Answer:
Explained below.
Step-by-step explanation:
Let X = number of trucks that will be going over the speed limit on I-77 South between Dobson and Elkin.
The probability of X is, p = 0.75.
A random sample of n = 5 trucks are observed on this stretch of I-77.
The random variable X follows a binomial distribution with parameters n = 5 and p = 0.75.
(a)
Compute the mean as follows:
[tex]\mu=n\times p=5\times 0.75=3.75[/tex]
The mean of this probability distribution is 3.75.
(b)
The mean of 3.75 implies that on average 3.75 trucks that will be going over the speed limit on I-77 South between Dobson and Elkin.
(c)
Compute the standard deviation as follows:
[tex]\sigma=\sqrt{np(1-p)}=\sqrt{5\times 0.75\times (1-0.75)}=0.968[/tex]
Thus, the standard deviation of this probability distribution is 0.97.
(d)
Compute the probability that exactly 3 of the observed trucks are speeding as follows:
[tex]P(X=3)={5\choose 3}(0.75)^{3}(1-0.75)^{5-3}\\\\=10\times 0.421875\times 0.0625\\\\=0.263671875\\\\\approx 0.2637[/tex]
Thus, the probability that exactly 3 of the observed trucks are speeding is 0.2637.
(e)
Compute the probability that less than 3 of the observed trucks are speeding as follows:
[tex]P(X<3)=P(X=0)+P(X=1)+P(X=2)\\\\=\sum\limits^{2}_{x=0}{{5\choose x}(0.75)^{x}(1-0.75)^{5-x}}\\\\=0.0009765625+0.0146484375+0.087890625\\\\=0.103515625\\\\\approx 0.1035[/tex]
Thus, the probability that less than 3 of the observed trucks are speeding is 0.1035.
The power generated by an electrical circuit (in watts) as a function of its current x xx (in amperes) is modeled by P ( x ) = − 15 x ( x − 8 ) P(x)=−15x(x−8)P, left parenthesis, x, right parenthesis, equals, minus, 15, x, left parenthesis, x, minus, 8, right parenthesis What current will produce the maximum power?
Given:
The power generated by an electrical circuit (in watts) as a function of its current x (in amperes) is modeled by
[tex]P(x)=-15x(x-8)[/tex]
To find:
The current which will produce the maximum power.
Solution:
We have,
[tex]P(x)=-15x(x-8)[/tex]
[tex]P(x)=-15x^2+120x[/tex]
Differentiate with respect to x.
[tex]P'(x)=-15(2x)+120(1)[/tex]
[tex]P'(x)=-30x+120[/tex] ...(i)
To find the extreme point equate P'(x)=0.
[tex]-30x+120=0[/tex]
[tex]-30x=-120[/tex]
Divide both sides by -30.
[tex]x=4[/tex]
Differentiate (i) with respect to x.
[tex]P'(x)=-30(1)+(0)[/tex]
[tex]P'(x)=-30<0[/tex] (Maximum)
It means, the given function is maximum at x=4.
Therefore, the current of 4 amperes will produce the maximum power.
Answer:
its 4 amperes
Step-by-step explanation:
khan said so
A carpenter cuts a circle out of a piece of wood. The radius of the circle is
about 23 inches. The carpenter cuts the circle into two semicircles. What is
the area of one semicircle to the nearest hundredth? Use 3.14 for
Answer:
830.53 in²
Step-by-step explanation:
To find the area of one semicircle, find the area of the full circle and divide it by 2:
Use the circle area formula, A = [tex]\pi[/tex]r²
Plug in 3.14 as pi, and plug in the radius:
A = [tex]\pi[/tex]r²
A = 3.14(23²)
A = 1661.06
Divide this by 2:
1661.06 / 2
= 830.53
So, the area of one semicircle is 830.53 in²
Answer:
850.53 in² is the answer
Multiply. −2⋅(4)⋅(−3)⋅(5) −120 −4 4 120
Answer:
-44120
Step-by-step explanation:
sally picked 6 and 2-thirds pounds of apples. She used 1-half of the apples she picked to make pies. Question How many pounds of apples did Sally use to make pies? Move numbers to the boxes to show the answer.
Answer:
[tex]3 \frac{1}{3}[/tex]
Step-by-step explanation:
We know that Sally picked 6 2/3 pounds of apples, which can be converted into an improper fraction: 20/3. Multiply 20/3 and 1/2. You will get 20/6, which is 3 1/3. Hope this helped :D
1) x+30 = 40
2) 30-20+2x=10
3) 3x-10+13=-2x+28
4) 13x-23-45=-7x+12
5) 2(x+4) = 10x+24
6) 3(x-5) = 1-(2x-4)
7) 5X -10 = 15
2
8) X + 4 = X + 6
3 2
1)x+30=40
x=40-30
Answer :x=10
2)30-20+2x=10
10+2x=10
2x=0
Answer: x=0
3)3x-10+13=-2x+28
3x+3=-2x+28
3x+2x+3=28
3x+2x=28-3
5x=28-3
5x=25
x=5
4)13x-23-45=-7x+12
13x-68=-7x+12
13x+7x-68=12
13x+7x=12+68
20x=12+68
20x=80
x=4
5)2(x+4)=10x+24
2x+8=10x+24
2x-10x+8=24
2x-10x=24-8
-8x=24-8
-8x=16
x=-2
6)3(x-5)=1-(2x-4)
3x-15=1-(2x-4)
3x-15=1-2x+4
3x-15=5-2x
3x+2x-15=5
3x+2x=5+15
5x=5+15
5x=20
x=4
7)5x-10=15
5x=15+10
5x=25
x=5
8)x+4=x+6
4=6
no solution
PLEASE MARK ME AS BRAINLIEST
Solve: 3(g − 2) = 8
Answer:
g=4⅔
Step-by-step explanation:
3(g - 2)=8
3g -6 = 8
3g= 8+6
3g= 14
[tex] \frac{3g}{3} = \frac{14}{3} [/tex]
g=4⅔
hope this helps
Step-by-step explanation:
3(g - 2) = 8
3(g - 2) = 8
+ 2 +2
3g = 8
3÷3= 0 8÷3 = 4.6
so your answer will be g= 4.6 (5 if you round it up) or if you need it in fraction form it will be 4 and 2/3
3/4 change 3/4 to a decimal show work
Answer:
0.75
Step-by-step explanation:
You just need to convert 3/4 into a decimal.
For example: If you get 3 out of 4 problems right on a quiz, in percent form it will be a 75%, in decimal form 0.75 because you'll move the percent sign 2 spaces to the left. That will then be a decimal if you're converting 75% to 0.75.
3 divided by 4 is also going to give you 0.75. Because, a "fraction slash" is the dividing point. So,
3/4 = 0.75
The altitude of a helicopter increase is 1000 feet every four minutes. What is the unit rate of change (feet per minute) of the altitude?
Answer:
250 feet per minute
Step-by-step explanation:
1000 divided by 4 is 250. You divide them by each other because if you multiply 250 feet by 4 minutes, you get 1000.
(brainliest?)
Which statement illustrates a simulation that could be used to generate samples of people on a game show selecting either door A, door B, or door C?
A. Flipping a coin and getting heads for door A or tails for door C.
B. Rolling a die; 1 or 2 represents door A, 3 or 4 represents door B, and 5 or 6 represents door C.
C. Creating a spinner divided into 4 equal parts. Label two parts door A, one part door B, and the third part door C.
D. Go to the game show and collect data for a month on which doors people chose.
Answer:
The correct option is;
B. Rolling a die; 1 or 2 represents door A, 3 or 4 represents door B, and 5 or 6 represents door C
Step-by-step explanation:
Given that an onloaded die has equal chances of getting either 1 or 2 or 3 or 4 or 5 or 6, the chances of getting a particular score is therefore 1/6
and the probability of getting a 1 or 2 = 1/6 + 1/6 = 2/6 = 1/3
Therefore, given that the probability, P[tex]_{door}[/tex] of opening door A, or door B, or door C is the probability of selecting 1 out of 3 given as follows;
P[tex]_{door}[/tex](door A) = 1/3
P[tex]_{door}[/tex](door B) = 1/3
P[tex]_{door}[/tex](door C) = 1/3
Therefore, given that the probability of selecting either door A or door B or door C is equivalent to the probability of getting a 1 or 2, or a 3 or 4, or a 5 or 6 on a die.
