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2 years ago

Write an equation to match the description. "three times the sum of a number and 12 is 35."

Mathematics

1 answer:

Nikitich [7]2 years ago

4 0

Answer:

$3 * (x + 12) = 35$

_____________

$\sf Solve~for~x$

Subtract 12 by the product(35) to find <em>x.</em>

$35 - 12 = 23$

_____________

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How do you reduce the ratio 250:400

Mkey [24]

You can divide by 10 and with that its simplified to 25;40...

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6 0

3 years ago

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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

Match the following items by evaluating the expression for x = -2.

jolli1 [7]

Answer:

X^-2= 1/4

X^-1=1/2

X^0=1

X^-1 = -2

X^2=4

Step-by-step explanation:

You’ll first have to plug in (-2) into x for the given expression and using the negative power rule since we have negative exponents; x^-a = 1/x^a You’ll start to plug in x^-2 into 1/2^2 simplify 2^2 to get 4 and for x^0 the rule of zero; x^0=1 Hopes this help and make sense

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3 years ago

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The cost of 9 scarves is $60.75. What is the unit price?

tiny-mole [99]

$6.75 hope this helps my dude

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4 years ago

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Is the square root of 53 a irrational or rational number

nevsk [136]

Pretty sure it’s irrational