Answers
[tex]\frac{1}{4}x + 2 = -3 + \frac{1}{2} x[/tex]
First, we will take [tex]\frac{1}{4}[/tex]x to the right hand side of the equation, and -3 to the left hand side. In doing so, their signs will change (that is, they will be subtracted from the side that they are moved to).
2 -(-3) = [tex]\frac{1}{2} x - \frac{1}{4} x[/tex]
2 + 3 = [tex]\frac{1}{4}[/tex]x
[tex]\frac{1}{4} x = 5[/tex]
Now, we will multiply both sides by 4, so as to find x.
[tex]\frac{1}{4} x[/tex] x 4 = 5 x 4
x = 20
Therefore, x = 20.
Related Questions
The sale price of ground beef at a local grocery store is $1.49 for the first pound and $1.09 for each additional pound. Which function rule shows how the cost of ground beef, y depends on the number of pounds, x?
Answers
Answer:
y=1.09x+0.4
Step-by-step explanation:
Let's assume that the price of beef stays the same for every pound of beef (the first pound is also $1.09)
Then, the equation would be, it y was the cost, and x was pounds:
y=1.09x
But, the price of beef is not the same for the first pound.
The first pound costs an extra 1.49-1.09=0.4 dollars a pound, so we will add that to the equation.
y=1.09x+0.4
A local charity organization held an event to celebrate its work for the past five years. A local newspaper reporter who attended the event asked 75 of the attendees about their contributions. The reporter computed the mean amount of money raised by the 75 attendees to be $18,500. In an article published by the local newspaper, the reporter was quoted as stating, "The members of the charity organization were successful in raising money for their cause. Last year, they raised a mean amount of $18,500!"
Part A: What is a statistical advantage of using the median of the reported amounts, rather than the mean, as the estimate of the typical amount raised? (4 points)
Part B: The newspaper editor felt the individuals who attended the event may be different from the organization as a whole. A more detailed survey of the members was planned to determine a better estimate of the amount of money raised. The staff developed two methods based on the available funds to carry out the survey.
Method 1: Send out an e-mail to all 10,530 members of the organization and ask them to complete an online form. The staff estimates at least 2,000 members will respond.
Method 2: Select a simple random sample of members of the organization and contact the selected members directly by phone. Follow up to ensure all responses are obtained. Because method 2 requires more time than method 1, the staff estimates that only 1,000 members of the organization can be contacted using method 2.
Which of the two methods would you select for estimating the average yearly amount raised by all 10,530 members of the charity organization? Explain your reasoning by comparing the two methods and by describing the effect of each method on the estimate.
Answers
Answer:
Part A. The statistical advantage of using the median is that the median is less effected by skewed data and outliers.
Part B. I would select method two because method one has a non-response bias and the sample individuals are not selected at random.
Step-by-step explanation:
Higher values pull averages up where medians just select the middle value and aren't necessarily pulled by outliers.
Non response biases happen when the individuals chosen choose not to answer or can volunteer to answer.
Sending out emails to everyone at the org is not choosing them at random.
A statistical advantage of using the median instead of the mean as the estimate of the typical amount raised is that the median is less sensitive to extreme values or outliers.
Method 1 would be the better choice for estimating the average yearly amount raised by all 10,530 members of the charity organization
What is a median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
Part A:
A statistical advantage of using the median instead of the mean as the estimate of the typical amount raised is that the median is less sensitive to extreme values or outliers.
In this case,
If there were a few attendees who contributed a very large amount of money, it would increase the mean and make it an overestimate of the typical amount raised.
However, the median would not be affected by the outliers, and it would give a better estimate of the typical amount raised by the majority of the attendees.
Part B:
Method 1 would be a better choice for estimating the average yearly amount raised by all 10,530 members of the charity organization.
This is because it would have a larger sample size than method 2, which would make the estimate more precise and reduce the sampling error.
Additionally,
Method 1 would include a broader range of members, including those who may not have attended the event or who may have contributed in other ways besides donating money.
Method 2, on the other hand, would have a smaller sample size and would only include a random subset of the organization's members, which could lead to sampling bias if the selected members are not representative of the larger population.
Furthermore, the follow-up required by method 2 would make it more time-consuming and potentially less cost-effective than method 1.
Thus,
Method 1 would be the better choice for estimating the average yearly amount raised by all 10,530 members of the charity organization because it would have a larger sample size, include a broader range of members, and be more cost-effective than method 2.
