Find the volume of the cylinder.

Answer:

y = -2x + 5

Step-by-step explanation:

Slope-intercept form: y = mx + b

The slope of the line, m, is -2 because the line shows a negative trend and moves right 1 unit every time a point moves down 2 units.

The y-intercept, b, is 5 because the line crosses that number once on the y-axis.

The probability of selecting a multiple of 2 or a multiple of 7 is 11/20 or 0.55 or √0.3025.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total number of outcome = 20

Total number of favourable outcome (multiple of 2 or a multiple of 7):

E = {2, 4, 6, 7, 8, 10, 12, 14, 16, 18, 20}

n(E) = 11

The probability = 11/20 = 0.55 or

= √0.3025

Thus, the probability of selecting a multiple of 2 or a multiple of 7 is 11/20 or 0.55 or √0.3025.

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Answer:

[tex]x=13[/tex]

Step-by-step explanation:

Step 1: Isolate the square root on the left hand side

 Radical already isolated

  √x-4 = x-10

Step 2: Eliminate the radical on the left hand side

Raise both sides to the second power

    (√x-4)2 = (x-10)2

    After squaring

    x-4 = x2-20x+100

Step 3: Solve the quadratic equation

    Rearranged equation

    x2  - 21x  + 104 = 0

    This equation has two rational roots:

      {x1, x2}={13, 8}

Step 4: Check that the first solution is correct

    Original equation

    √x-4 = x-10

    Plug in 13 for  x

     √(13)-4 = (13)-10

     Simplify

     √9 = 3

     Solution checks !!

    Solution is:

     x = 13

Step 5: Check that the second solution is correct

    Original equation

    √x-4 = x-10

    Plug in 8 for  x

     √(8)-4 = (8)-10

     Simplify

     √4 = -2

     Solution does not check

     2 ≠ -2

One solution was found :

     x = 13

Answer:

60 degrees

Step-by-step explanation:

since its a vertically opposite angle so angle 1 will equal angle 3

Answer:

60

Step-by-step explanation:

If an event is likely to occur, the probability that the event will occur is between 3/4 and 1.

Probability determines how likely it is that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

If the probability lies between 0 and 1/5, it is likely that the event would not occur. If the probability lies between 1/5 and 1, it is likely that the event would occur.

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Answer:

75% and 100%

Step-by-step explanation:

The probability spectrum is (the spaces are supposed to be equal):

|----------------------|--------------------|--------------------|---------------------|

0%                    25%               50%              75%                   100%

impossible   unlikely          equal            likely                  certain

Answer:

3/25

Step-by-step explanation:

1/5 x 3/5 = 3/25

Answer:

31.5 units.

Step-by-step explanation:

The area is the height times the base divided by 2.

9x7 = 63

63/2 = 31.5

Answer:

7/10

Step-by-step explanation:

There are 20 students in the class.

The scores are :

100, 95, 88, 62, 74, 90, 100, 58, 72, 60, 85, 90, 70, 72, 54, 100, 60, 80, 75, 51

* scores ≥ 70 have been highlighted in bold

Out the 20, 14 students have passed.

Hence, the fraction of students passed :

Answer:

4080 cm³

Step-by-step explanation:

Figure is of a cuboid

Given length (l) = 30cm

breadth (b) = 17cm

height (h) = 8cm

Volume of cuboid = l.b.h

= 30 × 17 × 8

= 4080 cm³

Answer:

6. The number is [tex]-5[/tex]

7. The two numbers are [tex]10[/tex] and [tex]11[/tex]

Step-by-step explanation:

Question six can be re-worded to create the following expression:

[tex]-2=\frac{4x+10}{5}[/tex]

Solve for x to find the number:

[tex]-2=\frac{4x+10}{5}\\-10=4x+10\\-20=4x\\\frac{-20}{4} = x\\-5 = x[/tex]

Question seven can be solved by first listing the constraints (assuming x is smaller than y):

To get the numbers, we can create a system of linear equations. First, solve for [tex]y[/tex] in each expression:

[tex]y = x+1[/tex]

[tex]2y = 3x-8\\y = \frac{3}{2}x - 4[/tex]

Solve for [tex]x[/tex]:

[tex]x+ 1 = \frac{3}{2}x - 4\\x + 5 = \frac{3}{2}x\\5 = \frac{3}{2}x - x\\5 = \frac{1}{2}x\\10 = x[/tex]

Solve for [tex]y[/tex]:

[tex]y = x + 1\\y = 10 + 1\\y= 11[/tex]

Answer:

see explanation

Step-by-step explanation:

(6)

let n be the number then the sum of 4 times the number and 10 is 4n + 10

so

[tex]\frac{4n+10}{5}[/tex] = - 2 ( multiply both sides by 5 to clear the fraction )

4n + 10 = - 10 ( subtract 10 from both sides )

4n = - 20 ( divide both sides by 4 )

n = - 5

(7)

let the consecutive integers be n and n + 1 , then

3n = 2(n + 1) - 8 ← distribute parenthesis and simplify right side

3n = 2n + 2 - 8

3n = 2n - 6 ( subtract 2n from both sides )

n = - 6 and n + 1 = - 6 + 1 = - 5

the 2 integers are - 6 and - 5

[tex]f(x)=x+10\\\\f(7)=(7)+10\\\\f(7)=17[/tex]

the answer is 17.

Answer:

The answer is 17, x±10 =10+7= 17

[tex]\huge\rm\underline{Answer}[/tex]

✧ Rational numbers are represented on the number line by dividing a unit into as many divisions as the denominator of the rational number

Here , Each unit is divided into 7 equal parts . It means denominator of the rational number is 7.

So , A represents -10/7

So , B represents -6/7

So , C represents 3/7

So , D represents 15/7

Hope it helps ~

Answer:

6.28 meters

Step-by-step explanation:

Circumference is the distance around the circle, given by:

C = pi•d

C = 3.14 • 2

C = 6.28 meters

Answer:

6.28 Meters

Step-by-step explanation:

2pi * r

= 2*3.14

= 6.28 Meters

Answer:

159.25cm²

Step-by-step explanation:

A=lw

A=12×10cm

The rectangle’s area is 120cm² 

First, substitute the given information into the equation for the area of a circle.

A=πr²

A=(3.14)(5²)

A=3.14×25

A=78.5

Next, because the figure is only half of a circle, divide this in two.

78.5/2= 39.25cm²

Asc=39.25cm²

Add the two areas together.

A=Ar+Asc

120cm²+39.25cm²

The area of the combined figure is 159.25cm²

Answer:

Amanda's percent of error: = .03 or 3% Dwyane's percent of error: = .02 = 2%

Looks like Amanda had the larger error.

Answer:

Reese's Peanut Butter Cups: 10.8

York Peppermint Patties: 2.6

Step-by-step explanation:

Let Reese's Peanut Butter Cups be r and York Peppermint Patties y.

Step 1: Make equations.

1) If you buy 3 bags of Reese's Peanut Butter Cups and 6 bags of York Peppermint Patties, it costs $48.

[tex]3r + 6y = 48[/tex]

2) If you buy 4 bags of Reese's Peanut Butter Cups and 3 bags of York Peppermint Patties, it costs $51.

[tex]4r + 3y = 51[/tex]

Step 2: Solve the system of equations.

We have system of equations. I'll solve them by elimination.

[tex](1.) \text{ } 3r + 6y = 48\\(2.) \text{ } 4r + 3y = 51[/tex]

Multiply the second equation with 2 so we'll get 6y.

[tex](1.) \text{ } 3r + 6y = 48\\(2.) \text{ } 8r + 6y = 102[/tex]

Now let's subtract second equation from first and solve for r.

[tex]3r - 8r + 6y - 6y = 48 - 102\\-5r = -54\\r = \frac{-54}{-5}\\r = \$10.8[/tex]

To get y let's substitute the value of r in first equation.

