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.
A LOT OF POINTS!!
Suppose you borrow $40,000 at 13% APR for a 12-year term to be paid monthly. Your monthly payment is $450.00.
How much of your first payment goes toward interest?
Make sure you show your work to earn full credit.
Answer:
You get $45,200 first with interest with the 5400 you made in 1 year that dedeucts
Step-by-step explanation:
PLEASE GIVE ME AN ANSWER!!!!ILL MARK BRAINLIEST ANSWER
Answer:
3 3/4
Step-by-step explanation:
3.75 square ft per hr.
5/8 x 6 = 3.75
8% of $796.25 is how much?
8/100*796.25
=63.7%
Answer:63.7%
Answer: Hello, there! your Answer is below
63.7 would Be the correct answer
Step-by-step explanation: Below Is Info About How to Calculate Precentage UwU
how to calculate percentage of a number. Use the percentage formula: P% * X = Y
Convert the problem to an equation using the percentage formula: P% * X = Y.
P is 10%, X is 150, so the equation is 10% * 150 = Y.
Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.
SAT scores: The College Board reports that in 2009, the mean score on the math SAT was 582 and the population standard deviation was =σ120. A random sample of 20 students who took the test in 2010 had a mean score of 515. Following is a dotplot of the 20 scores. (a) Are the assumptions for a hypothesis test satisfied? Explain. (b) If appropriate, perform a hypothesis test to investigate whether the mean score in 2010 differs from the mean score in 2009. Assume the population standard deviation is =σ120. What can you conclude? Use the =α0.10 level of significance and the critical value method.
Answer:
we can conclude that there is no significant evidence to conclude that the mean score in 2010 differs from the mean score in 2009.
Step-by-step explanation:
H0 : μ = 582
H1 : μ < 582
Test statistic :
T = (xbar - μ) ÷ σ/√n
Xbar = 515 ; n = 20 ; σ = 120
T = (515 - 582) ÷ 120/√20
T = -67 / 26.832815
T = 2.50
Pvalue at t score = 2.50 ; df = 19 is 0.0187
At α = 0.0187
Pvalue > α ; Hence, we fail to reject the Null
Hence, we can conclude that there is no significant evidence to conclude that the mean score in 2010 differs from the mean score in 2009.
Calculate the mass of NaOH in 0.2 moles of NaOH
Answer:
0.2M i.e
Step-by-step explanation:
how to solve by factoring
x^2 + x = 0
Answer:
x=0 and x=-1
Step-by-step explanation:
Given: x^2+x=0
Factor: x(x+1)=0
Use Zero Product Property: x=0 and x+1=0
Therefore, x=0 and x=-1
A bicycle is originally priced at $60. The online retailer gives a discount and the bicycle is now priced at $42. Enter the percentage discount for the cost of the bicycle.
Answer:
30% ywww
Step-by-step explanation:
What is the theoretical probability that the spinner below will land on 6 if someone spins it 48 times?
Answer:
1/4 or 12*
Step-by-step explanation:
There are 8 possibilities. 2 of them are 6.
2/8=1/4
1/4 of 48 is 12
*The theoretical probability doesn’t change no matter how many times you spin the spinner. It will always be 1/4. (Or 0.25, or 25%). That could be what they’re asking. If you spun it 48 times, it would probably land on a six 12 times. That could also be what they’re asking for. 12:48 = 1:4.
please help meeeee i will give brainlyest
Answer:
answer is 63 min
Step-by-step explanation:
math+calculator like and subscribe to yourmom.com31
Which number has the least absolute value?
what is the area of the shaded region? use 3.14 for pi
Answer:
13.8
Step-by-step explanation:
Area of square = πr²
=22/7 × 4²
=50.2
Area of square = l²
=8²
= 64
Area of shape is 64 - 50.2 = 13.8
Answer:
The answer is 13.8
Step-by-step explanation:
Yes
In sixteen years Paul will be 48 years old.
How old is he now?
Answer:
32 years old
Step-by-step explanation:
48-16=32
Answer:
Paul is 32 years old
Step-by-step explanation:
48 - 16 = 32
Kristin charges $30 to train a small dog, and $50 to train a big dog. If Kristin trains 15 small dogs and 6 big dogs, how much money will she make?
Answer:
$750
Step-by-step explanation:
We can set up the equation 30x + 50y = z where x = the amount of small dogs, y = the amount of big dogs, and z = the total.
After plugging in the x and y values to solve for z, we are left with the following equation:
30(15) + 50(6) = 750
7n - 4 (8n+4) = 159
Answer:
n = -7
Step-by-step explanation:
Use distributive property:
7n - 32n - 16 = 159
Combine like terms
-25n - 16 = 159
Add 16 to both sides to isolate variable n
-25n = 175
Divide both sides by -25 to isolate variable n
n = -7
Check your work:
7(-7) - 32(-7) - 16 = 159
-49 + 224 - 16 = 159
159 = 159
I need so much help help me please UwU
Answer:
Line A: y = 3x + 3
Line B: y = -1/3x + 3
Step-by-step explanation:
Line A points: (0, 3) and (1, 6)
Slope:
m=(y2-y1)/(x2-x1)
m=(6-3)/(1-0)
m= 3
y - y1 = m(x - x1)
y - 3 = 3(x - 0)
y - 3 = 3x
y = 3x + 3
Line B points: (0, 3) and (9, 0)
Slope:
m=(y2-y1)/(x2-x1)
m=(0-3)/(9-0)
m= -1/3
y - y1 = m(x - x1)
y - 3 = -1/3(x - 0)
y - 3 = -1/3x
y = -1/3x + 3
what is the shape identify in the image
Answer:
it is a triangular prism
Can someone give me a fake band name???
Answer:
loaded diper
Step-by-step explanation:
what is the area of a right triangle with sides 7ft 24ft and 25ft?
Answer:
84 ft^2
Step-by-step explanation:
[tex] \frac{7 + 24 + 25}{2} = 28[/tex]
The area is:
[tex] \sqrt{28 \times (28 - 7) \times (28 - 24) \times (28 - 25)} [/tex]
[tex] = 84 \: {ft}^{2} [/tex]
50 pts please help asap (:
Answer:
d. 8 units
Step-by-step explanation:
If AC = 16 units then the length of CB is 8 units because DB is perpendicular bisector from the centre of circle.
Answer: B
Step-by-step explanation: I took the quiz
Hope this helps
find the gradient of the line
with the equation 3x+4y=10
sin(30°)cos(45°) + cos(30°)sin(45°)
Step-by-step explanation:
sin(30°)cos(45°) + cos(30°)sin(45°)=1+√3/2√2
If Mike loses $5 per week, how much does he lose in 4 weeks?
Answer:
$ 20Step-by-step explanation:
[tex]1week \: = 5 \\ 4 \: weeks = x \\ \\ x = 20[/tex]
hope this helps you.
Can I have the brainliest please?
Have a nice day!
There are 4 roses for every 7 carnations in a bouqeuet. Mr rodriguez buys a bouqeuet with 12 roses in it. How many total flowers are in the bouqeuet Mr rodriguez bought?
Please explain step by step I dont get it.
Answer:
33 total flowers are in the bouquet Mr Rodriguez bough
Step-by-step explanation:
So for every 4 roses there are 7 carnations meaning the ratio is 4:7
4 times x = 12
x=3
So we do the same for carnations
7 x 3 = 21
Now we add to find the total
21+12=33
33 total flowers
-A sequence is a list of numbers or obje
What is a pattern?
-A pattern is a repetitive sequence and
numbers and almost everywhere you ca
What's More
A. Directions: Give the pattern rule of t
Rul
1. 1, 4, 7, 10, 13
2.2, 8, 32, 128, 512
Rul
Answer:
1. Add 3
2. Multiply 4
Step-by-step explanation:
Given
[tex](1)\ 1, 4, 7, 10, 13[/tex]
[tex](2)\ 2, 8, 32, 128, 512[/tex]
Required
The rule
[tex](1)\ 1, 4, 7, 10, 13[/tex]
This is a linear function because successive terms have a common difference
The common difference between each term is:
[tex]d = 4 - 1 = 3[/tex]
[tex]d = 7 - 4 = 3[/tex]
[tex]d = 10 - 7 = 3[/tex]
[tex]d = 13 - 10 = 3[/tex]
The above shows that 3 is [tex]added\ to\ each\ term[/tex] to get the next term.
Hence, the rule is: Add 3
[tex](2)\ 2, 8, 32, 128, 512[/tex]
This is a geometric function because successive terms have a common ratio
The common ratio between each term is:
[tex]r = 8/2 = 4[/tex]
[tex]r = 32/8 = 4[/tex]
[tex]r = 128/32 = 4[/tex]
[tex]r = 512/128 = 4[/tex]
The above shows that 4 [tex]is\ multiplied\ to\ each\ term[/tex] to get the next term.
Hence, the rule is: Multiply 4
Do 5 yd 12 yd 13 yd make a right angle?
If x=3 and y=7, evaluate the following expression: 100 − 3 ( 3 − 4x )
Answer:
[tex]100 - 3(3 - 4x) \\ = 100 - 3(3 - 4 \times 3) \\ = 100 -27 \\ = 73[/tex]
Answer:
873
Step-by-step explanation:
100 - 3 ( 3- 4x ) 97 ( 3 - 4×3 )97 (3 - 12 ) 97 × 9 873Tinisha is planning a birthday party. She can buy:
10 balloons, 8 cupcakes, and 8 hats for $50
5 balloons, 9 cupcakes, and 7 hats for $46, or
12 balloons, 7 cupcakes, and 9 hats for $51
Using b for the number of balloons, c for the number of cupcakes, and h for
the number of hats, write a system of equations to represent this situation.
Answer:
b+c+h=50
Step-by-step explanation:
Its the first one because you need to have the same amount of hats as cupcakes cause the hat really stands for people.
brainiest exchange give me and I will give you 2+2
Answer:
4
Step-by-step explanation:
and sure
Answer:
4
Step-by-step explanation:
The side lengths of a rectangle are all multiplied by 5. What happens to its perimeter?
Answer:
The perimeter is multiplied by 5.
Step-by-step explanation:
Perimeter of a rectangle:
The perimeter of a rectangle with sides l and w is given by:
[tex]P = 2(l + w)[/tex]
The side lengths of a rectangle are all multiplied by 5.
This means that [tex]l = 5l, w = 5w[/tex]. So
[tex]P_M = 2(5l + 5w) = 2*5(l+w) = 10(l + w)[/tex]
What happens to its perimeter?
The rate is:
[tex]\frac{P_M}{P} = \frac{10(l+w)}{2(l+w)} = 5[/tex]
The perimeter is multiplied by 5.
Pam and her grandma are planning to make a quilt together. The quilt will be made out of fabric squares that measure 6 inches on each side. The quilt will have 3 more squares along its longer edge than it will have along its shorter edge.
If there are x fabric squares along the quilt's shorter edge, find an expression for f(x), the length of the quilt's shorter edge in inches.
f(x)=
6x
Next, find an expression for g(x), the length of the quilt's longer edge in inches.
g(x)=
Which function can you use to find the area of the quilt in square inches?
Answer:
There are x squares on the shorter side, each square measures 6 inches.
The length of the shorter side is:
f(x) = x*6 = 6xThe length of the longer side is:
g(x) = (x + 3)*6 = 6x + 18The area of the quilt is:
A = 6x(6x + 18) = 36x² + 108x