Using the normal distribution, it is found that:
a) The probability that a randomly selected person spent more than $25 is of 0.3446 = 34.46%.
b) The probability that a randomly selected person spent between $12 and $21 is of 0.3307 = 33.07%.
c) The middle 95% of the amounts are between $13.2 and $32.8.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the costs of the meal are given as follows:
[tex]\mu = 23, \sigma = 5[/tex]
The probability that a randomly selected person spent more than $25 is one subtracted by the p-value of Z when X = 25, hence:
Z = (25 - 23)/5
Z = 0.4
Z = 0.4 has a p-value of 0.6554.
1 - 0.6554 = 0.3446 = 34.46%.
The probability that a randomly selected person spent between $12 and $21 is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 12, hence:
X = 21:
Z = (21 - 23)/5
Z = -0.4
Z = -0.4 has a p-value of 0.3446.
X = 12:
Z = (12 - 23)/5
Z = -2.2
Z = -2.2 has a p-value of 0.0139.
0.3446 - 0.0139 = 0.3307 = 33.07%.
The normal distribution is symmetric, meaning that the bounds of the middle 95% of values are given as follows:
2.5th percentile: X when Z = -1.96.97.5th percentile: X when Z = 1.96.-1.96 = (X - 23)/5
X - 23 = -1.96 x 5
X = $13.2
1.96 = (X - 23)/5
X - 23 = 1.96 x 5
X = $32.8
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is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.25 . If the flight is on time, the probability that her luggage will make the connecting flight is , but if the flight is 0.8 delayed, the probability that the luggage will make it is only 0.65
The probability that Rebecca's first flight was delayed is 75%.
What is probability?Probability is the ratio or odds of an expected outcome occurring when there are many possible outcomes.
Probability is always a fractional value lying between 0 and 1. When the expected outcome is certain, the probability is said to be one. When it is uncertain, the probability is zero.
Like ratios, probability is depicted as decimals, fractions, or percentages when there is no 100% certainty or uncertainty.
The probability of Rebecca's first flight leaving on time = 0.25
The probability of Rebecca's first flight being delayed = 0.75 (1 - 0.25)
= 75%.
Thus, it is 75% likely that Rebecca's first flight will be delayed.
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Question Completion:Suppose you pick her up at the Denver airport and her luggage is not there. What is the probability that Rebecca's first flight was delayed?
A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 60% pure antifreeze. The company wants to obtain 180 gallons of a mixture that contains 35% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be mixed?
The gallons of water and premium antifreeze solution that must be mixed are equal to 60 gallons and 120 gallons respectively.
How to determine the gallons of water and premium antifreeze solution?In order to calculate the gallons of water and premium antifreeze solution, we would assign variables to the gallons of water and premium 60% antifreeze that is required, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the gallons of water.Let the variable y represent the premium 60% antifreeze.Since the premium antifreeze solution contains 60% premium antifreeze, we have the following mathematical expression:
x + y = 180 ....equation 1.
0.60y = 0.40(180) ....equation 2.
From equation 2, we have:
0.60y = 0.40(180)
0.60y = 72
y = 72/0.60
y = 120 gallons of premium antifreeze.
For the gallons of water, we have the following:
x + y = 180
x = 180 - y
x = 180 - 120
x = 60 gallons of water.
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will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest
Area of the given figure is 27.852 in².
What is Area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
In the given figure there is a square.
First let us find the area of square, which has length of side 3 in
Area of square=3²=9
Now there are two semicircles with diameter 3 in.
Radius of semicircle = 3/2=1.5 in
Area of semicircle=2πr
=2×3.142×1.5
=9.426
As there are two semicircles
2×9.426
18.852
Area of figure is 9+18.852
27.852 in²
Hence, area of the given figure is 27.852 in².
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Function or not
x y
-10 5
4 -4
-8 6
7 5
-10 5
Answer: function
Step-by-step explanation: for ever input the is one output, even though -10,5 showed up multiple times it had the same input and output. So it’s a function …if I remember correctly.
If the 5 is negative on just one, it’s not a function.
so sorry if it’s wrong, best of luck :)
Kohler Corporation reports the following components of stockholders’ equity at December 31 of the prior year.
Common stock—$15 par value, 100,000 shares authorized, 50,000 shares issued and outstanding $ 750,000
Paid-in capital in excess of par value, common stock 70,000
Retained earnings 400,000
Total stockholders' equity $ 1,220,000
During the current year, the following transactions affected its stockholders’ equity accounts.
