What are the next three terms in the sequence 2, -4, 8, -16, 32, ...?

Answer:

w = [tex]\frac{V}{lh}[/tex]

Step-by-step explanation:

We can find the formula for the width by isolating w:

V = lwh

Divide each side by lh to isolate w:

[tex]\frac{V}{lh}[/tex] = w

Answer:

For the triangle, [tex]x=14[/tex]

For the rectangle, [tex]x=\frac{5}{2}[/tex]

Step-by-step explanation:

To solve for x in these equations, we have treat each side as it's just one number - add them all up.

The perimeter of a triangle will be the sum of all 3 of its sides.

So:

[tex]x + 4 + 2x - 3 + x = 57[/tex]

We can combine like terms to get

[tex]4x + 1 = 57[/tex]

Subtract 1 from both sides:

[tex]4x = 56[/tex]

Divide both sides by 4:

[tex]x = 14[/tex]

For the rectangle, the perimeter is [tex]2l + 2w[/tex], so we can add up the sides.

[tex]5x - 4 + 5x - 4 + 3x + 2 + 3x + 2 = 36[/tex]

Combine like terms:

[tex]16x - 4 = 36[/tex]

Add 4 to both sides:

[tex]16x = 40[/tex]

Divide both sides by 18:

[tex]x = \frac{40}{16}[/tex]

Simplifying this fraction gets us

[tex]\frac{5}{2}[/tex]

Hope this helped!

Answer:

(a) X(in '000s) = 4133, 2369, 1295, 928, 679.

(b) The mean number of passengers for these five cruise lines is 1880.8.

(c) The range of the data is 3454.

(d) The standard deviation of the data is 1414.75.

Step-by-step explanation:

We are given that in a recent year, the top five  cruise lines in the world had this many passengers:

4,133,000, 2,369,000, 1,295,000, 928,000, 679,000

(a) Let X = Number of passengers in the top five  cruise lines in the world

Representing each number in terms of thousands  of passengers below;

X(in '000s) = 4133, 2369, 1295, 928, 679

(b) The mean of the data is given by the following formula;

              Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]

Here, n = number of observations in data = 5

So, [tex]\bar X[/tex] = [tex]\frac{4133+2369+1295+928+679}{5}[/tex]

          = [tex]\frac{9404}{5}[/tex] = 1880.8

Hence, the mean number of passengers for these five cruise lines is 1880.8.

(c) The range of the data is calculated by the following formula;

             Range = Highest value - Lowest value

                         = 4133 - 679 = 3454

Hence, the range of the data is 3454.

(d) The standard deviation of the data is given by the following formula;

       Standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]

                      =  [tex]\frac{(4133-1880.8)^{2}+(2369-1880.8)^{2}+.......+(679-1880.8)^{2} }{5-1}[/tex]

                      =  1414.75

Hence, the standard deviation of the data is 1414.75.

Answer:

-18

Step-by-step explanation:

-3 (3)(2)

-9 * 2

-18

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ - 18}}}}}[/tex]

Step-by-step explanation:

Given, y = 3 , z = 2

To find : value of -3yz

plug the values of y and z

[tex] \sf{ - 3 \times 3 \times 2}[/tex]

Multiply the numbers : - 3 and 3

⇒[tex] \sf{ - 9 \times 2}[/tex]

Multiply the numbers : -9 and 2

⇒[tex] \sf{ - 18}[/tex]

Hope I helped!

Best regards!!

Answer:

The slope of the function is  ²/₃ and since the second derivative is zero, the concavity doesn't exist.

Step-by-step explanation:

Given;

x = 6t

y = 4t - 3

point t = 4

[tex]\frac{dy}{dx} = (\frac{dy}{dt} )/(\frac{dx}{dt} )=\frac{\frac{dy}{dt} }{\frac{dx}{dt}} \\\\\frac{dy}{dt} = 4; \frac{dx}{dt} = 6\\\\\frac{dy}{dx} =\frac{4}{6} = \frac{2}{3}[/tex]

The slope of the function is  ²/₃

take the second derivative of the function;

the second derivative will be zero since the first derivative is a constant value.

[tex]\frac{d^2y}{dx^2} = 0[/tex]

Since the second derivative is zero, the concavity doesn't exist.

Answer:

The solution to the given expression is -x³ + 9x + 6

Step-by-step explanation:

(9x - 4x² + 9) + (-x³ + 4x² - 3)

Since there is a positive sign in front of the second parentheses, then the terms inside will stay the same.

9x - 4x² + 9 - x³ + 4x² - 3

Group terms together that are alike. Also known as like terms.

