x -4)(x +4) = 0 . . . . . true for x=4, x=-4
x = 4, x = -4 are the equations of the vertical asymptotes
__
The zeros of a rational expression are the places where the numerator is zero:
4x = 0
x = 0 . . . . . . divide by 4
Find the equation for the line containing the points (-2,-5) and (6,3)
Answer:
y = x - 3
Step-by-step explanation:
Do rise/run to find the slope
8/8 = 1
y = x + b
Plug in a point to find the y-intercept
-5 = -2 + b
-3 = b
The equation will be y = x - 3
What is the measure of AC?
Enter your answer in the box.
Answer:
21
Step-by-step explanation:
Since angle ABC is an inscribed angle, its measure is half that of arc AC. Therefore:
[tex]2(3x-1.5)=3x+9 \\\\6x-3=3x+9 \\\\3x-3=9 \\\\3x=12 \\\\x=4 \\\\AC=3(4)+9=12+9=21[/tex]
Hope this helps!
Use the Inscribed Angle theorem to get the measure of AC. The intercepted arc AC is, 21°.
What is the Inscribed Angle theorem?We know that, Inscribed Angle Theorem stated that the measure of an inscribed angle is half the measure of the intercepted arc.
Given that,
The inscribed angle is, (3x - 1.5)
And the Intercepted arc AC is, (3x + 9)
So, We get;
(3x - 1.5) = 1/2 (3x + 9)
2 (3x - 1.5) = (3x + 9)
6x - 3 = 3x + 9
3x = 9 + 3
3x = 12
x = 4
Thus, The Intercepted arc AC is,
(3x + 9) = 3×4 + 9
= 21°
Learn more about the Inscribed Angle theorem visit:
brainly.com/question/5436956
#SPJ2
Solve for x. 9x-2c=k
What is the area of this triangle?
Answer:
Option (D)
Step-by-step explanation:
Formula for the area of a triangle is,
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
For the given triangle ABC,
Area of ΔABC = [tex]\frac{1}{2}(\text{AB})(\text{CD})[/tex]
Length of AB = [tex](y_2-y_1)[/tex]
Length of CD = [tex](x_3-x_1)[/tex]
Now area of the triangle ABC = [tex]\frac{1}{2}(y_2-y_1)(x_3-x_1)[/tex]
Therefore, Option (D) will be the answer.
what is the recursiveformula for this geometric sequence? 4,-12,36,108
Answer:
a[1] = 4
a[n] = -3·a[n-1]
Step-by-step explanation:
The sequence given is not a geometric sequence, since the ratios of terms are -3, -3, 3 -- not a constant.
If we assume that the last given term is supposed to be -108, then the common ratio is -3 and each term is -3 times the previous one. That is expressed in a recursive formula as ...
a[1] = 4 . . . . . . . . . . . first term is 4
a[n] = -3·a[n-1] . . . . . each successive term is -3 times the previous one
The maximum height of a vehicle that can safely pass under a bridge is 12 feet 5 inches. A truck measures 162 inches in height. Which best explains whether or not the truck can pass safely under the bridge?
162 inches is 13.5 feet or 13 feet 6 inches, so it would not fit underneath the bridge
Answer:
The truck cannot pass safely under the bridge. The truck is 13 inches taller than the maximum height.
Need help ASAP Thankyou!!!
Answer:
216
Step-by-step explanation:
To find the volume of the pyramid we have to do length * width * height / 3
The length is 9yd
The width is 8yd
The height is 9yd
So 9 * 9 * 8 = 648
648 / 3 = 216
The Environmental Protection Agency must visit nine factories for complaints of air pollution. In how many ways can a representative visit five of these to investigate this week? Since the representative's travel to visit the factories includes air travel, rental cars, etc., then the order of the visits will make a difference to the travel costs.
Answer:
The number of ways is [tex]\left 9}\atop } \right. P _5 = 15120[/tex]
Step-by-step explanation:
From the question we are told that
The number of factories visited is [tex]n = 9[/tex]
The number of factories to be visited by a representative r = 5
The number of way to visit the 5 factories is mathematically represented as
[tex]\left 9}\atop } \right. P _5 = \frac{9!}{(9-5)!}[/tex]
Where P represents permutation
=> [tex]\left 9}\atop } \right. P _5 = \frac{9 \ !}{4\ !}[/tex]
=> [tex]\left 9}\atop } \right. P _5 = \frac{9 *8*7 * 6 * 5 * 4!}{4\ !}[/tex]
=> [tex]\left 9}\atop } \right. P _5 = 15120[/tex]
Let f(x)= x^3 −6x^2+11x−5 and g(x)=4x^3−8x^2−x+12. Find (f−g)(x). Then evaluate the difference when x=−3 x=−3 .
Answer: (f-g)(x)= -138
Step-by-step explanation:
The life of an electric component has an exponential distribution with a mean of 8.9 years. What is the probability that a randomly selected one such component has a life more than 8 years? Answer: (Round to 4 decimal places.)