January 2 Purchased 6,000 shares of its own stock at $20 cash per share.
January 5 Directors declared a $2 per share cash dividend payable on February 28 to the February 5 stockholders of record.
February 28 Paid the dividend declared on January 5.
July 6 Sold 3,000 of its treasury shares at $24 cash per share.
August 22 Sold 3,000 of its treasury shares at $16 cash per share.
September 5 Directors declared a $2 per share cash dividend payable on October 28 to the September 25 stockholders of record.
October 28 Paid the dividend declared on September 5.
December 31 Closed the $428,000 credit balance (from net income) in the Income Summary account to Retained Earnings.
Required:
1. Prepare journal entries to record each of these transactions.
2. Prepare a statement of retained earnings for the current year ended December 31.
3. Prepare the stockholders’ equity section of the balance sheet as of December 31 of the current year.
1. The journal entries to record the transactions for Kohler Corporation are as follows:
Journal Entries:January 2 Debit Treasury Stock $90,0000
Credit Paid-in capital in excess $30,000 Cash $120,000
January 5 Debit Dividend $88,000
Credit Dividend Payable $88,000
January 5 Debit Retained Earnings $88,000
Credit Dividend $88,000
February 28 Debit Dividend Payable $88,000
Credit Cash $88,000
July 6 Debit Cash $72,000
Credit Treasury Stock $45,000
Credit Paid-inn Capital in excess $27,000
August 22 Debit Cash $48,000
Credit Treasury Stock $45,000
Credit Paid-inn Capital in excess $3,000
September 5 Debit Dividend $100,000
Credit Dividend Payable $100,000
September 5 Debit Retained Earnings $100,000
Credit Dividend $100,000
October 28 Debit Dividend Payable $100,000
Credit Cash $100,000
December 31 Debit Income Summary $428,000
Credit Retained Earnings $428,000
2. The preparation of the statement of retained earnings for the current year ended December 31 is as follows:
Kohler Corporation
Statement of Retained EarningsFor the current year ended December 31
Beginning balance $400,000
Dividends (88,000)
Dividends (100,000)
Income Summary 428,000
Ending balance $640,000
The preparation of the stockholder's equity section of the balance sheet as of December 31 of the current year is as follows:
Kohler Corporation
Stockholders' Equity Section of the Balance SheetAs of December 31 of the current year
Common stock—$15 par value, 100,000 shares authorized
50,000 shares issued and outstanding $ 750,000
Paid-in capital in excess of par value, common stock 70,000
Retained earnings 640,000
Total stockholders' equity $1,460,000
Transaction Analysis:January 2 Treasury Stock $90,0000 Paid-in capital in excess $30,000 Cash $120,000
January 5 Dividend $88,000 Dividend Payable $88,000 (50,000 - 6,000 x $2)
January 5 Retained Earnings $88,000 Dividend $88,000
February 28 Dividend Payable $88,000 Cash $88,000
July 6 Cash $72,000 Treasury Stock $45,000 Paid-inn Capital in excess $27,000 (3,000 x $24)
August 22 Cash $48,000 Treasury Stock $45,000 Paid-inn Capital in excess $3,000 (3,000 x $16)
September 5 Dividend $100,000 Dividend Payable $100,000 (50,000 x $2)
September 5 Retained Earnings $100,000 Dividend $100,000
October 28 Dividend Payable $100,000 Cash $100,000
December 31 Income Summary $428,000 Retained Earnings $428,000
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Please help!!
Will give 5 points asap
The probabilities are given as follows:
a) P(both marbles are red) = 0.167 = 16.7%.
b) P(red then green) = 0.111 = 11.1%.
c) P(green then blue) = 0.083 = 8.3%.
d) P(blue and red, any order) = 0.333 = 33.3%.
How to obtain a probability?The probability of an event in an experiment is calculated as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.
In this problem, the are nine marbles, of which four are red, hence the probability of both red is:
p = 4/9 x 3/8 = 0.167 = 16.7%.
(the marble is not replaced, hence for the second marble there will be eight possible marbles, of which 3 are red).
For red then green, the probability is:
p = 4/9 x 2/8 = 0.111 = 11.1%.
For green then blue, the probability is:
p = 2/9 x 3/8 = 0.083 = 8.3%.
For blue or red, there are two possible outcomes, blue then red or red then blue, hence:
p = 3/9 x 4/8 + 4/9 x 3/8 = 0.333 = 33.3%.
