Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)[/tex]
So this is divisible by 3.
Now, to prove that this is divisible by 9 = 3*3 we need to prove that
[tex]4^n+17[/tex] is divisible by 3. We will prove it by induction.
Step 1 - for n = 1
4+17=21= 3*7 this is true
Step 2 - we assume this is true for k so [tex]4^k+17[/tex] is divisible by 3
and we check what happens for k+1
[tex]4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17[/tex]
[tex]3\cdot 4^k[/tex] is divisible by 3 and
[tex]4^k+17[/tex] is divisible by 3, by induction hypothesis
So, the sum is divisible by 3.
Step 3 - Conclusion
We just prove that [tex]4^n+17[/tex] is divisible by 3 for all positive integers n.
Thanks
-1/5-(-3/8)=?
I need a step by step to solve this equation
Answer:
7/40
Step-by-step explanation:
Simplify the following:
-1/5 + 3/8
Hint: | Put the fractions in -1/5 + 3/8 over a common denominator.
Put -1/5 + 3/8 over the common denominator 40. -1/5 + 3/8 = (-8)/40 + (5×3)/40:
(-8)/40 + (5×3)/40
Hint: | Multiply 5 and 3 together.
5×3 = 15:
(-8)/40 + 15/40
Hint: | Subtract the fractions over a common denominator to a single fraction.
-8/40 + 15/40 = (-8 + 15)/40:
(-8 + 15)/40
Hint: | Subtract 8 from 15.
-8 + 15 = 7:
Answer: 7/40
Given f(x)=10-2x, find f(7)
Answer:
f(7)=10-14=-4
Answer=-4
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
f(x)=10-2x
Let x = 7
f(7) = 10 -2(7)
= 10 -14
= -4
which of these limits evaluate to 0?
===============================================
Work Shown:
Part I
[tex]\displaystyle \lim_{x \to 2}\frac{x-2}{x+2} = \frac{2-2}{2+2}\\\\\\\displaystyle \lim_{x \to 2}\frac{x-2}{x+2} = \frac{0}{4}\\\\\\\displaystyle \lim_{x \to 2}\frac{x-2}{x+2} = 0\\\\\\[/tex]
----------
Part II
[tex]\displaystyle \lim_{x \to 0}\frac{\sin(x)}{x+2} = \frac{\sin(0)}{0+2}\\\\\\\displaystyle \lim_{x \to 0}\frac{\sin(x)}{x+2} = \frac{0}{2}\\\\\\\displaystyle \lim_{x \to 0}\frac{\sin(x)}{x+2} = 0\\\\\\[/tex]
----------
Part III
[tex]\displaystyle \lim_{x \to 5}\frac{x}{x} = \lim_{x \to 5}1\\\\\\\displaystyle \lim_{x \to 5}\frac{x}{x} = 1\\\\\\[/tex]
New codes to destroy the First Order are known to exist. With probability 0.6, the codes are hidden by Leia; with probability 0.4, they are hidden by Han Solo. When Leia hides the codes, she hides them with BB-8 70% of the time and with C-3PO 30% of the time. Han Solo is equally likely to hide them with BB-8 and C-3PO a. What is the probability that the codes are with BB-8? b. Given that the codes are with C-3PO, what is the probability the codes were hidden by Han Solo?
Answer: (a). 0.62 (b). 0.53
Step-by-step explanation:
Let us start by defining some events seen:
Given;
L rep the event that codes hidden Leia
BB represents the codes hidden in BB-8
H is the event that codes hidden by Hah
C-3PO rep the codes hidden in C3PO
Giving the probabilities, we have that
P(L) = probability that codes are hidden by Leia = 0.6
P(H) = probability that codes are hidden by Hah = 0.4
where P(BB/L) = 70/10 i.e 70%
P(C-3PO/L) = 1 - P(BB/L) = 1 - 7/10 = 3/10
Also, P(BB/H) = 1/2 = P(C-3PO/H)
We can say that Han Solo is likely to hide them in aceta BB-8 and C-3PO
To begin,
(a). The question tell us to find the probability that the codes are with BB-8.
