Using the combination formula, it is found that the number of candidates that can get a unique number sequence is given by:
b. 45.
The order of the pieces is not important, hence the combination formula is used.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 2 pieces are taken from a set of 10, hence the number of sequences is given by:
[tex]C_{10,2} = \frac{10!}{2!8!} = 45[/tex]
Which means that option b is correct.
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Given various values of the linear functions f(x) and g(x) in the table, determine the y-intercept of (f- g)(x).
X -6 -4 -1 3 4
f(x) 15 11
5 -3 -5
g(x) -36 -26 -11 9 14
O (0,9)
O (0, 3)
O (0, -3)
O (0, -9)
The y-intercept of linear function (f- g)(x) is (0,9)
How to determine the y-intercept?The table of values is given as:
x -6 -4 -1 3 4
f(x) 15 11 5 -3 -5
g(x) -36 -26 -11 9 14
The equations of the functions is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2-x_1} * (x -x_1) + y_1[/tex]
So, we have:
[tex]f(x) = \frac{11 -15}{-4 + 6} * (x + 6) + 15[/tex]
Evaluate
f(x) = -2x + 3
Also, we have:
[tex]g(x) = \frac{-26 + 36}{-4 + 6} * (x + 6) - 36[/tex]
Evaluate
g(x) = 5x - 6
Next, we calculate (f - g)(x) using:
(f - g)(x) = f(x) - g(x)
This gives
(f - g)(x) = -2x + 3 - 5x + 6
Substitute 0 for x
(f - g)(0) = -2(0) + 3 - 5(0) + 6
Evaluate
(f - g)(0) = 9
Hence, the y-intercept of (f- g)(x) is (0,9)
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Are any of these funtions?
Answer: The first and the fourth option
Step-by-step explanation:
Every input of a function can have only one output.
Option one is a function.
See the attached image as to why option two is not a function.
Option three has two outputs for the input value of "20" meaning it is not a function.
Option four is a function.
Someone pls help me ASAP! Express the following as the sum of its partial fraction: 2x+4/x(x+2)(x-4)
[tex] \frac{2x + 4}{(x + 2)(x - 4)} [/tex]
Answer:
[tex]\dfrac{2x+4}{x(x+2)(x-4)} \equiv \dfrac{1}{2(x-4)}-\dfrac{1}{2x}[/tex]
Step-by-step explanation:
Partial FractionsWrite out the expression as an identity:
[tex]\begin{aligned}\dfrac{2x+4}{x(x+2)(x-4)} & \equiv \dfrac{A}{x}+\dfrac{B}{(x+2)}+\dfrac{C}{(x-4)}\\\\\implies \dfrac{x(2x+4)(x+2)(x-4)}{x(x+2)(x-4)} & \equiv \dfrac{Ax(x+2)(x-4)}{x}+\dfrac{Bx(x+2)(x-4)}{(x+2)}+\dfrac{Cx(x+2)(x-4)}{(x-4)}\\\\\implies 2x+4 & \equiv A(x+2)(x+4)+ Bx(x-4)+Cx(x+2)\end{aligned}[/tex]
Calculate the values of A, B and C using substitution:
[tex]\begin{aligned}2x+4 & = A(x+2)(x-4)+Bx(x-4)+Cx(x+2)\\\\x=4 \implies 12 & = A(0)+B(0)+C(24)\implies C=\dfrac{1}{2}\\\\x=-2 \implies 0 & = A(0)+B(12)+C(0) \implies B=0\\\\ x=0 \implies 4 & = A(-8)+B(0)+C(0) \implies A=-\dfrac{1}{2}\end{aligned}[/tex]
Replace A, B and C in the original identity:
[tex]\begin{aligned}\dfrac{2x+4}{x(x+2)(x-4)} & \equiv \dfrac{A}{x}+ \dfrac{B}{(x+2)}+\dfrac{C}{(x-4)}\\\\& \equiv -\dfrac{1}{2x}+\dfrac{1}{2(x-4)}\\\\\implies \dfrac{2x+4}{x(x+2)(x-4)}& \equiv \dfrac{1}{2(x-4)}-\dfrac{1}{2x}\end{aligned}[/tex]
For 33 hours of work, you are paid $245.85. how much would you receive for 39 hours?