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y - 4x = 5
8x - 2y = 16
Solve using system of equations
Answers
Answer:
No solution
Step-by-step explanation:
Let's solve this system using elimination through addition/subtraction. Multiply the second equation by (1/2), which results in the system
y - 4x = 5
4x - y = 8
--------------
0x + 0y = 13. This is NEVER true. This system of equation has NO SOLUTION.
The probability for event A is 0.4, the probability for event B is 0.2, and the probability of events A and B is 0.1. Why are the events are not independent?
Answers
Answer:
Since [tex]P(A \cap B) \neq P(A)P(B)[/tex], these events are not independent.
Step-by-step explanation:
Independent events:
Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this question, we have that:
[tex]P(A) = 0.4, P(B) = 0.2, P(A \cap B) = 0.1[/tex]
However
[tex]P(A)P(B) = 0.4*0.02 = 0.08[/tex]
Since [tex]P(A \cap B) \neq P(A)P(B)[/tex], these events are not independent.
Answer:
C
Step-by-step explanation:
edg 2020
Stir-fry is tony's favorite food to cook, but it always makes a lot of smoke! Tony needs to know the volume of his kitchen so he can buy a fan that is the right size. Tony's kitchen has a floor area of 85 square feet. The height of the ceiling is 8 feet. What is the volume of tony's kitchen?
Answers
Answer:
Volume = 680 ft³
Step-by-step explanation:
Given
Floor Area = 85 ft²
Height = 8 ft
Required
Volume of the Kitchen
To solve this, it'll be assumed that Tony's kitchen has a regular shape.
Having said that, the volume of Tony's kitchen is calculated as thus.
Volume = Floor Area * Height.
Substitute the values of floor area and height
Volume = 85ft² * 8ft
Volume = 680 ft³
Hence, the volume of Tony's kitchen is 680ft³
please please help me
Answers
Answer:
a) 22, b) i. 5/11, ii. 5/11, iii. 7/11
Step-by-step explanation:
a) 3+6+3+5+4+1 = 22 total number of students
b)
i. Number of girl/total number of students= 10/22 = 5/11
ii. blond hair/total number of students = 10/22 = 5/11
iii.
Number of girl/total number of students= 10/22 = 5/11
red hair/total number of students = 4/22 = 2/11
P(a girl or red hair) = 5/11 + 2/11 = 7/11
What is the answer? Plz need help
Answers
30x and 12 have a common factor of 6. So yes, this might have been the result of distributing the 6 in
6(5x - 2)
Answer:
30x - 12 = 2(15x - 6)
30x - 12 = 3(10x - 4)
30x - 12 = 6(5x - 2)
Step-by-step explanation:
30 and 12 have these factors in common: 2, 3, 6
There are three possible answers.
30x - 12 = 2(15x - 6)
30x - 12 = 3(10x - 4)
30x - 12 = 6(5x - 2)
3 POINSSSSSS
The bar graph shows the results of rolling a number cube (a die) 50 times. What is the probability of rolling an odd number? How does this compare with the theoretical probability of rolling an odd number?
Experimental Probability. Theoretical Probability
P(odd) = % P(odd) = %
Answers
Answer:
see below
Step-by-step explanation:
Experimental means what actually happened
P(odd) = (number of 1 + number of 3 + number of 5) / total
= (10+8+8) / 50
= 26/50
= 13/25 = 52%
Theoretical means what we expect to happen
P (odd) = (number of 1 + number of 3 + number of 5) / total
=(1+1+1)/6
=1/2 = 50%
We rolled an odd just a little more than the expected amount of times
Answer:
yes
Step-by-step explanation:
6. David leaves the house to go to school He walks 200 m west and 125 m
north. Calculate how far he is from the sting point.