First of all, we find P(BB).
P(BB) = P(L)*P(BB/L) + P(H)*P(BB/H)
solving this we get
P(BB) = 0.6*7/10 + 0.4*1/2 = 0.62
Therefore, the probability that the codes are with BB-8 = 0.62
(b). The second question says;
Given that the codes are with C-3PO, what is the probability the codes were hidden by Han Solo?
This tell us to find P(H/C-3PO)
P(H/C-3PO) = P(C-3PO/H)*P(H) / P(C-3PO/H) + P(C-3PO/L)*P(L)
inputting the values gives us;
P(H/C-3PO) = 1/2 * 0.4 / ( 1/2 *0.4 + 3/10 *0.6) = 0.53
SO we have that the probability the codes were hidden by Han Solo = 0.53
cheers I hope this was helpful!!
joseph wants to find the side length of a square that has an area of 150 feet. Should his answer be rational or irrational ? why ?
Answer:
i dont what it is can u tell me
Step-by-step explanation:
The length side is not a integer. Therefore, The answer is irrational.
What is the area of a square?The area of a square is given by the formula
A = side x side
In this problem we have
A = 150 square feet.
Now, substitute in the formula
150 = side^2
Now, take the square root both sides
side = √150
Then simplify
side = 5√6 feet
Remember that; A Rational Number is a number that can be made by dividing two integers. soThe length side is not a integer
Therefore, The answer is irrational.
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What is the diameter of the circle the area of the circle is 144 square root m2
Answer: 24 m
Step-by-step explanation:
Given: area of the circle is 144 π m² .
Area of a circle = [tex]\pi r^2[/tex], where r= radius of the circle.
Then, [tex]144\pi = \pi r^2[/tex]
Cancelling π from both sides , we get
[tex]144 = r^2[/tex]
Taking square root on both sides , we get'
[tex]12= r[/tex]
i.e. radius = 12 m
Then diameter = 2 (radius ) = 2 (12)= 24 m
Hence, the diameter of the circle is 24 m.
The diameter of the circle is 13.54cm
The formula for calculating the area of the circle is expressed as:
A = πd²/4
d is the diameter of the circle
GIven the following
A = 144m²
Substitute the area into the circle
144 = πd²/4
πd² = 144 * 4
πd² = 576
d² = 576/3.14
d² =183.44
d = 13.54cm
Hence the diameter of the circle is 13.54cm
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Simplify the expression: 7h+2+4
Answer:
[tex] \boxed{ \huge{ \bold{ \sf{ \boxed{7h + 6}}}}}[/tex]Step-by-step explanation:
[tex] \sf{7h + 2 + 4}[/tex]
Add the numbers
⇒[tex] \sf{7h + 6}[/tex]
Hope I helped!
Best regards!
Answer:
7h+6
Step-by-step explanation:
We are given the expression:
7h + 2 + 4
and asked to simplify.
In order to simplify an expression, we must combine like terms. In this expression, we have 2 constants, or terms without variables. The 2 constants and 2 and 4. Add 2 and 4.
7h + (2+4)
7h+6
There are no more like terms, so this expression is simplified.
The expression 7h+2+4 simplified is 7h +6
Using traditional methods it takes 98 hours to receive an advanced flying license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher believes the new technique may reduce training time and decides to perform a hypothesis test. After performing the test on 200 students, the researcher decides to reject the null hypothesis at a 0.01 level of significance. What is the conclusion?
Answer:
We conclude that the new technique reduces the training time that it takes less than 98 hours to receive an advanced flying license.
Step-by-step explanation:
We are given that using traditional methods it takes 98 hours to receive an advanced flying license. A researcher believes the new technique may reduce training time and decides to perform a hypothesis test.
After performing the test on 200 students, the researcher decides to reject the null hypothesis at a 0.01 level of significance.
Let [tex]\mu[/tex] = mean time to receive an advanced flying license.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 98 hours
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 98 hours
Here, the null hypothesis states that it takes 98 hours to receive an advanced flying license.
On the other hand, the alternate hypothesis states the new technique may reduce training time that it takes less than 98 hours to receive an advanced flying license.
Now, it is stated that after performing the test on 200 students, the researcher decides to reject the null hypothesis at a 0.01 level of significance. This means we don't have sufficient evidence to support the null hypothesis as our test statistics will fall in the rejection region.
Therefore, we conclude that the new technique reduces the training time that it takes less than 98 hours to receive an advanced flying license.
Will mark brainiest for simplest and most coherent answer. What does it mean if an x (input) or y (output) value doesn't make sense? What does it look like on a graph? What happens in the equation?
Answer:
I tried to answer but I still would like to know what doesn't make sense.
Considering the identity:
[tex]\sec^2\theta-\tan^2\theta=1 \implies |\sec\theta|\geq1[/tex]
[tex]$\forall\;\theta\in\mathbb{R}-\{(2n+1)\frac{\pi}{2}, n\in\mathbb{Z} \}$[/tex]
The identity is true whenever both sides are defined. It is not supposed to hold the values when we have division by zero, because it is undefined.
If the value doesn't make sense, it is probably not a function, or it is undefined by the given value of [tex]x[/tex].
Let's go back to the definition of function again:
A function relates a set of inputs and a set of allowable outputs where each input is related to only one output. It basically defines the relation of ordered pairs.
Hope it helped you a bit.
Use Lagrange multipliers to find three positive numbers whose sum is 210 and whose product is maximum. (Enter your answers as a comma-separated list.)
Answer: the three positive numbers are; 70, 70, 70
Step-by-step explanation:
Given that sum is equal = 210
Lets ( x, y, z ) be the three positive numbers
such that
x + y + z = 210
what is the maximum of xyz
take f(x,y,z) = xyz
Q(x,y,z) = 0
x + y + z -210 = 0
consider the function
F(x,y,z) = f(x,y,z) + λQ(x,y,z)
F = xyz + λ(x+y+z-210)
dF/dx = 0 ⇒ yz + λ(1) = 0 ⇒ λ = -yz ..............equ(1)
dF/dy = 0 ⇒ xz + λ(1) = 0 ⇒ λ = -xz.................equ(2)
dF/dz = 0 ⇒ xy + λ(1) = 0 ⇒ λ = -xy...............equ(3)
Now
equ(1)/equ(2) ⇒ λ/λ = -yz/-xz ⇒ x = +y
equ(1)/equ(3) ⇒ λ/λ = - yz/-xy ⇒ x = +z
⇒ y = z = x
by substitution
x + y + z = 210
x + x + x = 210
3x = 210
x = 210/3 = 70
∴ x, y, z = 70, 70 ,70
MAXIMUM
∛xyz = 70 { when x = y = z = 70}
Here is a sample distribution of hourly earnings in Paul's Cookie Factory: Hourly Earning $6 up to $9 $9 up to $12 $12 up to $15 Frequency 16 42 10 The limits of the class with the smallest frequency are: ______.
Answer:
$12 up to $15
Step-by-step explanation:
Given
Hourly Earning: $6 - $9 || $9 - $12 || $12 - $15
Frequency: 16 || 4 || 10
Required
Determine the limits of the least frequency;
First, we have to determine the lowest frequency;
From the table. the lowest frequency is:
[tex]Lowest = 10[/tex]
Next is to determine the corresponding class limits
The corresponding class limit is $12 up to $15
Mr. Ferret loves fresh, juicy, organic mole meat from Mole Foods grocery store. But his ability to purchase this tasty delicacy depends upon how much Mole Foods is currently charging per pound. The more Mole Foods charges, the less mole meat Mr. Ferret will buy. Use the ‑intercept equation to plot a line representing Mr. Ferret's demand curve.y =−2x+8
Answer:
It has a negative slope = -2
Step-by-step explanation:
Let y be the price and x be the quantity purchased . Then putting the value of x in the equation we can find the price= y
where y = −2x+8
x 0 1 2 3 4 5 6 7
y 8 6 4 2 0 -2 -4 -6
So we can plot the demand curve which has a negative slope.
