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2 years ago

7 (m+5) = 21 as a step by step problem?

Mathematics

2 answers:

Sever21 [200]2 years ago

8 0

Answer:

m=-2

Step-by-step explanation:

You want to isolate the variable on one side (m).

Divide each side by 7.

m+5=3

Subtract 5 from both sides

m=-2

lina2011 [118]2 years ago

6 0

Answer:

m = -2.

Step-by-step explanation:

First divide both sides by 7; m + 5 = 3.

Then subtract 5 from both sides; m = -2.

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In studies for a medication, 3 percent of patients gained weight as a side effect. Suppose 643 patients are randomly selected.

timofeeve [1]

Part a)

It was given that 3% of patients gained weight as a side effect.

This means

$p = 0.03$

$q = 1 - 0.03 = 0.97$

The mean is

$\mu = np$

$\mu = 643 \times 0.03 = 19.29$

The standard deviation is

$\sigma = \sqrt{npq}$

$\sigma = \sqrt{643 \times 0.03 \times 0.97}$

$\sigma =4.33$

We want to find the probability that exactly 24 patients will gain weight as side effect.

P(X=24)

We apply the Continuity Correction Factor(CCF)

P(24-0.5<X<24+0.5)=P(23.5<X<24.5)

We convert to z-scores.

$P(23.5 \: < \: X \: < \: 24.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 1.20) \\ = 0.051$

Part b) We want to find the probability that 24 or fewer patients will gain weight as a side effect.

P(X≤24)

We apply the continuity correction factor to get;

P(X<24+0.5)=P(X<24.5)

We convert to z-scores to get:

$P(X \: < \: 24.5) = P(z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P(z \: < \: 1.20) \\ = 0.8849$

Part c)

We want to find the probability that

11 or more patients will gain weight as a side effect.

P(X≥11)

Apply correction factor to get:

P(X>11-0.5)=P(X>10.5)

We convert to z-scores:

$P(X \: > \: 10.5) = P(z \: > \: \frac{10.5 - 19.29}{4.33} ) \\ = P(z \: > \: - 2.03)$

$= 0.9788$

Part d)

We want to find the probability that:

between 24 and 28, inclusive, will gain weight as a side effect.

P(24≤X≤28)=

P(23.5≤X≤28.5)

Convert to z-scores:

$P(23.5 \: < \: X \: < \: 28.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{28.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 2.13) \\ = 0.1494$

3 0

4 years ago

Two consecutive whole numbers such that the sum of their squares is 13

valina [46]

The square root of 169 is 13 and 170 is 13.03

5 0

3 years ago

Inverse of f(x)=-5x+15

Otrada [13]

f(x) = -5x - 15

Let y = f(x)

y = -5x - 15

Switch the x and y places, and solve for y:

x = -5y - 15

-5y = x + 15

y = (x + 15)/-5

y = -(x/5) - 3

So the inverse of : f(x) = -5x - 15 is

-x/5 - 3

5 0

4 years ago

Find the magnitude of the vectors {-4, 2} to the nearest tenth

Dimas [21]

$\bf \begin{array}{rllll}
\ \textless \ -4&,&2\ \textgreater \ \\
a&&b
\end{array}\implies 
\begin{array}{llll}
||\ \textless \ a,b\ \textgreater \ ||=\sqrt{a^2+b^2}\\\\
||\ \textless \ -4,2\ \textgreater \ ||=\sqrt{(-4)^2+2^2}
\end{array}$

5 0

4 years ago

Can someone please help me with this and make sure it’s correct

Len [333]

The answer is: B
Explanation: 8 is fixed, not related to the number of marbles.

5 0

3 years ago