Answers
Answer:
~235.8
Step-by-step explanation:
200^2 +125^2= distance traveled^2
55625= distance traveled^2
235.849528301
Angela works 18 hours a week for 12 weeks in the summer at the local swimming pool as a life guard. she earns $13 per hour. her employer takes 15 percent out of her check for federal income tax withholding and 6.2 percent for social security and 1.45 percent for medicare. she will receive 12 paychecks, one for each week she works. calculate angela’s weekly gross pay: calculate the amount taken out of angela’s check for federal income tax withholding: calculate the amount taken out of angela’s check for social security taxes: calculate the amount taken out of angela’s check for medicare taxes: calculate angela’s net paycheck using the calculations above: calculate angela’s total gross pay for all 12 weeks: calculate angela’s total net pay for all 12 weeks:
Answers
Answer:
Gross pay per week = $234
Federal income tax = $421.2
Social security = $174.96
Medicare =$40.71
net pay per week = $181
Total gross pay = $2,808
Total net pay = $2172
Step-by-step explanation:
Hi, to answer this question, first, we have to calculate Angela gross income per week:
18 hours per week x $13 per hour = $234 per week (gross)
234 x 12 =2,808
Amount taken ; multiply weekly gross pay by each percentage discount in decimal form (divided by 100)
Federal income tax = 234 x (15/100) = $35.1 (in 12 weeks = 35.1 x 12 = $421.2)
Social security = 234 x (6.2/100)= $14.508 (in 12 weeks = 14.5 x 12 = $174.96)
Medicare = 234 x (1.45/100)=$3.393 (in 12 weeks = 3.39x 12 = $40.71)
Total amount taken (per week)= 35.1+14.508+3.393=$53.001
Net pay per week = 234-53 = $181
For the total gross pay we have to multiply the weekly gross pay by the number of weeks (12)
Total gross pay = 234 x 12 =$2,808
Total net pay = 181 x 12 = 181 per week x 12 = $2172
The total number of subsets of a set A is 120 more than the total number of subsets of set B. The number of elements in the two sets respectively are
(A) 3, 7 (B) 4, 8 (C) 8, 4 (D) 7, 3
Answers
Answer:
(D) 7, 3
Step-by-step explanation:
If a set has 'n' elements, the total number of subsets is (2^n) - 1
So if set A has more subsets than set B, it needs to have more elements, so option (A) and (B) can't be correct.
So, checking option (C), we have:
Set A: number of subsets = 2^8 - 1 = 255
Set A: number of subsets = 2^4 - 1 = 15
Difference: 255 - 15 = 240
The difference is not 120, so this is not the correct option
Option (D):
Set A: number of subsets = 2^7 - 1 = 127
Set A: number of subsets = 2^3 - 1 = 7
Difference: 127 - 7 = 120
Correct option: (D)
A factory uses 3/4 of a barrel of raisins in each batch of granola bars. Yesterday, the factory
used 1 1/2 barrels of raisins. How many batches of granola bars did the factory make
yesterday?
Answers
Answer:
Step-by-step explanation:
3/4 * 2 = 1 1/2
The factory made two batches of granola bars.
Students measure objects in their desks and the data are shown in the line plot below. If the objects are to be connected end to end,what would be the total length?
Answers
This question is incomplete because it lacks the diagram of the line plot. Find attached to the answer, the diagram of the scatter plot.
Answer:
35/8 inches or 4 3/8 inches.
Step-by-step explanation:
Reading the line plot, the number of objects is plotted vertically while the length of the object is arranged horizontally on the line plot.
The total length is calculated as: summation of the (Number of objects × Length of the objects)
= [(1/8 ×0) + (1/4×0) + (3/8 × 2) + (1/2 ×3) + (5/8 × 1) + (3/4 × 2) +(7/8 × 0)] inches
=[ 0 + 0 + 3/4 + 3/2 + 5/8 + 3/2 + 0] inches
= 35/8 inches or 4 3/8 inches.
Therefore, the total length of the objects if they are connect end to end is 35/8 inches or 4 3/8 inches.
A group of students recorded how much money they earned per week for allowance to the nearest dollar. The students created the following histogram.
Which data set below was used to create this histogram?
A
$1, $2, $2, $3, $3, $3, $4, $4, $4, $4
Answered Incorrectly
B
$2, $3, $4, $5, $6, $7, $8, $10, $14, $15
C
$2, $4, $5, $7, $7, $9, $10, $14, $15, $20
D
$3, $4, $6, $7, $7, $8, $11, $14, $16, $17
Answers
Answer:
C
Step-by-step explanation
Answer:
c
Step-by-step explanation:
The answer to 7/12 divided by 2
Answers
Answer: 7/24
Step-by-step explanation: Think of the 2 as 2/1.
When dividing by a fraction, we can simply change, we can simply change the multiplication sig to division and take the reciprocal of the second fraction or flip the second fraction.
So our problem can be rewritten as [tex](\frac{7}{12})[/tex] [tex]x[/tex] [tex](\frac{1}{2})[/tex].
Now multiplying across the top and bottom we get 7/24.
Answer:
7/24
Step-by-step explanation:
the guy was right! (also khan said so)
John should drive to his workplace and back to home. On the way to the workplace it was raining, so he drove at a speed of 42mph. On the way back the rain was over so his speed was 54mph. What was John's average speed, for the whole trip?
