Probability of an event is the measure of its chance of occurrence. The event out of the listed events whose probability is 0.2957 is given by : Option C: [tex]P(0.25 \leq Z \leq 1.25)[/tex]
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z-score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p-value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
Using the z-table, we get the needed probabilities as:
Case 1:
[tex]P(-1.25 \leq Z \leq 0.25) = P(Z \leq 0.25) - P(Z \leq -1.25) \approx 0.5987 - 0.1056 = 0.4931[/tex]
Case 2:
[tex]P(-1.25 \leq Z \leq 0.75) = P(Z \leq 0.75) - P(Z \leq -1.25) \approx 0.7734- 0.1056=0.6678[/tex]
Case 3:
[tex]P(0.25 \leq Z \leq 1.25) = P(Z \leq 1.25) - P(Z \leq 0.25) \approx 0.8944 - 0.5987=0.2957[/tex]
Case 4:
[tex]P(0.75 \leq Z \leq 1.25) = P(Z \leq 1.25) - P(Z \leq 0.75) \approx 0.8944 - 0.7734 =0.1210[/tex]
Thus, the event out of the listed events whose probability is 0.2957 is given by : Option C: [tex]P(0.25 \leq Z \leq 1.25)[/tex]
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whats the answer for this!!
Evaluate the expression: 5x - 2w + t =
Answer:
Nothing further can be done with this topic
Step-by-step explanation:
Answer:
This answer is in its simplest form. There are no like terms in this equation.
what is the answer 1/5=2/10=5/
Answer:
2
5
Step-by-step explanation:
step 1 Multiply 1 by 2, and get 2, then we multiply 5 by 2 and get 10.
step 2 Since our denominators match, we can add the numerators.
Offering career academies in high schools has become more popular during the past 30 years because they help students prepare for work and postsecondary education. A principal at a large high school with a Science, Technology, Engineering, and Mathematics (STEM) Academy is interested in determining whether the status of a student is associated with level of participation in advanced placement (AP) courses. Student status is categorized as (1) STEM for students in the STEM program or (2) regular. A simple random sample of 200 students in the high school was taken and each student was asked two questions:
Are you in the STEM Academy?
In how many AP courses are you currently enrolled?
The responses of the 200 students are summarized in the table.
Level of Participation in Advanced Placement (AP) Courses Student Status
STEM Regular Total
No AP courses 17 31 48
One AP course 38 70 108
Two or more AP courses 20 24 44
Total 75 125 200
Part A: Calculate the proportion of STEM students who participate in at least one AP course and the proportion of regular students in the sample who participate in at least one AP course.
Part B: Is participating in two or more AP courses independent of student status?
Part C: Describe a method that could have been used to select a simple random sample of 200 students from the high school.
Part D: Is there any reason to believe there is bias in the method that you selected? Why or why not?
Part E: The responses of the 200 students are summarized in the segment bar graph shown.
Compare the distributions and what the graphs reveal about the association between level of participation in AP courses and student status among the 200 students in the sample. (5 points)
Part F: Do these data support the conjecture that student status is related to level of participation in AP courses? Give appropriate statistical evidence to support your conclusion. (10 points)
The proportion of STEM students who participate in at least one AP course is 0.19.
How to calculate proportionIt can be deduced that the proportion of STEM students who participate in at least one AP course will be:
= 38/200
= 0.19
The proportion of regular students in the sample who participate in at least one AP course will be:
= 70/200
= 0.35
Also, participating in two or more AP courses is independent of student status. This is because the p value is more than the 0.05.
A method that could have been used to select a simple random sample of 200 students from the high school is by writing all the registration numbers of the students in a container an randomly picking.
There is bias in the sampling because the convenience sampling is used. This doesn't give everyone an equal chance.
In conclusion, status is not related to level of participation in AP courses.
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Can someone help me please.
Step-by-step explanation:
2^x < 2x³ + 1 ?
that would mean
x < log2(2x³ + 1)
x < log2(2×(x³ + 1/2))
x < log2(2) + log2(x³ + 1/2)
x < 1 + log2(x³ + 1/2)
x - 1 < log2(x³ + 1/2)
for large x the "-1" and the "+ 1/2" are becoming relatively irrelevant for the inequality.
and the limes of this goes to
x < log2(x³)
which is not true for large x, as the logarithm turns into a very flat curve, while "x" just keeps growing with slope 1 and therefore outpaces the logarithm.
for x = 20 for example, 2^x is already way larger than 2x³.
the "cross-over" point is between x=11 and x=12.
from there on 2^x will quickly become much larger than 2x³ + 1.
subtract-5 from the additive inverse of 4
Answer:
-9
Step-by-step explanation:
The additive inverse of 4 is -4. Why? 4 + -4 = 0
-4 - 5 = -9
Answer:
i think -9
Step-by-step explanation:
Find the square root
Answer: the square root of 25 is 5
and also it’s an app called Desmos that finds the square root for you !
Work out m and c for the line: y − 3 x = 5
Answer:
Step-by-step explanation:
Write the equation in slope intercept form.
y = mx +c
y - 3x = 5
y = 3x + 5
m = 3 and c = 5
Find two values for x that make the inequality true.
-5x<2
giving brainliest answer quick
Answer: See below
Step-by-step explanation:
-5x<2 means -5x is less than 2, so a decimal under 0.4 (but not equal to) such as 0.3, 0.2, and 0.1 would all make the inequality true
Ex. Let x = 0.2
-5(0.2) < 2
1 < 2
1 is less than 2, so the inequality is true
help I dont get this at all
What is the sum of the expression below? (9c − 8d) + (2c − 6) + (− d + 3
Answer:
-1D
Step-by-step explanation:
1D + -4D + 2D = -1D
the midpoint of the segment as an ordered pair (5,8) (1,2)
Answer:
Midpoint :(3,5)Step-by-step explanation:
Mid point :
[tex] \frac{x_1 + x_2}{2} \: \frac{y_1 +y _2}{2} [/tex]
x1 = 5
y1 = 8
x2 = 1
y2 = 2
Midpoint :
[tex]( \frac{5 + 1}{2} \: \frac{8 + 2}{2} ) \\ ( \frac{6}{2} \: \frac{10}{2} )[/tex]
Simplify
[tex](3 \: 5)[/tex]
Find the lower quartile, upper Quartile and inter quartile range for the data : 9, 11, 15, 19, 17, 13, 7.
On arranging the given data in ascending order of their magnitudes, we get :
➙ 7 , 9 , 11 , 13 , 15 , 17 , 19
Clearly, n = 7, which is an odd number.
★ Lower Quartile (Q¹)
[tex] = > ( \frac{n + 1}{4} )term \: [/tex][tex] = > ( \frac{7 + 1}{4} ) \: term[/tex][tex] = > 2nd \: \: term \: = > 9[/tex]★ Upper Quartile (Q³)
[tex] = > ( \frac{3(7 + 1)}{4} ) \: term[/tex][tex] = > 6th \: term \: = > 17[/tex]★ Inter-Quartile range
⇒ Q³- Q¹
⇒ 17 - 9
⇒ 8
[tex]\huge\purple{✎﹏﹏﹏﹏﹏﹏﹏﹏﹏}[/tex]
During April it was recorded that there were 19 days when it rained, mostly cloudy on 6 days and sunny on 5 days inference in the future most of the days in the month of April will be rainy
Would you challenge or defend this 
Influence
Answer:
I would defend this
Step-by-step explanation:
This makes sense because April is the rainiest month of the year. It's even shown in the say that April showers bring May flowers.
What is the value of r in the equation?
Negative 1.5 (4 minus r) = negative 12
Answer: -4
Step-by-step explanation:
-1.5(4-r)=-12
Divide both sides by -1.5
4-r=8
-r=4
r=-4
Therefore, the value of r is -4
The hypotenuse of a 45°-45°-90° triangle measures 4 inches. What is the length of each leg?
Find the exact value of each.
Answer:
sin (20) = - 2[tex]\sqrt{10}[/tex]/ 7
Step-by-step explanation:
1- Find the trigonometric values
Hope this helps :)
Tell whether the table of values represents a linear function, an exponential function, or a quadratic funtion
Answer:
Step-by-step explanation:
if it is linear then it will be a straight line(gradient is the same)
if quadratic then curve(gradeint isnt the same)
y=mx+c
m=[y(2)-y(1)]/[x(2)-x(1)]
you can choose any 2 points from the table
m=2-0.4/0-1
m=-1.6
repeat but 2 different coordinates
m=0.4-0.08/-1--2==>-2.24
m=-2.24
different coordinate therefore quadratic
cant be exponential, because nothing is being raised to some power
Find the area of the composite figurep
Answer:
53.12 sq ft
Step-by-step explanation:
For triangle:
Base (b) = 8 ft
Height (h) = 7 ft
For semicircle:
Radius (r) = 8/2 = 4 ft
Area of the composite figure = Area of triangle + Area of semicircle.
[tex] = \frac{1}{2} bh + \frac{1}{2} \pi {r}^{2} \\ \\ = \frac{1}{2} (8)(7) + \frac{1}{2} (3.14)(4)^{2} \\ \\ = (4)(7) + (3.14)(8) \\ \\ = 28 + 25.12 \\ \\ = 53.12 \: {ft}^{2} [/tex]
REWARD: 50 points + Brainly to the best answer.
Check the file.
Answer:
a) No because the gallons and quarts of oil you and your friend bought is proportional.
b) Yes because the gallons and quarts of oil are no longer proportional.
c) 1 gallon of gasoline = $3.55
1 quart of oil = $5.00
Step-by-step explanation:
Let g = cost per gallon of gasoline
Let q = cost per quart of oil
a) Creating expressions from the given information:
10g + 2q = 45.50
5g + q = 22.75
From inspection, we can see that if we multiply the second equation by 2, it will give us the first equation. Therefore, they are proportional and we cannot determine the variables.
b) Creating expressions from the given information:
10g + 2q = 45.50
5g + q = 22.75
8g + 2q = 38.40
From inspection, we can see that the third equation is not proportional to equations 1 and 2. Therefore, we can use this equation with either of the other equations to determine the variables.
c)
Using equations 2 and 3 from the previous part (b):
5g + q = 22.75
8g + 2q = 38.40
Rewrite 5g + q = 22.75 to make q the subject:
⇒ q = 22.75 - 5g
Substitute into 8g + 2q = 38.40 and solve for g:
⇒ 8g + 2(22.75 - 5g) = 38.40
⇒ 8g + 45.5 - 10g = 38.40
⇒ 2g = 7.1
⇒ g = 3.55
Substitute found value for g into q = 22.75 - 5g and solve for q:
⇒ q = 22.75 - (5 x 3.55)
⇒ q = 5
Which of the following intervals includes only 4 data points?
1-6
0-5
1-4
1-5
Answer:
1-5
Step-by-step explanation:
5 - 1 = 4
Answer the questions below. Be sure to mark all answers that apply.
Answer:
Part A: Only 460 is divisible by 2
Part B: 385, and 460 are divisible by 5
Part C: Only 460 works for this one
10+10 in the best form
Answer:
20
Step-by-step explanation:
10+10=20
mod katie sampah kasih warn ke gw terus anj lu
9²+6²
ampe ga bisa dijawab bule iq nya 0
9² + 6²
→ 81 + 36
→ 117
Answer : 117
On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80). What are the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J? x = (StartFraction m Over m n EndFraction) (x 2 minus x 1) x 1 y = (StartFraction m Over m n EndFraction) (y 2 minus y 1) y 1 (40, 96) (85, 105) (80, 104) (96, 72).
The x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J is (85, 105).
Given
On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80).
CoordinatesThe coordinates point any point can be found by using the following formula.
[tex]\rm X=\dfrac{m}{m+n}(x_2-x_1)+x_1\\\\ Y=\dfrac{m}{m+n}(y_2-y_1)+y_1[/tex]
The x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J is;
[tex]\rm X=\dfrac{m}{m+n}(x_2-x_1)+x_1\\\\ X = \dfrac{3}{3+5}(-40-160)+160\\\\ X = 3 \times (-25)+160\\\\\X = -75+160\\\\ X = 85\\\\\ Y=\dfrac{m}{m+n}(y_2-y_1)+y_1\\\\ Y=\dfrac{3}{3+5}(80-120)+120\\\\Y =- 3\times 5 +`120\\\\Y=-15+120\\\\Y=105[/tex]
Hence, the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J is (85, 105).
To know more about co-ordinates click the link given below.
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Answer:
B
Step-by-step explanation:
Kiran's mother gets a restaurant bill for $25. She has a coupon for 15% off. After the discount is applied, she adds 20%
as a tip
What is the total after the discount and tip?
Answer:
the answer is 25.50
Step-by-step explanation:
so you multiply 25×.15 which gives 3.75.
you subtrct that from 25. 25-3.75=21.25.
then multiply 21.25 by .20. 21.25×.20=4.25
add that to 21.25 and you get 25.50
Answer:
25.50
Hope it helps
Are scales and slopes the same or different?
Answer:
same
Step-by-step explanation:
i just know i forgot where i know it
The 10 little piggies $600 per month on groceries. This is 15% of their
monthly budget. What is their monthly budget? *
Tim has a cat that cost $25, which is 20% more
than it cost last month...what did it cost last
month?
[tex][Hello,BrainlyUser][/tex]
Answer:
$20
Step-by-step explanation:
20% More = Markup
20% = .20
$25 * .20 = 5 ( Markup Price)
$25 - 5 = $20
Hence, last month the cost of the cat was $20.
[CloudBreeze]
(Due soon) Check each factorization to find the polynomial that does not have its GCF correctly factored out.
Choose the correct answer below.
12x^(2)+8x=4x(3x+2)
15x^(2)+12x+9=3(5x^(3)+4x+3)
4x^(4)+12x^(3)+18x^(2)=2x^(2)(2x^(2)+6x+9)
16x^(5)+24x^(2)=4x^(2)(4x^(3)+6)
Answer:
Option d
Step-by-step explanation:
Given options are ,
12x² + 8x = 4x( 3x + 2)Firstly find the GCF of 12x² and 8x .
The GCF of 12 and 8 is 4 , whereas the GCF of x² and x is x , So
→ GCF(12x² , 8x) = 4*x = 4x
Therefore the GCF is correctly factored out from the polynomial .
______________________________________
15x² + 12x + 9 = 3(5x² + 4x +3)Here GCF of 15x² , 12x and 9 , will be ;
GCF of 15,12 and 9 is 3 whereas of x² , x and 1 is 1
→ GCF = 3*1 = 3
Therefore the GCF is correctly factored out from the polynomial .
______________________________________
4x⁴+ 12x³ +18x² = 2x²(2x² + 6x + 9 )Here GCF of 4 , 12 and 18 is 2 and that of x⁴ , x³ and x² is x² . So ,
→ GCF = 2*x² = 2x²
Therefore the GCF is correctly factored out from the polynomial .
______________________________________
16x^5 + 24x² = 4x²( 4x³ + 6 )Here GCF of 16 and 24 is 8 and that of x^5 and x² is x² . So ,
→ GCF = 8*x² = 8x²
But they have factored out 4x² .
Therefore the GCF is " not " correctly factored out from the polynomial .
Option d is correct .
