21 Use mathematical induction to show that Σ Coti) = (nti) (nt²)/2 whenever 'n' is a non negative integen J=0

Answer:

4

Step-by-step explanation:

Whatever you multiply or divide to the numerator, you do to he denominator.

Here, 12 was divided by 4 to obtain 3 in the other fraction. So, the missing number has to be 16 divided by 4, which gives 4

Answer:

\(\frac{3}{4}\)

Step-by-step explanation:

In this question we are presented with  \(\frac{12}{16}\)  and we want to simplify to have a numerator of 3. When simplifying fractions it's important to do the operation on both the numerator and the denominator so,

\(\frac{12}{16}\)   →  Half the numerator and the denominator →  \(\frac{6}{8}\)  →  Half the numerator and the denominator again →  \(\frac{3}{4}\)

1) The reaction is single replacement

2) KI and Cl2

3) KCl and I2

4) Cl2 + 2KI → 2KCl + I2

A single replacement reaction, also known as a single displacement reaction, is a type of chemical reaction in which one element or ion in a compound is replaced by another element. The general form of a single replacement reaction is:

A + BC → B + AC

Single replacement reactions can also occur with non-metals, in which case the non-metal replaces another non-metal in a compound. For example, when chlorine gas (Cl2) is added to a solution of potassium iodide (KI), a single replacement reaction occurs:

Cl2 + 2KI → 2KCl + I2

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Using the Binomial probability distribution,

The probability that exactly two customers in the sample will default on their payments is 0.31..

We have given that,

4% of total customers a mortgage company default on their payments .

The probability of success i.e number of customers default on their payments (p) = 4%

= 0.04

The probability of failure (q) = 1-p = 1-0.04 = 0.06

Total number of customers in sample (n) = 20

we have to find out the probability that exactly two customers in the sample will default on their payments.

Using the Binomial probability distribution,

P(X=x)= ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

the required probability is P(X= 2 )

Now, P(X= 2) = ²⁰C₂(0.04)²(0.06)¹⁸

=> P(X=2) = 190 × 0.0016 × 1.0155 = 0.31

Hence, the required probability is 0.31

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Answer:

  42, 38, 34, 30

Step-by-step explanation:

You want the first 4 terms of the sequence described by ...

  an = 42 -4(n -1), n ∈ ℕ

You can write the first 4 terms of the sequence by evaluating the 'an' expression for n = 1, 2, 3, 4.

Or, you can recognize the expression describes a sequence with a first term of 42 and a common difference of -4. That is, each term is 4 less than the one before.

The terms you want are ...

  42, 38, 34, 30

__

Additional comment

The equation for the n-th term of an arithmetic sequence is ...

  an = a1 +d(n -1)

where a1 is the first term, and d is the common difference. Comparing this to the given equation, we see a1 = 42, d = -4.

<95141404393>

the numerators are both negative, the answer will be a negative number. The numerator of the first fraction (-5) divided by the numerator of the second fraction (5) is -1. Multiply this answer by the common denominator (18) to get the final answer: -5/2.

To solve this fraction division problem, first convert the fractions to have a common denominator. To do this, multiply the denominator of the first fraction (-1/3) by the denominator of the second fraction (6), and the denominator of the second fraction (6) by the denominator of the first fraction (-1/3). This will change the fractions to -5/18 and 5/18, respectively.

Next, divide the numerators of the fractions. Since the numerators are both negative, the answer will be a negative number. The numerator of the first fraction (-5) divided by the numerator of the second fraction (5) is -1.

Multiply this answer by the common denominator (18) to get the final answer: -5/2.

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Answer:

im pretty sure its right

Step-by-step explanation:

The height function for the baseball dropped from a stadium seat 77 feet above the ground is  s(t) = 77 - 16t^2.

To determine the height of the baseball after a given time, we need the specific function or equation that represents the relationship between the height and time. The problem statement mentions s(t) as the height function, but it does not provide the specific equation.

In general, when an object is dropped from a height and falls freely under the influence of gravity, the height function can be described by the equation:

s(t) = s0 - 16t^2

where s(t) represents the height of the object at time t, s0 is the initial height, and 16t^2 represents the distance traveled due to gravitational acceleration.

In this case, the initial height of the baseball is given as 77 feet above the ground, so we can substitute s0 = 77 into the equation:

s(t) = 77 - 16t^2

This equation represents the height of the baseball at any given time t in seconds.

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It can be concluded that the probability that all three students like pizza is more than 50% which implies that in a group of three students, it is more likely that all three will like pizza.

A school survey found that eight out of ten students like pizza. If three students are chosen at random with replacement, then we have to calculate the probability that all three students like pizza.

As given, P(likes pizza) = 8/10 = 0.8

We need to find the probability of three students liking pizza, which means the probability of an event happening thrice. This is a case of independent events with repetition.

Hence, the formula for independent events with repetition is used, which is: P(A and B and C) = P(A) × P(B) × P(C)

Where A, B and C are independent events. In this case, all three events are identical.

Hence, we have: P(A and A and A) = P(A)³ = (0.8)³ = 0.512

This implies that the probability that all three students like pizza is 0.512.

Therefore, if three students are chosen at random with replacement, the probability that all three students like pizza is 0.512 or 51.2%.

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Answer:

image = A = 35×35

preimage = B = 28×28

Scale factor = image/preimage

=

\( \frac{35}{28} \times \frac{35}{28} \)

=

\( \frac{5}{4} \times \frac{5}{4} \)

= 25/16

=

Complete Question

Carmen is putting together a business plan for her sandwich restaurant, Subs Away, so she can expand to another location. She wants to include some information about recent sales but only has certain information about last month's sales. She currently offers ham, turkey and vegetarian sandwiches. She sells the ham sandwiches for $10 each and the turkey sandwiches for $11.25.

Last Month's Vegetarian Sales

Total Sandwiches Sold 75

Total Income $712.50

How much does Carmen charge for the vegetarian sandwich?

Answer:

 \(X=9.5\)

Step-by-step explanation:

From the question we are told that:

Total Vegetarian Sandwiches Sold \(T_{vs}=75\)

Total Vegetarian Sandwiches Income \(T_{vi}=$712.50\)

Generally the equation for Cost of vegetarian sandwich is mathematically given by

 \(X=\frac{Total\ income\ from\ vegetarian\ sandwich}{No.\ of\ vegetarian\ sandwich\ sold}\)

 \(X=\frac{T_{vi}}{T_{vs}}\)

 \(X=\frac{712.50}{75}\)

 \(X=\$9.5\)

Answer:

you use disputation

Step-by-step explanation:

4 times 3x = 12x

4 times 6 = 24

The p-value for the given analysis of variance (ANOVA) test is approximately 0.0012.

To find the p-value for this ANOVA test, we need to consider the F-statistic (5.71) and degrees of freedom for groups (4) and error (35). Using an F-distribution table or an online calculator, input the F-statistic value and the degrees of freedom to obtain the p-value.

The p-value represents the probability of observing an F-statistic as extreme as the one calculated from your data, assuming the null hypothesis is true (i.e., all group means are equal).

In this case, the p-value of approximately 0.0012 indicates a very low probability of observing the given F-statistic if the null hypothesis were true, suggesting that there is a significant difference among the group means.

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If 150 town residents were asked about their age and yogurt , then the probability that a randomly selected customer prefers Swirl if age is at least 25 years old is 0.66 .

let X be = the selected customer that prefers swirled yogurt or is at least 25 years old ;

The sum of all the customers that are "at least 25 years old" = 21 + 30 + 24 = 75 ;

the sum of all the customers that " like Swirl Yogurt" is = 24 + 24 = 48 ;

the total number of residents = 150 students ;

So , the probability is calculated as : ( 75+48 -24)/150 = 0.66 .

Therefore , the required probability is 0.66 .

