Algebra 1A, I need help

The series converges, since |8/9| = 8/9 < 1.

Let [tex]S_n[/tex] denote the n-th partial sum of the series,

[tex]S_n=\displaystyle\sum_{k=0}^n\left(\frac89\right)^k[/tex]

[tex]S_n=1+\dfrac89+\left(\dfrac89\right)^2+\cdots+\left(\dfrac89\right)^n[/tex]

Multiply both sides by 8/9:

[tex]\dfrac89S_n=\dfrac89+\left(\dfrac89\right)^2+\left(\dfrac89\right)^3+\cdots+\left(\dfrac89\right)^{n+1}[/tex]

Subtract this from [tex]S_n[/tex] to eliminate all but the first term in

[tex]S_n-\dfrac89S_n=1-\left(\dfrac89\right)^{n+1}[/tex]

Solve for [tex]S_n[/tex]:

[tex]\dfrac19S_n=1-\left(\dfrac89\right)^{n+1}[/tex]

[tex]S_n=9-9\left(\dfrac89\right)^{n+1}[/tex]

As [tex]n\to\infty[/tex], the exponential term vanishes, so that

[tex]\displaystyle\lim_{n\to\infty}S_n=\sum_{k=0}^\infty\left(\frac89\right)^k=\boxed{9}[/tex]

Answer:

3/10. 0/0_____________

Answer:

235=30x-25

Step-by-step explanation:

235+25=30x-25+25

260=30x

260/30=30x/30

x=8.66 or 9 weeks

The equation is 30x + 25 = 235. And the number of weeks will be 7.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Greg is saving to purchase a tablet that costs $235. He as of now has $25 set aside. Every week, Greg procures $15 looking after children and $25 as a clerk, however, he burns through $10 on snacks.

Let x be the number of weeks. Then the equation is given as,

25x + 15x - 10x + 25 = 235

Simplify the equation, then the number of weeks is given as,

25x + 15x - 10x + 25 = 235

30x = 235 - 25

30x = 210

x = 210 / 30

x = 7 weeks

The equation is 30x + 25 = 235. And the number of weeks will be 7.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Answer:

5/136

Probability is the chance of an event happening.

Probability = (Favorable outcome)/(total outcome)

P(r and n) = 2/17 × 5/16

=(2 × 5)/(17 × 16)

= 10/272

= 5/136

Answer:

5/136, or about 3.68%

Step-by-step explanation:

There are 17 total books on the bookshelf and only two of them are reference books, so the probability that you randomly grab a reference book is 2 out of 17, or 2/17.

Now that you took out a reference book (and did not put it back) there are 16 books on the bookshelf and you know five of them are nonfiction. That means the probability of getting a nonfiction book on your second grab is 5/16.

To find the probability that both of these events happen, you multiply the two fractions together.

2/17 x 5/16 = 10/272, which can reduce to 5/136, or about 3.68%

Answer:

B: (5,1)

Step-by-step explanation:

So we have the system of equations:

[tex]x+y=6\text{ and}\\y+4=x[/tex]

We can solve this system using substitution.

Substitute the second equation into the first. Use x. So:

[tex](y+4)+y=6[/tex]

Combine like terms:

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

Subtract 4 from both sides:

[tex]2y=2[/tex]

Divide both sides by 2:

[tex]y=1[/tex]

So, the value of y is 1.

To find x, substitute this back into the second equation:

[tex]y+4=x[/tex]

Substitute 1 for y:

[tex]1+4=x[/tex]

Add:

[tex]x=5[/tex]

Therefore, our answer is (5,1).

The answer is B.

And we're done!

Answer:

p = 6

Step-by-step explanation:

Divide 6 by both sides to get p. 36/6 is equal to 6

Answer:  p =6

Step-by-step explanation:

if p times 6  is 36  or   6p =36  

Then to  find p divide both sides by 6

6p = 36

p = 6

Answer:

A conditional statement is false if hypothesis is true and the conclusion is false.

Step-by-step explanation:

Conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences.

Reasoning in maths is the process of applying logical and critical thinking to a mathematical problem in order to work out the correct strategy to use  in reaching a solution

A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences.

For this conditional statement, P is called the hypothesis and Q is called the conclusion.

“If P then Q” means that Q must be true whenever P is true.

We have a conditional statement If it is raining, we will not play.

Let, P: It is raining and Q: we will not play.

Then; If P is true, that is, it is raining and Q is false, that is, we played, then the statement P implies Q is false.

Hence,  conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences.

To learn more on Mathematical Reasoning click:

https://brainly.com/question/11679298

#SPJ2

Answer:

there is no sufficient evidence to prove that viscosity is not 3000

Step-by-step explanation:

Let's state the hypothesis.

Null hypothesis; H0: μ = 3000

Alternative hypothesis; μ ≠ 3000

The sample mean is;

x = (2781 + 2900 + 3013 + 2856 + 2888)/5 = 2887.6

Standard deviation σ = √variance = √[(2781 - 2887.6)² + (2900 - 2887.6)² + (3013 - 2887.6)² + (2856 - 2887.6)² + (2888 - 2887.6)²)(1/(5 - 1))]

σ = √((1/4)(11363.56 + 153.76 + 15725.16 + 998.56 + 0.16)

σ = 84.026

Formula for test statistic is given as;

t = (x - μ)/σ

t = (2887.6 - 3000)/84.026

t = -1.338

From online p-value calculator from t value attached, using DF = 5 - 1 = 4, two tail and a significance level of 0.05,we have;

The p-value is 0.251896.

This is greater than the significance level of 0.05.

Thus, we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to prove that viscosity is not 3000

Answer:

set y = 0 to get the x intercept,,,,,,,,,,   0 = 2x -3 =    x = 3/2 or 1.5

Step-by-step explanation:

Answer:

(-1, -4.8)

Step-by-step Explanation:

Let the point be P, which is 3/10 of the way from A to B. This means, it divides P into AP and PB in the ratio, 3:10 = AP/PB = 3/10.

Apply the formula for internal division to find the coordinates which is given as:

[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]

[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]

Where,

[tex] A(-4, -8) = (x_1, y_1) [/tex]

[tex] B(9, 6) = (x_2, y_2) [/tex]

[tex] m = 3, n = 10 [/tex]

Plug in the necessary values to find x and y coordinates for point P

[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]

[tex] x = \frac{3(9) + 10(-4)}{3 + 10} [/tex]

[tex] x = \frac{27 - 40}{13} [/tex]

[tex] x = \frac{-13}{13} [/tex]

[tex] x = -1 [/tex]

[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]

[tex] y = \frac{3(6) + 10(-8)}{3 + 10} [/tex]

[tex] y = \frac{18 - 80}{13} [/tex]

[tex] y = \frac{-62}{13} [/tex]

[tex] y = \frac{-62}{13} [/tex]

[tex] y = -4.8 [/tex]

The coordinates of the point 3/10 of the way from A to B are (-1, -4.8)

Answer:

(0.2,-2.3)

Step-by-step explanation:

Answer:

5.1 days

Step-by-step explanation:

[tex]3.4 \: miles = 1 \: day \\ 17.34 \: miles \: = x \: days[/tex]

Cross Multiply

[tex]3.4x = 17.34[/tex]

Divide both sides of the equation by 3.4

[tex] \frac{3.4x}{3.4} = \frac{17.34}{3.4} [/tex]

[tex]x = 5.1[/tex]

Answer:

5 Days and 1 Hour

Step-by-step explanation:

3,4 per day

So, for 17.34 miles;

      17.34/3.4 = 5 Days and 1 hour

Answer:

PS = 26 units

Step-by-step explanation:

Perimeter of rectangle = 94

2(4z - 2 + 3z) = 94

2(7z - 2) = 94

14z - 4 = 94

14z = 94 + 4

14z = 98

z = 98/14

z = 7

QR = 4z - 2 = 4*7 - 2 = 28 - 2 = 26

PS = QR (Opposite sides of rectangle)

PS = 26 units

Answer:

[tex]x=\frac{-2m-10}{-2m-7}[/tex]

Step-by-step explanation:

Step 1: Write out equation

3x = (2x - 2)(m + 5)

Step 2: FOIL

3x = 2xm + 10x - 2m - 10

Step 3: Subtract 2xm on both sides

3x - 2xm = 10x - 2m - 10

Step 4: Subtract 10x on both sides

3x - 2xm - 10x = -2m - 10

Step 5: Factor out x

x(3 - 2m - 10) = -2m - 10

Step 6: Combine like terms in parenthesis

x(-2m - 7) = -2m - 10

Step 7: Divide both sides by -2m - 7

[tex]x=\frac{-2m-10}{-2m-7}[/tex]

Answer:

$5,830

Step-by-step explanation:

Multiply the miles by the cost per mile.