We see from the values above that the slope is negative having a value equal to -2. This means that for every increase in the number of quantities there is a decrease in the price.
A deposit of $200 is made in an account at the beginning of each month at an annual interest rate of 3% compounded monthly. The balance in the account after n months is An = 200(401)(1.0025n ? 1).(Round your answers to two decimal places.)
(a) Compute the first six terms of the sequence {An}.
A1 = $
A2 = $
A3 = $
A4 = $
A5 = $
A6 = $
(b) Find the balance in the account after 5 years by computing the 60th term of the sequence.
A60 =
(c) Find the balance in the account after 15 years by computing the 180th term of the sequence.
A180 =
Complete questions:
A deposit of $200 is made in an account at the beginning of each month at an annual interest rate of 3% compounded monthly. The balance in the account after n months is An = 200(401)(1.0025^n - 1).(Round your answers to two decimal places.)
Answer:
Kindly check explanation
Step-by-step explanation:
Given the amount of balance in an account after. 'n' months using the eqation:
An = 200(401)(1.0025^n - 1)
(a) Compute the first six terms of the sequence {An}.
A1 = 200(401)(0.0025) = $200.50
A2 = 200(401)(1.0025^2 - 1) = $401.50
A3 = 200(401)(1.0025^3 - 1) = $603.00
A4 = 200(401)(1.0025^4 - 1) = $805.01
A5 = 200(401)(1.0025^5 - 1) = $1007.53
A6 = 200(401)(1.0025^6 - 1) = $10210.54
B) balance 5 years after n = 5 * 12 = 60
A60 = 200(401)(1.0025^60 - 1) = $12,961.67
C.) balance 15 years after ; n = 15 * 12 = 180
A180 = 200(401)(1.0025^180 - 1) = $45,508.02
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
6-x+1=x+5
O 2
O 3
O 6
O 12
Select the correct answer.
You reflect triangle PQR with vertices P(-2,-4). Q(-3,-1), and R(-4,-4), across the y-axis to get triangle P'Q'R'. What are the coordinates of triangle
P'Q'R?
Answer:
P' (2, -4)
Q' (3, -1)
R' (4, -4)
Step-by-step explanation:
Reflection in the y axis
(x, y) → (-x, y)
P(⁻²₋₄ ) → P'(²₋₄ ) ∴ P'(2, -4)
Q(⁻³₋₁ ) → Q'(³₋₁ ) ∴ Q'(3, -1)
R(⁻⁴₋₄ ) → R'(⁴₋₄ ) ∴ R'(4, -4)
A toxin increase from 12ppm to 16ppm. What percent increase is this?
A rectangle has opposite sides that are parallel and congruent. What is the measure of each interior angle in a rectangle?
Each interior angle of a rectangle measures 90°
What is a rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°). The opposite sides of a rectangle are equal and parallel.
According to the property of a rectangle, we have,
Opposite side equal and paralleleach interior angle right angleDiagonal are equal and bisects each other.Hence, Each interior angle of a rectangle measures 90°
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The areas of two similar octagons are 9 m² and 25 m². What is the scale factor of their side lengths? PLZ HELP PLZ PLZ PLZ
Answer:
[tex] \frac{3}{5} [/tex]
Step-by-step explanation:
Let the side length for the octagon having 9m² as area = x
Side length for the octagon having area of 25m² = y.
