Answer:
Part A- 6
Part B- 3
Part C- 3/22100
Step-by-step explanation:
Part A-
Use the permutation formula and plug in 3 for n and 2 for k.
nPr=n!/(n-k)!
3P2=3!/(3-2)!
Simplify.
3P2=3!/1!
3P2=6
Part B-
Use the combination formula and plug in 3 for n and 2 for k.
nCk=n!/k!(n-k)!
3C2=3!/2!(3-2)!
Simplify.
3C2=3!/2!(1!)
3C2=3
Part C-
It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.
I believe the answer is 3/22100
I honestly suck at probability but I tried my best.
The side length of the cube is s. Find the domain of the volume of the cube.
Answer:
-∞<x<∞
Step-by-step explanation:
volume of a cube=s^3
the domain is (-∞,∞) the domain is all the real number of s
help plsssssssssssss
Answer:
[tex]z = \frac{x}{y} [/tex]
Step-by-step explanation:
Let x be the price of carton of ice cream
Let y be the number of grams in carton
Let z be price per gram.
[tex]z = \frac{x}{y} [/tex]
Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.
Hope this helps ;) ❤❤❤
The area of a triangle is 14 square inches. The base is 28 inches. What is the height in inches? Do not include units in your answer.
Answer:
Hey there!
A=1/2bh
14=1/2(28)h
14=14h
h=1
Hope this helps :)
Answer:
the height is 1 inchStep-by-step explanation:
Area of a triangle is
[tex] \frac{1}{2} \times b \times h[/tex]
where b is the base
h is the height
From the question
Area = 14in²
b = 14 inches
So we have
[tex]14 = \frac{1}{2} \times 28 \times h[/tex]
which is
[tex]14 = 14h[/tex]
Divide both sides by 14
That's
[tex] \frac{14}{14} = \frac{14h}{14} [/tex]
We have the final answer as
h = 1
Therefore the height is 1 inch
Hope this helps you
Evaluate f(x) when x= 9
f(x) = {6x² +2 if 6
112 if 9
No solution
O 110
O 12
56
Answer:
[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]
[tex] f(x) = 12 , 9 \leq x <13[/tex]
And we want to evaluate f(x=9)
And for this case the answer would be:
[tex] f(9)= 12[/tex]
Best answer:
O 12
Step-by-step explanation:
For this problem we have the following function given:
[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]
[tex] f(x) = 12 , 9 \leq x <13[/tex]
And we want to evaluate f(x=9)
And for this case the answer would be:
[tex] f(9)= 12[/tex]
Best answer:
O 12
find the area under (sin x) bounded by x= 0 and x = 2π and x-axis
You probably want the unsigned area, which means you don't compute the integral
[tex]\displaystyle\int_0^{2\pi}\sin x\,\mathrm dx[/tex]
but rather, the integral of the absolute value,
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx[/tex]
[tex]\sin x[/tex] is positive when [tex]0<x<\pi[/tex] and negative when [tex]\pi<x<2\pi[/tex], so
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\int_0^\pi\sin x\,\mathrm dx-\int_\pi^{2\pi}\sin x\,\mathrm dx[/tex]
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=(-\cos x)\bigg|_0^\pi-(-\cos x)\bigg|_\pi^{2\pi}[/tex]
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\boxed{4}[/tex]
In a certain state, license plates each consist of 2 letters followed by either 3 or 4 digits. How many differen license plates are there that have no repeated letters or digits?
Answer:
26 × 26 × 10 × 10 × 10 = 676 , 000 possibilities
Step-by-step explanation:
There is nothing stating that the letters and numbers can't be repeated, so all 26 letters of the alphabet and all 10
digits can be used again.
If the first is A, we have 26 possibilities:
AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.
If the first is B, we have 26 possibilities:
BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ
And so on for every letter of the alphabet. There are 26 choices for the first letter and 26 choices for the second letter. The number of different combinations of 2 letters is: 26 × 26 = 676
The same applies for the three digits. There are 10 choices for the first, 10
for the second and 10 for the third:
10 × 10 × 10 = 1000
So for a license plate which has 2 letters and 3 digits, there are: 26 × 26 × 10 × 10 × 10 = 676 , 000 possibilities.
