Answer:
If not treated, the probability of at least 75 percent of 1400 students being infected is approximately equal to 1.
Step-by-step explanation:
Let Y be the no. of infections
The number of students who have been exposed to whooping cough is as follows:
n = 1400
n = 1400 and p = 0.8
nm = 1400 x 0.8
nm = 1120
n(1-m) = 1400 x (1-0.8)
n(1-m) = 280
Here,
Both nm and n(1-m) are greater than or equal to 10. So, we use normal distribution.
The mean and standard deviation of number of new infections is:
u = np
u =1400 x 0.8
u = 1120 = mean
SD = Standard Deviation
SD = [tex]\sqrt{1120(1-0.8)}[/tex]
SD = 14.966
The number of infections is distributed in an approximately normal way
N(1120,14.966)
75% of 1400 means 0.75 x 1400 = 1050
So,
Probability required.
P (Y[tex]\geq[/tex] 1050) = P (Y [tex]\geq[/tex] 1050 - 0.5) (Continuity Correction)
P (Y[tex]\geq[/tex] 1050) = P([tex]\frac{Y - u}{SD} \geq \frac{1049.5 - 1120}{14.966}[/tex])
P (Y[tex]\geq[/tex] 1050) = P(Z [tex]\geq[/tex] -4.71)
P (Y[tex]\geq[/tex] 1050) = P(Z [tex]\leq[/tex] 4.71)
Using the z table:
P (Y[tex]\geq[/tex] 1050) ≈ 1
Hence,
If not treated, the probability of at least 75 percent of 1400 students being infected is approximately equal to 1.
A researcher is trying to show evidence for extra-sensory perception (ESP). She performs a test in which the subject is asked 10 yes or no question whose answer depends on information which the subject has not observed. Suppose that for each test, in the absence of ESP, the subject gets each question correct with 50% probability a) In the absence of ESP, what is the probability that a given test subject will answer at least 8 out of 10 questions correctly
Answer:
The answer is "0.0547".
Step-by-step explanation:
[tex]P(Correct) = 0.50\\\\n = 10\\\\x = 8[/tex]
Using the binomial distribution:
[tex]\to P(x,n) = n_{C}_x \times p^x \times (1-p)^{(n-1)}\\\\\to P(x \geq 8) = 1 - P( \leq 7)[/tex]
Calculating the excel formula:
[tex]=BINOM.DIST(7,10,0.50,TRUE)[/tex]
[tex]\to P(x \geq 8) = 1 - 0.9453\\\\ \to P(x \geq 8) = 0.0547[/tex]
Suppose f is a linear function such that f(4)= 8 and f(9)= 1. Find the equation for f.
Find the area of the trapezoid.
Recall : (b + b) h
Answer:
36 Sq cm
Step-by-step explanation:
Area of the trapezoid
[tex] = \frac{1}{2} \{8 + (4 + 8 + 4) \} 3\\ \\ = \frac{1}{2} \{8 + 16 \} 3\\ \\ = \frac{1}{2} \times 24 \times 3\\ \\ = 12 \times 3 \\ \\ = 36 \: {cm}^{2} [/tex]
9 ft. 15 ft The volume of the figure is cubic feet. 15 ft. 15 ft
Answer:
4,050 cubic feet
Step-by-step explanation:
The figure is made up of a square pyramid and cube
Therefore:
Volume of the figure = volume of the square pyramid + volume of the cube
✔️Volume of the square pyramid = ⅓*a²h
a = 15 ft
h = 9 ft
Volume of square pyramid = ⅓*15²*9 = 675 ft³
✔️Volume of the cube = s³
s = 15 ft
Volume of the cube = 15³ = 3,375 ft³
✔️Volume of the figure = 675 + 3,375 = 4,050 cubic feet
The square pool was turned into a rectangular one and it's area was enlarged by a factor of 5 by enlarging one side of the pool by 3 meters and the other side by 14. What are the new dimensions of the pool?