Thus:
[tex] \frac{9}{25} = (\frac{x}{y})^2 [/tex] (area of similar polygons theorem)
The scale factor of their sides would be [tex] \frac{x}{y} [/tex]. Which is:
[tex] \sqrt{\frac{9}{25}} = \frac{x}{y} [/tex]
[tex] \frac{\sqrt{9}}{\sqrt{25}} = \frac{x}{y} [/tex]
[tex] \frac{3}{5} = \frac{x}{y} [/tex]
Scale factor of their sides = [tex] \frac{3}{5} [/tex]
Answer:
3:5
Step-by-step explanation:
when bisecting an angle, why must The Arc be drawn in the interior of the angle?
Answer:
It depends on the measure of the angle you are talking about
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 257.62 and a standard deviation of 62.1 (All units are 1000 cells/μ L.)
Using the empirical rule, find each approximate percentage below.
What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7 ?
What is the approximate percentage of women with platelet counts between 71.3 and 443.9 ?
a. Approximately 68 % of women in this group have platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7.
(Type an integer or a decimal. Do not round.)
b. Approximately ____ % of women in this group have platelet counts between 71.3 and 443.9.
(Type an integer or a decimal. Do not round.)
Answer:
(a) Approximately 68 % of women in this group have platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7.
(b) Approximately 99.7% of women in this group have platelet counts between 71.3 and 443.9.
Step-by-step explanation:
We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 257.62 and a standard deviation of 62.1
Let X = the blood platelet counts of a group of women
So, X ~ Normal([tex]\mu=257.62, \sigma^{2} =62.1^{2}[/tex])
Now, the empirical rule states that;
68% of the data values lie within the 1 standard deviation of the mean.95% of the data values lie within the 2 standard deviations of the mean.99.7% of the data values lie within the 3 standard deviations of the mean.(a) The approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7 is 68% according to the empirical rule.
(b) The approximate percentage of women with platelet counts between 71.3 and 443.9 is given by;
z-score of 443.9 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{443.9-257.62}{62.1}[/tex] = 3
z-score of 71.3 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{71.3-257.62}{62.1}[/tex] = -3
So, approximately 99.7% of women in this group have platelet counts between 71.3 and 443.9.
What is the square root of 190,290,390,545
Answer:
Step-by-step explanation:
Answer:
190 = 13.78
290 =17.02
390 = 19.74
545 = 23.34
Step-by-step explanation:
if you need simplest ratical let me know
Which of the following can be written as a fraction of integers? CHECK ALL THAT APPLY.
2.5
square root of 14
-1.25
5.33333...
square root of 16
null
0.6
Answer:
[tex]2.5[/tex] [tex]-1.25[/tex] [tex]\sqrt{16}[/tex] [tex]0.6[/tex]
Step-by-step explanation:
Required
Which of the given parameters can be represented as fraction of integers
Taking them one at a time;
1. 2.5
This can be rewritten as
[tex]2.5 = \frac{2.5}{1}[/tex]
Multiply numerator and denominator by 2
[tex]2.5 = \frac{2.5 * 2}{1 * 2}[/tex]
[tex]2.5 = \frac{5}{2}[/tex]
Hence, 2.5 can be represented as fraction of integers
2. √14
This can be rewritten as
[tex]\sqrt{14} = 3.74165738677...[/tex]
The ... implies that the decimal continues and this cannot be represented as a fraction
3. -1.25
This can be rewritten as
[tex]-1.25 = \frac{-1.25}{1}[/tex]
Multiply numerator and denominator by 4
[tex]-1.25 = \frac{-1.25 * 4}{1 * 4}[/tex]
[tex]-1.25 = \frac{-5}{4}[/tex]
Hence, -1.25 can be represented as fraction of integers
4. 5.33333.....
