Find the sum of the following series. 14 n=1 (2n+1)

A. 448
B. 256
C. 240
D. 224

Answer:

C

Step-by-step explanation:

A geometric series will only converge if - 1 < r < 1

sum to infinity = [tex]\frac{a}{1-r}[/tex]

The nth term formula for a geometric series is

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

The only summation with - 1 < r < 1 is C where r = - 0.2

Answer:  The correct option is

(C) [tex]\sum_{n=1}^{\infty}4(-0.2)^{n-1}.[/tex]

Step-by-step explanation:  We are give to select the geometric series that converges.

We know that

the general (n-th) term of a common geometric series is given by

[tex]a_n=ar^{n-1}.[/tex]

And the series converges if the modulus of the common ratio is less than 1, .e., |r| < 1.

Now, for the first infinite geometric series, we have

[tex]a_n=\dfrac{2}{3}(-3)^{n-1}.[/tex]

So, the common ratio will be

[tex]r=-3~~~\Rightarrow |r|=3>1.[/tex]

That is, the series will not converge. Option (A) is incorrect.

For the second geometric series, we have

[tex]a_n=5(-1)^{n-1}.[/tex]

So, the common ratio will be

[tex]r=-1~~~\Rightarrow |r|=1.[/tex]

That is, the series will not converge. Option (B) is incorrect.

For the third geometric series, we have

[tex]a_n=4(-0.2)^{n-1}.[/tex]

So, the common ratio will be

[tex]r=-0.2~~~\Rightarrow |r|=0.2<1.[/tex]

That is, the series will CONVERGE. Option (C) is correct.

For the fourth geometric series, we have

[tex]a_n=0.6(-2)^{n-1}.[/tex]

So, the common ratio will be

[tex]r=-2~~~\Rightarrow |r|=2>1.[/tex]

That is, the series will not converge. Option (D) is incorrect.

Thus, (C) is the correct option.

The definition of a number line is a straight line with a "zero" point in the middle, with positive and negative numbers listed on either side of zero and going on indefinitely.

Answer:

818.4 in²

Step-by-step explanation:

The area (A) of the shaded region is

A = area of circle - ( area of white sector + area of triangle )

  = ( π × 27.8²) - (π × 27.8² × [tex]\frac{210}{360}[/tex] +(0.5 × 27.8 ×27.8 × sin150°)

  = 2427.95 - (1416.30 + 193.21 )

  = 2427.95 - 1609.51 ≈ 818.4 in²

The probability that Craig will get a green gumdrop and a piece of butterscotch candy is 4/25.

To find the probability that Craig will get a green gumdrop and a piece of butterscotch candy, we need to calculate the probability of each event happening separately and then multiply those probabilities together.

There are 5 gumdrops in the first jar with 4 being green, so the probability of choosing a green gumdrop is 4/5. In the other jar, there are 5 pieces of candy with 1 being butterscotch, so the probability of choosing a butterscotch candy is 1/5. Multiplying these probabilities together gives us 4/5 × 1/5 = 4/25.

Answer:

29119.66666...+14561.3333...=43681, 209ft^2, not square feet.

Step-by-step explanation:

"One side of a rectangle is 3 feet shorter than twice the other side find the sides if the area is 209 feet squared"

Ok, so this is a tricky one- 209 feet squared, not 209 square feet, therefore the area is 209^2, or 43,681.

Next, let's define our variables-

x= the "other side"

z= 3 feet shorter than twice side

We can now make these (useful) equations

z=2x-3

43681= (2x-3)+x

We will focus on the latter for now-

Simplify

43681= (2x-3)+x

43681= 2x-3+x

43681= 3x-3

+3

43684=3x

/3

14561.3333...=x

z=2x-3

z=2*(14561.3333)-3

z=29119.66666....

29119.66666...+14561.3333...=43681

The answer would be....:B.90 ML

The volume of the solution should be given to a cat that weighs 8 lbs. is 9 ml. Thus, the correct option is D.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

The weight of the cat is 8 lbs. Therefore, the weight of the cat in kg will be,

Weight of cat = 8 lbs = (8×0.454) kgs = 3.632 kgs

Since for one kg, the recommended dose is 5 mg, therefore, the recommended dose for the cat will be,

Recommended dose for cat = 3.632kg × 5 = 18.16 mg

Now, as given that one ml of solution contains 2mg of drugs, therefore,

1 ml = 2mg

1 mg = 1/2 ml

18.16 mg = 18.16 × 1/2 = 9.08ml ≈ 9 ml

Hence, the volume of the solution should be given to a cat that weighs 8 lbs. is 9 ml. Thus, the correct option is D.

