In a list of measurements in increasing order: 4, 5, 6, 8, 10, and x, the value of x is 16.
To get the value of x, we will use algebraic expressions to demonstrate the given relationships.
If the median of these measurements is six sevenths times their arithmetic mean, then:
median = 6/7 x mean
Median (Md), is a single value at the middle of the data values arranged in increasing or decreasing order. On the other hand, arithmetic mean (μ) is the sum of the data values divided by its total number.
For the list of measurements in increasing order is 4, 5, 6, 8, 10, and x,
The median is between 6 and 8.
Md = 6+8/2
Md = 7
Evaluating the first equation using Md = 7:
median = 6/7 x mean
7 = 6/7 x mean
mean = 49/6
By definition,
mean = (4 + 5 + 6 + 8 + 10 + x)/6
Equating both equations for the mean:
49/6 = (4 + 5 + 6 + 8 + 10 + x)/6
49 = 33 + x
x = 16
Hence, the value of x is 16.
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Help please! (show steps too)
If the equation of the circle is [tex]x^{2} +y^{2}-8x+6=0[/tex] then the center and radius of the circle is (4,0) and [tex]\sqrt{10}[/tex] respectively
Given,
The equation,
[tex]x^{2} +y^{2}-8x+6=0[/tex]
Rearrange the equation
[tex]x^{2} -8x+6+y^{2} =0[/tex]
Add 10 on both sides
[tex]x^{2} -8x+16+y^{2} =10[/tex]
Change to standard form
[tex](x-4)^{2}+(y-0)^{2}=(\sqrt{10})^{2}[/tex]
Standard form of the equation of a circle is
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
Here the r is the radius of the circle and (h,k) is the center
So,
Center = (4,0)
Radius = [tex]\sqrt{10}[/tex]
Hence, if the equation of the circle is [tex]x^{2} +y^{2}-8x+6=0[/tex] then the center and radius of the circle is (4,0) and [tex]\sqrt{10}[/tex] respectively.
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Write the equation of a square root function that has been
shifted up 3 units and right 1 unit and contains the point
(5,7).
The equation of the square root function is g(x) = √(x - 1) + 3
How to determine the equation of the square root function?A square root function is represented as
f(x) = √x
The transformation rule is given as
Shifted up 3 units and right 1 unit
This can be represented as
(x - 1, y + 3)
So, we have
g(x) = f(x - 1) + 3
This gives
g(x) = √(x - 1) + 3
From the question, we have
It contains the point (5,7).
This means that
g(5) = 7
So, we have
g(5) = √(5 - 1) + 3
Evaluate
g(5) = 7
Hence, the equation of the square root function is g(x) = √(x - 1) + 3
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if i choose four cards from a standard $52$-card deck, with replacement, what is the probability that i will end up with one card from each suit?
The probability that i will end up with one card from each suit is 3/32.
Probability:
Probability refer the possibility of the event.
The formula for the probability of the event is,
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes
Given,
If i choose four cards from a standard 52-card deck, with replacement,
Then we need to find the probability that i will end up with one card from each suit.
In the first draw, we can take one card, if it is a spade one,
Then for the second draw we have 39 options
For the third draw we have 26 options
For the fourth draw we have 13 options,
So, the probability that i will end up with one card from each suit is
=> 1 x 39/52 x 26/52 x 13/52
=> 1 x 3/4 x 1/2 x 1/4
=> 3/32
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Tomás wants to tile a rectangular floor with square tiles that measure 12 inches on a side. The floor measures 10 feet 6 inches long by 8 feet 6 inches wide. If he is able to cut the tiles without waste, what is the minimum whole number of tiles Tomás needs to completely cover the floor?
There are 1176 is the minimum whole number of tiles Tomás needs to completely cover the rectangular floor.
Rectangle:
Rectangle means a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles.
Given,
Tomás wants to tile a rectangular floor with square tiles that measure 12 inches on a side. The floor measures 10 feet 6 inches long by 8 feet 6 inches wide.
