Assume the birth of a boy or a girl is equally likely. The probability that a single child is born a girl is 1/2. What is the probability that the next child born to the same familiy will also be a girl?

In this problem, the student can use the properties of a 45°-45°-90° triangle to determine that the hypotenuse KL is 7 * √2 which is approximately equal to 9.9.

In a triangle where you know one angle (45°) and one side (7 units) across from the right angle, it is a typical example of a situation where trigonometry can be used. In this case, you're dealing with a 45°-45°-90° triangle, also known as an isosceles right triangle. In such a triangle, the sides are in a specific ratio. The sides opposite the 45° angles are the same length (let's call it 'a'), and the hypotenuse is a√2.

Given that LM = 7 and angle K is 45°, triangle KLM is therefore an isosceles right triangle and KL (the hypotenuse) is equal to LM multiplied by √2. So, KL = 7 * √2 which approximately equals to 9.9.

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Answer:

52

Step-by-step explanation:

Suppose Joe had $J$ dollars to start with. Then Mary had $J + 2$ dollars. Since they both spent the same amount on their shirts, $\frac{2}{5} J - 1 = \frac{1}{3} (J + 2)$. Distributing, we get $\frac{2}{5} J - 1 = \frac{1}{3}J + \frac{2}{3}$. Isolating $J$ on the left side, $\frac{1}{15}J = \frac{5}{3}$. Therefore, $J = 25$. Thus, their original total amount of money was $J + (J + 2) = \boxed{52}$ dollars.

Answer:

Option A is correct

Step-by-step explanation:

In the given figure to draw the parallel line to AC passing through B we have to tell the next step.

As lines AC and AB given and we know if lines are parallel then alternate angles are equal.

Hence, if line through B parallel to AC drawn then alternate angles ∠BAC and ∠ABD equal.

∴ To draw parallel lines our next step is to use a protractor to measure ∠BAC so that the same angle through B is drawn results in equal alternate interior angles.

Hence, Option A is correct.

Answer:

To show: [tex]\sqrt{21}[/tex] is between 4 and 5

We know:

21 is lies between two consecutive integer  i.e, 16 and 25

We can write this as:

[tex]16 < 21 < 25[/tex]

or

[tex]\sqrt{16} <\sqrt{21}<\sqrt{25}[/tex]

Simplify:

[tex]4 < \sqrt{21} < 5[/tex]

⇒[tex]\sqrt{21}[/tex] lies between 4 and 5.

Therefore,  [tex]\sqrt{21}[/tex] is between [tex]\sqrt{16}[/tex] and [tex]\sqrt{25}[/tex] this means [tex]\sqrt{21}[/tex] lies between 4 and 5.

Answer:

We know that

[tex]16<21<25[/tex]

Because, 16 is less than 21 and 25 is more than 21.

Now, if we apply a square root to each part, we would have

[tex]\sqrt{16} < \sqrt{21}<\sqrt{25}[/tex]

Then, we solve each square root, except the square root of 21, because it doesn't have an exact result

[tex]4<\sqrt{21}<5[/tex], because [tex]\sqrt{16}=4[/tex] and [tex]\sqrt{25}=5[/tex]

So, basically, the reason why [tex]\sqrt{21}[/tex] is between 4 and 5 is beacuse 21 is between 16 and 25. Then, when you apply square roots to each part, you would find that the square root of 21 is between 4 and 5. That's the reason, the position.

Answer:

its D

Step-by-step explanation:

The margin of error can be calculated using the t statistic. The formula for margin of error is given as:

Margin of error = t * s / sqrt (n)                                 ---> 1

Where,

t = the t score based on the given confidence level and degrees of freedom

n = number of samples = 21

s = standard deviation = 7.1

Degrees of freedom = n – 1 = 21 – 1 = 20

Based on the standard probability tables for t, the t score is:

t = 0.860

Substituting into equation 1:

margin of error = 0.860 * 7.1 / sqrt (21)

margin of error = 1.33

The range is:

range = 30.1 ± 1.33

range = 28.77, 31.43

Therefore the commute time to work is between 28.77 minutes and 31.43 minutes.

Answer:

Step-by-step explanation:

Any equation that is equivalent to V = x(12 - 2x)(8 - 2x) is accepted. Any graph that is similar to the graph of the function is accepted.

Sample Student Response:

The box is a cube, so the volume is the length × width × height. The height is the side length of the cardboard, which is x.

The length is the original length minus two side lengths of the cutout, so the length is 12 - 2x.

Similarly, the width is the original width minus two side lengths of the cutout, so the width is 8 - 2x.

Answer: [tex]sec \theta[/tex].

Step-by-step explanation: Given expression : [tex]\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .[/tex]

We know,

[tex]sec \theta = \frac{1}{cos \theta}[/tex]

[tex]tan \theta = \frac{sin \theta}{cos \theta}[/tex]

Substituting those values in given expression, we get

[tex]\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .[/tex] =[tex]\frac{sin \theta\ \frac{1}{cos \theta} } {cos \theta\ \frac{sin \theta}{cos \theta} }[/tex]

= [tex]\frac{sin \theta \ cos \theta}{cos \theta \ cos \theta \ sin \theta}[/tex]

Crossing out [tex]sin \theta \ cos \theta[/tex] from top and bottom, we get

=[tex]\frac{1}{cos \theta }[/tex]

= [tex]sec \theta[/tex].

Answer:

The simplified form of the given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex] is  [tex]\sec\theta[/tex]

Step-by-step explanation:

Given: Expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex]

We have to writ the given expression in simplified form.

Consider , The given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex]

Since, we know,

[tex]\sec\theta=\frac{1}{\cos\theta}[/tex]

and  [tex]\tan\theta=\frac{\sin\theta}{\cos\theta}[/tex]

Substitute, we have,

[tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}=\frac{\sin\theta \cdot\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{\sin\theta}{\cos\theta} }[/tex]

Simplify, we have,

[tex]=\frac{\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{1}{\cos\theta} }[/tex]

Simplify further, we get,

[tex]=\frac{1}{\cos\theta}=\sec\theta[/tex]

Thus, The simplified form of the given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex] is  [tex]\sec\theta[/tex]

opposite angles have to equal 180

 so 180-111 = 69

 angle 2 is 69 degrees

The area of a computer monitor with dimensions of 13.93 inches by 10.45 inches is approximately 0.09381 square meters.

To calculate the area of your computer monitor, you first need to convert the dimensions from inches to meters because the area is asked for in square meters. There are approximately 0.0254 meters in an inch. So the width is 13.93 inches * 0.0254 m/inch equals to approximately 0.354 meters, and the height is 10.45 inches * 0.0254 m/inch equals to approximately 0.265 meters.  

Then, we can calculate the area using the formula: Area = width * height. Substituting the converted measurements into the formula: Area = 0.354 m * 0.265 m which equals to approximately 0.09381 square meters.

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