Answer:
a
mean [tex]\mu = 10[/tex] variance [tex]\sigma^2 = 6[/tex]
b
The binomial random variable x fall into this interval ranges from
- 5 to 5
c
[tex]P(6 \le x \le 14) = 0.8969[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 25[/tex]
The percentage that look for gas stations and food outlets that are close to or visible from the highway is [tex]p = 0.40[/tex]
Generally the mean is mathematically represented as
[tex]\mu = n * p[/tex]
=> [tex]\mu = 0.40 * 25[/tex]
=> [tex]\mu = 10[/tex]
The variance is mathematically represented as
[tex]\sigma^2 = np(1- p )[/tex]
=> [tex]\sigma^2 = 25 * 0.40(1- 0.40 )[/tex]
=> [tex]\sigma^2 = 6[/tex]
The standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{\sigma^2}[/tex]
[tex]\sigma = \sqrt{6}[/tex]
[tex]\sigma = 2.45[/tex]
The interval is evaluated as
[tex]p\pm 2 \sigma[/tex]
=> [tex]p - 2 \sigma\ \ \ , \ \ \ p + 2\sigma[/tex]
=> [tex]0.40 - 2 *2.45\ \ \ , \ \ \ 0.40 + 2* 2.45[/tex]
=> [tex]-4.5\ \ \ , \ \ \ 5.3[/tex]
The binomial random variable x fall into this interval ranges from
- 5 to 5
Generally
[tex]P(6 \le x \le 14) = P(\frac{ x - \mu }{\sigma } \le \frac{14 - 10}{{2.45}} ]-P[ \frac{ x - \mu }{\sigma } \le \frac{6 - 10}{2.45 } ][/tex]
[tex]P(6 \le x \le 14) = P(Z \le 1.63 ]-P[ Z \le -1.63 ][/tex]
[tex]P(6 \le x \le 14) = [1- P(Z > 1.63 ]] -[1- P[ Z > -1.63 ]][/tex]
From the z-table
[tex]P(Z > 1.63 ) = 0.051551[/tex]
And
[tex]P(Z >- 1.63 ) =0.94845[/tex]
=> [tex]P(6 \le x \le 14) = [1-0.051551] -[1-0.94845][/tex]
=> [tex]P(6 \le x \le 14) = 0.8969[/tex]
If f(x) = 2x + 3 for all values of x, what is the value of f(-3)?
Answer:
f(-3)= -3
Step-by-step explanation:
We are given the function:
f(x) = 2x+3
and asked to find f(-3). Essentially, we want to find f(x) when x is equal to -3.
Therefore, we can substitute -3 for each x in the function.
f(x)= 2x+3 at x= -3
f(-3)= 2(-3) +3
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction
Multiply 2 and -3.
f(-3) = (2*-3) +3
f(-3)= (-6)+3
Add -6 and 3.
f(-3)= (-6+3)
f(-3)= -3
If f(x)= 2x+3, then f(-3)= -3
what is the answer?
Answer/Step-by-step explanation:
Given:
Data set for sandwich calories=> 242, 290, 290, 280, 390, 350
Mean: the mean is given as sum of all values in the data set ÷ total no. of data set given
[tex] \frac{242 + 290 + 290 + 280 + 390 + 350}{6} = \frac{1,842}{6} = 307 [/tex]
Mean Absolute Value:
Step 1: find the absolute value of the difference between each value and the mean
|242 - 307| = 65
|290 - 307| = 17
|290 - 307| = 17
|280 - 307| = 27
|390 - 307| = 83
|350 - 307| = 43
Step 2: find the sum of all values gotten in step 1
65 + 17 + 17 + 27 + 83 + 43 = 252
Step 3: divide the result you get in step 2 by 6 to get the M.A.D
[tex] M.A.D = \frac{252}{6} = 42 [/tex]
The Mean Absolute Value represents or gives us an idea how spread the data set for the number of sandwich calories are.
Thus, averagely, the number of calories of sandwich at the restaurant are far from the mean caloric value by 42 calories.
simplify 8+7x9 I need help on this. plz give your best answers.
Answer:
[tex] \boxed{ \sf{ \bold{ \huge{ \boxed{71}}}}}[/tex]
Step-by-step explanation:
Using PEMDAS rule :
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Let's solve:
[tex] \sf{8 + 7 \times 9}[/tex]
Multiply the numbers
⇒[tex] \sf{8 + 63}[/tex]
Add the numbers
⇒[tex] \sf{71}[/tex]
Hope I helped!
Best regards!
69. A 10-foot-tall basketball hoop is 4 feet shorter than twice the height of a flag pole.
What is the height in feet of the flag pole?
Answer:
24 ft.
Step-by-step explanation:
10x2=20. 20+4=24
Answer:
24 FT.
Step-by-step explanation:
10x2=20. 20+4=24
Convert standard to slope-intercept forms. 1. Standard form: 10x − 7y = −8
Answer:
Step-by-step explanation:
-7y = -10x - 8
y = 10/7x + 8/7
Find the sum of a finite geometric series. A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50 percent of its previous height. The total vertical distance down the ball has traveled when it hits the ground the fifth time is meters.
Answer:
19.375 m.
Step-by-step explanation:
Before the first bounce it has travelled 10 meters.
Then after just hitting the ground the second time it has travelled 10 +1/2(10) = 15 m.
The common ratio is 0.5 and we want the sum of 5 terms
= a1 (1 - r^n) / (1 - r)
= 10 * (1 - 0.5^5) / (1 - 0.5)
= 19.375 m.
Find the interval in which f(x)=sinx−cosx is increasing or decreasing?
Answer:
There is no short answer.
Step-by-step explanation:
To find to intervals which f(x) increases or decreases, we first need to find it's derivative.
[tex]f(x) = sinx - cosx\\f'(x) = cosx - (-sinx) = cosx + sinx[/tex]
The function is increasing when it's value is > 0 and decreasing when it's value is < 0.
If we take a look at this graph, cosx+sinx is positive when they are both positive or when cosx is greater then sinx on the negative part.
I hope this answer helps.
Fraction that less then 5/6 dominater is 8
Answer:
1/8, 2/8, 3/8, 4/8, 5/8, 6/8
Step-by-step explanation:
If i have interpreted correct. You want to know a fraction with a denonminator of 8 that is less than 5/6
5/6=0.8333
Multiple Answers
1/8, 2/8, 3/8, 4/8, 5/8, 6/8
3 1/2 x 5 2/5 = Also explain how you got it
Answer:
Hello! Answer below.
Step-by-step explanation:
The answer to your question is:
18 9/10 or 18.9
Steps below...
You have to do this first.
1. Convert the mixed number to fraction.
2. [tex]7/2[/tex]
Multiplied by
[tex]27/5[/tex]
This will equal, 189/10
If you divide this the answer will be 18 9/10
So the answer is 18 9/10 or 18.9
Hope this helps!
By, BrainlyMagic
Use the diagram to answer the question.
P
Which of the following statements is true?
line s and line t intersect
line s and line t intersect at Point P
Point P is on line t and on line s
all of the above are true
Answer:
last option ie all of the above are true
Lines s and t are intersect at P. Therefor, option D is the correct answer.
What is intersection of line?In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.
Straight lines s and t are intersect at P.
P is called point of intersection.
Therefor, option D is the correct answer.
Learn more about intersection of lines here:
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which fractions are equivalent to 15/20
Answer:
[tex]\frac{3}{4}[/tex], [tex]\frac{30}{40}[/tex], [tex]\frac{45}{60}[/tex], [tex]\frac{60}{80}[/tex]....e.t.c are all equivalent fractions
Step-by-step explanation:
For the answer you need to know bout equivalent fractions
TO find equivalent fractions you have to multiply the numerator and denominator by the same amount
E.x.[tex]\frac{15}{20}=\frac{(15)(2)}{(20)(2)} =\frac{30}{40}[/tex]
Therefore [tex]\frac{30}{40}[/tex] is an equivalent fraction
Evaluate the triple integral ∭ 8x^2 dV, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1)
Answer:
2/15
Step-by-step explanation:
given that the triple integral = ∫∫∫ 8x^2 dv
and T is the solid tetrahedron with vertices : (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1)
hence the equation of the plane: x + y + z = 1
T [ (X,Y,Z) : 0≤x≤1, 0≤y≤1-x, 0≤z≤1-x-y ]
attached below is the detailed solution ( we multiply our answer after evaluation with the coefficient of 8 as attached to the initial expresssion)
By evaluating the triple integral where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1) the value calculated is 2/15.
Given :
The triple integral ∭ 8x^2 dV, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1).
The following calculation can be used to evaluate the triple integral:
[tex]\rm I = \int\int\int 8x^2dV[/tex]
T[(x,y,z) : [tex]0 \leq x \leq 1[/tex] ; [tex]0 \leq y \leq 1-x[/tex] ; [tex]0 \leq z \leq 1-x-y[/tex] ]
Now put the limits in the above integral.