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Answer:

Step-by-step explanation:

(5) x^2 + 16 is a perfect square binomial only if imaginary roots are allowed.

x^2 + 16 = (x + 4i)(x - 4i)

(6)  x^4 + 12x^2 + 36 is a perfect square trinomial.  

The square root of x^4 is x^2 and the square root of 36 is 6.

Experimenting, we find that  x^4 + 12x^2 + 36 = (x² + 6)²

so we can conclude that x^4 + 12x^2 + 36 = (x² + 6)(x² + 6) = (x² + 6)².

ANSWER

18. No extraneous solution.

19. The extraneous solution is x=-2

EXPLANATION

18. The given radical equation is:

[tex] \sqrt{3x - 2} = x[/tex]

Solving this radical equation yields

[tex]x=1,x=2[/tex]

We check for an extraneous solution by substituting each value into the equation.

Checking for x=1,

[tex] \sqrt{3 \times 1 - 2} = 1[/tex]

[tex]\sqrt{3- 2} = 1[/tex]

[tex]\sqrt{1} = 1[/tex]

[tex]1 = 1[/tex]

This is true.

Checking for x=2

[tex]\sqrt{3 \times 2- 2} = 2[/tex]

[tex]\sqrt{6- 2} = 2[/tex]

[tex]\sqrt{4} = 2[/tex]

[tex]2 = 2[/tex]

This is also true. Hence there is no extraneous solution.

19. The given radical equation is:

[tex] \sqrt{x + 6} = x[/tex]

Solving this equation yields,

[tex]x=3,x=-2[/tex]

Checking for x=3,.

[tex]\sqrt{3+ 6} = 3[/tex]

[tex] \sqrt{9} = 3[/tex]

3=3.

This is a true solution.

Checking for x=-2.

[tex]\sqrt{ - 2 + 6} = - 2[/tex]

[tex] \sqrt{4} = - 2[/tex]

[tex]2 \ne - 2[/tex]

Hence x=-2 is an extraneous solution.

Answer:

(4, - 2 )

Step-by-step explanation:

To find the x- coordinate substitute y = - 2 into the equation

y + 2 = - 3(x - 4), thus

- 2 + 2 = - 3x + 12

0 = - 3x + 12 ( subtract 12 from both sides )

- 12 = - 3x ( divide both sides by - 3)

4 = x

Answer:

b

Step-by-step explanation:

Answer: 26

Step-by-step explanation:

Add all together and the subtract by 12434.7 and you get 26 hope this helps!

Answer:

The value of x is x

Step-by-step explanation:

Answer: x = 5

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

The area= 25

The square root of 25=5

So we know that 2 sides are 5

5×4=20

Multiply 5 by 4 because squares have all sides of the same length, so the remaining 2 sides are 5.

Answer: [tex]-x^2-x+9[/tex]

Step-by-step explanation:

To simplify the given polynomial [tex]2x^2+6x-7x+8-3x^2+1[/tex] we need to add the like terms. Then we get:

[tex]2x^2+6x-7x+8-3x^2+1=(2x^2-3x^2)+(6x-7x)+(8+1)=-x^2-x+9[/tex]

Therefore, we get that the polynomial simplified is:

[tex]-x^2-x+9[/tex]

Which is a trinomial ( A polynomial that has three terms) of degree 2 (Because the highest exponent is 2).

Answer:

Final answer is [tex]-x^2-x+9[/tex].

Step-by-step explanation:

Given polynomial is [tex]2x^2+6x-7x+8-3x^2+1[/tex].

Now we need to simplify the given polynomial so we can begin with combining like terms.

[tex]2x^2+6x-7x+8-3x^2+1[/tex]

[tex]=2x^2-3x^2+6x-7x+8+1[/tex]

[tex]=(2-3)x^2+(6-7)x+(8+1)[/tex]

[tex]=(-1)x^2+(-1)x+(9)[/tex]

[tex]=-x^2-x+9[/tex]

Hence final answer is [tex]-x^2-x+9[/tex].

Answer:

25%

Step-by-step explanation:

Percentages are one of several ways of describing quantities' relationships to one another. Specifying one number as a percentage of another means specifying the fraction of the second quantity the first comprises. The percentage value is the number that, divided by 100, equals that fraction. To express the percentage as a whole number, round it accordingly. Some applications, however, don't require percentages as exact whole figures.