Answer:
$290.55
Step-by-step explanation:
We can use a ratio to solve
33 hours 39 hours
---------------- = -------------
245.85 x dollars
Using cross products
33 * x = 39* 245.85
33x=9588.15
Divide each side by 33
33x/33 = 9588.15-33
x =290.55
Someone help me with this
Answer:
radius = √35 mm or 5.916 mm
Explanation:
[tex]\sf area \ of \ circle = \pi r^2[/tex]Here:
area of circle: 110 mm²π taken as 22/7Solve for radius:
[tex]\rightarrow \sf \pi r^2 = 110[/tex]
[tex]\rightarrow \sf \dfrac{22}{7} r^2 = 110[/tex]
[tex]\rightarrow \sf r^2 = \dfrac{110(7)}{22} =35[/tex]
[tex]\rightarrow \sf r = \sqrt{35}[/tex]
Let's see
Area=110πr²=11022/7r²=110r²≈110(7)/22r²=770/22r=√770/22r=5.9mmDILATE TRIANGLES URGENTTTTTT
photo is inserted so work from that, the original triangle is the one in blue.
The Dilation is 0.76
What is dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape.
Dilation or scale factor= Dimension of new shape/ dimension of old shape
= Perimeter of new triangle(green)/ Perimeter of old Triangle (blue)
= 8.3/10.9
= 0.76
Hence, the scale factor is 0.76.
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Write and simplify the expression equivalent to 2(7x + 3) + 9x.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to simplify the expression 2(7x+3)+9x.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
We need to multiply 2 times 7x and 3, and then add 9x.So, let's compute...
\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\///\\\////\\\///\\\///\\\///\\\///\\\///\\\//\\//\\\/
After performing multiplication we obtain
[tex]\star~\mathrm{14x+6+9x}[/tex]
Now add 9x:
[tex]\star~\mathrm{23x+6}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
Mrs. Nygaard needs 12 hours to grade all of her students’ projects. She made a chart to show how much time she could spend grading the projects during the week.
Project Grading
Day
Hours Grading
Monday
1 and three-fourths
Tuesday
1 and one-half
Wednesday
1 and one-fifth
Thursday
2
Friday
1 and one-fourth
How many hours will Mrs. Nygaard need to work over the weekend to finish grading the projects?
Answer:
2
Step-by-step explanation:
I think Mrs. Nygaard would need 2 hours to work over the weekend to finish grading the projects .
a washing machine was reduced in sale by 15% the sale price is now £238 what was the original price?
Answer:
£280
Step-by-step explanation:
238/0.85
Look at the image below and figure it out i have 10 min
Answer:
The first one is Perimeter The second one is Area The third on is Volume.
Step-by-step explanation:
A box big enough to hold a computer is the area of something, A fence to go around the garden would be the perimeter, enough carpet to cover the floor is the volume
A fence to around a flower garden ---> perimeter
A box big enough to hold a computer ---> volume
Enough carpet to cover the floor ---> area
What is perimeter?Distance around the outside of a shape.
What is volume?The number of cubic units that make up a solid figure; the amount of space the figure occupies. In Cubic Units, or units³.
What is area?The space or surface enclosed in 2-dimensional shape.
Using these definitions, it can be said that the fence acts as a perimeter surrounding a flower garden. Each side has a length.
A box big enough enough to hold a computer is the amount of space in the box to make it big enough to hold the computer (The volume of the box).
The amount of carpet to cover the floor is acting as a 2-dimensional shape scenario as the carpet is likely a standard typical shape such as a rectangle or square. Overall, enough to occupy a standard-sized room.
The graph shows a probability distribution. What is P(X<3)?
The value of probability P(X<3) is 0.3 after calculating the area up to 3 option second is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a probability distribution shown in the picture.
To find the probability P(X<3) = area up to 3
From the probability distribution:
P(X<3) = (1/2)×3×(0.20)
P(X<3) = 1.5×0.20
P(X<3) = 0.3
Thus, the value of probability P(X<3) is 0.3 after calculating the area up to 3 option second is correct.
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Which is not a function?
Can give brainliest!!
Answer:
3
Step-by-step explanation:
A function cannot have two y values for any value of x
answer three has two y values for x =1
~Please help me with this q u e s t i o n~
Answer:
Point D
Step-by-step explanation:
[tex] \huge \qquad \sf Answer[/tex]
How to locate a point on a graph (x - y plane) :
The x - coordinate of a point on the graph shows its distance from y - axis and sign refers to its direction that is +ve sign means right side of y - axis and -ve sign means left side of y - axis.
We have been given its x - coordinate as 9, so the required point should be At a distance of 9 units from y - axis and in right side of y - axis.
And similarly, y - coordinate shows distance of point from x - axis, +ve for upward direction and -ve for downward direction.
and we have given the y - coordinate as 0, ao its distance from x - axis is 0. that means the point lies of x - axis.
And by Observing the points clearly we can figure out that the required point is D. that satisfy the condition.
what would i put in, in the blanks? please help, i don’t get this
The function f(x) is a logarithmic function with a horizontal asymptote of y=1. The range of the function is all real numbers greater than 1, and it is decreasing on its domain of x>0. The end behavior on the LEFT side is as x approaches zero, y approaches infinity, and the end behavior on the RIGHT side is as x approaches infinity, y approaches 1.
Which is the correct answer for 62 + ∛125 ?
Answer: 67
Step-by-step explanation:
∛125 = 5
62 + 5 = 67
Please help me fast and thank you if you do
Answer:
8 > u > 6
Step-by-step explanation:
We have to solve this inequality as 2 separate inequalities.
==============================================================
Inequality 1 :
⇒ 10 > 5u/4
⇒ 5u < 10 × 4
⇒ 5u < 40
⇒ u < 8 [Box 1]
============================================================
Inequality 2 :
⇒ 5u/4 > 15/2
⇒ 5u/2 > 15
⇒ u/2 > 3
⇒ u > 3 × 2
⇒ u > 6 [Box 2]
============================================================
Solution :
⇒ 8 > u > 6
add. express your answer in simplest form. 1/12 + 5/12
Answer:
The answer is 1/2
Answer:
1/2
Step-by-step explanation:
[tex]\frac{1}{12}+\frac{5}{12} = \frac{6}{12}\\ \\ \frac{6}{12} = \frac{1}{2}[/tex]They are both equivalent fractions. If you divide the numerator and denominator both by 6, you get 1/2.
Cut-1 Cut-2 Number of rope cutting 1 2 3 Resulting pieces 3 5 7 1.2.1 The number of pieces of ropes for FIVE cuts. 4 S
The answer to the all parts given below.
What is sequence?A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.
For 5 cuts number of pieces will be 11 pieces.
General formula:
Tn= 2n+1
For 153 rope pieces number of rope cutting
2n+1=153
2n= 152
n= 76
For 11 cuttings rope pieces will be
2(11)+1
= 23
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A line contains the points (3, 2) and (6, 0). What is the equation of the line?
A
y = 3x + 2
B
y = 2x - 2
C y = -2x+3
D
2/3x+4
On discovering that her family had a 70% risk of heart attack, Erin took a treadmill test to check her own potential of having a heart attack. The doctors told her that the reliability of the stress test is 67%. What is the probability that Erin will not have a heart attack and the test predicts that she will?
A.
0.099
B.
0.201
C.
0.231
D.
0.469
Serena constructed a wire barrier to protect her tomato plant from squirrels. The barrier is 2.5 feet from the tomato plant in every direction.
The shape of the barrier is a circle with a diameter of 5 feet. The correct option is the last option - A circle with a diameter of 5 feet
Determining shapeFrom the question, we are to determine the statement that describes the shape of the barrier
From the given information,
The barrier is 2.5 feet from the tomato plant in every direction.
This can be likened to a circle that has a radius of 2.5 feet.
Recall: Radius of a circle is the distance from the center of the circle to any point on it's circumference
If radius of a circle is 2.5 feet, the diameter will be 2 × 2.5 feet = 5 feet
Hence, the shape of the barrier is a circle with a diameter of 5 feet. The correct option is the last option- A circle with a diameter of 5 feet
Here is the complete question:
Serena constructed a wire barrier to protect her tomato plant from squirrels. The barrier is 2.5 feet from the tomato plant in every direction. Which statement describes the shape of the barrier?
A circle with a radius of 5 feet
A square with diagonals 5 feet long
A square with sides 5 feet long
A circle with a diameter of 5 feet
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e0.02t
where
The population of a town is modeled by the equation P = 16, 581e'
Prepresents the population tyears after 2000. According to the model, what
will the population of the town be in 2020?
CL
hypotenuse I think????????????????????????
Answer:
You have walked 7.0 steps
Step-by-step explanation:
You just add 4 steps by 3 steps, so 4+3=7
What is the median pumpkin weight?
Answer:
17
Step-by-step explanation:
The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have:
[tex]10, 12, 14, 16, 18, 20, 22, 24[/tex]
Since there is an even number of data values in this data set, there are two middle numbers. With 8 data values, the middle numbers are the data values at positions 4 and 5. These are 16 and 18. The median is the average of these numbers. We have
[tex]{\frac{ 16 + 18 }{2}}[/tex]
Therefore, the median is
[tex]17[/tex]
A person borrows $50000 loan from bank at a rate of 10% for 5 years compounded yearly.
a) Calculate the total amount paid after 5 years.
b) Find the interest paid.
[tex]\large\boxed{Formula: A= P(1+ \frac{R}{100}{)}^{T}}[/tex]
Let's substitute according to the formula.
[tex]A= 50000(1+ \frac{10}{100}{)}^{5}[/tex]
A= $80525.5
Now, we can find the interest paid
[tex]\large\boxed{I= A-P}[/tex]
We'll have to deduct the total amount from the principal amount.
Let's substitute according to the formula.
[tex]I= 80525.5-50000[/tex]
I= $30525.5
Hence, the total amount paid after 5 years is $80525.5 and $30525.5 was paid as interest.
Professor Hopkins is grading the final exam. She notices that the
mean test score is 71, and the standard deviation is 6. The test
scores were normally distributed.
If there were 300 students in the data sample, how many would
have a test score between 71 and 83?*
*Round your answer to the nearest whole value.
students
Answer:
143
Step-by-step explanation:
The interval of interest extends from the mean score (71) to 2 standard deviations above the mean (71+2(6) = 83). The area under the normal distribution curve in this interval can be found using a suitable table, probability app, spreadsheet, or web site. It can also be found using the "empirical rule", which tells you that the 95% of the area is within 2 standard deviations of the mean.
__
Since the curve is symmetrical, and we're only interested in the area above the mean, the empirical rule tells us that 95%/2 = 47.5% of the sample will be in the range of interest.
0.475 × 300 = 142.5 ≈ 143
143 students will have a score between 71 and 83.
__
The attachment shows a calculator output for the same calculation. You will notice it is slightly different from the "empirical rule," which is only an approximation. Either way, we find 143 students have scores in the range.
Find the measure of the angle indicated
Answer:
59°
Step-by-step explanation:
Well, as you can see from the figure, the line WU is a diameter which means that it is a straight line. So, Angle WSU is 180° (Because straight angles are 180°)
Also, angle WSU is formed by addition of angle VSW and VSU. The value of VSU is given in the picture. So,
∠VSW + ∠VSU = 180°
∠VSW = 180° - ∠VSU
∠VSW = 180° - 121 (Because ∠VSU is given 121°)
∠VSW = 59°
Therefore, angle VSW is 59 degrees.
So, here you go. I hope you understand my explanation. Have a good day.
- Eddie
is (0,0) a solution to this system? y ≤ x^2 + x - 4 y < x^2 + 2x + 1
( 0,0 ) is not the solution of the first inequality y≤x² +x-4 but ( 0,0) is the solution for the second inequality y <x²+2x+1.
What is inequality?
The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than’
Finding the solution for the inequality is as follows:-
y ≤ x² +x-4 by putting x and y equal to 0.
0 ≤ 0 + 0 -4
0 ≤ - 4
This is incorrect so (0,0) can not be the solution for this inequality.
y < x²+2x+1.
0 < 0 + 0 + 1
0 < 1
This inequality is showing the solution for (0,0)
Therefore ( 0,0 ) is not the solution of the first inequality y≤x² +x-4 but ( 0,0) is the solution for the second inequality y <x²+2x+1.
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hey guys my last question please answer :) peace and love guys
Looking at the problem statement, this question states for us to determine the range of the function that is provided in a graph is. Let us first determine what range is.
Range ⇒ Range is what y-values can be used in the function that is graphed. For example, if a line just goes up and down all the way to negative and positive infinity, then the range would be negative infinity to positive infinity as it includes all of the y-values in it's solutions.Now moving back to our problem, we can see that we have a vertex at (2, -5) and that the lowest y-values is at y = -5. Therefore the y-values would be anything greater than or equal to -5 and less than infinity because the lines go forever up in the positive-y-direction.
Therefore, the option that would best match the description that we provided would be option B, -5 ≤ y < ∞.
jasper