Here we need to find if he is able to cut the tiles without waste, what is the minimum whole number of tiles Tomás needs to completely cover the floor.
Here we have to convert the feet into inches for easy calculation,
1 feet = 12 inches
So, the length is ,
l = 120 + 6 = 126 inches
w = 96 + 6 = 112 inches
So, the area of the floor is,
=> l x w
=> 126 x 112
=> 14,112
Here we need to use 12inches square tile,
So,
=> 14112 / 12
=> 1176.
Therefore, there are 1176 tiles are need to cover the floor.
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Write and equations of the horizontal and vertical lines that pass though the given point.
(-3,2)
(1,4)
Answer:
Step-by-step explanation:
(-3, 2)
Horizontal is y = 2
Vertical is x = -3
In the same way (1, 4) is
y = 4
x = 1.
in a certain school, course grades range from 0 to 100. adrianna took 4 courses and her mean course grade was 90. roberto took 5 courses. if both students have the same sum of course grades, what was roberto’s mean?
Average of 5 courses is 72
• In simple words, average is the number which is the representative of the list of the numbers.
• Average of numbers is calculated by the sum of the numbers divided by total numbers.
We are given that
Number of courses took by Adrianna = 4
Average of her course grade = 90
Number of course took by Roberto = 5
We also know that , Both students have the same sum of course grades
Let the average of Roberto be x
Average = Sum / Total Subjects
Sum = Average * Total Subjects
So,
90 * 4 = x * 5
x = 360/5
x = 72
Therefore, average of Roberto is 72
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identity the restrictions on the domain of f(x)=x-1/x+4
Answer:
Answer is option A.
X cannot be equal to -4
Ryan has a points card for a movie theater.
• He receives 85 rewards points just for signing up.
• He earns 7.5 points for each visit to the movie theater.
.
• He needs 160 points for a free movie ticket.
Write and solve an equation which can be used to determine v, the number of visits
Ryan must make to earn a free movie ticket.
Answer:
anaaaa
Step-by-step explanation:
question 12(multiple choice worth 1 points) (04.01 lc) which set of ordered pairs represents a function? {(0, 1), (1, 3), (1, 5), (2, 8)} {(0, 0), (1, 2), (2, 6), (2, 8)} {(0, 0), (0, 2), (2, 0), (2, 4)} {(0, 2), (1, 4), (2, 6), (3, 6)}
The set of ordered pairs that represents a function is: {(0, 2), (1, 4), (2, 6), (3, 6)}
We know that a function defines a relation between input and output values.
In function for each input there is exactly one output.
We need to find the set of ordered pairs that represents a function.
We need to find the set of ordered pairs such that for each x value (x coordinate) there is unique y value (y coordinate).
1) {(0, 1), (1, 3), (1, 5), (2, 8)}
This set of ordered pairs cannot be a function.
As for x = 1, there are two output values 3 and 5.
2) {(0, 0), (1, 2), (2, 6), (2, 8)}
This set of ordered pairs cannot be a function.
As for x = 2, there are two output values 6 and 8.
3) {(0, 0), (0, 2), (2, 0), (2, 4)}
This set of ordered pairs cannot be a function.
As for x = 0, there are two output values 0 and 2.
and for x = 2, the output values are 0 and 4.
4) {(0, 2), (1, 4), (2, 6), (3, 6)}
This set of ordered pairs represents a function.
Here, for each input value there is unique output value.
Therefore, the set of ordered pairs that represents a function is: {(0, 2), (1, 4), (2, 6), (3, 6)}
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Parsons Bank offers two checking-account plans. The No Frills plan charges
25 cents per check whereas the Simple Checking plan costs $
5 per month plus
5 cents per check. For what number of checks per month will the Simple Checking plan cost less?
If the number of checks are greater than 25, the Simple Checking plan cost less.
We have two checking account plans at Parson's bank.
We have to determine for what number of checks per month will the Simple Checking plan cost less.
What is an Inequality in Mathematics ?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Let for x number of checks per month the simple checking plan cost less.
For No frills plan -
Charge per check - $0.25
Therefore, for x checks, it will cost - $0.25x
For Simple Checking plan -
Fixed monthly charges - $5
Charges per check - $0.50
Therefore - for x checks - $5 + $0.50x
Now - for Simple Checking plan to cost less than No frills plan -
5 + 0.05x < 0.25x
5 < 0.25x - 0.05x
5 < 0.2x
x > 25
Hence, if the number of checks are greater than 25, the Simple Checking plan cost less.
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The function h is defined by the following rule.
h(x) = -2x-5
Complete the function table.
X
-4
0
2
3
5
H(x)
?
?
?
?
?
Darren is purchasing a car that costs $11,000. He is taking out a simple interest loan at an annual rate of 3%. If he makes monthly payments over a period of 5 years, how much is his monthly payment?
Darren's monthly payment on car loan is $210.83
Given,
Cost of the car Darren purchased = $11000
The simple interest for the car loan = 3%
Time period of loan = 5 years
We have to find the monthly payment amount:
Simple interest = PRT / 100
Where,
P = Principal amount = $11000
R = Rate of interest = 3%
T = Time period = 5 years
Now,
SI = PRT / 100
SI = (11000 × 3 × 5) / 100
SI = 110 × 3 × 5
SI = 1650
Here, the simple interest for 5 years is $1650
Now,
Total amount to be paid after 5 years = Principal amount + Simple interest
A = P + SI
A = 11000 + 1650
A = 12650
The amount to be paid after 5 years is $12650
Next,
The monthly payment amount:
Number of months in 5 years = 12 × 5 = 60 months
So,
Monthly payment amount = Total amount after 5 years / Total months in 5 years
Monthly payment amount = 12650 / 60 = 210.83
That is, the monthly payment amount on car loan is $210.83
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For what value of k does the equation 2x^2 − 6x + k = 0 have exactly one solution?
Answer:
k = 2.25 or 9/4
Step-by-step explanation:
2x^2 - 6x + k = 0
2(x^2 - 3x + 2.25) = 0
x -1.5
x -1.5
-------------------------------------
(x - 1.5) (x - 1.5) = 0
x = 1.5 or 15/10 = 3/2
one solution
there are 20 colored markers in a package – 8 black, 4 blue, 4 red, 4 green. if two markers are selected at random, one after another, without replacement, find the probability that both will be blue.
If two markers are selected at random, one after another, without replacement, the probability that both will be blue = 0.0316
For given question,
there are 20 colored markers in a package – 8 black, 4 blue, 4 red, 4 green.
if two markers are selected at random, one after another, without replacement, we need to find the probability that both will be blue.
The probability that the selecting one blue marker is:
4/20
After selecting one blue marker, there are 19 markers in a package - 8 black, 3 blue, 4 red, 4 green.
The probability of selecting second blue marker would be,
3/19
So, the probability that both will be blue:
4/20 × 3/19
= 0.2 × 0.16
= 0.0316
Therefore, if two markers are selected at random, one after another, without replacement, the probability that both will be blue = 0.0316
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Which of the following is the equation of a line in slope-intercept form for a
line with slope = 2/3 and y-intercept at (0,-2)
The equation of the line with slope 2/3 and y-intercept at ( 0, - 2) is y = ( 2/3 )x - 2.
The slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible.
We have the slope 2/3 of a line and the y-intercept at ( 0, - 2 ).
Now, we know that
The slope-intercept form of the equation of a line with slope m and y-intercept at the point (0, c) is given by:
y = mx + c
The slope of the line is :
m = 2/3
And, the y-intercept is (0, c) = ( 0, -2)
Hence, the equation of the line in the slope-intercept form will be:
y = mx + c
y = ( 2/3 )x + ( - 2)
y = ( 2/3 )x - 2
Therefore, the slope-intercept form of the equation of the line is y = ( 2/3 )x - 2.
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a double decker bridge has two parallel levels connected by a network of diagonal girders. one of the girders makes 52 degrees angle with the lower level as shown in the figure. what is the measure of angle 1?
Answer: 128
Step-by-step explanation:
a whole supplementary angle adds up to 180 degrees
so 180
- 52
128
The function m(x) represents the amount of money (in dollars) it costs you to be a member at the YMCA after x monthsExplain the meaning of the following function notation using a sentence by connecting it to this situation:
m(0) = 50
The meaning of the function notation is the inital amount of money (in dollars) it costs you to be a member at the YMCA
How to explain the meaning of the function notation?The function is given as
m(x) represents the amount of money (in dollars) it costs you to be a member at the YMCA after x months
The function notation is given as
m(0)
The function notation m(0) implies that
We determine the value of m(x) when x = 0
This represents the x-intercept of the function
The x-intercept of the function is the initial value of the function
Hence, the meaning of the function notation is the inital amount of money (in dollars) it costs you to be a member at the YMCA
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976,733,776 divide 9
Answer:
108525975,11111111111111111111111
Answer: 108525975.111
Step-by-step explanation:
25 points plus brainliest
Answer:
hi awaz are u in india server ?
Stephen bought some peaches and crumbles to make peach cobbler. Peaches costs $1.80 per pound, and crumbles cost $2.50 per pound. Stephen spent a total of $19.40.
Part 1. Create an equation that can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased. Remember to define any variables used.
Part 2. Use the equation created in Part 1 to determine how many pounds of crumbles Stephen purchased if he purchased 8 pounds of peaches. You must show all steps to receive credit.
√x
The equation which can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased is 1.8x+2.5y=19.4 and if Stephen purchased 8 pounds of peaches then he also purchased 2 pounds of crumbles.
Given that the cost of peaches is $1.80 per pound and cost of crumbles is $2.50 per pound and the total expenditure done by Stephen is $19.40.
We are required to find the equation that can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased and find the number of crumbles that Stephen purchased if he had 8 pounds of peaches.
Suppose the number of pounds of peaches be x and the number of crumbles be y.
The equation will be as under:
x*1.80+y*2.50=19.40
1.80x+2.50y=19.40---------1
Put the value of x=8 to find the number of crumbles.
1.8 *8+2.50y=19.40
14.4+2.50y=19.40
2.50y=19.4-14.4
2.50y=5
y=5/2.5
y=50/25
y=2
Hence the equation which can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased is 1.8x+2.5y=19.4 and if Stephen purchased 8 pounds of peaches then he also purchased 2 pounds of crumbles.
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given the equation of :y-5=25/2=25/2(x+4) what is the slope of any line parallel? M= blank
The slope of the any line parallel to the line y-5 = 25/2(x+4) is equal and its value is 25 /2 .
The graph of the equation y =mx + c could be a line with m as slope, and c because the y-intercept.This type of the equation is termed the slope-intercept form, and therefore the values of m and c area unit real numbers.We have given equation y-5 = 25/2(x+4) .
On simplifying , we get
y - 5 = 25 x/2 +50
y = 25 x /2 +55
On comparing the above equation with slope intercept form y = mx + b ,
we get m = 25 / 2
All the lines which are parallel to any other line have equal slope.
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PLS HELP!!
what are the two equations to set up to solve the equation
| 3x -2 | = 19
3x - 2 =
insert in the box and 3x - 2 = insert in the box
The two equations to set up to solve the equation are 3x - 2 = 19 and 3x - 2 = -19
What are the two equations to set up to solve the equation?The equation is given as
|3x - 2| = 19
The above equation is an absolute value equation.
When it is split, the constant would be represented as positive and negative
So, the equivalent equations are
3x - 2 = 19 and 3x - 2 = -19
Hence, the two equations to set up to solve the equation are 3x - 2 = 19 and 3x - 2 = -19
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Pqrs and t are on line k such that q is the midpoint of pt, r is the midpoint of qt, and s is the midpoint of rt. If ps
Given the midpoint, the value of PT will be 10 2/7.
How to calculate the value?Q is the midpoint of PT,
so PQ = QT.
R is the midpoint of QT,
so QR=RT.
S is the midpoint off RT,
so RS=ST.
Let us say RS = ST = x .
Then, RT= RS + ST= x + x = 2x ,
so RT = QR = 2x
Then, QT = QR+RT = 2x+2x = 4x ,
and PQ = QT = 4x .
Then, PS= PQ+QR+RS=4x+2x+x=7x ,
and PT=PQ+QT=4x+4x=8x
The problem says that PS = 9
Therefore, 7x = 9 and x = 9/
PT = 8x = 8 × 9/7 = 10 2/7.
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P, Q, R, S, and T are on line k such that Q is the midpoint of segment PT, R is the midpoint of segment QT, and S is the midpoint of segment RT. If segment PS = 9, then what is PT?
x^2=a^2, what does x equal?
x=±a
1. take the square root of both sides
If wood flooring costs 39.97 per square yard, how much will it cost to cover a room 15 feet by 25 feet?
Answer:
$14988.75
Step-by-step explanation:
15 x 25 = 375
375 x $39.97 = $14988.75
Answer:
$14988.75
Step-by-step explanation:
25x15 = 375
375 x 39.97 = $14988.75
a box with a square base and a top is to be constructed from 10 square meters of material. find the dimensions which will maximize the volume that the box can hold.
A box with a square base and a top is to be constructed from 10 square meters of material. 40 square meters will maximize the volume that the box can hold.
What is volume?LSD use among secondary school understudies is a specific concern. More Volume is a proportion of consumed three-layered space. It is frequently evaluated mathematically utilizing SI inferred units or by different supreme units. Volume is characterized as the space involved inside the limits of an article in three-layered space. It is otherwise called the limit of article. Volume is a proportion of consumed three-layered space. It is frequently measured mathematically utilizing the SI determined unit, the cubic meter. The volume of a compartment is by and large comprehended to be the limit of the compartment, how much liquid (gas or fluid) that the holder could hold, instead of how much space the actual holder dislodges. Three layered numerical shapes are additionally relegated volumes.
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the angle of elevation to the top of a building in new york is 12° from the ground and 1 mile from the base of the building.
The height of the building is 1122.528 feet.
Angle of elevation:
Angle of elevation means an angle between the horizontal plane and oblique line from the observer's eye to some object above his eye.
Given,
The angle of elevation to the top of a building in New York is 12° from the ground and 1 mile from the base of the building.
Here we need to find the height of the building.
We know that,
The expression for the height of the building is,
h = tanΘ × x
Where the value of
tan Θ = 12°
x = 1 mile
So, When we apply the value on the formula,
The we get,
h = tan 12° x 1
So, apply the value of tan 12 degree,
h = 0.2126 x 1
h = 0.2126 mile
Simplify the above equation using the information
1 mile = 5280 ft.
That is equal to
h = 1122.528 feet.
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the ceo of a large company decides to survey the workers for their opinions about a new vacation policy. a sample of the population that gives each worker an equal chance of participating in the survey would be a(n): please choose the correct answer from the following choices, and then select the submit answer button. answer choices sample that includes half the workers. random sample. unrepresentative sample. sample that includes all the workers.
correct answer is random sample
A simple random sample, also known as an SRS, is a subset of people (also known as a sample) picked at random from a larger group of people (also known as a population) with an equal probability. It is a method of choosing a sample at random. Each subset of k people in SRS has the same chance of getting selected for the sample as any other subset of k people. [1] An objective sampling strategy is a straightforward random sample. Simple random sampling is a fundamental kind of sampling that may be used in combination with other, more sophisticated sampling techniques.
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The diameter of a circle is 36 meters. What is the circle's area? Use 3.14
Answer:
113.04
Step-by-step explanation:
1530 divided by 30? I will give you a Brainliest!
51
1530÷30=51
30x51=1530