Answer:
a) what is the probability that Neither will of these products launch ?
= 0.30
b) At least one product will be launched ?
= 0.70
Step-by-step explanation:
From the above question, we have the following information:
P(A) = 0.45
P(B) = 0.60
P(A ∩ B) = P(A and B) launching = 0.35
Step 1
We find the Probability that A or B will launch
P (A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 0.60 + 0.45 - 0.35
= 1.05 - 0.35
= 0.70
a) what is the probability that Neither will of these products launch ?
1 - Probability ( A or B will launch)
= 1 - 0.70
= 0.30
b)At least one product will be launched?
This is equivalent to the probability that A or B will be launched
P (A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 0.60 + 0.45 - 0.35
= 1.05 - 0.35
= 0.70
An 8×8×8 cm cube was painted red, and then broken up into small cubes with side lengths of 1 cm. How many small cubes have none of their faces painted red?
Answer:
216
Step-by-step explanation:
If you just paint the surface of the cube, then the inside of the cube would not have any of their faces painted red.
Just looking at the cube from a side view, you would realize that there would be a smaller cube, 6 x 6 x 6 (not 7 since you have to account for both the top side and the bottom side), and so that is the answer, 6 ^ 3, which is 216.
Answer:
216
Step-by-step explanation:
8 * 8 * 8 = 512
8 * 8 = 64
Each face is 64 cubes, overlapping at the edges, with 6 faces total.
16 + 12 = 28 for each overlapping cube on each side
64 * 6 = 384
384 - 2(28) = 328
Top & Bottom dealt with, overlap from them is 56 units total, 14 units on top and bottom of each face..
64 - 14 = 50
50 * 2 = 100
Front & Back dealt with.
328 - 100 = 228
64 - 28 = 36
36 * 2 = 72
228 - 72 = 156
...
OR
6^3 = 216
n a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of inches and a standard deviation of inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than inches. The probability that the study participant selected at random is less than inches tall is nothing. (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between and inches. The probability that the study participant selected at random is between and inches tall is nothing. (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than inches. The probability that the study participant selected at random is more than inches tall is nothing. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
Answer:
(a) The probability that a study participant has a height that is less than 67 inches is 0.4013.
(b) The probability that a study participant has a height that is between 67 and 71 inches is 0.5586.
(c) The probability that a study participant has a height that is more than 71 inches is 0.0401.
(d) The event in part (c) is an unusual event.
Step-by-step explanation:
The complete question is: In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than inches tall is nothing. (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 67 and 71 inches. The probability that the study participant selected at random is between and inches tall is nothing. (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 71 inches. The probability that the study participant selected at random is more than inches tall is nothing. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
We are given that the heights in the 20-29 age group were normally distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches.
Let X = the heights of men in the 20-29 age group
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean height = 67.5 inches
[tex]\sigma[/tex] = standard deviation = 2 inches
So, X ~ Normal([tex]\mu=67.5, \sigma^{2}=2^{2}[/tex])
(a) The probability that a study participant has a height that is less than 67 inches is given by = P(X < 67 inches)
P(X < 67 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{67-67.5}{2}[/tex] ) = P(Z < -0.25) = 1 - P(Z [tex]\leq[/tex] 0.25)
= 1 - 0.5987 = 0.4013
The above probability is calculated by looking at the value of x = 0.25 in the z table which has an area of 0.5987.
(b) The probability that a study participant has a height that is between 67 and 71 inches is given by = P(67 inches < X < 71 inches)
P(67 inches < X < 71 inches) = P(X < 71 inches) - P(X [tex]\leq[/tex] 67 inches)
P(X < 71 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{71-67.5}{2}[/tex] ) = P(Z < 1.75) = 0.9599
P(X [tex]\leq[/tex] 67 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{67-67.5}{2}[/tex] ) = P(Z [tex]\leq[/tex] -0.25) = 1 - P(Z < 0.25)
= 1 - 0.5987 = 0.4013
The above probability is calculated by looking at the value of x = 1.75 and x = 0.25 in the z table which has an area of 0.9599 and 0.5987 respectively.
Therefore, P(67 inches < X < 71 inches) = 0.9599 - 0.4013 = 0.5586.
(c) The probability that a study participant has a height that is more than 71 inches is given by = P(X > 71 inches)
P(X > 71 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{71-67.5}{2}[/tex] ) = P(Z > 1.75) = 1 - P(Z [tex]\leq[/tex] 1.75)
= 1 - 0.9599 = 0.0401
The above probability is calculated by looking at the value of x = 1.75 in the z table which has an area of 0.9599.