11,000 × $0.53 = $5,830

The cost to drive the car 11,000 miles is $5,830.

Answer:

[tex]3x^{2} -5x+6[/tex]

Step-by-step explanation:

Factor the numerator and it should be [tex](x+2)(3x^2-5x+6) / (x+2)[/tex]. Cancel out both the [tex]x+2[/tex] so that the denominator becomes a 1.

Answer:

$1.51

Step-by-step explanation:

take 4.26 and subtract 2.75.

Answer:

deretos

Step-by-step explanation:

Answer:

The answer is 18.

Step-by-step explanation:

Putting it straight into the calculator as you see it gives you 18.

Answer:

18

Step-by-step explanation:

Hope this helps : )

Answer:

3688

Step-by-step explanation:

Step 1:

4013 - 325 = 3688

Answer:

3688

Hope This Helps :)

Answer:

The answer is

Step-by-step explanation:

Area of a triangle is given by

[tex]A = \frac{1}{2} \times base \times height[/tex]

from the question

base = 16 m

height = 21 m

The area is...

[tex]A = \frac{1}{2} \times 16 \times 21 \\ = 8 \times 21 \: \: \: \: \: \: [/tex]

We have the final answer as

Hope this helps you

Answer:

Range: 8, 3, -7

Step-by-step explanation:

The Range is the second coordinate which is y.

Hope This Helps :)

Answer:

Step-by-step explanation:

Question (3)

The given expression is,

[tex]\frac{4(x-3)}{3}=20[/tex]

       Statements                Proof

1). [tex]\frac{4(x-3)}{3}=20[/tex]                1). Given

2). [tex]4(x-3)=60[/tex]           2). Multiplication property of equality

3). 4x - 12 = 60             3). Distributive property

4). 4x = 72                    4). Addition property of equality

5). x = 18                       5). Division property of equality

Question (4)

Equations are,

5x + 10 = 30 ------(1)

5(x + 10) = 30 ------(2)

From equation (1),

5x + 10 = 30

5x = 30 - 10

x = 4

From equation (2),

5(x + 10) = 30

(x + 10) = 6

x = 6 - 10

x = -4

Therefore, solutions of both the equations are different.

Answer:

(9, 6)

Step-by-step explanation:

Midpoint formula is:

Having coordinates of one end- and midpoint (-5, 12) and (2, 9):

we get the coordinates of the missing endpoint with coordinates (x₂, y₂):

So the missing point is: (9, 6)

☽------------❀-------------☾

Hi there!

~

[tex]\sqrt{42}[/tex] ≈ [tex]6.4807406984087...[/tex]

So [tex]\sqrt{42}[/tex] is irrational (since the decimal portion doesn't terminate or repeat)

❀Hope this helped you!❀

☽------------❀-------------☾

(The other person copied there answer from google!)

Answer: a.)Within your skills and abilities

Step-by-step explanation: i hope this helps :)

Knowing your personal strengths and weaknesses will help to keep your goal a. Within your skills and abilities.

Understanding what makes you tick is part of knowing yourself. It entails figuring out your priorities, talents, and limitations, as well as your habits, inclinations, and ways of thinking. The following is a list of the advantages and significance of understanding oneself

Knowing your personal strengths and weaknesses will help you

can change your personality flaws and improve on your weaknesses.

You’ll have more emotional intelligence, which is key to knowing others.

So, Knowing your personal strengths and weaknesses will help to keep your goal  Within your skills and abilities.

learn more about psychology here :

https://brainly.com/question/10980588

#SPJ2

Answer:

  5%

Step-by-step explanation:

Assuming the measurement is rounded to the nearest pound, there is the potential for the reported value to differ by 1/2 pound from the measured value. The precision of the measurement is thus ...

  (0.5 lb)/(10.0 lb) = 5/100 = 5%

__

Unless we know the cat's actual weight, we cannot determine the error in the measurement. If the cat actually weighs 10 pounds, the error is 0%.

Answer:

3(10)+30

(-30) (the amount she lost) +22 (the amount she gained)= -8

Glados lost 8 dollars while at the mall.

Answer:

v>5

Step-by-step explanation:

you will divide by negative 8 causing the value sign to flip and that gives you 5

Answer:

Step-by-step explanation:

it 28 by adding 6 +1 is 7 and times it by 4

7+3x=y I got this as the answer!