The number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.
When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.
The number of different permutations of n objects with m₁ repeated items, m₂ repeated items,...,mₙ repeated items can be computed as
m!/(m₁!)(m₂!)...(mₙ!)
Here, the letter 'KNICKKNACK' is a total of 10 letters with 4 K's, 2 N's, 1 I, 2 C's, and 1 A.
So, the number of possible arrangements is
(10!)/(4!*2!*1!*2!*1!) = (10*9*8*7*6*5*4!)/(4!*2*2) = 10*9*7*6*5*2 = 37800
Therefore the number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.
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You are given that cos(A)=−35, with A in Quadrant II, and cos(B)=817, with B in Quadrant I. Find cos(A−B). Give your answer as a fraction.
Expand cos(A - B) with the identity
cos(A - B) = cos(A) cos(B) + sin(A) sin(B)
A is in quadrant II, so sin(A) > 0, and B is in quadrant I, so sin(B) > 0. Using the Pythagorean identity, we get
cos²(A) + sin²(A) = 1 ⇒ sin(A) = + √(1 - (-3/5)²) = 4/5
cos²(B) + sin²(B) = 1 ⇒ sin(A) = + √(1 - (8/17)²) = 15/17
Then
cos(A - B) = (-3/5) × 8/17 + 4/5 × 15/17 = 36/85
cos (A - B) is 36/85
How to simply the identity
Expand cos(A - B) with the identity
You get, cos(A - B) = cos(A) cos(B) + sin(A) sin(B)
Since A is in quadrant II, so sin(A) > 0,
B is in quadrant I, so sin(B) > 0.
Using the Pythagorean identity, we get
cos²(A) + sin²(A) = 1
Make sin A the subject of formula
[tex]sin(A)^{2}[/tex] = ([tex]\sqrt{(1 - (-3/5}[/tex])²)
Find the square root of both sides, square root cancels square
[tex]sin A[/tex] = 4/5
Repeat the same for the second value
[tex]sin A^{2} = \sqrt{(1- 8/17)^2}[/tex]
[tex]sin A[/tex] = 15/17
Substitute values into cos(A - B)
cos(A - B) = cos(A) cos(B) + sin(A) sin(B) = (-3/5) * 8/17 + 4/5 * 15/17
cos (A - B) = 36/85
Therefore, cos (A - B) is 36/85
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Graph the line passing through (6, 1) whose slope is m = 3.
Answer: [tex]y=3x-17[/tex]
Step-by-step explanation:
use point-slope form:
[tex]y_{1} -y=m(x_{1} -x)[/tex]
[tex]y-1=3(x-6)[/tex]
[tex]y-1=3x-18[/tex]
[tex]y=3x-17[/tex]
Answer:
equation: y = 3x - 17
[image attached]
Step-by-step explanation:
we know that the equation for a line is y = mx + b
we are given a point, (6, 1)
remember that a point is (x, y)
we can plug these sample x and y values into our equation, replacing x and y
y = mx + b
1 = m6 + b
we know that m = 3 [this was a given], so we can plug this into our equation
1 = (3)(6) + b
1 = (18) + b
1 = 18 + b [we can now solve for "b"]
1 = 18 + b
-18 - 18
-17 = b
so, we can re-write our equation so that we can graph it:
y = 3x - 17
we can now plug in x-values to graph this:
(you'll see these written in the table on the graph)
y = 3(0) - 17
y = -17
y= 3(1) - 17
y = 3 - 17
y = -14
y = 3(2) - 17
y = 6 - 17
y = -11
y = 3(3) - 17
y = 9 - 17
y = -8
y = 3(4) - 17
y = 12 - 17
y = -5
y = 3(-1) - 17
y = -3 - 17
y = -20
y = 3(-2) - 17
y = -6 - 17
y = -23
y = 3(-3) - 17
y = -9 - 17
y = -26
[there is an image attached of my graph]
hope this helps!! :)
Find the solution to the following system by substitution.
5x + y = 20
y = 5x
A. (2,10)
B. (4,0)
C. (0,20)
D. (4,20)
Answer:
A. (2,10)
Step-by-step explanation:
5x + y = 20
y = 5x
The second equation is already solved for y, so substitute 5x for y in the first equation to find x.
5x + 5x = 20
10x = 20
x = 2
Now substitute 2 for x in the second original equation to find y.
y = 5(2)
y = 10
Answer: (2, 10) which is A.
Find two functions defined
implicity by this equation:
(x − 5)² − 3(y + 2)² = 4
Answer:
[tex] \frac{dy}{dy} = \frac{x - 5}{3y + 6} [/tex]
What is the value of x for the regular polygon shown below?
2x + 4
36
please help me :((((((
Answer:
Answer D
Step-by-step explanation:
It says to divide f(x)/g(x), which is displayed in D and if we find the domain it would be x is not equal to -1/4
Which statements about the system are true? Select two options.
y=-x-4
3y - x = -7
O The system has one solution.
O The system consists of parallel lines.
O Both lines have the same slope.
Both lines have the same y-intercept.
The equations represent the same line.
The system of equation has one solution
How to determine the true statements?The equations are given as:
y = -x - 4
3y -x = -7
Rewrite the first equation as:
y + x = -4
Add y + x = -4 to the second equation to eliminate x
4y = -11
Divide by 4
y = -11/4
Substitute y = -11/4 in y + x = -4
-11/4 + x = -4
Make x the subject
x = -4 + 11/4
Evaluate
x = -5/4
The above means that the system of equation has one solution
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Option A and B. The system has one solution and the system consists of parallel lines.
Slope of the linesThe slope of the lines is calculated as follows;
y = -x - 4
slope = - 1
3y - x = -7
3y = x - 7
y = x/3 - 7/3
slope = 1/3
Solution of the equationsy = -x - 4 ----(1)
3y - x = -7 ----(2)
solve (1) and (2)
3(-x - 4) - x = -7
-3x -12 - x = -7
-4x = 5
x = -5/4
y = -5/4 - 4
y = -5.25
Thus, the system has one solution and the system consists of parallel lines.
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Prove that < AOD and < BOD are supplementary
Angle AOD and < BOD are supplementary since they are both right angles which equal 180°.
What is a supplementary angle?It should be noted that a supplementary angle simply means an angle that adds up to 180°.
In this case, the angles given are both rights angles. This will be:
= 90° + 90°
= 180°
In this case, Angle AOD and < BOD are supplementary since they are both rights angles which equal 180°.
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Two buses leave a station at the same time and travel in opposite directions. One bus travels 14 miles faster than the other. If the two buses are 640 miles apart after 5 hours, what is the rate of each bus?
If the two buses are 640 miles apart after 5 hours. Then the rate of each bus will be 57 miles per hour and 71 miles per hour.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Two buses leave a station at the same time and travel in opposite directions.
One bus travels 14 miles faster than the other.
Let x be the speed of first bus. Then the speed of the second bus will be (x + 14).
If the two buses are 640 miles apart after 5 hours.
Then the rate of each bus will be
Then the relative speed of the buses will be
S = x + x + 14
S = 2x + 14
Then the value of x will be
2x + 14 = 640 / 5
2x + 14 = 128
2x = 114
x = 57 miles per hour
Then the speed of the other bus will be
⇒ 57 + 14
⇒ 71 miles per hour
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Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P ( X > 2 ) , n = 5 , p = 0.7
The value of the probability P(x > 2) is 0.8369
How to evaluate the probability?The given parameters are:
n = 5
p =0.7
The probability is calculated as:
[tex]P(x) = ^nC_x *p^x * (1 - p)^x[/tex]
Using the complement rule, we have:
P(x > 2) = 1 - P(0) - P(1) - P(2)
Where:
[tex]P(0) = ^5C_0 *0.7^0 * (1 - 0.7)^5[/tex]
P(0) = 1 *1 * (1 - 0.7)^5 = 0.00243
[tex]P(1) = ^5C_1 *0.7^1 * (1 - 0.7)^4[/tex]
P(1) = 5 *0.7^1 * (1 - 0.7)^4 = 0.02835
[tex]P(2) = ^5C_2 *0.7^2 * (1 - 0.7)^3[/tex]
P(2) = 10 *0.7^2 * (1 - 0.7)^3 = 0.1323
Recall that:
P(x > 2) = 1 - P(0) - P(1) - P(2)
So, we have:
P(x > 2) = 1 - 0.00243 - 0.02835 - 0.1323
Evaluate
P(x > 2) = 0.83692
Approximate
P(x > 2) = 0.8369
Hence, the value of the probability P(x > 2) is 0.8369
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Step 2 of 2 : Suppose a sample of 782 suspected criminals is drawn. Of these people, 548 were not captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list.
