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.
what are evidence that the himalayas mountains are still rising
Answer:
The Himalayas are still rising by more than 1 cm per year as India continues to move northwards into Asia, which explains the occurrence of shallow focus earthquakes in the region today. However the forces of weathering and erosion are lowering the Himalayas at about the same rate.
Step-by-step explanation:
we can tell that the himalayas are still rising because of the movement of india northwards into asia,so the more india moves to the north the more the himalayas rise by more than 1cm.
Which polynomial function has a root of 1 with
multiplicity 2 and a root of 6 with multiplicity 1?
Of(x) = (x - 1)(x – 6)
O f(x) = 2(x - 1)(x – 6)
O f(x) = (x - 1)(x - 1)(x – 6)
O f(x) = (x - 1)(x - 6)(x-6)
Answer:
The 3rd:
f(x) = (x - 1)(x - 1)(x – 6)
Step-by-step explanation:
Its roots are the x-values for which f(x)=0, that are:
x1=1
x2=1
x3=6
If f(x) = 6x - 4. what is f(x) when x = 8?
Answer:
44
Step-by-step explanation:
* means multiply
put 8 where the x is
6 * 8 - 4
48 - 4
44
someone help me for this algebra task please
answer needed fast! 15 points! in how many ways can 85 be written as the sum of 2 primes
What is the answer to this? Also, please provide an explanation.
Answer:
3 to the power of 4 equals 81 times 3 equals 243
Step-by-step explanation:
These dot plots show the weights (in kilograms) from a sample of leopards
and tigers.
Leopards
000
0000+
000000
00018
00
20
40
60
80
160
180
200
220
100 120 140
Weight (kg)
Tigers
000
2000
000000
2000
ooe
O
20
40
60
80
160
180
200
220
100 120 140
Weight (kg)
What are the differences between the centers and spreads of these
distributions?
Select two choices: one for the centers and one for the spreads.
No
Answer: A.Spreads: The weights of the tigers are more spread out.
B.Centers:The leopards have a lower median weight than the tigers
Step-by-step explanation:
On analyzing the dot plots, we find that the weight of Leopards are more spread out and the weight of Leopards has a lower median than Tiger.
What is median?Median is a statistical measure that determines the middle value of a dataset listed in ascending order. The measure divides the lower half from the higher half of the dataset.
Median of Weight of Leopard = 50 kg
Median of Weight of Tiger = 125 kg
This implies that the Leopards have a lower median weight than Tigers.
What is spread of data?
Spread describes the variation of the data. One of the measures of spread is range.
Range of weight of Leopards= 40 kg
Range of weight of Tigers = 90 kg
This implies that the weight of Tigers are more spread out.
Learn more about median here
brainly.com/question/21396105
#SPJ2
does anyone understand this? will give Brainly for correct answer
Answer:
[tex]x_{1}[/tex] = [tex]\frac{\pi }{6}[/tex] and [tex]x_{2}[/tex] = [tex]\frac{5\pi }{6}[/tex]
Step-by-step explanation:
Guys please help me if you don’t mind
Step-by-step explanation:
Step 1: The factors of -60 that add up to -11 are -15 and 4.
Step 2:
[tex]( 6{x}^{2} - 15x)( 4x - 10)[/tex]
Step 3:
[tex]3x(2x - 5) + 2(2x - 5)[/tex]
[tex](3x + 2)(2x - 5) [/tex]
In the equation 17x2 = 12x, the value of c is:
O
0 12
O 17
Answer:
ok ok ok ok ok ok ok
Step-by-step explanation:
Which of the following is equal to 5^1/3?
A. ^3√5 B. 5^3 C. √5•3 D. √5
Answer:
A. ^3√5 is the answer.
Step-by-step explanation:
5^( 1 / 3 ) = ^3√5
An angle in standard position measures 5п 8 radians. In which quadrant does the terminal side of this angle lie? O Quadrant I II Quadrant Quadrant IIT Quadrant IV
Answer:
I've attached a picture of a unit circle with the quadrant labeled.
Calculate the degree of 5п 8 radians:
[tex]\frac{5\pi }{8} =\frac{5*180}{8} =\frac{900}{8} =112.5[/tex]
Locate the general location of 112.5° on the unit circle:
It's between 120°([tex]\frac{2\pi }{3}[/tex]) and 90°([tex]\frac{\pi }{2}[/tex]).
Find the quadrant it lies in:
Quadrant II
The triangle below is isosceles. Find the length of side x in simplest radical form with a rational denominator.
Solution given:
it is a right angled isosceles triangle
so
perpendicular [p]=base[b]=5
hypotenuse [h]=x
we have
by using Pythagoras law
p²+b²=h²
5²+5²=h²
50=h²
h=[tex]\sqrt{50}[/tex]
x=[tex]\bold{5\sqrt{2}}[/tex]
What is the y-intercept of the line 10x - 5y = 40
10x - 5y = 40
-5y = -10x + 40 || : (-5)
y = 2x - 8
20 POINTS
Find the volume of the prism.
