I need help with these questions asap, I will post pictures if you know them all answer them in the order of the photos from 1-5 thank you.
Answers
Answer:
1. step 4
2.idk
3. step 2
4.-5n = 1 ---------> n= -1/5
n + 15 = -10 -------> -25
n/5 = -1/5 ------> n = -1
n - 13 = -12 ------> n = 1
5. cant see the drop down menu or possible answers
but if an answer is the addition one thing
then the second one is the subtraction thing
Step-by-step explanation:
Related Questions
Help me please I need answers
Answers
Answer:
[tex]\huge \boxed{\mathrm{\$ \ 7,533.33}}[/tex]
Step-by-step explanation:
There are 12 months in one whole year.
In one year, the person earns $96,600 with bonus.
The person gets a bonus of $6,200 during Christmas.
96,600 - 6,200 = 90,400
The person earns $90,400 yearly.
[tex]\frac{90,400}{12}[/tex] = 7,533.3333
Each month, the person earns $7,533.33, to the nearest cent.
Find X so that m is parallel to n. Identify the postulate or theorem you used. Please help with these 3 problems, I don’t understand it at all
Answers
the corresponding angles should be equal
so, [tex] 5x+15=90 \implies 5x=75\implies x=15^{\circ}[/tex]
A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. A 95% confidence interval for the difference between the population means is (1.4, 8.7). If the hypothesis test is based on the same samples, which of the following do you know for sure:
A: The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
B: The hypothesis µ1 = µ2 would be rejected at the 10% level of significance.
C: The hypothesis µ1 = µ2 would be rejected at the 1% level of significance.
A) A and B
B) A and C
C) A only
D) A, B, and C
Answers
Answer:
C) A only
Step-by-step explanation:
In statistics, the null hypothesis is the default hypothesis and the alternative hypothesis is the research hypothesis. The alternative hypothesis usually comes in place to challenge the null hypothesis in order to determine if the test is statistically significant or not.
Similarly,
In hypothesis testing, the confidence interval consist of all reasonable value of the population mean. Values for which the null hypothesis will be rejected [tex]H_o[/tex] .
Given that:
At 95% confidence interval for the difference between the population means is (1.4, 8.7).
The level of significance = 1 - 0.95 = 0.05 = 5%
So , If the hypothesis test is based on the same samples, The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
Hakim is making a mosaic
from square tiles. The area he
needs to fill measures 150 mm
by 180 mm. The tiles have side
lengths of 4, 6 or 8 mm and are
too small to cut. Which tiles
should Hakim use?
Answers
Answer:
6×6 tile
Step-by-step explanation:
First let's calculate the total area Hakim should fill.
Let A be that area.
The area is a rectangle so its area is the product of the length and the width.
● A = 180*150
● A = 27000 mm^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
The tiles Hakim has are all squares with different sides(4,6,8).
Let calculate the area of each tile.
Let A' , A" and A"' be the areas respectively of the 4,6 and 8 squares.
Since all tiles are squares, the area is the side times itself.
■■■■■■■■■■■■■■■■■■■■■■■■■■
● A' = 4^2 = 16 mm^2
● A" = 6^2 = 36 mm^2
● A"' = 8^2 = 64 mm^2
Divide the total area by each area and see wich one will give you a whole number.
●A÷A' = 27000÷16 = 1687.5
This isn't a whole number
● A÷A" = 27000÷36 = 750
This is a whole number, so it is the right tile.
● A+A"' = 27000÷64 = 421.875
This isn't the right tile.
Hakil should use the 6×6 tile
Hakim should use a tile of 6×6 side.
What is area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
Given that, Hakim is making a mosaic from square tiles. The area he needs to fill measures 150 mm by 180 mm. The tiles have side lengths of 4, 6 or 8 mm and are too small to cut.
To know that which tile fits best, we will divide the area of mosaic to the area of the tile, and see if we get a whole number if not a whole number then it should be cut, but we are restricted to do so, therefore we will look for the whole number,
Area of the mosaic = 150×180 = 27000 mm²
Area of the tile with side 4 mm = 4² = 16 mm²
Number of tile = 27000/16 = 1687.5 tiles. (not a whole number)
Area of the tile with side 6 mm = 6² = 36 mm
Number of tile = 27000/36 = 750 tile. (a whole number)
Hence, Hakim should use a tile of 6×6 side.
For more references on area, click;
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Transform the given parametric equations into rectangular form. Then identify the conic. x= -3cos(t) y= 4sin(t)
Answers
Answer:
Solution : Option D
Step-by-step explanation:
The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )
x = - 3cos(t) ⇒ x / - 3 = cos(t)
y = 4sin(t) ⇒ y / 4 = sin(t)
Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )
( x / - 3 )² = cos²(t)
+ ( y / 4 )² = sin²(t)
_____________
x² / 9 + y² / 16 = 1
Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.
From a group of 11 people, 4 are randomly selected. What is the probability the 4 oldest people in the group were selected
Answers
The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.
Given that:
Find how many ways the 4 oldest people can be selected from the group.
Since the 4 oldest people are already determined, there is only 1 way to select them.
n = 11 (total number of people in the group) and k = 4 (number of people to be selected).To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:
Number of ways to choose k items from n items :
C(n,k) = n! / (k!(n-k)!)
Calculate the total number of ways to select 4 people from the group:
Plugging n and k value from given data:
C(11,4 )= 11! / (4!(11-4)!)
On simplifications gives:
C(11, 4) = 330.
Calculate the probability:
Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people
Plugging the given data:
Probability = 1 / 330
Probability ≈ 0.00303 or 0.303%.
Therefore, the probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.
Learn more about probabilities here:
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How many ways are there to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants
Answers
Answer:
There are 6566 ways to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants.
Step-by-step explanation:
Given:
There are 5 types of croissants:
plain croissants
cherry croissants
chocolate croissants
almond croissant
apple croissants
broccoli croissants
To find:
to choose 22 croissants with:
at least one plain croissant
at least two cherry croissants
at least three chocolate croissants
at least one almond croissant
at least two apple croissants
no more than three broccoli croissants
Solution:
First we select
At least one plain croissant to lets say we first select 1 plain croissant, 2 cherry croissants, 3 chocolate croissants, 1 almond croissant, 2 apple croissants
So
1 + 2 + 3 + 1 + 2 = 9
Total croissants = 22
So 9 croissants are already selected and 13 remaining croissants are still needed to be selected as 22-9 = 13, without selecting more than three broccoli croissants.
n = 5
r = 13
C(n + r - 1, r)
= C(5 + 13 - 1, 13)
= C(17,13)
[tex]=\frac{17! }{13!(17-13)!}[/tex]
= 355687428096000 / 6227020800 ( 24 )
= 355687428096000 / 149448499200
= 2380
C(17,13) = 2380
C(n + r - 1, r)
= C(5 + 12 - 1, 12)
= C(16,12)
[tex]=\frac{16! }{12!(16-12)!}[/tex]
= 20922789888000 / 479001600 ( 24 )
= 20922789888000 / 11496038400
= 1820
C(16,12) = 1820
C(n + r - 1, r)
= C(5 + 11 - 1, 11)
= C(15,11)
[tex]=\frac{15! }{11!(15-11)!}[/tex]
= 1307674368000 / 39916800 (24)
= 1307674368000 / 958003200
= 1307674368000 / 958003200
= 1365
C(15,11) = 1365
C(n + r - 1, r)
= C(5 + 10 - 1, 10)
= C(14,10)
[tex]=\frac{14! }{10!(14-10)!}[/tex]
= 87178291200 / 3628800 ( 24 )
= 87178291200 / 87091200
= 1001
C(14,10) = 1001
Adding them:
2380 + 1820 + 1365 + 1001 = 6566 ways
given point (-6, -3) and a slope of 4, write an equation in point-slope form
Answers
Answer:
y = 4x + 21
Step-by-step explanation:
Hello!
Point-slope form is y - y1 = m(x - x1)
y1 is the y point
x1 is the x point
m is the slope
Put in what you know
y - -3 = 4(x - -6)
Subtracting a negative is the same as adding
y + 3 = 4(x + 6)
Distribute the 4
y + 3 = 4x + 24
Subtract 3 from both sides
y = 4x + 21
The answer is y = 4x + 21
Hope this helps!
Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.
a. (4,2,−4)
b. (0,8,15)
c. (√2,1,1)
d. (−2√3,−2,3)
Answers
Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:
[tex]\rho = \sqrt{x^{2}+y^{2}+z^{2}}[/tex]
[tex]\phi = cos^{-1}\frac{z}{\rho}[/tex]
For angle θ:
If x > 0 and y > 0: [tex]\theta = tan^{-1}\frac{y}{x}[/tex];If x < 0: [tex]\theta = \pi + tan^{-1}\frac{y}{x}[/tex];If x > 0 and y < 0: [tex]\theta = 2\pi + tan^{-1}\frac{y}{x}[/tex];Calculating:
a) (4,2,-4)
[tex]\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}[/tex] = 6
[tex]\phi = cos^{-1}(\frac{-4}{6})[/tex]
[tex]\phi = cos^{-1}(\frac{-2}{3})[/tex]
For θ, choose 1st option:
[tex]\theta = tan^{-1}(\frac{2}{4})[/tex]
[tex]\theta = tan^{-1}(\frac{1}{2})[/tex]
b) (0,8,15)
[tex]\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}[/tex] = 17
[tex]\phi = cos^{-1}(\frac{15}{17})[/tex]
[tex]\theta = tan^{-1}\frac{y}{x}[/tex]
The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = [tex]\frac{\pi}{2}[/tex]
c) (√2,1,1)
[tex]\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}[/tex] = 2
[tex]\phi = cos^{-1}(\frac{1}{2})[/tex]
[tex]\phi[/tex] = [tex]\frac{\pi}{3}[/tex]
[tex]\theta = tan^{-1}\frac{1}{\sqrt{2} }[/tex]
d) (−2√3,−2,3)
[tex]\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}[/tex] = 5
[tex]\phi = cos^{-1}(\frac{3}{5})[/tex]
Since x < 0, use 2nd option:
[tex]\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }[/tex]
[tex]\theta = \pi + \frac{\pi}{6}[/tex]
[tex]\theta = \frac{7\pi}{6}[/tex]
Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:
[tex]r=\sqrt{x^{2}+y^{2}}[/tex]
Angle θ is the same as spherical coordinate;
z = z
Calculating:
a) (4,2,-4)
[tex]r=\sqrt{4^{2}+2^{2}}[/tex] = [tex]\sqrt{20}[/tex]
[tex]\theta = tan^{-1}\frac{1}{2}[/tex]
z = -4
b) (0, 8, 15)
[tex]r=\sqrt{0^{2}+8^{2}}[/tex] = 8
[tex]\theta = \frac{\pi}{2}[/tex]
z = 15
c) (√2,1,1)
[tex]r=\sqrt{(\sqrt{2} )^{2}+1^{2}}[/tex] = [tex]\sqrt{3}[/tex]
[tex]\theta = \frac{\pi}{3}[/tex]
z = 1
d) (−2√3,−2,3)
[tex]r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}[/tex] = 4
[tex]\theta = \frac{7\pi}{6}[/tex]
z = 3
Maxwell Communications paid a dividend of $1.20 last year. Over the next 12 months, the dividend is expected to grow at 13 percent, which is the constant growth rate for the firm (g). The new dividend after 12 months will represent D1. The required rate of return (Ke) is 17 percent. Compute the price of the stock (P0). (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Answers
Answer:
The price of the stock is [tex]P_o = \$ 33.9[/tex]
Step-by-step explanation:
From the question we are told that
The dividend is [tex]k = \$ 1.20[/tex]
The expected growth rate is [tex]r = 13\% = 0.13[/tex]
The required rate of return is [tex]K_e = 17 \% = 0.17[/tex]
The new dividend after 12 months is mathematically represented as
[tex]D_1 = k * (1 + r)[/tex]
substituting values
[tex]D_1 = 1.20 * (1 + 0.13)[/tex]
[tex]D_1 = \$ 1.356[/tex]
The price of the stock the price of stock is mathematically represented as
[tex]P_o = \frac{D_1}{ K_e - r }[/tex]
substituting values
[tex]P_o = \frac{ 1.356}{ 0.17 - 0.13 }[/tex]
[tex]P_o = \$ 33.9[/tex]
how would you write six times the square of a number
Answers
Answer:
[tex]\huge \boxed{6x^2 }[/tex]
Step-by-step explanation:
6 times a number squared.
Let the number be [tex]x[/tex].
6 is multiplied to [tex]x[/tex] squared.
[tex]6 \times x^2[/tex]
The weight of an object on moon is 1/6 of its weight on Earth. If an object weighs 1535 kg on Earth. How much would it weigh on the moon?
Answers
Answer:
255.8
Step-by-step explanation:
first
1/6*1535
=255.8
Which choice shows the product of 22 and 49 ?
Answers
Answer:
1078
Step-by-step explanation:
The product of 22 and 49 is 1078.
Answer:
1078 is the product
Step-by-step explanation:
The lines below are parallel. If the slope of the green line is -4, what is the slope of the red line?
Answers
Answer:
-4
Step-by-step explanation:
Hey there!
Well the slopes of 2 parallel lines have the same slope,
meaning if the green line has a slope of -4 then the slope of the red line has a slope of -4.
Hope this helps :)
In a random sample of 205 people, 149 said that they watched educational television. Find the 95% confidence interval of the true proportion of people who watched educational television. Round intermediate answers to at least five decimal places.
Answers
Answer: Given a sample of 200, we are 90% confident that the true proportion of people who watched educational TV is between 72.1% and 81.9%.
Step-by-step explanation:
[tex]\frac{154}{200} =0.77[/tex]
[tex]1-0.77=0.23[/tex]
[tex]\sqrt{\frac{(0.77)(0.23)}{200} }[/tex]=0.049
0.77±0.049< 0.819, 0.721
The area of a rectangular garden if 6045 ft2. If the length of the garden is 93 feet, what is its width?
Answers
Answer:
65 ft
Step-by-step explanation:
The area of a rectangle is
A = lw
6045 = 93*w
Divide each side by 93
6045/93 = 93w/93
65 =w
Answer:
[tex]\huge \boxed{\mathrm{65 \ feet}}[/tex]
Step-by-step explanation:
The area of a rectangle formula is given as,
[tex]\mathrm{area = length \times width}[/tex]
The area and length are given.
[tex]6045=93 \times w[/tex]
Solve for w.
Divide both sides by 93.
[tex]65=w[/tex]
The width of the rectangular garden is 65 feet.
Which statement about the angle measures is true?
m_BAC + m2 ACB 85
m.BAC MACB 95
95°
m..BACA BC 85
m. BACIMBC 95
B
Answers
Answer:
Option (4)
Step-by-step explanation:
By the property of exterior angle of a triangle,
"Exterior angle of a triangle is equal to the sum of two opposite interior angles."
In the triangle ABC,
∠ACD is an exterior angle and ∠BAC and ∠ABC are the opposite interior angles.
m∠ACD = m∠BAC + m∠ABC
95° = m∠BAC + m∠ABC
Therefore, Option (4) will be the correct option.
You flip two coins. What is the probability
that you flip at least one head?
Answers
Answer:
[tex]\boxed{Probability=\frac{1}{2} }[/tex]
Step-by-step explanation:
The probability of flipping at least 1 head from flipping 2 coins is:
=> Total sides of the coins = 4
=> Sides which are head = 2
=> Probability = 2/4 = 1/2
Find the product of all solutions of the equation (10x + 33) · (11x + 60) = 0
Answers
Answer:
18
Step-by-step explanation:
Using Zero Product Property, we can split this equation into two separate equations by setting each factor to 0. The equations are:
10x + 33 = 0 or 11x + 60 = 0
10x = -33 or 11x = -60
x = -33/10 or x = -60/11
Multiplying the two solutions together, we get -33/10 * -60/11 = 1980 / 110 = 18.
The blue dot is at what value on the number line?
Answers
Answer:
-19
Step-by-step explanation:
By looking at the 2 numbers provided, -10 and -4, you can work out that there is a gap of 6 numbers as(-4) - (-10) = 6
There are 2 intervals between -10 and -4, so each interval is
6/2 = 3
a gap of 3
This means the number to the left of -4 is -7, then -10 which works.
From there, you count how many intervals there is between -10 and the ?
There are 3 intervals, so you have to decrease -10 by -3x3 or -9
Therefore the ? is -19
Another way is to just count it directly
The number directly left of -10 is going to be -13, then -16 and finally -19
g The intersection of events A and B is the event that occurs when: a. either A or B occurs but not both b. neither A nor B occur c. both A and B occur d. All of these choices are true. a. b. c. d.
Answers
Answer:
c. both A and B
Step-by-step explanation:
Given that there are two events A and B.
To find:
Intersection of the two sets represents which of the following events:
a. either A or B occurs but not both
b. neither A nor B occur
c. both A and B occur
d. All of these choices are true. a. b. c. d
Solution:
First of all, let us learn about the concept of intersection.
Intersection of two events means the common part in the two events.
Explanation using set theory:
Let set P contains the outcomes of roll of a dice.
P = {1, 2, 3, 4, 5, 6}
And set Q contains the set of even numbers less than 10.
