In second half of the month it rain by 1/12 of an inch.
Define Algebraic Expression
In mathematics, an expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)
Given,
The rainfall in Georgetown during the first half of the month was = 1/4 inch
The total rainfall for the month was = 1/3 of an inch
To get an answer for this, you need to subtract the amount of rainfall in first half from the total rainfall for the month. This would tell the how much it rained in the second half of the month.
= 1/3 - 1/4
= 4/12 - 3/12
= 1/12
Hence, In second half of the month it rain by 1/12 of an inch.
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A time-and-motion study measures the time required for an assembly-line worker to perform a repetitive task. The data show that the time required to bring a part from a bin to its position on an automobile chassis varies from car to car according to a Normal distribution with mean 11 seconds and standard deviation 2 seconds. The time required to attach the part to the chassis follows a Normal distribution with mean 20 seconds and standard deviation 4 seconds. The study finds that the times required for the two steps are independent. A part that takes a long time to position, for example, does not take more or less time to attach than other parts. Management's goal is for the entire process to take less than 30 seconds. Find the probability that this goal will be met for a randomly selected part.
The amount of time required for an assembly line worker to complete a repetitive task is measured using a time and motion study.
According to the data, the average time it takes to move apart from the bin to its place on a car's chassis is 11 seconds, while the standard deviation is 2 seconds.
If XX and YY are independent, the property mean and variance are as follows: X 1 = 11; sigma_X_1 = 2, X 1 = 2, mu_X_2 = 20, X 2 = 20, sigma_X_2 = 4, and X 2 = 4.
aX+bY = a X + b Y; sigma_aX+bY = a X + b Y; aX+bY 2 = a 2 X 2 + b 2 Y 2; and finally, we have the following results:
X 1 + X 2 = X 1 + X 2 = 11+20=31 sigma_X_1+X_2=sqrtsigma_X_1+sigma_X_2=sqrtsigma_X_1+sigma_X_2=sqrtsigma_X_2=sqrtsigma_X_2=sqrtsigma_X_2=sqrtsigma_X_1+
The value reduced by the mean and divided by the standard deviation is the z-score:
z=\dfrac{x-\mu} {\sigma} =\dfrac{30-4.4721} \approx - 0.22
z=σx−μ =4.472130−31
≈−0.22
Decide the relating esteem utilizing table A:
P (X_1+X_2 30) = P(Z-0.22) = 0.4129 P (X 1 30) = P(Z-0.22) = 0.4129
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Four transformations of the function f f (x x ) = 4x x + 5 are given below. For each transformation, drag the expression that shows the result of that transformation into the box under it. Math item stem image CLEAR CHECK (4x x + 5)3x x 4(3x x • x x ) + 5 4(x x + 3) + 5 3(4x x + 5) 4(3x x ) + 5 4x x + 3 + 5 f f (x x + 3) f f (x x ) + 3 3f f (x x ) f f (3x x )
The graphs and the equations are matched and mentioned above.
What is a mathematical function, equation and expression?Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is a graph of the function as shown in the image.
The function g(x) = f(x) + 2, is represented by graph [1].
The function h(x) = f(x + 2), is represented by graph [6].
The function k(x) = f(x) - 2, is represented by graph [3].
The function g(x) = f(x - 2), is represented by graph [5].
Therefore, the graphs and the equations are matched and mentioned above.
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Amelia has two sheets of construction people with length accent meters one piece of construction paper has a width of X +4. 5 cm and the other has a width of X +6. 25 cm right and expression to represent the the two pieces of construction paperwork cover
x² + 6.25x + 4.5x + 28.125, this expression represents the area the 2 pieces of construction paper will cover.
What is the quadratic equation?
A quadratic equation is any equation in algebra that can be rearranged in standard form as where x represents an unknown value and a, b, and c represent known numbers, with a 0.
We have,
Amelia has 2 sheets of construction paper with length x centimeters.
One piece of construction paper has a width of x+4.5 centimeters, and the other has a width of x+6.25 centimeters.
expression to represent the area the 2 pieces of construction paper will cover.