Answer:
[tex] P(X>8)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] F(x) = 1- e^{-\lambda x}[/tex]
And if we use this formula we got:
[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]
Step-by-step explanation:
For this case we can define the random variable of interest as: "The life of an electric component " and we know the distribution for X given by:
[tex]X \sim exp (\lambda =\frac{1}{8.9}) [/tex]
And we want to find the following probability:
[tex] P(X>8)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] F(x) = 1- e^{-\lambda x}[/tex]
And if we use this formula we got:
[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]
Ken runs 12 miles in a marathon. Every 3.5 miles, he stopes to take a drink. How many times does he stop during the marathon ?
Answer:
Brainleist!
Step-by-step explanation:
12/3.5
3.42857142857
round down so its 3!
The equation f(x) is given as x2_4=0. Considering the initial approximation at
x0=6 then the value of x1 is given as
Select one:
O A. 10/3
O B. 7/3
O C. 13/3
O D. 4/3
Answer:
The value of [tex]x_{1}[/tex] is given by [tex]\frac{10}{3}[/tex]. Hence, the answer is A.
Step-by-step explanation:
This exercise represents a case where the Newton-Raphson method is used, whose formula is used for differentiable function of the form [tex]f(x) = 0[/tex]. The expression is now described:
[tex]x_{n+1} = x_{n} - \frac{f(x_{n})}{f'(x_{n})}}[/tex]
Where:
[tex]x_{n}[/tex] - Current approximation.
[tex]x_{n+1}[/tex] - New approximation.
[tex]f(x_{n})[/tex] - Function evaluated in current approximation.
[tex]f'(x_{n})[/tex] - First derivative of the function evaluated in current approximation.
If [tex]f(x) = x^{2} - 4[/tex], then [tex]f'(x) = 2\cdot x[/tex]. Now, given that [tex]x_{0} = 6[/tex], the function and first derivative evaluated in [tex]x_{o}[/tex] are:
[tex]f(x_{o}) = 6^{2} - 4[/tex]
[tex]f(x_{o}) = 32[/tex]
[tex]f'(x_{o})= 2 \cdot 6[/tex]
[tex]f'(x_{o}) = 12[/tex]
[tex]x_{1} = x_{o} - \frac{f(x_{o})}{f'(x_{o})}[/tex]
[tex]x_{1} = 6 - \frac{32}{12}[/tex]
[tex]x_{1} = 6 - \frac{8}{3}[/tex]
[tex]x_{1} = \frac{18-8}{3}[/tex]
[tex]x_{1} = \frac{10}{3}[/tex]
The value of [tex]x_{1}[/tex] is given by [tex]\frac{10}{3}[/tex]. Hence, the answer is A.
Farhan has three pieces of rope with lengths of 140cm, 168cm and 210cm. He wishes to cut all the three pieces of ropes into smaller pieces of equal length and that there is no leftover rope. (i) What is the greatest possible length of each of the smaller pieces of rope? How many smaller pieces of rope can he get altogether?
give correct answer
Answer:
The greatest possible length is 14 cm.
The total number of smaller pieces is 37.
Step-by-step explanation:
The greatest common factor of these three numbers is 14.
Total number of smaller pieces = 10+12+15 = 37
Best Regards!
A professional employee in a large corporation receives an average of μ = 39.8 e-mails per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 38 employees showed that they were receiving an average of x = 33.1 e-mails per day. The computer server through which the e-mails are routed showed that σ = 16.2. Has the new policy had any effect? Use a 10% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee.
Answer:
Step-by-step explanation:
Null hypothesis: u = 39.8
Alternative: u =/ 39.8
Using a one sample z test: the formula is
z = x-u / (sd/√n)
Where x = 33.1 u = 39.8, sd= 16.2 and n = 38
Thus we have:
z = 33.1-39.8 / (16.2/√38)
z = -6.7 / (16.2/6.1644)
z = -6.7/ 2.6280
z= -2.5495
To be able to arrive at a conclusion, we have to find the p value, the p value at a 0.1 significance level for a two tailed test is 0.0108. This is way less than 0.1 thus we will reject the null and conclude that there has been a change (either way) in the average number of e-mails received per day per employee. Yes, the new policy had an effect.
Please answer this correctly without making mistakes I want genius,expert or ace people to answer this correctly
Answer:
It would decrease by 9.
Step-by-step explanation:
52 is the original mean or the initial mean.
43 is the final mean.
52-43 = 9
So 9 is the difference.
Hope this helped!
multiply and remove all perfect square roots. Assume y is positive. √12
Answer:
2√3
Step-by-step explanation:
Step 1: Find perfect square roots
√4 x √3
Step 2: Convert
2 x √3
Step 3: Answer
2√3
Can someone please help me with this problem?
Answer: -13
Step-by-step explanation:
c-2y
= -5-2(4)
= -5 - 8
= -13
Answer:
-13
Step-by-step explanation:
[tex]c=-5\\y=4\\c-2y=\\-5-(4*2)=\\-5-8=\\-13[/tex]
The expression is equal to -13 when [tex]c=-5[/tex] and [tex]y=4[/tex].