Answer:
Step-by-step explanation:
A coefficient is a number before the variable that shows how many groups of the variable there are. For example, 2b would be two groups of B.
The coefficients in this expression would be 4 (as in 4x) and 8 (as in 8y).
if f(x) = 2x - 4 find f(3x)
Answer: the answer would be 2
Step-by-step explanation: f(x) means that for every x you are going to multiply it by the value it gives you in this case it is 3.
2x3=6-4=2
Express 60 as the product of its prime factors.
60 = (Answer here)
Answer:
2x2x3x5= 60
I hope you like it
Answer:
2 X 2 X 3 X 5
Step-by-step explanation:
We divide 60 by 2 as many times as possible to get 60 = 15 x 2 x 2. 2 is a prime number so we don't need to break the 2's down any more. Instead we break 15 down. 15 doesn't divide by 2 so we try the next prime number: 3 Divide 15 by 3 to get 15 = 5 x 3, and so 60 = 5 x 3 x 2 x 2. Now we collect the factors, so our final answer is 60 = 5 x 3 x 22.
Given the speeds of each runner below, determine who runs the fastest.
i cant figure this out and its due soon pls help me
The person who runs fastest is Zach.
How to find the speed?Ron runs 9 feet per second: 9 ft/s
Zach runs 410 feet in 49 seconds:
410/49 ft/s
=8.36 ft/s
= 8.4 ft/s (Approximately)
Katie runs 1 mile in 412 seconds:
1 mile = 5280 ft
5280/412 ft/s
=12.8 ft/s
Noah runs 870 feet in 1 minute:
= 870/60 ft/s
= 14.5 ft/s
Hence,
Ron 9 feet per seconds
Zach 8.4 feet per seconds
Katie 12.8 feet per seconds
Noah 14.5 feet per seconds
So, Zach is the fastest.
Therefore the fastest is Zach.
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To compleate a task in 16 days a company needs 5 workers each working 6 hours per day
The company decides to have 8 people each working 4 hours per day
Assuming that each person works at the same rate
How many days will the task take to complete?
Answer:
10 days
Step-by-step explanation:
This is a type of proportion either direct or indirect .16 days for 5 workers.so for 8 workers the days will reduce .Now for 8 workers it will be 10daysThe identification of a relationship using
multiplication and the prediction of the value of one
quantity based on the value of another.
Utilizing multiplication to find relationships and predicting that value of one "Linear regression" is a quantity derived from the value of another.
Define the term Linear regression?The relationship in between magnitude of one parameter and that of a second is modeled by simple linear regression.
For instance, as X rises, Y also increases. or Y declines as X rises. 1 Regression defines the nature of the link, whereas correlation evaluates the strength of such a linking between two variables.Simple linear regression calculates the precise amount by which Y will alter when X alters by a specific amount. The variables X and Y remain interchangeable with the correlation coefficient. Regression uses a linear relationship, or a line, to try and predict any Y variable from the X variable:Y = b 0 + b 1 X.Thus, finding correlations via multiplication and assuming that the value of one "Linear regression" is a number obtained as from value of another
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help for the rest pls
Answer :
9 girls and 18 boys don't have a voucher
Step-by-step explanation :
There are 38 boys and 22 girls. The total number of children is 60. We know that 33 children have a voucher. 27 children don't have a voucher. ( 60 - 33 = 27 ) .
"Twice as many boys as girls do not have a voucher."
We can now make an equation.
The girls who do not have a voucher will be x, boys who don't have a voucher will be 2x, since it says twice as many boys.
We can now make our equation.
x + 2x = 27
Add x and 2x
3x = 27
Divide both sides by 3
x = 9
We know now that girls who don't have a voucher is 9.
The boys who don't have a voucher is 2x, so we plug 9 instead of x.
2(9) = 18.
18 boys do not have a voucher.
If you would like the rest for the frequency tree...
Total students : 60
Boys : 38
Boys who don't have a voucher : 18
Boys who have a voucher : 20
Girls : 22
Girls who don't have a voucher : 9
Girls who have a voucher : 13
Hope this helped.
Use the method of adding y-coordinates to graph the function.
f(x) = 3x - sin 4x
Graph of f(x) = 3x - sin 4x is using method of adding y-coordinates is attached below.
What is graphing method by adding ordinates?
