Answer:
a) [tex]28.5-1.993\frac{23.1}{\sqrt{75}}=23.18[/tex]
[tex]28.5+1.993\frac{23.1}{\sqrt{75}}=33.82[/tex]
b) For this case since the value 32.5 is in the confidence interval obtained then we can't conclude that the statement by Nielsen is wrong
Step-by-step explanation:
Information given
[tex]\bar X=28.5[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=23.1 represent the sample standard deviation
n=75 represent the sample size
Part a
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=75-1=74[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex] and the critical value would be [tex]t_{\alpha/2}=1.993[/tex]
Now we have everything in order to replace into formula (1):
[tex]28.5-1.993\frac{23.1}{\sqrt{75}}=23.18[/tex]
[tex]28.5+1.993\frac{23.1}{\sqrt{75}}=33.82[/tex]
Part b
For this case since the value 32.5 is in the confidence interval obtained then we can't conclude that the statement by Nielsen is wrong
In 1998, Mary Meagher set the women's world swimming record for the 100-m butterfly. She swam the distance in 57.93 seconds. On average, how long did she take to swim 10 m?
Answer:
5.793 s
Step-by-step explanation:
On average she swam 1/10 the distance in 1/10 the time.
She took an average of 5.793 seconds to swim 10 m.
___
10 m is 1/10 of 100 m
What is the slope of a line perpendicular to y=-7X?
O A.
4
B.
IN
N
O c.
4
O D.
PLZZZ HELP
Answer:
1/7
Step-by-step explanation:
y=-7X
The slope of this line is -7
Perpendicular lines have slopes that multiply to -1
-7 * m = -1
Divide each side by -7
m = -1 / -7
m = 1/7
The slope of the perpendicular line is 1/7
Answer:
1/7
Step-by-step explanation:
Perpendicular slope can be calculated by take the opposite/negative reciprocal of the given slope. This means multiply the given slope by -1 (so if it is negative it becomes positive and if it is positive then becomes negative) and then flip the numerator and denominator.
So -7 is the slope of the given equation (y = mx + b where is m is slope and b is the y-intercept).
to find perpendicular slope..
Step 1. Multiple -7 by -1 = 7
Step 2. Flip 7/1 to 1/7
Answer: 1/7 is perpendicular slope
Geometry please help. What is the perimeter of XYZ
Answer:
39
Step-by-step explanation:
Angle AQC, AQB and BQC are 120deg. (360/3=120). Therefore, Angle BZC, CXA and AYB are 60deg. Because, angle BZC is half of angle BQC. same for the other three angles. As, all 3 angles are 60deg, it is an equilateral triangle. So, YZ is 13 therefore as all 3 sides are equal its 13*3=39.
The solution is: 39 is the perimeter of XYZ.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
Here, we have,
Angle AQC, AQB and BQC are 120deg.
(360/3=120).
Therefore, Angle BZC, CXA and AYB are 60deg.
Because, angle BZC is half of angle BQC.
same for the other three angles.
As, all 3 angles are 60deg, it is an equilateral triangle.
So, YZ is 13
therefore as all 3 sides are equal
its 13*3=39.
Hence, 39 is the perimeter of XYZ.
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KEVIN HAS TWO PART-TIME JOBS. HE DELIVERS PIZZA FOR PEDRO'S PIZZERIA
AND MAKES $8 AN HOUR, PLUS $20 FOR DRIVING EXPENSES EACH WEEK. HE
ALSO DOES ODD JOBS FOR A LOCAL HARDWARE STORE, WHERE HE IS PAID $10
AN HOUR.
A. WRITE A SYSTEM OF EQUATIONS TO DESCRIBE THE SCENARIO WHERE H
REPRESENTS THE NUMBER OF HOURS KEVIN WORKS, AND A
REPRESENTS THE AMOUNT HE EARNS AT EACH JOB IN A WEEK. B. HOW MANY HOURS MUST KEVIN WORK AT EACH JOB SO THAT HIS EARNINGS FROM BOTH SIDES ARE THE SAME? C. WHAT WOULD HIS INCOME FROM EACH JOB BE IN THAT CASE?
Answer:
A. A = 8h + 10
A = 10h
B. 5 hours
C. $50
Step-by-step explanation:
A. https://brainly.com/question/17036764
Pizza Place: A = 8h + 10
Hardware Store: A = 10h
Since you had made a separate question for part A, I answered that.
B. Kevin's earnings is represented by A. Because we want the earnings for each job to be equal, set the two equations equal to each other. Solve for h.
8h + 10 = 10h
10 = 2h
5 = h
Kevin has to work 5 hours.
C. Plug 5 into each equation.
A = 8h + 10
A = 8(5) + 10
A = 40 + 10
A = 50
A = 10h
A = 10(5)
A = 50
Kevin will make 50 from each job.
Every weekday, Mr. Jones bikes from his home to his job. Sometimes he rides along two roads, the long route that is shown by the solid lines. Other times, he takes the shortcut shown by the dashed line.
A right triangle. The distance from the angle with measure 90 degrees to Job is 15 kilometers. From the angle to Home is a. They hypotenuse is 17 kilometers.
How many fewer kilometers does Mr. Jones bike when he takes the shortcut instead of the long route?
6 kilometers
8 kilometers
23 kilometers
32 kilometers
Mark this and return
Answer:
(A)6 kilometers
Step-by-step explanation:
First, we determine the value of a using Pythagoras Theorem.
[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\17^2=a^2+15^2\\a^2=17^2-15^2\\a^2=289-225\\a^2=64\\a^2=8^2\\a=8$ km[/tex]
Therefore:
Distance along the long route = 8 + 15 =23 km
Distance along the shortcut =17 km
Difference =23-17 =6km
Therefore, Mr. Jones bikes 6km less when he takes the shortcut instead of the long route.
Answer:
a
Step-by-step explanation:
on edge
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise Find the indefinite integral.
a) dx3x 2 + 2
b) x3 + 2x
c) dx6x 5 + 5
d) x6 + 5x
Answer:
a.) dx3x² + 2
Use the properties of integrals
That's
integral 3x² + integral 2
= 3x^2+1/3 + 2x + c
= 3x³/3 + 2x + c
= x³ + 2x + C
where C is the constant of integration
b.) x³ + 2x
Use the properties of integrals
That's
integral x³ + integral 2x
= x^3+1/4 + 2x^1+1/2
= x⁴/4 + 2x²/2 + c
= x⁴/4 + x² + C
c.) dx6x 5 + 5
Use the properties of integrals
That's
integral 6x^5 + integral 5
= 6x^5+1/6 + 5x
= 6x^6/6 + 5x
= x^6 + 5x + C
d.) x^6 + 5x
integral x^6 + integral 5x
= x^6+1/7 + 5x^1+1/2
= x^7/7 + 5/2x² + C
Hope this helps
A random sample of 11 students produced the following data, where x is the hours spent per month playing games, and y is the final exam score (out of a maximum of 50 points). The data are presented below in the table of values. x y 14 46 15 49 16 37 17 42 18 37 19 31 20 25 21 23 22 20 23 15 24 12 What is the equation of the regression line?
Answer:
y= -3.7x+100.94
Step-by-step explanation:
Generally this type of problems is solved by using a calculator or a spreadsheet. Now, getting the final equation depends on the model of calculator you are using, so I will suggest you look for the instructions on your calculator's instruction manual. I'll provide indications for using excel.
So first you need to input the table on an excel sheet. You can input them just the same way they were given to you. (See attached picture)
Once you inputed them, you can highlight them and go to the insert tab. There you can pick the scattering plot option. Once the scatterplot is graphed, you can right-click on the graph and a menu should appear. Pick the option add tendency line. Choose the line option and below, you can mark the option present equation on the graph and present the value of R. And that will be it! Excel will automatically provide you with the equation of the regression line you need.
Most scientific calculators nowaday can provide you with the equation, you just need to input the data and they will return the slope and y-intercept of the line.
There are other formulas you can use to find this regression by hand, but they are generally used in statistics courses.
Dominics two daughters both want to take gymnastics this year. It cost 90 per month per child. How much dose dominic need to budget for a year ( 12 months) of gymnastics for both daughters
Answer:
$2,160 is what he need for both daughters for 1 year
Step-by-step explanation:
90 x 2 = 180
180 x 12 = 2,160
Dominic need to budget a total of 2160 for a year of gymnastics for both daughters.
