Answer:
0.2389 = 23.89% probability that Yuki's time is faster than Zana's.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Subtraction of normal variables:
When normal variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
Yuki's times in this race are normally distributed with a mean 80 seconds and standard deviation of 4.2 seconds. Zana's times are also normally distributed with a mean of 85 seconds and a standard deviation of 5.6 seconds.
Yuki's is faster than Zana if the subtraction of Yuki by Zana is larger than 0.
The mean is:
[tex]\mu = 80 - 85 = -5[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{4.2^2 + 5.6^2} = 7[/tex]
Find the probability that Yuki's time is faster than Zana's.
This is P(X > 0), which is 1 subtracted by the pvalue of Z when X = 0.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - (-5)}{7}[/tex]
[tex]Z = 0.71[/tex]
[tex]Z = 0.71[/tex] has a pvalue of 0.7611
1 - 0.7611 = 0.2389
0.2389 = 23.89% probability that Yuki's time is faster than Zana's.
Given the definitions of f(x) and g(x) below, find the value of g(f(-1)).
f(x) = -4x – 7
g(x) = x² + 7x – 2
Answer:
-14
Step-by-step explanation:
[tex]f(x) = -4x – 7 \\ plug \: x = - 1 \\ f( - 1) = - 4( - 1) - 7 = 4 - 7 = - 3 \\g(x) = x² + 7x – 2 \\g(f( - 1)) = {( - 3)}^{2} + 7( - 3) - 2 \\ = 9 - 21 - 2 \\= - 14[/tex]
A recent hailstorm caused $1200 worth of body damage to Karen's car. Based
on Karen's insurance policy given below, how much money will Karen receive
after she files her claim?
Summary
Comprehensive Deductible: 333
Collision Deductible: 5550
Premium of $625 for 4 months
A. $625
B. $825
O C. $375
Ο Ο
D. $1200
Answer:B
Step-by-step explanation:
$825
NEED HELP ASAPPP PLS
Answer:
they are alternate interior angles to parallel lines.
Step-by-step explanation:
The reason for this is that they are alternate interior angles to parallel lines. The straight dotted lines that represent the line of sight of each individual are parallel to each other while the elevation line in this scenario would be considered the Transversal as it passes through both of them. This ultimately causes the angles between the transversal and the line of sight to be alternate interior angles which are equal to one another, as can be seen in the attached demonstration in the image below.
b. If the radius of a circle is r сm, what
is the measure of its circumference?
Answer:
[tex]2 \times \pi \: \times r[/tex]
is the circumference of the circle
Answer:
Step-by-step explanation:
If the radius of a circle is r cm then
circumference = 2πr
Victor drew trapezoid PQRS on a
coordinate plane. The coordinates of each
vertex are:
P(8,4) Q(10, 4) R(13, -1) S(8, -1)
tion
What is the length, in units, of side PS?
A. 2
B. 3
C. 4
D. 5
Answer:
Step-by-step explanation:
b
Answer:
b hope it helps make brainlliest ty
Step-by-step explanation:
can you make me brainlliest
The number of hours per week that the TV is turned on is determined for each family in a sample.
The mean of the data is 37 hours.
The median is 33.2 hours.
Twenty four of the families in the sample watched TV for less than 22 hrs per week.
The 16th percentile is 22hrs.
150 families participated in the study.
The first percentile is greater than or equal to 22 hours: True or False?
Answer:
False, the first percentile is less than 22 hours.
Step-by-step explanation:
xth percentile:
If a measure is said to be in the xth percentile, it means that x% of the measures are smaller than it, and (100-x)% are larger.
Twenty four of the families in the sample watched TV for less than 22 hrs per week. In the sample, there are 150 families.
This means that 22 is the:
24*100%/150 = 16th percentile.
The first percentile is greater than or equal to 22 hours: True or False?
The first percentile is less than the 16th percentile, which is 22. This means that this is false, the first percentile is less than 22 hours.
need you to check if answer is correct
Joe ran 3 miles yesterday and wants to run at least 15 miles this week. Write an inequality that can be used to determine the additional number of days Joe must run this week if each run is 3 miles. Then solve the inequality.
9514 1404 393
Answer:
3 +3d ≥ 15
d ≥ 4
Step-by-step explanation:
Since Joe runs 3 miles for each day he runs, the number of miles he runs in d days is 3d. That, added to the distance he has already run, will total the amount for the week. He wants that to be at least (greater than or equal to) 15 miles:
3 + 3d ≥ 15
__
We can divide by 3 to get ...
1 + d ≥ 5
d ≥ 4 . . . . . . . subtract 1
Joe must run at least 4 additional days this week to run at least 15 miles.
Find the volume of the pyramid.
Please Help!
Answer:
144cm
Step-by-step explanation:
Just search it up lol
In how many ways can 5 different novels, 4 different mathematics books, and 1 biology book be arranged on a bookshelf if: (a) The books can be arranged in any order? Your answer is: 3628800 (b) The mathematics books must be together and the novels must be together? Your answer is : 6 (c) The mathematics books must be together but the other books can be arranged in any order? Your answer is: 5040
Answer:
(a) 3628800 ways
(b) 17280 ways
(c) 120960 ways
Step-by-step explanation:
Given
[tex]Novels = 5[/tex]
[tex]Maths = 4[/tex]
[tex]Biology = 1[/tex]
[tex]Total = 10[/tex]
Solving (a): Arrangement with no restriction.
