Find the distance between A(5,-4) and B(5,-5)

Percentage of the student body exists at least 21 years old exists 50%.

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

As one moves away from the center, values start to taper off and the majority of values are concentrated in this area. In a normal distribution, the mean, mode, and median are identical measures of central tendency.

When given a normal or Symmetric distribution, the mean of the distribution exists at the center with 0.5 or 50% of the distribution to either side (right and left) of the distribution.

Therefore, if the mean = 21 ; then the percentage of student body with at least 21 years is the percentage to the left of the distribution, which exists 50%.

P(x ≤ 21) = 0.5 = 50%

Therefore, 50 percentage of the student body exists at least 21 years old

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The dimensions given are as follows;

Base a = 36

Base b = 30

Height = 20

The area is derived as follows;

The area therefore is 660 square inches

Answer: 0, 3, 0

Step-by-step explanation:

f(a) represents the value of f(x) at x=a.

Answer:

pi/6 and 11pi/6

Explanation

Given the trigonometry equation:

Add 2\sqrt[3] to both sides as shown;

Take the cos inverse of both sides

Since theta is between 0 and 2pi

theta = 360 - 30

theta = 330^0

Convert to radians

180^0 = pi rad

30^0 = x

180x = 30pi

x = 30pi/180

x = pi/6

Similarly;

180^0 = pi rad

330^0 = x

180x = 330pi

x = 330pi/180

x = 11pi/6

Hence the value of thets between 0 and 2pi are pi/6 and 11pi/6

Answer: Uncle Luke is at 50 years old

Step-by-step explanation: I went through trial and error first with simple t-charts.  In the first one, I simply implemented the piece of info that Luke was 5 times older than the nephew. But then, I realized that Luke would always be 5 years older than his nephew. Here was the info for that t-chart:

[tex]\left \{ {{N=1} \atop {L=5}} \right. \left \{ {{N=2} \atop {L=6}} \right. \left \{ {{N=3} \atop {L=7}} \right.[/tex]

Next, I tried a chart starting with the nephew at 2 years of age, and got an age gap of 8. This helped me realize that I would have to start at 4 years of age in order to have an age gap of 16
[tex]\left \{ {{N=2} \atop {L=10}} \right.[/tex]        |             [tex]\left \{ {{N=4} \atop {L=20}} \right. \left \{ {{N=5} \atop {L=21}} \right.[/tex]  (remember there are 1 increments)

Next, I realized that N=4, L=20 was 40 years ago, so if now the nephew was 44, we can increment 16 to get 50
44+16=50

Answer:

$39.33

Step-by-step explanation:

11.25 + 12.50 +12.50 = 36.25

36.25 + 8.5% = 39.33

4.5 = m + 2.75

Solving for m:

Subtract 2.75 from both sides:

4.5 - 2.75 = m + 2.75 - 2.75

1.75 = m

m = 1.75

Answer:

See below

Step-by-step explanation:

Length (L), volume (V), weight(W), or mass(M)

Mile     L

Cup           V

Pound   W

Centimeter L

Liter     V

Gram   M

Pint           V

Yard   L

Kilogram   M

Teaspoon  V

Milliliter    V

1. Mile

2. Cup

3. Pound

4. Centimeter

5. Liter

6. Gram

7. Pint

8. Yard

9. Kilogram

10. Teaspoon,

11. Milliliter

The kilometres that she has cycled in total by the end of the 18th week is 105.

Based on the information, this is an arithmetic sequence and the formula is illustrated as

= a + (n - 1)d

where a = first term = 20

d = common difference = 5

n = numbers = 18

Therefore, the 18th term will be:

= a + (n - 1)d

= 20 + (18 - 1)5

= 20 + (17 × 5)

= 20 + 85

= 105

The number of kilometers is 105 kilometers.

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The mark up percentage gained by the shopkeeper is 400%.

For the given question.

The cost of the item is $103.

The customer pays is $515.

The mark up percentage is -

mark up percentage = 515 - 103 / 103

mark up percentage = 4 × 100%

mark up percentage = 400 %.

Thus, the mark up percentage gained by the shopkeeper is 400%.

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3x^2 + 1 = 5x

3x^2 - 5x + 1 = 0

quadratic formula

where ax^2 + bx + c = 0

so

You can see that the 25 - 12 = 13 so the answers are A and B

Solve for b

-73 = b/7- 81

b= 56

-511=b-567

b-567=-511

b=-511+567

b=56

Solution 2

Add 81 to both sides.

-73+81= b/7

simplify -73+81 to 8

8=b/7

8*7=b

simplify 8*7 to 56

56=b

switch sides b= 56

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If the equation be -73 = b/7- 81 then the value of b is 56.

Solve for b

-73 = b/7- 81

b= 56

-511=b-567

b-567=-511

Hence,

b=-511+567

b=56

Solution 2

Add 81 to both sides.

-73+81= b/7

simplify -73+81 to 8

8=b/7

8*7=b

simplify 8*7 to 56

56=b

switch sides b= 56

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Answer:

4:8

Step-by-step explanation:

Equivalent ratios have the same simplified ratio.

The simplified ratio of 3:6 is 1:2. We can get it by dividing both sides of the ratio by a common factor of 3.

18:9 is incorrect because its simplified ratio is 2:1. Equivalent ratios have the same order.

4:8 is correct because dividing both sides of the ratio by 4 gives us 1:2.

11:12 is incorrect because it can not be simplified to give 1:2.

Answer:

r = 23.7

Step-by-step explanation:

17 = r - 6.7 ( add 6.7 to both sides )

23.7 = r

Answer:

6+4,8-6, 4x2,8-2

Step-by-step explanation:

The system of equations to represent this scenario is x + y = 20  and 2x + 4y = 70  .

In the question ,

it is given that

the total number of tables in the restaurant = 20 tables

let the number of round tables be "x"

let the number of rectangular tables be "y" .

number of person that can seat on a round table = 2

So , the number of person that can seat on "x" round tables = 2x person

number of person that can can seat on rectangular table = 4

So , the number of person that can seat on "y" rectangular tables = 4y person

since total number of table is 20

So , the equation is x + y = 20

and total number of person that can seat are 70 seats .

So , the equation is 2x + 4y = 70

Therefore , The system of equations to represent this scenario is x + y = 20  and 2x + 4y = 70  .

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The Nya will pay $46.42 for the sweater. The decimal equivalent of a 20 percent discount is 0.20. To calculate the savings in dollars, multiply the decimal discount by the item's price. For instance, if the item's original price is $24, you would multiply 0.2 by that amount to get $4.80.

We have been given that Nya wants to buy a sweater that had an original price of $55. The sweater is now discounted 20%.

the price of sweater after20% discount is 55-20% of 55

The price of the sweater after discount =55-(20/100*55)

The price of the sweater after discount=55-(0.20*55)

The price of the sweater after discount=55-11

The price of the sweater after discount=44

SO  The price of the sweater after discount is $44

Now let us find the price of sweater after adding 5.5% sales tax

The price of sweater after sales tax =44+(5.5/100*44)

The price of sweater after sales tax=44+(0.055*44)

The price of sweater after sales tax=44+2.42

The price of sweater after sales tax=46.42

$46.42 is paid for sweater after sales tax

Hence, The Nya will pay $46.42 for the sweater.

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Answer:

45%

Step-by-step explanation:

In a class of 20 students, 5 have a brother and 11 have a sister. There are 3 students who have a brother and a sister. What is the probability that a student who does not have a brother has a sister?

P (no bro / yes sis) = P(no bro) - P(sis and bro)

       = 12/20 - 3/20

       = 9/20

       or 45%

25

1) We must start by reminding the binomials. Since this question refers to a perfect square trinomial then we can write:

2) Now we can look at the expression. Let's start by dividing that 10 by 2, since we have to write that -10x as 2 times the product of x and the other term:

Note that the second term is 5²= 25

3) Hence, the answer is 25

A) distribution of x and its parameter(s) is (λ^x e^-λ ) / x!  

B) standard deviation of x is 1

C) probability that x is (inclusively) within one standard deviation of the mean of x is 0.7358

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

A) The poisson distribution with mean is followed by X = λ = 1

Therefore, ≈ (λ = 1)

Distribution of X is:

(λ^x e^-λ ) / x!   ,    x = 0, 1, 2, 3 ......

B) Standard Deviation of X is :

σx = √x = 1

C) Probability of X = P (-1 ≤ x ≤ 1)

P(x = 0) + P(x = 1)

= (1⁰ e⁻¹) / 0! + 1¹ e-¹ / 1!

= 2e⁻¹

= 0.7358

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Answer:

See below

Step-by-step explanation:

The  equation is

y = [tex]x^{2}[/tex] + x

x equals the step

We see steps: 1, 2,3 and 4

y equals the number of squares that you see in each step.

If you look at step 1, you see [tex]1^{2}[/tex] + 1 = 2

Step 2: [tex]2^{2}[/tex] + 2 = 6

Step 3: [tex]3^{2}[/tex] + 3 = 12

Step 4: [tex]4^{2}[/tex] + 4 = 20

Can you see at each step there is a square of the number and then a little extra?  That little extra equals the number of the stop.

In the equation

y = 4x -2

Step 1

y = 4(1) -2

y = 2  It works!

Step 2:

y = 4x -2

y = 4(2)  - 2

y = 8 - 2

y = 6  It works!

Step 3:

y = 4x -2

y = 4(3) - 2

y = 12 - 2

y = 10  It does not work!

Step 4:

y = 4x -2

y  = 4(4) - 2

y = 16 - 2

y = 14  It does not work!

The equation y= 4x -2  only worked for the first 2 steps.

Gabrielle is the correct one.

The largest positive integer m that divides both x and y is the GCF of two or more non-zero integers, x, and y. The GCF stands for the greatest common factor. Here, greatest might be changed to highest, and factor to divisor. Therefore, the greatest common factor is often referred to as the highest common divisor )(HCD), highest common factor (HCF), or greatest common divisor (GCD.

Fractions, which are frequently employed in daily life, are almost always utilized with GCF. Finding the GCF of the denominator and numerator will allow you to obtain the necessary reduced form for simplifying a fraction or ratio. The greatest number that can divide two numbers x and y is their GCF.

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Answer:

AAS

Step-by-step explanation:

Because of vertical angle theorem, angle rts and vtu are congruent. This means there are 2 congruent angles with a non-included side

Answer:

She will no longer owe the bank any money. She will have 100 dollars in profit.

Step-by-step explanation:

$24 x 6 hours a day means she makes 144 dollars a day.
144 dollars times 25 means she makes 3600 dollars over the 25 day period.

3600-3500(the amount she owed) is 100 dollars

The expression that represents the situation is 5/2(x) and the family uses  350 gallons of water for each week.

Showerheads:

The showerhead is a bathroom fixture that directs the flow of water in a bathroom shower.

Given,

Low flow showerheads use 2 1/2 gallons of water per minute.

And the family uses 2 1/3 hours per week.

Here we need to find the expression for this situation and we also need to find the amount of water used by the family.

First, we have to convert the mixed fraction into improper fraction, then we get,

2 1/2 =5/2

So, for one minute the showerhead use 5/2 gallon of water.

So, the expression for this situation is,

=> 5/2(x).

Where x represents the amount of time in minutes.

Now, we know that the family uses the showerhead for 2 1/3 hours per week.

So, we have to convert this mixed fraction into improper fraction,

2 1/3 = 7/3

We know that, 1 hour = 60 minutes.

So, 7/3 hours is equal to,

=> 7/3 x 60 = 7 x 20 = 140

Then, the amount of water used by the family is,

=> 5/2 (140)

=> 5 x 70

=> 350

Therefore, the amount of water used by the family is 350 gallons per week.

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Given the Cyclic Quadrilateral Theorem,

Opposite angles of a Cyclic Quadrilateral are supplementary(that is, they add up to 180°).

Therefore,

To obtain y,

Thus,

Therefore, the values are

m

m

m

1) Gathering the data

Strategy:

Running : 2x As he swims

Biking: 4x Runs

Runs = 3 miles

Then

2) Runs = 3 miles Swims = 6 miles Biking = 12 miles

The Total distance will be the sum of those activities:

3+6+12=21 miles

The radius of the snowball decreasing by -2.

What is rate?

A rate is the ratio of two related values expressed in various units. [1] If one of these numbers is used as the ratio's denominator and it is assumed that this quantity can be altered in a predictable way (i.e., is an independent variable), then the numerator of the ratio represents the rate of change in the other (dependent) variable.

Let r(t) be a function of the radius of the sphere over time.

The volume of the sphere over time is then [tex]v(t) = \frac{4}{3} \pi r(t)^3[/tex]

The rate of change of the volume is then  [tex]v'(t) = 4\pi r(t)^2r'(t)[/tex]

Comparing is to the surface area of the sphere [tex]s(t) = 4\pi r(t)^2[/tex],  it seems perfectly possible for the volume to decrease at a rate equal to  2s(t).

That just means that

[tex]v'(t) = -2s(t)\\4\pi r(t)^2r'(t) = -8\pi r(t)^2\\r'(t) = -2[/tex]

Therefore, the radius must shrink by two units of distance every unit of time, it is now obvious.

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The equation of the Pythagorean Theorem  in the triangle  is 25^2 = 24^2 + 7^2

From the question, the side lengths of the triangle are given as

25, 24 and 7

The Pythagorean Theorem states that:

Hypotenuse^2 = Sum of the squares of the other sides

Where

The other sides are the smaller sides

This in other words mean that:

Other sides = 24 and 7

Hypotenuse = 25

Substitute the known values in the above equation

25^2 = 24^2 + 7^2

Hence, the Pythagorean Theorem equation is 25^2 = 24^2 + 7^2

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The measure of each angle in the diagram is as follows:

When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.

Therefore, the measure of each angle in the diagram can be calculated as follows:

10y = 7x + 4 (vertically opposite angles)

3y + 11  = 4x -22(vertically opposite angles)

Therefore,

10y - 7x = 4

3y - 4x = -22 - 11

10y - 7x = 4

3y - 4x = -33

multiply equation(ii) by 1.75

10y - 7x = 4

5.25y - 7x = - 57.75

subtract equation(ii) from equation(i)

Hence,

4.75y = 61.75

y = 61.75 / 4.75

y = 13

Therefore,

10(13) - 7x = 4

130 - 7x = 4

130 - 4 = 7x

7x = 126

x = 126 / 7

x = 18

Therefore, the unknown angles are as follows;

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