Divide the first number the second. For instance, if you want to find what percentage 43 is out of 57, divide 43 by 57 to get 0.754386.

ANSWER

A.

[tex] \frac{1}{64} [/tex]

EXPLANATION

The given expression is:

[tex] {4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } [/tex]

Recall that:

[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]

We apply this property to obtain:

[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ - \frac{11}{3} - - \frac{2}{3} } [/tex]

Collect LCM

[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ \frac{ - 11 + 3}{3}} [/tex]

Simplify;

[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ \frac{ - 9}{3}} [/tex]

.

[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ - 3} [/tex]

[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = \frac{1}{ {4}^{3} } [/tex]

[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = \frac{1}{64} [/tex]

The first choice is correct

Answer:

y - 3 = a(x + 1)^2

Step-by-step explanation:

The vertex equation of a vertical parabola is:

y - k = a(x - h)^2.

If the vertex is at (-1, 3), then the equation becomes:

y - 3 = a(x + 1)^2, where a is a constant.

Next time, would you please share the answer choices.  Thank you.

Answer:

Step-by-step explanation:

all parabola have equation : y = a(x +1)²+3   a in R

Answer:

A rotation is when a shape rotates across the x or y axis on a coordinate plane :)

Step-by-step explanation:

the answer is 11.

use BEDMAS, and calculate the equation inside the brackets (answer to that is 44/15)

then divide it by 4/15 and you get 11

let's firstly convert the mixed fractions to improper fractions and proceed.

[tex]\bf \stackrel{mixed}{4\frac{1}{3}}\implies \cfrac{4\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{13}{3}}~\hfill \stackrel{mixed}{1\frac{2}{5}}\implies \cfrac{1\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{7}{5}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{recall that by PEMDAS, parenthesis first}~\hfill }{\left(\cfrac{13}{3}-\cfrac{7}{5} \right)\div \cfrac{4}{15}\implies \left(\stackrel{\textit{using an LCD of 15}}{\cfrac{(5)13-(3)7}{15}} \right)\div \cfrac{4}{15}\implies \left(\cfrac{65-21}{15} \right)\div \cfrac{4}{15}} \\\\\\ \left(\cfrac{44}{15}\right)\div \cfrac{4}{15}\implies \cfrac{44}{15}\times \cfrac{15}{4}\implies \cfrac{44}{4}\cdot \cfrac{15}{15}\implies 11\cdot 1\implies 11[/tex]

Answer:

Step-by-step explanation:

The formula of an area of a triangle:

[tex]A_\triangle=\dfrac{1}{2}ab\sin\theta[/tex]

a, b - adjacent sides

θ - included angle

=============================================

7.

a = 9in, b = 14in, θ = 85°

sin85° ≈ 0.9962

Substitute:

[tex]A_\triangle=\dfrac{1}{2}(9)(14)\sin85^o=\dfrac{1}{2}(126)(0.9962)\approx62.8 in^2[/tex]

8.

a = 12 in, b = 5 in, θ = 135°

sin135° = sin(180° - 45°) = sin45° ≈ 0.7071   used sin(180° - x) = sin(x)

Substitute:

[tex]A_\triangle=\dfrac{1}{2}(12)(5)\sin135^o=\dfrac{1}{2}(60)(0.7071)\approx21.2\ in^2[/tex]

Answer:

Step-by-step explanation:

Put x = -4 to f(x) = 2x² - x + 9:

f(-4) = 2(-4)² - (-4) + 9 = 2(16) + 4 + 9 = 32 + 4 + 9 = 45

Answer:

Step-by-step explanation:

The volume of a cone is

V = (1/3) * pi * r^2 * h

pi = 3.14

r = 3

h = 8

V = 1/3 * 3.14 * 3^2 * 8

V = 1/3 * 3.14 * 9 * 8

V = 75.36

V = 75.4

Answer:

38.

Step-by-step explanation:

range is taking the highest number subtracting it by the smallest

Answer:

the answer is 38

Step-by-step explanation:

you subtract the biggest number with smallest number

Answer:

C. or D. I would say D though.

Step-by-step explanation:

All you have to do is look at the total with both children and adults, then you can take that and divide it by the total of either children or adults and then you would get the answer D.

