If there are 25 students in a class - 11 are guys and 14 are girls what is the probability that one of the students on the class is a guy?

Answer:

[tex]\frac{A}{(x-1)} + \frac{B}{(x-9)}[/tex]

Step-by-step explanation:

Given the expression [tex]\dfrac{1}{(x-1)(x-9)}[/tex], we are to write the expression as a partial fraction. Writing as a partial fraction means rewriting the expression a s a sum of two or more expression.

Before we will do this we will need to check the nature of the function at the denominator whether it is linear, quadratic or a repeated function. According to the question, the denominator at the denominator is a linear function and since it is a linear function, we can separate both linear function without restriction as shown;

[tex]\dfrac{1}{(x-1)(x-9)} = \frac{A}{(x-1)} + \frac{B}{(x-9)}[/tex] where A and B are the unknown constant which are numerical values.

Answer:

x > 39 hours

Step-by-step explanation:

Let x be the number of hours she worked.

11x - is how much she would get paid for working for x hours

11x + 20 > 450

11x > 430

x > 39 hours

Hope that helped!!! k

Answer:

the answer is a and d

Step-by-step explanation:

6 + 6 + 2 +2 = 16

3 + 3 + 5 + 5 = 16

to find perimeter, double each factor and add :)

Answer:

The confidence interval consist of positive values, it implies that the mean length of male babies at birth is more than that of female babies.

Step-by-step explanation:

Consider the hypothesis for testing the difference in the mean length of male babies and female babies​ at birth:

H₀: There is no significant difference between the mean length of male babies and female babies​ at birth, i.e. μ₁ - μ₂ = 0.

Hₐ: There is a significant difference between the mean length of male babies and female babies​ at birth, i.e. μ₁ - μ₂ ≠ 0.

The decision rule based on the confidence interval is:

If the (1 - α)% confidence interval does not consist of the null value, i.e. 0 then the null hypothesis will be rejected.

The confidence interval for the difference in the mean length of male babies and female babies​ at birth is:

CI = (0.2 in, 2.7 in)

The confidence interval does not consist of the null value, i.e. 0.

Thus, the null hypothesis will be rejected.

Hence, concluding that there is a significant difference between the mean length of male babies and female babies​ at birth.

Since the confidence interval consist of positive values, it implies that the mean length of male babies at birth is more than that of female babies.

Answer:

The 95% confidence interval for the proportion opposing health care changes is (0.6082, 0.6918).

Step-by-step explanation:

The (1 - α)% confidence interval for the population proportion is:

[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

The information provided is:

[tex]\hat p=0.65\\n=500\\\text{Confidence level}=95\%[/tex]

The critical value of z for 95% confidence level is:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]

*Use a z-table.

Compute the 95% confidence interval for the proportion opposing health care changes as follows:

[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

     [tex]=0.65\pm 1.96\sqrt{\frac{0.65(1-0.65)}{500}}\\\\=0.65\pm 0.04181\\\\=(0.60819, 0.69181)\\\\\approx (0.6082, 0.6918)[/tex]

Thus, the 95% confidence interval for the proportion opposing health care changes is (0.6082, 0.6918).

Answer:

See below.

Step-by-step explanation:

It depends on the sentence or phrase. If the sentence includes an operation of numbers or something related to comparing numbers, then maybe it can be translated into symbols. If the sentence or phrase has nothing to do with quantities, or operations or comparison of quantities, then probably it can't.

Examples:

1) The boy went for a walk.

There's nothing to translate into symbols in this case.

2) I had $10 in my bank account, then I deposited n dollars. Now I have $30 in my account.

In this case, I can translate the sentence into an equation.

10 + n = 30

Answer:

[tex] {x}^{4} = 2880[/tex]

Step-by-step explanation:

[tex] {y}^{2} = 20 \: (eq . \: 1)[/tex]

[tex] {x}^{2} = {(2 \sqrt{3y)} }^{2} = 12y [/tex]

Putting value of eq. 1 in the following:

[tex] {x}^{4 } = {(12y)}^{2} = 144{y}^{2} = 144 \times 20 = 2880[/tex]

Answer:

60.36 steps West from centre

85.36 steps North from centre

Step-by-step explanation:

Refer to attached

Musah start point and movement is captured in the picture.

or 360°, so bearing of 315° is same as North-West 45°.

Note. According to Pythagorean theorem, 45° right triangle with hypotenuse of a has legs equal to a/√2.

How far West Is Musah's final point from the centre?

How far North Is Musah's final point from the centre?

Answer:

8

Step-by-step explanation:

3x = 24

Divide both sides by 3

3x/3 = 24/3

x = 8

The solution for x in the equation, 3x = 24 is 8.

To solve the equation 3x = 24 for x, we need to isolate x on one side of the equation. Here's how we can do that:

Start with the equation 3x = 24.

Divide both sides of the equation by 3 to isolate x. This gives us (3x)/3 = 24/3.

Simplify the equation: x = 8.

Therefore, the solution to the equation 3x = 24 is x = 8.

This means that if we substitute x with 8 in the original equation, we get 3(8) = 24, which is true.

Read more about equation here: https://brainly.com/question/29174899

#SPJ6

Answer:

23 miles per gallon

Step-by-step explanation:

414 miles = 18 gallons

=> 18/18 gallons = 414/18 miles

=> 1 gallon = 23 miles

So, she drove 23 miles per gallon.

Answer:

The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs

of crackers

Step-by-step explanation:

IQR of trail mix data = 105 - 90 = 15

The range of cracker data = 100 - 70 = 30.

Therefore, the first option is NOT TRUE.

To check if option 2 is correct, calculate the lower limit to see if 70 is below the lower limit. If 70 is below the lower limit, then it is an outlier in the trail mix data.

Thus, Lower Limit = [tex]Q_1 - 1.5(IQR)[/tex]

Q1 = 90,

IQR = 105 - 90 = 15

Lower Limit = [tex]90 - 1.5(15)[/tex]

Lower Limit = [tex]90 - 22.5 = 67.5[/tex]

70 is not less than the lower limit, therefore, 70 is not an outlier for the trail mix data. The second option is NOT TRUE.

The upper quartile of the trail mix data = 105.

The maximum value of the cracker data = 100.

Therefore, the third option is NOT TRUE.

Range can be used to determine how much variable there is in a data represented on a box plot. The greater the range value, the greater the variation.

Range of trail mix data = 115 - 70 = 45

Range of cracker data = 100 - 70 = 30.

The range value for the number of calories in trail mix is greater than that for cracker, therefore, the number of calories in the packs of trail mix have a greater variation than the number of calories in the packs

of crackers.

The fourth option is TRUE.

Answer: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

Answer:

Following are the answer to this question:

Step-by-step explanation:

Let, In the Bth place there are 8 values.

In point a:

There is no case, where it generally manages its next groom is = 7 and it will be arranged in the 2, that can be arranged in 2! ways. So, the total number of ways are: [tex]\to 7 \times 2= 14\\\\ \{(1,2),(2,1),(2,3),(3,2),(3,4),(4,3),(4,5),(5,4),(5,6),(6,5),(6,7),(7,8),(8,7),(7,6)\}\\[/tex][tex]\therefore[/tex] required probability:

[tex]= \frac{14}{8!}\\\\= \frac{14}{8\times7 \times6 \times 5 \times 4 \times 3\times 2 \times 1 }\\\\= \frac{1}{8\times6 \times5 \times 4 \times 3}\\\\= \frac{1}{8\times6 \times5 \times 4 \times 3}\\\\=\frac{1}{2880}\\\\=0.00034[/tex]

In point b:

Calculating the leftmost position:

[tex]\to \frac{7!}{8!}\\\\\to \frac{7!}{8 \times 7!}\\\\\to \frac{1}{8}\\\\\to 0.125[/tex]

In point c:

This option is false because

[tex]\to P(A \cap B) \neq P(A) \times P(B)\\\\\to \frac{12}{8!} \neq \frac{14}{8!}\times \frac{1}{8}\\\\\to \frac{12}{8!} \neq \frac{7}{8!}\times \frac{1}{4}\\\\[/tex]

Answer:

2.8

Step-by-step explanation:

Hey there!