[tex]3r + 6y = 48\\3 \cdot 10.8 + 6y = 48\\32.4 + 6y = 48\\6y = 15.6\\y = \$2.6[/tex]

Answer:

3

Step-by-step explanation:

Coefficient in the number behind the variable.

In 3x + 7,

x is the variable.

3 is the coefficient.

Answer:

4(3)(-2) = -24

Answer:

C) -24

Step-by-step explanation:

Given the expression: 4xy

Substitute the values above for the variables and multiply:

4(3)(-2)

12(-2)

-24

Final answer: -24

Hope this helps!

Answer: The median is 7 and the mode is 3

Step-by-step explanation:

Check the picture below.

Answer:

x = 10.9 cm

Step-by-step explanation:

Formula for a cone

Here, we are given :

Solving

Answer:

x ≈ 3.6 cm

Step-by-step explanation:

the volume (V) of a cone is calculated as

V = πr²h ( r is the radius and h the perpendicular height )

here diameter = 7 , so r = 7 ÷ 2 = 3.5 , V = 140 and h = x , then

π × 3.5² × x = 140

π × 12.25x = 140 ( divide both sides by 12.25π )

x = [tex]\frac{140}{12.25\pi }[/tex] ≈ 3.6 cm ( to 1 dec. place )

Answer:

Step-by-step explanation:

Since the x-axis is the line of symmetry, the missing vertex is the reflection of the given vertex over the line of symmetry.

Connect these points with the vertex on the x-axis to complete the triangle.

See the attachment

See attachment for the graph of g(x) = 1/2x^2

The equation of the function is:

g(x) = 1/2x^2

The above function is a quadratic function that has only one term

Next, we plot  the graph using a graphing tool

See attachment for the graph of g(x)

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Answer:

0.16666666666667.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

the standard form of a quadratic expression is ax² + bx + c ( a ≠ 0 )

(1)

(2x + 5)(x + 1)

each term in the second factor is multiplied by each term in the first factor, that is

2x(x + 1) + 5(x + 1) ← distribute parenthesis

= 2x² + 2x + 5x + 5 ← collect like terms

= 2x² + 7x + 5 ← in standard form (a = 2, b = 7, c = 5 )

(2)

(x - 2)(x + 2)

= x(x + 2) - 2(x + 2) ← distribute parenthesis

= x² + 2x - 2x - 4 ← collect like terms

= x² - 4 ← in standard form (a = 1, b = 0, c = - 4 )

Answer:

[tex]3^{n}+3^{n-1}[/tex]

Step-by-step explanation:

Since the sequence is geometric (it multiplies the previous number each time). The nth term sequence would be [tex]x^n + yn[/tex]

Because the sequence multiplies by 3 each time, The base number in that equation would be [tex]3^n +yn[/tex].

So [tex]3^n[/tex] of the equation would be:
[tex]3, 9, 27[/tex].

Compare the 2 equations:
4, 12, 36

3, 9 ,27

The difference between the 2 equations is: 1, 3, 9 which itself is a geometric sequence so the nth term of this new equation is: [tex]3^{n-1}[/tex].

Combine these 2 equations together and you get:

[tex]3^{n}+3^{n-1}[/tex].

Answer:

  9.  AB = (40/3)√3

  10.  BC = (20/3)√3

Step-by-step explanation:

The ratios of side lengths in the "special" 30-60-90° triangle are ...

  1 : √3 : 2

__

If D is the point where the altitude meets AB, then we have for the left triangle ...

  CD : AD : CA = 1 : √3 : 2 = 10 : 10√3 : 20

and, for the right triangle ...

  BD : CD : BC = 1 : √3 : 2 = (10/√3) : 10 : (20/√3)

and for the large triangle ...

  BC : CA : AB = 1 : √3 : 2 = (20/√3) : 20 : (40/√3)

__

The hypotenuse of ΔABC is AB, shown above to be ...

  AB = 40/√3 = (40/3)√3

__

The shorter leg of ΔABC is BC, shown above to be ...

  BC = 20/√3 = (20/3)√3

Answer:

Nothing provided

Step-by-step explanation: