Probability of an event is the measure of its chance of occurrence. The probability that the post box will outweigh the Kellogs box is 0.4129 approximately.
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z-score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] standard deviation [tex]\sigma[/tex])
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z-tables, the p-value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
What is the distribution of random variable which is sum of normal distributions?Suppose that a random variable X is formed by [tex]n[/tex] mutually independent and normally distributed random variables such that:
[tex]X_i = N(\mu_i , \sigma^2_i) ; \: i = 1,2, \cdots, n[/tex]
And if
[tex]X = X_1 + X_2 + \cdots + X_n[/tex]
Then, its distribution is given as:
[tex]X \sim N(\mu_1 + \mu_2 + \cdots + \mu_n, \: \: \sigma^2_1 + \sigma^2_2 + \cdots + \sigma^2_n)[/tex]
If, for the given case, we assume two normally distributed random variables as:
X = variable assuming weights of boxes of Post Corn Flakes
Y = variable assuming weights of boxes of Kellogs
Then, as per the given data, we get:
[tex]X \sim N(\mu = 64.1, \sigma = 0.5)\\Y \sim N(\mu = 63.9, \sigma = 0.4)[/tex]
Then, the probability that the Post box will outweigh the Kellogs box can be written as:
[tex]P(X > Y)[/tex]
Or,
[tex]P(X -Y > 0)[/tex]
We need to know about the properties of X-Y.
Also, since [tex]E(aX) = aE(X), Var(aX) = a^2Var(X)[/tex], thus,
[tex]-Y \sim N(-63.9, 0.4)[/tex]
As both are independent(assuming), thus,
[tex]X - Y \sim N(\mu = 64.1 - 63.9, \sigma = 0.5 + 0.4) = N(0.2, 0.9)[/tex]
Using the standard normal distribution, we get the needed probability as:
[tex]P(X -Y > 0) = 1 - P(X - Y \leq 0) \\P(X -Y > 0)= 1- P(Z = \dfrac{(X-Y) - \mu}{\sigma} \leq \dfrac{0 - 0.2}{0.9})\\P(X -Y > 0) \approx 1 - P(Z \leq -0.22)[/tex]
Using the z-tables, the p-value for Z = -0.22 is 0.4129
Thus, [tex]P(X > Y) = P(X - Y > 0) \approx 0.4129[/tex]
Thus, the probability that the post box will outweigh the Kellogs box is 0.4129 approximately.
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The probability that a randomly selected Post box outweighs a Kellogg's box is approximately 50%.
To find the probability that the Post box will outweigh the Kellogg's box, we need to calculate the difference in weights between the two brands and then determine the probability that this difference is positive.
Let X be the weight of a box of Post Corn Flakes and Y be the weight of a box of Kellogg's Corn Flakes.
We are given that:
- For Post Corn Flakes, X ~ N(μ = 64.1, σ = 0.5)
- For Kellogg's Corn Flakes, Y ~ N(μ = 63.9, σ = 0.4)
We want to find P(X > Y), which is the probability that a randomly selected box of Post Corn Flakes weighs more than a randomly selected box of Kellogg's Corn Flakes.
Now, let Z = X - Y. We are interested in finding P(Z > 0).
The mean and standard deviation of Z can be calculated as follows:
- Mean of Z: μ_Z = μ_X - μ_Y = 64.1 - 63.9 = 0.2 oz
- Standard deviation of Z: σ_Z =[tex]sqrt(σ_X^2 + σ_Y^2) = sqrt(0.5^2 + 0.4^2)= sqrt(0.25 + 0.16)= sqrt(0.41) = 0.64 oz[/tex]
Now, we standardize Z:
Z = (X - Y - μ_Z) / σ_Z
Therefore,
P(Z > 0) = P((X - Y - μ_Z) / σ_Z > 0)
= P((X - Y) > μ_Z)
= P((X - Y) > 0.2)
Now we look up the z-score corresponding to Z = 0.2:
z = (0.2 - μ_Z) / σ_Z
= (0.2 - 0.2) / 0.64
= 0
The probability that Z is greater than 0 is equal to the probability that the standardized Z-score is greater than 0, which is 0.5.
Therefore, the probability that the Post box will outweigh the Kellogg's box is 0.5 or 50%.
A hot air balloon descended 99.6 meters in 12 seconds . What was the balloons average rate of descent in meters per second ?
8.6 meters per second
Here's a graph of linear function. Write the equation that describes that function. Express it in slope-intercept form.
the y intercept is -3 because its touching (0,-3).