The ... implies that the decimal continues and this cannot be represented as a fraction
5. √16
[tex]\sqrt{16} = \±4[/tex]
This can be rewritten as
[tex]\sqrt{16} = \±\frac{4}{1}[/tex]
Multiply numerator and denominator by 2
[tex]\sqrt{16} = \±\frac{4 * 2}{1 * 2}[/tex]
[tex]\sqrt{16} = \±\frac{8}{2}[/tex]
Hence, √16 can be represented as fraction of integers
6. 0.6
This can be rewritten as
[tex]0.6 = \frac{0.6}{1}[/tex]
Multiply numerator and denominator by 10
[tex]0.6 = \frac{0.6 * 10}{1 * 10}[/tex]
[tex]0.6 = \frac{6}{10}[/tex]
Hence, 0.6 can be represented as fraction of integers
If m<1 is three less than twice the measure of <2, and <1 and <2 are supplementary angles, find each angle
measure.
Step-by-step explanation:
Hey there!!
Let angle 2 be x then,
measure of angle 1 is three less than twice of angle 2 = 2x-3.
Now, we have.
Measure of supplementary angle is 180°.
Angle 1 + angle 2 = 180°
x+(2x - 3)= 180°
3x -3=180°
3x= 180°+3°
[tex]x = \frac{183}{3} [/tex]
Therefore, x = 61°.
Now, angle 2 = 61°
angle 1 = (61×2-3)= 119°.
check (119°+61°=180°).
Hope it helps...
can you help me with these questions
Answer:
see below (I hope this helps!)
Step-by-step explanation:
41. √20 = √4 * 5 = √4 * √5 = 2√5
43. The sum of interior angles in a triangle is 180°, therefore, x = 180 - (75 + 64) = 41°.
45. 15 + 5(2x - 3) = 15 + 5(2x) + 5(-3) = 15 + 10x - 15 = 10x
47. Complementary angles have a sum of 90°, therefore, x = 90 - 48 = 42°.
X + 7
2x - 3
Perimeter:
Area:
Answer:
P=6x+8
A=2x^2+11x-21
Step-by-step explanation:
Perimeter:
P=2(x+7)+2(2x-3)
P=6x+8
Area:
A=(x+7)(2x-3)
A=2x^2+11x-21
A lamina occupies the disk x squared space plus space y squared space less or equal than 4. Find the mass, if the density at any point is proportional to its distance from the origin, where the proportionality constant is 3.
Answer: Mass of Lamina is (K/3)
Centre of mass is (3/8, 3pi/16)
Step-by-step explanation:
Find explanation in the attachments
DVD cases are sold in packages of 15. Padded mailing envelopes are sold in packets of 4.
What is the least number of cases and envelopes you could buy so that there is one case for each
envelope with none left over?
The least number of cases and envelopes you could buy, so that there is one case for each envelope with
none left over, is cases and envelopes.
Answer:
Step-by-step explanation: you want to divide the price of eatch to the pacets???
Solve it! Hurry
Will mark as brainliest
IF U TRY TO get the points free i would report u
Answer:
A. 3x^2+7x^2+2×3x ×7-84x = 3x^2+7x^2-2×3x×7
9x^2+49x^2+42x-84 x= 9x^2+49x^2-42x
9x^2+49x^2-42 = 9x^2+49 x^2-42x
verified
B.
Answer:
Give him or her brainlist
Step-by-step explanation:
^
|
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if you bought a stock last year for $59 and it risen 13% how much is the stock worth now
the corresponding amount in a 13% increase is: (59 * 13): 100 = $ 7.67
so the current stock price is: 59 + 7.67 = $ 66.67
anyone know this one
Answer:
Only B
Step-by-step explanation:
Did this in Khan Academy.
=> Also, there are 2 '-' symbols in the question.
In Option A, there is only 1 "-' symbol.
In Option B, there are 2 '-' symbols.
Option C says none of the above.
Since, Option B has 2 '-' symbols, it is the correct.