Write down the first 6 elements of the following sequence (where n ∈ Z+), then give a recursive definition for an. Do not forget the base case. (You do not need to prove it is correct).
a. an - 3n - 10
b. an= (1+(-1)^n)^n
c. an= 2n! (2)
Answer:
a. The first six terms are:
-7, -4, -1, 2, 5, 8
b. The first six terms are:
0, 2, 0, 2, 0, 2.
c. The first six terms are:
4, 8, 24, 96, 480, 2880
Step-by-step explanation:
a. an - 3n - 10
For n = 1
a1 = 3(1) - 10
= -7
For n = 2
a2 = 3(2) - 10
= -4
For n = 3
a3 = 3(3) - 10
= -1
For n = 4
a4 = 3(4) - 10
= 2
For n = 5
a5 = 3(5) - 10
= 5
For n = 6
a6 = 3(6) - 10
= 8
The first six terms are:
-7, -4, -1, 2, 5, 8
b. an= (1+(-1)^n)^n
For n = 1
a1 = (1+(-1)^1)^1
= 0
For n = 2
a2 = (1+(-1)^2)^1
= 2
For n = 3
a3 = (1+(-1)^3)^1
= 0
For n = 4
a4 = (1+(-1)^4)^1
= 2
For n = 5
a5 = (1+(-1)^5)^1
= 0
For n = 6
a6 = (1+(-1)^6)^1
= 2
The first six terms are:
0, 2, 0, 2, 0, 2.
c. an= 2n! (2)
For n = 1
a1 = 2(1!)(2)
= 4
For n = 2
a2 = 2(2!)(2)
= 8
For n = 3
a3 = 2(3!)(2)
= 24
For n = 4
a4 = 2(4!)(2)
= 96
For n = 5
a5 = 2(5!)(2)
= 480
For n = 6
a6 = 2(6!)(2)
= 2880
The first six terms are:
4, 8, 24, 96, 480, 2880
pleassssssssssssssssssssssssseeeeeeeeeeeeeeeeeeeeeeee helpppppppppppppp meeeeeeeee i giveeeee you bralienstttttt
Answer:
487 divide by 14
Step-by-step explanation:
have a nice day
if elf =gjh ef=12 and Lf=7.8 find ij
Answer:
IJ= 4.98
Step-by-step explanation:
EF = 12
KF = 6
LF = 7.8
LK = sqrt(7.8^2-6^2) = 4.98
IJ = LK (4.98)
please help as soon as possible:)
Answer:
h = 536 ftStep-by-step explanation:
To find the height h we use tan
tan ∅ = opposite / adjacent
From the question
The adjacent is 2000 ft
The opposite is h
So we have
tan 15° = h / 2000
h = 2000 tan 15
h = 535.89 ft
h = 536 ft to the nearest foot
Hope this helps you
What does it mean to say "correlation does not imply causation"? Choose the correct answer below. A. Two variables can only be strongly correlated if there existed a cause-and-effect relationship between the variables. B. The fact that two variables are strongly correlated does not in itself imply a cause-and-effect relationship between the variables. C. The fact that two variables are strongly correlated implies a cause-and-effect relationship between the variables. D. Two variables that have a cause-and-effect relationship are never correlated.
Answer:
B. The fact that two variables are strongly correlated does not in itself imply a cause-and-effect relationship between the variables.
Step-by-step explanation:
The term "correlation does not imply causation", simply means that because we can deduce a link between two factors or sets of data, it does not necessarily prove that there is a cause-and-effect relationship between the two variables. In some cases, there could indeed be a cause-and-effect relationship but it cannot be said for certain that this would always be the case.
While correlation shows the linear relationship between two things, causation implies that an event occurs because of another event. So the phrase is actually saying that because two factors are related, it does not mean that it is as a result of a causal factor. It could simply be a coincidence. This occurs because of our effort to seek an explanation for the occurrence of certain events.
Answer: B. The fact that two variables are strongly correlated does not in itself imply a cause-and-effect relationship between the variables.
Step-by-step explanation:
which linear inequality is represented by the graph
Answer:
The first choice.
Step-by-step explanation:
When you are using y≥, then this means that the positive area needs to be shaded, but as you can see, the negative area is shaded, so the symbol '≤' would best fit this.
