(10CQ) The series 1/49+1/64+1/81+ ... is divergent.

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

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.

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.

Answer:

The shape includes a curve.

Step-by-step explanation:

A polygon consists of joined straight lines - no curves.

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 :

Using 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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Abott make his first mistake in step 2

Calculation operations include multiply, divide, add, substract, etc.

In mathematical operations we can use the order of operation / calculation according to the principle of PEMDAS

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

PEMDAS

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Answer:

Its B

Step-by-step explanation:

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

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]

C ($56) - ($2) - ($3)

Answer:

I believe it's A

Step-by-step explanation:

Sorry if wrong ;-;

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.

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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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).

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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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.

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]

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

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.

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

Answer:

the answer is D

Step-by-step explanation:

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]

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

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]

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:

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]

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)

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

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.

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:

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

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:

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

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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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.

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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