The mean is 58.319 m/h and the standard deviation is 11.665 m/h of the vehicle speed if 5% of all vehicles travel less than 39.13 m/h and 10% travel more than 73.25 m/h.
The mean and standard deviation of the vehicle speed can be calculated by using the formula for z-score.
The z-score of measure X can be given as;
Z = X - μ / σ
In this case, 39.13 m/h is the 5th percentile; therefore when X = 39.13, Z has a p-value of 0.05, hence Z = -1.645
Z = X - μ / σ
-1.645 = (39.13 - μ) / σ
39.13 - μ = -1.645σ
μ = 39.13 + 1.645σ
Additionally, 73.25 m/h is the 90th percentile (100 - 10 = 90), therefore when X = 73.25, Z has a p-value of 0.9, hence Z = 1.28
1.28 = (73.25 - μ) / σ
73.25 - μ = 1.28σ
μ = 73.25 - 1.28σ
We can find the standard deviation by equalling both equations as follows;
39.13 + 1.645σ = 73.25 - 1.28σ
1.645σ + 1.28σ = 73.25 - 39.13
2.925σ = 34.12
σ = 34.12/2.925 = 11.665 m/h
Now the mean can be calculated as follows;
μ = 73.25 - 1.28σ
μ = 73.25 - 1.28(11.665)
μ = 58.319 m/h
To learn more about standard deviation; click here:
https://brainly.com/question/28225633
#SPJ4
I need help with this practice I attempted this and got 13.96? Make sure your answer is rounded to the nearest hundredth
Law of Cosines
Given two side lengths a and b of a triangle and the angle included by them θ, the length of the third side can be calculated as:
[tex]c^2=a^2+b^2-2ab\cos \theta[/tex]We have a = 14, b = 9, θ = 71°. Substituting:
[tex]\begin{gathered} c^2=14^2+9^2-2\cdot14\cdot9\cos 71^o \\ c^2=196+81-252\cdot0.325568 \\ c^2=194.956825 \\ c=\sqrt[]{194.956825} \\ c=13.96 \end{gathered}[/tex]The length of CD is 13.96
5. How many ways are there to distribute 10 indistinguishable candies among 4 different
children? Children may end up with no candies.
PLSSSSS HELP IT IS EXTREMELY URGENT PLSSSS
By application of the combination formula, there are 210 ways for distributing 10 indistinguishable candies among 4 children.
What is combination?Combination is the arrangement of objects in which order is not taken into account.
The applicable formula is:
n combination r = n!/[(n - r)!r!]
where n is the number of indistinguishable items (10 candies), and r is the possible number of recipients (4 kids).
Hence;
10 combination 4 = 10!/[(10 - 4)!4!] ways
10 combination 4 = 10!/(6! × 4!) ways
10 combination 4 = (10 × 9 × 8 × 7 × 6!)/(6! × 4 × 3 × 2 × 1) ways
10 combination 4 = 10 × 3 × 7 ways
10 combination 4 = 210 ways
Therefore, there are 210 ways for the 10 indistinguishable candies to be distributed among the 4 children by with the application of combination formula.
Learn more about combination here: https://brainly.com/question/11732255
#SPJ1
Use the following two points to answer parts a -c . (2, 3) , (- 1, - 6) a. Find the slope of the line passing through the two pointsb . Write an equation of a line passing through the two points in point slope form . c . Rewrite the equation of the line in slope -intercept form .
sSlope means the inclination of the line
Intercept is the point where the line touches the Y axis.
With his new trainer, jacob now bikes at an average speed of 21 mph. that is 5% faster than he averaged with his old trainer. how fast did he bike, on average, before training with the his new trainer?
The average before training with new trainer is 20 mph.
Let the average speed with old trainer be x. Forming the equation as per given information- Average speed with new trainer = 5% × Average speed with old trainer + Average speed with old trainer
Keep the values in formula to find the average speed with old trainer.