Well to find the amount of minutes needed to fill a 46.2 gallon bathtub we’ll divide.

46.2 / 16.5

= 2.8

2.58 minutes

Hope this helps :)

Answer:

x = -10

Step-by-step explanation:

(x - 3) - 2(x + 6) = -5

Distribute

x-3 -2x-12 = -5

Combine like terms

-x -15 = -5

Add 15 to each side

-x-15+15 = -5+15

-x=10

Multiply each side by -1

x= -10

Answer:

c

Step-by-step explanation:

Answer:

8 km

Step-by-step explanation:

            1 km

4 cm x -------- = 8 km

           0.5 cm

The actual cities are 8 km apart from each other at the scale 0.5 cm = 1 km.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

The distance between two cities on a map = 4 centimeters.

Also,  the scale

0.5 cm = 1 km

To find actual distance between cities, use ratio properly,

0.5 cm = 1 km

1 cm = 2 km

4 cm = 8 km

The distance between the actual cities is 8 km.

To learn more about Ratio on :

https://brainly.com/question/13419413

#SPJ2

Hello, there!!!!

Given that,

80°,3x° and 2x°are three angles on a st.line.

we have,

2x°+3x°+80°= 180° {The total sum of angles on a st. line is 180°}.

or, 5x°= 180°-80°

or, 5x°=100°

or, x= 100°/5

Therefore the value of x is 20°.

Hope it helps...

Answer:

I'm confused by this. What do they mean by prove?

Step-by-step explanation:

Step-by-step explanation:

はい、両側を削除して、3を掛けて7にします

Step-by-step explanation:

Given:

3n = 21

if we multiply both sides by 1/3, we will get:

3n = 21

3n x (1/3)= 21 x (1/3)

3n/3 = 21/3

n = 21/3

n = 7

Hence we can indeed solve for n by multiplying both sides by (1/3)

Answer:

x^3 - x^2 + 11x - 1

-x^3 - 8x^2 + 5x + 7

Step-by-step explanation:

Find the sum

(x^3+5x^2+3x-7)+(8x-6x^2+6)

=x^3+5x^2+3x-7+8x-6x^+6

Collect like terms

=x^3 +5x^2-6x^2+3x+8x-7+6

Add the like terms

= x^3 - x^2 + 11x - 1

Find the difference (7x-3x^2+2)-(x^3+5x^2+2x-5)

(7x-3x^2+2)-(x^3+5x^2+2x-5)

= 7x-3x^2+2-x^3-5x^2-2x+5

Collect like terms

= -x^3-3x^2-5x^2+7x-2x+2+5

Add the like terms

= -x^3 - 8x^2 + 5x + 7

Answer:

An example of when a continuity correction factor can be used is in finding the number of tails in 50 tosses of a coin within a given range .

and continuity correction factor is used when a continuous probability distribution is used on a discrete probability distribution

Step-by-step explanation:

An example of when a continuity correction factor can be used is in finding the number of tails in 50 tosses of a coin within a given range .

continuity correction factor is used when a continuous probability distribution is used on a discrete probability distribution,  continuity correction factor creates an adjustment on a discrete distribution while using a continuous distribution

Answer:

4450878

Step-by-step explanation:

Answer:

total amount paid = 32.5 + 28.9 + 24.95 = 86.35

20% of the total amount paid = 0.2 * 86.35 = 17.27

you tip 17.25$

Answer:

5⁻³ = 1/5³ = 1/125

Answer: 1/125

Step-by-step explanation:

Answer:

1. 36, 49, 64, 81

The pattern is going up by squares.  

