Can you help me complete the proof and also correct any mistakes in my work.

The probability that there are fewer than 3 tornadoes in a 14-year period is 0.992333

Let x = number of tornados

n = 14

p = 0.03

There are just two outcomes that can occur in these independent, fixed trials, and the success probability is 0.03

Consequently, we may determine the probability using the binomial distribution.

Here we want to find P( X < 3) = P( X < = 3-1) = P(X <=2)

Using Excel:

P( X <=2) = "=BINOMDIST(2,14,0.03,1)" = 0.992333

Be aware that the default Excel command to find binomial probabilities that are less than or equal is  "=BINOMDIST(x, n, p, 1)"

Therefore, 0.9923333 percent of the time there won't be more than 3 tornadoes in a 14-year period.

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Simplify the given expression as shown below

Answer:

644

Step-by-step explanation:

-4x23=-92

-92x-7=644

i hope this helped :)

Answer:

Q is greater than P by 291

Step-by-step explanation:

The terms of these Arithmetic Sequences are odd natural numbers, because their common difference is 2

And, sum of 'n' odd natural numbers starting from 1 = n²

P = 99² - (1) = 9800

Q = 101² - (1 + 3 + 5) = 10192

Q - P = 291

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Explanation:

A = probability of picking a 7

A = 1/4 since one card is labeled "7" out of four cards total

B = probability of picking an odd number

B = 2/4 = 1/2 because there are 2 cards that are odd (5 and 7) out of 4 cards total.

C = A*B = probability events A and B happen

C = (1/4)*(1/2)

C = 1/8

This only works when we put the first card back, which means each event is independent.

Let's draw the figure to better understand the scenario:

Let,

s = the measure of the sides of the square

For us to be able to determine the area, let's first find out the measure of its side.

We will be using the Pythagorean Theorem:

Let's now determine the area of the square:

Therefore, the area of the square is 16.

The measures of the frequency distribution is;

(A) Range = 7

(B) Mean = 29

(C) Mode = 12

(D) Median = 29

(E) Variance = 7.612

(F) Standard Deviation = 2.759

A) The range of a frequency distribution is;

Range = Highest Value - Lowest Value

Thus;

Range = 32 - 25

Range = 7

B) Mean is expressed as;

x' = ∑fx/∑f

x' = [(25 * 4) + (26 * 6) + (28 * 6) + (30 * 4) + (32 * 12)]

x' = 928/32

x' = 29

C) Mode is the value with the highest frequency and so in this case;

Mode = 12

D) Median is the middle term when arranged from lowest to highest. In this case, it is the 16.5th term. Thus; Median = (28 + 30)/2 = 29

E) Variance = 7.612

F) The standard deviation is;

σ = √Variance

σ = 2.759

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Answer:

C - 3/4

Step-by-step explanation:

This question has to do with the change in the subject of the formula.

So we will proceed thus:

The correct answer, therefore, is the third option:

Answer:

the transformation matt can from A

Hello!

What is a slope-intercept line:

 [tex]y = mx + b[/tex]

            [tex]slope = \dfrac{y_2-y_1}{x_2-x_1} =\frac{-4--2}{3-0} =-\dfrac{2}{3}[/tex]

           ==> value of y-intercept is '-2'

Thus the equation is [tex]y=-\dfrac{2}{3}x-2[/tex]

Hope that helps!

Answer: y=-2/3x-2

Step-by-step explanation:

1) Draw a triangle from one point to the next point.

For this example, I will use (-3,0) and (0,-2).

You can see that the number goes down 2 and right 3. From this, you can conclude that the rate is -2/3 using the equation rise/run.

2) Find the y-intercept

Looking at the graph, you can find that the y-intercept is (0,-2).

3) Fill in the y=mx+b

y=-2/3x-2

Answer:

[tex]15xy+6x[/tex]

Answer:

26

Step-by-step explanation:

PEMDAS

8 + 2 = 10

6 - 4 = 2

10 x 2 = 20

2 x 3 = 6

20 + 6 = 26

step 1

Find out the measure of angle P

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

P+Q+R=180 degrees

substitute given values

P+70+60=180

P=180-130

P=50 degrees

step 2

Applying the law of sines

QR/sin P=PR/sin 70

substitute given values

QR/ sin 50=5/sin 70

QR=(5/sin 70)*sin 50

Answer:

400

Step-by-step explanation:

4 x 10^, 20^2

Answer:

25 pounds  16 ounces = 6400

Step-by-step explanation:

Recall that:

Let Victoria's speed be v.

Therefore, Victoria's resultant speed upstream is v - 4 and her resultant speed downstream is v + 4.