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.6625, 0.7388).
What is confidence interval?A confidence interval is the mean of your estimate plus and minus the variation in that estimate.
Given sample, n= 782
As, 548 were not captured.
x= 548
So, p= 548/ 782
p = 0.7007
q= 1- 0.7007 = 0.2993
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
Now,
α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
For confidence level of 98% , z is 2.33
Now,
(0.70007 - 2.33√ (0.7007(0.2993))/782 , 0.70007 + 2.33 √(0.7007(0.2993))/782
= (0.6625, 0.7388)
Hence, 98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.6625, 0.7388).
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The price of 11 pizzas and 5 hamburgers is 40$. The price of 1
hamburger is 2.50$. What is the price of a hamburger?
Step-by-step explanation:
you mean, what is the price of a pizza, right ? and I guess it is pizza slices ...
1 hamburger = $2.50
5 hamburgers = 5×1 hamburger = 5×2.5 = $12.50
that leaves for the 11 pizzas (slices)
40 - 12.5 = $27.50
so, 1 pizza (slice) is
27.5 / 11 = $2.50
Answer:
One hamburger costs $2.50
One pizza also costs $2.50
Step-by-step explanation:
Let's say Nigel is the one purchasing lots of food for no reason.
Nigel bought 11 pizzas and 5 hamburgers for $40 (DAMMMM WHAT COUPON IS THAT??)
We can write this algebraically:
11p + 5b = 40
We know that the price of 1 Hamburger is $2.50.
Now we can plug that into out equation and find the price of one pizza:
11p + 5(2.50) = 40
11p + 12.5 = 40
11p = 27.5
p = 2.5
Now, we have the price of one pizza, $2.50
Which statements about the system are true? Select two options.
y=-x-4
3y-x = -7
The system has one solution.
The system consists of parallel lines.
Both lines have the same slope.
Both lines have the same y-intercept.
The equations represent the same line.
The slope for both the line is m= 1/3 and they are parallel lines , Option B and C are correct two options
The first equation is
y = (1/3)x-4 and not y = -x-4
(if the equation is not corrected then it will not have two true statements)
What is a System of Equation ?A system of equation is a set of equation which have a common solution
The given system of equation is
y = (1/3)x-4
3y -x = -7
3y = x-7
As it can seen from the standard equation of a line that
y =mx+c
so slope for both the line is m= 1/3
Therefore they are parallel lines
Thus , Option B and C are correct two options
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find the indicated side of the right triangle
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 3\sqrt3 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \tan(60) = \cfrac{x}{3} [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{3} = \dfrac{x}{3} [/tex]
[tex]\qquad \tt \rightarrow \: x = 3 \sqrt{3} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
At the end of 2 years, P dollars invested at an interest rate r compounded annually increases to an amount, A dollars, given by the following formula. Upper A equals Upper P (1 plus r )squared Find the interest rate if $32 increased to $50 in 2 years. Write your answer as a percent.
The interest rate will be equal to 24% in 2 years.
What is compound interest?Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-
Given that:-
Find the interest rate if $32 increased to $50 in 2 years.The interest rate will be calculated by using the following formula:-
[tex]A = P[1+\dfrac{r}{n}]^{nt}[/tex]
[tex]50=32[1+\dfrac{r}{1}]^{2}[/tex]
[tex]\dfrac{50}{32}=(1+r)^2[/tex]
1.56 = ( 1 + r )²
√1.56 = ( 1 + r )
r = 1.24 - 1
r = 0.24
r = 24%
Therefore interest rate will be equal to 24% in 2 years.