The function y = 3x - sin 4x is actually the sum of two functions, y = 3x and y = - sin 4x.
For every value in the domain, there is a corresponding value in the range so that the point (x, 3x - sin 4x) is on the graph of y = 3x - sin 4x.
According to the given question:
Follow these steps to graphing the function:
1. Open an Excel file. Label the first column "x-coordinates," the second column "y = 3x," the third column "y = -sin 4x," and the fourth column "y = 3x - sin 4x." Set each column to round to four decimal places.
2. Set up the first column to range from -2pi to 2pi by intervals of pi/4.
3. Fill in the second and third columns by utilizing the equations y = 3x and y = - sin 4x, respectively.
4. Fill in the fourth column by simply adding the second and third columns.
5. Graph y = 3x - sin 4x by using the x-coordinates from column A and the y-coordinates from column D.
Check the attachment below for the required graph obtained after plotting the points.
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At the bowling alley kai rented shoes and purchased 3 games of bowling for $6.50.
Jack rented shoes and purchases 5 games of bowling for $9.50 Caelan has $17 if she rents shoes how many games of bowling can she purchase
Caelan must spend a total cost of $ 17 for 10 bowling games.
How many bowling games can Caelan purchase?
The total cost consists in the sum of a fixed cost, represented by rent of shoes, and a variable cost, represented by the number of bowling games, whose model is presented below:
c' = c + r · n
Where:
c - Fixed cost, in monetary units.r - Cost of each rent, in monetary units.n - Number of rented games.First, construct the system of equations related to Kai and Jack:
Kai
c + 3 · r = 6.50
Jack
c + 5 · r = 9.50
Second, solve the system of linear equations by numerical methods:
(c, r) = (2, 1.5)
Third, write the resulting function:
c' = 2 + 1.5 · n
Fourth, evaluate the function for the situation of Caelan:
17 = 2 + 1.5 · n
1.5 · n = 15
n = 10
Caelan rents 10 bowling games for $ 17.
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If the line of best fit is y = 1.416x − 0.76, what is the residual value for the coordinate (10, 14)? −0.16 0.16 0.6 −0.6
The residual value is 0.6.
What is Residual?The estimated value of a fixed asset at the conclusion of its useful life or lease term is known as the residual value, also known as salvage value. In lease agreements, one of the lessor's main methods for figuring out how much the lessee must pay in periodic lease payments is the residual value.
Given:
y = 1.416x − 0.76
For (7, 8):
As, residual value = Measured value - Predicted value
or, residual value = (actual y-coordinate of the point) - (value of y from the
equation)
When x = 10:
So, the value of y from the equation,
[tex]y_1[/tex] = 1.416 x 10 - 0.76
[tex]y_1[/tex]= 14.16 - 0.76
[tex]y_1[/tex]= 13.4
and, actual y-coordinate of the point, [tex]y_2[/tex]= 14
Residual value = 14 - 13.4
Residual value = 14 - 13.4
Residual value = 0.6
Hence, the residual value is 0.6
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Answer:
0.6
Step-by-step explanation:
im taking the test rn
Arrange the pairs of points in increasing order of the slopes of the lines joining them.
(15, 30) and (20, 40)
(12, 32) and (18, 48)
(27, 12) and (72, 32)
(45, 15) and (60, 20)
(27, 2) and (243, 18)
(18, 63) and (24, 84)
(63, 9) and (84, 12)
↓
↓
↓
↓
↓
↓
The arrangement of the points in increasing order of the slopes are (27, 2) and (243, 18), (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40), (12, 32) and (18, 48), (18, 63) and (24, 84)
How to Arrange the points in increasing order of the slopes of the lines joining them?
Slope is defined as the change in y divided by the change in x. Mathematically:
Slope = (y2 - y1) / (x2 -x1)
To arrange the pair of points. You need to find the slope:
For (15, 30) and (20, 40):
x1 = 15, y1 =30 and x2 =20, y2=40
slope = (40-30)/(20-15) = 10/5 =2
For (12, 32) and (18, 48):
slope = (48-32)/(18-12) = 16/6 = 2.67
For (27, 12) and (72, 32):
slope = (32-12)/(72-27) = 20/45 = 0.44
For (45, 15) and (60, 20):
slope = (20-15)/(60-45) = 5/15 = 1/3 = 0.33
For (27, 2) and (243, 18):
slope = (18-2)/(243-27) = 16/216 = 0.07
For (18, 63) and (24, 84):
slope = (84-63)/(24-18) = 21/6 = 7/2 = 3.5
For (63, 9) and (84, 12):
slope = (12-9)/(84-63) = 3/21 = 1/7 = 0.14
Therefore, the pairs of points in increasing order of the slopes are (27, 2) and (243, 18), (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40), (12, 32) and (18, 48), (18, 63) and (24, 84)
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A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100shares at 50 per share was $33. 77 (AAII Journal, February 2006). The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.
a. Using the sample data, what is the margin of error associated with a 95% confidence interval?
b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share
a) The margin of error associated with a 95% confidence interval is 4.
b) The 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)
a) We are given with the information that the mean for 54 discount brokers is $50 for 100 shares is $33.77 Also the population standard deviation is $15.
The formula for margin of error is Z = zα/2 σ √ n
Now we know from our z-table that value of zα/2 for 95% confidence interval is 1.96
So, the value of error margin is zα/2 σ √ n =1.96 (15/√54) = 1.96 x 2.04
= 4
b) We know from part a that margin of error is 4.
Also, the mean price charged for a trade of 100shares at 50 per share was $33. 77
The value of confidence interval for population mean is,
x ± zα/2 σ √ n = 33.77 ± 4 = (29.77,37.77)
Thus, the 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)
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rationalise the denominator of \frac{26}{4+\sqrt{3}}
The rationalization of the denominator of the given fraction gives 8 -2√3
Rationalizing the denominatorFrom the question, we are to rationalize the denominator of the given fraction
The given fraction is
26 / (4+√3)
To rationalize the given expression, we will multiply both the numerator and the denominator of the fraction by the conjugate of the denominator.
The denominator is 4+√3
Thus,
The conjugate of the denominator is 4-√3
Now, multiply the numerator and the denominator by the conjugate.
That is,
(26 × (4-√3)) / ((4+√3) × (4-√3))
(104 - 26√3) / (16 - 3)
(104 - 26√3) / 13
= 104/13 - (26√3)/13
= 8 - 2√3
Hence,
The result of rationalizing is 8 -2√3
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,
Admission to the art museum is $3 per person. When the museum opened this
there was $150 on hand in the ticket booth. At closing time, there was $1254. How many
people paid admission today?
Had:
Tickets:
Total:
Step-by-step explanation:
so the ticket booth had $150 so $1254 -$150=$1104
so $1104 ÷ by $3 each person = to 368 people paid the admission
Had: $150
Tickets :368
Total :$1254
In 2005, there were 12,458 fish in Hound's Tooth
Lake. After years of drought, there were only
968 fish in 2010. Find the rate of change in the
population of fish for 2005–2010.
For the period 2005–2010, the drought caused a change in fish population of 2298 fishes each year.
Define the term rate of change?The term "rate of change" (ROC) describes the rate at which an object changes over time. Thus, it is not the amount of specific changes themselves but rather the acceleration and deceleration all changes (i.e., the rate).According to the specified question-
Hound's Tooth Lake had 12,458 fish in it in 2005.In 2010, there were just 968 fish after years of drought.Rate of change = (final number - initial number)/(final year - initial year)
Rate of change = (12,458 - 968)/(2010 - 2005)
Rate of change = -11490/5
Rate of change = -2298 fishes per year.
Negative sign shows there is a decline in the number.
Thus, for the time period 2005–2010, the drought caused a change in fish population of 2298 fishes each year.
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Choose the linear equation that is parallel to the following line y =−1/4 x − 1
Answer:
Any equation that has the same slope as this line will be parallel to it. The slope is -1/4, so whichever equation has -1/4 x in it will be parallel to the line.
a standard die is rolled three times. what is the probability of rolling a number less than 5 on the first two rolls, then an even number on the third roll?
2/216 or 1/108 is the probability of rolling a number .
How does probability explain work?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.The great thing about this question is that all three of those rolls are Independent Scenarios.
The probability of the first roll does not effect the outcome of the second or third roll
1/6 ( we want a 1, and there are 6 options.)
