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professor190 [17]

2 years ago

15

In a shipment of toys from a manufacturer. The probability that a toy is defective is 1/50. If Marie selects 2 toys from a shipm

ent. What is the probability that both toys are defective?

2 answers:

GrogVix [38]2 years ago

8 0

Answer: The required probability is $\dfrac{1}{2500}.$

Step-by-step explanation: Given that in a shipment of toys from a manufacturer, where

the probability that a toy is defective is $\frac{1}{50}.$

We are to find the probability that both toys are defective, if Marie selects 2 toys from a shipment.

Since the events of selecting toys from a shipment are independent of each other,

therefore, the required probability that both toys are defective, if Marie selects 2 toys from a shipment will be

$P=\dfrac{1}{50}\times\dfrac{1}{50}=\dfrac{1}{2500}.$

Thus, the required probability is $\dfrac{1}{2500}.$

sukhopar [10]2 years ago

7 0

The probability is 1/2500. (1/50)*(1/50)

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In the diagram of circle A, what is the measure of ∠XYZ?<br><br> 35°<br> 70°<br> 75°<br> 140°

Mademuasel [1]

Answer: First Option is correct.

Step-by-step explanation:

Since we have given that

Measure of arc WZ = 175°

Measure of ∠XAZ = 105°

We need to find the measure of ∠XYZ.

As we know the angle subtended at the center is the average of the measure of arc intercepted by it angle and its vertical angles.

$\frac{175^\circ+\angle XYZ}{2}=105^\circ\\\\175^\circ+\angle XYZ=210^\circ\\\\\angle XYZ=210^\circ-175^\circ\\\\\angle XYZ=35^\circ$

Hence, the value of ∠XYZ is 35°.

Hence, First Option is correct.

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2 years ago

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Which statements are true regarding triangle LMN? Check all that apply.

dimaraw [331]

Answer:

$NM = x$

$LM = x\sqrt{2}$

$tan (45) = 1$

Step-by-step explanation:

Step 1: Pythagoras Theorem

Pythagoras theorem relates the three sides of the triangle in such a way that the sum of the square of base and perpendicular is equal to hypotenuse, such as:

$LM^{2} =LN^{2} +NM^{2}$

Step 2: Trigonometric Functions

Only for a right angle triangle following three trigonometric relations are valid

$sin (\theta) = \frac{opposite}{hypotenuse}$

$cos (\theta) = \frac{adjacent}{hypotenuse}$

$tan (\theta)=\frac{sin (\theta)}{cos (\theta)} = \frac{opposite}{adjacent}$

Step 3: Verifying all the possible answers

A: Since, LN = x and using $tan (45) =1$

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{NM}{x} =1$

therefore, NM = x (true)

B: As NM = x therefore it can not be equal to $x\sqrt{2\\}$ .

C: Using Pythagoras Theorem

$LM^{2} =LN^{2} +NM^{2}$

$LM^{2} =x^{2} +x^{2}$

$LM^{2} =2x^{2}$

$LM = \sqrt{2x^{2}} = x\sqrt{2}$

It can also be proved using trigonometric relation

$cos (45) = \frac{x}{LM}$

$LM = \frac{x}{cos (45)}$

As, $\frac{1}{cos (45)}= \sqrt{2}$

Therefore

$LM = x\sqrt{2}$

D and E:

Using same approach similar to part A

Since, LN = x and NM = x

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{x}{x} =1$

Therefore, $tan (45) = 1$ and not equal to $\frac{\sqrt{2} }{2}$

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Roberta invested $600 into a mutual fund that paid 4% interest each year compounded annually. Write an exponential function of t

Oksanka [162]

Answer:

The exponential equation is <em>A = 600(1.04)^15</em>

<em></em>

The value of the mutual fund after 15 years is <em>$1,081</em>

Step-by-step explanation:

The value of the mutual fund after the number of years can be represented using the compound interest equation below;

A = P(1 + r/n)^nt

Where A is the value of the mutual fund after 15 years, P is the initial amount invested which is $600, r is the interest rate which is 4% or 0.04(4% = 4/100 = 0.04), n is the number of times we are compounding per year(which is 1 since it is a one time payment per year) and t is the number of years which is 15

Let's plug these values, we have;

A = 600(1 + 0.04/1)^15

A = 600(1.04)^15

A = $1,081 approximately

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Alisiya [41]

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The ordered pairs would be:
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Now, the equation for this would be $y = 2^{(x+1)}$

If we graph that, and we do the vertical line test, then we know this is a function.

It is a function because each x-value has a different y-value. There are no y-values that have the same x-values.

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