In a local ice sculpture contest, one group sculpted a block into a rectangular based pyramid. The dimensions of the base were 3 m by 5 m, and the pyramid was 3.6 m high. Calculate the amount of ice needed for this sculpture. A conical-shaped umbrella has a radius of 0.4 m and a height of 0.45 m. Calculate the amount of fabric needed to manufacture this umbrella. (Hint: an umbrella will have no base) A cone has a volume of 150 cm3 and a base with an area of 12 cm2. What is the height of the cone? Find the dimensions of a deck which will have railings on only three sides. There is 28 m of railing available and the deck must be as large as possible. A winter recreational rental company is fencing in a new storage area. They have two options. They can set it up at the back corner of the property and fence it in on four sides. Or, they can attach it to the back of their building and fence it in on three sides. The rental company has decided that the storage area needs to be 100 m2 if it is in the back corner or 98 m2 if it is attached to the back of the building. Determine the optimal design for each situation.

Answer:

A. 3 Days

Step-by-step explanation:

Just took the test hope this helps :)

Answer:

the answer on edge is A.3

Answer:

27_5_10/2

27_5_5

22_5

17

Answer:

Geometric sequence

Step-by-step explanation:

Because this is not adding or subtraction, but multiplication, this would be a geometric sequence.

Answer:

(0,-3)

Step-by-step explanation:

Answer:

she walked 6 miles.

Step-by-step explanation:

We know that Ruth walks at a speed of 4 mph and it took her 1.5 hours to walk from her home to the library (from 9 to 10.30).

We can solve this using a rule of three:

If she walks 4 miles in 1 hour, how many hours did she walk in 1.5 hours?

1 hour           4 miles

1.5 hours       x miles

Solving for x we get:

[tex]x=\frac{1.5(4)}{1} =6[/tex] miles

Thus, she walked a distance of 6 miles

The distance between her home and the library is the number of meters between them.

The distance walked is 6 m

The speed is given as:

[tex]\mathbf{Speed = 4mph}[/tex]

The time spent walking is calculated as:

[tex]\mathbf{Time = 10:30am - 9:00am}[/tex]

[tex]\mathbf{Time = 1.5\ hrs}[/tex]

So, the distance is calculated as:

[tex]\mathbf{Distance = Speed \times Time}[/tex]

Substitute known values

[tex]\mathbf{Distance = 4mph \times 1.5hrs}[/tex]

[tex]\mathbf{Distance = 6m}[/tex]

Hence, the distance walked is 6 m

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Answer:

$126

Step-by-step explanation:

The plot of land is worth $18,000 and the tax on the land is $0.70 per $100. You would divide 18000 by 100 which is 180. Then you would multiply 180*0.70 which is $126.

Step-by-step explanation:

Here, given that;

The total value of land us $18000.00

tax per $100.00 is $0.70

now,

$100.00 taxes $0.70

$18000.00 taxes ($18000.00÷100)/$0.70 (as in question given that the tax is charged in each $100)

= $126.

is the required tax amount.

Hope it helps..

Explanation:

The x intercepts here are -1, 2 and 3. This is where the graph crosses the x axis. We can determine these three values by solving f(x) = 0.

In other words, set (x-3)(x-2)(x+1) equal to zero and solve for x.

(x-3)(x-2)(x+1) = 0

x-3 = 0 or x-2 = 0 or x+1 = 0

x = 3 or x = 2 or x = -1

x = -1 or x = 2 or x = 3

When we expand out (x-3)(x-2)(x+1), there will only be one x^3 term and the coefficient for this term is positive 1. The positive leading coefficient indicates that the graph goes up forever as we move to the right. In other words, the graph grows forever after passing that dip between x = 2 and x = 3.

Another way you could phrase it is that "as x goes to infinity, y also goes to infinity". An informal way is to say "the graph rises to the right" to describe the end behavior.

Answer:

16 and 4

Step-by-step explanation:

Let (x+y) =20 and (x-y)=12 then:

Isolate for x in each equation

   x=20-y and x=12+y

Set the equations to equal each other since the value of x should be the same for both

   20-y = 12+y

Rearrange so that y is on one side and the numbers are on the other

   8 = 2y

   y= 8/2

   y= 4

Now  substitute the y- value back into either of the original equations

   x+y= 20

   x+4 = 20

Rearrange and isolate  x

   x = 20-4

   x = 16

So the two values are 16 and 4

Answer:

[tex]A.\ \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]

Step-by-step explanation:

Given

Let the two triangles be A and B

Sides of A: 4, 6 and 8.5

Sides of B: 6, 9 and 12.5

Required

Which set of ratio determines the dilation

To determine the dilation of  a triangle over another;

We simply divide the side of a triangle by a similar side on the other triangle;

From the given parameters,

A ------------------B

4 is similar to 6

6 is similar to 9

8.5 is similar to 12.5

Ratio of dilation is as follows;

[tex]Dilation = \frac{4}{6}[/tex]

[tex]Dilation = \frac{6}{9}[/tex]

[tex]Dilation = \frac{8.5}{12.5}[/tex]

Combining the above ratios;

[tex]Dilation = \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]

From the list of given options, the correct option is A,

Answer:

a

Step-by-step explanation:

Answer: Stratified Sampling

Step-by-step explanation: Stratified Sampling involves creating subdivisions of the population such that each subdivisions is seen as a subgroup or smaller chunk of the population which is split based on certain criteria or attribute. The stratified random sampling may be employed in delineating certain characteristics or to investigate further how a feature or characteristics vary between one subdivision to the other.

In the scenario above, the researcher made use of the stratified sampling by performing a random sampling selection of its subjects based on the different subdivisions of students available in the college

Answer:

Options (B) and (C)

Step-by-step explanation:

The given expression is [tex](d^{\frac{1}{8}})^5[/tex]

By simplifying this expression,

[tex](d^{\frac{1}{8}})^5[/tex]

= [tex](\sqrt[8]{d})^{5}[/tex]

Option (B)

Similarly,

[tex](d^{\frac{1}{8}})^5[/tex]

= [tex]d^{\frac{5}{8}}[/tex]

= [tex](d^{5})^{\frac{1}{8}}[/tex]

Option (C)

Therefore, Options (B) and (C) will be the correct options.

Answer:

83.33 cajas estándar de frambuesas y 51.67 cajas de lujo de frambuesas.

Step-by-step explanation:

Representemos el número de cajas como

A = caja estándar de frambuesas

B = caja de lujo de frambuesas

Caja estándar de frambuesas = $ 7 Caja de lujo de frambuesas = 10.

A + B = 135 ......... Ecuación 1

B = 135 - A

7A + 10B = 1100 ........... Ecuación 2

Sustituir

135 - A para B en la ecuación 2

7A + 10 (135 - A) = 1100

7A + 1350 -10A = 1100

7A - 10A = 1100-1350

-3A = - 250

A = 250/3

A = 83.33 cajas

Sustituye 83.33 por A en la ecuación 1

A + B = 135

83,33 + B = 135

B = 135 - 83.33 = 51.67 cajas

Por lo tanto, vendió,

83.33 cajas estándar de frambuesas y 51.67 cajas de lujo de frambuesas.

Answer:

Step-by-step explanation:

The given equation is expressed as

(x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12

Simplifying the right hand side of the equation, it becomes

[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)

x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)

(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)

4x/(x - 1)(x + 1)

Therefore,

4x/(x - 1)(x + 1) = 7/12

Cross multiplying, it becomes

4x × 12 = 7(x - 1)(x + 1)

48x = 7(x² + x - x - 1)

48x = 7x² - 7

7x² - 48x - 7 = 0

Applying the quadratic formula,

x = - b ± √(b² - 4ac)]/2a

from our equation,

b = - 48

a = 7

c = - 7

Therefore

x = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)

x = [48 ± √(2304 + 196]/14

x = (48 ± √2500)/14

x = (48 ± 50)/14

x = (48 + 50)/14 or x = (48 - 50)/14

x = 98/14 or x = - 2/14

x = 7 or x = - 1/7

Answer: The given equation is expressed as (x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12Simplifying the right hand side of the equation, it becomes[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)4x/(x - 1)(x + 1)Therefore, 4x/(x - 1)(x + 1) = 7/12Cross multiplying, it becomes4x × 12 = 7(x - 1)(x + 1)48x = 7(x² + x - x - 1)48x = 7x² - 77x² - 48x - 7 = 0Applying the quadratic formula,x = - b ± √(b² - 4ac)]/2a from our equation, b = - 48a = 7c = - 7Thereforex = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)x = [48 ± √(2304 + 196]/14x = (48 ± √2500)/14x = (48 ± 50)/14x = (48 + 50)/14 or x = (48 - 50)/14x = 98/14 or x = - 2/14x = 7 or x = - 1/7

