find the radius of convergence, r, of the series. [infinity] n2xn 6 · 12 · 18 · ⋯ · (6n) n = 1 r = find the interval, i, of convergence of the series. (enter your answer using interval notation.) i =

Answer:

240 students

Step-by-step explanation:

If 84 represents 35% then 100%=(84/35)(100)

240 students

The percent increase in the cost of the uniform from last year to this year is 25%.

To find the percent increase in the cost of the uniform from last year to this year, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100 to express the result as a percentage.

The difference between this year's price and last year's price is:

$65 - $52 = $13

The original price (last year's price) is $52.

So the percent increase in the cost of the uniform is:

percent increase = (difference / original price) x 100

percent increase = ($13 / $52) x 100

percent increase = 0.25 x 100

percent increase = 25%

Therefore, the percent increase in the cost of the uniform from last year to this year is 25%.

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Answer:

3.5 feet

Step-by-step explanation:

1 inch ≅ 0.083

42 inches = 3.5 feet

So, 42 inches is 3.5 feet.

Step-by-step explanation:

2, 2, 3, 4, 5, 5, 5, 6, 6, 7, 9, 10

_

2+2+3+4+5+5+5+6+6+7+9+10 = 64 ÷ 12 = 5.3

_

Mean: 5.3

Median: 5

The probability that a puppy is picked from the pet store is 0.375 or 37.5%.

To determine the probability of picking a puppy from the pet store, we need to take into account the relative frequency of puppies compared to the other pets.

According to the problem statement, puppies are chosen twice as often as the other pets. Therefore, we can assign a weight of 2 to each puppy and a weight of 1 to each of the other pets.

This means that the total weight of all the puppies is 6 x 2 = 12, while the total weight of all the other pets is (9+4+7) x 1 = 20.

To calculate the probability of picking a puppy, we need to divide the weight of all the puppies by the total weight of all the pets:

Probability of picking a puppy = Weight of all the puppies / Total weight of all the pets

= 12 / (12+20)

= 12 / 32

= 3 / 8

= 0.375

Therefore, the probability of picking a puppy from the pet store is 0.375 or 37.5%.

It's important to note that this probability assumes that all the pets are equally likely to be chosen, except for the fact that puppies are chosen twice as often.

If there are any other factors that could influence the likelihood of picking a certain pet, such as their position in the store or their visibility, this probability may not accurately reflect the true likelihood of picking a puppy.

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The x-value that makes the set of ratios equivalent include:

6      ⇒  2x : 48 = 3 : 12.

9      ⇒  2 : 3 = 6 : x

16     ⇒  12 : 15=x: 20

24     ⇒  4 : 7 = x : 42

In Mathematics and Geometry, a direct proportion simply refers to a mathematical expressions which is typically used to represent the equality of two (2) ratios.

By applying direct proportion to the given mathematical expressions, we have the following mathematical equation:

2 : 3 = 6 : x

2/3 = 6/x

By cross-multiplying, we have the following:

2x = 18

x = 18/2 = 9.

4 : 7 = x : 42

4/7 = x/42

By cross-multiplying, we have the following:

7x = 168

x = 168/7 = 24.

2x : 48 = 3 : 12

2x/48 = 3/12

x/24 = 1/4

x = 6

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1-The formula will be;C(n, 2) = n! / 2!(n - 2)! = n(n - 1) / 2, where n >= 2.

2-The probability that can happen if some of the providers will get down so then he can not do the job; P(B|A) = P(A ∩ B) / P(A) = P(B) / P(A), where P(A) ≠ 0.

Explanation:

1. Formula to represent the selection of the best two providers out of a set of providers:

In this case, we can use the combination formula which is given by;

C(n, r) = n! / r!(n - r)!  

Where n represents the total number of providers and r represents the number of providers to be selected.

Since we want to select the best two providers, we can plug in n = the total number of providers and r = 2 in the formula. Therefore, the formula becomes;

C(n, 2) = n! / 2!(n - 2)!

= n(n - 1) / 2, where n >= 2.

2. Formula to represent the probability of the provider not being able to do the job:

We can use conditional probability to represent the probability of a provider not being able to do the job given that some providers are down. The formula for conditional probability is given by;

P(A|B) = P(A ∩ B) / P(B)

where A and B are two events, P(A ∩ B) is the probability that both A and B occur and P(B) is the probability that event B occurs.

In this case, let's say that the probability of a provider being down is represented by event A, while the probability of the provider not being able to do the job is represented by event B. Then we can write;

P(B|A) = P(A ∩ B) / P(A)

where P(A ∩ B) is the probability that the provider is down and cannot do the job, and P(A) is the probability that the provider is down.

The probability of A ∩ B is usually given, so we only need to calculate P(A). Therefore, the formula becomes;

P(B|A) = P(A ∩ B) / P(A)

= P(B) / P(A), where P(A) ≠ 0.

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1. First formula to select best two providers:

                \(C(n, r) = n! / (r! (n - r)!)\).