Answer:
v=1/2(13.1+25.4)(17)(15)
v=1/2(38.5)(255)
v=4,908.7 ft³
OAmalOHopeO
(100 points)
4. MIke divided the group into 5 groups. If there were 28 people in each group how big was the original group?
a. What are they asking for? __________________
b. identify all the necessary numbers. __________________
c. write the equation or problem in numeric form. ______________
d. solve the math. ______________________________
e.write the answer. ______________________________
5. If he difference is 589 and the subtrahend is 339,what is the minuend?
a. What are they asking for? __________________
b. identify all the necessary numbers. __________________
c. write the equation or problem in numeric form. ______________
d. solve the math. ______________________________
e.write the answer. ______________________________
6. If the quotient is 17 and the dividend 765, what is the divisor?
a. What are they asking for? __________________
b. identify all the necessary numbers. __________________
c. write the equation or problem in numeric form. ______________
d. solve the math. ______________________________
e.write the answer. ______________________________
4. MIke divided the group into 5 groups. If there were 28 people in each group how big was the original group?
a. What are they asking for?
how big was the original group?
b. identify all the necessary numbers.
28,5
c. write the equation or problem in numeric form.
x=28*5
d. solve the math.
x=140
e.write the answer
. the original group contains 140 people.
5. If he difference is 589 and the subtrahend is 339,what is the minuend?
a. What are they asking for?
what is the minuend?
b. identify all the necessary numbers.
589,339
c. write the equation or problem in numeric form.
x=589-339
d. solve the math.
x=250
e.write the answer.
minuend=250
6. If the quotient is 17 and the dividend 765, what is the divisor?
a. What are they asking for?
what is the divisor?
b. identify all the necessary numbers.
17,765
c. write the equation or problem in numeric form.
x=765/17
d. solve the math.
x=45
e.write the answer.
divisor is 45.
4. Solution
a. How big was the original group?
b. 28 and 5
c. x = 28×5
d. x = 140
e. There are 140 people in original group.
5. Solution
a. What is the minuend?
b. 589 and 339
c. x = 589-339
d. x = 250
e. The minuend is 250.
6. Solution
a. What is the divisor?
b. 17 and 765
c. x = 765/17
d. x = 45
e. Hence, 45 is the divisor.
Determine the area of the triangle.
96.0 square units
16.9 square units
192.0 square units
97.5 square units
Answer:
A. 96.0 square units
Step-by-step explanation:
The formula for the area of a triangle when we know the side length of two sides and the measure of an included angle of a triangle is given as:
A = ½*a*b*Sin C
Where,
a = 13
b = 15
C = 80°
Plug in the values into the formula
A = ½*13*15*Sin 80
A = 96.0187559
A = 96.0 square units (nearest tenth)
Answer:A
Step-by-step explanation: I took the test
modrater give me answer
if 2x- 35273 = 5361925 than find the value of 1x
Answer:
[tex]2x - 35273 = 5361925 \\ 2x = 5361925 + 35273 \\ 2x = 5397198 \\ x = \frac{5397198}{2} \\ x = 2698599[/tex]
[tex]\displaystyle\ 2x-35273=5361925\\\\2x=53\underline{61925}+\underline{35273} \\\\2x=5397198\\\\\\x=\frac{5397198}{2} =2698599\\\\\underline{x=2698599\qquad }\\\\2\cdot 2698599-35273=5361925\\\\5397198-35273=5361925\\\\5361925=5361925[/tex]
Sam studied guinea pigs for his science fair project. He found that the amount of weight the guinea pigs gained varied directly with the number of calories they consumed.
The guinea pigs gained 1 ounce for every additional 218 calories in their diet. How many additional ounces would they gain if their diet was increased by 1,090 calories? Let W represent the weight in ounces, and let C represent the number of calories.
Answer: C= 1,090 and the W= 5.
Priya has planted a garden shaped like a right triangle. She knows that one leg of the triangle is 11 meters long and that the angle formed by that leg and the hypotenuse is 50 degrees . If Priya wants to build a fence around her garden. How many meters will she need? Round to the nearest hundredth and you must submit work to receive credit.
Answer:
She will need 41.22 meters.
Step-by-step explanation:
She knows that one leg of the triangle is 11 meters long and that the angle formed by that leg and the hypotenuse is 50 degrees .
The leg is adjacent to the hypothenuse. We know that the cosine of an angle [tex]\theta[/tex] is given by:
[tex]\cos{\theta} = \frac{l}{h}[/tex]
In which l is the length of the adjacent side and h is the hypothenuse.
Considering that we have [tex]\theta = 50, l = 11[/tex], we can find the hypothenuse.
Looking at a calculator, the cosine of 50 degrees is 0.6428.
So
[tex]0.6428 = \frac{11}{h}[/tex]
[tex]0.6428h = 11[/tex]
[tex]h = \frac{11}{0.6428}[/tex]
[tex]h = 17.11[/tex]
The other leg:
In a right triangle, with legs [tex]l_1[/tex] and [tex]l_2[/tex], and hypothenuse h, the pythagorean theorem states that:
[tex]l_1^2 + l_2^2 = h^2[/tex]
We already have one of the legs and the hypothenuse, so:
[tex]11^2 + l^2 = 17.11^2[/tex]
[tex]l^2 = 17.11^2 - 11^2[/tex]
[tex]l = \sqrt{17.11^2 - 11^2}[/tex]
[tex]l = 13.11[/tex]
How many meters will she need?