2. 1/162, 1/486, 1/1458

The pattern is 1/3n.

Step-by-step explanation:

1. Before the blank spaces started we were at 5^2, or 25.  Now, we have to find 6^2, 7^2, 8^2, and 9^2.  That would be 36, 49, 64, and 81. It goes up by squares.

2. As the pattern continues, each number in the sequence is multiplied by 1/3 create the next number in the sequence.

The two rolls of the number cube are independent events because

the result of 1 roll does not affect the result of the other roll.

To find the probability of two independent events, we first find

the probability of each event, then we multiply the probabilities.

We can find the probability of an event using the following ratio:

number of favorable outcomes/total number of outcomes

Since there is only one way to roll a 3 and there are six

possible outcomes, 1, 2, 3, 4, 5, and 6, the probability of rolling a 3 is 1/6.

Since there is also only one way to roll a 2 and there are

six possible outcomes, the probability of rolling a 2 would be 1/6.

Now we multiply the probabilities.

1/6 x 1/6 is 1/36.

So the probability of rolling a 3 and a 2 is 1/36.

Answer:

1/36

Step-by-step explanation:

Probability of rolling 3 in a dice = 1/6.

Probability of rolling 2 = 1/6

Since, 2 should be followed after 3; we multiply 1/6 and 1/6

1/6 x 1/6 = 1/36.

Answer:

The dice has 6 options:

if the outcome is 5, player wins 50

if the outcome is 6, player wins 200

if the outcome is another number, the player does not win anything.

Now, remember that the expected value can be written as:

E = ∑xₙpₙ

where xₙ is the event n, and pₙ is the probability of that event.

for a dice, the probabilty for each number is 1/6

The expected value is:

E = (1/6)*(0 + 0 + 0 + 0 + 50 + 200) = 41.66

The expected gain will be E - 100 (because the player pays 100 in order to play)

Then the expected gain is:

G = 41.66 - 100 = -58.33

The standard deviation can be written as:

s = √( ∑(x - x)^2/n)

where x is the mean, in this case the mean is:

(200 + 50 + 4*0)/6 = 41.66  and n = 6.

s = √( (1/6)*(4*(0 - 41.66)^2 + (50 - 41.66)^2 + (200 - 41.66)^2) ) = 73

So we have a lot of standard deviation on Y.

Answer:

Solution : Option B

Step-by-Step Explanation:

We have the following system of equations at hand here.

{ x = 5 cot(t), y = - 3csc(t) + 4 }

Now instead of isolating the t from either equation, let's isolate cot(t) and csc(t) --- Step #1,

x = 5 cot(t) ⇒ x - 5 = cot(t),

y = - 3csc(t) + 4 ⇒ y - 4 = - 3csc(t) ⇒ y - 4 / - 3 = csc(t)

Now let's square these two equations. We know that csc²θ - cot²θ = 1, so let's subtract the equations  as well. --- Step #2

( y - 4 / - 3 )² = (csc(t))²

- ( x - 5 / 1 )² = (cot(t))²  

___________________

(y - 4)² / 9 - x² / 25 = 1

And as we are subtracting the two expressions, this is an example of a hyperbola. Therefore your solution is option b.

Answer:

the unknown number is 1500

Step-by-step explanation:

let "a" be the unknown number we finding so from the above question we can deduce that

(80/100)*a=1200

80a=1200*100

80a=120000

a=120000/80

a=1500

Answer:

Step-by-step explanation:

x² + 5x - 24

To factorize first write 5x as a difference so that when subtracted will give you 5 and when multiplied will give you - 24

That's

x² + 8x - 3x - 24

Factorize x out

That's

x( x + 8) - 3(x + 8)

Factor x + 8 out

We have the final answer as

Hope this helps you

Answer:(x-3)(x+8)

Step-by-step explanation:

Answer: 64 fluid ounces

Step-by-step explanation:

1 pint=16 fl oz

16*4=64