(d) The event in part (c) is an unusual event because the probability that a study participant has a height that is more than 71 inches is less than 0.05.
Consider the following functions. f={(−1,1),(1,−2),(−5,−1),(5,3)} and g={(0,2),(−3,−4),(1,−2)} Step 1 of 4: Find (f+g)(1).
Answer:
-4
Step-by-step explanation:
(f+g)(1) = f(1) +g(1)
In each case, you need to locate the ordered pair with 1 as the first element.
(1, f(1)) = (1, -2) . . . . f(1) = -2
(1, g(1)) = (1, -2) . . . . g(1) = -2
f(1) +g(1) = (-2) +(-2) = -4
(f+g)(1) = -4
A department store offers two promotions. Promotion A says, "Buy one pair of shoes, get the second pair for half the price." Promotion B says, "Buy one pair of shoes, get $10 off the second pair." Jane wants to buy two pairs of shoes that cost $30 each. She can only use one of the promotions, A or B. Jane decides to use the promotion that will save her the most money. How many dollars does Jane save by picking one promotion over the other? (For example, if Jane spends $150 on her purchase by using one promotion and $100 on her purchase by using the other promotion, she saves $150-100=50$ dollars by using the second promotion over the first.)
Answer:
$5
Step-by-step explanation:
Using Promotion A, Jane would buy the first pair for $30 and the second for 1/2 * 30 = $15 for a total of 30 + 15 = $45. Using Promotion B, she would buy the first pair for $30 and the second for 30 - 10 = $20 for a total of 30 + 20 = $50. Since 45 < 50, Promotion A is the better deal, so Jane would save 50 - 45 = $5.
Help please!! Simplify the following expression
*4 + 3x3 - 2x - 5x2 - X+ x2 + x +1+7x4
O A. 8x4 +5x2 + 4x2 + 0x+1
B. 8x4 +5x + 4x2 +1
C. 8x4 + x2 - 4x + 0x
D. 8x4 + x2 - 4x2 +1
━━━━━━━☆☆━━━━━━━
▹ Answer
D. 8x⁴ + x³ - 4x² + 1
▹ Step-by-Step Explanation
Remove the opposites:
x⁴ + 3x³ - 2x³ - 5x² + x² + 1 + 7x²
Collect like terms:
8x⁴ + 3x³ - 2x³ - 5x² + x² + 1
8x⁴ + x³ - 5x² + x² + 1
8x⁴ + x³ - 4x² + 1
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
write the equation of a horizontal ellipse with a major axis of 30, a minor axis of 14, and a center at (-9,-7).
Answer: [tex]\dfrac{(x+9)^2}{225}-\dfrac{(y+7)^2}{49}=1[/tex]
Step-by-step explanation:
The equation for a horizontal ellipse is: [tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex] where
(h, k) is the centera is x-radiusb is the y-radiusGiven: major axis (diameter on x) is 30 --> x-radius (a) = 15 --> a² = 225
minor axis (diameter on y) is 14 --> y-radius (b) = 7 --> b² = 49
center (h, k) is (-9, -7)
Input those values into the equation for a horizontal ellipse and simplify:
[tex]\dfrac{(x-(-9))^2}{15^2}-\dfrac{(y-(-7))^2}{7^2}=1\\\\\\\large\boxed{\dfrac{(x+9)^2}{225}-\dfrac{(y+7)^2}{49}=1}[/tex]
for each of the following express the first quantity as a percentage of the second quantity 1 year ' 4 month
Answer:
300%
Step-by-step explanation:
1 year = 12 months
percent = part/whole * 100%
percent = 12/4 * 100% = 300%
Answer:
please can u follow me I've started following you
Which of the following statements about sets of numbers is true? (1 point)
All integers are whole numbers.
O All irrational numbers are integers.
O All rational numbers are natural numbers.
O All integers are rational numbers.
Answer:
-All integers are whole numbers.
-All rational numbers are natural numbers.
Step-by-step explanation:
The statement which is correct about the sets of numbers is:
All integers are rational numbers.
Option D is the correct answer.
What is a rational number?A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.
We have,
Natural number:
Natural numbers are positive integers or non-negative integers which start from 1 and end at infinity.
Integer:
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Whole number:
Whole numbers include all natural numbers and 0.
It does not include fractions, decimals, and negative integers.
Irrational numbers:
An irrational number is a type of real number which cannot be represented as a simple fraction.
It cannot be expressed in the form of a ratio.
Rational number:
A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.
From the above definition, we can say that,
- Some integers are whole numbers but not all integers are whole numbers.
- No irrational numbers are integers.
-Some rational numbers are natural numbers but not all rational numbers are natural numbers.
- Yes, all integers are rational numbers.
Thus the statement which is correct about the sets of numbers is:
All integers are rational numbers.
Option D is the correct answer.
Learn more about rational numbers here:
https://brainly.com/question/24398433
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The area of a square is 36cm2. What are the dimensions of the square? You must show your work. Pls tell me what the dimensions of the square are
Answer:
6 cm by 6 cm
Step-by-step explanation:
We know that the formula for area of a square is A = s² where A = area and s is the length of one side. We know that A = 36 so:
36 = s²
√36 = s
s = ±6
Note that s = -6 is an extraneous solution because you can't have a side length of -6, therefore the answer is s = 6 so the dimensions of the square are 6 cm by 6 cm.
The area of a square is found using the formula area = s^2, where s is the length of a side. ( a square has 4 equal sides).
Given the area you have:
36 = s^2
Find a by taking the square root of both sides:
S = sqrt(36)
S = 6
The square has a side length of 6 cm.
Emily thinks the perfect tomato sauce has 8 cloves of garlic in every 500 mL, of sauce. Raphael's tomato sauce has 121 cloves of garlic in every 900 mL of sauce. What will Emily think of Raphael's tomato sauce? Choose 1 answer: Choose 1 answer: (Choice A) A It is too garlicky. (Choice B) B It is not garlicky enough. (Choice C) C It is perfect.
Answer:
A
Step-by-step explanation:
Let's find the ml per garlic for each sauce. Emily's has 1 clove of garlic for 62.5 ml. Raphael's has 1 clove of garlic for 7.438... ml. So, A, it will be too garlicky.
Please Help
Function 1 is defined by the equation: p=r+7
Function 2 is defined by the table shown in the image below
Which function has a greater slope, function 1 or function 2?
Answer:
The slope of Function 2 (m=1.1) is greater than the slope of Function 1 (m=1).
Step-by-step explanation:
First, note that p is essentially the y and that r is the x. Thus, to make this easier to see, convert p to y and r to x. Thus:
[tex]y=x+7[/tex]
From the above equation, we can determine that the slope is 1. Thus, the slope of Function 1 is 1.
To find the slope of the table, simply use the slope formula. Use any two points. I'm going to use the points (0,8) and (10,19). Let (0,8) be x₁ and y₁, and (10,19) be x₂ and y₂. Therefore:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{19-8}{10-0}=11/10=1.1[/tex]
Thus, the slope of Function 2 is 1.1.
1.1 is greater than 1.
Thus, the slope of Function 2 is greater than the slope of Function 1.
Answer:
Function 2 has the greater slope
Step-by-step explanation:
If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 28 inches, what diameter pizza will reward you with the largest slice
Answer:
The diameter that will reward with the largest pizza is 14 in
Step-by-step explanation:
The perimeter of a sector of a circle is:
P = 2r + l
l = rθ
P = 2r + rθ
P=28 inches
28=2r + rθ
28-2r=rθ
θ=(28-2r/r)
=(2*14 - 2*r)/r
=2(14-r)/r
Area of the sector of the circle is:
A = r²/2 * θ
A = r²/2 * 2(14 - r)/r
A = r² * (14 - r)/r
A = r(14 - r)
A = 14r - r²
For the maximum area:
A = 14r - r²
A' = 14 - 2r
Set A' = 0
14 - 2r = 0
14= 2r
r = 7 in
The diameter (D) of the circle is twice of the radius:
D = 2r = 2 * 7= 14 in
The maximum area is:
A = 14r - r²
r = 7 in
A = 14 * 7 - 7²
A = 98 - 49
A = 49 in²
A box contains 40 tiles, and all identical
shape and size, numbered 1 through 40. If a
person picks out a single tile from the box
without looking, what is the probability the
number on the tile will be a prime number?
Answer:
32.5%
Step-by-step explanation:
Hey there!
To find the probability we first need to find the amount of prime numbers in the 1-40 set.
Prime - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
That’s 13 prime numbers.
Fraction - 13/40
Simplified is just 13/40.
13 / 40 = .325
Percent - 32.5%
Hope this helps :)
Write the quadratic in a verbal sentence. PLEASE HELP I’m super stuck!! If you can explain how to do this as well that would help so much!!