The graph goes right one and down five so the slope is -5
y=mx + b
y= -5x -3
Since the sample size is always smaller than the size of the population, the sample meana. must always be smaller than the population meanb. must be larger than the population meanc. must be equal to the population meand. can be smaller, larger, or equal to the population mean
Answer:
d. can be smaller, larger, or equal to the population mean
Step-by-step explanation:
The mean of the sample will depend upon which values are selected from the population to form the sample.
The sample mean can be any value below, above or equal to the population mean.
However, as more and more samples are taken and their means found, the mean of the sample means will approach the population mean.
Answer:
It can be smaller, larger, or equal to the population mean.Step-by-step explanation:
We know that the sample size is smaller than the size of the population, because it's a subset that must represent the population.
However, that doesn't mean the sample mean has to be smaller than the population mean, actually this stats can be smaller, equal or larger, it depends on another factors.
Therefore, the right answer is the last choice
It can be smaller, larger, or equal to the population mean.The layer cake has both vanilla and chocolate frosting. What percent of the surface area of the cake (not including the bottom) is chocolate? Round your answer to the nearest tenth of a percent. The radius is 6 in height for vanilla is 4 in height for chocolate is 4 in
Answer:
Step-by-step explanation:
2
Please help with this!!!!
The other angel is also equal to x and the sum of all angels need to be 360:
2x+90+26=360
2x=244
X=122
Answer:
The answer is 112
Step-by-step explanation:
Because seven ate nine :D but seriously 90+26+2x=360 so thats
116+2x=360 and 360-116 is 244 and you divide that by the remaining 2
and that gives you your answer of 112
Given that (x, y) = (5, 10), find r.
a.2√5
b.5√2
c.5√5
d.5√10
I am considering the point you have given is point on a circumference of a circle and center of circle is (0,0) and we have to calculate radius
so radius = root((x-h)^2 + (y-k)^2)
where (h,k) is center of circle
so r = root((5-0)^2+(10-0)^2)
= √(100+25) = √125 = 5√5
so answer is option c
The distance r from the point (5, 10) to the origin is calculated using the distance formula, resulting in r = 5√5. So, the correct answer is option (c) 5√5.
The student's question involves finding the distance r from a point to the origin in a coordinate system, given a point (x, y). Given the point (5, 10), we can calculate r using the distance formula [tex]r = \( \sqrt{(x - x_1)^2 + (y - y_1)^2} \).[/tex]
We want to find the distance r from the origin [tex](x_1,y_1)[/tex] = (0, 0) to this point (x, y) = (5, 10).
Substituting x = 5 and y = 10 into the equation, we get:
[tex]r = \( \sqrt{(5 - 0)^2 + (10 - 0)^2} \)\\ = \( \sqrt{5^2 + 10^2} \)\\ = \( \sqrt{25 + 100} \)\\ = \( \sqrt{125} \)\\ r = 5\sqrt{5}.[/tex]
Therefore, the correct answer is option (c) [tex]5\sqrt{5}[/tex].
Please answer this question only if you know it!
Answer:
d. 90°, 90°
Step-by-step explanation:
Both angles intercept 180° arc WZ. They are half the measure of the intercepted arc, hence both are 90°.
What is the distance to the earth’s horizon from point P?
Answer:
156.7 miles.
Step-by-step explanation:
The radius and the tangent at the point of contact form a right angle so we can apply the Pythagoras theorem:
( 3959 + 3.1)^2 = x^2 + 3959^2
x^2 = 3962.1^2 - 3959^2
x^2 = 24555.41
x = 156.7 miles.
The solution is : 156.7 miles is the distance to the earth’s horizon from point P.
What is distance?The distance between two points is the length of the line joining the two points. Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
here, we have,
from the given diagram, we get,
The radius and the tangent at the point of contact form a right angle so we can apply the Pythagoras theorem:
( 3959 + 3.1)^2 = x^2 + 3959^2
x^2 = 3962.1^2 - 3959^2
x^2 = 24555.41
x = 156.7 miles.
Hence, The solution is : 156.7 miles is the distance to the earth’s horizon from point P.
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3. Find the quotient of 5/31 divided by 15/23. Reduce your answer to the lowest fraction.
Answer:
The answer is 23/93
Step-by-step explanation:
In order to divide two fractions, we can flip the second one and multiply.