2. Second formula to write the probability of providers not being able to do the job:

                \(P(x) = (n C x) * p^x * (1 - p)^(n-x)\)

Solution:

Formula to represent the probability and selection of providers are as follows:

1.

First formula to select best two providers:

If you have a set of providers and you want to select the best two of them to do your jobs, you can use the combination formula.

The formula to select n elements from a set of r elements is given by the formula:

\(C(n, r) = n! / (r! (n - r)!)\),

where n = total number of providers

          r = number of providers you want to select.

In this case, you want to select the best two providers from a set of n providers. Therefore, the formula to select the best two providers is:

\(C(n, r) = n! / (r! (n - r)!)\)

2.

Second formula to write the probability of providers not being able to do the job:

If some of the providers will get down so then he can not do the job, the probability of this happening can be represented by the binomial probability formula.

The binomial probability formula is given by the formula:

\(P(x) = (n C x) * p^x * qx^(n-x)\)

where n = total number of providers,

          x = number of providers who cannot do the job,

          p = probability of a provider getting down,

         q = probability of a provider not getting down.

In this case, if some of the providers will get down, the probability of a provider getting down is given. The probability of a provider not getting down is 1 minus the probability of a provider getting down.

Therefore, the formula to write the probability of some of the providers not being able to do the job is:

\(P(x) = (n C x) * p^x * (1 - p)^(n-x)\)

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Answer:

Step-by-step explanation:

25, i think

The probability that a customer purchased popcorn, given that they purchased from stand B is 13.4%.

For the given question;

The data for the selling of the snack items at arena are given;

Snack Item    Hot Dogs  Nachos Popcorn Total Concession

Stand A          125            65          40           230

Stand B          218            119          52           389

Stand C          65             52          13             130

Total              408           236        105           749

Now the customer purchased the popcorn from stand B.

Thus, total number of snack at stand B = 389

Total number of popcorn at stand B = 52

Thus,

Probability = favourable outcome/total outcome

Probability = 52/386

Probability % = 52/386 × 100

Probability % = 13.4%.

Thus, the probability that a customer purchased popcorn, given that they purchased from stand B is 13.4%.

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Answer:

y>-2

Step-by-step explanation:

that is the answer

Answer:

3/4

Step-by-step explanation:

Answer:

The cost per ounce is $0.23

Step-by-step explanation:

Set up fraction:

ounce/cost

15.4/3.59 = 1/x

cross multiply

15.4x=3.59

x=3.59/15.4

x=0.233116883117

x=$0.23

The cost per ounce is $0.23

Answer:

$0.23

Step-by-step explanation:

\(\frac{15.4}{3.59} =.23.........\)

$0.23

Next year population of this city will be 237886

Let the current population of the city is X

Population in a city is the measure of the total living people in that city. Increase in population signifies the addition of living people while decrease in population signifies the subtraction of living people.

Net decrease in the population rate per year is 1.7%

According to the question, Present population of the city is 242000

Therefore, X = 242000

Now as per the question, next year population will be 1.7% less than this year population

Therefore, next year population will be

X - 1.7% of X

Here X = 242000

Therefore,

= 242000 - 1.7% of 242000

= 242000 - 0.017(242000)

= 242000 - 4114

= 237886

Decreased population is 237886

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Answer: C

\(\frac{3}{4}*\frac{1}{3}=\frac{3}{12}=\frac{1}{4}\)

Answer:

C. 184 square centimeters

Step-by-step explanation:

4 x 6 = 24

there are 2 of them so you leave it the same

5 x 10 = 50

there are 2 of them so

50 x 2 = 100

6 x 10 = 60

24 + 100 + 60 = 184

184 square centimeters

Answer:

x=2

Step-by-step explanation:

6x + 2 = 14

Subtract 2 from each side

6x+2-2 = 14-2

6x= 12

Divide by 6

6x/6 = 12/6

x=2

Answer:  x=2

Step-by-step explanation:

Answer:

2,350,000,000

Step-by-step explanation:

Answer:The number form of 2350 million is 2350000000. It can also be abbreviated as 2350M.

Step-by-step explanation:

Answer:

A,B,D

Step-by-step explanation:

Answer:

the person above me is right, it's A, B, and D

Step-by-step explanation:

The mathematical model that best fits the given data is option : y = 82.3 - 8.275x.

To construct a scatterplot and determine the mathematical model that best fits the given data, we will plot the points and analyze the trend.

Given Data:

x: 4, 8, 12, 16, 20

y: 40, 20, -11, -37, -97

Let's plot these points on a scatterplot:

(x, y) points:

(4, 40)

(8, 20)

(12, -11)

(16, -37)

(20, -97)

After plotting the points, we can analyze the trend in the data.

By observing the scatterplot, it is clear that a linear or quadratic model would not fit the data well since the points do not follow a straight line or a parabolic curve.

Next, we can try the logarithmic, exponential, and power models to see if any of them fit the data better.

Using a calculator or computer to perform the regression analysis, we find that the regression equation with the highest R² value is:

y = 82.3 - 8.275x

This equation corresponds to option : y = 82.3 - 8.275x

The regression equation represents a linear model that best fits the given data. The R² value indicates how well the model explains the variability in the data, and in this case, the linear model provides the highest R² value compared to the other models.

It's important to note that the specific values of the coefficients in the regression equation may vary slightly depending on the calculator or software used for the analysis. However, the overall best-fit model remains the same.

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Answer:

x=24

y=25

Step-by-step explanation:

3y =75 by alternate interior angles theorem

y =25

4x+9+75=180

4x+84=180

4x=96

x=24

Answer:

I think its -4.

Answer: \(\frac{1}{\sqrt 2}\)

Step-by-step explanation:

Note that \(\sin(A-B)=\sin A \cos B-\cos A \sin B\).

\(\implies \sin 80^{\circ} \cos 35^{\circ}-\cos 80^{\circ} \sin 35^{\circ}=\sin 45^{\circ}=\frac{1}{\sqrt{2}}\)

The correct statements are:

b) Ordering costs decrease with respect to lot size,

c) It is good to have fixed interval ordering systems for products that have independent demand,

e) Taxes and insurance costs can be considered as carrying costs of inventory,

f) Costs incurred for defective products identified after the products are shipped are classified as internal failure costs,

h) Costs of repairing faulty products under warranty are limited to external failure costs, and j) Under EOQ inventory model, there is an assumption which states that there is no possibility of inventory stockout to occur.

b) Ordering costs decrease with respect to lot size: Ordering costs involve the expenses incurred when placing orders for inventory, such as administrative costs, processing fees, and transportation costs.

When the lot size increases, the frequency of placing orders decreases, resulting in lower ordering costs per unit. This is because the fixed costs associated with ordering are spread over a larger quantity of inventory.

c) It is good to have fixed interval ordering systems for products that have independent demand: Fixed interval ordering systems involve placing orders at regular intervals, regardless of the inventory level.

This approach is suitable for products with independent demand, where the demand is unpredictable or sporadic. By setting fixed intervals, the company can ensure a consistent replenishment schedule and avoid stockouts while optimizing inventory levels.

e) Taxes and insurance costs can be considered as carrying costs of inventory: Carrying costs are the expenses associated with holding and storing inventory.

They include costs such as storage fees, insurance premiums, taxes on inventory, and the opportunity cost of tying up capital in inventory. Taxes and insurance costs directly impact the financial burden of inventory holding and are considered as components of carrying costs.

f) Costs incurred for defective products identified after the products are shipped are classified as internal failure costs: Internal failure costs are expenses incurred due to quality issues discovered within the company's operations.

In the context of inventory, costs related to defective products identified after they are shipped, but before reaching the customer, fall under internal failure costs. These costs include rework, scrap, and any necessary corrective actions taken to address the quality problems.

h) Costs of repairing faulty products under warranty are limited to external failure costs: External failure costs are the expenses incurred due to quality issues discovered by customers after the products have been delivered.

When faulty products are repaired under warranty, the costs associated with the repairs are considered external failure costs. This includes the direct costs of repairing or replacing the faulty products and any associated customer service expenses.

j) Under EOQ inventory model, there is an assumption which states that there is no possibility of inventory stockout to occur: The Economic Order Quantity (EOQ) model is a widely used inventory management technique.

It assumes that demand for the product is constant and known with certainty, there are no quantity discounts or price variations, and there is no possibility of stockouts occurring.

The assumption of no stockouts simplifies the calculations and ensures that the optimal order quantity obtained from the model will meet the demand without interruptions.

However, in real-world scenarios, stockouts can occur due to unforeseen factors, variability in demand, or supply chain disruptions.

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Answer:

4x+17=5

Step-by-step explanation:

The product of 4 and a number: Product means multiplication.

Therefore, we have 4 and any variable of your choice.(I used x)

plus 17: +17

Now we have 4x+17

Is: means equal (=)

Now we plug in what we have: 4x+17=5

Hope this helps! :)

Answer:

infinite

Step-by-step explanation:

\(\\ \sf\longmapsto 4(4x-2)+1=16x-7\)

\(\\ \sf\longmapsto 16x-8+1=16x-7\)

\(\\ \sf\longmapsto 16x-7=16x-7\)

\(\\ \sf\longmapsto 0=0\)

this may help you with your question

Answer:

Step-by-step explanation:

             Statements                                  Reasons

1). AD ≅ BC                                           1). Given

2). ∠D ≅ ∠C                                          2). Given

3). ∠DEA ≅ ∠CEB                                 3). Vertically opposite angles

4). ΔADE ≅ Δ BCE                                4). AAS postulate of congruence

5). AE ≅ BE                                           5). CPCTC

Hence, proved.

The half life formula is :

where N(t) = remaining quantity after t years

No = Original Quantity

t = time in years

T = half life in years

From the problem, we have :

N(t) = 30 grams

No = 100 grams

T = 674

Solve for t :

Take ln of both sides :

The answer is t = 1170.71 years

Answer:

f=11.52

Step-by-step explanation:

slove:f=\(\frac{8}{cos\frac{23\pi }{90} }\)

round the number:f =11.5

answer:f=11.52