21 = 5/100x + x
Multiplying the equation with 100
2100 = 5x + 100x
Performing addition
105x = 2100
Shifting 105 to Right Hand Side of the equation
x = 2100 ÷ 105
Performing division on Right Hand Side of the equation
x = 20
Thus, average speed with old trainer was 20 mph.
Learn more about percentage and average -
https://brainly.com/question/26215194
#SPJ4
What is the center of the hyperbola?
(y+3)^2/9 − (x−2)^2/2 = 1
Enter your answer by filling in the boxes.
The center of the hyperbola is (2, -3)
What is an hyperbola?A hyperbola is a curve that is open and that has two branches and it is symmetrical
How to solve the center of the hyperbola?The equation is given as
(y + 3)²/9 − (x − 2)²/2 = 1
A hyperbola is represented as
(y - k)²/a² − (x − h)²/b² = 1
Where the center of the hyperbola has the coordinates of (h, k)
The values of h and k in the given equation (y + 3)²/9 − (x − 2)²/2 = 1 are
h = 2 and k = -3
This means that:
(h, k) = (2, -3)
So, we have coordinates of the center to be (2, -3)
Hence, the center is (2, -3)
Read more about hyperbola at
https://brainly.com/question/28031641
#SPJ1
A train ticket in a certain city is 3.00. People eho use the train also have the option of purchasing a frequent rider pass for 18.75 each month. With the pass, each ticket costs only 2.25. Determine the number of times in a month the train must be used so that the total monthly cost without the pass is the same as the total monthly cost with the pass.
The number of times for which the train must be used so that the monthly cost without the pass is same as with the pass is; 6.25 times.
How to solve Word Problems using algebraic expressions.It follows from the task content that the regular train ticket costs, 3.00.
Therefore, the cost for travelling x times with the month is; 3x.
On this note, for the total monthly cost without the pass to be same as that with the pass; the equation which must hold is;
3x = 18.75
x = 18.75/3
x = 6.25 times.
Therefore, after taking the train 6.25 times, the cost without the pass is same as that with the pass.
Read more on word problems;
https://brainly.com/question/21405634
#SPJ1
a large industrial firm purchases several new word processors at the end of each year, the exact num- ber depending on the frequency of repairs in the previ- ous year. suppose that the number of word processors, x, purchased each year has the following probability distribution: x 0 1 23 f(x) 1/10 3/10 2/5 1/5 if the cost of the desired model is $1200 per unit and at the end of the year a refund of 50x2 dollars will be issued, how much can this firm expect to spend on new word processors during this year?
The money which is expected to spend on new word processors during this year is
The probability distribution is
x: 0 1 2 3
f(x) [tex]\frac{1}{10}[/tex] [tex]\frac{3}{10}[/tex] [tex]\frac{2}{5}[/tex] [tex]\frac{1}{5}[/tex]
If the cost of the desired model is $1200 per unit and at the end of the year a refund of 50x2 dollars
So total money spent in this year is [tex]1200x-50x^2[/tex]
Then the equation of expenses will be
[tex]\text{Expenses}=E(1200x-50x^2)[/tex]
We can rewrite it as
[tex]\text{Expenses}=E(1200x)-E(50x^2)[/tex]
[tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex] -----------------(1)
Now the mean of the probability distribution is ,
[tex]E(x)=\sum_{ }^{ }((x_i)(f(x_i))\\=(0\times\frac{1}{10})+(1\times\frac{3}{10})+(2\times\frac{2}{5})+(3\times\frac{1}{5})\\=\frac{3}{10}+\frac{4}{5}+\frac{3}{5}\\\\=\frac{3+8+6}{10}\\\\=\frac{17}{10}\\\\=1.7[/tex]
The variance of the function is
[tex]E(x)=\sum_{ }^{ }(x_i^2)(f(x_i)[/tex]
[tex]=(0^2\times\frac{1}{10})+(1^2\times\frac{3}{10})+(2^2\times\frac{2}{5})+(3^2\times\frac{1}{5})[/tex]
[tex]=\frac{3}{10}+\frac{8}{5}+\frac{9}{5}[/tex]
[tex]=\frac{37}{10}[/tex]
[tex]=3.7[/tex]
On substituting the values in equation (1)
[tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex]
[tex]=1200(1.7)-50(3.7)^2[/tex]
[tex]=2040-684[/tex]
[tex]=1855[/tex]
A similar probability distribution problem is given at
https://brainly.com/question/12913756
#SPJ4
Please help me dont know the answer
Answer:
First answer is obtuse
The second answer is scalene
Step-by-step explanation:
Obtuse is when an angle is over 90
Scalene since all the angles are different, all the side lengths are different.
a package boodins weighs 6.2 ounces. A package of rews weighs 9.97 ounces. how much more does a package of rews weigh than a package of boondins
Based on the package of boondins and the package of rews, the package of rews will have a weight in relation to the package of boondins that is 3.77 ounces
How to find the different in weights?To find how much more that the package of rews weighs over the boondins, deduct the weight of the package of boondins from the weight of a package of rews.
Weight of package of rews = 9.97 ounces
Weight of package of boondins = 6.2 ounces
The difference in the weight of the packages is:
= 9.97 - 6.2
= 3.77 ounces
Find out more on difference in weight at https://brainly.com/question/15207190
#SPJ1
The required difference in the package of the bodies and rews is 3.77 ounces.
As per the given in the question,
boudin is 6.2 ounces in weight and rews are 9.97 ounces in weight.
here,
As per observation, rews weighs more than bodies, and the difference between their weights is simply evaluated from the subtraction between the weight. So,
Weigh difference = weigh of rews - weigh of boodins
Substitute the value in the above equation,
Weigh difference = 9.97 - 6.2 = 3.77.
Thus, the required difference in the package of the bodies and rews is 3.77 ounces.
Learn more about Subtraction here:
https://brainly.com/question/2346316
#SPJ1
I figured x equals a specific number in every single question involving something like this. X is on all sides, there's no given number.
The angle x of the triangle is 60 degrees.
How to find the angles in a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is equals to 180 degrees.
A triangle can be classified base on the sides and angles. For example equilateral triangle, scalene triangle and isosceles triangle.
Therefore, the angle x of the triangle can be found as follows:
x + x + x = 180
3x = 180°
divide both sides of the equation by 3
3x / 3 = 180 / 3
x = 180 / 3
x = 60 degrees.
learn more on triangle here: https://brainly.com/question/25950519
#SPJ1
Answer:
the person below or above me is the answer. Yeah
Step-by-step explanation:
A model car is a 1/40 if the length of the real car is 5.5 m what is the length of the model car
Answer:
0.14 meters, or 140 mm
Step-by-step explanation:
(1/40) means that the model car will have dimensions that are (1/40) the original car.
Real car = 5.5 meters.
Model car = (1/40)*(5.5 m) = 0.14 meters, or 140 mm
Hello, I’m struggling with my geometry homework. It’s number 2
An inscribed circle is the largest circle contained in the polygon (triangle):
• Bisects two angles of the triangle.
,• The angle bisector will intersect at the intercenter.
Procedure
To draw the inscribed circle, we have to use the intercenter (O, in our case) as the center, pointing one of the compass points in O, and draw the circle touching the edges.
2) m angle2=x+88 50° 2 A) -8 C) 8 B) -7 D) 7
A
1) Since the sum of the interior angles of any triangle is 180º, and this is an isosceles triangle
2) Then the other angle, has the same measure 50º since this is an isosceles triangle, at least two congruent sides, and two congruent angles.