Answer: B

Step-by-step explanation:

Step-by-step explanation:

[tex]\sqrt{m^6}=\sqrt{m^{3\cdot2}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(m^3)^2}\qquad\text{use}\ \sqrt{a^2}=|a|\\\\=|m^3|\\\\\text{if}\ m\geq0,\ \text{then}\ \sqrt{m^6}=m^3\\\\\text{if}\ m<0,\ \text{then}\ \sqrt{m^6}=-m^3[/tex]

Answer:

1336 phones

Step-by-step explanation:

The average battery life of 2800 manufactured cell phones has a normal distribution.

The mean battery life is 14 hours, therefore: μ = 14 hours.

The standard deviation is 0.5 hours, therefore: σ = 0.5 hours.

To find the number of phones who have a battery life in the 13 to 14 range, we're going to ask for the help of a calculator. The probability of finding phones who have a battery life in the 13 to 14 range is: 0.4772. (See attached picture)

Therefore, the number of phones who have a battery life in the 13 to 14 range is: 0.4772×2800 = 1336,16 ≈ 1336 phones.

Final answer:

To find the number of phones with a battery life between 13 and 14 hours, calculate the z-scores, find the corresponding percentage using the standard normal distribution, and then multiply by the total number of phones, resulting in approximately 1336 phones.

Explanation:

The question asks for the number of cell phones with a battery life in the 13 to 14 hour range out of 2800 phones where the mean battery life is 14 hours with a standard deviation of 0.5 hours. The battery life is normally distributed.

To find this number, we need to calculate the z-scores for 13 and 14 hours and then determine the percentage of phones between those z-scores. The z-score for 13 hours is (13 - 14)/0.5 = -2 and for 14 hours is (14 - 14)/0.5 = 0. Using the standard normal distribution table, the area under the curve from -2 to 0 is approximately 47.7%. Therefore, the number of phones with battery life between 13 and 14 hours is 0.477 * 2800 ≈ 1336 phones.

A. 272 1/4 ft

B. 68 5/8 ft

Hope this helps!

Shannon and Leslie need to carpet 272.25 square feet in a room with an entertainment system that takes up 12.25 square feet. Therefore, they need to buy 12.25 square feet of carpet.

Shannon and Leslie are planning to carpet a square room that measures 16.5 feet by 16.5 feet. However, they need to account for an entertainment system that juts out into the room, taking up 3.5 feet by 3.5 feet of space.

A. Area of the space with no carpet:

To determine the area of the space with no carpet, we first calculate the area of the entertainment system:

Area of entertainment system = 3.5 feet * 3.5 feet = 12.25 square feet

Next, we subtract the area of the entertainment system from the total area of the room:

Total area of room - area of entertainment system = area of space with no carpet

272.25 square feet - 12.25 square feet = 260 square feet

Therefore, the area of the space with no carpet is 260 square feet.

B. Carpet needed for the room:

To calculate the amount of carpet Shannon and Leslie need to buy, we simply subtract the area of the space with no carpet from the total area of the room:

Total area of room - area of space with no carpet = area of carpet needed

272.25 square feet - 260 square feet = 12.25 square feet

Shannon and Leslie need to buy 12.25 square feet of carpet.

Answer:

y-intercept = (0,2).

Step-by-step explanation:

We have been given a table of the function g(x) as shown below:

x g(x)

0 2

1 6

2 10

Using that table we need to find about what is the y-intercept of the given function g(x).

By definition of y-intercept, we know that, y-intercept is the y-value or function value of g(x) value when x=0.

From table we see that g(x)=2 when x=0.

So the y-intercept = 2.

In point form we can write y-intercept as (0,2).

Answer: y= 4/3x-9

Step-by-step explanation:

The equation 8x - 6y = 54 can be converted to slope-intercept form (y = mx + b) by isolating y. The steps involve rearranging terms and simplifying to yield the equation: y = (4/3)x - 9.

First, you want to manipulate your equation: 8x - 6y = 54 into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Here are the steps:

Therefore, the equation 8x - 6y = 54 in slope intercept form is y = (4/3)x - 9.

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Answer:

Option D. [tex]cos(54\°)=\frac{0.5s}{7}[/tex]

Step-by-step explanation:

we know that

A regular pentagon can be divided into 5 isosceles triangles

The length side of the legs of one isosceles triangle is equal to the radius

The vertex angle of one isosceles triangle is equal to 360/5=72 degrees

The base angle of one isosceles triangle is equal to 54 degrees

Let

s------> the length side of the regular pentagon

so

[tex]cos(54\°)=\frac{(s/2)}{r}[/tex]

substitute the given value

[tex]cos(54\°)=\frac{(s/2)}{7}[/tex]

[tex]cos(54\°)=\frac{0.5s}{7}[/tex]