[tex]\rm I = \int\limits^1_0\int\limits^{1-x}_0\int\limits^{1-x-y}_0 {8x^2} \, dz \, dy \, dx[/tex]
[tex]\rm I = \int\limits^1_0\int\limits^{1-x}_0 {8x^2} (1-x-y) \, dy \, dx[/tex]
[tex]\rm I = 8 \int\limits^1_0\int\limits^{1-x}_0 {x^2-x^3-x^2y} \, dy \, dx[/tex]
[tex]\rm I = 8 \int\limits^1_0 {x^2(1-x)-x^3(1-x)-x^2\dfrac{(1-x)^2}{2}} \, dx[/tex]
[tex]\rm I = 8 \int\limits^1_0 {x^2-x^3-x^3+x^4-x^2\dfrac{(1+x^2-2x)}{2}} \, dx[/tex]
[tex]\rm I = 4\left( \int\limits^1_0 {2x^2-4x^3+2x^4-x^2-x^4+2x^3} \, dx\right)[/tex]
[tex]\rm I = 4\left( \int\limits^1_0 {x^2+x^4-2x^3} \, dx\right)[/tex]
[tex]\rm I = 4\left( {\dfrac{x^3}{3}+\dfrac{x^5}{5}-\dfrac{x^4}{2}} \right)^1_0[/tex]
[tex]\rm I = 4\left( {\dfrac{1}{3}+\dfrac{1}{5}-\dfrac{1}{2}} \right)[/tex]
[tex]\rm I = \dfrac{2}{15}[/tex]
By evaluating the triple integral where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1) the value calculated is 2/15.
For more information, refer to the link given below:
https://brainly.com/question/24308099
The circumference of Dion's bicycle tire is 56.52 inches. What is the diameter of Dion's bicycle tire? (Use 3.14 for i.)
Answer:
The answer is 18 inchesStep-by-step explanation:
Circumference of a circle = πd
where
d is the diameter of the circle
From the question
Circumference = 56.52 inches
π = 3.14
To find the diameter substitute the value of the circumstance into the above formula and solve for the diameter
That's
56.52 = πd
[tex]d = \frac{56.52}{\pi} \\ d = \frac{56.52}{3.14} [/tex]
We have the final answer as
d = 18 inchesHope this helps you
The diameter of Dion's bicycle tire is 18 inches.
CircumferenceThe length of the perimeter of the circle is known as the Circumference. Mathematically, [tex]C=2\pi r[/tex]
How to find the diameter of the bicycle tire?The circumference of the bicycle tire is 56.52 inches.
So,
[tex]2\pi r=56.52\\r=\dfrac{56.52}{2\times 3.14}\\r=9 inches[/tex]
So, the diameter of the bicycle tire is [tex]9\times 2= 18[/tex] inches.
Thus, the diameter of the bicycle tire is 18 inches.
Learn more about diameter here- https://brainly.com/question/5501950
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Water flows through a pipe at a rate of 6300 liters every 8.5 months. Express this rate of flow in cubic feet per hour. Round your answer to the nearest hundredth.
Answer:
0.04
Step-by-step explanation:
[tex] \dfrac{6300~L}{8.5~month} \times \dfrac{1000~cm^3}{1~Liter} \times \dfrac{1~ft^3}{(30.48~cm)^3} \times \dfrac{12~months}{1~year} \times \dfrac{1~year}{365.25~days} \times \dfrac{1~day}{24~hours} \times \dfrac{1~day}{24~hours} = [/tex]
[tex]= 0.04 \dfrac{ft^3}{hour}[/tex]
The value of the flow rate in cubic feet per hour is 0.04.
What is the rate of flow?The rate of the flow of the fluid is defined as the volume of the fluid flowing through the cross-section per unit of time. The unit of the flow rate is cubic feet per hour or cubic meter per hour etc.
Given that water flows through a pipe at a rate of 6300 liters every 8.5 months. Then the flow rate in cubic feet per hour will be calculated as below:-
1 litre = 0.0353 cubic feet
6300 litres = 6300 x 0.0353
6300 litres = 222.4 cubic feet
1 month = 730 hours
8.5 months = 6205 hours
The rate of flow in cubic per hour will be:-
Rate of flow = 222.4 / 6205 = 0.04 cubic feet per hour
Therefore, the value of the flow rate in cubic feet per hour is 0.04.
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If 512+14=x then x=23 Question 10 options: True False
How to solve 5(10 - 1) using order of operation
Answer:
45
Step-by-step explanation:
Answer: 45
Step-by-step explanation: Parentheses first.
10-1=9. Next is multiplication. 5(9)=45.
Simplify nine to the second power
Answer:
It would be 81
Step-by-step explanation:
[tex]9^{2}[/tex] is the same as 9 times 9. And 9 times 9 is 81.
