Luke is 5 years younger than 3 times Sydney's age, s. In this situation, what does 3s represent?
0 Luke's age
O Sydney's age
o three times Luke's age
O three times Sydney's age

Answer:

This question is not complete. Let me explain the concept of combination and permutation.

Step-by-step explanation:

The general formula for factorial is n! = n×(n - 1)×(n - 2)×...×2×1

0! = 1

Example 1:

How many different words can we make using the letters D, S, K and Z?

Solution:

We have 4 letters here.

Therefore, to get the possibility of the numbers, we will use:

4! = 4 x 3 x 2 x 1 = 24. We have 24 different words that can be made with the letters.

Permutation

The general formula for permutation is n P r = n! / (n - r)!

Example 2:

Find 5 [tex]P_{3}[/tex]

Solution: This will give 5!/(5-3)! = (5 x 4 x 3 x 2 x 1) / 2!

= 120 / 2 x 1 = 120 / 2 = 60

Combinations

The general formula for combination is n C r = n! / [ (n - r)! r! ]

Example 3:

Find 4[tex]C_{3}[/tex]

Solution: 4[tex]C_{3}[/tex] will give 4!/(4-3)!3! = (4 x 3 x 2 x 1) / 1!3!

= 24 / 1(3 x 2 x 1) = 24 / 6 = 4

Example 4: In Nigeria, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 followed by 3 letters from the alphabet. How many number plates will be formed if neither the digits nor the letters are repeated?

Solution: Note that we have 26 letters in the alphabet chart.

(9 P 4) × (26 P 3) = 9!/(9-4)! x 26!/(26-3)! = 47,174,400

Step-by-step explanation:

Hey, there!!

[tex] \frac{7}{3x} = \frac{2}{x + 5} [/tex]

By cross multiplication,

[tex]7.(x + 5) = 2 \times 3x[/tex]

[tex]7x + 35 = 6x[/tex]

[tex]7x - 6x = -35[/tex]

Therefore, x= -35.

Hope it helps...

Answer:

Here. I have graphed this for you. The points are at +3 and +3

Step-by-step explanation:

Answer:

354,500 square m

Step-by-step explanation:

Remaining area = Area of park - Area used for soccer and baseball field

= 560 * 700 - 250* 150

= 392,000 - 37,500

= 354,500 square m

Answer is fragment because is fragment walk block

Answer:

  b.  3 = 3/1

  c.  -4 = -4/1

Step-by-step explanation:

An integer can be written as a rational number with a denominator of 1. The denominator can be anything else, too, in which case the numerator must be multiplied by that same value.

__

b. 3 = 3/1 = 6/2 = 27/9

__

c. -4 = -4/1 = 8/-2 = -12/3

Answer:

400,000,000+30,000,000+200,000+90,000+100

Answer:

53 m^2

Step-by-step explanation:

53 m^2 is the area of the figure given!

So as given in the question that the sides meet at right angles.

we take the bottom of the upper rectangle as 5m, then the upper side of the lower rectangle will be 3+5+3= 11.

Now, by using the formula of the area of a rectangle that is Area = Height x width, we areas of the two rectangles. Then add both the areas.

Finally we get the area of the given figure!

Hope it helps you!

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Answer:

A = 53 m²

Step-by-step explanation:

A = A1 + A2

= 4m×5m + 3m×(3m + 5m + 3m)

= 20m² + 3m×11m

= 20m² + 33m²

= 53 m²

Answer: Volume = 40 cm3

Step-by-step explanation:

Answer:  14) 44°    15) 6.5

Step-by-step explanation:

Law of Cosines: a² = b² + c² - 2bc · cos A

Note: The letters can be swapped

14) Given: a = 7,  b = 6,  c = 10, A = ???

7² = 6² + 10² - 2(6)(10) · cos A

49 = 36 + 100 - 120 cos A

49 = 136 - 120 cos A

-87 =  - 120 cos A

0.725 = cos A

43.5° = A

15) Given: A = 21°,  b = 18,  c = 16

a² = 18² + 16² - 2(18)(16) · cos 21°

   = 324 + 256 - 576 cos 21°

   = 580 - 576 cos 21°

   = 42.26

[tex]a=\sqrt{42.26}[/tex]

   = 6.5

Answer:

D

Step-by-step explanation:

We know that we are adding the two expressions because the question says "sum" which means that we need to add. Let's combine like terms. We know that x + 2x = 3x and 5 + 3 = 8 so the answer is 3x + 8.

Answer:

D. 3x+8

Step-by-step explanation:

We want to find the sum of (x+5) and (2x+3). Sum means addition, so we must add the 2 expressions.

(x+5)+(2x+3)

Now, we must simplify by combining like terms.

First, combine the terms with variables.

(x+2x) + (5+3)

3x + (5+3)

Next, add the constants, or terms without variables.