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The given question is incomplete , the complete question is

The 150 residents of the town of wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. the results are displayed next.

     Age                               Chocolate      Vanilla      Swirl

under 25 years old                  22                 29             24

at least 25 years old                21                  30             24

What is the probability a randomly selected customer prefers Swirl Yogurt given he or she is at least 25 years old ?

Answer:

Step-by-step explanation:

Imfinite solutions

A gradient vector field represents the direction and magnitude of the gradient of a function at each point in the plane. The function f(x, y) = 2x^2 + 2y^2 corresponds to the gradient vector field plot labeled with the equation "f(x, y) = 2x^2 + 2y^2."

A gradient vector field represents the direction and magnitude of the gradient of a function at each point in the plane. The gradient vector field can be visualized by plotting vectors at different points, with the vectors pointing in the direction of the steepest ascent of the function.

In this case, the function f(x, y) = 2x^2 + 2y^2 represents a quadratic function with the coefficients 2 for both x^2 and y^2 terms. The gradient vector field plot that corresponds to this function would show vectors pointing away from the origin (0, 0) in all directions, indicating the direction of steepest ascent.

By matching the function f(x, y) = 2x^2 + 2y^2 with the gradient vector field plot labeled with the equation "f(x, y) = 2x^2 + 2y^2," we can visually observe the direction and magnitude of the gradient vectors associated with the function at each point in the plane.

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Answer:

y=-5

Step-by-step explanation:

Answer: just use pemdas

Step-by-step explanation:

2(-3*4)-10

-3*4=-12

s0

2*(-12)-10

2*-12=-24

so

-24-10=-34

Using pemdas

it's -34

The value of x for the length A'E' of the similar shape A'B'C'D'E' is equal to 6⅔.

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other.

The side A'E' corresponds to the side A'E' and also E'D' corresponds to the side ED so;

(7). A'E'/AE = E'D'/ED

x/10 = 6/9

x = (10 × 6)/9 {cross multiplication}

x = 20/3

x = 6⅔

Therefore, the value of x for the length A'E' of the similar shape A'B'C'D'E' is equal to 6⅔

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Answer:

60 inches

Step-by-step explanation:

the least common multiple of 12 and 10 is 60

you can use the prime factorization tree or a list method

1st multiple of 10: 10                               1st multiple of 12: 12

1st multiple of 10: 20                               1st multiple of 12: 24

1st multiple of 10: 30                               1st multiple of 12: 36

1st multiple of 10: 40                               1st multiple of 12: 48

1st multiple of 10: 50                               1st multiple of 12: 60

1st multiple of 10: 60                              

You can stop when a common multiple is reached

Answer:

I'm confused

Step-by-step explanation:

what is it

How do we help? theres no question??

Answer:

number 5 is y= 3    7-3=4x4=16

Step-by-step explanation:

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number can only be divided evenly by 1 and itself.

To find the multiples of a prime number, you can use the following steps:

For example, if the prime number is 5, the multiples of 5 are 5, 10, 15, 20, 25, and so on.

It's important to note that a prime number only has two divisors: 1 and itself. This means that a multiple of a prime number will never be a prime number.

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Technically, we don't have enough info so it could go either way.

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Explanation:

We can see that the sides are proportional to each other, but we don't know anything about the angles. We need to know if the angles are the same. If they are, then the hexagons are similar. If the angles are different, then the figures are not similar.

Right now we simply don't have enough info. So they could be similar, or they may not be. The best answer (in my opinion) is "not enough info". However, your teacher likely wants you to pick one side or the other. We can't pick "similar" so it's best to go with "not similar" until more info comes along the way.

Answer: It does not say what you want to figure out so I will just explain.

Step-by-step explanation: You can get 5,280 and divide it by 8 you will get 660 and you put three 660s on the length and 1 each on the width.

btw I got a document so you can understand.

Answer:

19, 23, 27, 31, 35,

Step-by-step explanation:

It's +4 each time.