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Black_prince [1.1K]
3 years ago
8

Which of the following statements about Pascal's Triangle are true?

Mathematics
1 answer:
Anarel [89]3 years ago
6 0

Answer:

1. It is symmetric

2. The second diagonal is the counting numbers

3. Any number in the triangle is the sum of the two numbers directly above it

Step-by-step explanation:

1. The first diagonal shows the counting numbers.

2. The sums of the rows give the powers of 2.

3. Each row gives the digits of the powers of 11

You might be interested in
Colton gave out a survey to some students in his school about their favorite color. 470 of those surveyed said their favorite co
Tanzania [10]

Answer:

500

Step-by-step explanation:

Convert percent to decimal:

94%=

100

94

​

=0.94

Move decimal 2 places to the left

Multiplying the decimal by the whole gives us the part:

0.94x=

0.94x=

470

0.94

0.94x = 0.94

470

​

Divide both sides by 0.94x=

500

7 0
2 years ago
After an extensive advertising campaign, the manager of a company expects the proportion of potential customers that recognize a
lina2011 [118]

Answer:

Step-by-step explanation:

Hello!

The study variable is:

X: number of customers that recognize a new product out of 120.

There are two possible recordable outcomes for this variable, the customer can either "recognize the new product" or " don't recognize the new product". The number of trials is fixed, assuming that each customer is independent of the others and the probability of success is the same for all customers, p= 0.6, then we can say this variable has a binomial distribution.

The sample proportion obtained is:

p'= 54/120= 0.45

Considering that the sample size is large enough (n≥30) you can apply the Central Limit Theorem and approximate the distribution of the sample proportion to normal: p' ≈ N(p;\sqrt{\frac{p(1-p)}{n} })

The other conditions for this approximation are also met: (n*p)≥5 and (n*q)≥5

The probability of getting the calculated sample proportion, or lower is:

P(X≤0.45)= P(Z≤\frac{0.45-0.6}{\sqrt{\frac{0.6*0.4}{120} } })= P(Z≤-3.35)= 0.000

This type of problem is for the sample proportion.

I hope this helps!

5 0
2 years ago
What is the range of the relation[(-5,0),(-4,-3),(-3,4),(-1,0),(-4,-1)]
vesna_86 [32]

The range is the set of values that the relation takes for the domain for which it is defined.

Is the set of values of the dependent variable.

In this case, we have the relation [(-5,0),(-4,-3),(-3,4),(-1,0),(-4,-1)]​.

The dependant variable takes the values: 0, -3, 4, 0 and -1. Some values are repeated.

We put the repeated values only once and sort to write the range.

Then, the range is R = {-3, -1, 0, 4}.

Answer: Range = {-3, -1, 0, 4}

4 0
1 year ago
F(x) =x2+2x-3 g(x)=3x-14
Leviafan [203]

The solution to the composite function f(g(x)) is 9x² - 78x  + 165.

<h3>What is composite function?</h3>

A composite function is generally a function that is written inside another function.

Function composition is an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g.

From the given composite function, the solution is determined as follows;

to solve for f(g(x)), we use the following methods.

f(x) = x² + 2x - 3, g(x) = 3x - 14

f(g(x)) = (3x - 14)² + 2(3x - 14) - 3

         = 9x² - 84x + 196  + 6x - 28 - 3

         = 9x² - 78x  + 165

Thus, the solution to the composite function f(g(x)) is 9x² - 78x  + 165.

Learn more about composite function here: brainly.com/question/10687170

#SPJ1

The complete question is below:

F(x) =x2+2x-3 g(x)=3x-14, find f(g(x))

8 0
1 year ago
Joelle is working on a school report in a word processor. She wants to place a figure which is 13.09 cm wide so it apperars cent
irga5000 [103]

Hello Croary

We would first need to subtract 13.09cm from  21.59cm which will be 8.5cm, with the left over space, divide in half

<u><em>8.5/2 = 4.25cm</em></u>

:)

6 0
3 years ago
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