Roy has a bag containing green, blue, red, brown, and black marbles. He randomly picks a marble and replaces it. He repeats this experiment 60 times and records the results in this table.

Answer:

Shannon's expression:

[tex]\frac{4.2 \times 10^{9} }{1.4 \times 10^{4} }[/tex]

Kristoph's expression:

[tex]\frac{4.2 \times 10^{2} }{1.4 \times 10^{-3} }[/tex]

Notice that both expression has the same coefficient numbers: 4.2 and 1.4. That means to have the same results, we just need to have the same powers.

Without dividing the complete expression, you can observe that both powers are the same, because each you subtract 9-4 = 5, and 2-(-3) = 5, both gives the same exponent to the power of 10.

Therefore, both expression give the same result, because they have the same numbers and the same powers.

Let's solve the division to have the result in scientific notation.

Shannon's expression:

[tex]\frac{4.2 \times 10^{9} }{1.4 \times 10^{4} }=3 \times 10^{9-4}=3 \times 10^{5}[/tex]

Kristoph's expression:

[tex]\frac{4.2 \times 10^{2} }{1.4 \times 10^{-3} }=3 \times 10^{2-(-3)}=3 \times 10^{5}[/tex]

The standard form refers to each number written without the power. To do so, we need to move the decimal points the number of spots as the exponent demands. Notice that the exponent is 5, that means, we need to move the decimal point 5 spots to the right.

[tex]3 \times 10^{5}=300000[/tex]

Therefore, the standard value of the expressions is 300,000.

Answer:

D. 75x+160<760

Step-by-step explanation:

The reason is 75 has to be a variable because it changes with time. The fee is a fixed rate that will not change no matter the time. All of these values must be less than 760 meaning the variable and constant must be less than (<) 760

Answer:

[tex]\frac{x^{2} }{36}+\frac{y^2}{16}=1[/tex]

Step-by-step explanation:

Center of the ellipse is at origin (0, 0)

So (h, k) = (0, 0)

Length of major axis = 12

2a = 12

⇒ a = 6

Length of minor axis = 8

⇒ 2b = 8

⇒ b = 4

Since focus is on the x-axis, so it's a horizontal ellipse.

Equation of the horizontal ellipse is in the form of,

[tex]\frac{(x-h)^{2} }{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

By substituting the given values of a, b, and (h, k)

[tex]\frac{(x-0)^{2}}{6^2}+\frac{(y-0)^2}{4^2}=1[/tex]

[tex]\frac{x^{2} }{36}+\frac{y^2}{16}=1[/tex]

Answer:

A

Step-by-step explanation:

edge

Answer:

25+(The number)

Step-by-step explanation:

Answer:

A) (x+8)(x-3)

Step-by-step explanation:

this is the answer

Answer: 3

Step-by-step explanation:

Evaluate is a fancy word for putting the value assigned into the equation and see what result you get.

[tex]-2x^2-4x+3\\x=-2[/tex]

[tex]-2(-2)^2-4(-2)+3\\-2(4)+8+3\\-8+8+3\\3[/tex]

To evaluate the expression −2x²−4x+3 for x=−2, substitute x with -2 and perform the operations: square x, multiply by -2, multiply -4 by x, and add the results to get the final answer of 3.

To evaluate the expression
−2x²−4x+3 when x=−2, we need to substitute x with −2 and then follow the order of operations, which is to perform exponentiation before multiplication and addition.

Thus, −2x²−4x+3 evaluates to 3 when x is −2.

Answer:

He walked 2.75 miles in one hour         (distance in miles)

He walked 2 miles 3960 feet  in one hour           (distance in feet and miles)

He walked 14520 feet  in one hour                  (distance in feet)

Step-by-step explanation:

Using proportion to solve;

Let x be the distance(in mile) walked in one hour

11 miles = 4 hours

  x         = 1 hour

cross-multiply

4×x = 11

4x = 11

Divide both-side of the equation by 4

4x/4 = 11/4

At the right-hand side of the equation, 4 will cancel-out 4 leaving us with just x

x =2.75 miles

He walked 2.75 miles in one hour

Converting it to feet and miles

1 mile = 5280 feet

0.75 mile  =  y

y = 0.75×5280

   =3960 feet

he walked 2 miles 3960 feet  in one hour

To convert  it to feet

1 mile = 5280 feet

2.75 miles  = x

x = 2.75×5280

x = 14520 feet

he walked 14520 feet  in one hour

Answer:

14.2, 2.8

Step-by-step explanation:

Answer:

The two triangles are related by SAS so the triangles are congruent by SAS

Step-by-step explanation:

The angle that is the same is between the two sides that are the same

The triangle is congruent by SAS

Answer:

2.7

Step-by-step explanation:

its the answer trust me

Answer:

81 meters.

Step-by-step explanation:

The height (in meters), h(x) of a hovercraft x seconds after takeoff, is modeled by:

[tex]h(x)=-3(x-3)^2+108[/tex]

We are to determine its height at the time of takeoff.

Now, at the time of takeoff, x=0.

We substitute x=0 to solve for h.

[tex]h(0)=-3(0-3)^2+108\\=-3(-3)^2+108\\=-3(9)+108\\=-27+108\\=81$ meters[/tex]

The height of the hovercraft at takeoff is 81 meters.

Answer:

It is 5 km/hour

Step-by-step explanation:

Let w represents the speed of the water

The speed can be found by following:

→ distance = speed x time → speed = distance / time (1)

If the boat goes downstream the total speed of the boat is the speed of the boat in still water + the speed of the water. Substitute the values into equation 1:

→ (the speed of the boat in still water + the speed of the water) = 120 / 4

Since the speed of the boat in still water is 25

→ 25 + w = 120 / 4

→ w + 25 = 30

→ w = 5

Answer:

D - 150

Hope it helped :)

Answer:

150=w

Step-by-step explanation:

The answer is a little bit wordy. w = the sum of 85 + the supplement of 115.

So the first thing to do is get the supplement of 115.

180 - 115 = 65

w = 85 + 65 (These two are the remote interior angles. W is equal to the sum of them).

w = 150

Answer:

  3171 square meters

Step-by-step explanation:

You want the surface area of a 35 m square pyramid that has a volume of 8820 cubic meters.

The volume is given by ...

  V = 1/3s²h

so the height of the pyramid is ...

  h = 3V/s² = 3(8820)/35² = 21.6 . . . . meters

The slant height of one triangular face of the pyramid is found from the Pythagorean theorem:

  c² = a² +b²

  c² = 21.6² + 17.5² = 772.81

  c = √771.81 ≈ 27.799 . . . . . . meters

The surface area of the pyramid is the sum of the area of the square base and the lateral area of the four triangular faces.

  SA = s² + 4(1/2)(sc) = s(s +2c)

  SA = 35(35 +2·27.8) = 3171 . . . . square meters

The surface area of the Louvre Pyramid is about 3171 square meters.

Answer:

y=1/2x+4/3

Step-by-step explanation:

1.) subtract -3x to the side the 3x is on and then put it on the side that has the 8 on it

2.) write it out as 6y=-3x+8

3.) divide by six to the whole problem

4.) simplify

Answer:

if the parabola is positive it would be facing up

Step-by-step explanation:

Answer:

pointed upward

Step-by-step explanation:

The coefficient of the quadratic term, a, determines how wide or narrow the graphs are, and whether the graph turns upward or downward. A positive quadratic coefficient causes the ends of the parabola to point upward.

Answer:

We divided the figure into 1 triangle and 3 rectangles (as shown in attached pic).