Hope this helps.
Which Graph represents the solution to the compound inequality 4x +8< -16 or 4x + 8 > 4
Answer:
option 3
Step-by-step explanation:
4x+8<-16
x<-6
4x+8_>-16
x_>-1
(it's more and equal .so the circle has to be shaded and move to the right of -1)
Answer:C
Step-by-step explanation:
Explain how the interquartile range of a data set can be used to identify outliers. The interquartile range (IQR) of a data set can be used to identify outliers because data values that are ▼ less than equal to greater than ▼ IQR Upper Q 3 minus 1.5 (IQR )Upper Q 3 plus IQR Upper Q 3 plus 1.5 (IQR )or ▼ less than equal to greater than ▼ IQR Upper Q 1 plus 1.5 (IQR )Upper Q 1 minus IQR Upper Q 1 minus 1.5 (IQR )are considered outliers.
Answer:
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Step-by-step explanation:
To identify outliers the interquartile range of the dataset can be used
Outliers can be identified as data values that are
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Using the interquartile range concept, it is found that:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
----------------------------
The interquartile range of a data-set is composed by values between the 25th percentile(Q1) and the 75th percentile(Q3).It's length is: [tex]IQR = Q3 - Q1[/tex]Values that are more than 1.5IQR from the quartiles are considered outliers, that is:[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]
Thus:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
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What linear function defines the following Arithmetic Sequence?
-8, -4, 0, 4, 8, ...
A : an = -8 + 4(n - 1)
B : an= 8 + 4(n - 1)
C : an = -8 - 4(n - 1)
D : an = 8 - 4(n - 1)
The linear equation defines the arithmetic sequence is an = -8 + 4(n - 1). The correct option is A.
What is an arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that, the sequence is -8, -4, 0, 4, 8, ...
a = -8
d = +4
The expression for the nth term will be written as,
an = a + ( n - 1 ) d
= -8 + ( n - 1 ) 4
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Part A Each time you press F9 on your keyboard, you see an alternate life for Jacob, with his status for each age range shown as either alive or dead. If the dead were first to appear for the age range of 75 to 76, for example, this would mean that Jacob died between the ages of 75 and 76, or that he lived to be 75 years old. Press F9 on your keyboard five times and see how long Jacob lives in each of his alternate lives. How long did Jacob live each time? Part B The rest of the potential clients are similar to Jacob, but since they’ve already lived parts of their lives, their status will always be alive for the age ranges that they’ve already lived. For example, Carol is 44 years old, so no matter how many times you press F9 on your keyboard, Carol’s status will always be alive for all the age ranges up to 43–44. Starting with the age range of 44–45, however, there is the possibility that Carol’s status will be dead. Press F9 on your keyboard five more times and see how long Carol lives in each of her alternate lives. Remember that she will always live to be at least 44 years old, since she is already 44 years old. How long did Carol live each time? Part C Now you will find the percent survival of each of your eight clients to the end of his or her policy using the simulation in the spreadsheet. For each potential client, you will see whether he or she would be alive at the end of his or her policy. The cells in the spreadsheet that you should look at to determine this are highlighted in yellow. Next, go to the worksheet labeled Task 2b and record either alive or dead for the first trial. Once you do this, the All column will say yes if all the clients were alive at the end of their policies or no if all the clients were not alive at the end of their policies. Were all the clients alive at the end of their policies in the first trial? Part D Next, go back to the Task 2a worksheet, press F9, and repeat this process until you have recorded 20 trials in the Task 2b worksheet. In the Percent Survived row at the bottom of the table on the Task 2b worksheet, it will show the percentage of times each client survived to the end of his or her policy, and it will also show the percentage of times that all of the clients survived to the end of their respective policies. Check to see whether these percentages are in line with the probabilities that you calculated in questions 1 through 9 in Task 1. Now save your spreadsheet and submit it to your teacher using the drop box. Are your probabilities from the simulation close to the probabilities you originally calculated?
Step-by-step explanation:
brain list me please......