To find the area(A) of a paper:
multiply its height by its width:
A = (x + 4.5) * (x + 6.25)
A = x² + 6.25x + 4.5x + (4.5) * (6.25)
A = x² + 6.25x + 4.5x + 28.125
hence, x² + 6.25x + 4.5x + 28.125, this expression represents the area the 2 pieces of construction paper will cover.
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A line passes through the point (4, -8) and has a slope of 5/2
Write an equation in slope-intercept form for this line.
help me pls this is due in 30 minutes
Answer:
y = (5/2)x - 18
Step-by-step explanation:
plug in the x, y, and m into the formula y=mx+b, solve for b, and create the formula y = (5/2)x - 18
[tex]y=mx+b[/tex]
m represents the slopeb represents the y-interceptSolving the QuestionWe're given:
passes through (4, -8)slope of [tex]\dfrac{5}{2}[/tex]Plug the slope, [tex]\dfrac{5}{2}[/tex], into [tex]y=mx+b[/tex]:
[tex]y=\dfrac{5}{2}x+b[/tex]
Now, to solve for b, plug in the given point (4, -8):
[tex]-8=\dfrac{5}{2}(4)+b\\\\-8=10+b\\b=-18[/tex]
Plug this into our equation:
[tex]y=\dfrac{5}{2}x-18[/tex]
Answer[tex]y=\dfrac{5}{2}x-18[/tex]
1. Jericho was stacking paper cups in a dispenser that was 32 centimeters high. The paper cups were 8 centimeters tall, and each paper cup after the first added 0.75 centimeters to the height of the stack. How many paper cups can Jericho fit in the dispenser?
2. Anthony has a collection of 56 red tokens and cold tokens. The number of gold tokens in his collection is 12 less than the number of red in his collection. How many red tokens does he have in his collection?
3. Catherine’s age is six more than half of Sally’s age . If the sun of their ages equals 30, how old is Catherine?
4. Robert was a participant at a quiz show where he needed to answer 20 questions three points were awarded for every correct answer and one point was deducted for every incorrect answer. If Robert and a total of 44 points, how many questions did he answer correctly?
The answers are 3, 34, 14 and 16
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given are the problems based on equation making and solving,
1) The equation for finding the number of cups will be =
x(8+07.5) = 32
Where x the number of cups.
x = 32/8.75 ≈ 3
Hence, The number of cups is 3
2) Let the number of Red tokens be R and Gold tokens be G, setting up the equation, we get,
R+G = 56
R-G = 12
Adding the equations,
R+R+G-G = 56+12
2R = 68
R = 34
Hence, The number of Red tokens is 34
3) Let the Sally's age be 2x, therefore, Catherine's age is 6+x
Setting the equations,
6+x+2x = 30
3x = 24
x = 8
Therefore, Catherine's age is 8+6 = 14
4) Let the numbers of answers Robert correctly answered be x,
Setting up the equation,
3x-1(20-x) = 44
3x-20+x = 44
4x = 64
x = 16
Therefore, he answered 16 questions correctly.
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a restaurant offers a dinner special for $25 per person plus a $5 per-person tip. Which expressions represent the special?
Rewrite log[(4)] using the properties of logarithms.
log[(4)] = 0.60205999132
Answer:
The value of log 4 to the base 10 is 0.6020. In this article, we will discuss the value of log 4 in terms of both natural logarithm and common logarithm in the logarithmic function. Logarithms are inverse of exponential functions.
Here is the value of log 4 with respect to base-10 and base-e.
Step-by-step explanation:
Now, let us discuss finding the value of log 4 using a common and natural log functions. Also, find the log of 4 to the base 2 here.
the belt (orbit) of the asteroids is located between . group of answer choices venus and mercury saturn and uranus jupiter and mars earth and mars
The main belt is not located between these all planets.
What is orbit?
A route that an object in space follows around another is known as an orbit. A satellite is a thing that orbits the earth. An Earth- or moon-like natural satellite is one possibility. Moons are satellites that orbit many planets. A man-made satellite is also possible, such as the International Space Station.
The belt of asteroids is located between the orbits of Mars and Jupiter. The asteroids in this region, known as the main belt, are made up of small rocky bodies that orbit the sun in a region between about 2.2 and 3.2 astronomical units (AU) from the sun.
The distance from the sun to the Earth is about 1 AU, and the distance from the sun to Venus is about 0.7 AU, so the main belt is located beyond the orbits of both Venus and Earth.
The orbits of Saturn and Uranus are much farther out from the sun, at distances of about 9.5 and 19.2 AU, respectively, so the main belt is not located between these planets.
Hence, The main belt is not located between these all planets.
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An object falls freely from rest under the influence of gravity. If air resistance is negligible, the ratio ofthe distances traveled during each 1-second time interval by the object during the first, second, and third seconds of its fall is
O 1:1:1
O 1:2:3
O 1:2:4
O 1:3:5
O 1:4:9
The correct answer is O 1:2:3. In a free-falling object, its acceleration due to gravity is constant.
What is distance?Distance is the physical separation between two points or objects. It is usually measured in miles, kilometers, or meters. Distance can be used to measure the length of a journey, the size of an area, or the difference between two locations. Distance is also used to measure the time taken to travel, the speed of an object, or the strength of a signal. Distance is an important concept in physics and mathematics, and it is fundamental to the understanding of the universe.
This means that the distance covered in each 1-second time interval is directly proportional to the square of the time elapsed. Therefore, the ratio of distances traveled during each 1-second time interval by the object during the first, second, and third seconds of its fall will be 1:2:3.
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2. Which system has an infinite number of solutions?
a. x+2=y
4= 2y-x
b. 2y + 6 = 4x
-3=y-2x
c. y+3=2x
4x=2y-3
d. y = 2x - 5
-2 = y - 2x
Answer: B
Step-by-step explanation:
Substitution method
solve the equation for Y by putting the variable on the left. -3 = y - 2x would become y = 2x - 3
Plug Y into the top equation. 2(2x - 3) + 6 =4x
4x - 6 + 6 = 4x
Combine like terms
4x - 0 = 4x
4x = 4x
Infinite Solutions
A newspaper article reported the results of a study comparing the proportions experiencing pain
relief using a new medication compared to using a placebo. The study showed that the proportion
experiencing pain relief was higher for the new medication (p1) when compared to the placebo
(p2). The researcher is quoted as saying that there was less than a 1 in 100 probability that the
observed differences in proportions was due to chance. The null hypothesis for this study is:
Answer:
there is no question here so how can i give you an answer?
Step-by-step explanation:
1. Use the unit circle to find the exact value of the inverse trig function. Remember the domain of inverse cosine is limited to to quadrants | and || (the top half of the unit circle)
2. Use the unit circle to find the exact value of the inverse trig function. Remember the domain of inverse sine is limited to to quadrants | and |V (the right side of the unit circle)
Answer:
A. 120 degrees.
B. 0 degrees.
Can you explain me how factorize this : (x+1)²+3(x+1)+x+1
The factorization of the given expression is obtained as (x + 1)(x + 5).
How to factorise an algebraic expression?In order to factorize an expression first find all the terms that have the common factors. Then, write those terms in the form of product of factors. This is the way to factorize an expression.
The given algebraic expression is (x + 1)²+ 3(x + 1) + x + 1
It can be factorized as follows,
(x + 1)²+ 3(x + 1) + x + 1
⇒ (x + 1)²+ 3(x + 1) + (x + 1)
⇒ (x + 1)²+ 4(x + 1)
In all the three terms the common factor is (x + 1).
Take (x + 1) as common to get,
(x + 1)(x + 1 + 4)
⇒ (x + 1)(x + 5)
Hence, the given algebraic expression can be factorized as (x + 1)(x + 5).
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The ECOA Valuations Rule requires lenders to issue a copy of the appraisal or written valuation to an applicant
The ECOA Valuations Rule requires lenders to issue a copy of the appraisal or written valuation to an applicant. This is true.
What is ECOA?Discrimination in any way related to a credit transaction is forbidden by the Equal Credit Opportunity Act (ECOA). It covers all credit extensions, including those given to corporations, partnerships, trusts, and small businesses. The ECOA outlaws discrimination.
According to the ECOA Valuations Rule, you have three business days from the time you receive an applicant's application to inform them that they have the right to a copy of the appraisals. You must provide the applicant with copies of all appraisals and other written valuations as soon as possible.
According to the ECOA Valuations Rule, creditors must inform applicants of their right to obtain copies of appraisals and written valuations
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The ECOA Valuations Rule requires lenders to issue a copy of the appraisal or written valuation to an applicant. True or false.
For each value of v , determine whether it is a solution to v/9+7=13
Write a statement that correctly interprets the confidence interval. Choose the correct answer below. O A. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion. B. 95% of sample proportions will fall between the lower bound and the upper bound. C. One has 95% confidence that the sample proportion is equal to the population proportion. D. There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
The sample proportion is 0.5507, standard error is 0.0151, margin error is 0.030 and population proportion fall between 0.521<p<0.58
A.
One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
The sample proportion, pcap = 0.5507
b) sample size, n= 1084
The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean.
standard error, SE = [tex]\sqrt{(pcap*(1-pcap)/n)}[/tex]
SE=[tex]\sqrt{(0.5507*(1-0.5507)/1084)}[/tex]= 0.0151
Given Cl level is 95%, hence [tex]\alpha =1-0.95=0.05[/tex]
[tex]\frac{\alpha }{2}= \frac{0.05}{2}= 0.025[/tex]
Zc=Z[tex](\frac{\alpha }{2} )=1.96[/tex]
Margin of errors, in statistics, is the degree of error in results received from random sampling surveys.
Margin of error, ME = zc×SE
ME= 1.96×0.0151
ME= 0.030
c) Cl= (pcap-z×SE, pcap+z×SE)
Cl = (0.5507-1.96×0.0151, 0.5507+1.96×0.0151)
Cl= (0.521, 0.58)
0.521<p<0.58
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I need help answering the question for math hw 13188 divided by 12
Answer:
1099
Step-by-step explanation:
Use a calculator
One angle measures 18°, and another angle measures (6d − 6)°. If the angles are complementary, what is the value of d? d = 2 d = 13 d = 31 d = 36.2
The value of d for the given angles will be equal to d = 13. The correct option is B.
What is the complementary angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Complementary angles are formed when the sum of two angles equals 90 degrees. 30 degrees and 60 degrees, for example, are complementary angles.
Given that one angle measures 18° and another angle measures (6d − 6)°.
The value of d will be calculated as,
18 + 6d - 6 = 90
6d + 12 = 90
6d = 90 - 18
6d = 78
d = 78 / 6
d = 13
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level of confidence,
represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained. It is denoted
left parenthesis 1 minus alpha right parenthesis times 100 %.
The alpha value is the threshold for statistical significance.
What is the level of confidence in probability and statistics?Confidence levels must be decided upon in advance when conducting a survey since they affect the survey's essential scope and error margin. Confidence intervals of 90, 95, and 99% are widely employed in surveys.
A determined statistical result that was based on a sample would likewise hold true for the entire population within the established confidence level if the confidence level were set at 95%.
The probability cutoff for statistical significance is the alpha value. Although p = 0.05 is the most typical alpha value, 0.1, 0.01, and even 0.001 have also been utilized. To choose which alpha value to utilize, it is best to look at the research articles that have been published on your subject.
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Robbie pulls a marble out of the bag. What is the probability that the marble will be blue?
1/8
1/2
1/3
1/4
Answer: 1/4
Step-by-step explanation:
To find the probability that Robbie will pull a blue marble out of the bag, we need to first determine the total number of marbles in the bag. Since there are 2 blue marbles, 4 red marbles, and 2 yellow marbles, the total number of marbles in the bag is 2 + 4 + 2 = 8.
Next, we need to determine the number of blue marbles in the bag. Since there are 2 blue marbles, the number of blue marbles in the bag is 2.
Finally, we can use these numbers to calculate the probability that Robbie will pull a blue marble out of the bag. The probability is equal to the number of blue marbles divided by the total number of marbles, which is 2 / 8 = 1/4. Therefore, the probability that Robbie will pull a blue marble out of the bag is 1/4.
Find the measures of angle
m∠1=___
m∠2=___
Applying the triangle sum theorem, the measures of the angles are:
m∠1 = 30°
m∠1 = 60°
What is the Triangle Sum Theorem?The triangle sum theorem states that we will always have a sum of 180 degrees when we add all interior angles of a triangle.
Therefore:
m∠2 = 180 - 90 - 30 [triangle sum theorem]
m∠2 = 60°
Angle 1 and Angle 2 are complementary angles, therefore:
m∠1 + m∠2 = 90
Substitute
m∠1 + 60 = 90
m∠1 = 90 - 60
m∠1 = 30°
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1 2 Write the equation of each parabola given below. Vertex (-2, 5); focus (-2,-8)
Answer:
Step-by-step explanation:Question Number 15:
The following transactions were completed during May, the second month of the business’s operations:
May
1. Shannon Burns made an additional investment in Dancing Music by depositing $3,000 in Dancing Music’s checking account.
1. Instead of continuing to share office space with a local real estate agency, Shannon decided to rent office space near a local music store. Paid rent for May, $1,600.
1. Paid a premium of $3,360 for a comprehensive insurance policy covering liability, theft, and fire. The policy covers a two-year period.
2. Received $1,200 on account.
3. On behalf of Dancing Music, Shannon signed a contract with a local radio station, KPRG, to provide guest spots for the next three months. The contract requires Dancing Music to provide a guest disc jockey for 80 hours per month for a monthly fee of $2,400. Any additional hours beyond 80 will be billed to KPRG at $40 per hour. In accordance with the contract, Shannon received $4,800 from KPRG as an advance payment for the first two months.
3. Paid $250 on account.
4. Paid an attorney $150 for reviewing the May 3rd contract with KPRG. (Record as Miscellaneous Expense.)
5. Purchased office equipment on account from One-Stop Office Mart, $5,000.
8. Paid for a newspaper advertisement, $200.
11. Received $600 for serving as a disc jockey for a college fraternity party.
13. Paid $500 to a local audio electronics store for rental of digital recording equipment.
14. Paid wages of $1,200 to receptionist and part-time assistant.
16. Received $1,100 for serving as a disc jockey for a wedding reception.
18. Purchased supplies on account, $750.
21. Paid $240 to Rocket Music for use of its current music demos in making various music sets.
22. Paid $500 to a local radio station to advertise the services of Dancing Music twice daily for the remainder of May.
23. Served as disc jockey for a party for $1,560. Received $400, with the remainder due June 4, 2006.
27. Paid electric bill, $560.
28. Paid wages of $1,200 to receptionist and part-time assistant.
29. Paid miscellaneous expenses, $170.
30. Served as a disc jockey for a charity ball for $1,200. Received $600, with the remainder due on June 9, 2006.
31. Received $2,000 for serving as a disc jockey for a party.
31. Paid $600 royalties (music expense) to Federated Clearing for use of various artists’ music during May.
31. Withdrew $2,000 cash from Dancing Music for personal use.
Dancing Music’s chart of accounts and the balance of accounts as of May 1, 2006 (all normal balances), are as follows:
Instructions
1. Enter the May 1, 2006 account balances in the appropriate balance column of a four-column account. Write Balance in the Item column, and place a check mark (✔) in the Posting Reference column. (Hint: Verify the equality of the debit and credit balances in the ledger before proceeding with the next instruction.)
2. Analyze and journalize each transaction in a two-column journal, omitting journal entry explanations.
3. Post the journal to the ledger, extending the account balance to the appropriate balance column after each posting.
4. Prepare a unadjusted trial balance as of May 31, 2006
5. Prepare adjusting journal entries. You will need the following additional accounts:
18 accumulated Depreciation—Office Equipment 22 Wages Payable
57 Insurance Expense 58 Depreciation Expense
The data needed to determine adjustments for the two-month period ending May 31, 2006, are as follows:
a. During May, Dancing Music provided guest disc jockeys for KPRG for a total of 110 hours. For information on the amount of the accrued revenue to be billed to KPRG, see the contract described in the May 3, 2006.
b. Supplies on hand at May 31, $170.
c. The balance of the prepaid insurance account relates to the May 1, 2006.
d. Depreciation of the office equipment is $100.
e. The balance of the unearned revenue account relates to the contract between Dancing Music and KPRG, described in the May 3, 2006.
f. Accrued wages as of May 31, 2006, were $130. Instructions
6. Post the adjusting entries, inserting balances in the accounts affected.
7. Prepare an adjusted trial balance.
8. Prepare a ten-column work sheet.
9. Prepare an income statement, a statement of owner’s equity, and a balance sheet. (Note: Shannon Burns made investments in Dancing Music on April 1 and May 1, 2006.)
10. Journalize and post the closing entries. The income summary account is #33 in the ledger of Dancing Music. Indicate closed accounts by inserting a line in both Balance columns opposite the closing entry.
11. Prepare a post-closing trial balance
|2x - 1|> 7.
|7-5x|<3
Answer:
1)x=2
2)4<x
3)x<4/5
4)1<x
H(y) models the leading number of home runs for season y of the National League between the years 2000-2010, according to the table.
Season Player # of Home Runs Team
2000 Sammy Sosa 50 Chicago
2001 Barry Bonds 73 San Francisco
2002 Sammy Sosa 49 Chicago
2003 Jim Thome 47 Philadelphia
2004 Adrian Beltre 48 Los Angeles
2005 Andruw Jones 51 Atlanta
2006 Ryan Howard 58 Philadelphia
2007 Prince Fielder 50 Milwaukee
2008 Ryan Howard 48 Philadelphia
2009 Albert Pujols 47 St. Louis
2010 Albert Pujols 42 St. Louis
Which number type is more appropriate for the domain of H?
The type of number is more appropriate for the domain of H would be;
2000 ≤ x ≤ 2010
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
Given that H(y) models the leading number of home runs for season y of the National League between the years 2000-2010,
The domain must lie in between 2000 Sammy Sosa 50 Chicago AND 2010 Albert Pujols 42 St. Louis
Then the Integers for as greater than 2000 and less than 2010.
The appropriate for the domain of H is
2000 ≤ x ≤ 2010
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Can someone please answer this problem for me.
Length of each Plan A workout: 4 hours and Length of each Plan B workout: 8 hours.
To find the length of each workout plan, we need to know the total amount of time that Deshaun spent on each plan. We can find this by adding up the number of clients who did each plan on Friday and Saturday and then multiplying by the total amount of time that Deshaun spent training his clients on each day.
On Friday, Deshaun had 4 clients who did Plan A and 8 who did Plan B, for a total of 4 + 8 = 12 clients.
On Saturday, Deshaun had 2 clients who did Plan A and 3 who did Plan B, for a total of 2 + 3 = 5 clients.
In total, Deshaun had 12 + 5 = 17 clients who did his workout plans.
Since Deshaun trained his Friday clients for a total of 17 hours and his Saturday clients for a total of 7 hours, the total amount of time that he spent on Plan A was 4 × 17 = 68 hours.
The total amount of time that he spent on Plan B was 8 × 17 = 136 hours.
Since there were 17 clients in total, the length of each Plan A workout is 68 / 17 = 4 hours.
The length of each Plan B workout is 136 / 17 = 8 hours.
Thus, the length of each Plan A workout is 4 hours, and the length of each Plan B workout is 8 hours.
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The distance is 1,163 miles and the driving is 17 hours and 38 minutes
Answer:
Step-by-step explanation:
17 hours multiplied by 60 (60 seconds in 1 minute) = 1020 minutes + 38 minutes = 1058 minutes.
Miles per hour = distance/time
1163/1058 = 1.10 miles per hour
Whats the answer ? I don’t know this please help?
3/2 is an example of a rational number which can be proved by the properties of rational number.
What is a Rational number?
Rational numbers are numbers which can be expressed as a fraction and also as positive numbers, negative numbers and zero. It can be written as p/q, where q is not equal to zero.
According to the given question:
An example of a rational number can be 3/2. It means integer 3 is divided by another integer 2
Check the following 3 properties of a rational number to determine if it is rational
1. If the number can be written in fraction form
2. If the numerator and denominator of the fraction are integers
3. And the denominator is not equal to zero
If any number satisfies these 3 conditions then it is said to be a rational number
Let's prove for our example that is 3/2
1. 3/2 is a fraction in which 3 is numerator and 2 is denominator
2. 3 and 2 are integers
3. the denominator 2 is not equal to zero.
Hence it is proved that 3/2 is a rational number.
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When solving a word problem using a system of equations, how many equations
must you create when there are two unknowns?
a) 1
b) 2
c) 3
d) 4
Answer:
The answer for the above question is:
b)2
When solving a word problem using a system of equations with two unknowns, you must create two equations. So, correct option is B.
The reason is that each unknown in the problem requires an equation to represent its relationship with the other variables.
For example, let's say you have two unknowns, x and y. You need two equations to define the relationships between these variables. These equations can be represented as:
Equation 1: x + y = 10 (This equation represents the relationship between x and y based on the given information in the problem.)
Equation 2: 2x - y = 4 (This equation represents another relationship between x and y based on additional information provided in the problem.)
With a system of two equations involving two unknowns, you can use algebraic methods such as substitution or elimination to solve for the values of x and y.
Having only one equation would not be enough to determine unique values for both x and y, as there would be an infinite number of possible solutions. On the other hand, having more than two equations might lead to over-determining the system, making it inconsistent or redundant.
Therefore, two equations are the minimum required to solve for two unknowns effectively. So, correct option is B.
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there are 365 days in a year, 24 hours per day, 12 months per year, and 60 minutes per hour. use these data to determine how many minuytes are in a month
A month has 43,800 minutes, according to the information given.
Multiplication is what?Multiplication in the context of integers or counting numbers is just repeated addition. Consequently, 3 x 5 equals:
5 is added to 0 and placed in the "accumulator."
For a total of three times, repeat operation (1).
As a/b times c/d = ac/bd, we can simply extend multiplication to rational integers. By the way, this definition enables us to say that multiplication is closed for rational numbers.
What distinguishes addition from multiplication?
Concentrating on the words "sum" and "product" in relation to "things that aren't numbers" is still beneficial. In logic, the terms "sum" and "product" have a non-numerical sense as the union and intersection of sets.
For instance, a "blue circle" is a reasonable outcome. It is where the "blue" and "circle" sets cross. The only components in the logical combination of the two sets would be those that are "blue" or "circular."
The no: of minutes in a month is 30*24*60=43200 minutes in a month
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a production line manager wants to determine how well the production line is running. he randomly selected 90 items from the assembly line and found that 8 were defective. (assume all conditions have been satisfied for building a confidence interval). find the 99% confidence interval to estimate the population proportion of items that are defective.
The 99% confidence interval to estimate the population proportion of items that are defective is (0.0116, 0.1662).
Sample size , n = 90
defective items , x = 8
Sample proportion = x / n
= 8/90 = 0.0889
= 1- 0.0889 =0.9111
At 99% confidence level the z is ,
α = 1 - 0.99 = 0.01 , α/ 2 = 0.01 / 2
= 0.005
Zα/₂ = Z0.005 = 2.576 ( Using z table )
Margin of error Formula, E = Zα/2× (sqrt(((p-hat× (1 - p-hat)) /n)
= 2.575 ×sqrt((0.0889*0.9111) /90 )
E = 0.0773
A 99% confidence interval is
p-hat - E < p < p-hat + E
=> 0.0889 - 0.0773 < p < 0.0889 +0.0773
=> 0.0116 < p< 0.1662
Hence, confidence interval is (0.0116, 0.1662).
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