This is the perimeter of the garden, which is the sum of its dimensions, of 11 meters, 13.11 meters and 17.11 meters. So
[tex]P = 11 + 13.11 + 17.11 = 41.22[/tex]
She will need 41.22 meters.
S.p=315 loss percent =10% c.p=rs=xc.p=?
Given:
S.P. = 315
Loss percent = 10%
To find:
The C.P.
Solution:
Let x be the C.P.
We have,
S.P. = 315
Loss percent = 10%
[tex]S.P.=C.P.-10\%\text{ of }C.P[/tex]
[tex]315=x-\dfrac{10}{100}x[/tex]
[tex]315=x-0.1x[/tex]
[tex]315=0.9x[/tex]
Divide both sides by 0.9.
[tex]\dfrac{315}{0.9}=x[/tex]
[tex]350=x[/tex]
Therefore, the cost price (C.P.) is 350.
HELP ASAP BRAINLIST AND 10POIMTS AND 5 STAR AND A THANKS BUT IF CORRECT
Answer:
V = 20 cm^3
Step-by-step explanation:
The volume of a prism is
V = l*w*h
V = 6*5*2/3
V = 20 cm^3
Step-by-step explanation:
hope it helps you.........
The math club sold 15 novelty erasers and made a profit of
$7. After another week, the club had sold a total of 25
erasers and made a profit of $15. Which equation models
the total profit, y, based on the number of erasers sold, X?
A. y - 15 = 0.8(x - 7)
B. y - 15 = 1.25(x - 7)
C. y - 7 = 0.8(x - 15)
D. y - 7 = 1.25(x - 15)
Whoever helps me I will mark brainliest.
Answer:
Option no. D is right. Because the congruence presented is more congruent
Question 2 of 10
If f(x) x/2-3 and g(x) = 4x^2 + x - 4, find (f + g)(x).
A. 4x+3x-7
B. 4x2+x-1
C. 66²-7
D. 4x + x-
Answer:
B
Step-by-step explanation:
pls help and explain answer!!
At a certain point in time, a physicist measures the
speed of a falling object to be 17.6 feet per second.
What is the equivalent speed in miles per hour?
(5280 feet = 1 mile)
Answer:
0.003 miles per hour
Step-by-step explanation:
Well since 5280 feet gives 1 mile den convert 17.6 feet per sec to miles per hr
plzzz help
thank u for those who help
Answer:
SAS
Step-by-step explanation:
As per the given diagram, the following facts are evident.
(BR) = (CR), Both sides have two small orange lines on them. This shows that these sides are congruent.
(<B) = (<C), this is shown by the box around both angles, indicating that both angles have a measure of (90) degrees.
(AB) = (AC), Both sides have one small orange line on them. This indicates that these sides are congruent to each other.
Therefore, the sides are congruent by the theorem (SAS); side-angle-side, congruence.
subtract 111 from 11010
Answer : I think it is 10899
what are the x-coordinates of the solutions? Choose all that apply.
a. -2
b. 1
c. -1
d. 0
Answer:
a. -2
c. -1
Step-by-step explanation:
these are the only values for x, where the 2 equations deliver the same y value.
in case of a. y = -2×-2 - 1 = 4 - 1 = 3
and y = 3¹ = 3
c. y = -2×-1 - 1 = 2 - 1 = 1
y = 3⁰ = 1
Write the trigonometric expression in terms of sine and cosine, and then simplify.
tan θ/(sec θ − cos θ)
Answer:
[tex]\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta} = \frac{1}{\sin\theta} = \csc\theta[/tex]
Step-by-step explanation:
We have the expression:
[tex]\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta}[/tex]
And we want to write the expression in terms of sine and cosine and simplify.
Thus, let tanθ = sinθ / cosθ and secθ = 1 / cosθ. Substitute:
[tex]=\displaystyle \frac{\dfrac{\sin\theta}{\cos\theta}}{\dfrac{1}{\cos\theta}-\cos\theta}[/tex]
Multiply both layers by cosθ:
[tex]=\displaystyle \frac{\left(\dfrac{\sin\theta}{\cos\theta}\right)\cdot \cos\theta}{\left(\dfrac{1}{\cos\theta}-\cos\theta\right)\cdot \cos\theta}[/tex]
Distribute:
[tex]\displaystyle =\frac{\sin\theta}{1-\cos^2\theta}[/tex]
Recall from the Pythagorean Theorem that sin²θ + cos²θ = 1. Hence, 1 - cos²θ = sin²θ. Substitute and simplify:
[tex]\displaystyle =\frac{\sin\theta}{\sin^2\theta} \\ \\ =\frac{1}{\sin\theta}[/tex]
We can convert this to cosecant if we wish.