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4+3 × (2 − 1) + 8 + (9-7)
Answer:
1
Step-by-step explanation:
Answer:17
Step-by-step explanation:
its just the order of operations aka PEMDAS If you want to know more about the order of operations just look it up. :)
Graph the equation y= - 7/2 x + 2 on the coordinate plane.
Step-by-step explanation:
your intercepts are:
y-intercept:
y = - 7/2x + 2
y = - 7/20 + 2
y = 2
( 0 , 2 )
x-intercept:
y = - 7/2x + 2
0 = - 7/2x + 2
-2 = - 7/2x
-7/2x = -2
2x = 2/7
x = 4/7
( 4/7 , 0 )
Write, solve and graph a compound inequality: An architect is designing a rectangular park. The perimeter of the park must be at least 5,000ft and less than 8,000ft. If the width is 8 less than half the length, what are the possible lengths of the park?
The inequality of the scenario is 10000 ≤ l² - 16l < 16000 and the length is 1672 feet
How to determine the inequality?The statements from the question are given as:
Shape = Rectangular park
Minimum perimeter = 5000 square ft
Maximum perimeter = Less than 8000 square ft
Also, we have
Width = 8 less than half the length
This means that
w = 1/2l - 8
The perimeter of a rectangle is
perimeter = 2 * (l + w)
So, we have
P = lw
This gives
P = 2 * (l + 1/2l - 8)
P = 2 * (1.5l - 8)
Open the brackets
P = 3l - 16
Substitute the known values in the above equation So, we have the following equation
5000 ≤ 3l - 16 < 8000
The above represents the inequality
See attachment for the graph
From the graph, we have the solution to be
l = 1672 (approximately)
Recall that:
w = 1/2l - 8
So, we have
w = 1/2 * 1672 - 8
Evaluate
w = 828
Hence, the possible length is 1672 ft
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Write an equation of the line passing through point P(0, -1) that is parallel to the line y = - 2x+3.
Answer:
[tex]y=-2x-1[/tex]
Step-by-step explanation:
If two lines are parallel, they have the same slope. In this case, it is -2
Using point-slope form, with a slope of -2 going to through point P(0,-1)
We have:
y+1=-2x
y = -2x - 1
:]
Juan scored a total of 37 points in the basketball game, and he scored p points in the second half of the game. Write an expression to determine the number of points he scored in the first half of the game. Then, find the number of points he scored in the first half of the game if he scored 11 points in the second half of the game.
for lunch three days ago, i had four tacos , each with a different kind of filling. Three of my tacos contained a green salsa. My friend clara had three burritos on the same day, each with a different kind of filling. Clara is vegetarian so none of her burritos had meat. together, how many tacos and burritos did we have?
Answer:
The answer to your question is,
7
Step-by-step explanation:
Function or not
x y
6 4
-8 2
9 -4
-3 8
6 -4
-6 4
Answer: not a function
Step-by-step explanation: one input has more than one output and to be a function it must have one output for every input.
I hope it’s right, best of luck :)
Can someone please find the area of the shaded area? Thanks! :) I’ll give brainly
Answer:
87 [tex]ft^{2}[/tex]
Step-by-step explanation:
11x9=99
99 ft is the area of the rectangle
Now we need the area of the triangle
4x6=24
24/2=12
12 ft is the area of the triangle so we subtract this from the area of the rectangle
99-12=87
Hopes this helps please mark brainliest
Una bolsa de palomitas contiene 438 calorias y sirve a 3.5 personas cuantas calorias hay en cada porcion?
The number of calories in each serving is 125.14 calories.
How to calculate the number of calories?The bad of popcorn has 438 calories. Also, it was stated that it can serve 3.5 people.
The number of calories for each serving will be the division of the calories given.
This will be:
Number of calories = Total calories / Number of people
= 438 / 3.5
= 125.14 calories
Each serving has 125.14 calories.
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Determine an nth degree polynomial that satisfies the aforementioned conditions.
The polynomial of p(x) is -24 (x² + 15x + 54) with the satisfying's conditions degree 3.
Given,
An nth degree polynomial p meets the requirements listed below:
p is of degree 3.
-9 is a zero, with multiplicity 2, of p.
-6 is a zero, with multiplicity 1, of p.
p(-1) = -960
We have to determine an nth degree polynomial that satisfier the conditions.