Adding up the area of them, we get the total area:

A = area of triangle + area of 3 rectangles

   =  base x height/2 + length1 x width1 + length2 x width2 + length3 x width3

   = 6 x (2 + 11 + 5 - 4 -3)/2 + 2 x 2 + 11  x (5 + 2) + 5 x 9

   = 159 (m2)

Hope this helps!

:)

Step 1) Split the figure into separate shapes

Triangle: 6 x 11

Small square: 2 x 2

Large rectangle (center): 16 x 7

Medium rectangle (bottom): 2 x 5

Step 2) Find the area of each shape

Triangle: A = 6 x 11 x 1/2 = 33

Small square: A = 2 x 2 = 4

Large rectangle (center): A = 16 x 7 = 112

Medium rectangle (bottom): A = 2 x 5 = 10

Step 3) Add the areas together

A = 33 + 4 + 112 + 10 = 159 square meters

Hope this helps! :)

Answer:

C is the answer

Step-by-step explanation:

If you graph them on a line the outcome will be a straight line making it functional and a proportion

The required set of ordered pairs are (0, 1), (1, 3), (2, 9), (3, 27). The correct option is (D).

An exponential function can be represented as y = aˣ. When x = 0, y = a⁰ = 1. The range of an exponential function is from zero to infinity for a > 0.

It is clear from the given options that, only options (B) and (D) satisfies the general expression y = aˣ at x = 0.

Now, both these options can be examined one by one as follows,

Option (B),

The ordered pairs are given as (0, 1), (1, 2), (2, 5), (3, 10).

Substitute the values in the general expression y = aˣ, first two pair are satisfied for a = 2 but the remaining two are not.

Option (D),

The ordered pairs are given as (0, 1), (1, 3), (2, 9), (3, 27).

Substitute the values in the general expression y = aˣ, all the pairs are satisfied for a = 3.

Thus, the correct option is found.

Hence, the set of ordered pairs which could be generated by an exponential function are (0, 1), (1, 3), (2, 9), (3, 27).

To know more about exponential function click on,

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Answer:

80 degrees

Step-by-step explanation:

1/2 = 2/4 = 3/6,4/8,5/10,6/12,7/14, etc.

Add 1 to the numerator. Add 2 to the denominator.

Answer:

Equivilent fractions of 2/4 include the following: 1/2, 3/6, 4/8, 5/10.

Step-by-step explanation:

The fraction 2/4 can be simplified to 1/2, because 2 is half of 4. And since 3 is half of 6, it can also be simplified to 1/2, making the fractions 2/4 and 3/6 equal to eachother.

I hope that makes sense :)

Answer:

1,395 sq feet

Step-by-step explanation:

lets start with the area of the green cube b×h. 15×15=225. 225×5= 1125. I got five because there are 5 visible faces on the cube. to find the area of a triangle you use the formula 1/2 bh 9×15= 135 multiply that by 2 instead of one half because you have four triangular faces. add your areas together and you get 1395

Answer: 1465

Step-by-step explanation:

225 base

225 for each wall  (x4)

540 area for the top

Answer:

4. 2 triangular faces, 9 edges, and 6 vertices

6. 2 rectangular faces, 12 edges, and 8 vertices

Step-by-step explanation:

Please mark brainliest :)

Answer:

If you still need the answer I think it's B

Step-by-step explanation:

The total surface area of the solid is 1466.4 square millimeters.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

The rectangular prism has a total surface area of:

2lw + 2lh + 2wh

= 2(16)(11) + 2(16)(10) + 2(11)(10)

= 352 + 320 + 220

= 892 square millimeters.

The triangular prism has a total surface area of:

2B + Ph

= 2(0.5bh) + (perimeter of base)h

= 2(0.5(11)(8)) + (11 + 8 + sqrt(11² + 8²))(16)

= 88 + 478.4

= 566.4 square millimeters.

Therefore,

The total surface area of the solid is:

892 + 566.4

= 1458.4 square millimeters,

which rounded to one decimal place is 1466.4 square millimeters.

Thus,

The total surface area of the solid is 1466.4 square millimeters.

Learn more about prism here:

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Answer:

.3333333

Step-by-step explanation:

There are 10 shirts

6 blue and 4 green

P (blue) =  blue shirts/ total

                6/10 = 3/5

Then there are 9 shirts left 5 blue and 4 green

P(blue) = blue shirts / total

              5/9

P(blue, no replace, blue) = 3/5 * 5/9 = 1/3

Tristan's fish tank is 1/2 yard long,  1/6 yard wide, and  1/3 yard high. (Note that the fish tank is in the shape of a rectangular prism and not a cube.) One way of finding the volume of the tank is by dividing the tank into cubic blocks. What should the side lengths of each cubic block used to find the volume be?

Answer:

the side lengths are 3 sides, 1 side and 2 sides  of each cubic block.

Step-by-step explanation:

The volume of the rectangular prism is:

[tex](1/2 \ yard) * (1/6 \ yard) * (1/3 \ yard) = 1/36 \ yard^3[/tex]

However: let's find their lowest common multiples to determine their side length.

Multiples of 2:   2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, ...

Multiples of 6:   6, 12, 18, 24, 30, ...

Multiples of 3:   3, 6, 9, 12, 15, 18, 21, 24, 27, 30,  ...

The lowest common multiple for 2 , 6 and 3 is 6 .

Then in terms of the side length of each cubic block; we have :

1/2 × 6 = 3

1/6 × 6 = 1

1/3 × 6 = 2

So the side lengths are 3 sides, 1 side and 2 sides  of each cubic block

Answer:

<

Step-by-step explanation: Since it just said you have less than and not equal to you can say its only less than.

Answer:

< Is the correct answer

Final answer:

To find the value of x for the given sequence, we must ensure the median remains 14. Since the median is the average of the third and fourth numbers in an ordered list of six numbers, x must be 16 because 9, 10, 12, 16, 20, 25 gives us a median of 14 (12 + 16 = 28; 28 / 2 = 14).

Explanation:

The student is asking to find the value of x in a sequence of numbers given that the median is 14. First, we place all the numbers in order: 9, 10, 12, x, 20, 25. Since there are six numbers, the median will be the average of the third and fourth numbers.

To have a median of 14, the sum of the third and fourth numbers must be 28 (since 14 = (third number + fourth number) / 2). Therefore, if the third number is 12, x must be 16 because 12 + 16 = 28.

The value of x that makes the median of the set equal to 14 is 16.

Answer:

500 cm²  

Step-by-step explanation:

You haven't presented any diagrams, so I assume the prism has the dimensions shown below.

Then the dimensions of the original piece of cardboard are as in the second figure.

The area of the cardboard is the same as the lateral area of the triangular prism.

The formula for the area of a rectangle is  

A = lw

 l = 9 cm + 9 cm + 7 cm = 25 cm

w = 20 cm

A = 25 cm × 20 cm = 500 cm²

The area of the piece of cardboard is 500 cm².

Answer:

The ratio is 16/65

Step-by-step explanation:

In this question, we are tasked with calculating what ratio represents the cosine of the angle  Q.

In a right angled triangle, there are usually three sides, the hypotenuse, the opposite and the adjacent. Also, there are three angles, 2 asides the ∠90°. The hypotenuse is the longest side which faces the ∠90°, the opposite is that side facing the angle we are interested in while the adjacent is the third side.

Hence we can have only a single hypotenuse, which is the longest side, two opposites(depending on the angle we are concerned about and two adjacents two based on the angle of interest

Firstly, please check attachment for diagrammatic representation.

The ratio for the cosine of an angle is = length of adjacent/length of hypotenuse

From the diagram, with respect to angle Q, the length of the adjacent is 16 while the length of the hypotenuse is 65.

Thus, the ratio representing the cosine of angle Q is 16/65