Step-by-step explanation:

Answer:

Option A.3

Step-by-step explanation:

If its rise over run the fraction should be right 2 up 6 makeing a fraction of

6/2 which equals 3

The line has a slope of 3

Answer:

9.48*

Step-by-step explanation:

This is a right triangle. The formula for solving the Hypotenuse, or the longest side of the right triangle is A^2 + B^2 = C^2. If we put the numbers from the problem into the formula this is what we get :

3^2 + 9^2 = C^2

9 + 81 = C^2

90 = C^2

9.48 = C

* This is rounded, the exact number is closer to 9.486832980505138. Your class should tell you what to round to.

Answer:

The answer would be A. 3√10 blocks

Step-by-step explanation:

I have had this question and its 3√10 blocks.
Hope this helps you other people :))

Answer:

2 root 17

Step-by-step explanation:

The square root of 68 in simplest radical form is 2√17

From the question, we have the following parameters that can be used in our computation:

The square root of 68

Mathematically, we have

The square root of 68 = √68

Expand 68

So, we have

The square root of 68 = √(4 * 17)

So, we have

The square root of 68 = √4 * √17

Evaluate

The square root of 68 = 2 * √17

Evaluate the products

The square root of 68 = 2√17

Hence, the square root of 68 is 2√17

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Answer:

second option

Step-by-step explanation:

Given

f(x) = (x - 7)(x + 4)(3x - 2)

To find the zeros let f(x) = 0, that is

(x - 7)(x + 4)(3x - 2) = 0

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 4 = 0 ⇒ x = - 4

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = [tex]\frac{2}{3}[/tex]

zeros are x = - 4, x = [tex]\frac{2}{3}[/tex], x = 7

Answer:

1) [tex]\boxed{Option \ 3}[/tex]

2) [tex]\boxed{Option \ 2}[/tex]

Step-by-step explanation:

A) [tex]x^2-5x+6[/tex]

Using mid term break formula

[tex]x^2-6x+x-6\\x(x-6)+1(x-6)\\Taking \ (x+6) \ as \ common\\(x-6)(x+1)[/tex]

B) [tex]\frac{-20p^{-5}qr^6}{16p^{-2}q^{-3}r^4}[/tex]

Solving it using the two rules: => [tex]\frac{a^m}{a^n} = a^{m-n} \ and \ a^m * a^n = a^{m+n}[/tex]

=> [tex]\frac{-5p^{-3}q^4r^2}{4}[/tex]

We need to put p in the denominator to cancel its negative sign

=> [tex]\frac{-5q^4r^2}{4p^3}[/tex]

Answer:

C and b

Step-by-step explanation:

First question:

The polynomial expression we want to factor is x^2-5x-6

Let's calculate the discriminant to find the roots. The discrminant is b^2-4ac

● b= -5

● a = 1

● c = -6

b^2-4ac= (-5)^2-4*1*(-6) = 25+24 = 49>0

So this polynomial expression has two roots since the discriminant is positive

Let x" and x' be the roots:

● x'= (-b-7)/2a = (5-7)/2= -1

● x"= (-b+7)/2a = (5+7)/2 =6

7 is the root square of the discrminant

The factorization of this pulynomial is:

● a(x - x') (x-x")

● 1*(x-(-1)) (x-6)

● (x+1)(x-6)

So the right answer is c

■■■■■■■■■■■■■■■■■■■■■■■■

Second question:

The expression is: (-20*p^(-5)*q*r^(6))/(16*p^(-2)*q^(-3)*r^3)

To make it easier we will simplify the similar terms one by one.

● Constant terms

-20/16 = (-5*4)/(4*4) = -5/4

● terms containing p

-p^(-5)/p^(-2) = p^(-5-(-2)) = p^(-3) =1/p^3

● terms containg q

q/q^(-3)= q(1-(-3)) = q^4

● terms containg r

r^6/r^4 = r^(6-4) = r^2

Multiply all terms together:

● -5/4 *1/p^3 *q^4 *r^2

● (-5*q^4*r^2)/(4p^3)

The right answer is b

I'm assuming you are asking if the above statements are true or false

Answer:

All true

Step-by-step explanation:

In the first statement, an equation may have different numbers on both sides of the equation after solving the equation such that we have 0=5 for instance given 1x=1x+5. This means that we cannot solve this equation and it cannot be true

In the second statement, an equation may be infinite meaning that is true for all values for the variables such that we have equal numbers on both sides of the equation 1=1, 4=4,0=0 for instance given equations like x−10+x=8+2x−18

In last statement, an equation is true if the variable equals a number meaning that the equation has one solution such as x=2 given an equation like 2x+4=8

Answer:

Step-by-step explanation:

A-domain (-∞,∞)

B- Range(0,∞)  the range is the set of values tat correspond with the domain

C- the y intercept (0,1) , y intercept is when x =0 (2/3)^0=1

D-the horizontal asymptote is x-axis y=0

E- the graph is always decreasing

F-it depend on the base

Answer:

  16 hours

Step-by-step explanation:

In the time it took Ruth to plant 5 bulbs, Terry planted 3 bulbs. So, Terry did 3/8 of the work of planting 8 bulbs in that time.

We expect that Terry alone would take 8/3 of the time that it took when working together with Ruth.

  (8/3)×(6 hours) = 16 hours . . . . . . for Terry to do the job alone

Answer:

Option B

Step-by-step explanation:

When we compare the number of shirt with it's cost, we find out that 8 shirts cost $120.

For more understanding, see the attached file.

To solve the equation, we need to let u = x²

A quadratic equation is an algebraic expression that takes the power of the second degree.

From the given parameter:

For us to be able to solve the given equation, we need to reduce the equation to a quadratic form.

This can be achieved by making an assumption that:

So, we will replace x² with u in the given equation.

By doing so, we have:

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Answer: Solve x4 – 17x2 + 16 = 0.Let u = xX 17x²✔ x²X -17x².

let u = x^2

Step-by-step explanation: just did it

Answer:

Option 3

Step-by-step explanation:

The curve goes infinitely downwards, so y is infinitely negative while x is limited at the y axis, or x=0 which is the asymptote.

Answer:

8

Step-by-step explanation:

8^3 = 8*8*8 = 512

la base = base = 8

Answer:

[tex]B. y=x^2+3 \\\\D.$ $x^2+3y=8[/tex]

Step-by-step explanation:

A quadratic function is a function in which the highest power of the unknown variable is 2.

Formally, a quadratic function is defined as a function of the form:

[tex]f(x)=ax^2+bx+c, a\neq 0[/tex]

From the given options, only B and D has the highest power as 2. Therefore, the equations that represent quadratic functions are:

[tex]B. y=x^2+3 \\\\D.$ $x^2+3y=8[/tex]

Answer:

The correct answer is A: 10

Step-by-step explanation:

We know that for Dance World the equation is y=15x and for Toe Tapper it is y=25+12.5x

Make a chart with both dance companies and compare the solutions to each equation. Like the one below.

        Dance World      /      Toe Tappers

A:10              $150        /       $150              

B:15              $225       /        $212.5

C:100            $1500      /       $1275

D:150             $2250     /       $1900

In conclusion, A:10 is the correct answer as both dance companies cost the same for 10 classes.

Sorry if this is really late, this is for the people who have the same question and need an answer too.

Answer:

A 10

Step-by-step explanation:

15x = 25 + 12.5x

2.5x = 25

x= 10

Answer:

[tex]\boxed{\sf Parallelogram}[/tex]

Step-by-step explanation:

A parallelogram has opposite parallel sides and it is a quadrilateral.

Answer:

This is a parallelogram

Step-by-step explanation:

This is also a quadrilateral.

Hope this helps.

Answer:

a^5.

Step-by-step explanation:

a^12 / a^7 = a^(12 - 7) = a^5.

Hope this helps!