Answer:
Number of term N = 9
Value of Sum = 0.186
Step-by-step explanation:
From the given information:
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}[/tex]
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}[/tex]
Number of term N = 9
The Value of the sum can be determined by using the expression for geometric series:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}[/tex]
here;
m = 5
n = 9
r = 0.5
Then:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =0.186[/tex]
For the given the geometric series, 3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³,
the responses are;
(1) The number of terms are 9
(2) The value of the sum is approximately 0.374
How can the geometric series be evaluated?The given geometric series is presented as follows;
3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³
(1) The number of terms in the series = 13 - 4 = 9
Therefore;
The number of terms in the series = 9 terms(2) The value of the sum can be found as follows;
The common ratio, r = 0.5
The sum of the first n terms of a geometric progression is presented as follows;
[tex]S_n = \mathbf{\dfrac{a \cdot (r^n - 1)}{r - 1}}[/tex]
The sum of the first 4 terms are therefore;
[tex]S_4 = \dfrac{3 \times (0.5^4 - 1)}{0.5 - 1} = \mathbf{ 5.625}[/tex]
The sum of the first 13 terms is found as follows;
[tex]S_{13} = \dfrac{3 \times (0.5^{13} - 1)}{0.5 - 1} = \mathbf{ \dfrac{24573}{4096}}[/tex]
Which gives;
The sum of the 5th to the 13th term = S₁₃ - S₄
Therefore;
[tex]The \ sum \ of \ the \ 5th \ to \ the \ 13th \ term =\dfrac{24573}{4096} - \dfrac{45}{3} = \dfrac{1533}{4096} \approx \mathbf{0.374}[/tex]
The value of the sum of the terms of the series is approximately 0.374Learn more about geometric series here:
https://brainly.com/question/12471913
by what number 7whole 2/3be divided to get 4whole1/3
Answer: 1 30/39
Step-by-step explanation:
Because y/x=z and y/z=x are true with the same values, simply do 7 2/3 divided by 4 1/3 to get 69/39.
Hope it helps <3
Find the probability of picking 1 consonant and 4 vowels when 5 letters are picked (without replacement) from a set of alphabet tiles.
Answer:
Ok, we have a total of 26 letters, and we want to select 5 of them.
Of the 26 letters, 21 are consonants and 5 are vowels.
Suppose that we want to have the consonant in the first selection, so the probability of picking a consonant is equal to the quotient between the number of consonants and the total number of letters.
p = 21/26
now a letter has been selected, so in the set, we have 25 letters left.
In the next 4 selections, we must select vowels.
In the second selection the probability is:
p = 5/25
in the third, the prob is:
p = 4/24 (we already selected one vowel before, so now we only have 4 vowels)
The fourth selection:
p = 3/23
and the last selection:
p = 2/22
The total probability is equal to the product of all the individual proabilities, so we have:
P = (2/22)*(3/23)*(4/24)*(5/25)*(21/26)
Now, remember that we said that the consonant must be in the first place, but it can be in any of the five places, so if we add the permutations of the consonant letter we have:
P = 5*(2/22)*(3/23)*(4/24)*(5/25)*(21/26) = 0.0018
PLEASE HELP ME UNDERSTAND!! ok, when i looked at other people converting sin, cos, tan, i realized this; cos(x) = y/z z = y cos(x) which is weird. why would you multiply cos by y instead of dividing cos by y?
Answer:
the real deal is that you mistook if
cos(x)=y/z gives y=zcos(x)
In a simple regression analysis for a given data set, if the null hypothesis β = 0 is rejected, then the null hypothesis ρ = 0 is also rejected. This statement is ___________ true. always
Answer:
Null hypothesis: [tex]\rho =0[/tex]
Alternative hypothesis: [tex]\rho \neq 0[/tex]
The statistic to check the hypothesis is given by:
[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]
And is distributed with n-2 degrees of freedom
And the statistic to check the significance of a coeffcient in a regression is given by:
[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]
For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:
Always
Step-by-step explanation:
In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:
Null hypothesis: [tex]\rho =0[/tex]
Alternative hypothesis: [tex]\rho \neq 0[/tex]
The statistic to check the hypothesis is given by:
[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]
And is distributed with n-2 degrees of freedom
And the statistic to check the significance of a coeffcient in a regression is given by:
[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]
For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:
Always
if -2x = -14 what is the value of x
Answer: x= 7
Step-by-step explanation:
-2x= -14 Divide both sides by -2
x= 7
check
-2(7) = -14
-14 = -14
Answer:
x = 7
Step-by-step explanation:
-2x = -14
Divide each side by -2
-2x/-2 = -14/-2
x = 7
PLEASE HELP
Divide. Write your answer using the smallest numbers possible. 47 pounds 13 ounces divided by 15 = ___pounds ___ounces
Answer:
3 pounds
51 ounces
Step-by-step explanation:
what is the slop of y= -5+4x
Hey there! :)
Answer:
m = 4.
Step-by-step explanation:
We are given the formula y = -5 + 4x. Rearrange the equation to be in proper slope-intercept form (y = mx + b)
Where 'm' is the slope and 'b' is the y-intercept. Therefore:
y = -5 + 4x becomes y = 4x - 5
The 'm' value is equivalent to 4, so the slope of the equation is 4.
Answer:
4
Step-by-step explanation:
because of y= mx + b where m is the slope
m= 4 in the equation
Dunno these answers
Answer:
its 9
Step-by-step explanation:
Answer:
c. 9i.
Step-by-step explanation:
[tex]\sqrt{-81}[/tex]
= [tex]\sqrt{-1 * 9 * 9}[/tex]
= [tex]\sqrt{-1 * 9^2}[/tex]
= [tex]9\sqrt{-1}[/tex]
The square root of -1 is the same thing as i.
= [tex]9i[/tex]
So, your answer is C.
Hope this helps!
Two passenger trains traveling in opposite directions meet and pass each other. Each train is 1 12 mi long and is traveling 50 mph. How many seconds after the front cars of the trains meet will their rear cars pass each other?
Answer:
Time taken = 6 sec (Approx)
Step-by-step explanation:
Given:
Total distance = 1/12 mi = 0.083333
Speed of train = 50 mph = 50 / 3600 = 0.01388889 mps
Find:
Time taken
Computation:
Time taken = Total distance / Speed
Time taken = Total distance / Speed of train
Time taken = 0.0833333 / 0.01388889
Time taken = 6 sec (Approx)
The height of a projectile launched upward at a speed of 32 feet/second from a height of 128 feet is given by the function h(t) = -16t^2 + 32t +128. How long will it take the projectile to hit the ground?
Answer:
It takes 4 seconds for the projectile to hit the ground
Step-by-step explanation:
The height of the projectile after t seconds is given by the following equation:
[tex]h(t) = -16t^{2} + 32t + 128[/tex]
How long will it take the projectile to hit the ground?
It happens when [tex]h(t) = 0[/tex]
So
[tex]h(t) = -16t^{2} + 32t + 128[/tex]
[tex]-16t^{2} + 32t + 128 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]-16t^{2} + 32t + 128 = 0[/tex]
So [tex]a = -16, b = 32, c = 128[/tex]
[tex]\bigtriangleup = 32^{2} - 4*(-16)*(128) = 9216[/tex]
[tex]t_{1} = \frac{-32 + \sqrt{9216}}{2*(-16)} = -2[/tex]
[tex]t_{2} = \frac{-32 - \sqrt{9216}}{2*(-16)} = 4[/tex]
Time is a positive measure, so:
It takes 4 seconds for the projectile to hit the ground
What is the correct slope and y-intercept for the following: y=-3x+8
━━━━━━━☆☆━━━━━━━
▹ Answer
Slope = -3
Y-intercept = 8
▹ Step-by-Step Explanation
y = mx + b
mx represents the slope.
b represents the y intercept.
therefore,
y = -3x + 8
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
[tex]\boxed{\mathrm{Slope:}-3 \: \: \: \:\: \mathrm{Y \: intercept:}8}[/tex]
Step-by-step explanation:
The general form of slope-intercept:
[tex]y=mx+b[/tex]
[tex]m:slope\\b:y \: intercept[/tex]
[tex]y=-3x+8[/tex]
[tex]m=-3\\b=8[/tex]
The slope is -3.
The y-intercept is (0, 8) or 8.
The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
Answer:
[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]
Step-by-step explanation:
[tex]Volume = Base \ Area\ * Height[/tex]
[tex]Height = \frac{Volume}{Base \ Area}[/tex]
Where [tex]Volume = x^4+4x^3+8x+4[/tex] and [tex]Area = x^3+3x^2+8[/tex]
Putting in the formula
[tex]Height = \frac{x^4 + 4x^3 + 3x^2 + 8x + 4}{x^3 + 3x^2 + 8}[/tex]
Doing long division, we get
[tex]Height = x + \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]
[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]
This is the simplifies form and it can't be further simplified.
Answer:
[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
Step-by-step explanation:
[tex]volume=base \: area \times height[/tex]
[tex]height=\frac{volume}{base \: area}[/tex]
[tex]\mathrm{Solve \: by \: long \: division.}[/tex]
[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]
[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]
[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
please please
please
please help
me. i am desperate
Answer:The answer is c
Step-by-step explanation:
find the maximal area of a right triangle with hypotenuse of length 8
Answer:
Max area is 16
Step-by-step explanation:
If A² + B² = C², then A² + B² = 64. The largest triangle area is when both A² and B² are equal to 32, so 32 + 32 = 64.
So equal side of the triangle is √32 or about 5.6568. The area of the triangle is then 1/2(5.6568 × 5.6568) or 16.
The maximal area of a right triangle is 90.496
What is differentiation?Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Given:
let the perpendicular be 'x'
and base be 'y'
Using Pythagoras theorem
x² + y² = 8²
x² + y² = 64
y²= 64- x²
y = √64-x²
Now, Area of triangle
= 1/2* base* height
=xy/2
=x *√64-x²*1/2
On differentiating both side
A' = 64-2x²/√64-x²*1/2
Setting derivative function equal to zero,
64= 2x²
32=x²
x=5.656
So, Area of triangle = x *√64-x²*1/2
= 90.496
Learn more about differentiation here:
https://brainly.com/question/24898810
#SPJ2
Which equation shows y-5=x converted to slope intercept form.
Answer:
C) y = x + 5
Step-by-step explanation
Add 5 to both sides
James determined that these two expressions were equivalent expressions using the values of x - 4 and x-6.
Which statements are true? Check all that apply.
7x+4 and 3x+5+4x-1
When x-2, both expressions have a value of 18.
The expressions are only equivalent for x = 4 and x-6.
The expressions are only equivalent when evaluated with even values.
The expressions have equivalent values for any value of x.
The expressions should have been evaluated with one odd value and one even value.
When x-0, the first expression has a value of 4 and the second expression has a value of 5.
The expressions have equivalent values if x - 8.
Answer:
1 - Correct
2 - incorrect
3- incorrect
4 - incorrect
5 - Correct
Step-by-step explanation:
Notice that
3x + 5 + 4x -1 = 3x + 4x + 5 -1 = 7x + 4
therefore the two expressions are equivalent for ANY number, specially x = 4 and x = 6 therefore
1 - Correct
Since that is true for all numbers
2 - incorrect
3- incorrect
4 - incorrect
The expressions are equivalent for all numbers therefore
5 - Correct
What is the equation of the line perpendicular to y=5x-3 that passes through the point (3, 5)?
Answer:
[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex]
Step-by-step explanation:
Hey there!
Well the slope of the perpendicular line is -1/5 because that's the reciprocal of 5.
Look at the image below ↓
By looking at the image we can conclude that the equation for the perpendicular line is,
[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex].
Hope this helps :)
Answer:
[tex]\boxed{y=-\frac{1}{5}x+\frac{28}{5}}[/tex]
Step-by-step explanation:
Part 1: Finding the new slope of the line
Perpendicular lines have reciprocal slopes of a given line - this means that the slope you are given in the first equation will be flipped and negated.
Because the slope is 5 in the first line, it gets flipped to become [tex]-\frac{1}{5}[/tex].
Part 2: Using point-slope formula and solving in slope-intercept form
Input the new slope into the slope-intercept equation: [tex]y=mx+b[/tex]. This results in [tex]y=-\frac{1}{5} x+b[/tex].
Then, use the point-slope equation to get b, or the y-intercept of the equation.
[tex](y-y_{1})=m(x-x_{1})[/tex]
[tex](y-5)=-\frac{1}{5}(x-3)\\\\y-5=-\frac{1}{5}x+\frac{3}{5} \\\\y=-\frac{1}{5}x+\frac{28}{5}[/tex]
Witch table represents a linear function ?
Answer:
If you compute the slope between any two points that must be the same, that's how you can tell if a table represents a linear function.
Remember that the slope between any two points (x1,y1), (x2,y2) is
slope = ( y2 - y1 ) / (x2 - x1)
Step-by-step explanation:
If you compute the slope between any two points that must be the same, that's how you can tell if a table represents a linear function.
Remember that the slope between any two points (x1,y1), (x2,y2) is
slope = ( y2 - y1 ) / (x2 - x1)
Find the 10th term of the following geometric sequence.
2, 10, 50, 250, ...
Answer:
3906250
Step-by-step explanation:
We can notice that the ratio is 5. 10/2 = 5
Each term gets multiplied by 5 to get the next term.
250 × 5 = 1250 (5th term)
1250 × 5 = 6250 (6th term)
6250 × 5 = 31250 (7th term)
31250 × 5 = 156250 (8th term)
156250 × 5 = 781250 (9th term)
781250 × 5 = 3906250 (10th term)
The 10th term of the geometric sequence is 3906250.
Please answer in the form of a number
Answer:
d ≈ 8.3
Step-by-step explanation:
This is kind of like the pythagorean theorem, but with one extra value. Thus, [tex]d^2=l^2+w^2+h^2[/tex].
Plug in the values to get:
[tex]d^2=2^2+7^2+4^2\\d^2=4+49+16\\d^2=69\\d=\sqrt{69} \\[/tex]
Thus d ≈ 8.3
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x2 + y2 = (4x2 + 2y2 − x)2
(0, 0.5)
(cardioid)
Answer:
y = x + 0.5
Step-by-step explanation:
This is a very trivial exercise, follow the steps below:
Step 1: Perform the implicit differentiation of the given equation
[tex]x^2 + y^2 = (4x^2 + 2y^2 - x)^2[/tex]
[tex]2x + 2y \frac{dy}{dx} = 2(4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\[/tex]
Step 2: Make dy/dx the subject of the formula, this will be the slope of the curve:
[tex]x + y \frac{dy}{dx} = (4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\x + y \frac{dy}{dx} = 32x^3 + 16x^2y \frac{dy}{dx} - 4x^2 + 16xy^2 + 8y^3\frac{dy}{dx} - 2y^2 - 8x^2 - 4xy\frac{dy}{dx} + x \\\\\frac{dy}{dx}(y + 4xy - 8y^3) = 32x^3 - 12x^2 + 16xy^2 - 2y^2\\\\\frac{dy}{dx} = \frac{32x^3 - 12x^2 + 16xy^2 - 2y^2}{y + 4xy - 8y^3}[/tex]
Step 3: Find dy/dx at the point (0, 0.5)
[tex]\frac{dy}{dx}|(0,0.5) = \frac{32(0)^3 - 12(0)^2 + 16(0)(0.5)^2 - 2(0.5)^2}{(0.5) + 4(0)(0.5) - 8(0.5)^3}\\\\\frac{dy}{dx}|(0,0.5) =\frac{-0.5}{-0.5} \\\\\frac{dy}{dx}|(0,0.5) =1\\\\m = \frac{dy}{dx}|(0,0.5) =1[/tex]
Step 4: The equation of the tangent line to a curve at a given point is given by the equation:
[tex]y - y_1 = m(x-x_1)\\\\y - 0.5 = 1(x - 0)\\\\y = x + 0.5[/tex]
If four times the brother's age is subtracted from three times the sister's age, the difference is 17. Give an equation that represents this statement using bbb as the age of the brother and s as the age of the sister.
Answer:
3s-4bbb=17
Step-by-step explanation:
brother=4bbb
sister=3s
3s-4bbb=17
Solve for y in terms of x.
IN
2
y - 4 = x
Oy= = x + 6
Oy
y = -x + 4
Oy
y = -x + 6
O
y =
X+ 4
Answer:
[tex]\boxed{\mathrm{Option \ 4}}[/tex]
Step-by-step explanation:
Given that
[tex]y-4 = x[/tex]
Adding 4 to both sides
[tex]y-4+4 = x+4\\[/tex]
[tex]y = x+4[/tex]
4, 12, 36,what is 3 other remaining sequence
Answer:
108, 324, 972
Step-by-step explanation:
This sequence is multiplying by ✖️3.
4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972
Hope this helps!
how many two third ounce slice of cheese in twenty four ounce package
Answer: 36
Step-by-step explanation:
Simply do 24/(2/3) to get 36 2/3 ounce slices.
Hope it helps <3
4.5/y = 12.5/4 PLEASE HELP!!! SOS
Answer:
y = 1.44
Step-by-step explanation:
What are you aiming to do here? Please share all instructions with each problem.
If you want to solve 4.5/y = 12.5/4 for y: Multiply both sides by 4y:
18 = 12.5y. Then y = 1.44
This function to calculate the area of a rectangle is not very readable. Can you refactor it, and then call the function to calculate the area with base of 5 and height of 6? Tip: a function that calculates the area of a rectangle should probably be called rectangle_area, and if it's receiving base and height, that's what the parameters should be called.
Answer:
Here is the refactored function:
def rectangle_area(base, height):
area = base * height
return area
print("The area is ", rectangle_area(5,6))
Step-by-step explanation:
The above program has a function rectangle_area that takes two variables base and height as parameters. The function then computes the area of rectangle by multiplying the values of base and height. The result of the multiplication is assigned to the variable area. Then the function returns the resultant area.
print("The area is ", rectangle_area(5,6)) statement calls rectangle_area() method by passing values of base and height i.e. 5 and 6 to compute the area. The output of this program is:
The area is 30
Note that the use of rectangle_area function name describes what the function does i.e. it computes the area of rectangle. By naming the parameters as base and height that clearly depicts that in order to compute rectangle are we need the base and height of rectangle. So this makes the code readable.
Which best describes the meaning of the statement if A then B
Answer:
[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]
Step-by-step explanation:
You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as "negation of a" or " b" in mathematical terms is written like this
[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]
You can show that they are logically equivalent because they have the same truth table.
WHY CAN'T ANYONE HELP ME: ( Two computer disks and three notebooks cost $29. However, five computer disks and four notebooks cost $48. Find the price of each.
Answer:
Disks = $4 each and Notebooks = $7 each
Step-by-step explanation:
-4(2D + 3N = 29)
3(5D + 4N = 48)
-8D - 12N = -116
15D + 12N = 144
7D = 28
D = $4
2(4) + 3N = 29
8 + 3N = 29
3N = 21
N = $7
An ice sculpture is melting at a constant rate. It's weight changes -1 4/5 pounds every hour. What is the total change in weight of the sculpture after 3 1/2 hours?
Answer:
It will decrease by 6 3/10 lbs in the 3 1/2 hours
Step-by-step explanation:
The rate is -1 4/5 lbs per hour
The time is 3 1/2 hours
Multiply to find the weight change
-1 4/5 * 3 1/2
Change to improper fractions
- ( 5*1 +4) /5 * ( 2* 3+1)/2
- 9/5 * 7/2
-63/10
Changing back to a mixed number
-6 3/10
It will decrease by 6 3/10 lbs in the 3 1/2 hours
Answer:
-6 3/10 pounds
Step-by-step explanation:
The weight of ice sculpture changes -1 4/5 pounds every 1 hour.
In 3 1/2 hours, multiply the time with the weight.
-1 4/5 × 3 1/2
Multiply.
-9/5 × 7/2
-63/10 = -6 3/10