Answer:
2⁹ = 512
Step-by-step explanation:
2⁹ = 2*2*2*2*2*2*2*2*2 = 512
Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively
Answer:
[tex]x_n=7(-3)^{n-1}[/tex]
Step-by-step explanation:
First, write some equations so we can figure out the common ratio and the initial term. The standard explicit formula for a geometric sequence is:
[tex]x_n=ar^{n-1}[/tex]
Where xₙ is the nth term, a is the initial value, and r is the common ratio.
We know that the second and fifth terms are -21 and 567, respectively. Thus:
[tex]a_2=-21\\a_5=567[/tex]
Substitute them into the equations:
[tex]x_2=ar^{(2)-1}\\-21=ar[/tex]
And:
[tex]a^5=ar^{(5)-1}\\567=ar^4[/tex]
To find a and r, divide both sides by a in the first equation:
[tex]r=-\frac{21}{a}[/tex]
And substitute this into the second equation:
[tex]567=a(\frac{-21}{a} )^4[/tex]
Simplify:
[tex]567=a(\frac{(-21)^4}{a^4})[/tex]
The as cancel out. (-21)^4 is 194481:
[tex]\frac{567}{1}=\frac{194481}{a^3}[/tex]
Cross multiply:
[tex]194481=567a^3\\a^3=194481/567=343[/tex]
Take the cube root of both sides:
[tex]a=\sqrt[3]{343} =7[/tex]
Therefore, the initial value is 7.
And the common ratio is (going back to the equation previously):
[tex]r=-21/a\\r=-21/(7)\\r=-3[/tex]
Thus, the common ratio is -3.
Therefore, the equation is:
[tex]x_n=7(-3)^{n-1}[/tex]
find the length of segment AB
Answer:
AB = 10.77 units
Step-by-step explanation:
If the extreme ends of a line segment are [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex].
Then the length of the segment joining these extreme ends will be,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
If the extreme ends of the line segment AB are A(-3, 1) and (7, 5).
Measure of AB = [tex]\sqrt{(7+3)^2+(5-1)^2}[/tex]
AB = [tex]\sqrt{100+16}[/tex]
AB = [tex]\sqrt{116}[/tex]
AB = 10.77 units
Therefore, length of the segment AB will be 10.77 units.
The overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8.6 cm
a. Find the probability that an individual distance is greater than 214.80 cm.
b. Find the probability that the mean for 1515 randomly selected distances is greater than 204.00 cm
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
a. The probability is
(Round to four decimal places as needed.)
b. The probability is
(Round to four decimal places as needed.)
c. Choose the correct answer below.
A. The normal distribution can be used because the original population has a normal distribution.
B. The normal distribution can be used because the probability is less than 0.5
C. The normal distribution can be used because the mean is large.
D. The normal distribution can be used because the finite population correction factor is small
Answer:
(a) the probability that an individual distance is greater than 214.80 cm is 0.1401.
(b) The probability that the mean for 15 randomly selected distances is greater than 204.00 cm is 0.2482.
(c) The normal distribution can be used because the original population has a normal distribution.
Step-by-step explanation:
We are given that the overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8.6 cm.
(a) Let X = the overhead reach distances of adult females.
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean reach distance = 205.5 cm
[tex]\sigma[/tex] = standard deviation = 8.6 cm
So, X ~ Normal([tex]\mu=205.5,\sigma^{2} =8.6^{2}[/tex])
Now, the probability that an individual distance is greater than 214.80 cm is given by = P(X > 214.80 cm)
P(X > 214.80 cm) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{214.80-205.5}{8.6}[/tex] ) = P(Z > 1.08) = 1 - P(Z [tex]\leq[/tex] 1.08)
= 1 - 0.8599 = 0.1401
The above probability is calculated by looking at the value of x = 1.08 in the z table which has an area of 0.8599.
(b) Let [tex]\bar X[/tex] = the sample mean selected distances.
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean reach distance = 205.5 cm
[tex]\sigma[/tex] = standard deviation = 8.6 cm
n = sample size = 15
Now, the probability that the mean for 15 randomly selected distances is greater than 204.00 cm is given by = P([tex]\bar X[/tex] > 204.00 cm)
P([tex]\bar X[/tex] > 204 cm) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{204-205.5}{\frac{8.6}{\sqrt{15} } }[/tex] ) = P(Z > -0.68) = 1 - P(Z [tex]\leq[/tex] 0.68)
= 1 - 0.7518 = 0.2482
The above probability is calculated by looking at the value of x = 0.68 in the z table which has an area of 0.7518.