We can finally write
x+88 +50 +50 = 180
x +188 =180 subtract 188 from both sides
x= 180-188
x= -8
3) So x=-8 is the answer.
suppose that the members of a student governance committee will be selected from the 40 members of the student senate. there are 18 sophomores, 12 juniors and 10 seniors who are members of the student senate. in how many ways can the governance committee be selected, if it must be made up of 2 sophomores, 2 juniors and 3 seniors? assume that each of the sophomores, each of the juniors and each of the seniors is equally likely to be selected for the committee. a. 339 b. 1211760 c. 2160 d. 18643560 e. 25920
Assuming that each of the sophomores, each of the juniors and each of the seniors is equally likely to be selected for the committee, there are b. 1211760 ways can the governance committee be selected, if it must be made up of 2 sophomores, 2 juniors and 3 seniors. The committee can be selected in 1,211,760 ways.
Combination formula:
Cn,x is the number of different combinations of x objects from a set of n elements, given by:
Cnₓ= n!÷ x! (n-x!)
In this problem:
2 sophomores from a set of 18.
2 juniors from a set of 12.
3 seniors from a set of 10.
They are independent, so we can just multiply them, thus:
T= C₁₈,₂ × C₁₂,₂× C₁₀,₃ = 18! ÷2!6! × 12!÷ 2!10! × 10!÷ 3!×7! = 1211760
The committee can be selected in 1,211,760 ways.
To know more about combinations, refer:
brainly.com/question/24650047
#SPJ4
NOBODY'S ANSWERING MY QUESTION, HELLO? I WILL GIVE BRAINLIEST :(
Answer:B
Step-by-step explanation:
Answer:
(C) I and III only.
Step-by-step explanation:
Hello! It's me again! Let's help you with this question too!
Now, let's start understanding what information is given to us.
[tex]a < b < 0[/tex]
This means that, some integer a is lower than some integer b and b is lower than 0. So right out of the gate, both integer a and b are both negative numbers. Here, we can evaluate all 3 possibilities like so:
I. [tex]\frac{a}{b} > 0[/tex]
To start, let's see if this is true. The simplest way is to substitute values into integer a and b to where [tex]a < b < 0[/tex] holds true as well. For this example, we can say [tex]a=-2[/tex] and [tex]b=-1[/tex]. If we evaluate as such, it would be:
[tex]\frac{-2}{-1} > 0[/tex]
[tex]2 > 0[/tex]
From this example, 2 is higher than 0. Meaning this is true. Now, it'll be true for every value due to something called the fraction rule. Fraction rule is simply just stating that, if the numerator and denominator both have a negative sign, they cancel each other out and become a positive fraction. So, we can say I. is true.
II. [tex]-b > -a[/tex]
This is simple to prove, all it's saying is that negative integer b is always going to be higher than negative integer a. Using our same example from I. we can substitute as such and evaluate:
[tex]-(-1) > -(-2)[/tex]
[tex]1 > 2[/tex]
Here, we can see that 1 is not greater than 2 and no matter what numbers you substitute, that will always be the case because you're essentially putting the lowest number first and seeing if it's greater than the lower number. So II. is false.
III. [tex]0 < \frac{b}{a} < 1[/tex]
Now this one is a bit more difficult. However, there isn't much we need to do here. This is saying that 0 is lower than [tex]\frac{b}{a}[/tex] but [tex]\frac{b}{a}[/tex] is lower than 1. Let's split this into 2 parts.
Part 1: [tex]0 < \frac{b}{a}[/tex]
This isn't the same as I. as the numerator and denominators have switched. Let's use the values we've set back in I. to see if this holds true:
[tex]0 < \frac{-1}{-2}[/tex]
[tex]0 < \frac{1}{2}[/tex]
From here, we find that it is true. And it also holds true that it is less than 1. We can use another set of values to see if this still holds. Let's try [tex]a=-7[/tex] and [tex]b=-3[/tex]:
[tex]0 < \frac{-3}{-7}[/tex]
[tex]0 < \frac{3}{7}[/tex]
As you can see here, using the fraction rule. So long as there is an integer a and b are different (they always will be because of [tex]a < b < 0[/tex]), regardless of what they will be, it will always give us a fraction answer. And a fraction answer will always be lower than 1. Therefore, III. is also true.
So, the answer to this question is C. I and III only
Solve for x to the nearest tenth.
Answer:
x = 11.2 cms.
Step-by-step explanation:
I infer that the units are in centimeters.
8-3 = 5
One side = 5 cm
Other side = 10 cm
By the Pythagorean Theorem:
x² = 5² + 10²
x² = 25 + 100
x² = 125
√x² = √125
x = 11.18 cms
To the nearest tenth:
x = 11.2 cms
The graphs of the fuctions f and g are shown below, find all values of x for which f(x) < g(x). 30 points!!!
Answer: [tex]-10 < x < 0, x > 12[/tex]
Step-by-step explanation:
[tex]f(x) < g(x)[/tex] when the graph of [tex]f(x)[/tex] is below the graph of [tex]g(x)[/tex].
Hello, is there any way I can get some assistance in my practice work? I need to find the width of the backyard and how much the fence in the backyard will cost
Given that the backyard is rectangular and the length is 56 feet while the area is 1400 square feet. Recall that the area A of a rectangle is the product of the length L and the width B.
A = L * B
Hence the width B may be found from
1400 = 56 * B
B = 1400/56
B = 25 feet
b. If the fencing cost $10 per foot then because a rectangle has two lengths and two widths,
the total cost to fence the backyard will be
= $10 * 2(56 + 25)
= $1,620
Write the equation of the line passing through the point (6,-9) that is perpendicular to the line y=1/2x+11.
The line that is perpendicular to the equation of a line given is y = -2x + 3
What is the equation of a perpendicular line?The equation of a perpendicular line can be found using the slope of the line first and then applying the points through which the line passes through.
For the given question, the equation of the line is y = 1/2x + 11 and the point is (6, -9).
To find an equation of a line;
Identify the slope.Identify the point.Substitute the values into the point-slope form, y − y₁ = m ( x − x₁) . y − y₁ = m (x − x₁) .Write the equation in slope-intercept formThe equation of the line can be modified into y - y₁ = m(x - x₁)
substituting the values into the equation above gives y = -2x + 3
Learn more on the equation of line here;
https://brainly.com/question/13763238
#SPJ1
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
The three options you would pick is
y2 – 5y = 750
750 – y(y – 5) = 0
(y + 25)(y – 30) = 0
Step-by-step explanation:
Hope this helps! :))
Triangle ABC is congruent to triangle XYZ. In AABC, AB = 12 cm and AC = 14 cm. In AXYZ, YZ = 10 cm and XZ = 14
!
cm.
The perimeter of triangle ABC that is congruent to triangle XYZ is: 36 cm.
What are Congruent Triangles?Triangles that are congruent to each other have corresponding side lengths that have the same lengths that are equal to each other.
What is the Perimeter of a Triangle?The sum of all the three sides of a triangle is equal to the perimeter of the triangle.
Since triangle ABC is congruent to triangle XYZ, their corresponding side lengths will also be congruent to each other. That is, they will have the same lengths.
Therefore:
Side AB = side XY = 12 cm [corresponding congruent sides]
Side AC = side XZ = 14 cm [corresponding congruent sides]
Side BC = side YZ = 10 cm [corresponding congruent sides]
Find the perimeter of triangle ABC by adding all three triangles together.
Perimeter of triangle ABC = side AB + side AC + side BC
Perimeter of triangle ABC = 12 + 14 + 10
Perimeter of triangle ABC = 36 cm
Learn more about congruent triangles on:
https://brainly.com/question/2938476
#SPJ1
A group of people were asked if they owned a dog. 191 responded "yes", and 485 responded "no".Find the probability that if a person is chosen at random, they own a dog. 191485 294191 191676
Given:
There are given that the number of people who said yes is 191 and who said no is 485.
Explanation:
According to the given question:
The total number of people is:
[tex]191+485=676[/tex]That means the total outcome is 676.
Now,
The probability that the person is chosen own dog is:
[tex]P=\frac{The\text{ number of people who have their own dog}}{\text{Total number of outcomes}}[/tex]So,
[tex]P=\frac{191}{\text{6}76}[/tex]Final answer:
Hence, the correct option is C.
Answer:
191/676.
Step-by-step explanation:
The total number of people asked is 191 + 485
= 676.
So. the required probability
= number of people owning a dog/ total number of people
= 191/676.
Rewrite (156 + 243) using factoring
A. 3(52 + 81)
B. 6(24 + 40)
C. 12(13 + 21)
D. 18(9 + 13)
Write your answer as a fraction in simplest form.
910+(−45)=
Answer:
-44.09
Step-by-step explanation:
Trust bro i am passing collage math at 15
Which equation can be rewritten as x + 4 = x²? Assume x > 0.
Answer:
We have been given an equation . We are also told that x is greater than 0. We are asked to choose the equation that can be written as our given equation.
Since x is greater than, so we will take positive root on both sides of our given equation as:
Upon looking at our given choices, we can see that option C is same as our answer.
Step-by-step explanation:Therefore, option C is the correct choice.
Answer:2=x
Step-by-step explanation:
x+4=x^2
0+4=x^2
Square root 4 = square root x^2
2=x
Write an equation in standard form of the line that passes through the given points.
7. (-3, 2); m = 1
Answer:
y=x+1
Step-by-step explanation:
y-y1=m(x-x1)
y-2=1(x+3)
y-2=x+3
y=x+1
insert parentheses to make the expression true
4×2+3×2=32
Answer:
4 * ( 2 + 3 * 2) = 32
Step-by-step explanation:
The strategy I used in this question is generally trial and error. The most important thing here to remember is to follow the order of operations. If you think a little out of the box, then you will see the answer. To solve, first multiply 3*2, then add two, which should result in 8. 4*8 is 32, which makes the equation true.
If f(x) = 5x, what is f¹(x)?
O f¹(x) = -5x
○ f¹(x) = -1/2 x
0 r²(x) = ²/1 x
O f¹(x) = 5x
The value of f¹(x) = x/5
What is function?
A function in maths is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.
We are given f(x) = 5x
and we are to find inverse of f(x).
Replace f(x) by y.
So,
y = 5x
Isolate x
x = y/5
Replace x by f'(y)
So,
f'(y) = y/5
Replace all occurrences of y by x.
So,
f'(x) = x/5
Therefore, the inverse of function f(x) = 5x is f'(x) = x/5
To know more about functions, visit:
https://brainly.com/question/9676733
#SPJ9
Simplify by combining like terms. 9x + 6 - 4x - 2x + 1 - 15
9x + 6 - 4x - 2x + 1 - 15
9x - 4 x- 2x = (9-4-4)x = 3x
6 +1 -15 = -8
____________
Answer
3x -8
______________
Please tell me if you can see the updates
ok
________________
Which list shows the absolute values in order from greatest to least select each correct answer.
A: | 11 7/10 |, | 11 3/5 |, | 10 3/10 |
B: | -3 1/3 |, | -3 2/3 |, | 2 2/3 |
C: | -1 5/6 |, | 1 7/12 |, | 1 5/12 |
D: | -6 5/7 |, | -6 3/7 |, | 5 2/7 |
Please help I will give 100!
Step-by-step explanation:
A./11.7/,/22.6/,10.3/
11.7<22.6>10.3
B./-10.3/,/-10.7/,/7.3/
10.3<10.7>7.3
C./-2.5/,/1.42/,/1.25/
2.5>1.42>1.25
D./-9.3/,/-9/,/7.43/
9.3>9>7.43
therefore the answer is C and D