3x+ 8

The sum of (x+5) and (2x+3) is 3x+8. This makes choice D the correct answer.

Answer:

8/-24=-3

-3/-24=8

I hope this is the answer

Answer:

B. 5

Step-by-step explanation:

Answer is: B. 5

Answer:

the answer is 4) 10π/9 inches

Step-by-step explanation:

all answers have π on the nominator but i could not insert it for some reason

[tex]Question 7 options:\\1) \frac{40}{3}inches \\2) \frac{5}{3} inches\\3) \frac{100}{3} inches \\4) \frac{10}{9} inches[/tex]

A circle is a curve sketched out by a point moving in a plane. The length of the arc with a central angle of 100° and a radius of 2 inches is 3.49 inches.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Given that the radius of the circle is 2 inches, while the angle made by the arc at the centre of the circle is 100°. Therefore, the length of the arc can be written as,

Length of the arc = 2 × π × R × (θ/360°)

                              = 2 × π × 2 inches × (100°/360°)

                              = 10π / 9  inches

                              = 3.49 inches

Hence, the length of the arc with a central angle of 100° and a radius of 2 inches is 3.49 inches.

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Answer:

The size of file downloaded is  88 megabytes.

Step-by-step explanation:

Given that:

Average rate of downloading the file = [tex]r[/tex]

Time taken to download = [tex]t[/tex]

Formula for the size of file downloaded = [tex]r.t[/tex]

Rate of downloading, [tex]r = 800\ kilobytes/sec[/tex]

Time taken, [tex]t[/tex] = 110 seconds

To find:

Size of file downloaded in megabytes = ?

Solution:

First of all, let us apply the given formula to find the size of file downloaded:

Size of file downloaded = [tex]r.t[/tex]

Size of file downloaded = 800 kilobytes seconds [tex]\times[/tex] 110 seconds =

88000 kilobytes.

Now, let us convert the unit kilobytes to megabytes to find the answer.

Conversion formula:

1000 kilobytes = 1 megabyte

Let us use unitary method to find the number of megabytes in 88000 kilobytes.

1 kilobytes = [tex]\frac{1}{1000}[/tex] megabytes

88000 kilobytes = [tex]\frac{1}{1000} \times[/tex] 88000 megabytes

[tex]\Rightarrow[/tex] 88 megabytes.

Therefore, the size of file downloaded is  88 megabytes.

Answer:

800/1000*110

Step-by-step explanation:

Answer:

12 [tex]units^{2}[/tex]

Step-by-step explanation:

square: 2 x 2 = 4 units sq

small triangle: 2 x 2 = 4, 4 / 2 = 2 units sq

big triangle: 2 x 6 = 12, 12 / 2 = 6 units sq

4 + 2 + 6 = 12 units sq

Answer:

12 units²

Step-by-step explanation:

we need to notice that the shape has two right triangles and a rectangle

the area of right triangles is b*h/2 and of the rectangle side*length

area of first triangle

Base=2

Height=2

[tex]A=\frac{2*2}{2} =2[/tex]

Area of the square

Side=2

Length=2

[tex]A_2=2*2=4[/tex]

Area of the second triangle

Base=2

Height=6

[tex]A_3=\frac{2*6}{2} =6[/tex]

so we need to add all three areas

[tex]A_T=A_1+A_2+A_3\\\\A_T=2+4+6=12\\\\A_T=12[/tex]

So the area is 12 units²

Answer:

The range is 77.

The variance is 739.8.

The standard deviation is 27.2.

Step-by-step explanation:

The data provided, in ascending order is as follows:

S = {11 , 14 , 23 , 31 , 40 , 60 , 63 , 68 , 75 , 77 , 88}

The range of a data set is the difference between the maximum and minimum values.

From the above data set we know,

Maximum = 88

Minimum = 11

Compute the range as follows:

Range = Maximum - Minimum

           = 88 - 11

           = 77

The range is 77.

Compute the mean of the data as follows:

[tex]\bar x=\frac{1}{n}\sum x_{i}=\frac{1}{11}\times [11+14+23+...+88]=50[/tex]

Compute the variance as follows:

[tex]\sigma^{2}=\frac{1}{n-1}\sum (x_{i}-\bar x})^{2}[/tex]

    [tex]=\frac{1}{11-1}\times [(11-50)^{2}+(14-50)^{2}+...+(88-50)^{2}]\\\\=\frac{1}{10}\times 7398\\\\=739.8[/tex]

The variance is 739.8.

Compute the standard deviation as follows:

[tex]\sigma=\sqrt{\frac{1}{n-1}\sum (x_{i}-\bar x})^{2}}=\sqrt{739.8}=27.199265\approx 27.2[/tex]

The standard deviation is 27.2.

The increasing the value of m increases the line’s intersection with the y-axis. intersection with the x-axis which is stepness

The steps are as follow:

Therefore the increasing the value of m increases the line’s intersection with the y-axis. intersection with the x-axis which is stepness

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Answer: C

Step-by-step explanation:

Answer: C. "How do you like this great new TV show?"

The term "great" put in there skews the question to make people think the show is great, when it may not be. So people may have a tendency to say they really like the show when they may not.

Or perhaps they may like the show (somewhat) but the fact that they can sense the bias built into the question makes them decide to say opposite and say they don't like the show. Maybe this sort of scenario would have them rebel in a way.

Either way, the use of "great" is likely to alter the opinion of people answering the question.

Answer: $3.68

Step-by-step explanation:

Answer:

[tex] \frac{9}{14} [/tex]

Step-by-step explanation:

Evaluate, [tex] -\frac{3}{2} [/tex] ÷ [tex] -\frac{7}{3} [/tex] by first changing the operation from division to multiplication and flipping the fraction by your right upside down.

Thus,

[tex] -\frac{3}{2} * -\frac{3}{7} [/tex]

Negative multiplied by negative = positive

[tex] \frac{3*3}{2*7} = \frac{9}{14} [/tex]

Answer:

Both variables Can tell you the degree to which a linear relationship exists between two variables.

Step-by-step explanation:

Correlation and regression are two statistical concepts that are closely related and complement each other. They are powerful tools used in modern-day machine learning and artificial intelligence.

Correlation evaluates the linear relationship between two variables, using regression as a tool to assess the degree at which a dependant variable changes ( either increasing or decreasing ) based on the value of an independent variable.

The correlation coefficient is the degree of the linear relationship between two variables, ranging from zero ( for non-linear) to one ( for highly linear).

Answer:

5.009, 5.09, 5.7, 5.7081

Answer:

5.009, 5.09, 5.7, 5.7081

Answer:

n = 10

Step-by-step explanation:

3n1!/(n-4)! = (n-1)!/( n-1-5)

3n(n-1)(n-2)(n-3)(n-4) / N-4 -------- case1 ( cancel ( n-4) from top and bottom)

= (n-1)(n-2)(n-3)(n-4)(n-5)(n-6) / n-6 --------- case 2 ( Cancel n-6 from top and

                                                                                 bottom and also cancel n-1,

                                                                                  n-2, n-3 with case 1)

3n = ( n-4)(n-5)

3n = n² - 5n - 4n + 20

3n =  n² - 9n + 20

0 = n² - 9n - 3n + 20

0 = n² - 12n + 20

0 = (n-2)(n-10)

n = 2  ( not valid)       n = 10

Therefore n = 10

Answer: y > (5/2)*x - 3

Step-by-step explanation:

Ok, the thins we should notice.

The line is shaded, so the values of the line are not solutions of the inequality, then we should use < or >.

The shaded part is above the line, so we have:

y > a*x + b.

A linear relationship can be written as:

f(x) = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Now, we know that our line passes through the points (0, -3) and (2, 2)

Then the slope is:

a = (2 -(-3))/(2 - 0) = 5/2.

f(x) = (5/2)*x + b.

To find the value of b, we can replace the values of one of the points in the equation, let's use the point (0, -3)

f(0) = -3 = (5/2)*0 + b

-3 = b

Then the line is:

f(x) = (5/2)*x - 3

Then the inequality is:

y > (5/2)*x - 3

I don't know how to commit on these posts but the guy above is wrong.

Answer:

[tex]\sin O \approx 0.919[/tex], [tex]\sec O \approx -2.539[/tex] and [tex]\tan O = -\frac{7}{3}[/tex].

Step-by-step explanation:

Given a point (x, y) with respect to origin and in rectangular coordinates, the exact value of sine, secant and tangent functions are, respectively:

[tex]\sin O = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex]

[tex]\sec O = \frac{1}{\cos O} = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex]

[tex]\tan O = \frac{\sin O}{\cos O} = \frac{y}{x}[/tex]

Given that [tex]x = -3[/tex] and [tex]y = 7[/tex], the exact values of sine, secant and tangent are:

[tex]\sin O = \frac{7}{\sqrt{(-3)^{2}+7^{2}}}[/tex]

[tex]\sin O \approx 0.919[/tex]

[tex]\sec O = \frac{\sqrt{(-3)^{2}+7^{2}}}{-3}[/tex]

[tex]\sec O \approx -2.539[/tex]

[tex]\tan O = \frac{7}{-3}[/tex]

[tex]\tan O = -\frac{7}{3}[/tex]

Answer:

12.8 cm^2

Step-by-step explanation:

Angle subtended by the sector=70

Radius of the circle= 21 cm

Area of the sector =[tex]\frac{given angle}{360}[/tex] x [tex]\pi r^{2}[/tex]

                              =    [tex]\frac{70}{360}* \frac{22}{7}*21\\\\\frac{70}{360 } *22*3\\\frac{77}{6}\\ 12.8[/tex]