Answer:
n = 8
Step-by-step explanation:
Follow the question when turning the word equation into an equation
Because we know this is a quadratic equation, the product is a result of n multiplied by itself
[tex]n^{2} -4=60[/tex]
Solve for n
[tex]n^{2} =64[/tex]
[tex]\sqrt{n^{2} } =\sqrt{64}[/tex]
n = 8
 evaluate the expression for k=6 -18+2k=
Answer:
-6
Step-by-step explanation:
-18 + 2k wherre k = 6
=> -18 + 2(6)
=> -18 + 12
=> -6
if 2x-y=2, what is the value of 9^x/3^y?
1) 3
2) 9
3) 27
4) 81
Work Shown:
(9^x)/(3^y)
( (3^2)^x )/(3^y)
( 3^(2x) )/( 3^y )
3^(2x-y)
3^2 .... use the equation 2x-y = 2
9
If A and B are independent events with P( A) = 0.60 and P( B) = 0.70, then P( A or B) equals: a. 1.00 b. 0.42 c. 0.88 d. 1.30
Answer:
The correct option is D
P(A or B) = 1.30
Step-by-step explanation:
Given two independent (or mutually exclusive) events with P(A) = 0.60, and P(B) = 0.70
P(A or B) = P(A) + P(B)
= 0.60 + 0.70
= 1.30
This is however absurd, as the probability of an event can only be less than or equal to 1, and not less than 0.
Based on the information given, the value of then P(A or B) will be D. 1.30.
From the information given, A and B are independent events with P( A) = 0.60 and P( B) = 0.70.
Then, the value of P(A or B) will be calculated thus:
= 0.60 + 0.70
= 1.30
In conclusion, the correct option is D.
Learn more about probability on:
https://brainly.com/question/24756209
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips.
Required:
a. Determine the 26th percentile for the number of chocolate chips in a bag.
b. Determine the number of chocolate chps in a bag that make up the middle 96% of bags.
Answer:
(a) The 26th percentile for the number of chocolate chips in a bag is 1185
(b) The number of chocolate chips in a bag that makes up the middle 96% of the bags is between 1020 and 1504
Step-by-step explanation:
From the question, we have the following values:
μ =1262 and σ =118
(a) Let the value of x represents the 26th percentile. So the 26th percentile means 26% data is less than x. We can use the standard normal table to get the particular z-value that corresponds to this percentile.
P( Z<-0.65 )=0.2578 which is approximately 0.26
So for 26th percentile z-score will be -0.65.
Mathematically;
z-score = (x-mean)/SD
-0.65 = (x-1262)/118
-76.7 = x -1262
x = 1262-76.7 = 1185.3
This value is approximately 1,185
(b) Using a graph of standard normal distribution curve, if middle is 96% , then at both tails 2% each.
From z-table, we can find the closest probability;
P(-2.05<z<2.05) = 0.96
So we have two x values to get from the individual z-scores
-2.05 = (x-1262)/118
x = 1020(approximately)
For 2.05, we have
2.05 = (x-1262)/118
x = 1262 + 2.05(118) = 1504 (approximately)
I will be honest I'm having a major brain fart.. What's the line called and what's it do again? it's separating numbers.. Looks like this
29
---
3
I know I'm stupid for this one... I've been up for 30 hours studying and now I can't remember this.. I need sleep but can't till i figure this out now...
Answer:
fraction bar. separates numerator and denominator in a fraction
Answer:
basically a dividing symbol, but specifically used for fractions
Step-by-step explanation:
Is the sequence {81, 27, 9, 3, 1, …} arithmetic or geometric?
Answer:
Geometric
Step-by-step explanation:
That is a geometric sequence, because the each number divided into 3. As we know if the pattern are multiply or divided it will be geometric, if it is sum or subtract will be arithmetic.
hope this helps
if u have question let me know in comments
The given sequence is geometric. The common ratio of the geometric sequence is 1/3.
What is geometric progression?A geometric progression (G.P.) is a sort of sequence in which each successive term is obtained by multiplying the prior term by a set number known as a common ratio.
This progression is also known as a pattern-following geometric sequence of integers.
The given sequence in the problem is;
81, 27, 9, 3, 1, …
Due to the fact that each number is split into three, that sequence is geometric. The pattern will be geometric if it is multiplied or divided, and arithmetic if it is the result of addition or subtraction.
The common ratio of the sequence is found as;
[tex]\rm r = \frac{27}{81} =\frac{9}{27} =\frac{3}{9} =\frac{1}{3} =\frac{1}{3}[/tex]
The common ratio of successive terms is equal.
Hence, the given sequence is geometric.
To learn more about the geometric progression, refer to https://brainly.com/question/14320920.
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Use the model to show to help find the sum 0.34 plus 0.49
Answer/Step-by-step explanation:
The idea to use in solving this problem using the model, is to express the number of shaded boxes in fraction form.
Thus, the blue red shaded boxes has 34 boxes shaded out of 100 boxes. This represents [tex] \frac{34}{100} [/tex]. This will give us 0.34.
The other shaded boxes represents [tex] \frac{49}{100} = 0.49 [/tex].
Using the model, we can solve 0.34 + 0.49.
Add both fractions together.
[tex] \frac{34}{100} + \frac{49}{100} = \frac{34+49}{100} [/tex]
[tex] \frac{83}{100} = 0.83 [/tex]
which artistic tradition was founded by Masaccio
Answer:
Renaissance Naturalism
Step-by-step explanation:
just took the quiz
5^2x+4×5^-x+1-125=0
Answer:
Take 5^x as y.
Now the question becomes a simple equation.
y + 20y - 125 = 0.
21y = 125.
Thus, y = 125/21.
Now resubstituting we get,
5^x = 125 /21.
Taking log on both sides,
xlog5 = log 125 - log 21
x = (log125/log5) - (log21/log 5)
x= 3- 1.89
Christina's time for a race was 22.3 seconds. Another runner's time was 4.41 seconds faster. Write and evaluate an equation with a variable to find the difference between Christina's time and the other runner's time.
Answer:
[tex]Difference = 4.41[/tex]
Step-by-step explanation:
Given
Represent Christina's time with C and the other runner's time with R
C = 22.3
R = 4.41 + C
Required
Determine the difference using an equation
The difference between both runner's time is as follows;
[tex]Difference = R - C[/tex]
Substitute 4.41 + C for R
[tex]Difference = 4.41 + C - C[/tex]
[tex]Difference = 4.41[/tex]
Hence, the difference is 4.41 seconds
tan inverse 1/4 +tan inverse 2/7 = 1/2 cos inverse 3/5
Answer:
The equation is always false
Step-by-step explanation:
arctan1/4+arctan2/7=1/2arccos3/5
0.24497866+0.27829965=1/2(0.92729521)
0.52327832 =0.46364760
not equivalent and will never be.
A lottery exists where balls numbered 1 to "20" are placed in an urn. To win, you must match the balls chosen in the correct order. How many possible outcomes are there for this game?
Answer: 1860480
Step-by-step explanation:
Initially, there are 20 balls where 5 must be chosen in order.
The number of possible outcomes may be calculated using the concept of permutations.
The formula for permutations is:
nPr =n!/(n−r)!
where n represents the number of items and r represents the number of items to be selected.
The number of ways of selecting 5 balls in order out of 20 is:
20P5 = 20!/15!
= 1860480
To conclude, there are 1860480 possible outcomes.
A line runs tangent to a circle at the point (4, 2). The line runs through the origin. Find the slope of the tangent line.
Answer:
Slope of the tangent line (m) = 1 / 2
Step-by-step explanation:
Given:
Point A = (4,2)
Origin point = (0,0)
Find:
Slope of the tangent line (m)
Computation:
Slope of the tangent line (m) = (y2-y1) / (x2-x1)
Slope of the tangent line (m) = (2-0) / (4-0)
Slope of the tangent line (m) = 2 / 4
Slope of the tangent line (m) = 1 / 2
A Ferris wheel has a diameter of 42 feet it rotates 3 times per minute approximately how far will a passenger travel during a 5 minute ride
Answer:
1978.2 or 630π feet
Step-by-step explanation:
The Ferris wheel will rotate 3 * 5 = 15 times during the 5 minute ride and the radius is 42 / 2 = 21 feet. Since C = 2πr, r = 21 and π ≈ 3.14, C = 2 * 3.14 * 21 = 131.88. However, this only accounts for one rotation so the answer is 131.88 * 15 = 1978.2 or 630π feet.
All of Ralph’s ranch land was divided equally among his six children whose daughter land portion of the ranch land was divided among her four children how much of Roslyn was in Inherited by 1 of Lynn’s children
Answer: 1/24 of Ralph's land
Step-by-step explanation:
Ralph gave each of his children a 6th of his land.
= 1/6
Lynn being his daughter got 1/6 of his land. She then shared it to her 4 children.
Children got 1/4 of Lynn's land which is 1/6 of Ralph's land.
Lynn's children therefore got;
= 1/4 * 1/6
= 1/24 of the land
the area of triangle ABC is 31 1/4 square centimeters. What is the measure of b?
Answer:
102 cm
Step-by-step explanation:
