Answer:
24
Step-by-step explanation:
The topic here is COMBINATORICS.
The parent topic is PERMUTATIONS & COMBINATORICS.
Permutation deals with arrangement in a definite order while, as stated in the question here, definite order in not needed in Combinatorics.
Now, the multiplication rule of counting, also known as the rule of product, talks about the multiplication of the figures that represent the different ways of doing something.
For example, in this question, the robot needs to attach 4 wires to a circuit board. If you know how Physics or Electricity works, you'll that truly this is a combination matter and not permutation.
Putting/Connecting the 4 wires together (in a square shaped circuit for instance), the arrangement RGBY is different from RGYB or RBGY.
So there will be more ways to connect or combine these wires, than if we were to follow a definite rule like: "Red and Green must always stay together".
So using the multiplication rule of counting to determine 4 choices for the Red wire, 3 choices for the Green wire, 2 choices for the Blue wire, and 1 choice for the yellow wire, we have:
R4 x G3 x B2 x Y1 = 4 x 3 x 2 x 1 = 4! = 24
The term "4!" means "Four Factorial".
Which function has lowest rate of change?
5x – 2y = 15 (or) Cost of 5 pencils is 15 dollars
O Algebraic Function
O Verbal Description
Both the functions
O None of the choices
Answer:
A: Algebraic Function
Step-by-step explanation:
Algebraic function is given as;
5x – 2y = 15
Since we are dealing with rate of change, let's make y the subject first and find dy/dx.
Thus;
2y = 5x - 15
y = (5x/2) - 15/2
dy/dx = 5/2
dy/dx = 2.5
The verbal function is given as;
Cost of 5 pencils is 15 dollars
Thus, rate of 1 pencil = 15/5 = 3 pencils per dollar
We can see that the lowest rate of change is 2.5 and it is the algebraic function.
Question 3 of 28
What is the length of IN in the right triangle below?
M
19
N
O A. 442
B. 442
O c. 1200
D. 280
Answer:
Option C. √280
Step-by-step explanation:
From the question given above, the following data were obtained
MN = 19
ML = 9
LN =?
We can obtain the value of LN by using the pythagoras theory as illustrated:
M ² = ML² + LN²
19² = 9² + LN²
361 = 81 + LN²
Collect like terms
361 – 81 = LN²
280 = LN²
Take the square root of both side
LN = √280
Therefore, the length of LN is √280
Explain how the given graph is deceptive.
Complete the statements based on the bar graph.
By not starting the horizontal axis at 0, the
bar appears to be about one-fourth the height of the Pecan bar. The
bar appears to be about one-half the height of the Pecan bar. The
bar appears to be less than one-half the height of the Pecan bar. This misleads the viewer to
the number of each type of nut used
Ans:
Pine Nut
Walnut
Almond
Understimate
Answer:
In the picture below.
Step-by-step explanation:
From the commenter and answer above, confirmed on edge 2022.
Find the length of the arc. Round your answer to the nearest tenth
Answer:
12.6 mi
Step-by-step explanation:
Arc length = 2πr (Θ/360)
2π(12) (60/360)
= 12.6 mi
Answered by g a u t h m a t h
The American Management Association is studying the income of store managers in the retail industry. A random sample of 49 managers reveals a sample mean of $45,420. The standard deviation of the population is known to be $2,050.
a). Compute a 95% confidence interval, as well as the margin of error.
b). Interpret the confidence interval you have computed.
Answer:
a) The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.
b) The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.
Step-by-step explanation:
Question a:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{2050}{\sqrt{49}} = 574[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 45420 - 574 = $44,846.
The upper end of the interval is the sample mean added to M. So it is 45420 + 574 = $45,994.
The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.
Question b:
The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.
Find the missing side of the triangle
Answer:
approximately 12.7
Step-by-step explanation:
using phythagoras rule,
hyp²=opp²+ adj²
15²=x² + 8²
225=x² + 64
x²=225 - 64
x²= 161
x=12.7
OR
sin ø= 8/15
sin ø=0.53333333
ø=sin(inverse) of 0.53333333
ø=0.563⁰
therefore angle opposite 8 is 0.563
tan 0.563= 8/x
x tan 0.563=8
x= 8/tan 0.563
x= 12.7
Find the length of the segment indicated. circles 4
I need more information, comment on my "answer".
Find the difference: -18 - (-18)
Answer:
0
Step-by-step explanation:
-18-(-18)
= -18+18 [(+) + (+)=(+)]
=0 [(-) + (-)=(-)]
1. Write the polynomial function that models the given situation.A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.
2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.