Q = {2, 4, 6, 8}
Common elements are {2, 4, 6}
So, intersection of P and Q:
[tex]P \cap Q[/tex] = {2, 4, 6}
Explanation using Venn diagram:
Please refer to the image attached in the answer area.
The shaded region is the intersection of the two sets P and Q.
When we apply the above concept in events, we can clearly say from the above explanation that the intersection of two events A and B is the event that occurs when both A and B occur.
So, correct answer is:
c. both A and B
Answer:
C.
Step-by-step explanation:
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 3%. Suppose a random sample of 10 LED light bulbs is selected. What is the probability that
Answers
Answer:
The probability that none of the LED light bulbs are defective is 0.7374.
Step-by-step explanation:
The complete question is:
What is the probability that none of the LED light bulbs are defective?
Solution:
Let the random variable X represent the number of defective LED light bulbs.
The probability of a LED light bulb being defective is, P (X) = p = 0.03.
A random sample of n = 10 LED light bulbs is selected.
The event of a specific LED light bulb being defective is independent of the other bulbs.
The random variable X thus follows a Binomial distribution with parameters n = 10 and p = 0.03.
The probability mass function of X is:
[tex]P(X=x)={10\choose x}(0.03)^{x}(1-0.03)^{10-x};\ x=0,1,2,3...[/tex]
Compute the probability that none of the LED light bulbs are defective as follows:
[tex]P(X=0)={10\choose 0}(0.03)^{0}(1-0.03)^{10-0}[/tex]
[tex]=1\times 1\times 0.737424\\=0.737424\\\approx 0.7374[/tex]
Thus, the probability that none of the LED light bulbs are defective is 0.7374.
Find the missing coordinate
Answers
Answer:
(0, -10a)
Step-by-step explanation:
From the picture attached,
Coordinates of a point have been given as (-10a, 0)
x-coordinate → distance of the point from the origin on x-axis
y-coordinate → distance of the point from the origin on y-axis
Therefore, distance of the given point on x-axis = -10a [(-) sign denotes the negative side of the x-axis]
Distance of the other point with unknown coordinates (x, y) (on y-axis) from the origin = y
And y = 10a
Therefore, coordinates of the unknown point will be (0, -10a).
[Here (-) sign denotes the negative side of the y-axis]
A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 140 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month? Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fatal Accidents 8 15 9 8 13 6 17 15 10 9 18 12
Answers
Answer:
There is enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month, as the Variance is 14 and the Standard Deviation = 4 approximately.
There is a high degree of variability in the mean of the population as explained by the Variance and the Standard Deviation.
Step-by-step explanation:
Month No. of Mean Squared
Fatal Accidents Deviation Difference
Jan 8 -4 16
Feb 15 3 9
Mar 9 -3 9
Apr 8 -4 16
May 13 1 1
Jun 6 -6 36
Jul 17 5 25
Aug 15 3 9
Sep 10 -2 4
Oct 9 -3 9
Nov 18 6 36
Dec 12 0 0
Total 140 170
Mean = 140/12 = 12 Mean of squared deviation (Variance) = 170/12 = 14.16667
Standard deviation = square root of variance = 3.76386 = 4
The fatal accidents' Variance is a measure of how spread out the fatal accident data set is. It is calculated as the average squared deviation of the number of each month's accident from the mean of the fatal accident data set. It also shows how variable the data varies from the mean of approximately 12.
The fatal accidents' Standard Deviation is the square root of the variance, and a useful measure of variability when the distribution is normal or approximately normal.
Help me please thank you
Answers
Answer:
x = 7
Step-by-step explanation:
The angles are alternate interior angles, so for the lines to be parallel, the angle measures must be equal.
7x - 7 = 4x + 14
3x = 21
x = 7
S varies inversely as G. If S is 8 when G is 1.5, find S when G is 3. a) Write the variation. b) Find S when G is 3.
Answers
Step-by-step explanation:
a.
[tex]s \: = \frac{k}{g} [/tex]
[tex]8 = \frac{k}{1.5} [/tex]
[tex]k \: = 1.5 \times 8 = 12[/tex]
[tex]s = \frac{12}{g} [/tex]
b.
[tex]s = \frac{12}{3} [/tex]
s = 4
The angles of a quadrilateral are (3x + 2), (x-3), (2x+1), and 2(2x+5). Find x.
