Answer:
a) A score of 65 is in the 79.67th percentile.
b) A score less than 70 is below the 95.25th percentile.
c) 20.33% of the scores are greater than 65.
d) 95.25% of scores are less than 70.
e) 45.25% of the scores are between 50 and 60.
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.
The mean is 60 and the standard deviation is 6.
This means that [tex]\mu = 60, \sigma = 6[/tex]
a. what is the percentile rank of the score 65?
This is the p-value of Z when X = 65.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{65 - 60}{6}[/tex]
[tex]Z = 0.83[/tex]
[tex]Z = 0.83[/tex] has a p-value of 0.7967.
Thus: A score of 65 is in the 79.67th percentile.
b. what is the percentile of the score less than 70?
Below the p-value of Z when X = 70. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 60}{6}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525.
Thus: A score less than 70 is below the 95.25th percentile.
c. what is percent of the scores is greater than 65?
The proportion is 1 subtracted by the p-value of Z when X = 65.
From item a, when X = 65, Z has a p-value of 0.7967
1 - 0.7967 = 0.2033
0.2033*100% = 20.33%
20.33% of the scores are greater than 65.
d. what percent of scores is less than 70?
The proportion is the p-value of Z when X = 70, which, from item b, is of 0.9525.
0.9525*100% = 95.25%
95.25% of scores are less than 70.
e. what percent of the score is between 50 and 60?
The proportion is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 50.
X = 60
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 60}{6}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5.
X = 50
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{50 - 60}{6}[/tex]
[tex]Z = -1.67[/tex]
[tex]Z = -1.67[/tex] has a p-value of 0.0475.
0.5 - 0.0475 = 0.4525
0.4525*100% = 45.25%
45.25% of the scores are between 50 and 60.
pls answer with explanation!
The manager of a small baseball stadium uses the equation y = 9000 -2.4x to model the relationship between y, the number of unfilled seats in the
stadium, and x, the number of cars in the parking lot. According to the model, how many cars will be in the parking lot when there are no unfilled seats in the stadium?
Answer:
3,750 cars.
Step-by-step explanation:
We are given that the equation:
[tex]y=9000-2.4x[/tex]
Models the relationsip between y, the number of unfilled seats in the stadium, and x, the number of cars in the parking lot.
We want to determine the number of cars in the parking lot when there are no unfilled seats in the stadium.
When there are no unfilled seats in the stadium, y = 0. Thus:
[tex]0=9000-2.4x[/tex]
Solve for x. Subtract 9000 from both sides:
[tex]-2.4x=-9000[/tex]
Divide both sides by -2.4:
[tex]x=3750[/tex]
So, there will be 3,750 cars in the parking lot when there are no unfilled seats in the stadium.
Find the area of the compound shape
Answer:
15 units²
Step-by-step explanation:
The figure is a trapezoid, whose area (A) is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height and b₁, b₂ the parallel bases
Here h = 3 , b₁ = 3, b₂ = 7 , then
A = [tex]\frac{1}{2}[/tex] × 3 × (3 + 7) = 1.5 × 10 = 15 units²
Key West, Florida to Seattle, Washington is 3,518 miles. If it
takes 51 hours to drive there, what is the average speed?
Answer:
69 miles/hour
Step-by-step explanation:
Average speed = Total distance travelled / Total time taken
Distance travelled = 3,518 miles
Time taken = 51 hours
Average speed = Total distance travelled / Total time taken
= 3,518 miles / 51 hours
= 68.980392156862
Approximately,
Average speed = 69 miles/hour
Answer: 69 miles/hour
Step-by-step explanation:
pls help w explanation!!
A town with a population of 5,000 is being divided
into two voting districts: District X and District Y.
The populations of the two districts must differ by no
more than 500 people. Which of the following
systems represents all possible values for the
population x of District X and the population y of
District Y?
A) x-y ≤ 500 and x+y =5,000 B) x-y =500 and x+y ≤ 5,000 C) -500 ≤ x - y ≤ 500 and x+ y =5,000 D) -250 ≤ x - y ≤ 250 and x + y = 5,000
Answer:
A is the Answer
Step-by-step explanation:
Since the population is being split up into 2 divisions out of 5,000.
This means District X and Y must add up 5000.
[tex]x + y = 5000[/tex]
District X and Y must differ no more than 500 people.