(c) The normal distribution can be used in part (b), even though the sample size does not exceed 30 because the original population has a normal distribution and the sample of 15 randomly selected distances has been taken from the population itself.
NEED HELP ASAP!! Angles of Elevation and Despression! Need to find y! Round to the nearest tenth!!
Answer:
[tex] y = 178.3 ft [/tex]
Step-by-step explanation:
y is opposite to the reference angle, 27°.
350 ft is adjacent to the reference angle, therefore:
[tex] tan(27) = \frac{y}{350} [/tex]
Multiply both sides by 350
[tex] tan(27)*350 = \frac{y}{350}*350 [/tex]
[tex] tan(27)*350 = y [/tex]
[tex] 178.3 = y [/tex] (to nearest tenth)
[tex] y = 178.3 ft [/tex]
Put these fractions in order of size, smallest to largest:
4/3, 3/4, 3/8, 5/8, 7/6
Answer:
3/8, 5/8, 3/4, 7/8, 4/3
Step-by-step explanation:
What are the x - intercepts for the expression (x-4)(x+5)
Answer: It will be 4 or -5.
Step-by-step explanation:
Answer:
x = 4, -5
Step-by-step explanation:
Step 1: Write out expression
0 = (x - 4)(x + 5)
Step 2: Find roots
x - 4 = 0
x = 4
x + 5 = 0
x = -5
We are trying to come up with a regression model that predicts university GPA. Is high school GPA a significant predictor for university GPA?
Answer:
No.
Step-by-step explanation:
High school GPA is not a significant predictor of University GPA.
The Grade Point Average obtained at the end of high school education has almost nothing (in my opinion, it has nothing to do with) to do with grades that the scholar will obtain in college. Many scholars find it difficult adjusting to the social and academic life demands of tertiary institution.
A good predictor for university Grade Point Average would be:
The CGPA (Cumulative Grade Point Average) obtained by the student(s) in each year/session/level/part in the university.
This will be a significant predictor for university GPA.
4-2(3+2)
2
How do you do this help me
Answer:
-46Step-by-step explanation:
[tex]4 - 2(3 + 2) ^{2} \\ 4 - 2( {5}^{2} ) \\ 4 - 2(25) \\ 4 - 50 = - 46[/tex]
Identify the center and radius for the equation y2 = -8x – x2 – 24 – 6y.
Answer:
Hey there!
This circle would have a center at (-4, -3) and a radius of 1.
Let me know if this helps :)
solve for y:y= [-7-6]
answers:
(a)-13 (b)13 (c)1 (d) -1 (e) none of these
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Hi my lil bunny!
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[tex]y= [-7-6][/tex]
[tex]y = -13[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
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Have a great day/night!
❀*May*❀
Jin tried to evaluate 5 + 2 x 9 step-by-step.
5+2 x 9
Step 1: =7 x 9
Step 2: =63
Find jin’s mistake
A: step 1
B: step 2
C: Jin did not make a mistake
Answer:
5 + 2 x 9
Step 1 = 7 x 9
Step 2 = 63
Step-by-step explanation:
= 5 + 2 x 9
= 5 + ( 2 x 9 )
= 5 + 18
= 23
Step 2 = 7 x 9
= 63
Step 3 = 63
C. jin did not make a mistake
Sorry i'm wrong :)
A painter rented a wallpaper steamer at 9 a.m. and returned it at 4 p.m. He paid a total of $28.84. What was the rental cost per hour?
Greetings,
I hope you and your family are staying safe and healthy!
Answer: $4.12 per hour
Step-by-step explanation:
So, 9am to 4pm is 7 hours
Why? Because you go from 10am, 11am, 12pm, 1pm, 2pm, 3pm, and 4pm.
So now all we have to do is to divide the amount he paid by the number of hours.
Like this:
[tex]\frac{28.84}{7} = 4.12[/tex]
Therefore,
The rental cost per hour is $4.12
-----------------------------------
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Can someone help me solve the maze?
Answer:
see attached
Step-by-step explanation:
This is asking you to recognize the symbols used to designate a point, line segment, ray, angle, line, and plane.
The point is designated by its letter.
A line segment is designated by the letters of its endpoints, with an overline.
A ray is designated by the endpoint and a point on the ray. The endpoint is listed first. The letters have an arrow over them pointing in the direction from the endpoint.
An angle is designated using the symbol ∠. If three letters are used to identify the angle, the middle one is the vertex.
A line is designated using its name, or by the letters of two points on the line. If the letters are used, there may be a double-ended arrow over them.
A plane is designated by 3 non-collinear points, for example, "plane ABC". It may also be designated by the name of the plane.