The mixed number of 2.81 is 2 whole number 81 by 100 or [tex]2\frac{81}{100}[/tex].
What is whole number?
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.
Given number is 2.81.
The number 2.81 can be written as 2 + 0.81.
The number of digits after decimal point is 2.
To convert 0.81 into fractional form, divide 81 by 100.
2 + 0.81 = 2 + (81/100)
The mixed number of 2.81 is [tex]2\frac{81}{100}[/tex].
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John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic?w(w – 2) = 48w(w + 2) = 482w(w – 2) = 482w(w + 2) = 48
The equation to solve the width of rectangle created by John from 48 square centimetre tiles is w(w+2) = 48
and the greatest width in centimetres use for mosaic is 6 cm.
We have given that
John wants to create a mosaic of rectangular shape.
total area of tile(A) = 48 square centimetre
let l and w be length and width of rectangle
length of rectangle is 2 cm longer than width then length of rectangle (l) =( w+2) cm
Area oa rectangle (A) = l × w
=> (w+2) × w = 48
=> w²+ 2w = 48
which is quadratic equation , solve it
w² + 2w - 48 = 0
=> w² - 6w + 8w - 48 = 0
=> (w-6) (w+8) = 0
=> w = 6, -8
Hence, the required equation is w(w+2) = 48 and width of rectangle is 6cm.
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Based on the 90% confidence interval of (8.21, 11.75) points, which of the following are reasonable 95% confidence intervals for the population mean difference in exam scores before and after taking an exam prep course? Select any that may apply: 83, 12.13) points 53, 11.83) points (8.45, 11.51) points (8.63, 11.33) points Cannot be determined with the information given: Saved
The reasonable 95% confidence intervals for the population mean difference is (7.83, 12.13) , the correct option is (a) .
In the question ,
it is given that ,
90% confidence interval is given as (8.21 , 11.75)
using this interval , we have to find the 95% confidence interval .
Now, [tex]x_{d}[/tex] - E = 8.21
[tex]x_{d}[/tex] + E = 11.75 , where E is the margin of Error .
Solving the equations ,
we get ,
E = 1.77 and [tex]x_{d}[/tex] = 9.98
So , the margin of error E is given as
E = [tex]t_{\frac{0.10}{2},15 } \times \frac{S.D.}{\sqrt{n} }[/tex]
we have to find standard deviation from this ;
given n = 16 and [tex]t_{\frac{0.10}{2},15 }[/tex] = 1.7531
Substituting in the margin of error equation ,
we get ,
S.D. = (1.77 × 4)/1.7531
= 4.0386
So , the 95% confidence interval is given as [tex]x_{d}[/tex] ± [tex]t_{\frac{0.10}{2},14 } \times \frac{S.D.}{\sqrt{n} }[/tex] .
from t table , [tex]t_{\frac{0.10}{2},14 }[/tex] = 2.1314
Substituting ,
we get ,
CI = (9.98 ± 2.1314×4.0386/√16)
= (9.98 ± 2.1519)
= ( 9.98 - 2.1519 , 9.98 + 2.1519)
= (7.83 , 12.13)
Therefore , the correct option is (a) (7.83 , 12.13) .
The given question is incomplete , the complete question is
Based on the 90% confidence interval of (8.21, 11.75) points, which of the following are reasonable 95% confidence intervals for the population mean difference in exam scores before and after taking an exam prep course? Select any that may apply:
(a) (7.83, 12.13)
(b) (7.53, 11.83)
(c) (8.45, 11.51)
(d) (8.63, 11.33)
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Explain why 1/2 is not equivalent to 2/5.
Answer:
as you can see on the picture, they both have same rectangle
1st figure is i divide it by 2 and shade 1 to get 1/2
2nd figure is I divide it by 5 and shade 2 to get 2/5
if we use LCD:
1/2 will become 5/10
2/5 will become 4/10
Therefore, proved that 1/2 is not equivalent to 2/5, on the other hand, 1/2 is greater than 2/5CREDITS:heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Britney is buying a shirt and a hat at the mall. The shirt costs $31.18, and the hat costs $18.32. If Britney gives the sales clerk $100.00, how much change should she receive? (Ignore sales tax.)
The change she should receive is $50.50 and we can find it by using simple cost and price calculations.
What is selling price?
Selling price is the amount of money that a seller charges for a product or service. It is the amount of money that a buyer pays for a product or service. The selling price is determined by a variety of factors, such as the cost of production, the perceived value of the product or service, the market demand for the product or service, competitive pricing in the market, and the profit desired by the seller. The selling price may also be affected by the availability of financing options for buyers, taxes, and other applicable fees. The selling price is an important factor in marketing and promoting a product or service. It must be set at the right level to attract buyers and ensure that the seller can make a profit.
Selling price for a shirt = $31.18
Selling price for a hat = $18.32
Total amount she have = $100
Total selling price (for both) = $49.50
So, the remaining amount = $100 - $49.50
= $50.50
So, the change she should receive = $50.50
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Tommy made s sandwiches for them to eat when they get hungry. Tommy put 3 slices of turkey and 3 slices of ham on each sandwich.
Pick all the expressions that represent how many slices of meat Tommy used on the sandwiches.
Answer:
Step-by-step explanation:het
14. Solve for t by factoring: t² - 2t - 15 =
Mr. Brooks spent one over two of an hour making gingerbread cookies and one over fourths of an hour breaking the cookies. She then spent 45 minutes decorating the cookie. How many total minutes did she spend on her gingerbread cookies
90 minutes
Step-by-step explanation:
1/2 an hour = 30 minutes
1/4 an hour = 15 minutes
45+15=60
60+30=90
You invest $60,000 in the stock market. Since you are a math genius, you have found the secret key
to great returns. You average 22% return on your money. Assume daily compounding (n=365).
Using the compound interest equation: A = P(1 + )"
nt
How much money will be in the account in 15 years?
Answer: $1,184,537.217
Step-by-step explanation:
You just multiply the number by 1.22 every year.
For example: year 1 (60,000 * 1.22)= 73,200
Year 2: (73,200 *1.22) =89,304
and so on until year 15 is reached.
suppose you calculate a 95% confidence interval for a proportion to to be: 0.17 to 0.97. determine the margin of error
The margin of error with a confidence interval of 0.17 to 0.97 is 0.4.
An indicator of the extent of random sampling error in survey results is the margin of error. In other words, the percentage point difference between the results and the actual population value is indicated by the margin of error. The confidence interval form is given by Confidence Interval = [lower confidence interval limit, upper confidence interval limit]. The confidence interval's total width divided by two is the margin of error.
Here, 95% confidence interval = [0.17, 0.97]. Then, the margin of error is,
[tex]\begin{aligned}\text{Margin of error (E)}&=\frac{\text{(upper confidence interval limit-lower confidence interval limit)}}{2}\\&=\frac{0.97-0.17}{2}\\&=\frac{0.8}{2}\\&=0.4\end{aligned}[/tex]
The answer is 0.4.
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help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee
find each of the shaded areas under the standard normal curve. round the answers to four decimal places. part 1 of 4 0.61 the area of the shaded region is .
(a) The area of the shaded region is 0.2709.
(b) The area of the shaded region is 0.3520.
(c) The area of the shaded region is 0.5555.
(d) The area of the shaded region is 0.6197
What is standard normal curve?
The horizontal axis is approached but never touched by the standard normal curve as it extends indefinitely in both directions. The center of the bell-shaped standard normal curve, which has a z=0 slope, is. Nearly all of the standard normal curve's area lies between z = 3 and z = 3.
The shaded area under the standard normal curve are,
1) Find, P[Z > 0.61 ]
= P[Z > 0.50]
= 1 - P[Z < -0.50]
= 1 - 0.7291 ( use z table)
= 0.2709
The area of the shaded region is 0.2709.
2) Find, P[Z < -0.38 ]
= P[Z < -0.38 ]
= 0.3520 ... ( use z table)
The area of the shaded region is 0.3520.
3) Find, P( -0.58 < Z < 0.98 )
= P(Z < 0.98 ) - P(Z < -0.58 )
= 0.8365 - 0.2810 ......(using z-table)
= 0.5555
The area of the shaded region is 0.5555.
4) Find , P( -0.11 < Z > 0.98 )
= 1 - P(Z < 0.98 ) - P(Z < -0.11 )
= 1 - ( 0.8365 - 0.4562 ) ......(using z-table)
= 1 - 0.3803
= 0.6197
Hence, the area of the shaded region is 0.6197.
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For y=|x|, explain why the range of the graph is not all real numbers.
The range is the set of all possible y-values that could come from the equation y = |x|.
Since the absolute value only results in 0 or positive numbers, the range cannot include any negative real numbers.
|3| = 3
|0| = 0
|-3| = 3
Therefore the range is not all real numbers, since all negative real numbers are excluded from the range.
The range is y ≥ 0.
A bag contains 8 red marbles, 7 white marbles, and 8 blue marbles. You draw 3 marbles out at random without replacement. Find the following probabilities and round your answers to 4 decimal places.
a. the probability that all the marbles are red
b. the probability that none of the marbles are red
The probability that all the marbles are red is 0.0156 and The probability that none of the marbles are red is 0.2109.
Given ,
bag contains 8 red marbles
7 - white marbles
8 - blue marbles.
a.The probability that every marble is red is
8/23 * 7/22 * 6/21
= 0.0156.
b.The likelihood that no red marbles are present is
15/23 * 14/22 * 13/21
= 0.2109.
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savings should be treated as another type of gross income. net income. tax. expenditure.; an income is measured as all money; compound interest is usually better than simple interest because it pays; what is part of the third step in troubleshooting a computer problem?; which expenditure will be the same whether you lease or buy a new vehicle?; which statement is most accurate about the hourly pay a worker receives brainly; which are affected by the factors of production? choose three answers.; what is the role of the three questions of economics
The answers of given statements are
a) option (A) i.e Net income.
b) The funds grow faster in case of compund interest.
c) Establish a theory of probable cause is third step
d) Gas and insurance
e) It is the rate for each day that is worked.
f) The production factors are labour, land etc.
g) Three basic questions related to economy are
What will be produced?how will it be produced?
how will the output society produces be distributed?
We have given some statements,
a) Saving should treated as an another type -->
Net income
After all sales-related expenses have been taken out, the remaining earnings are referred to as net income. Savings is the act of holding money for use in the future; it does not include paying for an item or service up front. The saving reffered as net income, or income after all expenses.
b) Compound interest is usually better than simple interest because it pays -->or allows funds to grow at a faster rate than they would in an account with a simple interest rate.
c) Third step in troubleshooting a computer problem is :
Step 3. Establish a theory of probable cause. Eliminate the simple and obvious possible causes.
d) Gas and insurance is expenditure will be the same whether you lease or buy a new vehicle.
e) Hourly pay is the rate for each day that is worked and is often calculated upon the number of hours the labor has been given to the factory.
f)The factors of production are
landlaborcapital, and entrepreneurship.g) An economic system is any system of allocating scarce resources. Economic systems answer three basic questions:
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A translation maps the point A(-4,7) to the point A'(6,11). Which of the following are the B cordinates of the point B
(4,15) under the same translation
The coordinates of B' are (14, 19) when coordinate of B are (4, 15)
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
Translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.
Given that after translation the point A(-4,7) to the point A'(6,11)
(x,y)---->(x+10, y+4)
A(-4,7)---->(-4+10, 7+4)=A'(6, 11)
Now we need to find coordinates of B' when B is (4, 15)
(4,15)--->(4+10, 15+4)=(14, 19)
Hence, the coordinates of B' are (14, 19) when coordinate of B are (4, 15)
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You have been given the task of organizing a poll regarding an upcoming election. The object is to estimate the proportion of the country that will vote to keep the current government in power. You have been told to collect a sample and find a 95% confidence interval for the proportion. This interval is allowed to have a margin of error of 3%. A preliminary investigation suggests that the proportion of people that will vote to keep the current government is 0.74. a) Calculate the minimum sample size that is required in this survey. Give your answer as a whole number. Someone working on your team reports that the information suggesting that the proportion of people that will vote to keep the current government is equal to 0.74 is out of date. In fact, some recent events in politics mean that there is no safe guess at what the proportion might be. b) Based on this new information, calculate the minimum sample size that is required in this survey. Give your answer as a whole number.
The confidence interval for the task of organizing the poll for the upcoming elections be,
(222.117 , 257.883)
Given, You have been given the task of organizing a poll regarding an upcoming election.
The object is to estimate the proportion of the country that will vote to keep the current government in power.
You have been told to collect a sample and find a 95% confidence interval for the proportion.
This interval is allowed to have a margin of error of 3%. A preliminary investigation suggests that the proportion of people that will vote to keep the current government is 0.74.
We have to find the confidence interval,
Subtract 1 from your sample size. 10 – 1 = 9.
Subtract the confidence level from 1, then divide by two.
(1 – .95) / 2 = .025
For 9 degrees of freedom df and α = 0.025, margin of error is 2.262.
Divide your sample standard deviation by the square root of your sample size.
25 / √(10) = 7.90569415
Now, Multiply 2.262 × 7.90569415 = 17.8826802
For the lower end of the range
240 – 17.8826802 = 222.117
For the upper end of the range
240 + 17.8826802 = 257.883
Hence, the confidence interval be (222.117 , 257.883)
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How many ways are there to choose six tiles that spell the word WATERS?
Answer:
0
Step-by-step explanation:
Find the sixth number in this sequence. (a.) The fourth number is equal to 3x10. (b.) The second number is equal to 10+6. (c.) The Third number is halfway between the second and fourth numbers. (d.) The fifth number is 7 more than the fourth number.
The sixth term of the sequence 9, 16,23,30,37 is 44
What is arithmetic sequence?An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 2, 4, 6, 8, 10, 12.. . is an arithmetic progression with a common difference of 2.
The nth term of an arithmetic sequence is given as a+(n-1)d. Where d is the common difference and a is the first term.
fourth term = 30
second term = 16
third term = (30+16)/2 = 46/2 = 23
therefore d= 30-23 = 7
a = 16-7 = 9
therefore the sixth term = 9+(6-1)7= 9+5×7 = 9+35= 44.
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An employee receives a salary increase of 8% at the end of each full year working with a company. If the employee receives an initial salary of $35,400, which equation represents the employee’s salary, S, after t years since the employee began working with the company?
The equation that represents the employee’s salary, S, after t years since the employee began working with the company is S(t) = 35400 * (1.08)^t
How to determine the equation that represents the employee’s salaryFrom the question, we have the following parameters that can be used in our computation:
Initial salary = 35400
Raise = 8%
Number of years = t
The equation that represents the employee’s salary is calculated as
Salary = Initial salary * (1 + raise)^Number of years
Substitute the known values in the above equation, so, we have the following representation
Salary = 35400 * (1 + 8%)^t
So, we have
S(t) = 35400 * (1.08)^t
Hence, the equation is S(t) = 35400 * (1.08)^t
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how to i find the decimal for 3√2 on a calculator its suppose to be 4.242 what do i put in what are the steps i can't figure it out.
Step-by-step explanation:
3√2 means 3 times the square root of 2.
Enter 2. Press the square root key to get square root of 2.
You should see 1.4142135
Now multiply by 3.
You should get 4.2426405
SOMEONE HELP ME
Solve. 35.1 = 12.9 + 10.2x Enter your answer as a mixed number in simplest form in the box.
Solving the expression 35.1 = 12.9 + 10.2x gives x to be 2 3/17
What is algebraic expression?A group of numbers or variables coupled with the operations +, -,, or form an expression.
Algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that simply contain numbers and mathematical operators.
How to find the value of xThe given algebraic expression is 35.1 = 12.9 + 10.2x
solving for x
35.1 - 12.9 = 10.2x
10.2x = 22.2
x = 22.2/ 10.2
x = 2 3/17 as a mixed number in simplest form
the value of x is 2 3/17
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The members of a sewing circle are making blankets to give to shelters. This week, they made 49 twin-size blankets and 49 queen-size blankets, using a total of 441 yards of fabric. Last week, the members completed 21 twin-size blankets and 48 queen-size blankets, which required 405 total yards of fabric. How much fabric is used for the different sizes of blankets?
8 twin-size blanket , y = 1 queen-size blankets will be the fabric used
According to the given information
let
x = number of yards of fabric required to make a twin-size blanket.
y = the number of yards of fabric required to make a queen-size blanket
This week, they used 441 yards of cloth to create 49 twin-size blankets and 49 queen-size blankets:
49x + 49y = 441
The group members finished 21 queen-size blankets and 48 twin-size blankets last week, using 405 yards of cloth altogether:
48x + 21y = 405
Solving the two equations
1029x + 1029y = 9261
2352x + 1029y = 19845
hence
Solving the above two equations
We get
1323x = 10584
x = 8
Putting the value of x in above one equation
y = 1
8 twin-size blanket , y = 1 queen-size blankets will be the fabric used
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Solve for n.
4.8 = 3n
If necessary explain in the simplest way possible.
The value of n is 1.6 if 4.8=3n by using simplest method.
What is meant by simplest equation?A mathematical equation links the two phrases on either side of the sign. It typically simply has an equal sign and one variable. similar to 2x - 4 = 2. Simple equations are used to demonstrate the relationship between two terms when they are positioned on each side of an equal sign. Simple equations are all used to follow the four mathematical operations of addition, subtraction, multiplication, and division.
By employing the shorthand symbol for "equal to" (=), it ensures that both expressions of the equation are equal. Equations utilize arithmetic operations like addition, subtraction, division, and multiplication to balance the expressions on both sides.
4.8=3n
Dividing on both sides with 3, we get
3n/3=4.8/3
n=1.6
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Which number sentence is true?
A.
B.
C.
D.
Answer:
you forgot the sentences dude
Find the missing variable in the following question.
If there is direct variation and y=75 when x=25, find x when y=48
x=16
x=14
x=10
x=12
Hence, [tex]x=16[/tex] when [tex]y=48[/tex].
What is the direct variation?
A direct variation, also called direct proportion is a relationship between two variables [tex]x[/tex] and [tex]y[/tex] that can be written as [tex]y = kx[/tex], [tex]k\neq 0[/tex].
Here given that,
The direct variation and [tex]y=75[/tex] when [tex]x=25[/tex],
As we know that,
[tex]y[/tex]α[tex]x[/tex]
[tex]y=kx[/tex]
[tex]75=k(25)\\\\k=\frac{75}{25}\\\\k=3[/tex]
So, when [tex]y=48[/tex]
[tex]y=kx\\\\48=3x\\\\x=\frac{48}{3}\\\\x=16[/tex]
Hence, [tex]x=16[/tex] when [tex]y=48[/tex].
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What is the AREA of this composite figure?
A. 134 square units
B. 72 square units
C. 234 square units
D. 102 square units
E. 132 square units
Answer:
102
Step-by-step explanation:
As we know that the area of triangle is 1/2 × base × height so A.TQ
1) finding the triangle area = 1/2 × base × height
= 6 × 5.
= 30
2) finding the area of rectangle = l×b
= 12 × 6
= 72
Now to find total area is 72 + 30 which will be 102
so the answer is = 102
Lucy and Zaki each throw a ball at a target. an image What is the probability that both Lucy and Zaki miss the target?
The Probability of both Zack and Lucy missing the target will be 0.48
Let the probability of Lucy and Zack missing the target be = P(L) and P(Z), respectively. So, If the probabilities of Zack and Lucy missing the target are as follows-
P(L) = 0.6 and
P(Z) = 0.8
then, the probability of both Lucy and Zack missing the target will be,
P(L) × P(Z) i.e.
0.6×0.8 = 0.48
Probability is basically a method to find out the possibility of likelihood of a certain outcome. In mathematics, it was introduced by Pierre and Cardano in the seventeenth century.
The complete question is-
The probabilities of Lucy and Zack hitting or missing the target are given in the following image. As per that, what will be the probability of both Lucy and Zack missing the target?
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Show and explain how replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions as the one shown.8x + 7y = 394x - 14y = -68
Answer:
Solution of the given equation by elimination method is x=0.5 and y=5.
Step-by-step explanation:
8x + 7y = 39 --------------(1)
4x - 14y = -68 ------------(2)
Multiply the equation 2 by -2, then add the equations along.
Equation (2) multiply by -2 : -8x +28y = 136
8x + 7y = 39 --------------(1)
-8x +28y = 136-----------(2)
Add these equations to eliminate x:
0x+35y=175
35y=175
y=5
Substitute y=5 in 8x+7y=39:
8x+(7)(5) =39
8x+35=39
8x=39-35
8x=4
X=8/4
x=0.5
Solution of the given equation by elimination method is x=0.5 and y=5.
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Can you please help me
Answer:
The answer is b!
Step-by-step explanation:
the answer is A .
the open end of the arrow points to the bigger variable. When the variable is included there will be a line under the arrow
The Mean Corporation manufactures a line of unassembled furniture. Based on historical evidence, the customer service manager knows that the proportion of customers that have not had any problems with assembling the furniture at home is 0.63.
Improvements have been made to the instructions provided with the furniture, and the customer service manager believes that this will increase the proportion of customers that can assemble the furniture without problems (TT) to above 0.63. A hypothesis test is conducted in order to find out.
The null and alternative hypotheses are:
H0: Pi symbol = 0.63
HA: Pi symbol > 0.63
To run the test, the manager randomly selects a sample of 102 people and asks them to assemble a piece of furniture produced by the Mean Corporation. The proportion of people in this sample that succeed is 0.67. You may find this standard normal table useful throughout this question.
a)Calculate the test statistic (z). Give your answer to 2 decimal places.
z =
b)Calculate the P-value. Give your answer as a decimal to 4 decimal places.
P =
The test statistic z = 0.84 and P-value is 0.2005 when there is a line of unassembled furniture produced by The Mean Corporation.
Given that,
There is a line of unassembled furniture produced by The Mean Corporation. The customer care manager is aware that 0.63 of customers have had no issues putting together their furniture at home based on past data.
The null and alternative hypotheses are:
H₀: π = 0.63
H₁: π > 0.63
We have to find
(a) Calculate the test statistic (z).
(b) Calculate the P-value.
We know that,
a) z = p - π / √(π(1-π)/n)
= 0.67 - 0.63 / √(0.63×0.37/102)
= 0.04 / 0.0478
= 0.84
b) p value(one tailed) is 0.2005.
Therefore, The test statistic z = 0.84 and P-value is 0.2005 when there is a line of unassembled furniture produced by The Mean Corporation.
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