So this means that X and Y total people difference cannot be over 500 people. So the equation for this is
[tex]x - y \leqslant 500[/tex]
A shows this so A is the answer.
Find the coefficient of x^4 in the expansion of (x−9)^8
Please I need help!!
Answer:
459270
is the coefficientWhat is the capacity of a rectangular tank calculated to the nearest litre? Length: 85cm Width: 65cm Height: 30cm
Answer:
Capacity of the rectangular tank in litres is 165.75l
Step-by-step explanation:
Volume of the tank
[tex] = lbh[/tex]
[tex] = 85 \times 65 \times 30[/tex]
[tex] = 165750 {cm}^{3} [/tex]
Capacity of the tank
[tex] = 165750ml[/tex]
[tex] = 165.75l[/tex]
Calculate the sum of the integers from 52 to 108
Answer:
4560
Step-by-step explanation:
The radius of a circle is 6 cm. What is its diameter?
Answer:
Step-by-step explanation:
d=2r=2, 6 =12
diameter=12
Select the correct equations.
Identify all of the linear functions.
2x + 5y = 13
-Xº = 3y + 10
3(2x + y) = 14
y = 13 - 2x
2 = y + x
y = x+7
The a oranial price of a skate broad was reduced by 15 dollars .the new price is 49 dollars if p=the stakebroads oranail price in dollars what mathematical sentence expresses the information
a.49-p=15
b.15-p=49
c.15+p=49
d.p-15=49
Answer:
d. p - 15 = 49
Step-by-step explanation:
p = original price
The price was reduced by 15 dollars.
The new price is p - 15.
The new price is 49.
p - 15 = 49
Answer: d. p - 15 = 49
A menu at a local diner has 12 appetizers, 8 entrees, and 4 choice of desserts. How many different meal combinations are possible when you select one appetizer, one entrée, and one dessert from the menu?
Answer:
12* 8 * 4 = 384
Step-by-step explanation:
what is the measure of the angle formed by a side of the given angle and the given angle's bisector:27?
Answer:
Step-by-step explanation:
An angle is cut in half by the bisector.
Since the given angle is 172, its bisector creates 2 equal angles.
2x = 172 Divide both sides by 2
x = 172/2
x = 86
What is the length of leg s of the triangle below?
45
4-12
90°
45
Answer:
A
Step-by-step explanation:
Using the cosine ratio in the right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{s}{4\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
s × [tex]\sqrt{2}[/tex] = 4[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
s = 4 → A
a. 1.3
b. 9.6
c. 13
d. 1
Answer: I believe the answer would be 1.3
HOWEVER, if you do have to round to the nearest tenth then the answer would be 1
Step-by-step explanation:
2x+7 = 12x - 6
(subtract 2x from both sides)
7 = 10x - 6
(add 6 to both sides)
13 = 10x
(divide 13/10)
1.3 = x
PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS ANSWERRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
Answer:
ssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
¼. 1000
Step-by-step explanation:
25% = 25/100
= 1/4
Therefore,
25% of 1,000 is the same as
1/4. 1000
modrater give answer
if 27x = 45263514282 than find the value of 200x
═══════ღ❦ღ══╮
[tex]\boxed{ \sf{Answer}} [/tex]
↦ First find the value of x
[tex]27x = 45263514282 \\ x = \frac{45263514282}{27} \\ x = 1676426454.89[/tex]
↦ Now, find the value of 200x
[tex]x = 1676426454.89 \\ 200x = 200 \times 1676426454.89 \\ 200x = 335285290978[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Given that,
→ 27x = 45263514282
Then we have,
To find the required value of 200x.
Before that,
find the required value of x.
→ 27x = 45263514282
→ x = 45263514282/27
→ [x = 1676426454.89]
Now we can,
Solve for the value of 200x.
→ 200x
→ 200 × (x)
→ 200 × (1676426454.89)
→ 335285290978
Hence, 200x is 335285290978.
Anyone know the answer
Vertical ship up three and two to the right and the square root will flip
so options I is wrong
II is right
III is right
IV is wrong
THUS THE ANSWER IS OPTION II III
4
Help me with this problem
Answer:
The answer is 180 - 65
Step-by-step explanation:
We got 180, because that is the number of degree's in a line
so 180 - 65 is 115 degrees, that's your answer :)
if the slope of one of these perpendicular lines is -4/5 the slope of the other line is ____
Calculate the exact value of number one
Answer:
3/ 20
Step-by-step explanation:
4 1/5 × 1/3 - 1 1/4
= 21/5 × 1/3 - 1/5
= 7/5 - 5/4 = 28 - 25/ 20 = 3/20
= 3/20
Solve for x. Round to the nearest tenth, if necessary.