What is Multiplication?Multiplication is one of the basic mathematical operations which includes a number added repeatedly to times of the other number. The final answer is called the product of the numbers.
Multiplication is usually denoted as '×' sign.
a × b indicates that a is added repeatedly upto b times.
Cost for the gymnastics per month per child = 90
In order to find the cost per month for both daughters, we need to multiply 90 with 2.
Cost for the gymnastics per month for 2 daughters = 2 × 90 = 180
To find the total cost for an year, we need to multiply 180 with 12.
Total cost for the year = 180 × 12 = 2160
Hence the total budget for Dominic to send both the daughter in a year is 260.
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the pie chart on the left shows the mean of transport 60 people use every morning to get to work. How many people use the train to go to work
Answer:
I wanna end myself bye random stranger.
There is a 0.9986 probability that a randomly selected 27-year-old male lives through the year. A life insurance company charges $174 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $90 comma 000 as a death benefit. Complete parts (a) through (c) below. a. From the perspective of the 27-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving? The value corresponding to surviving the year is $ negative 173.76. The value corresponding to not surviving the year is $ 125.76.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
There is a 0.9986 probability that a randomly selected 27-year-old male lives through the year. A life insurance company charges $174 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $90 comma 000 as a death benefit. Complete parts (a) through (c) below.
a. From the perspective of the 27-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
b. If the 27 -year-old male purchases the policy, what is his expected value?
c. Can the insurance company expect to make a profit from many such policies? Why? From the point of view of the insurance company, the expected value of the policy is
Answer:
a. The life insurance company charges $174 for insuring if the male survives
Value(survive) = -$174
The life insurance company pays $90,000 for insuring if the male does not survive.
Value(not survive) = $89,826
b. The expected value for a 27-year-old male is
E(x) = -$48
c. The expected value for the insurance company is
E(x) = $48
Step-by-step explanation:
The probability that a randomly selected 27-year-old male survives is given by
P(survive) = 0.99864
The probability that a randomly selected 27-year-old male does not survive is given by
P(not survive) = 1 - P(survive)
P(not survive) = 1 - 0.99864
P(not survive) = 0.0014
a. From the perspective of the 27-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
If 27-year-old male survives:
The life insurance company charges $174 for insuring if the male survives
Value(survive) = -$174
If 27-year-old male does not survive:
The life insurance company pays $90,000 for insuring if the male does not survive.
Value(not survive) = $90,000 - 174
Value(not survive) = $89,826
b. If the 27-year-old male purchases the policy, what is his expected value?
The expected value for a 27-year-old male is given by
E(x) = P(survive)×Value(survive) + P(not survive)×Value(not survive)
E(x) = 0.9986×-174 + 0.0014×89,826
E(x) = -$48
The negative sign indicates that it is a loss from the perspective of the 27-year-old male.
c. Can the insurance company expect to make a profit from many such policies? Why? From the point of view of the insurance company, the expected value of the policy is
The expected value for the insurance company is given by
E(x) = 0.9986×174 + 0.0014×-89,826
E(x) = $48
The positive sign indicates that it is a profit from the perspective of the insurance company.
Want Brainliest? Get this correct Which of the following is the quotient of the rational expressions shown below?
Answer:
B. 3x+15 / 4x+10
Step-by-step explanation:
[tex]\frac{3x+}{2x+5}[/tex] X [tex]\frac{x+5}{2x}[/tex] -> multiply by the reciprocal
[tex]\frac{3x}{2x+5}[/tex] X [tex]\frac{x+5}{2x}[/tex] -> reduce the expression
[tex]\frac{3}{2x+5}[/tex] X [tex]\frac{x+5}{2}[/tex] -> multiply the fractions
[tex]\frac{3(x+5)}{2(2x+5)}[/tex] -> remove parenthesis
and you get:
[tex]\frac{3x+15}{4x+10}[/tex]
-Hope this helps :)
what is the square root of -16
Answer:
Step-by-step explanation:
[tex]\sqrt{-16}=\sqrt{16i^{2}}\\\\ =\sqrt{4^{2}*i^{2}}\\\\=4i[/tex]
Eighteen telephones have just been received at an authorized service center. Six of these telephones are cellular, six are cordless, and the other six are corded phones. Suppose that these components are randomly allocated the numbers 1, 2, . . . , 18 to establish the order in which they will be serviced. (Round your answers to four decimal places.)