Answers
Order the following expressions by their values from least to greatest.
b-a
a -0.5
a
Answers
Answer:
a
a -0.5
b -a
i believe that is the order but i could be wrong
Answer:
hi there !!
the correct answer should be: a - 0.5, a, b - a
Step-by-step explanation:
first let's show -0.5 on the number line.
now let's show b - a on the number line.
the given expressions are ordered by their values below.
4.16×10^−5 divided by 8.0×10^−4 in scientific notation
Answers
Answer: 13/250 or 0.052
Step-by-step explanation:
4.16 (1/100000)/ 8 (10^-4)
Then keep doing order of operations and dividing down.
Answer:
5.2*10^-2
Step-by-step explanation:
4/7 of the students in a classroom are boys. If there are twelve girls in the class, how many total students are there?
Answers
Answer:
28 students total.
Step-by-step explanation:
Let's use a ratio:
boys : girls
4 : 3
16 : 12
To find the total, we need to add 16 and 12 which equals 28
Answer:
28 students
Step-by-step explanation:
If 4/7 of the students are boys,
then 1- 4/7 = girls
7/7 -4/7 = 3/7
total students *3/7 = girls
total students * 3/7 = 12
Multiply each side by 7/3
total students * 3/7 *7/3 = 12*7/3
total students = 28
every natural number is a whole number why?
Answers
Answer:
Step-by-step explanation:
0 is whole number and 1 is natural number they both end in infinity. So there is only 0 in whole number but not in natural number.thats why every natural number is whole number
Natural numbers are the counting
numbers and they are always positive.
The set of natural numbers begin at 1 and go on indefinitely.
The natural numbers look like {1, 2, 3, 4, 5, ...}.
When we include 0 in the set of natural numbers, the new set,
{0, 1, 2, 3, 4, ...} is called the set of whole numbers.
Notice that all natural numbers are
included within the set of whole numbers.
We can represent the relationship between these
two sets of numbers using a diagram.
The bigger circle below represents the set of whole numbers
and all natural numbers will appear within the set of whole numbers.
In summary, natural numbers are the same as whole numbers except for the fact that whole numbers include 0.
Plz, help me plz!!!!!!
Which triangles are congruent?
Image below
Answers
Answer:
B. Triangles A and C
Step-by-step explanation:
Let's find the missing angle of all Triangles:
Triangle A: 180-110-30=40°
Triangle B: 180-30-45=105°
Triangle C: 180-110-40=30°
All triangle angles in numerical order:
ΔA: 30, 40, 110
ΔB: 30, 45, 105
ΔC: 30, 40, 110
We see that only ΔA and ΔC are congruent with the same angle sizes.
The are both have the same measurements
Jake and Becky measured the circle-shaped part of a sun they drew on the sidewalk.
The diameter of the circle is 70 centimeters. What is the approximate area of the circle?
(Use 3.14 for Pi)
Answers
Answer:
3847
Step-by-step explanation:
To get your radius
diameter/2= 70/2=35.
Radius=35
Area=πr^2 =3.14x 35x35= 3846.5
approximately=3847
The radius of a cylindrical water tank is 6.5 ft, and its height is 11 ft. What is the volume of the tank? Use the value 3.14 for pie, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.
Answers
Answer:
Step-by-step explanation:Idon't say you have to mark my ans as brainliest but my friend if it has helped you don't forget to thank me...
The volume of the cylindrical water tank with the given value of radius and height to the nearest whole number is 1459ft³.
What is a cylinder?
A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )
Given the data in the question;
Radius r = 6.5ftHeight h = 11ftConstant pi π = 3.14Volume of the cylindrical water tank V = ?We substitute our values into the expression above.
V = π × r² × h
V = 3.14 × (6.5ft)² × 11ft
V = 3.14 × 42.25ft² × 11ft
V = 1459ft³
The volume of the cylindrical water tank with the given value of radius and height to the nearest whole number is 1459ft³.
Learn more on volume of cylinder here: brainly.com/question/16788902
PLZZZZZZZZZZ HELP MEEEEEEEE
Answers
Answer:
D
Step-by-step explanation:
[tex]2x^2+2x+12=3x^2-x+2\\2x+12=x^2-x+2\\x^2-3x-10=0\\(x-5)(x+2)=0\\x=5, -2[/tex]
The correct answer is choice D. Hope this helps!
Answer:
{-5, 2}
Step-by-step explanation:
[tex]2x^{2} + 2x + 12 = 3x^{2} -x + 2[/tex] move everything to the right side
[tex]-2x^{2} -2x-12=-2x^{2} -2x-12[/tex] add line 1 and 2 to get the below equation
[tex]0 = x^{2} -3x -10[/tex] find multiples of -10 that add to give you -3
to get -10 we have to have (+)(-)
{-5, 2}
what is the slope of the line that passes through the points (-4,-4) and (-4,-9)? Write your answer in simplest form
Answers
Answer:
undefined
Step-by-step explanation:
We can find the slope of a line using two points by
m = (y2-y1)/(x2-x1)
= (-9- -4)/(-4 - -4)
= (-9+4)/(-4+4)
= -5/0
When we divide by zero, our solutions is undefined
The slope is undefined
Need help ASAP. WILL MARK BRAINLIEST.
Answers
Answer:
Circumference = 2 x 3.14 x radius = 27 (in)
=> radius = 27/(2 x 3.14) = 4.3 (in)
=> Area = 3.14 x radius^2 = 3.14 x 4.3^2 = 58.1 (in2)
Answer:
58 inches^2
Step-by-step explanation:
The formula for the area of a circle is [tex]\pi *radius^{2}[/tex]
To work out the area of this circle you would first need to divide the circumference of 27 by pi, this gives you 8.594. This is because the formula for the circumference is: [tex]\pi *diameter\\[/tex] and so by dividing the circumference by pi we are isolating the value of the diameter.
Then now that we have worked out the diameter we can now begin to work out the area, however in order to work out the area we must work out the radius. You can do this by dividing the diameter by 2, which gives you 4.297.
Then to work out the area you would multiply pi by the radius of 4.297 squared, this gives you 58.01 [tex]inches^{2}[/tex].
The next step is to round it to the nearest whole number, this gives you 58.
1) Divide 27 by pi.
[tex]27/\pi =8.594[/tex]
2) Divide 8.594 by 2.
[tex]8.594/2=4.297[/tex]
3) Multiply pi by 4.297 squared.
[tex]\pi *4.297^{2} =58.01[/tex]
4) Round to the nearest whole number.
58 square inches
Which is a name for the angle shown? Select all that apply
Answers
Answer:
D
Step-by-step explanation:
Well, the angle is an acute angle and <CDE is what would connect to make an acute angle. Easy.The name for the angle shown is ∠D and ∠CDE.
What is Coordinate system?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
An angle is formed when two straight lines or rays meet at a common endpoint.
An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Angles formed by two rays lie in the plane that contains the rays.
Angles are also formed by the intersection of two planes.
The name of the angle are ∠D and ∠CDE.
Hence, the name for the angle shown is ∠D and ∠CDE.
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1. Express as a unit rate
a) Serena walks 4 km in 1 h.
Answers
Answer:
Step-by-step explanation:
Serena walks 4 km in 1 h.
That means:
1) She walks 4 km per hour.
2) She spends 1/4 = 0.25 hour per mile.
Have a good day.
We can write this as:
4 kilometers/1 hour
The unit rate is already simplified so there is nothing else to do.
Answer: 4km/1hr
Best of Luck!
The volume of an oblique pyramid with a square base is V units3 and the height is h units.
An oblique pyramid with a square base has a volume of V units cubed and a height of h units.
Which expression represents the area of the base of the pyramid?
StartFraction 3 V Over h EndFraction units2
(3V – h) units2
(V – 3h) units2
StartFraction V Over 3 h EndFraction units2
Answers
Answer:
StartFraction 3 V Over h EndFraction units2Step-by-step explanation:
volume of an oblique square pyramid V = 1/3 * b * H where;
b is the base area of the pyramid
H is the height of the pyramid
To determine the expression that represents area of the base of the pyramid, we will make the variable 'b' the subject of the formula from
V = 1/3 bH
[tex]V=\frac{bH}{3}[/tex]
Cross multiplying we have;
[tex]3V = bH\\[/tex]
Dividing both sides by H we have;
[tex]\frac{3V}{H} = \frac{bH}{H} \\b = \frac{3V}{H}units^{2}[/tex]
This gives the correct expression for the base area of the pyramid
Answer:
A.
Step-by-step explanation:
A 4-foot long steel pipe consists of two concentric cylinders, with the inner cylinder hollowed out. The radius of the outside of the pipe is 6 inches and the radius of the inside of the pipe is 5.75 inches.
A. Determine the volume of metal used to build the pipe
B. If the pipe is to be powder-coated on the inside and outside surfaces, what is the total surface area to be powder-coated?
Answers
Answer:
Step-by-step explanation:
The radius of the outside of the pipe is 6 inches and the radius of the inside of the pipe
is 5.75 inches
Determine the volume of metal used to build the pipe.
