Select the correct answer from each drop-down menu.
The figure shown consists of a square pyramid on top of a square prism. The surface area of the figure is 432 cm2. The height of the prism is three times the height of the pyramid.


Find the heights of the pyramid and the prism.

The height of the pyramid is
cm.

The height of the prism is
cm.

Given:

The given expression is

[tex](-4)^{-3}[/tex]

To find:

The value of given expression.

Solution:

We have,

[tex](-4)^{-3}[/tex]

Applying the negative exponents rule, we get

[tex](-4)^{-3}=\dfrac{1}{(-4)^3}[/tex]     [tex][\because a^{-n}=\dfrac{1}{a^n}][/tex]

Expanding the exponent, we get

[tex](-4)^{-3}=\dfrac{1}{(-4)(-4)(-4)}[/tex]  

[tex](-4)^{-3}=\dfrac{1}{-64}[/tex]  

[tex](-4)^{-3}=-\dfrac{1}{64}[/tex]  

The value of given expression is [tex]-\dfrac{1}{64}[/tex].

Therefore, the correct option is A.  

Answer:

a

Step-by-step explanation:

-1/64

Answer:

1. a. 1,000 = 10³ = 10 × 10 × 10

b. 100 × 100 = 10² × 10² = 10 × 10 × 10 × 10

2. a. 3 × 10² = 300

b. 2.16 × 10⁴ = 21,600

c. 800 ÷ 10³ = 0.8

d. 754.2 ÷ 10² = 7.542

Step-by-step explanation:

3. a. 1,000

There are 3 zeros in 1000. This is equivalent to 10 raised to the power of 3. Writing this in multiplication sentence using 19 as the only factor, we would have:

1,000 = 10³ = 10 × 10 × 10

b. 100 × 100

Using the same logic as explained in (a) above, we would have:

100 × 100 = 10² × 10² = 10 × 10 × 10 × 10

2. a. 3 × 10²

Convert 10² to 100 and multiply both numbers

3 × 10² = 3 × 10 × 10 = 3 × 100 = 300

b. 2.16 × 10⁴

2.16 × 10 × 10 × 10 × 10 = 2.16 × 10,000

Multiplying both numbers, since we have 4 zeros, move the decimal point 4 places to the right.

2.16 × 10,000 = 21,600

c. 800 ÷ 10³ = 800 ÷ 10 × 10 × 10

800 ÷ 1,000

There are 3 zeros in 1000, since we are dividing, move the decimal point 3 places to the left.

800 ÷ 1,000 = 0.8

d. 754.2 ÷ 10² = 754.2 ÷ 10 × 10

754.2 ÷ 100

Move the decimal point 2 places to the left.

754.2 ÷ 100 = 7.542

Answer:

The population in 14 weeks is 232 fishes

Step-by-step explanation:

The equation for exponential growth is f(x) = a·(1 + r)ˣ

Where;

a = The starting population size = 3

r = The rate at which the population of grows

x = The number of periods to of change of the population

Therefore, we have;

f(6) = 31 = 3 × (1 + r)⁶

31/3 = (1 + r)⁶

㏑(31/3) = 6㏑(1 + r)

(㏑(31/3))/6 =㏑(1 + r)

1 + r = e^((㏑(31/3))/6) ≈ 1.476

1 + r ≈ 1.476

Therefore, the population in 14 weeks is given as follows;

f(14) = 3 × (1.467)¹⁴ ≈ 232.574

Given that we the information is with regard of living things, such that there are no fractions, we round down to the nearest whole number as follows;

f(14) ≈ 232

The population in 14 weeks = 232 fishes.

Answer:

use distance formula

Step-by-step explanation:

think it proves helpful for you

Answer:

You kidding right!

Anyways your answee is 1+1=2

Answer:

2

Add 1 and 1, and that is 2, I don't know why, but it is.

Simple I know, and I get that this is a joke, but please don't post jokes too often, thanks very much.

Hope this helps?

Step-by-step explanation:

first a quick check that we really deal with 100 events (experiment results).

14+19+16+16+17+18 = 100

perfect.

so, based on this particular die its own probabilty distribution of the 6 different possible outcomes shows that there might be some imbalances inside the die, or its outside dimensions are not exactly the same, or simply the process of rolling the die is not neutral (not fully random).

in any case, it seems there are some deviations from the normal expected behavior of 1/6 per number.

so, the observed experimental probabilty of rolling a 1 is

(as always, desired cases / total cases)

14/100 = 7/50 = 0.14

which is a little bit less then 1/7.

Answer:

The sum of area of two smaller squares is equal to the area of bigger square

An equation using a, b, and c with exponents is [tex]c^2=a^2+b^2[/tex]

Step-by-step explanation:

Let a be the side of the smallest square , b be the side of other smaller square and c be the side of biggest square

Area of square with side a = [tex]Side^2 = a^2[/tex]

Area of square with side b = [tex]Side^2 = b^2[/tex]

Area of square with side c =[tex]Side^2 = c^2[/tex]

Refer the attached figure

In triangle ABC

[tex]\angle A = 90^{\circ}[/tex]

So, We can use Pythagoras theorem over here

AB = a = Base

AC = b = Perpendicular

BC = c = Hypotenuse

[tex]Hypotenuse^2=Perpendicular^2+Base^2\\c^2=a^2+b^2[/tex]

So, The sum of area of two smaller squares is equal to the area of bigger square

An equation using a, b, and c with exponents is [tex]c^2=a^2+b^2[/tex]

Answer:

2

Step-by-step explanation:

form of functions

f(x) = ax2 + bx + c

which means ² is the greatest exponent of a quadratic function

Step-by-step explanation:

The length of arc KNJ is the circumference of the entire circle minus the measure of the 48 degree arc.

This means the central angle of this sector KNJ is 360-48=312.

Using the arc length formula, we get the arc length is (2)(pi)(16)(312/360)=416pi/15.

Answer:

25

Step-by-step explanation:

Answer: you would simple multiply the cost c which is fifty bucks times the number of p people

Step-by-step explanation: how much would it cost for 6 people to go to the fair to solve this you would just set up the equation 6 * 50 and solve from there

5 pairs of jeans for $87.50.

=> 1 pr costs = 87.50 : 5 = $17.50

How much would he need to pay for 9 pairs of jeans?

= 17.50 x 9 = $157.50

Answer:

157.5

Step-by-step explanation:

87.50/5=17.5

17.5x9=157.5

Answer:

There could be a total of 63 vehicles, 35 cars and 28 trucks

Answer:

28 trucks

35 cars

63 total cars and trucks

Step-by-step explanation:

trucks : cars

4 : 5

Use a proportion.

x/4 = 35/5

x/4 = 7

x = 28

28 trucks

35 cars

63 total cars and trucks

Answer:

75%

Step-by-step explanation:

[tex]\frac{15}{20}[/tex] as a percent = 75%, or 0.75 in decimal form.

Answer:

1+1=2

Step-by-step explanation:

easy lol

Answer:

1.5

Step-by-step explanation:

Answer:

1.5 or 3/2

Step-by-step explanation:

y-y over x-x and you get you answer.

Answer:

log ( 100 )

6 !

3 !

log ( 7 )

Answer:

8

Step-by-step explanation:

1) 5(16+2)/6

80+10/6

80+1.6

=8

2) 5(16+2)

80+10/6

90/6

=8

Step-by-step explanation:

A

Answer:

6*(5+10)

Step-by-step explanation:

6*(5+10)

6*15

90

Answer:

I=Prt

Step-by-step explanation:

The simple interest formula is given as;

          I  = Prt

where I is the simple interest

           p is the principal

           r is the percentage rate

          t is the duration

Simple interest accrues on the principal of either a loan or an investment. This amount is payable after a duration of time.

Principal is the amount borrowed or invested in a business

Rate is the percentage commission to be paid on the amount borrowed

Time is the duration of the borrowing.

Answer:

2

(

5

+

3

)

(

2

5

2

−

1

5

+

9

)

Step-by-step explanation:

The given expression 250m³ +54 can be written in the form, 2(5m + 3)(5m² - 15m + 3²)

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression, 250m³ +54

⇒ 250m³ +54

It can be written as,

⇒ 2×125×m³ +  2×27

Now, 2 can take common

⇒ 2(125×m³ + 27 )

⇒  2(5³×m³ + 3³ )

⇒  2(5m³ +  3³ )

It is known that, it is like algebraic identity

a³ + b³  =  (a + b)(a² - ab + b²)

Similarly, given expression can be written in form of identity

2(5m³ +  3³ ) = 2(5m + 3)(5m² - 15m + 3²)

Hence, it can be expressed as 2(5m + 3)(5m² - 15m + 3²)

To know more about Expressions check:

brainly.com/question/16804733

#SPJ2

Answer:

hey so i did your questions on a sheet of paper, hope you can understand it, let me know if you cant

also, good luck with school and stay safe!! :)

The greatest length of the considered pendent is given by: Option A: 1.25 cm

Suppose the considered function is [tex]y = f(x)[/tex]

Then, we will plot points as [tex](x,y) =(x,f (x))[/tex] for all values of 'x' which are in domain of the function.

For this case, the given function's graph (the graph of [tex]y = \dfrac{x^2}{20}[/tex] ) is shown below.

We're given that the largest dimension is of 10 units.

Let this be the line segment parallel to the x-axis, intersecting y-axis at [tex]y = y_0[/tex]

Now, since the curve is symmetric over (as for x or -x, we get same y), so the line segment that is parallel to x axis also intersects the graph at symmetric places. Let those points be in front of [tex]x_0[/tex] and [tex]-x_0[/tex]

For those inputs, the output is [tex]y = y_0[/tex],

Also, we have length of the line segment as of 10 units, this is the difference between those symmetric inputs.

Thus, we get two equations:

[tex]x_0 - (-x_0) = 10[/tex]

[tex]f(x_0) = y_0 = \dfrac{x_0^2}{20}[/tex]

From first one, we get:

[tex]x_0 = 10/2= 5[/tex]

Thus, we get:

[tex]f(x_0) = y_0 = \dfrac{x_0^2}{20}\\\\f(5) = y_0=\dfrac{25}{20} = 1.25[/tex]
Since the length of y_0 is the shortest distance from x-axis to that parallel line segment, this is the second dimension needed.

Thus, the greatest length of the considered pendent is given by: Option A: 1.25 cm

Learn more about functions here:

https://brainly.com/question/10166124

Answer:

12

Step-by-step explanation:

16 x3/4 is 48/4 or 48 divided by 4, or 12.