Answer:
Its B: Rolling a die; 1 or 2 represents door A, 3 or 4 represents door B, and 5 or 6 represents door C.
Step-by-step explanation:
They have to be evenly probable so its B
edge 2020
-4 5/6 + (3 1/3) =
How dI you do this?
How are lines KL and MN related?
O The lines intersect at point K.
O The lines are parallel.
O The lines are perpendicular.
O The lines do not have slopes,
The lines KL and MN perpendicular to each other.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
If a line passes through two points, then the slope of the line is
m = y2-y1/x2-x1
From the given graph it is clear that coordinates of points on line KL are K(-8,2) and L(6,2).
The slope of line KL is
m = 0
The slope of line KL is 0, it means it is a horizontal line.
From the given graph it is clear that coordinates of points on line MN are M(-4,8) and N(-4,-6).
The slope of line MN is
m = 1/0
The slope of line MN is 1/0 or undefined, it means it is a vertical line.
We know that vertical and horizontal lines are perpendicular to each other.
Therefore the lines KL and MN perpendicular to each other.
To learn more on slope click:
brainly.com/question/3605446
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3x-100 what does x equal?
2. Express each of the following percentages as
a decimal.
(a) 4%
(b) 633%
Answer:
a. 0.04
b. 6.33
Step-by-step explanation:
a. If we want to convert into decimal we need to divide it by 100 then answer will 0.04
4/100 = 0.04
b. If we want to convert into decimal we need to divide it by 100 then answer will 6.33
633/100 = 6.33
Suppose there is a 1.7f drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 49.9f what will be the temperature when the plane reaches am altitude of 4,000ft?? The temperature will be_____F (type an integer or a decimal)
Answer:
[tex]43.1 ^{\circ}F[/tex]
Step-by-step explanation:
Give that for every 1000 feet increase in the height there is a drop of [tex]1.7 ^{\circ}F[/tex] in temperature.
So, the rate of temperature drop with respect to height, R = 1.7/1000 [tex]^{\circ}F/\text{ft}[/tex].
If the change in height is [tex]\Deltah[/tex][tex]\Delta h[/tex] feet, the temperature drop,
[tex]\Delta T= \Delta h R \;^{\circ}F\cdots(i)[/tex]
The temperature on the ground is 49.9 [tex]^{\circ}F[/tex].
At the ground, the height is 0, so the change in height, \Delta h when the plane reaches an altitude of 4,000 feet, is
\Delta h =4000-0=4000 feet
Now, from equation (i), the temperature drop
[tex]\Delta T= 4000 \times \frac {1.7}{1000}=6.8\;^{\circ}F.[/tex]
Hence, the temperature at an altitude of 4000 feet [tex]= 49.9-6.8=43.1 \;^{\circ}F[/tex].
In rhombus JKLM, if m
Pls help question is in the pic. Please give a right answer thx :D
Answer:
61.2
Step-by-step explanation:
In 1999, Marks & Spencer, a British department store, created the biggest sandwich ever made. The tuna and cucumber sandwich was in the form of a triangular prism. Suppose each slice of bread was 8 inches thick. Find each measure to the nearest tenth. a. The surface area in square feet of the sandwich when filled b. The volume of filling in cubic feet to the nearest tenth
Answer:
A) 19.2 ft^2
B) 28.9 ft^3
Step-by-step explanation:
Thickness = 8 inches
Assuming the triangular prism is made up of an equilateral triangle hence all sides are equal
lets assume the side = 10 inches
lets assume the thickness as the height of the prism = 8 inches
Assume length of the rectangle(l) = 5 feet
A) The surface area of the sandwich triangular prism
total surface area = bh + 2ls + lb
= 10*8 + 2(5*10) + ( 5 * 10 )
= 80 + 100 + 50 = 230 inches = 19.2 ft^2
B ) The volume of filing in cubic feet to the nearest tenth
V = [tex]\frac{1}{4} h \sqrt{-a^4 +2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4}[/tex] ------- 1
where : a = b = c = 10 inches
h = 8 inches
input the given values into the equation 1 above
V= 346.41 inches ^3 = 28.9 ft^3
which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"
Answer:
Let x be that number.