5/31 ÷ 15/23
5/31 × 23/15 = 23/93
The math teacher asked Edith, "How old are you?" "Sixty years less than five times my brother's age," she answered. "That doesn't help me," replied the teacher. "Yes, it does," said Edith, "He and I are twins!" How old is Edith?
x= twin 1 and 2
x=5x-60
x-5x=-60
-4x=-60
x=15
check 15=5(15)-60
15=75-60
15=15
Jodie wants to buy a shirt regularly priced at $20. The shirt is on sale for 15% off the regular price. Which equation can be used to determine s , the sale price of the shirt, not including tax? A s = 20 – (20)(0.15) B s = 20 – (20 + 0.15) C s = 20(0.15) D s = 20 + 0.15
Answer:
it's A
Step-by-step explanation:
you toke the price and times it by the decimal of the discount
Answer:
0.150 x $20 = $ 3.00.
Step-by-step explanation:
You want to buy something that costs $20, and it's on sale for 15% off. What is the item's sale price?
First, convert the 15% to a real mathematical number. For percents, this is always done by dividing the 15% by 100%, or 15% / 100% = 0.150.
Second, find out what 15% of $20 is. This is the amount of the sale discount. This is always found by mulitplying 0.150 by the item's cost $20. So for this sale, you'll save $ 3.00 on this item.
This means, the cost of the item to you is $17.00$
Draw a number line and mark all described points on it. Numbers that are both larger than –2 and smaller than 3.
To mark the points on a number line that are both larger than -2 and smaller than 3, you would mark off the points at -1, 0, 1, and 2 on this line.
Explanation:To draw a number line and mark all points that are both larger than -2 and smaller than 3, follow these steps:
Draw a straight horizontal line. This is your number line. Mark an arbitrary point as 0, the origin. To the left and right of 0, begin to mark off equal intervals representing integers. Choose a numbering system where points to the right of 0 are positive and those to the left are negative. Your description requires numbers that are larger than -2 and smaller than 3. So you would mark off the points -1, 0, 1, and 2 on the number line. Learn more about Number Line here:
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To mark all points larger than -2 and smaller than 3 on a number line, draw a straight line with equal intervals, labeling -2 and 3, and shade in the area between them. For constructing a histogram, divide the data range into intervals, then draw and label bars on the y-axis to reflect the count of data points within each interval.
Explanation:
To draw a number line and mark all points that are both larger than –2 and smaller than 3, begin by drawing a horizontal line. Use a ruler to keep the line straight. Place tick marks at regular intervals, and label them with numbers from less than -2 to greater than 3, ensuring that -2 and 3 are clearly marked on the line. The numbers larger than -2 but smaller than 3 will be between these two points. Shade this region to indicate all the numbers that meet the condition.
Next, if you need to construct a histogram, you first need a set of data to work with. Once you have your data, determine the range of data and divide this range into five to six intervals. On the horizontal axis, or the x-axis, represent these intervals. Then, count how many data points fall within each interval. On the vertical axis, or the y-axis, draw bars for each interval with heights corresponding to the number of data points in each interval. Use your ruler for precision and label the axes to show the scale.
A man spends 80% of his salary and saves the rest. He saves $1080 a month. Find his salary
Find the value of C so that (x-3) is a factor of the polynomial p(x)
In general, you have that [tex](x-x_0)[/tex] is a factor of a polynomial [tex]p(x)[/tex] if and only if [tex]p(x_0)=0[/tex]
So, we want [tex]p(3)=0[/tex]. We have
[tex]p(3) = -3^3+ 9c -4\cdot 3 +3 = -27+9c-12+3 = 9c-36[/tex]
So, we have
[tex]p(3) = 0 \iff 9c-36 = 0 \iff x = \dfrac{36}{9} = 4[/tex]
Answer:
c = 4
Step-by-step explanation:
Given that (x - 3) is a factor of p(x) then x = 3 is a root and p(3) = 0
p(3) = - (3)³ + c(3)² - 4(3) + 3 = 0, hence
- 27 + 9c - 12 + 3 = 0
9c - 36 = 0 ( add 36 to both sides )
9c = 36 ( divide both sides by 9 )
c = 4
Find the sum of the series 14+11+8+5........-82
The sum of this finite arithmetic series is -1122.
The sum of the arithmetic series 14+11+8+5...-82 is -1122. This is obtained by identifying the number of terms in the series, the first term, the last term and the common difference, then substitifying these values into the sum formula for an arithmetic series.
Explanation:The series provided is an arithmetic series, where each term decreases by 3 from the previous one. The formula to find the sum of an arithmetic series is S = n/2 * (a + l) where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
In this case, the difference between consecutive terms is -3, the first term a = 14, and the last term l = -82. We find the number of terms by using the relation, l = a + (n-1)*d where d is the common difference. By substituting the given values, we can find that n = 33 terms. Substituting these values into the sum formula gives: S = 33/2 * (14 - 82) = -1122.
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where Q and R are polynomials and the degree of R is less than the degree of B.
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{a(x)}{b(x)}[/tex]
= [tex]\frac{2x^2-5x+6}{x-3}[/tex]
= 2x + 1 + [tex]\frac{9}{x-3}[/tex]
quotient q(x) = 2x + 1 and remainder r(x) = 9
What is the value of x in the equation 3(2x + 4) = −6? (4 points)
−3
1
12
19
3(2x+4)=-6 6x+12=-6
- 12. -12
6x = -18
÷6. ÷6
x= -3
Answer:
-3
Step-by-step explanation:
3(2x+4)= -6
6x+12= -6
6x= -18
x= -3
Find the diagonal of the rectangle solid with the given measures. I = 3, w = 5, h = 5
Hope this HELP:)))
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What are the period and amplitude of the function?
Question 1 options:
period: 5; amplitude: 3
period: 5; amplitude: 4.5
period: 6; amplitude: 3
period: 6; amplitude: 4.5
➷ The period is the distance from one part of the function to the same part of it.
In this case, the period is 5
The amplitude is the half the distance from the largest and smallest value
3 + 6 = 9
9/2 = 4.5
In this case, the amplitude is 4.5
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Let f(x)=6/−2+2e^−0.3x . What is f(−4) ?
DID THE TEST
ANSWER: 1.3
Answer:
[tex]f(-4)=1.3[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\frac{6}{-2+2e^{-0.3x}}[/tex]
we know that
f(-4) is the value of the function for x=-4
substitute x=-4 in the function
[tex]f(-4)=\frac{6}{-2+2e^{-0.3(-4)}}[/tex]
[tex]f(-4)=\frac{6}{-2+2e^{1.2}}[/tex]
[tex]f(-4)=1.3[/tex]
Answer:
1.94
Step-by-step explanation:
We substitute -4 into as x in the equation, but first what is e?
e is a term that represents the base of a natural logarithm and is a irrational number, its called Euler's number. e is equivalent to:
[tex]e=2.718[/tex]
We can substitute -4 into the equation
[tex]=6/(-2+2*(2.718^(-0.3*-4)))[/tex]
[tex]=6/(-2+2*(2.718^(1.2)))[/tex]
[tex]=6/(-2+2*2.54)[/tex]
[tex]=6/(3.09)[/tex]
[tex]=1.94
Therefore f(-4)=1.94
Simplify the expression (Picture provided)
Answer:
c. 1
Step-by-step explanation:
The given expression is
[tex]\cos(x) \csc(x) \tan(x)[/tex]
We express everything in terms of sine and cosine to obtain;
[tex]\cos(x) \times \frac{1}{\sin(x)} \times \frac{\sin(x)}{\cos(x)}[/tex]
We cancel out the common factors to obtain;
[tex]\frac{1}{1} =1[/tex]
Answer:
cos(x)csc(x)tan(x) = 1
Step-by-step explanation:
We have given a trigonometric expression.
cos(x)csc(x)tan(x)
We have to simplify the above expression.
Since, we know that
Tan(x) is ratio of sin(x) and cos(x).
Tan(x) = sin(x)/cos(x)
csc(x) is reciprocal of sin(x).
csc(x) = 1/sin(x)
Putting above values in given expression,we have
cos(x)csc(x)tan(x) = cos(x) × 1/sin(x) × sin(x)/cos(x)
cos(x)csc(x)tan(x) = 1 which is the answer.
Winona got her hair cut for $21. She left a 15% tip for the hair stylist. What is the total amount of money Winona paid?
Answer:
$24.15
Step-by-step explanation:
What you do is you take 15% and make it into a decimal which is .15.
Then you times it by $21. 21*.15=3.15.
You then take the $3.15 and add it to $21 to get
$24.15 as your answer.
Winona left a 15% tip for her $21 haircut, resulting in a tip of $3.15. When added to the cost of the haircut, it means she paid a total of $24.15.
Explanation:The question is asking us to find out how much Winona paid in total for her haircut, including a 15% tip. To find the amount of the tip, we can multiply the cost of the haircut (which is $21) by 15% (or 0.15 in decimal form): $21 * 0.15 = $3.15. To find the total amount Winona paid, we simply add the cost of the haircut to the tip: $21 + $3.15 = $24.15. So, Winona paid a total of $24.15 for her haircut.
