Answer:
The 10th percentile is 66.42.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
X ~ N(70, 14).
This means that [tex]\mu = 70, \sigma = 14[/tex]
Suppose that you form random samples of 25 from this distribution.
This means that [tex]n = 25, s = \frac{14}{\sqrt{25}} = 2.8[/tex]
Find the 10th percentile.
This is X when Z has a pvalue of 0.1, so X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1.28 = \frac{X - 70}{2.8}[/tex]
[tex]X - 70 = -1.28*2.8[/tex]
[tex]X = 66.42[/tex]
The 10th percentile is 66.42.
A basketball player has a 60% chance of making each free throw. What is the probability that the player makes exactly
three out of six free throws?
Find the value of x in the triangle shown below 3 6
5
√18
√27
4
a^2 + b^2 = c^2
In this case we're looking for C
so
(3)^2 + b^2 = (6)^2
9 + b^2 = 36
b^2 = 36-9
√b^2 = √27
b = 3√3
Answer:
the answer is actually d= 27
Step-by-step explanation:
What is the answer to this please????
Answer:
your answer will be
y=40 x +20
Step-by-step explanation:
have a nice day/night ^_^
If you divide me by 9, the remainder is 4. I am a multiple of 10. What two-digit number am I?
Answer:
40?
Step-by-step explanation:
i tried
Highest common factor of 15 30 and 45
Step-by-step explanation:
I believe it is 15...all the numbers can be divided by 15, since 15 is the smallest number it is also the highest common factor only because 30 and 45 can be divided by 15
.......hope it helps!
Answer:
15
Step-by-step explanation:
Find the prime factors for each number as:
45 =3 × 3 × 5
30 = 2 × 3 × 5
15 = 3 × 5
Now identify the common factors and determine the GCF:
Therefore:
HCF = 3 × 5 = 15
Answer choices please help
240
200
240
280
if ABCA-QRS, what must be the measure of <A
Answer:
m<A is 33
Step-by-step explanation:
126+21+x=180
147+x=180
180-147=x
x=33
Name the two congruent triangles
Answer:
∆ABE ≅ ∆DCE by SAS Congruence Theorem.
Step-by-step explanation:
The diagram given indicates the following:
<E ≅ <E (vertical angles)
AE ≅ DE
BE ≅ CE
Thus, an included angle, <E, and two side lengths, AE and BE, in ∆ABE are congruent to an included angle, <E, and two corresponding side lengths, DE and CE, in ∆DCE. By the SAS Congruence Theorem, both angles are congruent to each other.
Therefore:
∆ABE ≅ ∆DCE by SAS Congruence Theorem.
Help please!
Factoring Quadratics
Factor the following quadratic expressions into two binomials. Show your work.
1. x + 34x + 64
2. x - 14x + 40
3. X2 + 8x - 48
4. x2 - 17% - 60
5. 2x + 13x + 20
6. 5x? - 13x + 6
7. 8x + 14x - 15
8.-8x? - 20x + 12
Answer:
Step-by-step explanation:
Sry but I only did 1,2,5,6,7&8
But am not sure if am correct just try
ags of sugar come in 3 sizes.
Small bag: A 250 g bag costs 64p.
Medium bag: A 575 g bag costs £1.25.
Large bag: A 1.25 kg bag costs £2.54.
Find the cost per gram for each bag of sugar.
Round your answers to 3dp.
Write which size of bag is best value for money in the comment box.
Answer:1 gram of the small bag costs 0.256p ,1 gram of the medium bag costs 0.217p and 1 gram of the big bag costs 2. 032p
Step-by-step explanation:
Which equation can be used to describe the pattern in the table
Answer:
I feel like its C.
Step-by-step explanation:
Answer:
the answer is C
Step-by-step explanation:
because all the a values are 5 more than b
Help please!! I’ll give best answer brainliest!!
Answer:
D, The last one
Step-by-step explanation:
What fraction is equivalent to 8%
2/25
4/50
8/100
this are the smallest fractions equivalent to 8%
Answer:
8/100
Step-by-step explanation:
8% = 0.08 = 8/100
let me know if you need more of an explaination <33
PLAZ HELPPP PWETRYYY PSLOD
Answer:
=
Step-by-step explanation:
whatever comes out of an absolute value is always positive so 8=8
Ms. Smith mixes orange juice with seltzer in a ratio of 3:1. If she uses 48 ounces of orange juice, how many ounces of seltzer does she need?
Answer:
16 oz
Step-by-step explanation:
the ratio is 3 oz of oj to 1 oz of seltzer.
I pretty much just divided 48 by 3.
I hope this is correct and I hope it helps you!
How do I solve 5x/6=-8 to get the answer
Answer:
Download photo math
Step-by-step explanation:
Need help please help me
Help fast pleaseeeee
we will find the area of triangle with sides 5y,6y and 9y using herons formula
Your business loan has a variable interest rate. Next month the annual rate will jump from 6.3% to 7.8%. Your balance is
$1,620,000. How much will your monthly payment go up?
Answer:
$2,025
Step-by-step explanation:
The monthly payment will be increased by $2,025.
What is an amount?
The quantity of money anyone has is termed as the amount. Your monthly payment based on the rate of 6.3% per annum is:
= (6.3% * 1,620,000 ) / 12 months
= 102,060 / 12
= $8,505
Now that the rate has gone up to 7.8% per annum, the payment is:
= (7.8% * 1,620,000 ) / 12 months
= 126,360 / 12
= $10,530
Payment went up by:
= 10,530 - 8,505
= $2,025
Therefore the monthly payment will be increased by $2,025.
To know more about the amount follow
https://brainly.com/question/25109150
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The graph of triangle ABC is shown below:
What is the area, in square units, of triangle ABC?
Answer:
36 square units
Step-by-step explanation:
Height = 9
Base = 8
Area of a triangle = A = 1/2bh
Plug in
1/2 (8) (9) = 4 x 9 = 36
Kate’s father is a baker at the Morning Muffin Bakery. This morning the oven wasn’t working correctly and 2 dozen muffins burned. Kate’s father gave ¼ of what was left to Kate to take to school. He wrapped up ½ of the remaining muffins and sold them to the grocery store down the street. He then wrapped ⅓ of what was remaining and gave them to the coffee shop to sell. That left Kate’s father with a dozen muffins to sell at the bakery. How many muffins did Kate’s dad bake?
Answer:
64
Step-by-step explanation:
Step 1: 12 divided by 3 = 4. 12+4 = 16.
I need to know what ⅓ of 12 is so I can continue the problem without messing up.
Step 2: 16*2 = 32.
Half of however many are left is 16.
Step 3: 32 divided by 4 is 8. 32+8 is 40. Two dozen is 24. 40 + 24 = 64.
Now we know the answer.
Boom.
Solve the equation. The symbol "^" mean "raised to the second power"
C^2=28.2+42.1
Answer:
Step-by-step explanation:
c^2=28.2 + 42.1
SOLVE FOR A
A=logc (703/20), c ≠ 1 and C > 0
SOLVE FOR C
{ c = - (700/20) 1/a, A ≠ 0 and Numberator (A) bmod 2 = 0 and denominatior (A)bmod 2=1 SOOOOOOO a ≠ 0
Ava bought 2 sandwiches for a total of $5.25, a bowl of soup for $3.00, and a bag of chips for $1.25. How much change did she get back if she paid with a $20.00 bill?
Answer:
Step-by-step explanation:
5.25
3.00
1.25
_____
$ 9.50
- 20.00
_______
$10.5
What is the area of this shape
Pleasee helppp it’s due todayyy
Answer:
88 is a solution to 1/8 x =11, since a solution means that x is equal to that number, so in this scenario, x=88. When substituted(88*0.125), the same answer, 11, is obtained.
Step-by-step explanation:
Calculate the area, in terms of x and in simplest form, of the rectangle shown below.
5x + 4
2x - 5
5x +4 the x is 2 the answer to this is 14
2x-5 the x is 4 the answer to this is 13
A rectangular prism has a length of 1 1/4 centimeters, a width of 4 centimeters, and a heigh of 3 1/4 centimeters What is the volume of the prism? Enter your answer in the box as a simplified mixed number or a decimal
Answer:
Step-by-step explanation:
V=lbh=1 1/4×4×3 1/4
=5/4×4×13/4
=65/4
=16 1/4 cm³
=16.25 cm³
Volume of a rectangular prism can be found by multiplying all three dimensions of the prism together: V = lwh
WILL MARK BRAINLIEST!!!
(03.03)
The description below represents Function A and the table represents Function B:
Function A
The function is 2 more than 5 times x.
Function B
x
y
−1
2
0
5
1
8
Which statement is correct about the slope and intercept of the two functions? (1 point)
Select one:
a. Their slopes are equal but y-intercepts are not equal.
b. Their slopes are not equal but y-intercepts are equal.
c. Both slopes and y-intercepts are equal.
d. Neither slopes nor y-intercepts are equal.
Function b? Honestly, I need these points.
solve for x: -3(x+7)=5 . Explain how you solved for x and how you know your answer is correct
Answer:
Step-by-step explanation:
-3(x+7)=5
1. Multiply 3 and x+7 , you will get -3x-21=5
2. Add 21 on both sides, you will be left with -3x=26
3. Divide both sides with -3, and x will equal to -26/3
The length of a rectangle is increasing at a rate of 4 meters per day and the width is increasing at a rate of 1 meter per day. When the length is 10 meters and the width is 23 meters, then how fast is the AREA changing
Answer:
[tex]\displaystyle \frac{dA}{dt} = 102 \ m^2/day[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Area of a Rectangle: A = lw
l is lengthw is widthCalculus
Derivatives
Derivative Notation
Implicit Differentiation
Differentiation with respect to time
Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle l = 10 \ meters[/tex]
[tex]\displaystyle \frac{dl}{dt} = 4 \ m/day[/tex]
[tex]\displaystyle w = 23 \ meters[/tex]
[tex]\displaystyle \frac{dw}{dt} = 1 \ m/day[/tex]
Step 2: Differentiate
[Area of Rectangle] Product Rule: [tex]\displaystyle \frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]Step 3: Solve
[Rate] Substitute in variables [Derivative]: [tex]\displaystyle \frac{dA}{dt} = (10 \ m)(1 \ m/day) + (23 \ m)(4 \ m/day)[/tex][Rate] Multiply: [tex]\displaystyle \frac{dA}{dt} = 10 \ m^2/day + 92 \ m^2/day[/tex][Rate] Add: [tex]\displaystyle \frac{dA}{dt} = 102 \ m^2/day[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Implicit Differentiation
Book: College Calculus 10e