Answer:
Jacob:
Alive 69-70
alive 79-80
alive 62-63
alive 73-74
alive 78-Died 79
Carol:
alive 88-89
alive 67-68
alive 99-100
alive 73-74
alive 94- Died 95
Step-by-step explanation:
According to genetic theory, there is a very close to even chance that both children in a two child family will be of the same gender. Here are two possibilities.
(i). 24 couples have two children. In 16 or more of these families, it will turn out that both children are of the same gender.
(ii). 12 couples have two children. In 8 or more of these families, it will turn out that both children are of the same gender. Which possibility is more likely and why?
Answer:
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Step-by-step explanation:
(i) probability with 16 success out of 24 = 16/24 = 2/3
(ii) (i) probability with 8 success out of 12 = 8/12 = 2/3
Since the two experiments have the same probability, the observed probabilities are the same.
HOWEVER, since the theoretically probability is 1/2, 16.7% less than the experimental results, the number N of trials comes into play.
Using the binomial distribution,
(i)
p = 1/2
N = 24
x = 16 (number of successes)
P(16,24) = C(24,16) p^16* (1-p)^8
= 735471* (1/65536)*(1/256)
= 0.0438
(ii)
p = 1/2
N = 12
x = 8 (number of successes)
P(8,12) = C(12,8) p^8* (1-p)^4
= 495*1/256*1/16
= 0.1208
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Note: It would help to mention the topic you're on so answers will correspond to what is expected. Here we cover probability and binomial distribution.
What property do rectangles and parallelograms always share?
Find the measure of the indicated angle to the nearest degree.
PLEASE HELP ASAP
Answers
A. 26
B. 42
C. 64
D. 48
Answer:
The answer is option C
Step-by-step explanation:
To find the indicated angle we use sine
sin ∅ = opposite / hypotenuse
From the question
The opposite is 37
The hypotenuse is 41
So we have
sin ? = 37/41
? = sin-¹ 37/41
? = 64.4805
? = 64° to the nearest degreeHope this helps you
Answer:
C.) 64
Step-by-step explanation:
I got it correct on founders edtell
Connor has a collection of dimes and quarters with a total value of $6.30. The number of dimes is 14 more than the number of quarters. How many of each coin does he have?
Answer:
14 Quarters and 28 dimes
Step-by-step explanation: 14 quarters $3.50
28 dimes is $2.80 total is $6.30
The same bedroom furniture set costs $1,500 in both Florida and Alabama. The table gives a breakdown of the taxes someone would pay when purchasing the furniture set in either state. Alabama Florida State of Alabama: 4.225% County Tax: 1.375% City Tax: 3.0% State of Florida: 6.5% County Tax: 1% City Tax: 1.625% Which statement is true? A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations.
Answer:
A: True
B, C and D: False
Step-by-step explanation:
We have a total sales tax for Alabama that is:
[tex]T_A=4.225+1.375+3=8.6[/tex]
The total sales tax for Florida is:
[tex]T_F=6.5+1+1.625=9.125[/tex]
The total sales tax is greater in Florida than in Alabama.
A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE
The sales tax difference in this purchase can be calculated as:
[tex]1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8[/tex]
B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)
C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)
The amount of sales tax in Alabama is:
[tex]ST_A=1500\cdot T_A=1500\cdot 0.086=129[/tex]
D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).
What is the next term of the geometric sequence? 1, 2, 4, 8, 16,
Answer: 32
Step-by-step explanation:
and click Submit
By visual inspection, determine the best fitting regression model for the
scatterplot.
