The domain is the set of all possible values of x-variable
The range is the set of all possible values of y-variable
From the picture, the x-values and y-values vary from -4 to 4. Then, the range of the graph is the same as the domain. (True)
the school buys pencils for .20 each. it sells the pencils for .25 each. how much profit does the store make if it sells five dozen pencils
The stor buys the pencils for 0.20 and sells them for 0.25.
The difference between these two values represents the profit per pencil:
0.25-0.20= 0.05
The store profits 0.05cents per pecil sold.
One dozen equals 12 pencils, multiply it by 5 to know how many pencils are in 5 dozens:
12*5=60
The store sold 5 dozen pencils, this means they sold 60 pencils.
Multiply the profit per pencil by the total number of pencils sold to get how much they made:
60*0.05=3
For the 5 dozen pencils sold, the store made $3 profit.
ΔQRS is an isosceles triangle. What is the length of RT¯¯¯¯¯
R
T
? Round to the nearest hundredth. Enter your answer in the box.
\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22\)
22. Choose ALL the expressions that are equal to 18m+36*
3(15m+33)
6(3m+6)
2(9m+18)
6(3m+30)
3(6m+12)
18(m+2)
Answer:
6(3m + 6)
mark me brainliest
Which sign makes the following statement true?
1/4 _____ 5/16
Answer:
2. <
Step-by-step explanation:
To compare these two fractions we can first find them a common denominator. A common denominator between 4 and 16 is 16.
To get from 16 from 4 we multiply by 4 so we do the same to the numerator, changing 1/4 to 4/16.
5/16 already has a denominator of 16 so we can leave that one as is.
4/16___5/16
In this form it is obvious that 5/16 is the larger fraction because 5 is larger than 4, meaning that 5/16 is larger than 1/4.
Write the phrase, 6 divided by p, as an algebraic expression
divisiond i v i s i o n
6p6 over p
p6
Answer:
p/6 division
Step-by-step explanation:
if an angle is obtuse, what type of angle is the supplement
A tank is full of water. Find the work (in ft-lb) required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3. (Round your answer to the nearest whole number.) 3 ft6 ft12 ft A frustum of a cone with a spout is given. The smaller radius is 3 ft, the larger radius is 6 ft, and the height is 12 ft.
The work required to pump the water out of the spout is approximately 64,307,077 ft-lb
To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.
First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.
Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:
V = (1/3)π(12)(9 + 36 + 18) = 270π ft³
Now, we can calculate the weight of the water using the density of water:
Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb
Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):
Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²
Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:
Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft
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What is the coefficient of X when solved3x - 6(5x+3) = 9x+6
The coefficient of x in 3x - 6(5x+3) = 9x +6 is -36
What is coefficient?Coefficient is a number that is being multiplied by the variable. for example in 5x² + 6x there are two terms which are x² and x, they are variables and the coefficient of x² is 5 and coefficient of x is 6.
Similarly, for us to get the coefficient of x , we need to simplify the expression.
3x -6(5x+3) = 9x +6
3x -30x -18 = 9x + 6
collecting like terms
-27x -9x = 6 +18
-36x = 24
therefore the coefficient of x is -36
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Find the midpoint of a line segment with
endpoints A(-5, 5) and B(2, -5). Leave your answer
in fraction form.
Show your own work
Answer:
(-3/2, 0)
Step-by-step explanation:
You want the midpoint of line segment AB with end points A(-5, 5) and B(2, -5).
MidpointThe midpoint of a line segment has coordinates that are the average of the end point coordinates.
M = (A +B)/2
M = ((-5, 5) +(2, -5))/2 = (-5+2, 5-5)/2 = (-3, 0)/2
M = (-3/2, 0)
The midpoint of the line segment is (-3/2, 0).
Ralph chase plans to sell a piece of property for $145000. He wants the money to be paid off in two ways a short term note at 11% interest and a long term note at 8% interest. Find the amount of each note if the total annual interest paid is $13850.
Given :
Price of property , P = $145000 .
Money paid off in two ways a short term note at 11% interest and a long term note at 8% interest.
Total interest , I = $13850 .
To Find :
The amount of each note .
Solution :
Let , x money is paid off in 11 % interest rate and ( 145000-x) in 8% interest rate.
Therefore , their sum of interest in mathematics is given by :
\(\dfrac{11x}{100}+\dfrac{8(145000-x)}{100}=13850\\\\11x+1160000-8x=1385000\\\\3x=225000\\\\x=\$75000\)
Therefore , the amount of note is $75000 and $70000 for 11% and 8% interest rate respectively .
Hence , this is the required solution .
The following are the annual incomes (in thousands of dollars) for 8 randomly chosen, U.S. adults employed full-time.
44, 44, 54, 54, 65, 39, 54, 44
Send data to calculator
(a) What is the mean of this data set? If your answer is not an
integer, round your answer to one decimal place.
(b) What is the median of this data set? If your answer is not
an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are
their values? Indicate the number of modes by clicking in the
appropriate dircle, and then indicate the value(s) of the
mode(s), if applicable.
0
Zero modes
one mode:
Two modes:
Answer:
(a) To find the mean of the data set, sum up all the values and divide by the total number of values.
44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398
Mean = 398 / 8 = 49.75
Rounded to one decimal place, the mean of this data set is 49.8.
(b) To find the median of the data set, i need to arrange the values in ascending order first:
39, 44, 44, 44, 54, 54, 54, 65
The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:
(44 + 54) / 2 = 98 / 2 = 49
Rounded to one decimal place, the median of this data set is 49.0.
(c) To determine the modes of the data set, identify the values that appear most frequently.
In this case, the mode refers to the value(s) that occur(s) with the highest frequency.
From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.
In this exercise, do not attempt formal mathematical derivations, which would actually involve some subtle issues when we go beyond discrete random variables. Rather, use your understanding of the concepts involved. For each one of the statements below, indicate whether it is true or false.
(a) The law of iterated expectations tells us that E [E[X|Y]] = E[X]. Suppose that we want apply this law in a conditional universe, given another random variable Z, in order to evaluate E [X2]. Then: EE[X|Y, 2]|2] = E[X2] y E[E[X|Y]|2] =E[X2] V EE[X|Y,Z]] =E[X2]
(b) Determine whether each of the following statements about the quantity E[g(X,Y)|Y,Z) is true or false. The quantity E[9(X,Y)|Y, 2) is: • a random variable y a number y a function of (X,Y) y a function of (Y,Z) | a function of Z only
Solution :
From the given equation :
E[ E (X|Y) ] = E (X)
a). Then,
E[ E [ X|Y,Z] | Z] = E [ X|Z ]
---- True
E [ E [ X|Y ] | Z ] = E [ X|Z ]
---- False
E [E [X | Y,Z ]] = E [X|Y ]
---- False
b). Th quantity E [ g (X,Y) | Y,Z ] is ,
A random variable ----- TrueA number ----- FalseA function of (X,Y) ----- FalseA function of (Y,Z) ----- TrueA function of Z only ------- FalseThe low of iteration tell the following statement are true E[ E [ X|Y,Z] | Z] = E [ X|Z ] . A random variable y . A function of (Y,Z)
From the given equation the law of iterated expectations
\(E[ E (X|Y) ] = E (X)\)
Therefore We have to find a)
What is the definition of iteration?Iteration is the repetition of a process in order to generate a sequence of outcomes.
So by using the low of iteration we can say that,
E[ E [ X|Y,Z] | Z] = E [ X|Z ] ---- True
E [ E [ X|Y ] | Z ] = E [ X|Z ] ---- False
E [E [X | Y,Z ]] = E [X|Y ] ---- False
b). Th quantity E [ g (X,Y) | Y,Z ] is ,
For a random variable y this is ----- True
For a number ----- False
For a function of (X,Y) ----- False
For a function of (Y,Z) ----- True
For function of Z only ------- False
Therefore,The low of iteration tell the following statement are true E[ E [ X|Y,Z] | Z] = E [ X|Z ] . A random variable y . A function of (Y,Z)
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3,998-(-7)= can you please help me with this problem
Answer:
4005
Step-by-step explanation:
3,998 - (-7) = ?
Two negative signs will make a positive sign.
3,998 - (-7) = 3998 + 7 = 4005
So, the answer is 4005
How many edges does the figure have?
3
4
5
8
Answer:
4 points
Step-by-step explanation:
if you look its only 4, 1 on top, and 3 around.
How many solutions does this equation have? –4c = 3c + 7
Answer: c=-1
Step-by-step explanation:
-4c=3c+7
0=7c+7
-7=7c
-1=1c
c=-1
Answer:-
Step-by-step explanation:
1=c
6. A company car purchased for $39,600 depreciates at 12% per annum. What is the car
worth after 3 years?
Answer:
$26,986.29
Step-by-step explanation:
We can use the formula for calculating the depreciation of an asset over time:
wor
\(\bold{D = P(1 - \frac{r}{100} )^t}\)
where:
D= the current value of the asset
P = the initial purchase price of the asset
r = the annual depreciation rate as a decimal
t = the number of years the asset has been in use
In this case, we have:
P = $39,600
r = 12% = 0.12
t = 3 years
Substituting these values into the formula, we get:
\(D= 39,600(1 - \frac{12}{100})^3\\D= 39,600(1 - 0.12)^3\\D= 39,600*0.88^3\\D= 39,600*0.681472\\D=26986.2912\)
Therefore, the car is worth approximately $26,986.29 after 3 years of depreciation at a rate of 12% per annum.
Answer:
$26,986.29
Step-by-step explanation:
As the car's value depreciates at a constant rate of 12% per annum, we can use the exponential decay formula to create a function for the value of the car f(t) after t years.
Exponential Decay formula\(\boxed{f(t)=a(1-r)^t}\)
where:
f(t) is the value of the car (in dollars) after t years.a is the initial value of the car.r is the depreciation rate (as a decimal).t is the time period (number of years after purchase).In this case, the initial value is $39,600, and the rate of depreciation is 12% per year. Therefore, the function that models the value of the car after t years is:
\(f(t)=39600(1-0.12)^t\)
\(f(t)=39600(0.88)^t\)
To calculate the value of the car after 3 years, substitute t = 3 into the function:
\(\begin{aligned} f(3)&=39600(0.88)^3\\&=39600(0.681472)\\&=26986.2912\\&=26986.29\;(\sf 2\;d.p.)\end{aligned}\)
Therefore, the car is worth $26,986.29 after 3 years.
Lamont and Carmela both wrote an expression to show the area of the shaded region.
Lamont wrote: 6(m-2)
Carmela wrote: 6m-12
Whose expression is correct?
Answer:
Both expressions are correct
6(m-2) = 6m-12
Lamont's expression is factoring or factorising
Carmela's expression is expanding
what is a factor of 84 but not a multiple of 3
Answer:
2
Step-by-step explanation:
A rectangular prism has the dimensions shown below.
3 cm
3 cm
12 cm
What is the volume of the rectangular prism?
Answer:
108 cubic cm
Step-by-step explanation:
Multiply 3, 3, and 12. Just multiply the dimensions of the cubes.
Write the equation in slope-intercept form.
y+3 - 2(x-1)
Answer:
y = 2x - 5
Step-by-step explanation:
\(y+3=2(x-1)\\y+3=2x-2\\y+3-3=2x-2-3\\y=2x-5\)
Determine the values of the parameter s for which the system has a unique solution, and describe the solution. x 1 - 5 sx 2
Answer:
\(s \ne \±2\)
\(x_1 = \frac{3s - 2}{3(s^2 -4)}\)
\(x_2 = \frac{2(s- 6)}{5(s^2 - 4)}\)
Step-by-step explanation:
Given
\(3sx_1 +5x_2 = 3\)
\(12x_1 + 5sx_2 =2\)
Required
Determine the value of s
Express the equations as a matrix
\(A =\left[\begin{array}{cc}3s&5\\12&5s\end{array}\right]\)
Calculate the determinant
\(|A|= (3s*5s -5 *12)\)
\(|A|= (15s^2 -60)\)
Factorize
\(|A|= 15(s^2 -4)\)
Apply difference of two squares
\(|A|= 15(s -2)(s + 2)\)
For the system to have a unique solution;
\(|A| =0\)
So, we have:
\(15(s -2)(s+2) = 0\)
Divide both sides by 15
\((s -2)(s+2) = 0\)
Solve for s
\(s -2 = 0\ or\ s +2 = 0\)
\(s = 2\ or\ s = -2\)
The result can be combined as:
\(s =\±2\)
Hence, the system has a unique solution when \(s \ne \±2\)
Next, we solve for s using Cramer's rule.
We have:
\(mat\ x_1 = \left[\begin{array}{cc}3&5\\2&5s\end{array}\right]\)
Calculate the determinant
\(|x_1| = (3 * 5s - 5 *2)\)
\(|x_1| = 15s - 10\)
So:
\(x_1 =\frac{|x_1|}{|A|}\)
\(x_1 = \frac{15s - 10}{15(s -2)(s+2)}\)
Factorize
\(x_1 = \frac{5(3s - 2)}{15(s -2)(s+2)}\)
Divide by 5
\(x_1 = \frac{3s - 2}{3(s -2)(s+2)}\)
\(x_1 = \frac{3s - 2}{3(s^2 -4)}\)
Similarly:
\(mat\ x_2 =\left[\begin{array}{cc}3s&3\\12&2\end{array}\right]\)
Calculate the determinant
\(|x_2| = 3s * 2 - 3 * 12\)
\(|x_2| = 6s- 36\)
So:
\(x_2 =\frac{|x_2|}{|A|}\)
\(x_2 = \frac{6s- 36}{15(s -2)(s+2)}\)
Factorize
\(x_2 = \frac{6(s- 6)}{15(s -2)(s+2)}\)
Divide by 3
\(x_2 = \frac{2(s- 6)}{5(s -2)(s+2)}\)
\(x_2 = \frac{2(s- 6)}{5(s^2 - 4)}\)
169 divided by 13 and also please explain it
Answer:
13
Step-by-step explanation:
169/13 = How many times does 13 go into 169?
13*13 = 169
Answer: 13
Step 1:
Start by setting it up with the divisor 13 on the left side and the dividend 169 on the right side like this:
1 3 ⟌ 1 6 9
Step 2:
The divisor (13) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top:
0
1 3 ⟌ 1 6 9
Step 3:
Multiply the divisor by the result in the previous step (13 x 0 = 0) and write that answer below the dividend.
0
1 3 ⟌ 1 6 9
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.
0
1 3 ⟌ 1 6 9
- 0
1
Step 5:
Move down the 2nd digit of the dividend (6) like this:
0
1 3 ⟌ 1 6 9
- 0
1 6
Step 6:
The divisor (13) goes into the bottom number (16), 1 time(s). Therefore, put 1 on top:
0 1
1 3 ⟌ 1 6 9
- 0
1 6
Step 7:
Multiply the divisor by the result in the previous step (13 x 1 = 13) and write that answer at the bottom:
0 1
1 3 ⟌ 1 6 9
- 0
1 6
1 3
Step 8:
Subtract the result in the previous step from the number written above it. (16 - 13 = 3) and write the answer at the bottom.
0 1
1 3 ⟌ 1 6 9
- 0
1 6
- 1 3
3
Step 9:
Move down the last digit of the dividend (9) like this:
0 1
1 3 ⟌ 1 6 9
- 0
1 6
- 1 3
3 9
Step 10:
The divisor (13) goes into the bottom number (39), 3 time(s). Therefore put 3 on top:
0 1 3
1 3 ⟌ 1 6 9
- 0
1 6
- 1 3
3 9
Step 11:
Multiply the divisor by the result in the previous step (13 x 3 = 39) and write the answer at the bottom:
0 1 3
1 3 ⟌ 1 6 9
- 0
1 6
- 1 3
3 9
3 9
Step 12:
Subtract the result in the previous step from the number written above it. (39 - 39 = 0) and write the answer at the bottom.
0 1 3
1 3 ⟌ 1 6 9
- 0
1 6
- 1 3
3 9
- 3 9
0
Step-by-step explanation:
Hope this helps!! :))
4. In a mixture of 45 litters, the ratio of sugar solution to salt solution is 1:2. What is the
amount of sugar solution to be added if the ratio has to be 2:1?
Answer:
15
Step-by-step explanation:
The amountt of sugar and salt would be x and 2x
x+2x=45x
so sugar solution =15 and salt solution =30
ratio =2:1 then sugar =30 salt =15
The amount of sugar solution to be added =30-15=15
Solve the following equations by graphing. Give your answer to the nearest tenth.
Remember that
when solving a system of equations by graphing, the solution is the intersection of both graphs
so
Part A
we have
3(2^x)=6x-7
that is the same that
y=3(2^x)
y=6x-7
The solution is the x-coordinate of the intersection point in both graphs
using a graphing tool
There are no intersection points
that means
The system has no solution
Part B
we have
10x+5=-x+8
y=10x+5
y=-x+8
The solution is the x-coordinate of the intersection point in both graphs
using a graphing tool
The solution is x=0.27hope anyone help me please
9514 1404 393
Answer:
a) Lahulspiti: -8; Srinigar: -2; Shimla: 5; Ooty: 14; Bengahuru: 22
b) 30
c) 6
d) yes; no
Step-by-step explanation:
a) The values are read from the graph.
__
b) 22 -(-8) = 22 +8 = 30 . . . . difference between highest and lowest
__
c) -2 -(-8) = -2 +8 = 6 . . . positive difference
(Technically, the difference between L and S is L - S = (-8) -(-2) = -6.)
__
d) -2 + 5 < 5 . . . . true
-2 + 5 < -2 . . . . false
if the area of the origional rectangle is 7ft by 15ft and the scale is going by 1 inch to 2000 feet, what's the area of the scale rectangle?
Answer:
you should try searching it up
Step-by-step explanation:
What conclusions can you draw from the graph?
Answer:
My best conclusion (simply put) is that you had a higher score than the average class.
Step-by-step explanation:
It obvious that the green dots is above the averages of both bars. It would be safe to think that you scored higher than the average of the entire class in both predictions and parabolas.
how do you find the surface area and volume of a cylinder
The surface area of a shape is the sum of the area of all of its faces. To find the area of a cylinder, you need to find the area of its bases and add that to the area of its outer wall. The formula for finding the area of a cylinder is A = 2πr2 + 2πrh.
Step-by-step explanation:Surface area of a cylinder = 2πr 2 + 2πrh Volume of a cylinder = πr 2 h You need to know the radius and height to figure both the volume and surface area of a cylinder. Answers for volume problems should always be in cubic units. Answers for surface area problems should always be in square units.Exercises 1-6 sketch the convex set formed by the intersections of the half-space determined by the given inequalities. Also indicate whether the convex set is bounded x+y <5 2x +Y < 8 X2 0, y 2 0 I-><-2 2*-> < 0 3x +> < 6 X20, > 2 0
The given equations sketch out to form a convex set. Both sets are bounded.
1)
Here we see that the darkened area is the intersection region. Since the system is bounded by x ≥ 0 and y ≥ 0, we can say that this is a bounded region.
Then we see that in the bouned region, whatever two points we take, the line segment joining them, it will always lie in the convex space. Hence this is a convex set.
2)
Here we see that the darkened region in the first Quadrant will be the intersection space. Since x and y are greater than or equal to 0, we get a bounded region. Hence the solution is bounded.
Hence here we see any 2 points in the space will result in a line segment lying in the space. Hence this is a convex set.
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A certain type of kickboard scooter comes in silver, red, 2
or purple with wheel sizes of 125 millimeters or 180
millimeters. Determine the total number of color-wheel size combinations.
(This is probability and I’m having such a hell of a time figuring it out pls help)
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.
Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:
Total combinations = Number of color options × Number of wheel size options
Total combinations = 4 colors × 2 wheel sizes
Total combinations = 8
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
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