3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.
Answer:
1. (12 - 2x)(11 - 2x)x
2. 4(11 - 2x)²(x + 1)
3. π(x³ + 15x² + 63x + 81)
Step-by-step explanation:
1. Write the polynomial function that models the given situation.
A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.
Since the length of the rectangle is 12 units and its width 11 units and squares of x by x units are cut from its corners, it implies that a length x is cut from each side. So, the length of the open box is L = 12 - 2x and its width is w = 11 - 2x.
Since the cut corners of the rectangle are folded, the side x which is cut represents the height of the open box, h. so, h = x
So, the volume of the open box V = LWh = (12 - 2x)(11 - 2x)x
2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.
Since the square has sides of 24 units and squares of x + 1 by x + 1 units are cut from its corners, it implies that a length x + 1 is cut from each corner and the length 2(x + 1) is cut from each side. So, the length of side open box is L = 24 - 2(x + 1) = 24 - 2x - 2 = 24 - 2 - 2x = 22 - 2x = 2(11 - x)
Since the cut corners of the square are folded, the side x + 1 which is cut represents the height of the open box, h. so, h = x + 1
Since the area of the base of the pen box is a square, its area is L² = [2(11 - 2x)]²
So, the volume of the open box V = L²h = [2(11 - 2x)]²(x + 1) = 4(11 - 2x)²(x + 1)
3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.
The volume of a cylinder is V = πr²h where r = radius and h = height of cylinder.
Given that r = x + 6 and h is 3 units more than r, h = r + 3 = x + 6 + 3 = x + 9
So, V = πr²h
V = π(x + 3)²(x + 9)
V = π(x² + 6x + 9)(x + 9)
V = π(x³ + 6x² + 9x + 9x² + 54x + 81)
V = π(x³ + 15x² + 63x + 81)
A factory makes twenty-three million, five hundred fifty candies each month. This number in standard form is
Answer:
23,000,550
Step-by-step explanation:
A million has six zeroes, so twenty three million is
23,000,000
Since five hundred fifty is not in the thousands, it replaces the last trio of zeroes.
We have the number in standard form as
23,000,550
Answer:
23000550
Step-by-step explanation:
Please help I need this done ASAP
10 points + crown for whoever has the most accurate answer
Part a)
Time:distance
1:3
Part b)
6 hours
Part C)
81km
Answered by Gauthmath must click thanks and mark brainliest
One book is 4cm thick, find out how many such books can be placed in a space of 53cm.
It takes 12 people 15 hours to complete and certain job.how many hours would it take 18 people, working at the same rate to complete 2/5 of the same job?
Answer:
9 hours
Step-by-step explanation:
12 people take 15 hours to complete one job. First let's ask how long it would take 18 people working at the same rate to complete the same job? We can use proportions to answer this
[tex]\frac{12 people}{15 hours} = \frac{18 people}{x hours}\\x = \frac{18\times15}{12} = 22.5[/tex]
Now we know that one job takes 18 people 22.5 hours, so 2/5 of the job would take
[tex]\frac{18\times15}{12} \times \frac{2}{5} = 9[/tex]
Factor.
64x^12 + 27y^3
Answer:
answer is (4x^4+3y)(16x^8-12x^4y+9y^2)
Step-by-step explanation:
State if the scenario involves a permutation or a combination. Then find the number of possibilities.
A team of 15 basketball players needs to choose two players to refill the water cooler.
Permutation/Combination:
Answer:
Answer:
Permutation ; 210 ways
Step-by-step explanation:
Permutation and combination methods refers to mathematical solution to finding the number of ways of making selection for a group of objects.
Usually, selection process whereby the order of selection does not matter are being treated using permutation, while those which takes the order of selection into cognizance are calculated using combination.
Here, selecting 2 players from 15 ; since order does not matter, we use permutation ;
Recall :
nPr = n! ÷ (n - r)!
Hence,
15P2 = 15! ÷ (15 - 2)!
15P2 = 15! ÷ 13!
15P2 = (15 * 14) = 210 ways
Solve 2x^2+5x+5=0 round solutions to the nearest hundredth.