O A Quadratic
O B. Linear
OC Exponential
OD. No pattern
Answer:
quadratic
Step-by-step explanation:
This graph has a parabola form wich is a propertie for qaudratic functions
Answer:
A
Step-by-step explanation:
Solve the equation for the indicated variable. C=680x/h^2 for x
Answer:
C h^2 / 680 = x
Step-by-step explanation:
C=680x/h^2
Multiply each side by h^2
C h^2=680x/h^2 * h^2
C h^2=680x
Divide each side by 680
C h^2 / 680=680x/680
C h^2 / 680 = x
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
The complete question is;
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
(a) less than 10 minutes
(b) longer than 5 minutes
(c) between 8 and 15 minutes
Answer:
A) P (x < 10) = 0.6700
B) P (x > 5 ) = 0.9406
C) P (8.0000 < x < 15.0000) = 0.6332
Step-by-step explanation:
A) we are given;
Mean;μ = 8.9 minutes
Standard deviation;σ = 2.5 minutes
Normal random variable;x = 10
So to find;P(x < 10) we will use the Z-score formula;
z = (x - μ)/σ
z = (10 - 8.9)/2.5 = 0.44
From z-distribution table and Z-score calculator as attached, we have;
P (x < 10) = P (z < 0.44) = 0.6700
B) similarly;
z = (x - μ)/σ =
z = (5 - 8.9)/2.5
z = -1.56
From z-distribution table and Z-score calculator as attached, we have;
P (x > 5 ) = P (z > -1.56) = 0.9406
C)between 8 and 15 minutes
For 8 minutes;
z = (8 - 8.9)/2.5 = -0.36
For 15 minutes;
z = (15 - 8.9)/2.5 = 2.44
From z-distribution table and Z-score calculator as attached, we have;
P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332
Find the dimensions of a rectangle with area 512 m2 whose perimeter is as small as possible. (If both values are the same number, enter it into both blanks.)
Answer:
√512 by √512Step-by-step explanation:
Length the length and breadth of the rectangle be x and y.
Area of the rectangle A = Length * breadth
Perimeter P = 2(Length + Breadth)
A = xy and P = 2(x+y)
If the area of the rectangle is 512m², then 512 = xy
x = 512/y
Substituting x = 512/y into the formula for calculating the perimeter;
P = 2(512/y + y)
P = 1024/y + 2y
To get the value of y, we will set dP/dy to zero and solve.
dP/dy = -1024y⁻² + 2
-1024y⁻² + 2 = 0
-1024y⁻² = -2
512y⁻² = 1
y⁻² = 1/512
1/y² = 1/512
y² = 512
y = √512 m
On testing for minimum, we must know that the perimeter is at the minimum when y = √512
From xy = 512
x(√512) = 512
x = 512/√512
On rationalizing, x = 512/√512 * √512 /√512
x = 512√512 /512
x = √512 m
Hence, the dimensions of a rectangle is √512 m by √512 m
if the focus of an ellipse are (-4,4) and (6,4), then the coordinates of the enter of the ellipsis are
Answer:
The center is (1,4)
Step-by-step explanation:
The coordinates of the center of an ellipse are the coordinates that are in the middle of the two focus.
Then if we have a focus on [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], we can say that the coordinates for x and y can be calculated as:
[tex]x=\frac{x_1+x_2}{2}\\ y=\frac{y_1+y_2}{2}[/tex]
So, replacing [tex](x_1,y_1)[/tex] by (-4,4) and [tex](x_2,y_2)[/tex] by (6,4), we get that the center is:
[tex]x=\frac{-4+6}{2}=1\\ y=\frac{4+4}{2}=4[/tex]
Question 16 (5 points)
Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
i think its b
???
Step-by-step explanation:
im sorry if im wrong im not very confident on my answer :(
Answer:
D
Step-by-step explanation:
Most logical looking if you look at the formula, the last number has to be smaller than the one before, so.
A deep-sea diver is in search of coral reefs.he finds a beautiful one at an elevation of -120 4/7feet. While taking pictures of the reef he catches sight of a manta ray. He swims up 25 3/7feet to check it out.what is the diver's new elevation?
Answer:-95 1/7 feet
Step-by-step explanation:
-120 4/7+25 3/7=-95 1/7 feet
What is the slope of the line graphed below?
(3, 3) (0,-6)
Answer:
3
Step-by-step explanation:
Use this equation
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] substitute
-6-3/0-3 subtract
-9/-3 simplify
-3/-1 two negitives cansle out
3/1=3
Hope this helpes, if it did, please consider giving me brainliest, it will help me a lot. If you have any questions, feel free to ask.
Have a good day! :)
Answer:
3
Step-by-step explanation:
To find the slope, we use the slope formula
m= ( y2-y1)/(x2-x1)
= ( -6 -3)/(0 -3)
= -9/-3
= 3
Noah tried to prove that cos(θ)=sin(θ) using the following diagram. His proof is not correct.
Answer:
The first statement is incorrect. They have to be complementary.
Step-by-step explanation:
You can't say the measure of angle B is congruent to theta because it is possible for angles in a right triangle to be different.
You can only say that what he said is true if the angle was 45 degrees, but based on the information provided it is not possible to figure that out.
The other two angles other than the right angle in a right triangle have to add up to 90 degrees, which is the definition of what it means for two angles to be complementary. A is the correct answer.
Answer:
[tex]\boxed{\sf A}[/tex]
Step-by-step explanation:
The first statement is incorrect. The angle B is not equal to theta θ. The two acute angles in the right triangle can be different, if the triangle was an isosceles right triangle then angle B would be equal to theta θ.
in the number 23.45 the digit 5 is in ?
Answer: hundredths place
Step-by-step explanation:
The _________ measures the strength and direction of the linear relationship between the dependent and the independent variable.
Answer:
Correlation Coefficient
Step-by-step explanation:
Given that is both the median and altitude of , congruence postulate SAS is used to prove that is what type of triangle?
A.
equilateral
B.
scalene obtuse
C.
isosceles
D.
scalene acute
Answer:isosceles is the correct
Step-by-step explanation:
According to the given conditions the triangle ABC is an isosceles triangle.
What is an isosceles triangle?An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.
Given that, BD is median and altitude in the triangle ABC, and we are asked to find that what type of the triangle ABC will be if we prove triangles ADB and CBD congruent by SAS rule,
So, the proof is as follows,
AD = CD [definition of median]
∠ ADB = ∠ CDB [definition of altitude]
BD = BD [reflexive property]
∴ Δ ADB ≅ Δ CBD by SAS rule
AB = BC by CPCT
According to the definition of an isosceles triangle we can say that, ABC is an isosceles triangle.
Hence, according to the given conditions the triangle ABC is an isosceles triangle.
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find the coordinates of the vertices of the triangle after a reflection across the line y = -1 and then across the line x = -2
Answer: A) N'=(-2, 2) M'=(-1, 0) L'=(-5, -2)
Step-by-step explanation:
N = (-2, -4) M = (-3, -2) L = (1, 0)
Reflection over y = -1
N' = (-2, 2) M' = (-3, 0) L' = (1, -2)
Reflection over x = -2
N'' = (-2, 2) M'' = (-1, 0) L'' = (-5, -2)
Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?
Answer:
The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is [tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex].
The domain of the function is all real numbers and its range is between -4 and 5.
The graph is enclosed below as attachment.
Step-by-step explanation:
Let be [tex]z (x) = \cos x[/tex] the base formula, where [tex]x[/tex] is measured in sexagesimal degrees. This expression must be transformed by using the following data:
[tex]T = 180^{\circ}[/tex] (Period)
[tex]z_{min} = -4[/tex] (Minimum)
[tex]z_{max} = 5[/tex] (Maximum)
The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of [tex]2\pi[/tex] radians. In addition, the following considerations must be taken into account for transformations:
1) [tex]x[/tex] must be replaced by [tex]\frac{2\pi\cdot x}{180^{\circ}}[/tex]. (Horizontal scaling)
2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:
[tex]\Delta z = \frac{z_{max}-z_{min}}{2}[/tex]
[tex]\Delta z = \frac{5+4}{2}[/tex]
[tex]\Delta z = \frac{9}{2}[/tex]
3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)
[tex]z_{m} = \frac{z_{min}+z_{max}}{2}[/tex]
[tex]z_{m} = \frac{1}{2}[/tex]
The new function is:
[tex]z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)[/tex]
Given that [tex]z_{m} = \frac{1}{2}[/tex], [tex]\Delta z = \frac{9}{2}[/tex] and [tex]T = 180^{\circ}[/tex], the outcome is:
[tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex]
The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.