(a) What is the probability that all the cordless phones are among the first twelve to be serviced?
(b) What is the probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced?
(c) What is the probability that two phones of each type are among the first six serviced?
Answer:
a) 0.0498
b) 0.1489
c) 0.1818
Step-by-step explanation:
Given:
Number of telephones = 6+6+6= 18
6 cellular, 6 cordless, and 6 corded.
a) Probability that all the cordless phones are among the first twelve to be serviced:
12 are selected from 18 telephones, possible number of ways of selection = ¹⁸C₁₂
Then 6 cordless telephones are serviced, the remaining telephones are: 12 - 6 = 6.
The possible ways of selecting thr remaining 6 telephones = ¹²C₆
Probability of servicing all cordless phones among the first twelve:
= (⁶C₆) (⁶C₁₂) / (¹⁸C₁₂)
[tex] = \frac{1 * 924}{18564} [/tex]
[tex] = 0.0498 [/tex]
b) Probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced:
Here,
One type must be serviced first
The 6 remaining to be serviced can be a combination of the remaining two types.
Since there a 3 ways to select one type to be serviced, the probability will be:
= 3 [(⁶C₁)(⁶C₅) + (⁶C₂)(⁶C₄) + (⁶C₃)(⁶C₃) + (⁶C₄)(⁶C₂) + (⁶C₅)(⁶C₁)] / ¹⁸C₁₂
[tex] = \frac{3 * [(6)(6) + (15)(15) + (20)(20) + (15)(15) + (6)(6)]}{18564}[/tex]
[tex] = \frac{2766}{18564} [/tex]
[tex] = 0.1489 [/tex]
c) probability that two phones of each type are among the first six:
(⁶C₂)³/¹⁸C₆
[tex] \frac{3375}{18564}[/tex]
[tex] =0.1818 [/tex]
Carly owns a T-shirt shop. She pays $2.25 for each shirt.
Carly prints a picture on each shirt. The printing costs
her $1.00 per shirt. She sells the shirts for $10.50 each.
How much is the markup on each shirt?
Answer:
Total number of T-shirts= 200
Cost per T-shirt (without shipping ) = $2.80
Shipping cost per t-shirt ; 5% of a T-shirt = 0.05 *2.80 = $0.14
Total cost of T-shirt (shipping included) = 2.80 +0.14 = $2.94
Markup = 150% of total cost = 1.50 * 2.94 = $4.41
To get the price at which Michelle will sell each T-shirt , add total cost to the markup; 2.94 +4.41 = 7.35.
Therefore, selling price will be $7.35
Evaluate 9 x 8 = (10 x 8) - ( blank x 8) =80 - blank = blank
Answer:
see below
Step-by-step explanation:
9 x 8 = (10 x 8) - ( blank x 8) =80 - blank = blank
We are replacing 9 with 10 minus something
9 = 10 -1
9 x 8 = (10 x 8) - ( 1 x 8)
80 - 8
72
Pediatricians prescribe 5ml of cough syrup for every 25lb of a child’s weight. How many milliliters of cough syrup will the doctor prescribe for Jocelyn, who weighs 45lb?
Answer:
x=9
Step-by-step explanation:
for this sort of a problem, I would set up a proportion
5/25=x/45
multiply both sides by 25 and 45
45*5=x*25
225=25x
x=9
Find dy/dx by implicit differentiation.
x^2/x+y=y^2+7
Answer:
dy/dx = (2x − y² − 7) / (2xy + 3y² + 7)
Step-by-step explanation:
x² / (x + y) = y² + 7
x² = (x + y) (y² + 7)
Take derivative of both sides with respect to x. Use power rule, product rule, and chain rule.
2x = (x + y) (2y dy/dx) + (y² + 7) (1 + dy/dx)
Simplify.
2x = (2xy + 2y²) dy/dx + y² + y² dy/dx + 7 + 7 dy/dx
2x = (2xy + 3y² + 7) dy/dx + y² + 7
2x − y² − 7 = (2xy + 3y² + 7) dy/dx
dy/dx = (2x − y² − 7) / (2xy + 3y² + 7)
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Answer:
The picture on the bottom right.