Answer:
-0.56
Step-by-step explanation:
HELP keep saying im getting wrong
instruction find the perimeter of the polygon
Answer:
perimeter = 50
Step-by-step explanation:
Tangents to a circle from an external point are congruent , then
perimeter = (8 + 8) + (10 + 10) + (7 + 7) = 16 + 20 + 14 = 50
In June 2005, a CBS News/NY Times poll asked a random sample of 1,111 U.S. adults the following question: "What do you think is the most important problem facing this country today?" Roughly 19% of those sampled answered "the war in Iraq" (while the rest answered economy/jobs, terrorism, healthcare, etc.).
Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country. We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll.
What are the appropriate hypotheses in this case?
Answer:
The appropriate null hypothesis is [tex]H_0: p = 0.25[/tex]
The appropriate alternative hypothesis is [tex]H_1: p < 0.25[/tex]
Step-by-step explanation:
Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country.
At the null hypothesis, we test if the proportion is still the same, that is, of [tex]\frac{1}{4} = 0.25[/tex]. So
[tex]H_0: p = 0.25[/tex]
We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll.
Decreased, so at the alternative hypothesis, it is tested if the proportion is less than 0.25, that is:
[tex]H_1: p < 0.25[/tex]
Simplify: −4(b+6)−2b(1−4b
Step-by-step explanation:
-4b-24-2b+8b2
8b2-6b-24=0
I need to know the answer ASAP
Answer:
Step-by-step explanation:
A study was conducted in order to estimate ?, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be ? = 3.6 hours.
A similar study conducted a year earlier estimated that ?, the mean number of weekly hours that U.S. adults use computers at home, was 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year.
Using a 95% confidence interval of (7.7, 9.3), our conclusion is that:
a. the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.
b. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.
c. the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
d. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
e. None of the above. The only way to reach a conclusion is by finding the p-value of the test.
Answer:
d. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
Step-by-step explanation:
Mean was of 8 hours, test if it has changed:
At the null hypothesis, we test if it has not changed, that is, the mean is still of 8, so:
[tex]H_0: \mu = 8[/tex]
At the alternative hypothesis, we test if it has changed, that is, the mean is different of 8, so:
[tex]H_1: \mu \neq 8[/tex]
Using a 95% confidence interval of (7.7, 9.3), our conclusion is that:
8 is part of the confidence interval, which means that the study does not provide evidence that the mean has changed, and the correct answer is given by option d.
Which of the following graphs is described by the function given below?
y = x2 - 6x-7
Answer:
A
Step-by-step explanation:
We are given the function:
[tex]\displaystyle y = x^2 - 6x - 7[/tex]
And we want to determine its graph.
One of the most important features of a quadratic is its vertex. So, we can start by finding the vertex using the formulas:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -6, and c = -7.
Find the x-coordinate of the vertex:
[tex]\displaystyle x = -\frac{(-6)}{2(1)} = 3[/tex]
Substitute this back into the equation to find the y-coordinate:
[tex]\displaystyle y(3) = -16[/tex]
Therefore, our vertex is at (3, -16).
The only graph whose quadratic's vertex is at (3, -16) is Graph A. Thus, our answer is A.
Which functions represent a vertical stretch of the parent function, f(x) = 1/x? Check all that apply.
g(x) = 3/x
g(x) = -2/x
g(x) = 1/4x
g(x) = 5/2x
g(x) = 1/2x
Answer:
[tex]g(x) = \frac{3}{x}[/tex]
[tex]g(x) =-\frac{2}{x}[/tex]
[tex]g(x) =\frac{5}{2x}[/tex]
Step-by-step explanation:
Given
[tex]f(x)=\frac{1}{x}[/tex]
Required
Which represents vertical stretch of f(x)
The transformation is represented as:
[tex]g(x) = a* f(x)[/tex]
Where:
[tex]|a| > 1[/tex]
So, the functions are:
[tex]g(x) = \frac{3}{x}[/tex] ---- [tex]|3| > 1[/tex]
[tex]g(x) =-\frac{2}{x}[/tex] --- [tex]|-2|>1[/tex]
[tex]g(x) =\frac{5}{2x}[/tex] --- [tex]|\frac{5}{2}| > 1[/tex]
Answer:
the other person is correct if you need them quick it is a b and d
Step-by-step explanation:
!!I NEED THE ANSWER PLS!!
Which of the following represents the divisor and the dividend for the
synthetic division problem below?
- 3/ 2 4 -4 6
A. -3 and -2x2 - 4x2 + 4x-6
B. x+3 and -2x2 - 4x +47-6
C. X+3 and 2x + 4x2 - 4x+6
D. *-3 and 2x2 + 4x2 - 4x+6
Answer:
B
Step-by-step explanation:
B . x+3 and -2x2 - 4x +47-6
B . x+3 and -2x2 - 4x +47-6
The divisor and the dividend for the given synthetic division problem are : [tex]x+3[/tex] and [tex]2x^3+4x^2-4x+6[/tex]
What is synthetic division?"It is a way of dividing one polynomial by another polynomial of first degree."