1/6 ( We want a 3, and there are 6 options
2/6 ( We want a 5 or 6, and there are 6 options)
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asking help for a friend again
To find the parallel line of y =3z+6 passing through the slope intercept points (-2,5).
For a line to be parallel to another line, by definition it must have the same slope.
Because the equation is in the slope-intercept form we can use the slope of the line.
The slope- intercept form of a linear equation is :
y=mx+b
Where m is the slope and b is the y− intercept value.
Therefore, for the given equation, the slope is 3.
Now we can use the point slope formula to determine the equation for the parallel line.
The point - slope formula states: (y−y1)=m(x−x1)
Where m is the slope and (x1,y1) is a point the line passes through.
Substituting the slope from the given line and the given point gives:
y−5=3(x+2)
Transforming this to the slope-intercept form by solving for y gives:
y−5=3x+6
y−5+5=3x+6+5
y=3x+11
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a box contains tiles. each tile has certain properties: each tile is made of wood or plastic. each tile is red, yellow, or blue. each tile is a triangle, square, pentagon, or circle. there is exactly one tile for each combination of properties. for example, there is one red circle that is made of wood. steve chooses one tile, and ellen chooses a different tile. what is the probability that the two chosen tiles differ with respect to all three properties?
1/24 is the probability that the two chosen tiles differ with respect to all three properties
1/2 chance that the tiles materials will be different (wood or plastic). 1/3 chance exists that the tiles will have different colors (r, y or b) 1/4 chance where the tile shapes will change (t, s, p or c)the probability that all three attributes of the two tiles will be different.1/2 * 1/3 * 1/4 = 1/24 The probability of an event occurring is a measure of its likelihood. It assesses the likelihood of an event. P(E) = Number of Favourable Outcomes/Total Outcomes is the probability formula.
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Find the missing side lengths. Leave your answers as radicals in simplest form
Answer:
Step-by-step explanation:
Hi Mia, are you aware that the last name Hamilton is a famous math person? :) anyway,
The triangle in the picture is an isosceles triangle, we know that b/c the angle of the one is 45° meaning the other side must also be a 45° angle. So we know the two sides are the same length.
side n = 7 [tex]\sqrt{2}[/tex] / 2
then use Pythagoras to find m
[tex]c^{2}[/tex] = ( 7 [tex]\sqrt{2}[/tex] / 2)^2 + ( 7 [tex]\sqrt{2}[/tex] / 2)^2
[tex]c^{2}[/tex] = 49*2/4 + 49*2/4
[tex]c^{2}[/tex] = 49/2 + 49/2
[tex]c^{2}[/tex] = 98/2
[tex]c^{2}[/tex] = 49
c = 7
side m = 7 :) nice, huh ?
a) Sin X = O/H
Sin 45 = [tex]7\sqrt{2}[/tex]/2/H
H= [tex]7\sqrt{2}[/tex]/2/ Sin 45
m= 7
b) cos X = A/H
cos 45= A/7
A= cos45*7
n= 4.95
Write a linear function f with the given values f(0) = 2, f(3) = -1
The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.
What is Linear Function?
A straight line on the coordinate plane is represented by a linear function.
The linear function formulas are:
y = mx + b (slope-intercept form)y−y1 = m(x−x1) (point-slope form)Ax + By = C (standard form)xa+yb = 1 (intercept form)Here, we have
The given functions are f(0)=2 and f(3) = -1
For f(0) = 2
Coordinate: (0,2)
y-intercept, c: 2
For f(3) = -1
Coordinate: (3,-1)
gradient or slope, m when x₁ = 0, y₁ = 2, x₂ = 3, y₂ = -1
=( y₂-y₁)/(x₂-x₁)
= ( -1 -2)/(3 - 0)
= -3/3
= -1
The linear equation is in the slope-intercept form, y=mx+c
f(x) = -x+2, where -1 is the slope and 2 is the y-intercept.
Hence, The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.
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Raymond sings in a choir called the Seaville Songbirds. For every 5 modern songs they learn, the choir leader teaches them 3 classical songs.
