A circle has radius of 12 inches. What is the length of the arc subtended by a central angle
of 7/6 radians? Round to the nearest ioth.

[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

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

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:

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:

  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:

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 )

[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:

0.525 is the number.

X = Y/P%

X = 0.84/160%

p = 160%/100 = 1.6

X = 0.84/1.6

X = 0.525

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:

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:

Step-by-step explanation:

Let h be the height of the door

and w be its width

The statement “The height of the door is I foot more than twice its width”

can be translated mathematically like this :  h = 2w + 1

Let’s solve the equation for w:

h = 2w + 1

⇔ 2w = h - 1

[tex]\Leftrightarrow w=\frac{h-1}{2}[/tex]

now , if the door is 7 feet high then it’s width is equal to :

[tex]\Rightarrow \frac{7-1}{2} =\frac{6}{2} =3 \ ft[/tex]

Answer:

3 feet

Step-by-step explanation:

It mentions that the height of the door is 1 foot more than twice its width.

The width of a door of height 7 feet will be :

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:

m = [tex]\frac{1}{2}[/tex] , c = [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

y + 2x = 4 ( subtract 2x from both sides )

y = - 2x + 4 ← in slope- intercept form

with slope m = - 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (3, 4 ) into the partial equation

4 = [tex]\frac{3}{2}[/tex] + c ⇒ c = 4 - [tex]\frac{3}{2}[/tex] = [tex]\frac{5}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{2}[/tex] ← equation of line

with m = [tex]\frac{1}{2}[/tex] and c = [tex]\frac{5}{2}[/tex]

Answer:

300000

30000

3000

300

Step-by-step explanation:

Use the zero's trick for 10's.

The product of the given multiplications are 300000, 30000, 3000 and 300

Multiplication is when you take one number and add it together a number of times.

Example: 5 multiplied by 4 = 5 + 5 + 5 + 5 = 20. We took the number 5 and added it together 4 times. This is why multiplication is sometimes called "times".

Given that are four multiplication, 10000x30, 1000x30, 100x30 and 10x 30,

We know,

Multiplication by multiples of 10, 100, 1000, 10000:

We multiply the multiplicand by the non-zero digit of the multiplier. Then we add the same number of zero to the extreme right of the product as the multiplier has.

For example :-

26 × 10000 = 260000

524 × 10000 = 5240000

Therefore,

10000 x 30 = 300000

1000 x 30 = 30000

100 x 30 = 3000

10 x 30 = 300

Hence, the product of the given multiplications are 300000, 30000, 3000 and 300

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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!

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:

0.16666666666667.

Step-by-step explanation:

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:

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:

Nothing provided

Step-by-step explanation:

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:

Using the normal distribution, it is found that the life span of an appliance that has a z-score of –3 is of 24 months.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the parameters are given as follows:

[tex]\mu = 48, \sigma = 8, Z = -3[/tex].

Hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-3 = \frac{X - 48}{8}[/tex]

X - 48 = -24

X = 24.

The life span of an appliance that has a z-score of –3 is of 24 months.

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Answer:

Using the normal distribution, it is found that the life span of an appliance that has a z-score of –3 is of 24 months.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean  and standard deviation  is given by:

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, the parameters are given as follows:

.

Hence:

X - 48 = -24

X = 24.

The life span of an appliance that has a z-score of –3 is of 24 months.

Answer:

Candy is 21 years old

Step-by-step explanation:

If Alisa is 16 years old, that would mean that Barbara would be 8, since she is half of Alisa's age.

If we add 5 to Alisa's age, we get 21. To find the average of their ages, we add them all up, and divide by how many people there are (3).

16+8+21=45

45÷3=15

Hope this helps!

Age of Ailsa is 20 years. Then Candy's age will be 15 years.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

Ailsa is twice as old as Barbara. Ailsa is 5 years younger than Candy. The average age of Candy, Ailsa, and Barbara is 15.

Let 'x' be the age of Ailsa, 'y' be the age of Barbara, and 'z' be the age of Candy. Then the equations are given as,

x = 2y                                    ...(1)

x - 5 = z                                 ...(2)

(x + y + z) / 3 = 15                  ...(3)

From equations (1), (2), and (3), then

x + x / 2 + x - 5 = 45

(5/2) x = 50

x = 20

Then the age Candy is calculated as,

z = 20 - 5

z = 15

Age of Ailsa is 20 years. Then Candy's age will be 15 years.

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Answer: The median is 7 and the mode is 3

Step-by-step explanation:

Check the picture below.

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

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.

Answer:

  3, 4

Step-by-step explanation:

The expanded form of the given product is found using the distributive property. An equivalent form can be found using the commutative property of multiplication.

__

  7(2 -3n) = 7(2) +7(-3n) = 14 -21n . . . . . . . matches 3

Swapping the factors gives ...

  7(2 -3n) = (2 -3n)·7 . . . . . . . . . . matches 4

__

About the other choices

1. The value is not the same as 14 -21n. It appears to have been the result of (more or less) adding 7 to the coefficients inside parentheses.

2. It is a common mistake to eliminate parentheses after applying the outside factor to the first term only. That seems to be what happened here. The distributive property says you apply the factor to all the terms inside parentheses.

5. The sum of terms (2 -3n) has been incorrectly replaced by the product of terms (2)(-3n).

Part A

The yard is a quadrilateral with the following corner points

I'll label those points A through D in the order presented above.

From A to B is 40 feet since 40-0 = 40. We can subtract the y coordinates because the x coordinates are the same.

In short: side AB is 40 feet long.

The length of side BC is not as simple. We'll need the distance formula.

[tex]B = (x_1,y_1) = (0,40) \text{ and } C = (x_2, y_2) = (40,50)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-40)^2 + (40-50)^2}\\\\d = \sqrt{(-40)^2 + (-10)^2}\\\\d = \sqrt{1600 + 100}\\\\d = \sqrt{1700}\\\\d = \sqrt{100*17}\\\\d = \sqrt{100}*\sqrt{17}\\\\d = 10\sqrt{17}\\\\d \approx 41.2311\\\\[/tex]

Segment BC is exactly [tex]10\sqrt{17}[/tex] feet long, which is about 41.2311 feet.

Use the distance formula again to find the distance from point C(40,50) to D(50,0)

[tex]C = (x_1,y_1) = (40,50) \text{ and } D = (x_2, y_2) = (50,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(40-50)^2 + (50-0)^2}\\\\d = \sqrt{(-10)^2 + (50)^2}\\\\d = \sqrt{100 + 2500}\\\\d = \sqrt{2600}\\\\d = \sqrt{100*26}\\\\d = \sqrt{100}*\sqrt{26}\\\\d = 10\sqrt{26}\\\\d \approx 50.9902\\\\[/tex]

Lastly, the side AD is exactly 50 feet because 50-0 = 50. We can subtract x coordinates because the y coordinates are the same. Use of the distance formula from A to D should show a result of 50 exactly.

We have these side lengths:

AB = 40

BC = 41.2311 (approximate)

CD = 50.9902 (approximate)

AD = 50

Add up those four sides and we'll get the perimeter of the quadrilateral.

AB+BC+CD+AD = 40+41.2311+50.9902+50 = 182.2213

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

Part B

The garden is a rectangle that is 15 feet across horizontally (since subtracting x coordinates gives us 25-10 = 15) and 20 feet vertically (since subtracting y coordinates gives us 35-15 = 20).

This 15 by 20 rectangle has an area of 15*20 = 300 square feet.

The deck is a trapezoid with the parallel bases of 20 feet up top and 35 feet down below. Like before, we subtract x coordinates to find the horizontal distance (since the y coordinates are the same). The height of this trapezoid is 15 feet. Subtract the y coordinates to find the height.

The area of the trapezoid is

A = h*(b1+b2)/2

A = 15*(20+35)/2

A = 412.5

That decimal value is exact.

Add it onto the area of the rectangle

412.5+300 = 712.5