Answer:
9.4
Step-by-step explanation:
cos 32° = 8/x
x = 8/ cos 32°
= 8/ 0.8480
= 9.4
The value of the variable 'x' using the cosine formula will be 9.4 units.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The value of 'x' is given by the cosine of the angle ∠VWU. And the cosine of an angle is the ratio of the base and hypotenuse of the right-angle triangle. Then we have
cos 32° = 8 / x
x = 9.4
The value of the variable 'x' using the cosine formula will be 9.4 units.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ7
express 8cm as fraction of 2metres.
Answer:
4/200 is the answer
what is the length of KM ? no links . HELP
Answer:
40 units
Step-by-step explanation:
9x-5=7x+7
9x-7x=7+5
2x=12
x=6
6x+4
6(6)+4
36+4
40
2+2
f re e
points or whatever
Answer:
2+2 = 4
Step-by-step explanation:
Hope this helps.
Answer:
2 + 2 is 4 my guy
Step-by-step explanation:
thx for the points
Use the quadratic formula to find the solution to the quadratic equation given
below.
X^2-x+1/4=0
Answer:
[tex]\displaystyle x=\frac{-1}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]\displaystyle x=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]Step-by-step explanation:
Step 1: Define
Identify
x² + x + 1/4 = 0
↓ Compare to Standard Form
a = 1, b = 1, c = 1/4
Step 2: Solve for x
Substitute in variables [Quadratic Formula]: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1^2 - 4(1)(\frac{1}{4})}}{2(1)}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1 - 4(1)(\frac{1}{4})}}{2(1)}[/tex][√Radical] Multiply: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1 - 1}}{2(1)}[/tex][√Radical] Subtract: [tex]\displaystyle x=\frac{-1 \pm \sqrt{0}}{2(1)}[/tex][√Radical] Evaluate: [tex]\displaystyle x=\frac{-1 \pm 0}{2(1)}[/tex]Simplify: [tex]\displaystyle x=\frac{-1}{2(1)}[/tex]Multiply: [tex]\displaystyle x=\frac{-1}{2}[/tex]please tell me the answer to this, thanks
Step-by-step explanation:
Hey there!
The equation is: 2x + 3y -12=0 (i)
From the given equation;
Slope (m) = (-coeff.of X)/(coeff.of y)
m = -2/3
Now; Let the missing component be "a".
The equation also can be written in;
The equation also can be written in;(y-8) = -2/3(x-a) (using one point formula)
3y - 24 = -2x + 2a
2x +3y -2a -24 = 0………(ii)
Since both equation are made from same coordinates, equating equation (i) and (ii).
2x + 3y -12= 2x +3y -2a -24
Cancel like terms,
-2a - 24 = -12
or, -2a = 12
or, a = -6.
Therefore, the missing value is -6.
Check:
Putting the value "a" in equation (ii).
2x + 3y -2(-6) -24 = 0
or, 2x+3y -12 = 0 (which is equal to equation (i).
Hope it helps!
evaluate f(x)=1/4x for x=-5
option 1. -1/20
option 2. -1 1/4
option 3. 20
option 4. -4/5
Answer:
option 2. -1 1/4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 1/4x
Step 2: Evaluate
Substitute in x [Function f(x)]: f(-5) = 1/4(-5)Multiply: f(-5) = -5/4Simplify: f(-5) = -1 1/4What is the classification for this polynomial? X2y+3x3
Answer:
quadratic
Step-by-step explanation:
hope you got it
ANSWER PLZ ILL GIVE BRAINLIEST FIRST PERSON WHO ANSWER IM BEGGING
Answer:
The slope is 9.
Step-by-step explanation:
Answer:
Slope = 9
Step-by-step explanation:
Slope intercept form is y = mx +b (where m is slope and b is y intercept).
Here, m= 9 (slope) and b=0 (y intercept)
Vincent has $5 bills and $20 bills. He has a total of 24 bills and the total amount is $210. How many
$5 bills does he have?