-x³ + (-4x² + 4x²) + 9x + (9 - 3)'

Combine like terms.

-x³ + 9x + 6

Answer:

- [tex]x^{3\\}[/tex] + 9x + 6

Step-by-step explanation:

First, you need to combine like terms. Like terms, when dealing with exponents can be categorized by their powers.

hIn this case, 9x stands alone, because there is no other coefficient with the power of just x.

9x

Next, we can look at the -4x^2. The other similar coefficient is + 4x^2. We can combine both of those, which will equal out to 0.

Next, you have 9. It can be combined with -3, since none of them have an exponent attached. It will equal 6

9x + 6

We also have a -x^3 left over. There is no like term to combine with it, so we can leave it as is.

Our problem now looks like

9x + 6 - [tex]x^{3}[/tex]

You can rearrange them in the proper order, so it will look like,

- [tex]x^{3}[/tex] + 9x + 6.

And there you have it!

Answer:

The probability that a student owns a laptop or a desktop is 92%.

Step-by-step explanation:

We are given that the probability that an online student owns a laptop is 0.82 and the probability that a student owns a desktop is 0.65. The probability that a student owns both is 0.55 .

And we have to find the probability that a student owns a laptop or a desktop.

Let the probability that a student owns a laptop = P(L) = 0.82  

The probability that a student owns a desktop = P(D) = 0.65

The probability that a student owns both laptop and desktop = P(L [tex]\bigcap[/tex] D) = 0.55

Now, the probability that a student owns a laptop or a desktop is given by = P(L [tex]\bigcup[/tex] D)

         P(L [tex]\bigcup[/tex] D) = P(L) + P(D) - P(L [tex]\bigcap[/tex] D)

                        = 0.82 + 0.65 - 0.55

                        = 0.92 or 92%

So, the probability that a student owns a laptop or a desktop is 92%.

Answer:

i tried to answer but the question made no sense

Step-by-step explanation:

Answer:

11/20

Step-by-step explanation:

six over ten =6/10=0.6

one over two =1/2=0.5

so one number that can be between them is 0.55

which is 55/100=11/20

Answer:

adjacent / hypotenuse cos x° = g divided by h is right

Step-by-step explanation:

If   [tex]tanx^{o} = \frac{6}{g}[/tex] and [tex]sinx^{o} = \frac{6}{h}[/tex]  then  [tex]cosx^{o} = \frac{g}{h}[/tex] .

By right angled triangle we have,

  Trigonometric ratios as

 Given  [tex]sinx^{o} = \frac{6}{h}[/tex]  and [tex]tanx^{o} = \frac{6}{g}[/tex]

              opposite = 6, hypotenuse = h, adjacent = g

                  [tex]cosx^{o}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]  [tex]=\frac{g}{h}[/tex]

Learn more about Trigonometry :

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Answer:  10) 40°      11) 9.9

Step-by-step explanation:

[tex]\text{Law of Sines:}\quad \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

10) Given: a = 31,  b = 20, A = 84°

[tex]\dfrac{\sin 84^o}{31}=\dfrac{\sin B}{20}\\\\\\\dfrac{20\sin 84^o}{31}=\sin B\\\\\\\sin^{-1}\bigg(\dfrac{20\sin 84^o}{31}\bigg)=B\\\\\\39.9^o=B[/tex]

11) Given: a = 18,  A = 105°, B = 32°

[tex]\dfrac{\sin 105^o}{18}=\dfrac{\sin 32^o}{b}\\\\\\b=\dfrac{18\sin 32^o}{\sin 105^o}\\\\\\b=9.87[/tex]

Answer:

8+10+4+6+y /5=6

find lcm which is 5

(8+10+4+6+y/5)5=(6)5

8+10+4+6+y=30

28+y=30

y=30-28

y=2

Answer:

Widths are 2, 4, 5

Border or the perimeter of all these rectangles = 16

Perimeter of a rectangle

=> 2 ( L + W)

W = Width

L = Length

Area of a rectangle

=> L x W

First rectangle

Perimeter =  2(L+W)

=> 2 (L + 2) = 16

=> 2L + 4 = 16

=> 2L + 4 - 4 = 16 - 4

=> 2L = 12

=> 2L/2 = 12/2

=> L = 6

Length of the First Rectangle = 6

Area = L x W

=> 6 x 2 = 12

Area of the First Rectangle = 12

Second rectangle

Perimeter =  2( L + W)

=> 2 (L + 4) = 16

=> 2L + 8 = 16

=> 2L + 8 - 8 = 16 - 8

=> 2L = 8

=> 2L/2 = 8/4

=> L = 4

Length of the Second Rectangle = 4

Area = L x W

=> 4 x 4

=> 16

Area of the Second Rectangle = 16

Third Rectangle

Perimeter = 2 (L + W)

=> 2 (L + 5) = 16

=> 2L + 10 = 16

=> 2L + 10 - 10 = 16 - 10

=> 2L = 6

=> 2L / 2 = 6/2

=> L = 3

Length of the Third Rectangle = 3

Area = L x W

=> 3 x 5

=> 15

Area of the Third Rectangle = 15

To find which figure covers more spaces, we need to which figure has more area.