Hence the time of journey upstream is given by:

And the time of journey downstream is given by:

Since the time of journey upstream is the same as the time of journey downstream, it follows that:

Therefore, Victoria's speed is 46 mph

Answer:

See below

Step-by-step explanation:

Period = 1/2 year    total 4years = 8 periods

i = interest per period in decimal form = .12/2 = .06

initial deposit = ?

Final value = 60 000

60 000 = ? ( 1 + .06)^8

? = 37644.74

Given h(x), find h(4x) as shown below

Solution

The mean of the internal body temperature of the 12 abducted aliens is given by;

Differentiate using the product rule:

g. We take out the constant:

So:

Now

Substituting the derivatives found:

Simplify:

Answer:

Two parallel lines has the same slope.

The given line:

Is written in the form y=mx+b where m is the slope.

The slope is 8

To find the parallel line you need to write the given options in the form y=mx+b by solving y, as follow:

Slope is -1/8 (it is not parallel to given line)

_______________

Slope is 1/8 (it is not parallel to given line)

________________

Slope is -8 (it is not parallel to given line)

Answer:

264.9 in³

Explanation:

The volume of a cone can be calculated using the following equation:

Where π is approximately 3.14, r is the radius of the cone and h is the height.

So, replacing r by 5 in and h by 10.125 in, we get:

Therefore, the volume of the cone is 264.9 in³

Answer:

A. 1 over z raised to the twelfth power

Step-by-step explanation:

Hope this helps! :))
Please tell me if this is incorrect

Answer:

1 over z raised to the twelfth power

Step-by-step explanation:

we have the expression

Multiply in cross

Simplify

z^2-4=(z+2)(z-2) -----> difference of squares

z^2+z-12=(z+4)(z-3)

substitute in the above expression

Simplify

we know that

There are: 9 ways to put the first trophy.

8 ways to put the second trophy after putting the first one.

7 ways to put the third trophy after putting the second one.

6 ways .............the third one

5 ways --------> the fourth

4 ways------> 5

3 ways -----> 6

2 ways ----> 7

1 ways-----> 8

therefore

n!

where n=9

9!=9*8*7*6*5*4*4*2*1

9!=362,880

the answer is

Answers:

[tex]\cos(\theta) = \frac{-3\sqrt{5}}{7}\\\\\tan(\theta) = -\frac{2}{3\sqrt{5}} = -\frac{2\sqrt{5}}{15}\\\\\csc(\theta) = \frac{7}{2}\\\\\sec(\theta) = -\frac{7}{3\sqrt{5}} = -\frac{7\sqrt{5}}{15}\\\\\cot(\theta) = \frac{-3\sqrt{5}}{2}\\\\[/tex]

=================================================

Explanation:

We're given that [tex]\sin(\theta) = \frac{2}{7}\\\\[/tex]

Plug that into the pythagorean trig identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\[/tex] and solve for cosine to find that [tex]\cos(\theta) = \frac{-3\sqrt{5}}{7}\\\\[/tex]

I skipped steps in solving so let me know if you need to see them.

Keep in mind that cosine is negative in quadrant 2

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Once you've determined cosine, divide sine over cosine to get tangent

[tex]\tan(\theta) = \sin(\theta) \div \cos(\theta)\\\\\tan(\theta) = \frac{2}{7} \div \frac{-3\sqrt{5}}{7}\\\\\tan(\theta) = \frac{2}{7} \times -\frac{7}{3\sqrt{5}}\\\\\tan(\theta) = -\frac{2*7}{7*3\sqrt{5}}\\\\\tan(\theta) = -\frac{2}{3\sqrt{5}}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{3\sqrt{5}*\sqrt{5}}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{3*5}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{15}\\\\[/tex]

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To determine cosecant, we apply the reciprocal to sine.

[tex]\sin(\theta) = \frac{2}{7} \to \csc(\theta) = \frac{1}{\sin(\theta)} = \frac{7}{2}\\\\[/tex]

Similarly, secant is the reciprocal of cosine

[tex]\cos(\theta) = \frac{-3\sqrt{5}}{7} \to \sec(\theta) = \frac{1}{\cos(\theta)} = -\frac{7}{3\sqrt{5}} = -\frac{7\sqrt{5}}{15}\\\\[/tex]

Depending on your teacher, rationalizing the denominator may be optional.

Lastly, cotangent is the reciprocal of tangent

[tex]\tan(\theta) = -\frac{2}{3\sqrt{5}}\to \cot(\theta) = \frac{1}{\tan(\theta)} = \frac{-3\sqrt{5}}{2}[/tex]

------------------

Side notes:

Sine and cosecant are the only things positive in Q2

Everything else (cosine, tangent, secant, cotangent) are negative in Q2.