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Karolina [17]
3 years ago
13

There are three consecutive integers. Four times the smallest integer is equal to six more than three times the smallest integer

. What is the smallest of the 3 integers?
Mathematics
1 answer:
Nana76 [90]3 years ago
4 0

Let the smallest integer equal x - 1, the next one equal x, and the last one equal x + 1.

4(x-1) = 3(x-1) + 6

x-1 = 5

x = 6

The smallest integer is x - 1, which is equal to 5. Thus, the smallest of the three integers is 5.

You might be interested in
According to the National Institute of Allergy and Infectious Diseases, approximately 7% of U.S. children 4 years of age or youn
Yuliya22 [10]

Answer:

0.337 = 33.7% probability that one of the eight children has a food allergy.

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they have a food allergy, or they do not. The probability of a child having food allergy is independent of any other child. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

7% of U.S. children 4 years of age or younger have a food allergy.

This means that p = 0.07

A day care program has capacity for 8 children in that age range.

This means that n = 8

What is the probability that one of the eight children has a food allergy?

This is P(X = 1).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{8,1}.(0.07)^{1}.(0.93)^{7} = 0.337

0.337 = 33.7% probability that one of the eight children has a food allergy.

6 0
3 years ago
What is the completely factored form of f(x)=x^3-7x^2+2x+4
xxMikexx [17]

Solution, \mathrm{Factor}\:x^3-7x^2+2x+4:\quad \left(x-1\right)\left(x^2-6x-4\right)

Steps:

x^3-7x^2+2x+4

Use\:the\:rational\:root\:theorem,\\a_0=4,\:\quad a_n=1,\\\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:4,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\\\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:4}{1},\\\frac{1}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x-1,\\\left(x-1\right)\frac{x^3-7x^2+2x+4}{x-1}

\frac{x^3-7x^2+2x+4}{x-1}

\mathrm{Divide}\:\frac{x^3-7x^2+2x+4}{x-1},\\\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}x^3-7x^2+2x+4\mathrm{\:and\:the\:divisor\:}x-1\mathrm{\::\:}\frac{x^3}{x},\\\mathrm{Quotient}=x^2,\\\mathrm{Multiply\:}x-1\mathrm{\:by\:}x^2:\:x^3-x^2,\\\mathrm{Subtract\:}x^3-x^2\mathrm{\:from\:}x^3-7x^2+2x+4\mathrm{\:to\:get\:new\:remainder},\\\mathrm{Remainder}=-6x^2+2x+4,\\Therefore,\\\frac{x^3-7x^2+2x+4}{x-1}=x^2+\frac{-6x^2+2x+4}{x-1}

\mathrm{Divide}\:\frac{-6x^2+2x+4}{x-1},\\\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}-6x^2+2x+4\mathrm{\:and\:the\:divisor\:}x-1\mathrm{\::\:}\frac{-6x^2}{x}=-6x,\\\mathrm{Quotient}=-6x,\\\mathrm{Multiply\:}x-1\mathrm{\:by\:}-6x:\:-6x^2+6x,\\\mathrm{Subtract\:}-6x^2+6x\mathrm{\:from\:}-6x^2+2x+4\mathrm{\:to\:get\:new\:remainder},\\\mathrm{Remainder}=-4x+4,\\\mathrm{Therefore},\\\frac{-6x^2+2x+4}{x-1}=-6x+\frac{-4x+4}{x-1}

\mathrm{Divide}\:\frac{-4x+4}{x-1},\\\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}-4x+4\mathrm{\:and\:the\:divisor\:}x-1\mathrm{\::\:}\frac{-4x}{x}=-4,\\\mathrm{Quotient}=-4,\\\mathrm{Multiply\:}x-1\mathrm{\:by\:}-4:\:-4x+4,\\\mathrm{Subtract\:}-4x+4\mathrm{\:from\:}-4x+4\mathrm{\:to\:get\:new\:remainder},\\\mathrm{Remainder}=0,\\\mathrm{Therefore},\\\frac{-4x+4}{x-1}=-4

\mathrm{The\:Correct\:Answer\:is\:\left(x-1\right)\left(x^2-6x-4\right)}

\mathrm{Hope\:This\:Helps!!!}

\mathrm{-Austint1414}

8 0
3 years ago
Setting StartFraction 7 over 3 EndFraction equal to which ratio would result in a valid proportion?
pochemuha

Answer:

Option C is correct

Step-by-step explanation:

In this question, we are asked to select which of the options have the same value as 7/3

We examine the options one urge other.

Option A

9/49; This is wrong as it cannot be divided further to yield while multiples

Option B

18/42; Dividing through by 6 will yield 3/7 which is not same as 7/3; This makes this option wrong too

Option C

42/18; dividing through by 6 will yield 7/3 which makes this option correct

Option D

49/9; This is a dead end as it cannot be divided further to give whole number multiples

6 0
3 years ago
Read 2 more answers
What are two ratios equivalent to 10:85
guajiro [1.7K]

Answer:

2 : 17

1 : 8.5

6 0
3 years ago
A 15m long ladder reached a window 9m high from the ground on placing it against a wall at a distance x. Find the distance of th
Ilya [14]

Answer:

12 meters

Step-by-step explanation:

Given That :

Length of ladder = 15m

Height of wall =. 9 m

Using Pythagoras rule :

Adjacent² = hypotenus² - opposite²

Adjacent² = 15² - 9²

Adjacent² = 225 - 81

Adjacent² = 144

Adjacent = sqrt(144)

Adjacent, x = 12

8 0
3 years ago
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