We simply count each book with no restriction. i.e. 10 books
So, the number of arrangement is:
[tex]Arrangement =10![/tex]
[tex]Arrangement =10*9*8*7*6*5*4*3*2*1[/tex]
[tex]Arrangement =3628800[/tex]
Solving (b): Maths book together and Novels together
First, arrange the 4 maths books as:
[tex]Maths = 4![/tex]
Next, arrange the 5 novels as:
[tex]Novels = 5![/tex]
Lastly, take the 4 maths book as [1], the 5 novels as [1] and the remaining [1] biology book.
So, we have: 3 books
Arrange 3 books, we have:
[tex]Books = 3![/tex]
Total arrangement is:
[tex]Total = 4! * 5! * 3![/tex]
[tex]Total = 4*3*2*1 * 5*4*3*2*1 * 3*2*1[/tex]
[tex]Total = 17280[/tex]
Solving (c): Maths book together
First, arrange the 4 maths books as:
[tex]Maths = 4![/tex]
Next, take the 4 maths book as [1], then the remaining 6 books (i.e. 5 novels and 1 biology)
So, we have: 7 books
Arrange 7 books, we have:
[tex]Books = 7![/tex]
Total arrangement is:
[tex]Total = 4! * 7![/tex]
[tex]Total = 4*3*2*1 * 7*6*5*4*3*2*1[/tex]
[tex]Total = 120960[/tex]
Please help me with this question.
Answer:
A
Step-by-step explanation:
F(-2)= 4(-2)-1= -9
G(-2)= (-2)^2-3= 1
f(-2)-(g-2)= -9-1= -10
Write the number six and a half thousand in figures
Answer:
Step-by-step explanation:
6500 is the correct answer
The normal rainfall in September for Denver is 1.24 inches. The normal rainfall for Miami in September is 7.63 inches. The normal rainfall in January for Miami is 2.01 inches. The normal rainfall in January for Denver is 6.91 inches.
To the nearest tenth of an inch, how much more rain does Miami get in September than it gets in January?
Answer:
5.60 inches
Step-by-step explanation:
7.63 - 2.01 = 5.62
5.62 ≈ 5.6
Tell me if there is any missing information in the question because the information for Denver seems useless and there probably something missing
Helpp I’m begging ty
Answer:
40
Step-by-step explanation:
i asked siri
20 POINTS HELP!!
What value of x and y make the polygon below a parallelogram
Answer:
Step-by-step explanation:
3x = 12
x=4
x+y =5y
4+y = 5y
4 = 4y
1=y
Answer:
x-5 = y
72 -5 = 67
y=67
x = 72
Step-by-step explanation:
In a parallelogram, the diagonals bisect each other.
That being the case,
6x = 72
x = 12 In a parallelogram, the diagonals bisect each other.
That being the case,
6x = 72
x = 12 and the diagonals measure
144 and 134
i hope this helps!! ^_^
In triangle ABC, m∠A=(2x)∘, m∠B=(3x+1)∘, and m∠C=(3x−5)∘.
What is the value of x?
Answer:
x = 23
Step-by-step explanation:
A triangle contains 180°. So, simply create the equation m∠A + m∠B + m∠C = 180° and solve for x.
2x + 3x + 1 + 3x - 5 = 180
8x - 4 = 180
8x = 184
x = 23
The value of x in triangle ABC, where m∠A=(2x)∘, m∠B=(3x+1)∘, and m∠C=(3x−5)∘ is 23.
What is triangle angle sum theorem?According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees.
In triangle ABC,
m∠A=(2x)∘, m∠B=(3x+1)∘, m∠C=(3x−5)∘.As, the sum of all the angles of triangle is equal to the 180 degree. Thus,
[tex]m\angle A+m\angle B +m\angle C=180^o\\(2x)+(3x+1)+(3x-5)=180\\2x+3x+3x=180+5-1\\8x=184\\x=\dfrac{184}{8}\\x=23^o[/tex]
Thus, the value of x in triangle ABC, where m∠A=(2x)∘, m∠B=(3x+1)∘, and m∠C=(3x−5)∘ is 23.
Learn more about the triangle angle sum theorem here;
https://brainly.com/question/7696843
#SPJ2
Write a decimal that is less than 3.45 but greater than 3.0. helppp!
Answer:
any decimal between 3.0 and 3.45. You can,use 3.25 if u don't wanna think about it
Answer:There are mutipal answers but here’s one 3.1
Step-by-step explanation:
An item costs $34 it has a sales tax
rate of 5%. What is the amount of
sales tax for that item?
tax
0.00
+/-
Answer:
$1.70
Step-by-step explanation:
34 x 0.05 = 1.70
$1.70 is the tax
Padma's three fastest times in the 50-meter backstroke event were 49.06 seconds, 49.55 seconds, and 48.97 seconds. What is the difference, in seconds, between her two fastest times?
