Using the normal distribution, it is found that:
a) The 65th percentile is of 37.31.
b) The 90th percentile is of 42.68.
c) There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.
d) There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.
In a normal distribution 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]
It 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, which is the percentile of X.In this problem:
The mean is of 35, hence [tex]\mu = 35[/tex]The standard deviation is of 6, hence [tex]\sigma = 6[/tex]Question a:
The 65th percentile is X when Z has a p-value of 0.65, so X when Z = 0.385.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.385 = \frac{X - 35}{6}[/tex]
[tex]X - 35 = 0.385(6)[/tex]
[tex]X = 37.31[/tex]
The 65th percentile is of 37.31.
Question b:
The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 35}{6}[/tex]
[tex]X - 35 = 1.28(6)[/tex]
[tex]X = 42.68[/tex]
The 90th percentile is of 42.68.
Question c:
The probability is the p-value of Z when X = 38 subtracted by the p-value of Z when X = 28, hence:
X = 38:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{38 - 35}{6}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915.
X = 28:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 35}{6}[/tex]
[tex]Z = -1.17[/tex]
[tex]Z = -1.17[/tex] has a p-value of 0.121.
0.6915 - 0.121 = 0.5705.
There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.
Question d:
The probability is the p-value of Z when X = 44 subtracted by the p-value of Z when X = 41, hence:
X = 44:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{44 - 35}{6}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
X = 41:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{41 - 35}{6}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
0.9332 - 0.8413 = 0.0919
There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.
A similar problem is given at https://brainly.com/question/24663213
PLEASE HELP!! Which ordered pair corresponds to point A?
A) (-1,-2)
B) (2,1)
C) (-1,2)
D) (1,2)
Answer:
D) (1,2)
Step-by-step explanation:
This is because point A is identified as (1,2), giving it's plotted point
Jayla made 36 sugar cookies for the class party. Before you got to class the teachers ate 9 cookies, and then your classmates ate 1/3 of the remaining cookies. How many cookies are left for you to eat?
Answer:
9 cookies are left
Step-by-step explanation:
36 - 9 = 27
27 · 1/3 = 9
What is mode in math.
Answer:
the number that appears the most in a data set
Step-by-step explanation:
example
3,4,5,2,3,3,3,7,7
Mode:3
− 11/12 + p = 1/6
what does p =
Answer:
13/12
Step-by-step explanation:
p=1/6+11/12=(2+11)/12=13/12
Circle A has been enlarged to create circleA prime . The picture below shows the diameters of both circles.
Based on the information in the picture, what scale factor was used to create circle A prime ?
Answer:
Step-by-step explanation:
9514 1404 393
Answer:
5/2
Step-by-step explanation:
The ratio of the diameters is equal to the scale factor:
sf = (15 in)/(6 in) = 5/2
The scale factor used to create circle A' is 5/2.
At the Lincoln County Animal Shelter, there are currently 6 dogs and 4 cats. Write the ratio of cats to dogs in simplest form as a fraction.
Answer:
2/3
Step-by-step explanation:
4 cats / 6 dogs = 2/3
simplify by dividing by 2
How many bagels can you buy for $50?
Answer: about 120??
Step-by-step explanation: pls leave a thanks if helped <3
Answer: 120 bagels
Step-by-step explanation:
$50/$5 = 10 dozens of bagels
10 dozens x 12 = 120 bagels in total
What is the slope of the line that passes through the points (9, 1) and (17, 2)
A: 8/15
B: 8/1
C: 1/8
D: 15/8
Answer:
C
Step-by-step explanation:
Slope of a line that goes trough the points (x1=9, y1=1) and (x2=17, y2=2)
m= (y2-y1)/(x2-x1) = (2-1) / (17-9) = 1/8
Can someone help me with this question, please explain your answer. :D
Answer:
21/8 yards
Step-by-step explanation:
If Sarah wants to make her own costume she will need 21/8 yards of yarn.
To get this, you multiply 2 by 8 and get 16.
Next, you will add 5 onto 16 and get 21.
Keep your 21 and put is as your numerator.
Now take your 8 and put it as your denominator.
Solve for the value of n
Answer:
n = 8
Step-by-step explanation:
Both given angles are verticale angles therefore they are congruent, so;
9n = 8n + 8
(9n - 8n) = 8
n = 8
Hope this helps!
Point P has coordinates (-2.5,3). Point Q is a reflection of point P across the x-axis. What are the coordinates of the point Q? Which quardrant is it in?
Answer:
Q = (-2.5, -3), quadrant 3
Step-by-step explanation:
Reflection across the x-axis changes the sign of the y-coordinate.
Q = (-2.5, -3)
With two negative coordinates, point Q is in Quadrant III.
_____
Additional comment
Point P has a negative x-coordinate and a positive y-coordinate, so is located northwest of the origin in Quadrant II. The quadrant that is southwest of the origin is Quadrant III, which is where points in Quadrant II are reflected to when they are reflected across the x-axis.
Solve for g.
7 − –3g = 13
g =
Answer: g=2
Step-by-step explanation:
Remove the parentheses
7- (-3)g=13
Move the constant to the right
7+3g=13
Calculate
3g=13-7
Divide both sides
39=6
Answer:
g=2
n a school of 600, a survey was conducted with 10% of the population. The survey was conducted to narrow the choices for the new mascot. What was the frequency of Bears, if the following was the result of the survey?
Bears=22
Panthers=15
Beavers=2
Jaguars=21
Answer:
37%
Step-by-step explanation:
10% of 600 students is 60 students surveyed and 22 people chose bears. So to find the percent out of 60 just divide 22 by 60
22/60=.36666
move the decimal to get about 37%
hope this helps
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,699 was collected on the sale of 1,179 tickets. How many of each type of ticket were sold?
Answer:
Step-by-step explanation:
The Answer 3182121
Find and intercept the slope of this line.
Step-by-step explanation:
the 4th answer option is correct.
the slope of the line is expressed as the ratio
y coordinate change / x coordinate change
when going from one point to the other.
You have 2\3 of a pizza left from yesterday. You divide it into 4 equal pieces. What fraction of the pizza is each piece?
====================================================
Explanation:
Let's say for example this pizza had 6 slices to start with. Two-thirds of this is (2/3)*12 = 4 slices. So you have 4 slices left over from yesterday. Then let's say you hand one slice to each of your four friends. Each friend would have 1/6 of the original pizza.
The pic of the question is down below
Show all working
Answer:
GF ≈ 11.2HD ≈4.3∠HDE ≈68.8°Step-by-step explanation:
The relevant trig relations are ...
Tan = Opposite/Adjacent
Sin = Opposite/Hypotenuse
These tell us ...
tan(43°) = GH/DG
GH = DG·tan(43°) = (12 cm)·tan(43°) ≈ 11.2 cm
and ...
sin(HDE) = EH/ED = (11.2 cm)/(12 cm)
∠HDE = arcsin(11.2/12) ≈ 68.8°
The length HD can be found from ...
tan(68.8°) = HE/HD
HD = HE/tan(68.8°) = (11.2 cm)/tan(68.8°) ≈ 4.3 cm
_____
Additional comments
The values shown in the solution here are rounded according to the problem statement. The values actually used in the calculations are the full-precision calculator values. Rounding is only done on the final answers.
I need help with this also I had was to repost it again because someone deleted it
Answer: 8:05
Step-by-step explanation:
Answer: 8:05
Step-by-step explanation:
can you guys help me
5x3+7=50? this is g.e.m.d.a.s
Answer:
It's 27
Step-by-step explanation:
5x3 = 15 + 7 =27
What is an equation in point-slope form of the line shown in the graph, using the point (1, 5)?
Answer:
The point-slope form is
y
+
6
=
1
5
(
x
−
4
)
or
y
+
5
=
1
5
(
x
−
9
)
, depending on which point you use. If you solve for
y
to get the slope-intercept form, both equations will convert to
y
=
1
5
x
−
34
5
Step-by-step explanation:
Aubree is making different shades of pink paint to use for an art project. A batch of dark pink uses 2.5 cups of red paint and 1.5 cups of white paint. A batch of light pink uses 0.75 cup of red paint with 1.25 cups of white paint. She begins with a gallon of red and a gallon of white paint. How much of each color paint will she have left if she makes a batch of dark pink and light pink every day for a week?
Answer:
Cups of red paint for a batch of dark pink - 2.5
Number of gallons of red paint that she starts with - 1
Cups of red paint for a batch of light pink - i did not get that one
Step-by-step explanation:
Main St. Fair thinks your wheel is broken – the 3 outcomes (Big, Small, and No prize) are not coming out exactly equal. Your wheel maker says that’s normal – the numbers should be close to each other but probably not exactly equal. Who do you think is right? Explain.
Answer:
Step-by-step explanation:
(Fill in the blank)
If the triangle is equilateral, find the value of x.
(9x - 3)
x = _#
(numerical response only)
Answer:
x>1/3
Step-by-step explanation:
unless you are missing something else on the question.
equilateral means all sides are the same
so if one side is 9x-3 the other sides should also be 9x-3
9x-3=0
9x=3
x=1/3
The volume of a cylinder closed at the one end is 1056cm cube. If its height is 21cm, and the radius is 4, find the total surface area
Answer:
578 cm^2
Step-by-step explanation:
The surface area is given by one circle of radius 4 (the other is missing!), plus a "rectangle" (the lateral surface) of sides 21 and [tex]2\pi \times 4[/tex] (the length of the circumference at the base). Adding them up we get:[tex]\pi \times4^2 + 21\times 2\pi\times4 = 184\pi \approx 578 cm^2[/tex]
in the equation f(x) = 5x + 6,6 is called?
Answer:
the y-intercept
Step-by-step explanation:
Step-by-step explanation:
Since f(x) = 5x + 6 is in the slope-intercept form (y = mx + c), then that would make 6 the y-intercept.
Can I have help please
Step-by-step explanation:
the gradient describes the slope or steepness of the line joining two points.
it is expressed as the ratio of
y coordinate change / x coordinate change
so, we need to find 2 good points (typical with integer coordinates) per line to see how y and x changes between them.
for A I see e.g. (1, 1) and (2, 4)
for B I see e.g. (0, 5) and (1, 1)
so, for A
x changes by +1 (from 1 to 2)
y changes by +3 (from 1 to 4)
the slope or gradient of A : 3/1 = 3
and for B
x changes by +1 (from 0 to 1)
y changes by -4 (from 5 to 1)
the slope or gradient of B : -4/1 = -4
Write an equation for the line in slope intercept form
Answer:
y=4x+2
Step-by-step explanation:
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Let B be the basis of P3 consisting of the Hermite polynomials in Exercise 21, and let p.t / D 7 ! 12t ! 8t 2 C 12t 3. Find the coordinate vector of p relative to B.
To calculate the relative vector of B we have to:
[tex]P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right][/tex]
The coordenates of:
[tex]p(t)= 12t^3-8t^2-12t+7[/tex], with respect to B satisfy:
[tex]C_1(1)+C_2(2t)+C_3(-2+4t^2)+C_4(-12t+8t^3)= 7-12t-8t^2+12t^3[/tex]
Equating coefficients of like powers of t produces the system of equation:
[tex]\left \{ {C_1-2C_3=7} \atop {2C_2-12C_4=-12} \right. \\\left \{ {{4C_3=-8} \atop {8C_4=12}} \right.[/tex]
After solving this system, we have to:
[tex]C_1=3\\C_2= 3\\C_3= -2\\C_4= \frac{3}{2}[/tex]
And the result is:
[tex]P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right][/tex]
Learn more: brainly.com/question/16850761
-
1.) -x + 5y = 49
X =
X - 4y = - 39
-
=
Answer: (1,10)
Step-by-step explanation:
Assuming these are the correctly written equations:
-x + 5y = 49, and
x - 4y = -39
I'll rewrite them:
5y = x + 49
y = (1/5)x + (49/5)
-4y = -x -39
y = (1/4)x + (39/4)
=====
I'll assume the question is to find the point these two lines intersect (?).
See the attached graph. They intersect at (1,10).
identify an equation in point-slope form for the line perpendicular to y = 2x + 8 that passes through (-3,9)
Answer:
y - 9 = m(x + 3)
Step-by-step explanation:
Given a line whose slope is m, the slope of a new line that is perpendicular to the given line is the negative reciprocal of m: -1/m
Given y = 2x + 8, we see that the slope is 2 and figure that the negative reciprocal of that is -1/2. This is the slope of the desired perpendicular line.
We can write the equation of this perpendicular line most easily by using the point-slope form y - k = m(x - h), where (h, k) represents the point:
y - 9 = m(x + 3)