[tex] - 8 \div (x + 3)[/tex]
The quotient is the result of dividing a number by another. In this case, the numbers are - 8 and x + 3.
Write the equation of the line in point-slope form that passes through the
given point with the given slope.
(-4, 3); m = 2
Answer:
y = 2x + 11
plug the values into y = mx+b:
3 = 2(-4) + b
solve, and you get
3 = -8 + b
b= 3+8 = 11
so, the equation is y = 2x+11
Rachel earned $ 34 $34dollar sign, 34 in 4 44 hours at her job today. She wants to know how much she could earn ( e ) (e)left parenthesis, e, right parenthesis tomorrow if she works 10 1010 hours at the same hourly rate. How much will Rachel earn in 10 1010 hours? $
Answer:
Rachel earn $85 in 10 hours.
Step-by-step explanation:
Rachel earned $34 in 4 hours at her job today. It means we can find his earning in 1 hour.
1 hour = $(34/4)
= $8.5
He earns $8.5 in an hour.
To find his earning in 10 hours, multiply $8.5 by 10. So,
Earning = $8.5 × 10
= $85
Hence, Rachel earn $85 in 10 hours.
Answer:
85
Step-by-step explanation:
I am right
How do you make comparisons between an equation and a graph?
Answer:
here is a hint
Step-by-step explanation:
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Compare slope of an equation and slope of a line on graph and compare y-intercepts.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
For linear equation,
Compare slope of an equation and slope of a line on graph and compare y-intercepts.
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Therefore, compare slope of an equation and slope of a line on graph and compare y-intercepts.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
Seth is trying to pay off his credit card. He plans to pay it off in 24 months. Interest on the card is compounded monthly at a fixed annual rate of 11.6%. Seth currently has a balance of $18,875 on his credit card. Use the formula for the sum of a finite geometric series to determine Seth’s approximate monthly payment.
A.
Seth’s approximate monthly payment will be $753.97.
B.
Seth’s approximate monthly payment will be $834.75.
C.
Seth’s approximate monthly payment will be $884.99.
D.
Seth’s approximate monthly payment will be $868.35.
Answer:
$884.99
Step-by-step explanation:
Just took the quiz and this was the right answer. :)
Answer:
884.99
Step-by-step explanation:
Round 0.00208815 to 3 significant figures
What’s the highest common multiple?
Answer:
HCF = 90
Step-by-Step explanation:
2 × 3⁴× 5 = 810
2³× 3²× 5²= 1800
Find the prime factorization of 810
810 = 2 × 3 × 3 × 3 × 3 × 5
Find the prime factorization of 1800
1800 = 2 × 2 × 2 × 3 × 3 × 5 × 5
To find the HCF, multiply all the prime factors common to both numbers:
Therefore, HCF = 2 × 3 × 3 × 5
HCF = 90
Which of the following is r^2 + 4s evaluated for r = 4 and s = 1.5?
14
30
38
22
Answer:
22
Step-by-step explanation:
Once you fill in the variables your equation will look like this::4^2+4(1.5)::you will the go multiply both parts of the equation leaving you with 16+6 and when you add those together you get 22.
Hope This Helps!
help me pleaseeeeeeeeeeeeeeeeeeeeeee
Enter the correct answer in the box by replacing the values of m and b.
Answer:
f(x) = -2x + 5 Plato
Step-by-step explanation:
9) Draw a graph of the linear equation y= -2/-5x +3
find the cube of 2.9
[tex] {2.9}^{3} \\ 2.9 \times 2.9 \times 2.9 \\ 8.41 \times 2.9 \\ 24.389[/tex]
Answer:The cube of [tex]2.9[/tex] is [tex]24.389[/tex].
Which of the following is both a perfect square and a perfect cube?
64
16
81
1,000
I know the answer is 64, but how? Can someone please explain me to me how to work this out?