Based on the given ratio of modern and classical songs learned, the number of modern songs learned if 9 classicals have been learned is 15
What is the number of modern songs learned?Number of modern songs they learn = 5Number of classical songs = 3If the choir has learned 9 classical songs;
Number of modern songs learnt = xEquate the ratio of the number of modern songs to the number of classical songs
5 : 3 = x : 9
5/3 = x/9
cross product5 × 9 = 3 × x
45 = 3x
divide both sides by 3
x = 45/3
x = 15
In conclusion, the number of modern songs they have learned if they learn 9 classical songs is 15
Complete question:
Raymond sings in a choir called the Seaville Songbirds. For every 5 modern songs they learn, the choir leader teaches them 3 classical songs.
If the choir has learned 9 classical songs, how many modern songs have they learned?
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Can someone please help me
i need to find the diameter and the area of this equation[tex]A=\pi \frac{d}{2} x^{2}[/tex]
Answer:
Step-by-step explanation:
given the equation y(t)= -14t + 500, what is y (25)
The value of the equation y(t) at y(25) is 150
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Equations can be linear, quadratic or polynomials.
if y(t) = -14t + 500
The y(25) means substitute t = 25 into the equation
y(25) = -14(25) + 500
y(25) = -350 + 500
y(25) = 150
In conclusion, the value of y(25) is 150
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. Which is the better investment?
a. $1,200 at 9% simple interest for 2 years
b. $1,200 at 8% compound interest for 2 years
Answer:
200 at 9% simple interest for 2 years
Answer:
a
Step-by-step explanation:
Hope it helps and have a nice day!!!! :)
The perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle.
Solve the equation for the variable w
When you have done that
state the value of 'w' if the perimeter of the rectangle is equal to 37 feet and the length is equal to 4 feet.
hurrryyyy pls
Answer:
14.5 feet
Step-by-step explanation:
To make subject as 'w' and solving:To make the subject as 'w', isolate w.
To isolate 'w', subtract 2L from both sides .2L + 2W =P
2W = P - 2L
Now, divide both sides by 2.[tex]\sf W = \dfrac{P-2L}{2}\\\\W =\dfrac{P}{2}-\dfrac{2L}{2}\\\\ \boxed{W = \dfrac{P}{2}-L}[/tex]
P = 37 feet
L = 4 feet
[tex]\sf W =\dfrac{37}{2}-4\\\\[/tex]
= 18.5 - 4
W = 14.5 feet
Determine the smallest integer value of x in the solution of the following inequality.
-4x - 1 ≤ 13
Answer:
-3.5
Step-by-step explanation:
-4x-1+1≤ 13+1
-4x/-4 ≤ 14/-4
x≤ -3.5
. suppose the sides of a rectangle are changing with respect to time. the first side is changing at a rate of 2 in./sec whereas the second side is changing at the rate of 4 in/sec. how fast is the diagonal of the rectangle changing when the first side measures 16 in. and the second side measures 20 in.? (round answer to three decimal places.)
Diagonal of rectangle is changing by the rate of 4.373 in. /sec.
What is rate of change ?Rate of change (ROC) is the rate at which a variable changes over a particular period of time
To find the average rate of change, divide the change in the y-values by the change in the x-values . Finding the average rate of change is especially useful for identifying changes in measurable values such as average speed or average velocity.
A ratio is a special ratio in which the two terms have different units.
Calculationthe calculation part is shown in the below picture attached .
so after seeing the solution we come to an answer of = 4.373 in./sec
therefore diagonal of rectangle is changing by the rate of 4.373 in. /sec
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Tammy installs bathroom tiles. Her current job requires tiles that are equilateral triangles and all the tiles have to be congruent to each other. She has a big sack of tiles all in the shape of equilateral triangles. Although she knows that all the tiles are equilateral, she is not sure they are all the same size. What must she measure on each tile to be sure they are congruent? Explain.
Step-by-step explanation:
one side.
as each tile is guaranteed an equilateral triangle, all sides are equally long. measuring 1 side clarifies therefore the overall size of the tile.
the angles are the same in any case, as every equilateral triangle (no matter its size) has only angles of 60°.
so, if any side has the same length as the side lengths of the other triangles, then the checked triangle is congruent with the others.
the profit y (in dollars) for a business from selling x games is represented by y=33x graph the equation
THIS IS URGENT!!! SOMEONE PLEASE RESPOND!!!!
ty!
Answer: check the image attached
Step-by-step explanation:
Hope this helps
Answer:
Just point the graph on Y=33x+0
Step-by-step explanation:
There's no B or starting point, so you would just plant the point on 0,33