[tex] \boxed{ \tt{the \: dimensions \: are : }}\\ \boxed{ \tt{b = 9 \: meters} }\\ \boxed{ \tt{l = 20 \: meters}}[/tex]
[tex]5 {s}^{2} = (3 + s) \times (14 + s) \\ 5 {s}^{2} = {s}^{2} + 17s + 42 \\ {4s}^{2} - 17s - 42 = 0 \\ s = \frac{ - ( - 17) + \sqrt{ {( - 17)}^{2} - 4(4)(42)} }{2(4)} \\ s = \frac{17 + 31}{8} \\ s = 6 \\ hence \to \:the \: dimensions \: are : \\ b = s + 3 = 6 + 3 = 9 \: meters \\ l = s + 14 = 6 + 14 = 20 \: meters[/tex]
The new dimensions of the pool are; Width = 9 and Length = 20.
What is rectangular figure?A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.
It is given that the square pool was turned into a rectangular one and it's area was enlarged by a factor of 5 by enlarging one side of the pool by 3 meters and the other side by 14.
[tex]5s^2 = (3+s)(14 +s)\\\\5s^2 =s^2+ 17s + 42\\\\4s^2 - 17s - 42 = 0\\\\[/tex]
The root of the expression;
[tex]s = \dfrac{-(-17) + \sqrt{-17^2 - 4(4)(42)} }{2(4)} \\\\s = 6[/tex]
The dimensions are;
Width = 3 + s = 9
Length = 14 + s = 20
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Find the measure of 46.
t
56°/1249
46
te
s6 = [?]
Answer:
56°
Step-by-step explanation:
1st reason= alternate angles.
2nd reason= 124 and angle 6 is co-interior angles which means that little are shoudk adds up to 180.
180-124=56
Need help :C
A bakery in Hong Kong regularly orders carton of cranberries from Australia. The net weight (in ounces) of
cranberries of a random sample of 20 cartons were as follow:
160 170 170 190 210 240 240 240 270 280
290 290 300 420 500 520 530 610 630 650
(c) The bakery orders the cranberries from Australia with currency exchange rate of AUD 1 to HKD 5.8.
For each ounce of Australia cranberries costs AUD 2 and the fixed shipping fee of each carton is HKD
80. Find the mean, standard deviation, range, and third quartile of the payment (in HKD) of ordering a
carton of cranberries from Australia to Hong Kong.
Answer:
i) Mean = 1933.1817
ii) Range = 5684
iii) Third quartile = 6054
Step-by-step explanation:
Given data :
currency exchange rate : 1 AUD = 5.8 HKD
cost of each ounce = 2 AUD
Fixed shipping cost for each carton = 80 HKD
number of cartons = 20
next determine the total cost of the 20 cartons in HKD
= ∑(weight in ounce * cost of each ounce *exchange rate) +fixed shipping cost
= ∑ ( 160*2*5.8 + 80 ) + -------------- + (650 *2*5.8 + 80 ) ----------------- ( 1 )
= 81756 HKD
i) find the mean value ( X )
= Total cost / number of cartons
= 81756 / 20 = 4087.8
ii) Find the standard deviation
= [tex]\sqrt{\frac{(1936-4087.8)^2+-----+(7620-4087.8)^2}{20-1} }[/tex] note: std = √∑(xi-X )^2 / (n-1)
= 1933.1817
iii) Find the range
Range = highest cost - lowest cost ( values gotten from equation 1 )
= 7650 - 1936
= 5684
iv) Determine the third quartile
third quartile = 6054
attached below is the detailed solution
Elena went to a sporting goods store that
was having a sale. She bought a tennis
racket and 3 cans of tennis balls. How much
will she pay for everything, including tax?
Are there any other numbers to this question? I will be glad to help.
Someone help me please
Answer:
1440°
Step-by-step explanation:
the formula used for this is (n-2)×180° where n=# of sides in the polygon
If your Uncle Jack was on his roof, and he wanted you to help him down, would you help your Uncle Jack off?
Find f'(x) for the given function.
f(x) = 5/3-x
Answer:
The derivative is:
[tex]f^{\prime}(x) = -\frac{5}{x^2-6x+9}[/tex]
Step-by-step explanation:
We are given the following function:
[tex]f(x) = \frac{5}{3-x}[/tex]
Derivative of a quotient:
Suppose we have a quotient:
[tex]f(x) = \frac{g(x)}{h(x)}[/tex]
The derivative is:
[tex]f^{\prime}(x) = \frac{g^{\prime}(x)h(x) - h^{\prime}(x)g(x)}{h(x)^2}[/tex]
In this question:
Numerator [tex]g(x) = 5, g^{\prime}(x) = 0[/tex]
Denominator [tex]h(x) = 3 - x, h^{\prime}(x) = -1[/tex]
So
[tex]f^{\prime}(x) = \frac{0(3-x) - 5}{(3 - x)^2} = -\frac{5}{x^2-6x+9}[/tex]
The derivative is:
[tex]f^{\prime}(x) = -\frac{5}{x^2-6x+9}[/tex]
10(2x - 4) + 5 = 2x - 8
Step-by-step explanation:
10(2−4)+5=2−8
10(2x-4)+5=2x-810(2x−4)+5=2x−8
Solve
1
Distribute
10(2−4)+5=2−8
20−40+5=2−8
2
Add the numbers
3
Add
35
3535
to both sides of the equation
4
Simplify
5
Subtract
2
2x2x
from both sides of the equation
On a standardized exam, the scores are normally distributed with a mean of 135 and a
standard deviation of 20. Find the Z-score of a person who scored 115 on the exam.
Answer:
-1
Step-by-step explanation:
mean, mu = 135.
Standard deviation = 20
X = 115
use the z score formula : [tex]z = \frac{x-mu}{standard deviation}[/tex]
to get (115-135)/20 = -1
One number is 7more than twice the other number. If the sum of the two numbers is 25, find the two numbers.
Answer:
6 and 19
Step-by-step explanation:
x+2x+7=25
3x=18
x=6
the other number is 19
The sum of two numbers is 80.6. One of
the numbers is 9 times the other. What
are the two numbers?
What is the y-intercept of this line? Acellus, 10 points for answer.
Answer:
y-intercept is ( 0 , 5 )
Step-by-step explanation:
Statistics Question. Use the Desmos graphing calculator to find the least-squares regression line for the dataset in the table:
Given:
The table of values.
To find:
The least-squares regression line for the data set in the table by using the desmos graphing calculator.
Solution:
The general form of least-squares regression line is:
[tex]\hat{y}=mx+b[/tex] ...(i)
Where, m is the slope and b is the y-intercept.
By using the desmos graphing calculator, we get
[tex]m\approx 2.55,b\approx -6.435[/tex]
Substitute these values in (i).
[tex]\hat{y}=(2.55)x+(-6.435)[/tex]
[tex]\hat{y}=2.55x-6.435[/tex]
Therefore, the correct option is A.
The graph of regression line is attached below.
The equation of regression line is [tex]y=2.55x-6.435[/tex]
Equation of regression line:A graphing calculator is a calculator device that has the ability to display plotted graphs for complex equations.
First we have to enter the given table in graphing calculator,
After entering the data given into table,
We get, m= 2.55 and b= -6.435
So that, the equation of regression line is [tex]y=2.55x-6.435[/tex]
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Using the formula for the difference of squares, calculate: (100 - 3)
(100 + 3).
Answer:
97
Step-by-step explanation:
Answer:
Step-by-step explanation:
Explanations are below
Step 1
(100-3) Observe the equation
Step 2
(100-3) Simplify
100-(+3)
100-3
Answer: 97
CAN SOMEONE ANSWER THIS! Find the lateral surface area of the cylinder. Round your answer to the nearest hundredth. A) 315.04 in2 B) 370.62 in2 C) 395.84 in2 D) 408.92 in2
Answer:
C) 395.84 in^2
Step-by-step explanation:
I took the test
Help me with number
4,5,6,7
Answer
number
4.D
5.B
6.C
7.BHopes this helpWhich is proportional
Answer:
B
Step-by-step explanation:
It goes up the same amount ($0.75) for every bar you get.
The diameter of the planet Mercury is 4.87×103 kilometers. The diameter of the planet Venus is 1.21×104kilometers. The diameter of the planet Earth is 1.28×104 kilometers. The diameter of Mars is 6.79×103 kilometers. Which planet has the smallest diameter?
Question 2 options:
Mars
Mercury
Venus
Earth
Answer: Venus
Step-by-step explanation:
Answer:
Mercury, then MarsStep-by-step explanation:
Given diameters of planets:
Mercury ⇒ 4.87 × 10³ km = 4 870 kmVenus ⇒ 1.21 × 10⁴ km = 12 100 kmEarth ⇒ 1.28 × 10⁴ km = 12 800 kmMars ⇒ 6.79 × 10³ km = 6 790 kmCompared, we see the smallest value belongs to Mercury
The second smallest planet is Mars
If a student were going to write about their favorite food, they would want to include sensory language that focuses on. help please
Answer:
Here are the answers
Step-by-step explanation:
1. taste and smell
2. they allow the reader to feel as if he or she is in the story
3. touch
4. to make the writing more interesting and vivid, to provide greater detail to a narrative
Language Arts 6 B Unit 7 Lesson 13
Students would want to include sensory language which describes in the solution part that focuses on writing about their favorite food.
What is sensory language?Sensory Language is a word or words used to evoke mental imagery and help the reader visualize the tale or poetry. Imagery is a literary method that appeals to the reader's senses, whereas Sensory Language is a writing style and how writers utilize words to generate images for the readers.
When writing about their favorite food, a student might want to include sensory language that focuses on how the food looks, smells, tastes, feels, and sounds. This can help to paint a vivid picture for the reader and make the experience of reading about the food more immersive.
For example, if the student's favorite food is pizza, they might describe the golden, crispy crust; the savory, spicy tomato sauce; the gooey, melted cheese; the spicy sausage and bell peppers; and the satisfying crunch that it makes when they take a bite. They might also describe the way the warm, comforting aroma of the pizza fills the room as it cooks, or the way the different textures and flavors come together in each bite to create a satisfying and delicious meal. By using descriptive language that focuses on the senses, the student can help the reader to better understand and share in their love of the food.
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Name
Use the given information to answer Problems 7-11.
Leon and Jacey work for a florist. They each program a drone
to deliver boxes of flowers to neighbors. With Leon's program,
he must manually attach the box to the drone. With Jacey's
the drone can pick up one box at a time from a pile.
program,
ram
Please help!!
Answer:
#7: 30 seconds On The Graph The Drone Has Not Moved and The Time Is At 30 Seconds :)
#8 : 20 Seconds On The Graph All The times go Up by 20 So that is the only Possible answer
#9: Leon Drone Is Faster Look At The Graph 60 Seconds = 10 Feet And Jacey's Graph its 80 Seconds For 10 Feet And I could Go On
#10 The Time In Seconds
#11 With slow speed you can guarantee it will not be broken or damaged
I Hope This Helps :) Please Give Brainiest If It Makes Sense To You !
Thanks :)
simplify fully (9(x+7))÷(3(x-1))
Answer:
3x + 60
Step-by-step explanation:
9(x + 7) ÷ 3(x - 1) =
9x + 63 ÷ 3x - 3 =
9x ÷ 3x + 63 - 3 =
3x + 60
Note: For the third equation which is 9x ÷ 3x and etc, you have to put alphabets and numbers at one side seperately to be able to simplify easily.
If cotton candy sells for $4 per bag and the booth is
open for 12 hours, how many bags does the owner
have to sell to break even?
Answer:
Here ya go ! :)
Step-by-step explanation:
Evaluate and simplify the expression when r=2 and s=3
Answer:13
Step-by-step explanation:plug in the the numbers
Answer:20
Step-by-step explanation:
I’m smart
Manny bought 5 pounds of dog food for $8.00. At this rate, how much would 15
pounds cost? *
Answer:
24 dollars
Step-by-step explanation:
each pound is $1.60 and 15 times $1.60 equals 24
Answer:
$24
Step-by-step explanation:
5/8=15/x
cross product
8*15=5*x
120=5x
x=120/5
x=24
Pls help, i will give brainliest:
Consider the graphs which summarize the data on the number of hours per week of television viewing by two groups: 12-17 year-old Girls and 12-17 year-old Boys. Choose all that are correct.
The median for the girls is 16.
The median for the boys is 22.
The interquartile range for the girls is 28
The interquartile range for the boys is 16
The difference between the medians as a multiple of the IQR is 1/4
Answer:
a,b,e
Step-by-step explanation:
Answer:
B, D, E
OR
The median for the boys is 22
The interquartile range for the boys is 16
The difference between the medians as a multiple of the IQR is 1/4
Step-by-step explanation:
I just did it and got it right
1) How many ink cartridges can you buy with 77 dollars if one cartridge costs 11 dollars ?