What is dividend?"The value that is divided by another value to get the result. "
What is divisor?"The value that divides another number either completely or with a remainder."
For given question,
We have been given a synthetic division problem.
- 3/ 2 4 -4 6
We need to represent the divisor and the dividend for the given synthetic division problem.
We know that, to perform synthetic division, here are the steps:
- The leading coefficient of the divisor should also be 1.
- Express the dividend in standard form.
- Write the leading coefficient in the dividend.
- Place the product of the number you brought down and the number in the division box in the preceding column.
- Write the result at the bottom of the row.
So, the divisor of the given synthetic division form would be,
x - (-3) = x + 3
And the dividend of the given synthetic division form would be,
There are four leading coefficient.
This means the dividend polynomial must be of degree 3.
From the leading coefficients 2 4 -4 6
[tex]2x^3+4x^2-4x+6[/tex]
Therefore, the divisor and the dividend for the given synthetic division problem are : [tex]x+3[/tex] and [tex]2x^3+4x^2-4x+6[/tex]
Learn more about the synthetic division here:
https://brainly.com/question/11850611
#SPJ2
Help on 3,5,7,9,11,13.15,17, please thank you
Answer:
3. 6a+60
5. 25+5w
7. 90-10t
11. 4.5-12c
13. f-2
15. 12z+1.5
Step-by-step explanation:
3.
6(a+10)
Multiply 6 by both factors in the parentheses, in this case, a and 10.
6*a = 6a
6*10 = 60
6(a+10) = 6a + 60
I only put the step- by- step explanation for #3, but you should be able to figure the rest out with that.
Determine the value of X. Please explain the answer
We have two lines from the same point.
These two lines are also tangents to same circle which implies that they are of the same length.
That is 2x - 1 = 9
2x = 9 +1 = 10
x =10/2
x = 5
The dotplots below display the scores for two classes on a 30-point statistics quiz. Class A has 26 students and Class B has 25 students.
2 dot plots. For Class A, the dots are spread out more. For Class B, the dots are more grouped together.
Which statement best compares the variability of the quiz scores for Class A and Class B?
The scores on the quiz for Class A have more variability than the scores for Class B.
The scores on the quiz for Class B have more variability than the scores for Class A.
The scores on the quiz for Class A have less variability than the scores for Class B.
The scores on the quiz for Class B have about the same variability as the scores for Class A.
I think its (A), The scores on the quiz for Class A have more variability than the scores for Class B. Can someone check me?
The statement that best compares the variability of the quiz scores for Class A and Class B is A; The scores on the quiz for Class A have more variability than the scores for Class B.
How does the dot plot work?Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.
LEt suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.
The dot plot is skewed to the right due to majority of the data occur to the right of the dot plot.
An outlier is a number that is way smaller or way larger than that of other numbers in a data set. Outliers usually occur with a frequency of one.
For Class A the dots are spread out more.
For Class B, the dots are more grouped together.
Here, Looking at the dot plot, it can be seen that the numbers that range from 16 to 21 have only one dot.
The statement that best compares the variability of the quiz scores for Class A and Class B is A; The scores on the quiz for Class A have more variability than the scores for Class B.
To learn more about outliers, please check: brainly.com/question/27197311
SPJ2
Please Answer This!!! I NEEEDDD TOOO KNOWWWWW ANSWER!!!
Answer:
77.5
Step-by-step explanation:
Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B
Trong một lớp học có $35$ sinh viên nói được tiếng Anh, $25$ sinh viên nói được tiếng Nhật trong đó có $10$ sinh viên nói được cả tiếng Anh và tiếng Nhật. Mỗi sinh viên trong lớp nói được ít nhất một trong hai: tiếng Anh hoặc tiếng Nhật. Hỏi sỹ số của lớp là bao nhiêu
Answer:
please write this question in English then I give answer
What's the value of n if 13+19= n+25
.
.
..
.
.............
Answer:
[tex]13+19=n+25[/tex]
[tex]n+25=13+19[/tex]
Add 13+19= 32
[tex]n+25=32[/tex]
Now Subtract 25 from both sides
[tex]n+25-25=32-25[/tex]
[tex]n=7[/tex]
OAmalOHopeO