Step-by-step explanation:
There are eight compartments and seven of it is shaded and the other one five of the eight compartments are shaped.
I hope this helps :)
4 -letter "words" are formed using the letters A, B, C, D, E, F, G. How many such words are possible for each of the following conditions? (a) No condition is imposed. (b) No letter can be repeated in a word. (c) Each word must begin with the letter A (d) The letter C must be at the end. (e) The second letter must be a vowel.
Answer: a) 2401 b) 840 c)343 d)343 e) 686
Step-by-step explanation:
a) Total are 7 letters
There are 4 possible places in 4-letter word for each of 7 letter.
So total amount of the words is
7*7*7*7= 2401
b) No letter can be repeated mens that in 1st place can stay any of 7 letters,
in 2-nd place- any of 6 letters
in 3-rd place- any of 5 letters
in 4-th place any of 4 letters
Total amount of words is
7*6*5*4=840
c) It is not written if the letters can be repeated. Assume that they can.
1st place occupied by letter A. So at 2-nd, 3-rd and 4th places can stay any of 7 letters
Total amount of words is
1*7*7*7=343
d) Similar case like c). At 1-st ,2-nd, 3-rd can stay any of 7 letters, and at 4th place the letter C (1 letter). Total amount of words is
7*7*7*1=343
e) There are 2 vowels A and E.
So at 1st place can stay any of 7 letters, at 2-nd place -any of 2 letters, at 3-rd place- any of 7 letters and at 4th place any of 7 letters. Total amount of words is
7*2*7*7=686
The total number of 4-letter words possible is 2401
The total number of 4-letter words possible with no letter repeated is 840
The total number of 4-letter words possible with the first letter being A is 343
The total number of 4-letter words possible with the letter C at the end is 294.
The total number of 4-letter words possible with the second letter being a vowel is 1029.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
(a) No condition is imposed:
There are 7 choices for the first letter, 7 choices for the second letter, 7 choices for the third letter, and 7 choices for the fourth letter.
The total number of 4-letter words possible.
7 × 7 × 7 × 7 = 2401
(b) No letter can be repeated in a word:
For the first letter, there are 7 choices.
For the second letter, there are only 6 choices left (since we cannot repeat the first letter). Similarly, for the third letter, there are only 5 choices left, and for the fourth letter, there are only 4 choices left.
The total number of 4-letter words possible with no letter repeated.
7 × 6 × 5 × 4 = 840
(c) Each word must begin with the letter A:
For the first letter, there is only 1 choice (the letter A). For the second letter, there are 7 choices (since any letter can be used).
For the third letter, there are 7 choices, and for the fourth letter, there are 7 choices.
The total number of 4-letter words is possible with the first letter being A.
1 × 7 × 7 × 7 = 343
(d) The letter C must be at the end:
For the fourth letter, there is only 1 choice (the letter C).
For the first letter, there are 7 choices (since any letter can be used).
For the second letter, there are 7 choices, and for the third letter, there are 6 choices (since the letter C cannot be used).
The total number of 4-letter words possible with the letter C at the end.
7 × 7 × 6 × 1 = 294
(e) The second letter must be a vowel:
For the first letter, there are 7 choices (since any letter can be used). For the second letter, there are 3 choices (the vowels A, E, and I).
For the third letter, there are 7 choices, and for the fourth letter, there are 7 choices.
The total number of 4-letter words possible with the second letter being a vowel.
7 × 3 × 7 × 7 = 1029
Thus,
The total number of 4-letter words possible is 2401
The total number of 4-letter words possible with no letter repeated is 840
The total number of 4-letter words possible with the first letter being A is 343
The total number of 4-letter words possible with the letter C at the end is 294.
The total number of 4-letter words possible with the second letter being a vowel is 1029.
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The water was pumped out of a backyard pond. What is the domain of this graph?
Two dice are rolled. Determine the probability of the following: rolling a 6 or doubles
Answer as an exact fraction = 5/18
Answer as an approximate decimal = 0.2778
Answer as an approximate percentage = 27.78%
============================================================
Explanation:
x = result of the first die
y = result of the second die
(x,y) paired together shows the results of both dice at the same time.
Something like (x,y) = (4,2) means we got 4 on the first die and 2 on the second die.
--------
Let's list the ways of rolling a 6
(1,5)(2,4)(3,3)(4,2)(5,1)There are 5 ways to roll a 6. Each pair listed has the property x+y = 6.
--------
List all the ways of getting doubles
(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)There are 6 ways to roll doubles. Each pair mentioned has x = y.
--------
We have 5+6 = 11 items listed above. However, there are only 10 unique pairs though because (3,3) was listed twice. So we could say 5+6-1 = 11-1 = 10.
This is out of 6*6 = 36 different ways to roll the two dice. The probability is therefore 10/36 = 5/18.
Using a calculator, 5/18 = 0.2778 = 27.78%
KARUNA OPENED A CANDY SHOP AND SELLS CHOCOLATE AND PEANUT
BUTTER FUDGE BY THE POUND. THE CHOCOLATE FUDGE COSTS $3.20 PER
POUND AND THE PEANUT BUTTER FUDGE COSTS $3.00 PER POUND. ON A
GIVEN DAY KARUNA'S CANDY SHOP SELLS 15.5 POUNDS OF FUDGE FOR A
GROSS PROFIT OF $48.50
A WRITE A SYSTEM OF EQUATIONS TO DESCRIBE THE SCENARIO WHERE C
REPRESENTS THE NUMBER OF POUNDS OF CHOCOLATE FUDGE SOLD,
AND P REPRESENTS THE NUMBER OF POUNDS OF PEANUT BUTTER
FUDGE SOLD
B. HOW MANY POUNDS OF PEANUT BUTTER FUDGE DID KARUNA'S CANDY
SHOP SELL?
Answer:
A. System of equations:
[tex]3.2C+3P=48.5\\C+P=15.5[/tex]
B. 5.5 pounds of peanut butter fudge were sold.
Step-by-step explanation:
Given:
Cost of chocolate fudge = $3.20
Cost of peanut butter fudge = $3.00
Total pounds sold = 15.5
Total gross profit = $48.50
C is the number of pounds of chocolate fudge sold.
P is the number of pounds of peanut butter fudge sold.
To find:
System of equations and number of pounds of peanut butter fudge sold = ?
Solution:
As per given conditions:
1. [tex]C+P=15.5[/tex]
Gross profit from Chocolate fudge: [tex]3.20 \times C[/tex]
Gross profit from Peanut Butter fudge: [tex]3.00 \times P[/tex]
Total gross profit = [tex]3.20C+3.00P = 48.50[/tex]
So, the system of equations is:
[tex]3.2C+3P=48.5\\C+P=15.5[/tex]
2. To find P.
Let us solve the equations.
Multiply 2nd equation with 3 and subtracting from 1st equation:
[tex]0.2C = 48.5- 3 \times 15.5\\\Rightarrow 0.2C = 48.5- 46.5\\\Rightarrow C = 10\ pounds[/tex]
Putting in 2nd equation:
[tex]10+P=15.5\\\Rightarrow P =5.5\ pounds[/tex]
So, the answer is:
5.5 pounds of peanut butter fudge were sold.
A standard 52-card deck of French playing cards consists of four suits: hearts, spades, clubs, and diamonds. There are 13 cards of each suit; each suit has cards of rank 2 through 10, along with an ace, king, queen, and jack. Typically, hearts and diamonds are the red suits, while spades and clubs are the black suits. Four cards are drawn from the deck, one at a time, without replacement. a) The second card drawn is from a red suit. Based on this information, what is the probability it is a heart
Answer:
P = 0.5
Step-by-step explanation:
Let's call A the event that the second card is red suit and B the event that the second card is a heart.
