How do you decide which rational number operations to use to solve problems

The sum of the geometric progression is the sum S₃ = 32

The sum of terms of a geometric progression is given by

Sₙ = a(rⁿ - 1)/(r - 1) where

Given the geometric progression, aₙ = 4(2)ⁿ⁻¹ comparng it with the general term of a geometric sequence aₙ = arⁿ⁻¹, then

Now, we desire S₃, that is Sₙ when n = 3.

So, S₃ = a(r³ - 1)/(r - 1)

= 4(2³ - 1)/(2 - 1)

= 4(8 - 1)/1

= 4(8)

= 32

So, the sum S₃ = 32

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Answer:

C Linear Growth is the correct option.

Step-by-step explanation:

Equation:

x*4 + 20 = y

Have a nice day!

Answer:

linear growth

because the equation's slope is constant and equal 4

The probability is 21.6931 %

Explanation:

Total amount of callers: 18 + 23 + 40 +58 +50 = 189 callers

Amount of callers 25 or younger : 18 + 23 = 41 callers

Percentage of callers 25 or younger : 41 * 100 / 189 = 21.6931 %

Given the frequency and number of possible outcomes, the number of days that must pass before it becomes probable that Janice will have had to pick up lunch at least once is 8.

Note that the probability of any of the staff at the office picking the food is 1/8.

Even if She does not pick up lunch on her first day or second, the number of days that must pass to make sure that Janice picks up lunch AT LEAST once is 1 in 8 days.

The formula to compute the probability of an event is equivalent to the ratio of favorable outputs to the total number of outputs. It is to be noted that probabilities always range between 0 and 1.

The expression is given as:

P (E) = f/O; where

P(E) is the Probability of an event E happening;

f =  The number of possible outcomes for an event (frequency)

n = Total number of outputs that are likely

Hence,

P(E) = 1/8

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Mike's speed driving to his office is 45 miles/hour, which is 10 miles less than his average speed driving back.

Speed is an average value of a scalar measurement of the distance covered over the time taken.

Speed is the equation,  r = d/Δt, where r = speed or rate, d = distance, and Δt is the change in time.

Thus, when the distance covered by a traveler is divided by the time consumed, one can determine the average speed for the travel.

Distance from Mike's home to his office = 40 miles

Distance to and from = 80 miles (40 miles x 2)

Hours covered from office = 1.6 hours

Average speed for the trip = 50 miles/hour (80/1.6)

Average speed to return home = 55 miles/hour

Average speed to office = 45 miles/hour (55 - 10)

Thus, Mike's speed of driving to his office is 45 miles/hour.

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What is Mike's speed driving to his office?

Answer:

wheres the angle? explain.

Step-by-step explanation:

...

Answer:

  2.5%

Step-by-step explanation:

You want the percentage below 335 if the distribution is normal with a mean of 555 and a standard deviation of 110, using the empirical rule.

The z-score of 335 is ...

  Z = (X -µ)/σ

  Z = (335 -555)/110 = -220/110 = -2

The empirical rule tells you that 95% of the distribution is between Z = -2 and Z = 2. That is, 5% of the distribution is evenly split between the tails Z < -2 and Z > 2. Half that value is in each tail.

  P(X < 335) = 5%/2 = 2.5%

The percentage of people taking the test who score below 335 is 2.5%.

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Answer: 55 minutes

Step-by-step explanation:

First, you would have to subtract 5 from 225 because there are already 5 monsters there.

225-5= 220

Next, you would have to divide 220 by 4 to find the amount of minutes.

220/4= 55

The total value of the furniture sold by Joyce last week is A = $ 6,733.33

Given data ,

Let's call the value of the furniture Joyce sold "x".

She receives 10% commission on the first $1,200 of sales, which is $120:

Commission on first $1,200 = 0.1 * 1200 = 120

The remaining sales that she earns commission on is the difference between the total value of the furniture sold and the first $1,200:

Remaining sales = x - 1200

She earns 15% commission on the remaining sales, which is 0.15 times the remaining sales:

Commission on remaining sales = 0.15 * (x - 1200)

Her total earnings from commission last week was $950. So we can write an equation:

Commission on first $1,200 + Commission on remaining sales = $950

Substituting the expressions we found for the two commissions, we get:

120 + 0.15(x - 1200) = 950

120 + 0.15x - 180 = 950

On simplifying the equation , we get

0.15x - 60 = 950

0.15x = 1010

x = 6,733.33

Hence , the value of the furniture Joyce sold last week was $6,733.33

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Answer:

probability of getting exactly 500 heads= 1

Step-by-step explanation:

If a coin is tossed, the probability of obtaining a head = 0.5

If a coin is tossed, the probability of obtaining a tail= 1- probability of obtaining a head

If a coin is tossed, the probability of obtaining a tail=1-0.5

If a coin is tossed, the probability of obtaining a tail=0.5

So if 1000 coin are tossed, the probability of getting exay 500 heads which is already the half of 1000 is 1

Answer:

E(29/4,3)

Step-by-step explanation:

Given that,

Segment CD has point E located on it such that CE:ED = 3:5

The coordinates of C and D are (5, -6) and (11,18) respectively.

We need to find the coordinates of E. Let the coordinates are (x,y). Using section formula to find it as follows :

\((x,y)=(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2})\\\\(x,y)=(\dfrac{3(11)+5(5)}{3+5},\dfrac{3(18)+5(-6)}{3+5})\\\\=\dfrac{29}{4},3\)

So, the coordinates of E are (29/4,3).

The probability of the baseball player getting exactly 4 hits out of 10 times at bat is approximately 0.161, or 16.1%.

To calculate the probability of a baseball player getting exactly 4 hits out of 10 times he was up at bat, we need to use the binomial probability formula.

The binomial probability formula is given by:P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k hits

n is the total number of trials (in this case, the player's 10 times at bat)

k is the number of successful trials (in this case, 4 hits)

p is the probability of success in a single trial (in this case, the player's batting average, 0.298)

(1 - p) is the probability of failure in a single trial

Plugging in the values:

P(X = 4) = C(10, 4) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Using the combination formula C(n, k) = n! / (k! * (n - k)!):

P(X = 4) = 10! / (4! * (10 - 4)!) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Calculating the values:

P(X = 4) ≈ 0.161

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-10369

too lazy but that's the exact value

Answer:

Step-by-step explanation:

(-2)³ *(-4)² * 3⁴ = (-8) * 16 * 81

                      = -10368

Answer:

Step-by-step explanation:

14 mins

this is because if we divide 2 but 1/2 you would get 4

since she can run 1/2 a mile in 3 1/2 mins

we should multiply the 3 1/2 buy 4

this would lead to the answer 14

Answer:

Step-by-step explanation:

7 + 3 ( v - 2u )/u + 1

u = 2 and v = 5

7 + 3(v - 2u)/u + 1

7 + 3 ((5) - 2(2)) / (2) + 1

→ 7+3 ((5) -2 (2)) = 10

→ (2) + 1  = 3

10/3

Answer:

10/3

Step-by-step explanation:

u = 2

v = 5

7 + 3(v - 2u)

= 7 + 3(5 - 2*2)

= 7 + 3(5 - 4)

= 7 + 3(1)

= 7 + 3

= 10

u + 1

= 2 + 1

= 3

7 + 3(v - 2u)/u + 1

= 10/3

An expression that gives the perimeter of the rectangular pool is,

⇒ P = 2 (5x - 4)

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The area of a rectangular pool is,

⇒ 6x²− 11x + 3

Now, We can factor as;

⇒ 6x²− 11x + 3

⇒ 6x²− (9 + 2) x + 3

⇒ 6x²− 9x - 2x + 3

⇒ 3x(2x - 3) - 1 (2x - 3)

⇒ (3x - 1) (2x - 3)

Hence, An expression that gives the perimeter of the rectangular pool is,

P = 2 [ (3x - 1) + (2x - 3) ]

P = 2 [ 3x - 1 + 2x - 3 ]

P = 2 (5x - 4)

Thus, An expression that gives the perimeter of the rectangular pool is,

P = 2 (5x - 4)

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Answer:

cos

( 390 ) − 4 cot ( − 45 ) sin ( 330 )

Step-by-step explanation:

Answer: Estimated the standard deviation α  = 5.35

Step-by-step explanation:

According to Empirical rule, the largest value is approximately:

ц + 3α

And the smallest value is approximately:

ц + 3α

Based on the given figures in the question, we can say

ц + 3α = 140.6

ц - 3α = 108.5

Now subtracting these two; we have

ц + 3α - ( ц - 3α  ) = 140.6 - 108.5

ц + 3α - ц + 3α = 32.1

6α = 32.1

α = 32.1 / 6

α = 5.35

Estimated the standard deviation α  = 5.35

Answer:

$7.50

Step-by-step explanation:

Each shell is $0.75. You buy ten. Ten times 0.75 is 7.5

Answer:

$7.50

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

\(x + 2 = 16 \\ x = 16 - 2 \\ x = 14\)

Like this ？？？

Answer:

16 = 2 + 14

Step-by-step explanation:

Sum means to add to numbers, so we are finding x + 2 = 16.

x + 2 - 2 = 16 - 2

x = 14

Answer:

36352.0

Step-by-step explanation:

For 256x142 = 36352.0

There is none actually

To find the limit of a convergent sequence, we can simply take the limit as n approaches infinity. Let's calculate the limits for each of the given sequences:

A. \(\sf\:\lim_{n \to \infty} \frac{5n}{n+7} \\\)

To find the limit, we divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{5n/n}{(n+7)/n} = \frac{5}{1} = 5 \\\)

Therefore, the limit of the sequence A is 5.

B. \(\sf\:\lim_{n \to \infty} \frac{4-7n}{8+n} \\\)

Again, divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{4/n - 7}{8/n + 1} = \frac{0 - 7}{0 + 1} = -7 \\\)

So, the limit of sequence B is -7.

C. \(\sf:\lim_{n \to \infty} \frac{8n - 500\sqrt{n}}{2n + 800\sqrt{n}} \\\)

Divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{8 - 500\sqrt{n}/n}{2 + 800\sqrt{n}/n} \\\)

As n approaches infinity, the terms involving \(\sf\:\sqrt{n}/n \\\) tend to 0:

\(\sf\:\lim_{n \to \infty} \frac{8 - 500(0)}{2 + 800(0)} = \frac{8}{2} = 4 \\\)

Therefore, the limit of sequence C is 4.

To summarize:

A. The limit of sequence A is 5.

B. The limit of sequence B is -7.

C. The limit of sequence C is 4.

X = 30. Plug thirty into the equation to get -11 = -30 + k. Add 30 to both sides to get 19 = k.

K = 19

Answer:

1.75x?

Step-by-step explanation:

I'm not sure if it has to be multiple numbers

Answer:

there are 195 girls

Step-by-step explanation:

the equation is: 364= 2x+26

subtract 26 from both sides and you get 338

338 divided by 2 is 169, therefore there are 169 boys.

169+26 more girls is 195

169+195= 364

Answer:

She has 12 inches wood left

Step-by-step explanation:

The mean for the number of people with the genetic mutation in such groups of 600 is 18.

Given that,

About 3% of the population has a particular genetic mutation.

This means that for any group of people, 3% of the people has a particular genetic mutation.

This is a binomial distribution.

Probability that people having genetic mutation = 3% = 0.03

Random sample size = 600

Mean for a binomial distribution can be calculated as,

Mean = n × p

         = 600 × 0.03

         = 18

Hence the mean number of people having genetic mutation is 18.

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Answer:

[6, 8).

Step-by-step explanation:

When we are looking for the range of a function by just looking at the graph, we have to define from what point to what point the graph move vertically. On the other hand, if we were looking for the domain, we would state from where to where the graph moves horizontally.

In this case we have to analyze the graph vertically, since we are looking for the range of the function. Therefore, if we take a look at the line we can notice that it goes from y=6 to y=8. Therefore the range should be from 6 to 8.

Now, this result must be expressed in interval notation, meaning that we have to state whether the values of each end are contained or not by the function. The graph already tells us about it., because it marks it with the closed or open dots. In the case of the number 6, we have a closed dot, means that the function contains the number 6. For the other end we have an open dot, means that the function doesn't contain the number 8.

Applying internal notation, the range of this function is:

[6, 8).

Learn more about interval notation here:

1. https://web.nmsu.edu/~kberver/Unit1/Unit18.html#:~:text=An%20interval%20is%20closed%20if,used%20for%20an%20open%20endpoint.

2. https://brilliant.org/wiki/interval-notation/#:~:text=Interval%20notation%20is%20a%20way,inequality%20or%20system%20of%20inequalities.

The odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Since Jenny won a charity raffle, and her prize will be randomly selected from the 9 prizes shown below, and the prizes include 7 rings, 1 camera, and 1 headset, to find the odds against Jenny winning a headset, and find the odds in favor of Jenny winning a headset, the following calculations must be performed:

· 1 headset out of 9 total prizes

· 1/9 = headset

· 1/9 x 100 = 11.11%

· 100 - 11.11 = 88.89%

Therefore, the odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.