Answer:
(a)
[tex]\mu=54[/tex]
The standard deviation is
[tex]\sigma=6.6543[/tex]
(b)
[tex]\mu=246\\\sigma=6.6543[/tex]
Here sample size is large and np and n(1-p) are both greater than 30. So we can use a normal approximation of binomial distribution. z-score for Y = 234.5 (using continuity correction) is
[tex]z=-1.73[/tex]
So the approximate probability that at least 235 people in the sample will still be in the Rewards Program after the first four weeks is
[tex]P(Y\geq 235)=P(Y\geq 234.5)=P(z\geq -1.73)=0.9582[/tex]
Step-by-step explanation:
Let X is a random variable that shows the number of people who would drop out of the Rewards Program within four weeks. Here X has binomial distribution with parameters n = 300 and p = 0.18.
(a)
The mean number of people who would drop out of the Rewards Program within four weeks in a sample of this size is
[tex]\mu=np=300\cdot 0.18=54[/tex]
The standard deviation is
[tex]\sigma=\sqrt{np(1-p)}=\sqrt{300\cdot 0.18\cdot 0.82}=6.6543[/tex]
(b)
Let Y is a random variable that shows the number of people in the sample who will still be in the Rewards Program after the first four weeks. Here Y has a binomial distribution with parameters n= 300 and p=0.82. So mean of Y is
[tex]\mu=np=300\cdot 0.82=246\\\sigma=\sqrt{np(1-p)}=\sqrt{300\cdot 0.18\cdot 0.82}=6.6543[/tex]
Here sample size is large and np and n(1-p) are both greater than 30. So we can use a normal approximation of binomial distribution. z-score for Y = 234.5 (using continuity correction) is
[tex]z=\frac{Y-\mu}{\sigma}=\frac{234.5-246}{6.6543}=-1.73[/tex]
So the approximate probability that at least 235 people in the sample will still be in the Rewards Program after the first four weeks is
[tex]P(Y\geq 235)=P(Y\geq 234.5)=P(z\geq -1.73)=0.9582[/tex]
Help please thank you very much
Answer: [tex]2\sqrt{7}[/tex]
When writing this on a keyboard, you would say 2*sqrt(7)
========================================================
Explanation:
The formula we'll use is
A = 0.5*p*q*sin(R)
where R is the angle between sides p and q.
The diagram shows that p = x+4 is opposite angle P, and q = x is opposite angle Q. Convention usually has the uppercase letters be angles, and the lowercase letters as the sides.
Plug in the given values and simplify to get the following
A = 0.5*p*q*sin(R)
A = 0.5*(x+4)*x*sin(60)
A = 0.5*(x+4)*x*sqrt(3)/2 ..... use the unit circle
A = 0.25*(x^2+4x)*sqrt(3)
A = (0.25x^2+x)*sqrt(3)
Set this equal to the given area of A = sqrt(27) and solve for x
A = (0.25x^2+x)*sqrt(3)
(0.25x^2+x)*sqrt(3) = A
(0.25x^2+x)*sqrt(3) = sqrt(27)
(0.25x^2+x)*sqrt(3) = 3*sqrt(3) .... see note1 at the very bottom
0.25x^2+x = 3
(1/4)x^2+x = 3
x^2+4x = 12 .... see note2 at the very bottom
x^2+4x-12 = 0
(x+6)(x-2) = 0
x+6 = 0 or x-2 = 0
x = -6 or x = 2
A negative side length doesn't make sense, so we ignore x = -6. The only solution here is x = 2.
Since x = 2, this means we have the following side lengths so far
p = RQ = x+4 = 2+4 = 6q = PR = x = 2Now apply the law of cosines to find the missing side.
r^2 = p^2 + q^2 - 2*p*q*cos(R)
r^2 = 6^2 + 2^2 - 2*6*2*cos(60)
r^2 = 36 + 4 - 24*1/2
r^2 = 40 - 12
r^2 = 28
r = sqrt(28)
r = sqrt(4*7)
r = 2*sqrt(7)
Side PQ is exactly 2*sqrt(7) units long
This approximates to 2*sqrt(7) = 5.2915
------------------------------------
Footnotes:
Note1: sqrt(27) = sqrt(9*3) = sqrt(9)*sqrt(3) = 3*sqrt(3)Note2: I multiplied both sides by 4 to clear out the fractionWhich conversions from scientific notation to standard notation are true? Select the four correct answers
The options are missing, so i have attached them.
Answer:
options B, E, G & H are correct.
Step-by-step explanation:
A) We are given;
1.71 × 10³ = 0.00171
For this conversion, the exponent attached to 10 is positive. This means we will have to move the decimal point to the right of 1.71 three times because the exponent is 3.
Thus, the proper conversion is;
1.71 × 10³ = 1710
B) We are given;
8.05 × 10^(5) = 805000
For this conversion, the exponent attached to 10 is positive. This means we will have to move the decimal point five times to the right of 8.05 because the exponent is 5.
Thus, the proper conversion is;
8.05 × 10^(5) = 805000
C) We are given;
2.4 × 10⁴ = -24000
For this conversion, the exponent attached to 10 is positive. This means we will have to move the decimal point four times to the right of 2.4 because the exponent is 4.
Thus, the proper conversion is;
2.4 × 10⁴ = 24000
D) We are given;
8.25 × 10^(-3) = -8250
For this conversion, the exponent attached to 10 is negative. This means we will have to move the decimal point three times to the left of 8.25 because the exponent is -3.
Thus, the proper conversion is;
8.25 × 10^(-3) = 0.00825
E) We are given;
7.09 × 10^(-6) = 0.00000709
For this conversion, the exponent attached to 10 is negative. This means we will have to move the decimal point six times to the left of 7.09 because the exponent is -6.
Thus, the proper conversion is;
7.09 × 10^(-6) = 0.00000709
F) We are given;
3.99 × 10^(5) = 300,099
For this conversion, the exponent attached to 10 is positive. This means we will have to move the decimal point five times to the right of 3.99 because the exponent is 5.
Thus, the proper conversion is;
3.99 × 10^(5) = 399,000
G)We are given;
8 × 10^(7) = 80,000,000
For this conversion, the exponent attached to 10 is positive. This means we will have to move the decimal point seven times to the right of 8 because the exponent is 7.
Thus, the proper conversion is;
8 × 10^(7) = 80,000,000
H) We are given;
1.03 × 10^(-4) = 0.000103
For this conversion, the exponent attached to 10 is negative. This means we will have to move the decimal point four times to the left of 1.03 because the exponent is -4.
Thus, the proper conversion is;
1.03 × 10^(-4) = 0.000103
Looking at all the options as well as the proof I got, only options B, E, G & H are correct.
Given the function f(x) = 0.5|x - 4| + 6, for what values of x is f(x) = 7
Answer:
6 or 2
Step-by-step explanation:
f(x) = 0.5|x - 4| + 6
0.5|x - 4| + 6 = 7
0.5|x - 4| = 7-6
0.5|x - 4| = 1
|x - 4| = 2
x -4 = ± 2
x-4 = 2 ==> x = 6
x-4 = -2 => x = 2
so the value of x = 6 or 2
Which is the graph of g(x) =[x+3]?
Answer:
B
Step-by-step explanation:
math
A hemispherical tank is filled with water and has a diameter of 4 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?
9514 1404 393
Answer:
1046 pounds
Step-by-step explanation:
The volume of the hemisphere is given by the formula ...
V = 2/3πr³
where r is the radius, or half the diameter.
The radius is (4 ft)/2 = 2 ft, so the volume of the tank is ...
V = (2/3)π(2 ft)³ = 16/3π ft³ ≈ 16.755 ft³
Then the weight of the water in the tank is ...
(16.755 ft³)(62.4 lb/ft³) ≈ 1045.52 lb
The total weight of the water is about 1046 pounds.
10 ft
8 ft
Find the perimeter of this figure to
the nearest hundredth. Use 3.14 to
approximate a.
P = [?] ft
9514 1404 393
Answer:
40.56 ft
Step-by-step explanation:
The length of the semicircle of diameter 8 ft is ...
(1/2)(π)(d) = (π/2)(8 ft) = 4π ft ≈ 4×3.14 ft = 12.56 ft
Then the sum of the lengths of all of the sides of the figure is ...
P = 10 ft + 8 ft + 10 ft + 12.56 ft = 40.56 ft
The perimeter of the figure is about 40.56 ft.
Hurry which one
A. 112
B. 282
C. 315
D. 456
Answer:
It is B.282
Step-by-step explanation:
use "Calculator Soup"
https://www.calculatorsoup.com/calculators/geometry-solids/surfacearea.php
Jasmine recorded the number of minutes she spent doing homework each day during the months of March and April
The box plot shows her data for March
March
0
5
10
15
20
25
30
35
40
45
50
Time Spent Doing Homework (minutes)
Her data for April is given in the table
0 5 10 15
20 25 30 30 30
30 30 30 30
35 40 40 40 45
45 45 45 50 50 55 60 65 65 75
Select all true statements about the data
DA Jasmine spent more minutes doing homework during the month of April.
B
The mean value
greater for the month of April
C. The median value is greater for the month of April
D. Based on the interquartile range, there is greater variability for the month of April
Answer:
Option A,B,C and D is correct
Step-by-step explanation:
As we can see , the data set for April month has longer time duration taken for completing homework as compared to the time taken during the month of April. Hence, option A is correct.