=> Rectangle 2 has the largest area = 16

Answer:

Irrational

Step-by-step explanation:

Can't be put into a fraction.

Answer:

5

Step-by-step explanation:

Hi,

f(12)= 12/2 -1 = 6 -1 = 5

Thanks

Answer:

5

Step-by-step explanation:

f(x) = x/2 - 1

Let x = 12

f(12) = 12/2  -1

       = 6-1

       = 5

Answer:

n + 5

Step-by-step explanation:

"The sum of a number and 5" can be written symbolically as n + 5.

Answer:

false

Step-by-step explanation:

hope this helps✨

Answer: 9 to 4

Step-by-step explanation:

Using the grids you can count them to see what the width is.

The width is 9 units and the height is 4 units so the ration will be  9 to 4

The ratio of width of the rectangle to the height of the rectangle is 9 to 4.

A rectangle is a quadrilateral with four sides and four angles. It is a type of geometric shape characterized by its properties, including having opposite sides that are equal in length and all angles measuring 90 degrees (right angles).

In the given rectangle, there are 4 units or boxes in the height.

There are 9 units or boxes which makes width of the rectangle.

Hence, the ratio of width of the rectangle to the height of the rectangle is 9 to 4.

To learn more on Rectangles click here:

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Answer:

2.33 Seconds

Step-by-step explanation:

The equation y = -6t^2 - 10t + 56 expresses the height of a ball at a given time, t, on the planet Mars.  We are also given that the ball is thrown with a velocity of 10 feet per second with the initial height of 56 feet.

To find the amount of time to reach the ground, we can say that the time being found will be when the ball is on the ground, or when y = 0.  So we simply set our equation to 0 and solve for t.

y = -6t^2 - 10t + 56

0 = -6t^2 - 10t + 56

0 = -1 (6t^2 + 10t + -56)

0 = -1 (3t - 7) (2t + 8)

(3t - 7) = 0  OR (2t + 8) = 0

3t = 7         OR  2t = -8

t = 7/3        OR    t = -4

Since time will not be negative, we will want to choose the positive solution for this quadratic equation.

Hence, the amount of time for the ball to hit the ground will be 7/3 seconds or 2.33 seconds.

Cheers.

Answer:

2.33

Step-by-step explanation:

Setting $y$ to zero, we find the following:

\begin{align*}

-6t^2 - 10t + 56 &= 0 \\

\Rightarrow \quad 6t^2 + 10t - 56 &= 0 \\

\Rightarrow \quad 3t^2 + 5t - 28 &= 0 \\

\Rightarrow \quad (3t-7)(t+4) &= 0.

\end{align*}As $t$ must be positive, we can see that $t = \frac{7}{3} \approx \boxed{2.33}.$

Answer:

$24.35

Step-by-step explanation:

sale price⇒ total price-discount price

s.p=$24.60-25/100                              ∴25%⇒25/100

s.p⇒$2460/100-25/100                           ∴24.60⇒2460/100

s.p⇒$24.35

           ⇒$24.35

Answer:

there is insufficient evidence to support the claim that more than 10% of the employees are paid minimum wage.

Step-by-step explanation:

Given that:

A marketing organization claims that more than 10% of its employees are paid minimum wage.

The null hypothesis is:

[tex]H_o : p = 10[/tex]

The alternative hypothesis is:

[tex]H_1 : p > 10[/tex]

If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted

i.e Decision Rule: fails to reject the null hypothesis

Then the interpretation of the decision is that, there is insufficient evidence to support the claim that more than 10% of the employees are paid minimum wage.

Answer:

a) Cost of a chicken shawarma wrap?

$10.99

b) Cost of one order of spiced potatoes?

$4.99

Step-by-step explanation:

Cost of a chicken sharwarma wrap = a

Cost of an order of spiced potatoes = b

Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.

3a + 2b = $42.95 .............Equation 1

Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.

5a + 4b = $74.91 ................Equation 2

So we have:

3a + 2b = $42.95 .............Equation 1

5a + 4b = $74.91 ................Equation 2

We use Elimination method to solve for this.