Answers
Answer:
3x+2+x-3+2x+1+2(2x+5)=360
10x+10=360
x=35
sorry to keep asking questions
Answers
Answer:
y = [tex]\sqrt[3]{x-5}[/tex]
Step-by-step explanation:
To find the inverse of any function you basically switch x and y.
function = y = x^3 + 5
Now we switch x and y
x = y^3 +5
Solve for y,
x - 5 = y^3
switch sides,
y^3 = x-5
y = [tex]\sqrt[3]{x-5}[/tex]
Answer:
[tex]\Large \boxed{{f^{-1}(x)=\sqrt[3]{x-5}}}[/tex]
Step-by-step explanation:
The function is given,
[tex]f(x)=x^3 +5[/tex]
The inverse of a function reverses the original function.
Replace f(x) with y.
[tex]y=x^3 +5[/tex]
Switch variables.
[tex]x=y^3 +5[/tex]
Solve for y to find the inverse.
Subtract 5 from both sides.
[tex]x-5=y^3[/tex]
Take the cube root of both sides.
[tex]\sqrt[3]{x-5} =y[/tex]
A blue die and a red die are thrown. B is the event that the blue comes up with a 6. E is the event that both dice come up even. Write the sizes of the sets |E ∩ B| and |B|a. |E ∩ B| = ___b. |B| = ____
Answers
Answer:
Size of |E n B| = 2
Size of |B| = 1
Step-by-step explanation:
I'll assume both die are 6 sides
Given
Blue die and Red Die
Required
Sizes of sets
- [tex]|E\ n\ B|[/tex]
- [tex]|B|[/tex]
The question stated the following;
B = Event that blue die comes up with 6
E = Event that both dice come even
So first; we'll list out the sample space of both events
[tex]B = \{6\}[/tex]
[tex]E = \{2,4,6\}[/tex]
Calculating the size of |E n B|
[tex]|E n B| = \{2,4,6\}\ n\ \{6\}[/tex]
[tex]|E n B| = \{2,4,6\}[/tex]
The size = 3 because it contains 3 possible outcomes
Calculating the size of |B|
[tex]B = \{6\}[/tex]
The size = 1 because it contains 1 possible outcome
It is known that 80% of all brand A external hard drives work in a satisfactory manner throughout the warranty period (are "successes"). Suppose that n= 15 drives are randomly selected. Let X = the number of successes in the sample. The statistic X/n is the sample proportion (fraction) of successes. Obtain the sampling distribution of this statistic.
Answers
Answer:
P (x= 5) = 0.0001
P(x=3) = 0.008699
Step-by-step explanation:
This is a binomial distribution .
Here p = 0.8 q= 1-p = 1-0.8 = 0.2
n= 15
So we find the probability for x taking different values from 0 - 15.
The formula used will be
n Cx p^x q^n-x
Suppose we want to find the value of x= 5
P (x= 5) = 15C5*(0.2)^10*(0.8)^5 = 0.0001
P(x=3) = 15C3*(0.2)^12*(0.8)^3 = 9.54 e ^-7= 0.008699
Similarly we can find the values for all the trials from 0 -15 by substituting the values of x =0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15.
The value for p(x = 5) is 0.0001 and the value for p(x = 3) is 0.008699.
It is given that the 80% of all brand A external hard drives work in a satisfactory manner throughout the warranty period.
It is required to find the sampling distribution if n =15 samples.
What is sampling distribution?It is defined as the probability distribution for the definite sample size the sample is the random data.
We have p =80% = 0.8 and q = 1 - p ⇒ 1 -0.8 ⇒ 0.2
n = 15
We can find the probability for the given x by taking different values from 0 to 15
the formula can be used:
[tex]\rm _{n}^{}\textrm{C}_x p^xq^{n-x}[/tex]
If we find the value for p(x = 5)
[tex]\rm _{15}^{}\textrm{C}_5 p^5q^{15-5}\\\\\rm _{15}^{}\textrm{C}_5 0.8^50.2^{10}[/tex]⇒ 0.0001
If we find the value for p(x = 3)
[tex]\rm _{15}^{}\textrm{C}_3 0.8^30.2^{12}\\[/tex] ⇒
Similarly, we can find the values for all the trials from 0 to 15 by putting the values of x = 0 to 15.
Thus, the value for p(x = 5) is 0.0001 and the value for p(x = 3) is 0.008699.
Learn more about the sampling distribution here:
https://brainly.com/question/10554762
