Answer:
The step-by-step procedure to solve this question is given, using the normal approximation to the binomial distribution.
Step-by-step explanation:
We use the normal approximation to the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In the U.S., 45% of adults over 65 suffer from one or more of the conditions considered in the study.
This means that [tex]p = 0.45[/tex]
Mean and standard deviation for the approximation, for a sample of n:
[tex]\mu = E(X) = np = 0.45n[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{0.45*0.55n}[/tex]
Calculate the probability that fewer than 320 out of the n
Using continuity correction, this is [tex]P(X < 320 - 0.5) = P(X < 319.5)[/tex], which is the pvalue of Z when X = 319.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{319.5 - 0.45n}{\sqrt{0.45*0.55n}}[/tex]
Just have to replace the value of n, find Z, and then find its pvalue.
A picture is mounted on a frame measuring 25 centimeters by
15 centimeters. It has a border of 3 centimeters round it. Find the area
and perimeter of the picture.
25 cm
13 cm
A=kW
P-HIWAW
3 cm
picture 3 cm
115 cm
13 cm
cm
Answer:
I think it's 1,125 and 4485
Step-by-step explanation:
25x13x3
115x13x3
An electrical shop reduces display goods by 5% .A display TV is sold for £380. what is the usual price of the tv
Answer:
380-5%
Step-by-step explanation:
Answer:
£399
Step-by-step explanation:
personally its easier to find 1% first then multiply it by how many percent are needed to be found.
380/100=1%
380/100=3.8
3.8x5=5%
3.8x5=19
380+19=usual price
380+19=199
circumference of circle 132cm find the area of circle is
Answer: 1386 sq.cm.
Step-by-step explanation:
2Pi r= 132
2 * 22/7 * r = 132
r = 21
Area = pi * r * r
= 22/7 * 21 * 21
= 1386 sq.cm.
Hope this helps :))
Translate the phrase into an algebraic expression: the ratio of 12x and 19y
Answer:
228 x y or x^2+3x+2
Step-by-step explanation:
the ratio of 12x 19y
assume that of today, the aanualized interst rate on a three year security is 10 % and the annualized interest rate on a two year security is 7%. use this information to estimate the one year forward rate two years from now
Answer:
The shoes belonging to my three uncles are always dirty.
What is the CIRCUMFERENCE of this pie?
Give an approximate answer by using 3.14 for π.
SHOW YOUR WORK!
Can you help me image is here which 2 Should I drag
Answer:
for 6, you drag 36. for 7, you drag 42.
Step-by-step explanation:
It is using time tables by x6
please answer all the questions for brainliest and 40 points also if you don't answer the question on correctly I will report and you will not get anything
1. Patrick made a scale drawing of a newly planned hotel.
The height of the scale drawing is 27 inches. The actual height of the hotel would be _________ ( Responses: 54, 243, 270, 600) _________ meters.
2. Mr. Twain asked the students in his class to redraw the figure below using a scale factor of 3. Then, he asked students to tell him one of the new side lengths of the figure. Some student responses are below.
Student Response
Mark 5 in.
Samantha 6 in.
Divia 1.3 in.
Cheng 0.9 in.
Candice 11.7 in.
Select the student that answered Mr. Twain's question correctly.
A. Mark
B. Divia
C. Cheng
D. Candice
3. Louis is constructing a scale model of a regulation size soccer field that measures 90 meters wide and 120 meters long. If the longest side of his model is 24 cm long, what is the width of the model?
A. 4.5 cm
B. 18 cm
C. 22.5 cm
D. 32 cm
4. Two sides of a triangle are 2 inches and 7 inches. Which could be the length of the third side? Select Yes or No for each measurement.
Yes No
5 inches
6 inches
8 inches
10 inches
5. A triangle has a side 3.5 inches in length, a 34° angle, and a 49° angle. Which of the following statements about this triangle are false? Select two that apply.
A. This triangle must have two sides that are 3.5 inches in length.
B. This triangle is an obtuse triangle.
C. This triangle could be a scalene triangle.
D. This triangle is an isosceles triangle.
6. Select the figure that can be formed when a cube is cut by a plane parallel to its base.
A. line
B. square
C. trapezoid
D. triangle
7. Select all figures that can be formed when a rectangular pyramid is cut by a plane parallel to its base.
A. point
B. rectangle
C. trapezoid
D. triangle
8. This is a cylinder.
Select all figures that can be formed by a vertical slice perpendicular to the bases of the cylinder.
A. circle
B. line segment
C. rectangle
D. oval
9. A family just removed a big tree from their backyard. The diameter of the circular hole left behind is 7 feet across. Approximately how many square feet of grass will the family need if they want to cover the area where the tree once was?
A. 22 ft²
B. 39 ft²
C. 44 ft²
D. 154 ft²
Answer:
2. is b
3.is d
4.is b
5
Step-by-step explanation:
I've done these before
have a good grade
10 points pls answer!
Answer:
a
Step-by-step explanation:
8x-20 and 3x together will equal 90
Answer:
The answer is D
Step-by-step explanation:
pls help i dont get it
giving brainliest ! *easy*
pi = 180
3(180) 540
-------- = -------
5 5
Answer is 108 degrees
What is the answer for this quiestion
Answer:
What up why is there no question
Step-by-step explanation:
Five friends went out to lunch. They each
started with the same amount of money,
and they each spent $3 on lunch. They
ended with a combined total of $45. How
much did each of them have at the start?
Answer:
Each friend started with $9
Step-by-step explanation:
45 / 5 = 9
Find the measure of 45.
*5 = [?]
Answer:
angle7 = 80 (because vertically opposite angles are always equal)
angle7 + angle5 = 180 (because is a straight line)
80 + angle5 = 180
angle5 = 180 - 80
angle5 = 100
The total area of a rectangle is represented by (x²+9 x+18) sq units.Find the expression for the dimensions of the rectangle.
Answer:
x+3 units and x+6 units
Step-by-step explanation:
Give the total area of a rectangle is represented by (x²+9 x+18) sq units.F
Factorize
x²+9 x+18
- x^2 + 6x + 3x + 18
= x(x+6) + 3(x+6)
= (x+3)(x+6)
Since Area = Length * Width
The dimensions of the rectangle are x+3 and x+6 units
[tex]82.5.5. \div \times 552.6365 |. < 5 \geqslant 6 > { {0}^{?} }^{2} | [/tex]
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]
Jordyn is weighing the ingredients on a kitchen scale to make bread. The bowl weighs 1 12 pounds. He adds several scoops of flour. the total weight of the bowl and the flour is 2 34 pounds. If each cup weighs 516 pound, how many cups of flour does he add?
Answer:
4 POUNDS OF FLOUR
Step-by-step explanation:
The number of cups of flour he added is 4.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Bowl weight = 1(1/2) pounds
Number of cups of flour weight = x pounds
Now,
Total weight = 2(3/4) pounds
1(1/2) + x = 2(3/4)
x = 11/4 - 3/2
x = (11 - 6)/4
x = 5/4
Now,
Weight of each cup of flour = 5/16 pounds
Now,
The number of cups of flour.
= 5/4 ÷ 5/16
= (5 x 16) / (4 x 5)
= 4
Thus,
The number of cups of flour is 4.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
PLEASE ANSWER!!!!!!!!!
Answer:
1/15
Step-by-step explanation:
no. of students who participate in all of the three activities is 2.
So, the possibility is 2/15 = 1/15
Ans: 1/15
Divide using a common factor of 2 to find an equivalent fraction for 2/6
A: 1/6
B: 1/3
C: 3/6
D: 2/3
I hate math
Answer:
The answer is D
Step-by-step explanation:
2. Write the coefficient of 'a' in each of the '-24 ab2c
Answer:
The numerical coefficient in the expression 4x2y−23xy+25xy2 is 4,2−3,25 respectively
The numerical coefficient in the expression 3−5x2y+47xyz+3 is 3−5,47 respectively.
3 is a constant term.
Help! See the question below!
Determine the mean, standard deviation, and five number summary of each data set round to the nearest hundredth, if necessary
I'll do problem 3 to get you started.
---------------------------------------------------------
Part 1) Finding the mean:
The mean is found by adding up all the numbers and dividing by n, where n is the number of items in the set.
We sum the numbers to:
5+8+5+9+6+15+9+3+8+7+10+12 = 97
Then we divide over n = 12
mean = sum/n = 97/12 = 8.083333 approximately
This rounds to 8.08
---------------------------------------------------------
Part 2) Finding the standard deviation:
I'm assuming your teacher is talking about the population standard deviation, as opposed to the sample standard deviation.
First subtract each value from the mean. It helps to make a table as shown in the attachment below.
Column A is the original data set. Column B is when we subtract each data item x from the mean M.
Column C is where we square each item in column B.
Adding up everything in column C leads to 118.916666666667 which is approximate. This value is highlighted in the table diagram. Divide this over n = 12 to get 9.90972222222222 which is also approximate
The last step is to apply the square root to that and we get 3.1479711279
This rounds to 3.15
---------------------------------------------------------
Part 3) Finding the min:
From here on out, we have fairly simple calculations and don't need to involve a spreadsheet or any complicated formulas.
The min value is the smallest value of the set. So that would be 3
---------------------------------------------------------
Part 4) Finding the value of Q1, first quartile:
Sort the items in ascending order, ie from smallest to largest.
You should get this set: {3, 5, 5, 6, 7, 8, 8, 9, 9, 10, 12, 15}
There are n = 12 items here, so the median is between slot 12/2 = 6 and slot 7. The values in slot 6 and 7 are the two copies of '8'. That must mean the median is (8+8)/2 = 8.
Now break up the set into two equal halves
L = {3, 5, 5, 6, 7, 8} = lower half of six items
U = {8, 9, 9, 10, 12, 15} = upper half of six items
The median of set L is exactly the value of Q1, so that would be (5+6)/2 = 11/2 = 5.5; note how this is exactly between the two middle most values of 5 and 6.
---------------------------------------------------------
Part 5) Finding the median:
We found that earlier in part 4. The median is 8.
---------------------------------------------------------
Part 6) Finding the value of Q3, third quartile:
Focus on set U = {8, 9, 9, 10, 12, 15}, which was the upper set of values, ie values larger or equal to the median.
The middle two values here are the '9' and '10'. The median is at the midpoint of these values: (9+10)/2 = 19/2 = 9.5
We have Q3 = 9.5
---------------------------------------------------------
Part 7) Finding the max:
The max is the largest item in the original set
Refer to the sorted set {3, 5, 5, 6, 7, 8, 8, 9, 9, 10, 12, 15} and we see that 15 is the max.
---------------------------------------------------------
Part 8) Finding the IQR (interquartile range):
Subtract the values of Q3 and Q1 to get the IQR
IQR = Q3 - Q1
IQR = 9.5 - 5.5
IQR = 4
---------------------------------------------------------
Part 9) Finding the range:
The range is a similar idea as the IQR; however, we'll subtract the max and min this time.
Range = max - min = 15 - 3 = 12
The range is 12.
The range, IQR and standard deviation all help us determine the spread of the data. The larger the value gets, the more spread out the data is.
---------------------------------------------------------
Summary:
Mean = 8.08 (approximate)Standard Deviation = 3.15 (approximate)Min = 3Q1 = 5.5Median = 8Q3 = 9.5Max = 15IQR = 4Range = 12Side note: The phrase "five number summary" refers to the five values of: min, Q1, median, Q3, max. All of which are needed to form a box-and-whisker plot.
Factorise 12u-uv please help lol
Answer:
u(12-v)
Step-by-step explanation:
12u and -uv both have a factor of u in common, so we can pull it out to give us the factored expression u(12-v).
Note on factoring:
Remember, it's just using the distributive property in reverse! We can get our original expression back by distributing the u to the 12 and the -v.
64 Books on 4 Shelves how maany books per Shelf?
Answer:
256
Step-by-step explanation:
Answer:
16 is the answer because 64/4 is 16 so 16*4 is 64 meaning that there are 16 books on each shelf
Step-by-step explanation:
hope this helped
If you bike for 3 hours at 10 mph and then walk for 1hr at 2mph, what would be your average speed
Answer:
it depends how fat you are....BUT the average speed would be 8 I THINK but i might be right
Step-by-step explanation:
K.8 Complete a table and graph a proportional relationship 7th grade math
but it has to be in a zooom bc its alot of questions
Answer:
Someone gave me da link to dis
Step-by-step explanation:
which expressions are equivalent to 2 to the power of 6? Choose ALL that apply
How do you find slopes of two points for example (9, 6) and (4, 4)?
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Use the following equation:
slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Let:
[tex](x_1 , y_1) = (4 , 4)\\(x_2 , y_2) = (9 , 6)[/tex]
Plug in the corresponding numbers to the corresponding variables:
m = [tex]\frac{6 - 4}{9 - 4} = \frac{2}{5}[/tex]
[tex]\frac{2}{5}[/tex] is your slope.
Answer:
[tex]m = \frac{2}{5} [/tex]
Step-by-step explanation:
Slope is equal to the change in y over the change in x, or rise over run.
[tex]m = \frac{change \: in \: y}{cahnge \: in \: x} [/tex]
The change in x is equal to the difference in x-coordinates and the change in y is equal to the difference in y-coordinates.
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
Substitute in the values of x and y into the equation to find the slope.
[tex]m = \frac{4 - (6)}{4 - (9)} [/tex]
Simplify.
[tex]m = \frac{2}{5} [/tex]
Therefor, the answer is m = 2/5.
True or false: As long as its argument is restricted to [0,2pi] the polar form of a complex number is not unique.
Some say its true, some say its false. I'm sure one of the answers I looked at is correct, but some teachers probably purposefully left a one star
Answer:
true
Step-by-step explanation:
i think