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Given: a || b, transversal k
Prove <3 = <6
By the property of corresponding angles ∠3 ≅ ∠5.
What is transversal line?In geometry, a transversal is any line that intersects two straight lines at distinct points.
If two parallel lines are cut by a transversal, then each pair of corresponding angles are equals.
That is, ∠3 = ∠5 and ∠4 = ∠6.
Therefore the given angles ∠3 and ∠5 are equal.
Hence ∠3 ≅ ∠5 .
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Design a real life activity for the Intermediate Phase in which learners will be required to apply the associative property of multiplication over addition.
The associative property of adding or multiplying can be represented by (a + b) + c = a + (b + c) and a * (b * c) = (a * b) * c
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The associative property states that when adding or multiplying it can be represented by:
(a + b) + c = a + (b + c)
For multiplication:
a * (b * c) = (a * b) * c
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Which of the following staements must be true about this diagram check all that apply
Answer:Since, according to the Exterior Angle theorem, In a triangle the sum of any two adjacent interior angles is equal to the exterior angle of the triangle.
And, here is the exterior angle of the triangle, while , , and are the interior angles of the triangle.
Thus, according to the theorem,
.
⇒
and
Therefore, options B, C, E are correct.
The function f(x) = 40(0.9)x represents the deer population in a forest x years after it was first studied. What was the deer population when it was first studied?
a. 44
b.40
c. 36
d.49
Answer:
36
Step-by-step explanation:
40*.9
What is one possible value of 2x
Answer:
really good
Step-by-step explanation:
thanks for your help you with that do not have a copy of the receipt for your time to help you with theAn auto mechanic charges (C) an initial fee of $50 and then $40 per hour. The graph of this model would be:
a curved line that increases but then decreases.
a straight line that decreases only.
a straight line that increases only.
None of these choices are correct.
The graph of this model would be a straight line that increases only option third is correct.
What is a line graph?A line graph is a graph made up of segments of straight lines that connect the depicted data points.
We have:
An auto mechanic charges (C) an initial fee of $50 and then $40 per hour.
Let T be the total fee and h is the number of hours
T = 50 + 40h
The above equation represents a graph of a straight line as the slope of the line is positive.
m = 50
Thus, the graph of this model would be a straight line that increases only option third is correct.
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The table below shows the results of a screening program organized by Level 300 students of the department physiotherapy of the College Health Sciences of the University of Ghana. Complete the table and answer the questions below it using your understanding of probability and its applications to biomedical data.
True Diagnosis for presence of E. Coli
Test results Disease No Disease Total
Positive 35 15
Negative 10 60
Total
a. What is the efficiency of the test? 3 marks
b. What is the sensitivity of the screening kit? 3 marks
c. What is the specificity of the screening kit? 3 marks
d. What is the predictive value (PPV) of the test? 3 marks
e. What is the negative predictive value (NPV) of the test? 3 marks
(15 marks)
2. In double blinded randomized control trial for hypertensive patients attending Cocoa Clinic, thirty (30) 50-59-year-old were admitted into an intervention program for 6 weeks. During the trial, the average improvement in their systolic blood pressure was 15. The average improvement in systolic blood pressure in the general population of hypertensive patients is 20 with a standard deviation of 2.
i. What are the null and alternative hypotheses in this RCT? (2 marks)
ii. What tail is required in this test? (2 marks)
iii. What is the most appropriate statistical test for this study? (2 marks)
iv. State the assumptions of the test. (2 marks)
v. Test the above hypothesis using the appropriate statistical tool (7 marks)
Critical value =3.6
Help solve and get 20 pts! (Math)
Which linear equation has a slope of 3 and a y-intercept of -2?
y = 3x + 2
y = 3x - 2
y = -2x + 3
y=-2x-3
Answer:
y = 3x - 2
Step-by-step explanation:
The number beside the x is the slope. The number at the end of the equation is the y-intercept.
All the answers are in this form:
y = mx + b
m is the slope.
b is the y-intercept.
With a 3 filled in for slope and -2 filled in for the y-intercept, you get:
y = 3x + -2
is the same as,
y = 3x - 2
What is the partial fraction decomposition of StartFraction 7 x squared + 14 Over (x squared + 3) squared EndFraction?
