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3 years ago

A number decreased by 18 is equal to the product of the number and 7.

2 answers:

4 0

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Define x:
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Let the number be x

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Construct Equation :
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x- 18 = 7x

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Take away x from both sides :
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-18 = 7x - x

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Combine like terms :
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-18 = 6x

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Switch sides :
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6x = -18

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Divide by 6 on both sides :
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x = -3

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Answer; The number is -3.
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Leno4ka [110]3 years ago

4 0

Hi there! The answer is x = - 3

A number decreases by 18 can be written as
$x - 18$

The product of the number and 7 can be written as
$7 \times x = 7x$

We get the following equation
$x - 18 = 7x$

Now subtract x from both sides.
$- 18 = 6x$

Switch sides
$6x = - 18$

Divide both sides by 6.
$x = - 18 \div 6 = - 3$

Therefore, the answer is x = -3

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"Rebecca walks 100 feet in a straight line. She then turns 20 degrees to her left and walks another 100 feet, and then turns 20

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Answer:

1,800 ft

Step-by-step explanation:

Rebecca will walk in the pattern of a regular polygon with 'n' sides and internal angles of 160 degrees (180 at a straight line - 20 degrees from each turn).

The equation that describes the internal angle of a regular polygon is:

$A = \frac{(n-2)*180}{n}$

For A = 160 degrees:

$160n=(n-2)*180\\(180-160)n=360\\n=18\ sides$

If each side is 100 ft long, the total distance that Rebecca has walked is:

$d = 18*100\\d=1,800\ ft$

She walked 1,800 ft.

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Answer:

a) $P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

b) $E(X) = np = 4*0.75=3$

c) $Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

d) $P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=4, p=1-0.25=0.75)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

$P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

Part b

The expected value is givn by:

$E(X) = np = 4*0.75=3$

Part c

For the standard deviation we have this:

$Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

Part d

For this case the sample size needs to be higher or equal to 9. Since we need a value such that:

$P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

We can verify this using the following code:

"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.

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