Option B is also correct because most of the instance of time taken for doing homework is greater for month of April as compared to the month of March
Median value for the month of march = 25 and median value for the month of April is (30+35)/2 = 32.5. Hence, Option C is correct
There is greater variability for the month of April. Hence, option D is correct
Help me plz I’m too slow for this
Answer:
160 units²
Step-by-step explanation:
Surface area of the square pyramid = a² + 2al
Where,
a = side length of the square = 8
l = slant height of the triangular face = 6
Plug in the values
Surface area of the square pyramid = 8² + 2*8*6
= 64 + 96
= 160 units²
An electronics firm claims that the proportion of defective units of a certain process is 5%. A buyer has a standard procedure of inspecting 15 units selected randomly from a large lot. On a particular occasion, the bury found 5 items defective. a) What is the probability of this occurrence, given that the claim of 5% defective is correct
Answer:
0.0006 = 0.06% probability of this occurrence
Step-by-step explanation:
For each unit, there are only two possible outcomes. Either it is defective, or it is not. The probability of an unit being defective is independent of any other unit, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
An electronics firm claims that the proportion of defective units of a certain process is 5%.
This means that [tex]p = 0.05[/tex]
A buyer has a standard procedure of inspecting 15 units selected randomly from a large lot.
This means that [tex]n = 15[/tex]
a) What is the probability of this occurrence?
Probability of 5 defective items, whch is P(X = 5). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{15,5}.(0.05)^{5}.(0.95)^{10} = 0.0006[/tex]
0.0006 = 0.06% probability of this occurrence
A tire on a car has an outside diameter of 3 6.90 inches what angle in radians does the tire turn while traveling 1 mile
Answer:
well... uhm...its...uhm... 39.9
Step-by-step explanation:
The ______ are (is) used to determine the amount of money that an organization would save if it used a particular test in place of the test it currently uses to select employees.
Answer:
The correct answer is the "Brogden-Cronbach-Gleser formula".
Step-by-step explanation:
Brogden introduced the BCG approach towards the conclusion of the nineteenth century as well as developed it considerably mostly throughout a 1965 guidebook by Cronbach as well as Gleser.This model was used to determine the monetary value of another profit derived from either the usage of the content or the selection criterion beneath defined parameters.A tree with a height of 8 ft casts a shadow 14 feet long on the ground. How high is another tree that casts a shadow which is 21 feet long?
Answer:
12
Step-by-step explanation:
Do 8 divided by 14 =0.571428571
times that by 21 = 12
A bakery offers a sale price of $2.80 for 6 muffins. What is the price per dozen?
The price per dozen muffins is
Answer:
$5.60 or 5.52
Step-by-step explanation:
Step one multiply 2 to 2.80 (Since 6 muffins cost $2.80, a dozen should be 6 times 2. Because a dozen is 12, so half of a dozen is 6, and multiply half by 2 and, you will get the answer.)
[tex]2 \times 2.80 = 5.60[/tex]
If a seed is planted, it has a 75% chance of growing into a healthy plant.
If 6 seeds are planted, what is the probability that exactly 4 don't grow?
Answer:
It is binomial:
p= 0.75 = 75%
1-p = 0.25 = 25%
N = 10
k=7
"seven successes in 10 trials"
(10 choose 7) (0.75)^7 ( 0.25)^3 =
(10*9*8 / 3*2) * (0.75)^7 ( 0.25)^3 =
(5*3*8) (0.75)^7 ( 0.25)^3
120 (0.75)^7 ( 0.25)^3
= 0.25028228759765625
or just over 25%
Step-by-step explanation:
I need help with this math problem please
Answer:
C) 3(x+7)²
Step-by-step explanation:
Answer:
A) (3x + 21)(x + 7)
Step-by-step explanation:
If we look at the equation we can see that it is a quadratic equation, therefore we can factor it in the following way...
[tex]3x^{2} + 42x + 147 = 3x^{2} + 21x + 21x + 147 = 3x(x + 7) + 21(x + 7) = (3x + 21)(x + 7)[/tex]
Therefore the answer is A)
What are the domain and range of the function hx) = 5x+3+1?
-10
8
2.
-10
6
4
-8
10
- 2
6
s
-10
O domain: all real numbers greater than 1
range: all real numbers
O domain: all real numbers
Step-by-step explanation:
domain : i think is x > 4/3
range : y >4
Write a story to match the equation x + 2 1/2 = 10 . Explain what x represents in your story. Solve the equation. Explain or show your reasoning.
x + 2 1/2 = 10
x + 0.5 = 10
x = 9.5
Someone donated 2 toys and one-half of a toy. Someone donated a random out of toys and we had 10 toys in total.
x equal that mystery amount of toys that were dontated.
Are 1/3 and 3/6 equal equivalent fractions?
Please help is for now 6
Answer:
-2g-11
Step-by-step explanation:
2(3g-4)-(8g+3)
6g-8-8g-3
-2g-11
Simplify 3 Square root of 3 multiplied by 6 square root 6
Answer:
54√2
Step-by-step explanation:
3√3 * 6√6
number x number = 6 * 3 = 18
root * root = √18 = √3^2 *.2 = 3√2
18 * 3 = 54
54√2
Geometry. BD is tangent to circle O at C, mAEC=280, and mACE=80. Find mDCE.(The figure is not drawn to scale.)
A. 100
B. 50
C. 120
D. 60
Mike is building a model of a classic car: a '67 Chevy Impala. The scale is 1 in : 48 in. The actual length of the car is 213.2 inches. How long will the model be? Round to the nearest tenth.
2. On this spinner, the pointer is spun once. The colour is recorded.
The pointer is spun a second time. The colour is recorded.
a) Suppose you win if you spin the same colour on both spins.
What are your chances of winning?
b) Suppose you win if you spin two different colours.
What are your chances of winning?
Answer:
A=25% B=75%
Step-by-step explanation:
So first lets make a sample space. (Im using red, blue, green, and yellow)
rr, rb, rg, ry
br, bb, bg, by
gr, gb, gg, gy
yr, yb, yg, yy
So for A its 4/16 or 1/4=25%
For B its 12/16=3/4=75%
The number of adults at an amusement park, measured in hundreds of people, is represented by the function a(w)=−0.4w^2+5w+9, where w is the number of weeks since the amusement park opened for the season.
The number of children at the same amusement park, measured in hundreds of people, is represented by the function c(w)=−0.2w^2+9w+12, where w is the number of weeks since the amusement park opened for the season.
What function, f(w) , can be used to determine how many more children than adults are at the amusement park any week during the season?
Answer:
0.2w^2+4w+3
Step-by-step explanation:
a(w)=−0.4w^2+5w+9
c(w)=−0.2w^2+9w+12
We want to find the how many more children than adults
f(w) = c(w) - a(w)
= −0.2w^2+9w+12 - ( −0.4w^2+5w+9)
Distribute the minus sign
= −0.2w^2+9w+12 +0.4w^2-5w-9
Combine like terms
= 0.2w^2+4w+3
You need a 30% alcohol solution. On hand, you have a 780 mL of a 15% alcohol mixture. You also have 90%
alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution?
You will need ____ mL of the 90% solution?
PLEASE HELP!!! BRAINLIEST! FOR MY FINAL!!!
Answer:
195 mL of the 90% solution
Step-by-step explanation:
Let the number of mL of 90% mixture = x
Hence, our equation is
780mL × 15% + x mL × 90% = (780mL + x) 30%
117 + 0.9x = 234 + 0.3x
Collect like terms
0.9x - 0.3x = 234 - 117
0.6x = 117
x = 117/0.6
x = 195 mL
Therefore, You will need 195 mL of the 90% solution
ASAP PLEASE HELP!! EMERGENCY!!
A standard six sided die is rolled two times. use a tree diagram or organized list to write out the sample space.
Well, you can come up with 1,2,3,4,5,6 from the die. Its rolled twice so those numbers can happen two times. So we can use a tree diagram to write it out
Die
/|\
1-----1------2------2-----3--------3------------------4-----4-------5----------5---------6------6
Should look something like this. Connect the lines from die to each number, I can't draw them on the computer but hopefully this helps!
The size of the sample space is 36. And the sample space is given below.
What is a sample?A sample is a group of clearly specified components. The number of items in a finite sample is denoted by a curly bracket.
A standard six-sided die is rolled two times.
Then the size of the sample space will be
Size of sample = 6 x 6
Size of sample = 36
Then the sample is given below.
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
More about the sample link is given below.
https://brainly.com/question/350477
#SPJ2
Area of shaded region
Answer:
what are you asking
Step-by-step explanation:
help with this please :(
I don't like the ones where we have to approximate, but you did say please.
That's a right triangle, relative to x we're give the opposite leg 6.1, and the adjacent leg 5.1, so
tan x = opposite/adjacent = 6.1/5.1
x = arctan (6.1/5.1)
x ≈ 50.1°
Answer: 50.1
We leave out the degree sign because it's not part of x -- it's written separately at L.
Simplify the expression:
10+10v–10+10v
Answer:
20v
Step-by-step explanation:
answer
20 v. hope helpful answer. 10+10v-10+10 =20