Answer:
0.51 seconds
Step-by-step explanation:
49.55 - 49.06 = 0.51 seconds
Factor this trinomial.
x²+x-2
A. (x - 2)(x - 1)
B. (x-2)(x + 1)
O C. (x + 2)(x - 1)
D. (x + 2)(x + 1)
Answer:
(x−1)(x+2)
Step-by-step explanation:
The middle number is 1 (1x) and the last number is -2.
Factoring means we want something like
(x+_)(x+_)
We need two numbers that...
Add together to get 1
Multiply together to get -2
Try -1 and 2:
-1+2 = 1
-1*2 = -2
Fill in the blanks in
(x+_)(x+_)
with -1 and 2 to get...
(x-1)(x+2)
Hope this helps!
For males in a certain town, the systolic blood pressure is normally distributed with a
mean of 120 and a standard deviation of 8. What is the probability that a randomly
selected male's systolic blood pressure will be less than 108, to the nearest
thousandth?
Answer:
0.89
Step-by-step explanation:
The probability that a randomly selected male's systolic blood pressure will be less than 108 is 0.25.
What is Probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Here, mean = 110, standard deviation = 8
P = [tex]\frac{x_{mean}-x }{SD}[/tex]
P = (110 - 108)/8
P = 2/8 = 0.25
P(Z<0.25) = 0.5 - 0.25 = 0.25
Thus, The probability that a randomly selected male's systolic blood pressure will be less than 108 is 0.25.
Learn more about Probability from:
https://brainly.com/question/14210034
#SPJ2
In ΔABC, the sum of the measures of ∠A and ∠B is 47°. What is the measure of ∠C ?
Question 1 options:
133°
47°
86°
143°
94°
Answer:
133
Step-by-step explanation:
A + B = 47
A + B + C = 180
47 + C = 180
C = 180 - 47
C = 133
If the given figure is rotated 180° around the origin, what are the new coordinates of point Z?
please I really need help with this.
Answer:
New coordinates of the point Z are (-6, 9)
Step-by-step explanation:
If a point (x, y) is rotated 180° about the origin, coordinates of the image point is given by the rule,
(x, y) → (-x, -y)
Coordinates of the vertex Z → (6, -9)
Following the same rule,
Z(6, -9) → Z'(-6, 9)
Therefore, coordinates of the new (image) point will be (-6, 9).
PLEASE HELP!
In the figure below, m∠R is 66°, and m∠T is 122°.
Note: Figure is not drawn to scale.
What is m∠Q?
A.
58°
B.
56°
C.
24°
D.
124°
Answer:
B. 56°
Step-by-step explanation:
We are given that m∠R is 66° and m∠T is 122°.
We can apply the supplementary rule since ∠S and ∠T are a linear pair. So, we can use ∠T to find ∠S through 180° - 122° = 58°.
Now, we can use ∠R and ∠S to find ∠Q.
66° + 58° = 124°
180° - 124° = 56°
Answer:
m∠Q is 56°.
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the two interior angles that are not adjacent to that exterior angle.
In this case, ∠T is an exterior angle of the triangle, and ∠Q and ∠R are the two interior angles that are not adjacent to ∠T.
So, the measure of ∠T is equal to the sum of the measure of ∠Q and the measure of ∠R.
Therefore, m∠Q is 56°.
What’s the slope???? Please help meee!
Answer:
The slope is 0.
Step-by-step explanation:
Suppose we have two points in a data set, the slope is given by the change in the output divided by the change in the input.
In this question:
Two points: (0,-20) and (1,-20)
Change in the output: -20 - (-20) = -20 + 20 = 0
Change in the input: 1 - 0 = 1
Slope: 0/1 = 0
The slope is 0.
Solve: 18^(x^(2)+4x+4)=18^(9x+18)
x = -2
x = 7
x = –2 and x = 7
no solution
Is this the problem?
[tex]18x^{2+4+4} = 18^{9x+18}[/tex]
Answer
The Answer is C
x=-2 and x=7
BC is included between?
Answer:C
Step-by-step explanation: goobaldy gock
Answer:
the answer is B not C you're welcome
Von de som en bona pays 1. West End the stor 10 years when it is
The balance after 10 years is $
Answer:
10$
Step-by-step explanation:
Eloise can fertilize her lawn in t hr. What is the rate at which she does this job?
Answer:
1 / t
Step-by-step explanation:
The rate at which a job, chore or a certain task is executed is expressed as the reciprocal of the time taken to complete such task. That is ;
Rate = 1 / time taken
From the scenario above, the time taken = t hours
Then the rate at which work is done can be expressed as :
1 / t
Solve the following problems. It may be helpful to set up an equation. The sum of two numbers is 13, the difference is 4. What are the numbers? pls help
Answer:
y = 4 1/2
x = 8 1/2
Step-by-step explanation:
x + y = 13
x - y = 4
substitution method: let x = 4+y
4+y + y = 13
2y = 9
y = 4 1/2
x = 8 1/2