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I will mark brainliest!
Answer:
-5
Step-by-step explanation:
Point P represents -5. You can see that the line counts up in increments of 2. P is in between -6 and -4. It must be -5.
The correct answer is -5
As we can see from the picture, we have the number -4 before P and -6 after P. Which would mean -5 is the correct answer.
I hope this helps! :)
Have a wonderful day!
-LizzyIsTheQueen
A company offers you a job with an annual salary of $70 000 for the first year and a 5% raise every year after. Approximately how much money in total would you earn in 5 years of working there?
$386794
$87500
$89340
$367500
Answer:
$89340
Step-by-step explanation:
70,000 (1 + .05)^5Answer:
$386794
Step-by-step explanation:
To find how much we're going to make in total after working for 5 years in the company, we can solve it by calculating for the total amount after each year.
So in the first year we get.
$70,000
To get how much we get in the 2nd year we add the extra 5%.
2nd year salary = (70000 x 0.05) + 70000
2nd year salary = 73500
Now we continue to do that until the 5th year
3rd = (73500 x 0.05) + 73500
3rd = 77175
4th = (77175 x 0.05) + 77175
4th = 81033.75
5th = (81033.75 x 0.05) + 81033.75
5th = 85085.44
Now we add them all up to get the total.
70000 + 73500 + 77175 + 81033.75 + 85085.44
We get:
$386794.19 or $386794
(4x + 3) + (-2x + 4)
Answer:
(4x + 3) + (-2x + 4) = 2x + 7Step-by-step explanation:
(4x + 3) + (-2x + 4)
= 4x + 3 - 2x + 4 combine like terms
= (4x - 2x) + (3 + 4)
= 2x + 7
A falcon flew 112 miles in the same time that an eagle flew 56 miles.What is the difference in the distances the two birds traveled?
the falcon flew 56 miles more than the eagle
Answer:
the eagle flew 56 miles less than the falcon
Step-by-step explanation:
112-56=56
Last year Jo paid ?245 for her car insurance. This year she has to pay ?883 for her car insurance. Work out the percentage increase in the cost of her car insurance.
Answer:
The increase as a percentage is (2.60)(100%) = 260%
Step-by-step explanation:
The premium increase from last year is ($883 - $245), or $638.
The increase as a ratio is then $638/$245, or 2.60.
The increase as a percentage is (2.60)(100%) = 260%
Jenny bought gas for her car gas cost 3.45 pee gallon jenny bought 12.2 gallons what was the total cost for jennys gas
Answer:
$42.09
Step-by-step explanation:
1. multiply the cost per gallon (3.45) by the gallons purchased (12.2)
3.45*12.2 = 42.09
Answer:
42.09
Step-by-step explanation:
12.2×3.45
!!!!!!!!!!!!!!!!!I could use some help please uwu!!!!!!!!!!!
use the iterative rule to find the 7th term in the sequence~
an=30-4n
a7=___
thankyou!~bangtanboys7
Answer:
Step-by-step explanation:
Just substitute in 7 for the n.
30-4(7)
30-28
2
The 7th term in the sequence is 2.
(please give brainliest?)
The 7th term in the sequence defined by aₙ = 30 - 4n, substitute n with 7 and solve to get a₇ = 2. Thus, the 7th term is 2.
To find the 7th term in the sequence defined by the iterative rule aₙ = 30 - 4n, we need to substitute n with 7.
Start with the formula:⇒ aₙ = 30 - 4n
Substitute n with 7:⇒ a₇ = 30 - 4(7)
Calculate the result:⇒ a₇ = 30 - 28
The 7th term is:⇒ a₇ = 2
So, the 7th term in the sequence is 2.
Complete question:
Find the 7th term in the sequence
aₙ = 30 - 4n
Write the equation for the inverse of y = cos 2x
Answer:
Inverse = (arcos x) / 2.
Step-by-step explanation:
y = cos 2x
2x= arcos y
x = (arcos y) / 2.
Inverse = (arcos x) / 2.
The equation for the inverse of y = cos 2x is obtained by switching the x and y variables and solving for y, resulting in y = arccos (x) / 2.
Explanation:The inverse of a function switches the roles of the x and y variables, so the first step to finding the inverse of y = cos 2x is to switch the x and y in the equation, giving us x = cos 2y. Now, we simply solve for y. The equation x = cos 2y is equivalent to 2y = arccos (x) where arccos is the inverse cosine function. Therefore, the final answer is y = arccos (x) / 2. This is the equation for the inverse of y = cos 2x.
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