Now, that we see that, we can eliminate the 2nd and 4th option.
Now, looking at points (0, 2) and (2, 3), the slope is 1/2 <-- rise over run.
So, the first option will be correct!
Hope this helps:)
Answer:
You have selected the correct one!
Step-by-step explanation:
I don’t know if this is right, I’m stuck. Help!
Answer:
C
Step-by-step explanation:
According to SohCahToa, cosine is adjacent over the hypotenuse.
The adjacent when looking from angle b, is 21.
The hypotenuse of this triangle is 29.
So Cos B=21/29
Copy the problem, mark the givens in the diagram. Given: CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC, Prove: CR ≅ HS
Help urgently needed
Explanation:
1. CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC — given
2. ∆CRH ~ ∆HSC — AA similarity theorem
3. ∠SCH ≅ ∠RHC — corresponding angles of similar triangles are congruent
4. CH ≅ HC — reflexive property of congruence
5. ∆CRH ≅ ∆HSC — SAS congruence theorem
6. CR ≅ HS — CPCTC
Suppose the results indicate that the null hypothesis should not be rejected; thus, it is possible that a type II error has been committed. Given the type of error made in this situation, what could researchers do to reduce the risk of this error? Choose a 0.01 significance level, instead of a 0.05 significance level. Increase the sample size.
Answer:
Increase the sample size.
Step-by-step explanation:
Increasing the sample size is the best way to reduce the likelihood of a type II error.
The type II error occurs when a hypothesis test accepts a false null hypothesis. That is, it fails to reject the null hypothesis that is false.
In such a situation, to increase the power of the test, you have to increase the sample size used in the test. The sampling size has the ability to detect the differences in a hypothesis test.
We have a bigger chance of capturing the difference if the sample size is larger, and it also increases the power of the test.
Segments AC and BD are diameters of circle O. Circle O is shown. Line segments A C and B D are diameters. Angle A O D is 73 degrees. What is the measure of Arc A D B? 107° 146° 253° 287°
Answer:
253°
Step-by-step explanation:
The central angle whose rays intercept a diameter of the circle has measure 180 deg.
m<AOD = 73 deg
m<DOB = 180 deg
m<ADB = m<AOD +m<DOB = 73 deg + 180 deg = 253 deg
The measure of an arc of a circle is equal to the measure of the central angle that subtends it.
m(arc)AOD = m<AOD = 253 deg
Answer: 253°
The solution is, the measure of Arc A D B is 253°.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
Here, we have,
given that AC and BD are diameters of circle O.
AC and BD intersect at point C the centre of the circle.
The central angle of a circle is the angle based at the circle's center. In other words, the vertex of the angle must be at the center of the circle. A central angle is formed by two radii that start at the center and intersect the circle itself.
The central angle whose rays intercept a diameter of the circle has measure 180 deg.
m<AOD = 73 deg
m<DOB = 180 deg
m<ADB = m<AOD +m<DOB = 73 deg + 180 deg = 253 deg
The measure of an arc of a circle is equal to the measure of the central angle that subtends it.
m(arc)AOD = m<AOD = 253 deg
Answer: the measure of Arc A D B is 253°.
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For each statement, write the null and alternative hypotheses. State which hypothesis represents the claim. 17. Evaluate the limit, if it exists. Show work. lim→5 2−3−10 2−10
Answer:
Identify what you want to prove and you can test using ANOVA, Chi Square, F test ..... among many.
Step-by-step explanation:
Null and alternative hypothesis are always understood in terms of experiments.
In simple words,
null hypothesis = The results of your experiment are due to chance
alternative hypothesis = The results of your experiments are NOT due to chance
Therefore, identify what you want to prove and you can test using ANOVA, Chi Square, F test ..... among many.
find the number if 7/3 of it is 5 5/6
Answer: [tex]\dfrac{5}{2}.[/tex]
Step-by-step explanation:
To find: The number if [tex]\dfrac{7}{3}[/tex] of it is [tex]5\dfrac{5}{6}[/tex].
Let x be the number.
Then, as per the statement, we have
[tex]\dfrac{7}{3}x=5\dfrac{5}{6}[/tex]
Simplify [tex]5\dfrac{5}{6}[/tex] as [tex]\dfrac{5\times6+5}{6}=\dfrac{35}{6}[/tex]
Then, [tex]\dfrac{7}{3}x=\dfrac{35}{6}[/tex]
Multiply 3 on both sides, we get
[tex]7x=\dfrac{35}{2}[/tex]
Divide both sides by 7, we get
[tex]x=\dfrac{35}{2\times7}\\\\\Rightarrow\ x=\dfrac{5}{2}[/tex]
Hence, the number is [tex]\dfrac{5}{2}.[/tex]
We will see that the mixed number is:
N = 2 + 1/2
How to find the number?
We want to find a number N such that 7/3 times N is equal to 5 + 5/6.
So we just need to solve:
(7/3)*N = (5 + 5/6)
If we multiply both sides by 3/7, we get:
(3/7)*(7/3)*N = (3/7)*(5 + 5/6)
N = 15/7 + 15/42
If we multiply and divide the first fraction by 6, we get:
N = (6/6)*15/7 + 15/42 = 90/42 + 15/42
N = 105/42
Now we can write:
105 = 42 + 42 + 21
Replacing that in the fraction we would get:
N = 105/42 = (42 + 42 + 21)/42 = 42/42 + 42/42 + 21/42 = 2 + 21/42
N = 2 + 1/2
If you want to learn more about mixed numbers, you can read:
https://brainly.com/question/1746829
Sophie saw a dress she liked on sale for $15 off. The original price of the dress was $96. What is the sale price of the dress?
If there is $15 off on the dress and the original price of the dress was $96 the sale price of the dress will be $81.
What is the application of subtraction?In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.
Given that Sophie discovered a dress she liked that was $15 off. The dress cost $96.
The sale price of the dress is obtained by subtracting the original price from the price discount on the dress,
= $96 - $15
=$ $81
Thus, if there is $15 off on the dress and the original price of the dress was $96 the sale price of the dress will be $81.
Learn more about the application of subtraction here:
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g Which distribution is used to compute the p-value, if one of the alternative hypotheses of the test is true?Group of answer choices
Answer:
Probability distribution
Step-by-step explanation:
Probability distribution is the function which describes the likelihood of possible values assuming a random variable. Alternative hypothesis is a statement which we accept or reject based on the null hypothesis. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
What is the slope of the line
described by Y = 6X + 2?
A. 6
B. 2
C. 3
D. -6
E. 12
Answer:
A . 6Step-by-step explanation:
[tex]\mathrm{For\:a\:line\:equation\:for\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is\:}\mathbf{m}\\m=6[/tex]
Solving by fractions
Answer:
x = -8, 8
Step-by-step explanation:
Set y = 0 to find the x intercepts
0 = x^2 -64
Add 64 to each side
64 = x^2
Take the square root of each side
±sqrt(64) = sqrt(x^2)
±8 =x
Brainliest for whoever gets this correct! What is the sum of the rational expressions below?
Answer:
second option
Step-by-step explanation:
x / x - 1 + 3x / x + 2
= x(x + 2) / (x - 1)(x + 2) + 3x(x - 1) / (x - 1)(x + 2)
= (x² + 2x) / (x² + x - 2) + (3x² - 3x) / (x² + x - 2)
= (4x² - x) / (x² + x - 2)
A sample of 250 observations is selected from a normal population with a population standard deviation of 25. The sample mean is 20. Determine the standard error of the mean. (Round your answer to 3 decimal places.)
Answer:
The standard error of the mean is [tex]\sigma _{\= x } = 1.581[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 250
The standard deviation is [tex]\sigma = 25[/tex]
The sample mean is [tex]\= x = 20[/tex]
The standard error of the mean is mathematically represented as
[tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x } = \frac{25 }{\sqrt{250} }[/tex]
[tex]\sigma _{\= x } = 1.581[/tex]
The rate of earnings is 6% and the cash to be received in four years is $20,000. The present value amount, using the following partial table of present value of $1 at compound interest, is
Answer:
$15,842
Step-by-step explanation:
We use the Present value formula
Present Value = Future value/(1 + r)ⁿ
r = 6% = 0.06
n = 4 years
Future value = $20,000
Present value = 20,000/(1 + 0.06)⁴
= $15841.873265
≈ $15,842
Find the measure of each interior angle of a regular polygon with 10 sides.
Answer:
add up c
Step-by-step explanation:
Students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. The students collect a random sample of 47 students. The mean of the sample is 12.3 units. The sample has a standard deviation of 1.9 units. What is the 95% confidence interval for the average number of units that students in their college are enrolled in
Answer:
The 95% confidence interval for the average number of units that students in their college are enrolled in is :
Confidence Interval ( 11.76, 12.84).
Step-by-step explanation:
The formula for a Confidence Interval is:
C. I = μ ± z × σ/√n
Where
z = z score
μ is the sample mean
σ is the sample standard deviation
n = number of samples
We were given a 95% confidence interval
The z score for a 95% confidence interval = 1.96
μ = 12.3 units
σ = 1.9
n = 47 students
C. I = μ ± z × σ/√n
C.I = 12.3 ± 1.96 × 1.9/√47
C.I = 12.3 ± 0.5432012283
Hence,
Confidence interval = 12.3 ± 0.5432012283
12.3 - 0.5432012283 = 11.756798772 Approximately ≈ 11.76
12.3 + 0.5432012283 = 12.843201228
Approximately ≈ 12.84
Therefore, the 95% confidence interval for the average number of units that students in their college are enrolled in is :
Confidence Interval ( 11.76, 12.84).
Help me fast please
give the coordinates(enclose the coordinates in parentheses) of the
foci,vertices,and convertices of the ellipse with equation x²/169 + y²/25 = 1
Answer:
[tex]\frac{x^2}{169} +\frac{y^2}{25}=1[/tex]
If we compare this to the general expression for an ellipse given by:
[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2}=1[/tex]
We can see that the vertex is [tex] V=(0,0)[/tex]
And we can find the values of a and b like this:
[tex] a=\sqrt{169}=13, b=\sqrt{25}=5[/tex]
in order to find the foci we can find the value of c
[tex] c =\sqrt{169-25}=\sqrt{144}=12[/tex]
The two focis are (12,0) and (-12,0)
The convertices for this case are: (13,0) and (-13,0) on the x axis
And for the y axis (0,5) and (0,-5)
Step-by-step explanation:
For this problem we have the following equation given:
[tex]\frac{x^2}{169} +\frac{y^2}{25}=1[/tex]
If we compare this to the general expression for an ellipse given by:
[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2}=1[/tex]
We can see that the vertex is [tex] V=(0,0)[/tex]
And we can find the values of a and b like this:
[tex] a=\sqrt{169}=13, b=\sqrt{25}=5[/tex]
in order to find the foci we can find the value of c
[tex] c =\sqrt{169-25}=\sqrt{144}=12[/tex]
The two focis are (12,0) and (-12,0)
The convertices for this case are: (13,0) and (-13,0) on the x axis
And for the y axis (0,5) and (0,-5)
Which of the following lines are parallel to 2Y - 3X = 4?
A. Y = 2/3 X + 4
B. Y = 6/4 X
C. 2Y=8-3X
Answer:
B. Y = 6/4 X
Step-by-step explanation:
Well to find its parallel line we need to put,
2y - 3x = 4 into slope-intercept.
+3x to both sides
2y = 3x + 4
Now we divide everything by 2,
y = 3/2x + 2
So a line that is parallel to the given line will have the same slope but different y intercept, meaning we can cross out choices A and C.
To check look at the image below ↓
Thus,
answer choice B. Y = 6/4 X is correct.
Hope this helps :)
On a coordinate plane, triangle P Q R has points (3, 0), (1, negative 2), (4, negative 2). Triangle PQR is reflected over the line y = x. What is the coordinate of the image point R’? R’(2, 4) R’(–2, –4) R’(2, –4) R’(–2, 4)
Answer:
R'(- 2, 4 )
Step-by-step explanation:
Under a reflection in the line y = x
a point (x, y ) → (y, x ) , thus
R(4, - 2 ) → R'(- 2, 4 )
Answer:
R'(- 2, 4 )
Step-by-step explanation:
I got it right on edg
A passcode can have 5 or 6 digits. Digits can be repeated and leading 0s are allowed. So, 1234 would be a 4 digit code that is different from 01234, which is a 5 digit code. How many different passcodes are possible
Answer:
The number of passcodes possible is 1,100,000
Step-by-step explanation:
Here , we want to calculate the number of different possible passcodes.
For the five digit code,
each number in the code has a possibility of choosing from the digits 0 to 9, so this means that each of the numbers in the code has 10 options.
So for a five digit code, the number of possible choices would be 10 * 10 * 10 * 10 * 10 = 10^5
For a six digit code, the number of possible choice would be 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10^6
So for 5 or 6 digits code, the number of possible choices would be;
10^5 + 10^6 = 10^5(1 + 10)
= 11(10^5) = 1,100,000
The number of passcodes possible is 1,100,000
Calculation of the no of passcode:For the five-digit code, the no of possible choices should be [tex]10^5[/tex]
For the six-digit code, the no of possible choices should be [tex]10^6[/tex]
So, the possible choices should be
[tex]10^5 + 10^6 = 10^5(1 + 10)\\\\= 11(10^5)[/tex]
= 1,100,000
Hence, The number of passcodes possible is 1,100,000
Learn more about code here: https://brainly.com/question/24418415
n rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=11 and BC=2, what is the area of the shaded region? Write your answer as a decimal, if necessary.
Answer:
Step-by-step explanation:
Hello!
For the rectangle ABCD
AB= DC= 11
BC= AD= 2
Point E lies halfway between AB and CD
The shaded are forms two triangles, I'll refer to the upper triangle as "Triangle one" and the lower triangle will be "triangle 2"
The area of a triangle is calculated as
[tex]a= \frac{bh}{2}[/tex]
b= base
h= height
Triangle 1
b₁= AB= 11
[tex]h_1= \frac{BC}{2}= \frac{2}{2}= 1[/tex]
[tex]a_1= \frac{b_1h_1}{2}= \frac{11*1}{2}= 5.5[/tex]
Triangle 2
b₂= DC= 11
[tex]h_2= \frac{BC}{2}= \frac{2}{2} = 1[/tex]
[tex]a_2= \frac{b_2h_2}{2}= \frac{11*1}{2}= 5.5[/tex]
Now you add the areas of both triangles to get the area of the shaded region:
a₁ + a₂= 5.5 + 5.5= 11
Since point E is halfway to all sides of the rectangle, even tough it doesn't see so, the shaded area is equal to half the area of the rectangle:
area= bh= DC*AD= 11*2= 22
area/2= 22/12= 11
I hope this helps!
For the functions f(x)=2x−5 and g(x)=3x2−x, find (f∘g)(x) and (g∘f)(x).
Hi,
f°g means : apply first g then f . so calculate "g" and then use result as "x" in f.
g°f means : you apply first f then g
so : f°g = 2(3x²-x) -5 = 6x²-2x- 5
To improve in math, you need practice. have a try with g°f :)
give the answer in comments, and I will tell you if you are correct.
good luck.
Graph the equation below by plotting the y-intercept and a second point on the line. When you click Done, your line will appear
Answer:
Step-by-step explanation:
Equation of the line has been given as,
[tex]y=\frac{3}{2}x-5[/tex]
By comparing this equation with the y-intercept form of the equation,
y = mx + b
Slope of the line 'm' = [tex]\frac{3}{2}[/tex]
and y-intercept 'b' = -5
Table for the points to be plotted on a graph will be,
x y
-4 -11
-2 -6
0 -5
2 -4
4 -3
By plotting y-intercept (0, -5) and any one of the points given in the table we can get the required line.
Answer: actually the answer to this question is (0, -5) and ( 2, -2)
Step-by-step explanation: I just took the test on Plato and got it right :)
I need help! I don’t understand and need helping
Answer:
125
Step-by-step explanation:
30+25+x=180
55+x=180
x=180-55
x=125
Answer:
x = 64.3Step-by-step explanation:
To find x we use tan
tan ∅ = opposite / adjacent
From the question
x is the adjacent
30 is the hypotenuse
So we have
tan 25 = 30/x
x = 30/tan 25
x = 64.33
x = 64.3 to the nearest tenth
Hope this helps you
BRAINLIEST ANSWER GIVEN Write a system of equations describing the situation. Do not solve the system. Two numbers add up to 14 and have a difference of 4.
Answer:
[tex]x+y =14\\x-y =4[/tex]
Step-by-step explanation:
[tex]Let -the -unknown- numbers -be ; x -and; y\\x+y =14\\x-y =4[/tex]