The final decomposition of the given partial fraction is; 7 + (-7/(x² + 3))
How to decompose partial fractions?We are given the polynomial fraction (7x² + 14)/(x² + 3) to decompose.
Now, due to the fact that the degree of the numerator is not less than the degree of the denominator, we will perform polynomial long division to get;
(7x² + 14)/(x² + 3) = 7 + (-7/(x² + 3))
Now, the second term (-7/(x² + 3)) cannot be decomposed further and as such, we say that our final decomposition of the given partial fraction is;
7 + (-7/(x² + 3))
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Which of the following is NOT a rational expression?
The expression that is not rational is the first one:
[tex]f(x) = \frac{6x}{4}[/tex]
Which of the given expressions is not rational?A rational expression is something of the form:
[tex]f(x) = \frac{q(x)}{p(x)}[/tex]
Such that q(x) can be any polynomial, and p(x) is a polynomial of at least degree 1.
This means that we need to have the variable "x" on the denominator.
Then is easy to recognize the expression that is not rational, is the one that does not have x on the denominator, which is the first one:
[tex]f(x) = \frac{6x}{4}[/tex]
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Answer: B
Step-by-step explanation:
I took the test and this was the correct answer
let p be the perimeter of a rectangle, and let one side of the rectangle be x
PLEASE SHOW WORK
That is the length in terms of p and x.
L = p/2 - x
How to get the length of the other side in terms of x and p?
For a rectangle of length L and width W, the perimeter is:
P = 2*(L + W).
Here we know that the perimeter is p, so P = p, and let's say that the width is x.
Then we can write:
p = 2*(L + x)
Solving for L:
L = p/2 - x
That is the length in terms of p and x.
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What is the value for y?
What is the value of x?
Enter your answer in the box.
x =
Equiangular triangle A B C. Angles A, B, and C are marked congruent. The length of side A C is labeled as 5 x minus 22. The length of side A B is labeled as 4 x minus 10. The length of side B C is labeled as 3 x plus 2.
Enter your answer in the box.
y =
An isosceles triangle A B C with horizontal base B C and vertex A is above the base. Side A C and C B are labeled with single tick mark. All the three angles are labeled. Base angles C A B is labeled as 50 degrees and angle C B A is labeled as 2x degrees. The angle A C B is labeled left parenthesis 5 y plus 10 right parenthesis degrees.
1. The value of x in the equilateral triangle is: 12
2. x = 25; y = 14
What is an Equilateral Triangle?If a triangle has three sides that are marked congruent, then the triangle is an equilateral triangle.
1. Since triangle ABC is an equilateral triangle and its sides are equal, therefore:
5x - 22 = 3x + 2 [congruent sides]
Solve for x
5x - 3x = 22 + 2
2x = 24
2x/2 = 24/2
x = 12
The value of x is: 12.
2. Base angles of an isosceles triangle are congruent, therefore:
2x = 50
x = 50/2
x = 25
Thus, using the triangle sum theorem, we have:
2x + 50 + 5y + 10 = 180
Plug in the value of x and find y
2(25) + 50 + 5y + 10 = 180
50 + 50 + 5y + 10 = 180
110 + 5y = 180
5y = 180 - 110
5y = 70
y = 70/5
y = 14
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Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 2.0. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003?
Answer:
1,887,436,800
Step-by-step explanation:
f(t) = a·b^t
f (t) = number of cases at year t
a = starting value = 1800 in 1983
b = growth factor = 2
t = years since 1983 = 2003 - 1983 = 20
f(t) = 1800·(2)^20 =
1,887,436,800
wyzant
philip p
when finding the margin of error of the mean of a normally distributed population from a sample, what is the critical probability, assuming a confindence level of 58%
The critical probability, assuming a confindence level of 58% is 0.79.
How to calculate probability?From the information given, the confidence level is 58%. The alpha will be:
= 1 - (58/100)
= 1 - 0.58
= 0.42
The critical probability will be:
= 1 - (0.42/2)
= 1 - 0.21
= 0.79
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