Multiply Equation 1 by coefficient of b in Equation 2

Equation 2 by coefficient of b in Equation 1

3a + 2b= $42.95 .............Equation 1 × 4

5a + 4b = $74.91 ................Equation 2 × 2

12a + 8b = 171.80..............Equation 3

10a + 8b = 149.82..............Equation 4

Subtract Equation 3 from Equation 4

2a = 21.98

a = 21.98/2

a = 10.99

Therefore, a = Cost of Chicken sharwarma wrap = $10.99

Subtitute 10.99 for 9in Equation 1

3a + 2b = $42.95 .............Equation 1

3(10.99) + 2b = 42.95

32.97 + 2b = 42.95

2b = 42.95 - 32.97

2b = 9.98

b = 9.98/2

b = 4.99

b = Cost of an order of spiced potatoes = $4.99

Hence,

The cost of a chicken sharwarma wrap = $10.99

The cost of an order of spiced potatoes = $4.99

Answer:

6.7 seconds

Step-by-step explanation:

Let's calculate the maximum height covered by the object

Max height= U²Sin²tita/2g

Where g is acceleration due to gravity

Max height= 40²(sin90)²/(2*9.81)

Max height= 1600/19.62

Max height=81.55 m

Total max height= 30+81.55

Total max height= 111.55 m

Time t it will take to travel from the max height at acceleration of 4.9 m/s²

S= ut + ½at²

u= 0 at Mac height

S= 111.5 m

111.5 = ½(4.9)t²

223/4.9= t²

45.5= t²

6.745 seconds= t

6.7 seconds= t

Answer:

6:2 or 1:3

Step-by-step explanation:

Not really sure how to explain this, but I hoped this helped!

Step-by-step explanation:

Let the rate of boarding a dog and a cat be x and y respectively.

Now,

Further solving the two equations :

Y = $ 18.75

X = $ 28.25

Answer: the first term is 45

Step-by-step explanation:

Step 1: The formular for the nth term is ar^n-1 and since we're solving for the third term ar^3-1 = ar² which is equal to 20

So ar²= 20 and we make this equation i

Step 2: the formular for the sum of infinity is Sn = a/(1-r) and according the question the sum of infinity is equals to 3 *A ( A means the first term)

Further simplification gives us

3a= a/(1-r)

We simplify Futher by multiplying both sides by (1-r)

3a.(1-r) = a/(1-r).(1-r)

3a(1-r)=a

= 3a-3ar=a

Make 3ar the subject of the formula

3ar= 2a and lets make this equation (ii)

Step 3: From the first equation since ar²=20, let's make a the subject of the formula by dividing both sides by r²

Ar²/r² = 20/r²

A=20/r²lets make this equation (iii)

Step 4: subtitle a as 20/r² into equation (ii)

Since 3ar=2a

Then 3.(20/r²).r = 2. 20/r²

= (60/r²) .r = 40/r²

60/r = 40/r2

Multiplying both sides by r² gives us

60r = 40

Divide both sides by 20 gives us

= 3r= 2

Divide both sides by 3 gives us

= r = 2/3

Step 5: substitute r for 2/3 in equation i

ar²= 20

a. (2/3)2 = 20

= a.4/9 = 20

= 4a = 180

= a = 180/4

a = 45

Answer:

Option (A)

Step-by-step explanation:

If a function 'f' is an odd function,

f(-x) = -f(x)

If a function 'f' is an even function,

f(-x) = f(x)

In this question given function is,

f(x) = [tex]\frac{220}{x^3}[/tex]

To check the given function is odd or even,

f(-x) = [tex]\frac{220}{(-x)^{3} }[/tex]

      = [tex]-\frac{200}{x^{3}}[/tex]

Therefore, from the definition of even and odd functions,

Function 'f' is an odd function.

Option (A) will be the correct option.

Answer:

30

Step-by-step explanation:

Formula is 1/2bh

6 times 10 = 60

60 divided by 2 equals 30

Answer:

⇒30 in²

Step-by-step explanation:

area ofΔ⇒1/2×length×width

              ⇒ 1/2×6 in×10 in

              ⇒1/2×60in²

               ⇒30 in²

Answer:

(3rd listed choice) Paula's notes are incorrect. Step 4a should be "If the result does not define y as a function of x, then f does not have an inverse," and step 4b should be "If the result defines y as a function of x, then f has an inverse."

Step-by-step explanation:

If f(y) = x can be solved for a relation for y that is a function, then f(x) has an inverse. It will be the function defined by y.

Answer:

thee correct answer is in number.C. 36

Answer:

D

Step-by-step explanation: