Answers
Answer:
False
Step-by-step explanation:
We have the serie:
[tex]\frac{1}{49}+ \frac{1}{64} + \frac{1}{81}+...[/tex]
To test whether the series converges or diverges first we must find the rule of the series
Note that:
[tex]7^2 = 49\\\\8^2 = 64\\\\9^2 = 81[/tex]
Then we can write the series as:
[tex]\frac{1}{7^2}+ \frac{1}{8^2} + \frac{1}{9^2}+...[/tex]
Then:
[tex]\frac{1}{7^2}+ \frac{1}{8^2} + \frac{1}{9^2}+... = \sum_{n=7}^{\infty}\frac{1}{n^2}\\\\\sum_{n=7}^{\infty}\frac{1}{n^2} = \sum_{n=1}^{\infty}\frac{1}{(n+6)^2}[/tex]
The series that have the form:
[tex]\sum_{n=1}^{\infty}\frac{1}{n^p}[/tex]
are known as "p-series". This type of series converges whenever [tex]p > 1[/tex].
In this case, [tex]p = 2[/tex] and [tex]2 > 1[/tex]. Then the series converges
Related Questions
The volume of a prism is 48 cubic centimeters. If the length is 2 centimeters and the width is 4 centimeters. What is the height?
Answers
Answer:
6
Step-by-step explanation:
volume is (lwh) since youre trying to find the height just multiply the 2 and 4 together to get 8. Then divide 8 by 48 to get your height.
The following shape is NOT a polygon because:
Answers
Answer:
The shape includes a curve.
Step-by-step explanation:
A polygon consists of joined straight lines - no curves.
Match each expression to its equivalent expression with a rational denominator.
Answers
Answer: BCDA
Step-by-step explanation:
[tex]\dfrac{1}{\sqrt[4]{3x^3y^5}}\\\\\\\text{Since it is a 4th root, you need 4 on the "inside" to make 1 on the "outside"}\\=\dfrac{1}{y\sqrt[4]{3x^3y}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{1}{y\sqrt[4]{3x^3y}}\bigg(\dfrac{\sqrt[4]{3^3xy^3} }{\sqrt[4]{3^3xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{\sqrt[4]{3^3xy^3} }{y(3xy)}\\\\\\\boxed{=\dfrac{\sqrt[4]{3^3xy^3} }{3xy^2}}\quad Option\ B[/tex]
[tex]\dfrac{3}{\sqrt[4]{3^3x^{11}y^{13}}}\\\\\\\text{Since it is a 4th root, you need 4 on the "inside" to make 1 on the "outside"}\\=\dfrac{3}{x^2y^3\sqrt[4]{3^3x^3y}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{3}{x^2y^3\sqrt[4]{3^3x^3y}}\bigg(\dfrac{\sqrt[4]{3xy^3} }{\sqrt[4]{3xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{3\sqrt[4]{3xy^3} }{x^2y^3(3xy)}\\\\\\\boxed{=\dfrac{\sqrt[4]{3xy^3} }{x^3y^4}}\quad Option\ C[/tex]
[tex]\dfrac{2}{\sqrt[6]{2x^7y^5}}\\\\\\\text{Since it is a 6th root, you need 6 on the "inside" to make 1 on the "outside"}\\=\dfrac{2}{x\sqrt[6]{2xy^5}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{2}{x\sqrt[6]{2xy^5}}\bigg(\dfrac{\sqrt[6]{2^5x^5y} }{\sqrt[6]{2^5x^5y}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{2\sqrt[6]{32x^5y} }{x(2xy)}\\\\\\\boxed{=\dfrac{\sqrt[6]{32x^5y} }{x^2y}}\quad Option\ D[/tex]
[tex]\dfrac{4}{\sqrt[6]{2^5x^5y^9}}\\\\\\\text{Since it is a 6th root, you need 6 on the "inside" to make 1 on the "outside"}\\=\dfrac{4}{y\sqrt[6]{2^5x^5y^3}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{4}{y\sqrt[6]{2^5x^5y^3}}\bigg(\dfrac{\sqrt[6]{2xy^3}}{\sqrt[6]{2xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{4\sqrt[6]{2xy^3} }{y(2xy)}\\\\\\\boxed{=\dfrac{2\sqrt[6]{2xy^3} }{xy^2}}\quad Option\ A[/tex]
Tom had $56. He bought a soda for $2 and 2 cookies for $3. Which expression correctly shows the total money Tom has left? A. $56 + (?$2) + (?$3) B $56 + (?$2) ? (?$3) C $56 ? (?$2) ? (?$3) D $56 ? (?$2) + (?$3)
Answers
C ($56) - ($2) - ($3)
Answer:
I believe it's A
Step-by-step explanation:
Sorry if wrong ;-;
please help me!!!!!!!
Answers
Answer:
I would think the answer would be 35
Step-by-step explanation:
Step 1: Round your answer to 2 decimal places.
Step2: Divide or Multiply your answer you got by 2.
cos42= 35/y
y=35/cos42
y= 47.10
is the answer
Find the point of intersection of the lines: y = 4x + 1 and y = – 2x + 4 A. (2 , 9) B. ( 1 2, 3 ) C. (1 , 2) D. ( 1 4, 2)
Answers
Answer:
B. (1/2, 3)
Step-by-step explanation:
It is perhaps easiest to try the point values in the equations.
A — 4·2+1 = 9; -2·2 +4 ≠9 . . . . not the answer
B — 4·1/2 +1 = 3; -2·(1/2) +4 = 3 . . . . this is the answer
we need go no further since we have the answer
To find the point of intersection, solve the system of equations formed by the two lines. Substituting x=1 into either equation gives y=5. Therefore, the point of intersection is (1,5).
Explanation:To find the point of intersection of two lines, we need to solve the system of equations formed by the two lines. In this case, the equations are y = 4x + 1 and y = -2x + 4.
Setting the equations equal to each other, we have 4x + 1 = -2x + 4. Solving for x, we get x = 1.
Substituting x = 1 into either of the original equations, we find y = 4(1) + 1 = 5. Therefore, the point of intersection is (1, 5).
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Problem Page Manuel drove 871 miles in 13 hours. At the same rate, how long would it take him to drive 603 miles?
Answers
Answer:
9 hours.
Step-by-step explanation:
Average rate = distance / time
= 871 / 13
= 67 mph
So the time to travel 603 miles
= distance / rate
= 603 / 67
= 9 hours.
the graph of F(x), shown below, has the same shape as the graph of G(x)=x^4. but it is shifted 3 units to the right. which is its equation.
Answers
Answer:
C. F(X) = (X - 3)⁴
Step-by-step explanation:
Hope this helps you.
The graph of F (x) will be;
⇒ F (x) = (x - 3)⁴
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The function G (x) is,
⇒ G (x) = x⁴
And, The function of G (x) is shown in figure.
And, It is shifted 3 units to the right.
Now,
Here, The function G (x) is,
⇒ G (x) = x⁴
Since, The function of G (x) is shown in figure.
And, It is shifted 3 units to the right.
So, The function of F(x) become;
⇒ F (x) = (x - 3)⁴
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You have 6 large candy bars. You want to split each one into thirds. How many candy bar pieces will you then have?
Answers
Answer:
[tex]18\ pieces[/tex]
Step-by-step explanation:
step 1
Divide each large candy bar into thirds
so
[tex]\frac{1}{3}[/tex]
Now for each large candy bar you have 3 pieces of [tex]\frac{1}{3}[/tex]
step 2
Find the total number of candy bars pieces by proportion
[tex]\frac{1}{3}\frac{bar}{pieces} =\frac{6}{x}\frac{bar}{pieces}\\ \\x=6*3\\ \\x=18\ pieces[/tex]
Final answer:
To determine the total number of candy bar pieces after splitting 6 large bars into thirds, you multiply 6 by 3 resulting in 18 pieces.
Explanation:
The student's question is about dividing candy bars into thirds. If you start with 6 large candy bars and want to split each one into thirds, you end up with 6 groups of 3 pieces. To find the total number of candy bar pieces, you multiply the number of candy bars by the number of pieces you want to make from each bar, which is:
6 bars × 3 pieces per bar = 18 pieces.
Therefore, after splitting all the large candy bars into thirds, you will have a total of 18 candy bar pieces.
Holly has a rectangular garden that measures 12 m wide by 14 m long. She wants to increase the area to 255 m? by increasing the width and length by the same amount. What will be the length (longer dimension) of the new garden? Enter your answer in the box.
Answers
Answer:
255 square meters
Step-by-step explanation:
Present area = 12 * 14 = 168 square meters
The area has to increase by a factor of 255 / 168 = 1.5178571429
Therefore, the width and length are increased by a factor of the
square root of 1.5178571429 = 1.2320134508
So the width becomes
12 * 1.2320134508 = 14.7841614091
and the length becomes
14 * 1.2320134508 = 17.2481883107
That's roughly 14.78 by 17.25 and the area equals
14.78 * 17.25 = 255 square meters
Answer: The answer is 17
Step-by-step explanation:
find the missing sides. Brainliest!!
Answers
Answer:
1. x = 28; y = 14√3
2. x = 9√2
Step-by-step explanation:
For these, it is helpful to remember that the side lengths of a 30°-60°-90° triangle have the ratio 1 : √3 : 2, and those of a 45°-45°-90° triangle have the ratio 1 : 1 : √2.
1. 14 is the shortest side, and x is the longest side, so ...
x = 2·14 = 28
y = (√3)·14 = 14√3
__
2. 18 is the longest side and x is the shortest side of this 45°-45°-90° triangle, so ...
x·√2 = 18
x = 18/√2 = 18·(√2)/2 = 9√2
Triangle ABC has vertices at A(–2, 3), B(–3, –6), and C(2, –1). Is triangle ABC a right triangle? If so, which angle is the right angle? No, the triangle has no right angles. Yes, the right angle is angle A. Yes, the right angle is angle B. Yes, the right angle is angle C.
Answers
Answer:
Yes, the right angle is angle C.
Step-by-step explanation:
The given triangle has vertices at A(–2, 3), B(–3, –6), and C(2, –1).
Recall the slope formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The slope of the line going through AC is
[tex]m_{AC}=\frac{-1-3}{2--2}=-1[/tex]
The slope of the line going through BC s
[tex]m_{AC}=\frac{-1--6}{2--3}=1[/tex]
The product of the slopes of AC and BC is [tex]-1\times1=-1[/tex]
This means line AC is perpendicular to BC at C.
Hence the triangle ABC is right angled at C.
Answer:
Yes, the right angle is angle C.
Step-by-step explanation:
What term describes this polygon ?
Answers
Answer:
Step-by-step explanation:
The last one
I hope I helped you.
Polygons are closed figures based on a plane that are characterized by their sides and angles. Without an image or description of the polygon, it's impossible to identify the specific polygon indicated.
Explanation:In mathematics, polygons are divided based on many factors such as the number of sides, length of sides, angle measures, etc. However, without the image or description of the polygon, I can't definitively tell what polygon you're referring to. For example, a polygon could be anything from a triangle (3 sides) to a decagon (10 sides). Remember, a polygon is basically a closed figure formed by three or more sides in a plane.
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I dont understand anything
Answers
Answer:
D
Step-by-step explanation:
Answer:
The correct answer options are D and E.
Step-by-step explanation:
We are to determine whether which of the given data sets in the answer options are continuous.
For this, we need to know what a continuous data set is.
A data set which have no definite end to its value but keep on continuing.
Here, the data sets given in A, B and C have definite starting and ending points.
While D and E are continuous sets as its values are continuing.
13 ? start fraction, 13, divided by, 10, end fraction of a number is what percentage of that number?
Answers
Answer:
The percentage is [tex]130\%[/tex]
Step-by-step explanation:
Let
x-----> the number
we have
[tex]\frac{13}{10}x=1.3x[/tex]
To find the percentage multiply by 100
[tex]1.3*100=130\%[/tex]
(4CQ) Determine whether the series 3/2+9/8+27/32+...is convergent or divergent.
Answers
Answer:
The series is convergent ⇒ answer (a)
Step-by-step explanation:
* The series is 3/2 + 9/8 + 27/32 + ........
- It is a geometric series with:
- first term a = 3/2 and common ratio r = 9/8 ÷ 3/2 = 3/4
* The difference between the convergent and divergent
in the geometric series is :
- If the geometric series is given by sum = a + a r + a r² + a r³ + ...
* Where a is the first term and r is the common ratio
* If |r| < 1 then the following geometric series converges to a / (1 - r).
- Where a/1 - r is the sum to infinity
* The proof is:
∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number
∴ r^n approach to zero
∴ S = a(1 - 0)/(1 - r) = a/(1 - r)
∴ S∞ = a/1 - r
* If |r| ≥ 1 then the above geometric series diverges
∵ r = 3/4
∴ r < 1
∴ The series is convergent
A real estate broker's base salary is $18,000. She earns a 4% commission on total sales. How much must she sell to earn $55,000 total? Show your work and explain your reasoning in the space provided below.
Answers
The salary of the real estate broker = $18,000
Commission earned on total sales = 4% or 0.04
Total income earnings = $55,000
Let the total sales be = x
Equation becomes :
[tex]18000+0.04x=55000[/tex]
[tex]0.04x=55000-18000[/tex]
[tex]0.04x=37000[/tex]
[tex]x=925000[/tex]
Hence, the real estate broker must sell $925,000 worth of real estate to earn $55,000.
To earn $55,000 total, the real estate broker must sell $925,000 in total.
Explanation:To find out how much the real estate broker must sell to earn $55,000 total, we need to consider both her base salary and her commission. Let's set up an equation to solve for the total sales needed:
$18,000 + 0.04x = $55,000
Subtracting $18,000 from both sides gives:
0.04x = $37,000
Dividing both sides by 0.04 gives:
x = $925,000
Therefore, the real estate broker must sell $925,000 in total to earn $55,000.
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Find the inverse function of that problem! Please!!
Answers
Answer:
[tex]y=\frac{\sqrt{x} -8}{-2}[/tex]
Step-by-step explanation:
To find an inverse, switch x and y values in the equation. Then solve for y.
[tex]F(x) = (8-2x)^2\\x = (8-2y)^2\\\sqrt{x} = 8 - 2y\\\sqrt{x} -8 = -2y\\\frac{\sqrt{x} -8}{-2} =y[/tex]
23 points help asap!
Find the unit price and choose the better buy.
80 oz bottle of cleaner for $13.60
70 oz bottle of cleaner for $13.30
90 oz bottle of cleaner for $18.00
60 oz bottle of cleaner for $10.80
Answers
Answer:
60
Step-by-step explanation:
ITS THE BEST ONE
an 80 oz bottle of cleaner for $13.60 is the better buy because usually it would be about $40 for that size bottle
Which is true about the functional relationship shown in the graph?
Answers
Answer:
D
Step-by-step explanation:
For linear graphs, we say that the y-axis (y) is a function of the x-axis (x).
The y-axis shows earnings and the x-axis shows time worked (in hours). Thus, we can say that earnings is a function of the number of hours worked.
Looking at the answer choices, D is the correct choice.
Answer:
D
Step-by-step explanation:
I got it correct on A P E X
Simplify the expression. log(1/7)
Answers
Answer:
d. [tex]\frac{1}{7}[/tex]
Step-by-step explanation:
The given logarithm is
[tex]10^{\log(\frac{1}{7})}[/tex]
Recall that the common logarithm has a base of 10.
[tex]10^{\log(\frac{1}{7})}=10^{\log_{10}(\frac{1}{7})}[/tex]
Recall also that;[tex]p^{(\log_pa)}=a[/tex]
[tex]10^{\log(\frac{1}{7})}=10^{\log_{10}(\frac{1}{7})}=\frac{1}{7}[/tex]
Which situation describes DEPENDENT events? A) A die is rolled, the outcome is recorded, then a coin is tossed. B) A die is rolled, the outcome is recorded, then the same die is rolled again. C) A spinner is spun once, the outcome is recorded, then it is spun again. D) A card is drawn from a deck, then a second card is drawn from the same deck. Eliminate
Answers
Answer:
the answer is D
Step-by-step explanation:
[tex](x-4)^{2} ^+(y-3)^{2} =16[/tex]
Find the center and radius
(explanation please, I need help)
Answers
an equation for a circle has formula
(x-m)² + (y-n)² = r²
where (m,n) is its center
and r is its radius
so, the equation has center (4,3) and radius 4
the equation is derived from the pythagorean theorem
Please answer at least one of these questions!! Please state which question you answered too. Will give brainliest!
Answers
Answer:
15. 4.9 cm
17. 6.63 cm
Step-by-step explanation:
15. A perpendicular bisector is a segment which divides another in half. Since JH is 9.8 then each of the two segments it divides into is 4.9.
17. The segments within the circle form a right angle. Triangle CRS as a right triangle must follow the Pythagorean theorem which says the square of each leg adds to the square of the hypotenuse.
a² + b² = c²
Here a is unknown, b = 10 and c = 12.
a² + 10² = 12²
a² + 100 = 144
a² = 44
a = √44 = 6.63
An elevator has a placard stating that the maximum capacity is 23252325 lblong dash—1515 passengers. So, 1515 adult male passengers can have a mean weight of up to 2325 divided by 15 equals 155 pounds.2325/15=155 pounds. If the elevator is loaded with 1515 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 155155 lb. (Assume that weights of males are normally distributed with a mean of 161 lb161 lb and a standard deviation of 31 lb31 lb.) Does this elevator appear to be safe?
Answers
Answer:
0.7734; no, it does not.
Step-by-step explanation:
To find this probability we will use a z-score. We are dealing with the probability of a sample mean being larger than a given value; this means we use the formula
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
Our x-bar in this problem is 155, as that is the sample mean we are trying to find the probability of. Our mean, μ, is 161 and our standard deviation, σ, is 31. Our sample size, n, is 15. This gives us
[tex]z=\frac{155-161}{31\div \sqrt{15}}=\frac{-6}{8.0042}=-0.75[/tex]
Using a z table, we see that the area under the curve less than this, corresponding with probability less than this value, is 0.2266. This means that the probability of the sample mean being larger than this is
1-0.2266 = 0.7734, or 77.34%.
Since there is a 77.34% chance of the passengers having a mean weight that is too heavy, this elevator is not safe.
The probability that the elevator is overloaded using the normal distribution principle is 0.7870
Given the Parameters :
Mean, μ = 161Standard deviation, σ = 31 Sample size, n = 15X = 155Using the relation :
Zscore = (xbar - μ) ÷ (σ/√(n))
Zscore = (155 - 161) ÷ (31/√15)
Zscore = - 0.796
The probability that lift is overloaded can be expressed thus :
P(Z ≥ - 0.796) = 1 - P(Z ≤ - 0.796)
Using a normal distribution table ; PP(Z ≤ - 0.796) = 0.2130
P(Z ≥ - 0.796) = 1 - 0.2130
P(Z ≥ - 0.796) = 0.7870
Therefore, the probability that weight is overloaded is 0.7870
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Determine the slope of the line that has the following coordinates: (-3, 6) (4,-2)
Answers
Answer: [tex]m=-\frac{8}{7}[/tex]
Step-by-step explanation:
To calculate the slope of the line that has the coordinates given in the problem you must use the formula shown below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given the points (-3, 6) (4,-2), when you substitute them into the eequation shown above, you obtain that the slope is the following:
[tex]m=\frac{-2-6}{4-(-3)}\\m=-\frac{8}{7}[/tex]
Answer:
[tex] - \frac { 8 } { 7 } [/tex]
Step-by-step explanation:
We are given the following two points on a line and we are to find the slope of this line:
(-3, 6) and (4,-2)
We know the formula of the slope is given by:
[tex] \frac { y_2 - y_1 } { x_2 - x_1 } [/tex]
Substituting the given coordinates in the above formula to get:
Slope = [tex] \frac { - 2 - 6 } { 4 - - 3 } = - \frac { 8 } { 7 } [/tex]
Abott simplified an expression. His work is shown below.
Step 1
Step 2
Step 3
Step 4
45.5
In which step did Abott make his first mistake?
step 1
step 2
step 3
step 4
Mark this and return
Save and Exit Next Submit
Answers
Abott make his first mistake in step 2
Further explanationCalculation operations include multiply, divide, add, substract, etc.
In mathematical operations we can use the order of operation / calculation according to the principle of PEMDAS
P: Parentheses ⇒ ( ) E: Exponents (powers, square roots, etc.)⇒√,² MD: Multiplication and Division ⇒ x and : AS: Addition and Subtraction ⇒ + and -Multiplication and division or addition and subtraction are interchangeable/rank equally so the calculations/equation operations should be done from left to right
Abbot expression :
9.5 : 0.25 + + 4(0.25+0.5) + 6
Step 1 : 9.5 : 0.25 + + 4(0.75) + 6
Step 2 : 38 + 10(0.75)
Step 3 : 38 + 7.5
Step 4 : 45.5
From the Abott steps it can be concluded that the error occurred in step 2, because the number 4 must be multiplied first with the number in parentheses (ie 0.75)
The correct steps should:
step 1: Step 1: 9.5: 0.25 + 4 (0.75) + 6
Step 2: 38 + 3 + 6
Step 3: 38 + 9
Step 4: 47
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PEMDAS
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Answer:
Its B
Step-by-step explanation:
translate inequality: "half of the sum of a number and five is a maximum of ten"
Answers
Answer:
[tex]\frac{1}{2} (x+5)\leq 10[/tex]
Step-by-step explanation:
Half the sum of (1/2 * ) a number and five (x + 5) is a maximum of 10 (less than or equal to).
Answer:[tex]\frac{x+5}{2}\leq 10[/tex]
Step-by-step explanation:
upper text bottom text left text right text this is for min word req problem in picture
Answers
Replace x in the second equation with the value of x from the first one.
x = -3y
x + y = -6
-3y + y = -6
Simplify:
-2y = -6
Divide both sides by -2:
y = -6 / -2
y = 3
Now replace Y with 3 in one of the equations to solve for x:
x = -3y = -3(3) = -9
X = -9, Y = 3
(-9,3)
Solve by using proper methods. Show your work.
Determine the principal P that must be invested at 7%, compounded monthly, so that $200,000 will be available for retirement in 15 years?
Answers
Answer:
$70,201.38
Step-by-step explanation:
To determine the principal amount, we can use the formula:
[tex]P=\dfrac{A}{(1+\frac{r}{n})^{nt}}[/tex]
A = $200,000
r = 7% or 0.07
t = 15 years
n = 12
Now let's substitute our values.
[tex]P=\dfrac{200,000}{(1+\frac{0.07}{12})^{12(15)}}[/tex]
[tex]P=\dfrac{200,000}{(1.00583333333)^{12(15)}}[/tex]
[tex]P=70,201.38[/tex]
So the principal needed to get 200,000 in 15 years is $70,201.38.