6. Andre and Elena are each saving money. Andre starts with $100 in his savings account and adds $5 per week. Elena starts with $10 in her savings account and adds $20 each week.
a. After four weeks, who has more money in the
who has more money in their savings account? Explain how you know.
b. after how many weeks will Andre and Elena have the same amount of money in their savings
accounts?

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.

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

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:

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:

15

Step-by-step explanation:

Answer:

y = -5

Step-by-step explanation:

You are solving for y. You want to know which value of y makes the equation true. You must end up with y alone on the left side equaling a number.

12y + 25 = -35

First, subtract 25 from both sides.

12y + 25 - 25 = -35 - 25

12y = -60

Now divide both sides by 12.

12y/12 = -60/12

y = -5

Answer: y = -5

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: 26

Step-by-step explanation:

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

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:

Answer:

C log (20) - log (3)

Step-by-step explanation:

log (a/b) = log (a) - log (b)

log (20/3) = log (20) - log (3)

Answer: C. log (20) - log (3)

Step-by-step explanation: a p e x /\ dude above me is right too

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: 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.

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

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:

b

Step-by-step explanation:

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:

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:

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:

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.

Answer:

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

Step-by-step explanation:

Answer: [tex]y=-\frac{1}{2}x+6[/tex]

Step-by-step explanation:

The equation of the line is slope-intercept form is:

[tex]y=mx+b[/tex]

Where m is the slope and b thte y-intercept.

The lines are parallel, then they have the same slope.

Solve for "y"  from  [tex]2x+4y=10[/tex] to find the slopes of the lines :

[tex]2x+4y=10\\4y=-2x+10\\y=-\frac{1}{2}x+\frac{5}{2}[/tex]

The  value of the slopes of the lines is:

[tex]m=-\frac{1}{2}[/tex]

Substitute the slope and the point into the equation of the line and solve for "b":

[tex]2=-\frac{1}{2}(8)+b\\2=-4+b\\b=6[/tex]

Then the equation of this line is:

[tex]y=-\frac{1}{2}x+6[/tex]

The answer is:

The equation of the new line will be:

[tex]y=-0.5x+6[/tex]

or

[tex]y=-\frac{1}{2}x+6[/tex]

To solve the problem, we need to remember the slope intercept form of a line.

The slope intercept form of a line is given by the following equation:

[tex]y=mx+b[/tex]

Where,

y, is the function.

x, is the variable of the function.

m, is the pendant of the line.

b, is the y-axis intercept of the line.

So, we are given the line that will be parallel to the line that we are looking for:

[tex]2x+4y=10\\4y=-2x+10\\4y=-2(x-5)\\y=\frac{-2}{4}*(x-5)\\\\y=-\frac{1}{2}*(x-5)\\\\y=-\frac{1}{2}x+\frac{5}{2}[/tex]

Where,

[tex]m=-\frac{1}{2}[/tex]

Then,

We need to use the same slope to guarantee that the new line will be parallalel to the given line-

So, our new line will have the following form:

[tex]y=-\frac{1}{2}x+b[/tex]

We need to substitute the given point to isolate "b" in order to guarantee that the line will pass through.

Now, substituting the given point,  to calculate"b", we have:

Calculating b, we have:

[tex]2=-\frac{1}{2}8+b[/tex]

[tex]2=-4+b[/tex]

[tex]2+4=b[/tex]

[tex]6=b[/tex]

Hence, we have that the equation of the new line will be:

[tex]y=-0.5x+6[/tex]

or

[tex]y=-\frac{1}{2}x+6[/tex]

Proving that the line will pass through the given point, by substituting it into its equation, we have:

[tex]2=-0.5(8)+6[/tex]

[tex]2=-4+6[/tex]

[tex]2=2[/tex]

So, since the equality is satisfied, we know that the line pass through the new line.

Have a nice day!

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]

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

Answer: 314÷13

..............................................................................

Answer:

13/314

Step-by-step explanation:

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).

The quadratic formula is [tex]\frac{-b+-\sqrt[2]{b^2-4ac}}{2a}[/tex]

and in the equation ax^2+bx+c=0

so now all you have to do is substitute the numbers into the quadratic formula

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:

(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:

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

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].

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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