Let the polynomial be p(x) whose zero are -9 and -6
a be the coefficient.
p(x) = a (x+9) (x+6)
p(x) = a(x² + 6x + 9x + 54)
p(x) = a(x² + 15x + 54)
Now, take x = -1
p(-1) = a (-1² + 15 x -1 + 54)
-960 = a ( 1 - 15 + 54)
-960 = a x 40
a = -960/40
a = -24
We get,
p(x) = -24 (x+9) (x+6)
p(x)= -24 (x² + 15x + 54)
Therefore, the polynomial of p(x) is -24 (x² + 15x + 54) with the satisfying's conditions degree 3.
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Find the perimeter of the rectangle. The drawing is not to scale.
Answer: 190
Step-by-step explanation:
first you add 29 + 29 and you get 58. Next, you add 66 + 66 which is 132 then you add the 2 sums together and get 190. :)
Find the inverse of f(x) = 1/ x + 8
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{f(x)}{y}~~ = ~~\cfrac{1}{x+8}\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~\cfrac{1}{y+8}} \implies y+8=\cfrac{1}{x}\implies {\large \begin{array}{llll} \stackrel{f^{-1}(x)}{y}=\cfrac{1}{x}-8 \end{array}}[/tex]
An account has a rate of 1.9%. Find the effective annual yield if the interest is compounded quarterly.
Answer:
1.914 %
Step-by-step explanation:
Compounded quarterly means 4 periods per year = n
interest in decimal form per period i = .019/4 = .00475
Formula
annual yield = ( 1+ i)^n -1
(1+ .00475)^4 -1 = .01914 = ~ 1.914%
Maxine's credit card has an APR of 21.99%. If her current monthly balance, before interest, is $2,586.50, what will her monthly interest charge be?
According to the given APR, the monthly interest charge is $47.46
APR
Basically, APR refers the refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors.
Given,
Maxine's credit card has an APR of 21.99%.
Here we have to find the monthly interest charge if her current monthly balance, before interest, is $2,586.50.
While we looking into the given question, we have identified the following,
APR = 21.99%
For one month the APR is calculated as,
APR = 21.99 / 12
APR = 1.8325%
When we convert this into decimal form then we get,
=> APR = 1.8325/100
=> APR = 0.01835
And the current monthly balance is $2,586.50,
So, the interest change for the month is
=>2,586.50 x 0.01835
=> 47.46
Therefore, the monthly interest charge is $47.46.
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A local lighthouse is 170 feet tall. During a visit to the lighthouse Xavier, who is 6
feet tall, cast a shadow that was 1.8 feet long. How long, in feet, was the shadow
that the lighthouse cast?
Answer: 51 ft
Step-by-step explanation:
This is a Similar Triangles problem (geometry)
Draw 2 triangles with the sides correctly labeled.
Set up your ratios
170/6 = x/1.8
Solve for x
28.3 = x/1.8
x = 51 ft (length of shadow cast by the lighthouse)
358.584 divided by 9.92
Answer:
36.147580645161
Step-by-step explanation:
Hope it helps you
A manager samples the receipts of every sixth person who goes through the line. Out of 40 people, 3 had a mispriced item. If 750 people go to this store each day, how many people would you expect to have a mispriced item ?
Answer:
f
Step-by-step explanation:f
The equation of the line that goes
through the point (3, 1) and is
perpendicular to the line
2x + 4y = 5 can be written in the
form y
y = mx + b where m= and b=
The equation of the line that goes through the point (3, 1) and is perpendicular to the line 2x + 4y = 5 can be written in the form y = mx + b where m= 2 and b= -5.
According to the question,
We have the following information:
Points = (3,1)
Equation of the line: 2x+4y = 5
Now, converting this line into y = mx+b form:
4y = -2x+5
y = -2y/4+5/4
y = -y/2+5/4
Now, the slope of this line is -1/2.
Slope of the line perpendicular to this line will be 2 (-1/m).
Now, the equation of the line will be:
(y-y') = m(x-x')
x' = 3 and y' = 1
y-1 = 2(x-3)
y-1 = 2x-6
y = 2x-6+1
y = 2x-5
The value of m is 2 and b is -5.
Hence, the equation of the line that goes through the point (3, 1) and is perpendicular to the line 2x + 4y = 5 can be written in the form y = mx + b where m= 2 and b= -5.
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How do I write this out?
The magnitude of the second earthquake, using an logarithmic function, is of:
5.77.