So, the probability that the second card is a heart given that is a red suit is calculated as:
P(B/A) = P(A∩B)/P(A)
Additionally, the probability P(A∩B) that the second card is a red suit and is a heart is equal to the probability P(B) that the second card is a heart. So,
P(B/A) = P(B)/P(A)
Then, P(A) is equal to 0.5 because half of the cards are red cards and P(B) is equal to 0.25 because a quarter of the cards are red. Finally, P(B/A) is equal to:
P(B/A) = 0.25/0.5 = 0.5
I'm having trouble finding the missing number. Please simplify the resulting fraction. Thank you in advance. : 0) 7/8 = ?/48
Answer:
42
Step-by-step explanation:
7/8 = x / 48
We need to get a common denominator
Multiply the left side by 6
7/8 *6/6 = x/48
42/48 = x/48
Since the denominators are equal, the numerators must be equal
42 =x
Answer:
42
Step-by-step explanation:
7/8=42/48
Cross products: 7(48)=8x
Anyone know how to solve 7 and 11
Answer:
7. f⁻⁻¹(x)=x-3 11. f⁻⁻¹(x)= 2x/(1-x)
Step-by-step explanation:
to find the inverse of an expression:
1. change f(x) to y.
2. switch the x and y values.
3. solve to find y.
So....
7.) f(x)=x+3 11.) f(x)= x/(x+2)
y=x+3 y=x/(x+2)
x=y+3 x=y/(y+2)
f⁻⁻¹(x)=x-3 f⁻⁻¹(x)= 2x/(1-x)
can someone please help me with this
Hope you understand :)
Answer:
DF = 3.0
<E = 31°
<F = 59°
Step-by-step explanation:
1. Use the Pythagorean Theorem to find side DF.
a² + b² = c²
5² + b² = 5.83²
25 + b² = 33.9889
b² = 8.9889
b = √8.9889
b = 2.998149429
b = 3.0
Side DF is equal to 3.0.
2. Use SOHCAHTOA to find the measure of <E. We know two sides: adjacent (5) and hypotenuse (5.83). So, we will use cosine.
Cosine = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{5}{5.83}[/tex] = 0.8576329331
Take the inverse cosine to find <E in degrees.
cos⁻¹ (0.8576329331) = 30.95 = 31°
<E is equal to 31°.
3. Add the two angles and subtract from 180° or use SOHCAHTOA to find the measure of <F.
90° + 31° + x = 180°
121° + x = 180°
x = 59°
or
We know two sides: adjacent (3.0) and hypotenuse (5.83). So, we will use cosine.
Cosine = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{3.0}{5.83}[/tex] = 0.5145797599
Take the inverse cosine.
cos⁻¹(0.5145797599) = 59.03063031 = 59°
<F is equal to 59°.
Hope that helps. :)
In a certain city, the monthly cost of residential electric service is given by the function C = 0.08n = 14, where n is the number of kilowatt hours (kWh) used 8 cents is the cost per kWh, and 14 is a fixed charge. Find the monthly bill if 600 kWh were used. $
Answer:
b and I will be there at work and I will be there at work and I will be there at work and I will
Step-by-step explanation:
you are not going to be able to make it to the meeting tonight but I can tomorrow if you have time
My soccer team has 16 players. I have to choose a starting lineup of a goalie and 10 regular players (the regular players are interchangeable). How many different starting lineups can i choose? *the answer is not 4368*
Answer:
3003
Step-by-step explanation:
We want to find out how many ways we can choose 10 players among 15 players (since the goalie is not interchangeable)
The number of different lineups you can have can be found by using combination:
[tex]^{15}C_{10} = \frac{15!}{(15 - 10)! 10!}\\ \\= \frac{15!}{5! * 10!} \\\\= 3003[/tex]
There are 3003 different lineups that can be chosen.
17. Write the greatest and the smallest 4-digit numbers using four different digits
with the conditions as given:
( Digit 7 is always at units place.
Answer:
Greatest number = 9867
Smallest number = 1027
Step-by-step explanation:
Greatest number:
- - - 7
In order to form the greatest number, we should simply put the greatest available digit at the thousands place, the second greatest at the hundreds place and the third greatest at the tens place (which would be 9, 8, and 6 respectively).
9867
Smallest number:
- - - 7
In order to form the greatest number, we should simply put the lowest available digit at the thousands place (excluding zero since a number can't start with a zero), put zero at the hundreds place and the third lowest at the tens place (which would be 1, 0, and 2 respectively).
1027
what is the remainder when x+ - 2x2 – 3x – 7 is divided by x + 2?
x+-2*2-3x-7
x+4-3x-7
x+1.x-7
x.x-7
2x-7