Piecewise Function - The domain is split

Answer:

61 rows

Step-by-step explanation:

Set up a proportion:

[tex]\frac{15}{22}[/tex] = [tex]\frac{x}{90}[/tex]

Cross multiply:

22x = 1350

x = 61.36

= approx. 61 rows

Answer:

x = 5

Step-by-step explanation:

0.5x + 3.5 = 6

0.5x = 6 - 3.5

0.5x = 2.5

x = 2.5 / 0.5

x = 5

Answer:

subtract 5

Step-by-step explanation:

subtract 5 from each side of the equal sign..

Answer:

the answer is subtract 5

Step-by-step explanation:

Answer:

[tex]34.12 * 11 = 375.32[/tex]

Step-by-step explanation:

Given

11 * 34.12

Required

Multiply

To start with, we have to ignore the decimal points;

So, we have

    3412

  *      11

---------------

   3 4 1 2

3 4 1 2

------------------------

3 7 5 3 2

The next step is as follows;

34.12 is in 2 decimal places

11 is has no decimal (0 decimal place)

Add the decimal places together

[tex]Decimal\ Place = 2 + 0 = 2[/tex]

This implies that the result will be in 2 decimal placed;

Hence:

[tex]34.12 * 11 = 375.32[/tex]

Answer:

4 OR 4.5 SECONDS

Step-by-step explanation:

Answer:

the rectangle's width is approximately 3.39 inches

and the length is approximately 13.56 inches.

Step-by-step explanation:

Recall that the area of a rectangle is Length times Width

If we name the length "L" and the width "W", we have:

L * W = 46

Also: "the length is 4 times the width" can be written in math form as:

L = 4 * W

and now we can replace the length L by 4 * W in the formula for the area:

[tex]L\,*\,W = 46\\(4\,W) \,W = 46\\4\,W^2=46\\W^2=\frac{46}{4} =11.5\\W=\sqrt{11.5} \\W\approx 3.39[/tex]

and now we find the value of L:

[tex]L=4\.(3.39) = 13.56[/tex]

Therefore, the rectangle's width is approximately 3.39 inches

and the length is approximately 13.56 inches.

Answer:

Step-by-step explanation:

f(x) = x² - 2x - 24

g(x) = x + 4

To find (f-g)(x) subtract g(x) from f(x)

That's

(f-g)(x) = x² - 2x - 24 - ( x + 4)

(f-g)(x) = x² - 2x - 24 - x - 4

Group like terms

We have

(f-g)(x) = x² - 2x - x - 24 - 4

Simplify

We have the final answer as

Hope this helps you

Answer:

(4,7)

Step-by-step explanation:

f(x)=5x-13

Let this equal to 7

7=5x-13  

Add 13 to each side

7+13 = 5x-13+13

20 = 5x

Divide by 5

20/5 = 5x/5

4 =x

The ordered pair is

(4,7)

Answer:

Negative change

Step-by-step explanation:

Given

[tex]Monday\ Temperature = 5\ deg[/tex]

[tex]Thursday\ Temperature = -8\ deg[/tex]

First, we need to calculate the overall change in temperature

This is calculated by subtracting the initial temperature from the final temperature

[tex]Overall\ Change = Thursday\ Temperature - Monday\ Temperature[/tex]

[tex]Overall\ Change = -8\ deg - 5\ deg[/tex]

[tex]Overall\ Change = -13\ deg[/tex]

The overall change shows a negative change in the temperature.

This is as a result of a drop in temperature from Monday to Thursday

Answer:

Translation

Step-by-step explanation:

The object is only moved, which is what happens when a translation occurs

Answer:

the vetrex

Step-by-step explanation:

Answer:

16 * √3 cm² or approximately 27.71 cm²

Step-by-step explanation:

Given the 8 cm length of the diagonal and the 30° (π/6 radians) angle with one of the sides, we can calculate the width and height of the rectangle using:

8 * cos(π/6) = 8 * ((√3)/2) = 4 * √3

8 * sin(π/6) = 8 * (1/2) = 4

Multiply those two values together to get the area and you get

16 * √3 cm²

Answer:

4/9

Step-by-step explanation:

0.4444... can be written as a geometric series with first term 0.4 and common ratio 0.1.  Each new digit is 0.1 times the previous digit.

                               0.4

Then 0.4444... = ------------ = 0.4/0.9 = 4/9

                             1 - 0.1

You may check this result by dividing 4 by 9 on a calculator.

Answer:

People like oranges

Step-by-step explanation:

Given:

Mo likes oranges. Jai likes oranges. Ben likes oranges.

We have a few different options;

Option A: People don't like other fruit, such as apples. This can't be possible because we have only been given people who like oranges.

Option B: People on like oranges. This can't be possible because only is the case where people do not like any fruit except oranges, and we are not sure of this.

Option C: People like oranges. This can be possible because Mo, Jai, and Ben likes oranges

Option D: People like fruit. This can't be possible because we are not sure if people like all fruits or not

People like oranges.

the action or process of inducting someone to a position or organization.

We have a few different options;

Option A: People don't like other fruit, such as apples. This can't be possible because we have only been given to people who like oranges.

Option B: People like oranges. This can't be possible because only is the case where people do not like any fruit except oranges, and we are not sure of this.

Option C: People like oranges. This can be possible because Mo, Jai, and Ben like oranges

Option D: People like fruit. This can't be possible because we are not sure if people like all fruits or not

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Answer:

-1.5

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

-1.5

-1 1/2

-6/4

Answer:

3L

Step-by-step explanation:

Perimeter is the sum of side lengths

Since the triangle is equilateral, it has all sides equal and each has length of L

So perimeter is:

La mentalidad de crecimiento, ya que a diferencia de la mentalidad fija, nos permite ver en otras personas la mentalidad de mejorar y perseverar.

Answer:

10 miles

Step-by-step explanation:

3a/5 + 4 = a

a = race long

4 = a - 3a/5

4 = 5a/5 - 3a/5

4 = 2a/5

4*5/2 = a

a = 10

The length of the entire race is 10 miles.

Let length of race = r

Miles left after running 3/5 of race :

We can solve the expression thus :

r - 3r/5 = 4

r - 3r = 4 * -5

r - 3r = -20

-2r = -20

divide both sides by -2 to isolate r

r = 10

Hence, the length of the entire race is 10 miles.

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Answer:

Answer: $428.00

Step-by-step explanation: First, we need to calculate the person’s total hours, (30 x 2 = 60 hours) then the money per hour (60 x 9) then take away the taxes and account deductions.

Answer:

C

Step-by-step explanation:

Since the exponent on the 10 is negative, we need to move the decimal point to the left instead of the right. After moving the decimal point on the 2.5 to the left 4 places, we see that the answer is 0.00025.

Integration

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Double Integrals

Polar Coordinates Conversions:

Integral Conversion [Polar Coordinates]:
[tex]\displaystyle \iint_T {f(x, y)} \, dA = \iint_R {f(r, \theta)r} \, dr \, d\theta[/tex]

The formatting of the question was thrown off, so I have defined it down below.

We are given an integral and asked to convert to polar coordinates as well as evaluate it:
[tex]\displaystyle \int \limits^{8}_{-8} \int \limits^{\sqrt{64 - x^2}}_{0} \sin(x^2 + y^2) \, dy \, dx[/tex]

It would be quite difficult to evaluate the given integral using conventional methods, so we apply polar conversion to evaluate the integral. Let's start out by converting the function and the bounds.

[Bounds] Cartesian to Polar:

[tex]\displaystyle \left \{ {{-8 \leq x \leq 8} \atop {0 \leq y \leq \sqrt{64 - x^2}}} \right \longrightarrow \left \{ {{0 \leq r \leq 8} \atop {0 \leq \theta \leq \pi}} \right[/tex]

[Function] Cartesian to Polar:

[tex]\displaystyle f(x ,\ y) = \sin(x^2 + y^2) \longrightarrow f(r ,\ \theta) = \sin r^2[/tex]

Now that we've converted to polar coordinates, we can convert the integral using our integral conversion listed under "Multivariable Calculus":

[tex]\displaystyle \int \limits^{8}_{-8} \int \limits^{\sqrt{64 - x^2}}_{0} \sin(x^2 + y^2) \, dy \, dx \longrightarrow \int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta[/tex]

We can now evaluate the polar integral using basic integration techniques listed under "Calculus":

[tex]\displaystyle \begin{aligned}\int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta & = \int \limits^{\pi}_{0} \underbrace{\int \limits^{8}_{0} r \sin r^2 \, dr \, }_{u = r^2 ,\ du = 2r \, dr} d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \int \limits^{8}_{0} 2r \sin r^2 \, dr \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \int \limits^{r = 8}_{r = 0} \sin u \, du \, d\theta \\\end{aligned}[/tex]

[tex]\displaystyle \begin{aligned}\int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta & = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( - \cos u \bigg) \bigg| \limits^{r = 8}_{r = 0} \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( - \cos r^2 \bigg) \bigg| \limits^{r = 8}_{r = 0} \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( - \cos 64 + 1 \bigg) \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( 1 - \cos 64 \bigg) \, d\theta \\\end{aligned}[/tex]

[tex]\displaystyle \begin{aligned}\int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta & = \frac{1}{2} \bigg(1 - \cos 64 \bigg) \bigg( \theta \bigg) \bigg| \limits^{\pi}_{0} \\& = \boxed{ \frac{\pi}{2} \bigg( 1 - \cos 64 \bigg) }\end{aligned}[/tex]

∴ the integral equals:
[tex]\displaystyle \boxed{ \frac{\pi}{2} \bigg( 1 - \cos 64 \bigg) }[/tex]

[tex]\displaystyle \int \limits^{8}_{-8} \int \limits^{\sqrt{64 - x^2}}_{0} \sin(x^2 + y^2) \, dy \, dx = \boxed{ \frac{\pi}{2} \bigg( 1 - \cos 64 \bigg) }[/tex]

___

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Topic: Multivariable Calculus

Unit: Double Integrals

Answer:

1:6

Step-by-step explanation:

1 yard = 3 feet. 4 yards = 12 feet.

Ratio of 2 feet:12 feet = 1:6 Ans D

The ratio of 2 feet to 4 yards is 1 : 6

The ratio is given as:

Ratio = 2 feet : 4 yards

Convert yard to feet

Ratio = 2 feet : 4 * 3 feet

Evaluate

Ratio = 2 feet : 12 feet

Divide the ratio

Ratio = 1 : 6

Hence, the ratio of 2 feet to 4 yards is 1 : 6

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Answer: y= -2.5

Step-by-step explanation:

Distribute the -2 and 3 into the parentheses. -6 + 6 cancels out so you are left with 3y on the right side. Add 2y to the right side leaving you with -2=5y. Divide both sides by -2

Answer:

Step-by-step explanation:

[tex] \sf{ - 2(y + 1) = 3(y - 2) + 6}[/tex]

Distribute -2 through the parentheses

Similarly, Distribute 3 through the parentheses

⇒[tex] \sf{ - 2y - 2 = 3y - 6 + 6}[/tex]

Since two opposites add up to zero , remove them

⇒[tex] \sf{ - 2y - 2 = 3y}[/tex]

Move 3y to Left hand side and change it's sign

Similarly, move -1 to right hand side and change it's sign

⇒[tex] \sf{ - 2y - 3y = 2}[/tex]

Collect like term

⇒[tex] \sf{ - 5y = 2}[/tex]

Divide both sides of the equation by -5

⇒[tex] \sf{ \frac{ - 5y}{ -5 } = \frac{2}{ - 5} }[/tex]

Calculate

⇒[tex] \sf{ - 0.4}[/tex]

Hope I helped!

Best regards!

Step-by-step explanation:

(i) Sum the forces at point M in the x direction.

∑F = ma

-T sin 30° − T sin 30° + 5 N = 0

2T sin 30° = 5 N

T = 5 N

(ii) Sum the forces on the ring in the x direction.

∑F = ma

T sin 30° − N = 0

N = 2.5 N

Sum the forces on the ring in the y direction.

∑F = ma

T cos 30° − mg − Nμ = 0

Nμ = T cos 30° − mg

2.5 μ = 5 cos 30° − 2

μ = 0.932

(iii) Sum the forces on the ring in the y direction.

∑F = ma

T cos 30° − m₁g − m₂g + Nμ = 0

m₂g = T cos 30° − m₁g + Nμ

m (10) = 5 cos 30° − 2 + (2.5)(0.932)

m = 0.466 kg

Answer:

The true statements are;

(i) m - n = n - m

(ii) +m (-n) = m - n

(iii) 0 = m - n

Step-by-step explanation:

We are given that m and n are both integers and we have to select all the statements that are true if m and n are also equal to each other.

(i) The given situation is: m - n = n - m

LHS = m - n

       = m - m   {because m and n are equal}

       = 0

RHS = n - m

       = n - n   {because m and n are equal}

       = 0

Hence, the given statement is true because LHS = RHS = 0.

(ii) The given situation is: +m (- n) = m - n

LHS = +m (- n)

       = m - n

       = m - m  {because m and n are equal}

       = 0

RHS = m - n

       = n - n   {because m and n are equal}

       = 0

Hence, the given statement is true because LHS = RHS = 0.

(iii) The given situation is: 0 = m - n

LHS = 0

RHS = m - n

       = m - m   {because m and n are equal}

       = 0

Hence, the given statement is true because LHS = RHS = 0.

(iv) The given situation is: m + n = 0

RHS = 0

LHS = m + n

       = m + m   {because m and n are equal}

       = 2m

Hence, the given statement is not true because LHS [tex]\neq[/tex] RHS.

#1) m - n = n - m

#2) +m (-n) = m - n

#3) 0 = m - n

hope this HELPS!!!!!!!

Complete Question

An urn contains eight red, six white, and four green balls. Four balls are drawn at random.

(a) The probability that all four balls are red is

(Type an integer or a decimal. Round to two decimal places as needed.)

(b) The probability that there are exactly two red balls and exactly two green balls is

(Type an integer or a decimal. Round to two decimal places as needed.)

(c) The probability that there are exactly two red balls or exactly two green balls is

Answer:

(a) The probability that all four balls are red is

0.023

(b) The probability that there are exactly two red balls and exactly two green balls is

0.055

(c) The probability that there are exactly two red balls or exactly two green balls is

1.398

Step-by-step explanation:

An urn contains

Red balls = 8

White balls = 6

Green balls = 4

Total number of balls = 18 balls

(a) The probability that all four balls are red is?

The probability that a ball drawn is red = 8/18

The probability of drawing a ball that is not red = 1 - 8/18 = 10/18

The probability that all the 4 balls drawn are red = 8/18 × 7/17 × 6/16 x 5/15

= 1680/73440

= 0.022875817

Approximately = 0.023

(b) The probability that there are exactly two red balls and exactly two green balls is

There are 6 ways by which this can be achieved. Where R = Red balls and G = Green Balls

RRGG

GGRR

RGRG

GRGR

RGGR

GRRG

P(Exactly two red balls and two green balls) = P(Exactly two red balls × Exactly two green balls)

=[ (8/18 × 7/17) ×( 4/16 × 3/15)] × 6 ways

= 672/73440 × 6 ways

= 0.0091503268 × 6 ways

= 0.0549019608

Probability of drawing out exactly two two red balls and two green balls is

= 0.055

(c) The probability that there are exactly two red balls or exactly two green balls is

P(Exactly two red balls or two green balls) = P(Exactly two red balls + Exactly two green balls)

P(Exactly two red balls or two green balls) = P(Exactly two red balls or Exactly two green balls)

=[ (8/18 × 7/17) + ( 4/16 × 3/15)] × 6 ways

=0.1830065359 + 0.05

= 0.2330065359 × 6 ways

= 1.3980392154

≈1.398

Answer:

$3,636.70

Step-by-step explanation:

Given the following:

Initial price of Gold (A) = $2500

Rate of appreciation (r) = 5.5% = 0.055

Worth of gold in 7 years will be?

Period (p) = 7

Using the compound interest formula :

Let F = final amount

F = A( 1 + r/n)^nt

n = number of times Appreciation occurs per period.

Since rate compounds yearly, then, n = 1

F = $2500( 1 + 0.055/1)^(7*1)

F = $2500(1 + 0.055)^7

F = $2500(1.055)^7

F = $2500(1.454679161133794609375)

F = $3636.6979

Amount in 7 years = $3,636.70