How to obtain the magnitude of the earthquakes?The magnitude of an earthquake is given by the logarithmic rule presented as follows:
[tex]M = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]
The first earthquake had a magnitude of 3.9, hence it's energy is obtained as follows:
[tex]3.9 = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]
[tex]\log{\left(\frac{E}{E_0}\right)} = \frac{3.9 \times 3}{2}[/tex]
[tex]\log{\left(\frac{E}{E_0}\right)} = 5.85[/tex]
The logarithm and the base 10 are inverse functions, hence the base 10 is applied to both sides to isolate the energy variable as vollows:
[tex]\frac{E}{E_0} = 10^{5.85}[/tex]
[tex]E = 707945.784E_0[/tex]
For the second earthquake, it's energy was 650 times greater, hence:
[tex]E = 707945.784 \times 650E_0 = 460164760E_0[/tex]
Hence it's magnitude is obtained as follows:
[tex]M = \frac{2}{3}\log{\left(\frac{460164760E_0}{E_0}\right)}[/tex]
M = 5.77.
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A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 23 mg every six hours. Complete parts (a) and (b) below.
a. Following this dosage, how many 12.2 mg chewable tablets would be taken in a week?
b. This antihistamine also comes in a liquid form with a concentration of 12.2 mg/10 mL.. Following the prescribed dosage, how much liquid antihistamine should a 100-pound person
take in a week?
a. A 100-pound person could take tablets in a week.
(Round to the nearest whole number
as needed.)
b. A 100-pound person could take mL in a week
(Round to the nearest whole number as needed.)
a) The number of 12.2 mg chewable tablets would be taken in a week is 53.
b) The liquid antihistamine should a 100-pound person taken in a week is 528ml
What is meant by ratio and proportion?An ordered pair of numbers a and b, denoted as a / b, is a ratio if b is not equal to 0. A proportion is an equation that equalizes two ratios.. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls.
Given that a typical dose for a 100-pound person is 23 mg every six hours.
100 pounds person - 23 mg - 6hrs
For 1 day it is 24 hrs
7 days-168hrs
Therefore,
a) For 6 hrs - 23 mg
168 hrs- ?
X=(23×168)/6
=644 mg
For 1 tablet -12.2 mg
=644/12.2
= 52.786≈53 tablets
The number of 12.2 mg chewable tablets would be taken in a week is 53.
b) If 12.2 mg equals to 10 ml then
644mg =(10/12.2)×644 ml
=527.87 ml≈528ml
The liquid antihistamine should a 100-pound person taken in a week is 528ml
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in the fruit bowl there are 12 bananas 8 apples and 4 oranges. do for every one orange there are ___ bananas
For every 1 orange in the fruit bowl there are three bananas.
According to the question,
We have the following information:
In the fruit bowl there are 12 bananas, 8 apples and 4 oranges.
Now, in order to find the number of bananas in this fruit bowl for 1 orange can be as written below:
4 oranges = 12 bananas
Now, to find the number of bananas for 1 orange, we will divide the total number of bananas by the number of oranges.
So, we have the following expression:
1 orange = 12/4 bananas
1 orange = 3 bananas
Hence, for every 1 orange in the fruit bowl there are three bananas.
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Describe the function‘s end behavior. f(x)=−10+6x^5+4x^3
as x→ ∞, f(x)→
as x→ −∞, f(x)→
Possible answers for both are:
-∞
∞
0
an asymptote
We have an odd degree polynomial wit a positive leading coefficient, then the end behavior is:
as x → ∞, f(x) → ∞
as x → -∞, f(x) → -∞
What is the end behavior of the function?Here we have the function:
f(x) = -10 + 6x^5 + 4x^3
Notice that this is a polynomial of degree 5 (odd degree).
When we have a odd degree polynomial, we know that:
If the leading coefficient is positive, then the end behavior is:
as x → ∞, f(x) → ∞
as x → -∞, f(x) → -∞
If instead, the leading coefficient is negative, then:
as x → -∞, f(x) → ∞
as x → ∞, f(x) → -∞
For the case of:
f(x) = −10+6x^5+4x^3
The leading coefficient is 6, so it is positive, then the end behavior of our function is:
as x → ∞, f(x) → ∞
as x → -∞, f(x) → -∞
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What is the slope of a line perpendicular to the line whose equation is 2x+3y=24 Fully simplify your answer.
Answer:
y = -2/3 x + 8
Step-by-step explanation:
here is the answer in the image above
2(g-1)=2g-1
A. No solution
B. 1 solution
C. Indefinitnely solution