The mean of 3 consecutive terms in an arithmetic sequence is 10, and the mean of their squares is 394. What is the largest of the 3 terms?

Answer:

D) 704 in.²

Step-by-step explanation:

The area is height × width.

So, the area =32 × 22 = 704 in.²

Answer:

Option 4 is the image of the given figure.

Step-by-step explanation:

We are given that,

The shape EFGHCD is transformed to form another shape.

From the options, we see that,

Figure 2 and 3 does not have the same vertices as that of the figure.

So, they are discarded.

Since, after transforming a figure, we get a new figure.

So, the vertices cannot have same name as that of the original figure.

So, option 1 is discarded.

Thus, we get,

Option 4 is the image of the given figure after transformation as shown below.

A cube with side lengths measuring 7 inches means that each side of the cube is 7 inches long.

To find the volume of the cube, you multiply the length, width, and height of the cube since all sides are equal:

Volume = length × width × height

For a cube, all these measurements are the same, so you can simply cube the length of one side:

Volume = 7 inches × 7 inches × 7 inches

Volume = 7³ cubic inches

Volume = 343 cubic inches

So, the volume of the cube is 343 cubic inches.

A cube with side lengths measuring 7 inches implies that each side of the cube is 7 inches long.

To find the volume of the cube, we use the formula for the volume of a cube, which is side length cubed.

Since all sides of a cube are equal, we simply cube the length of one side: 7 inches × 7 inches × 7 inches. This equals 7³ = 343 cubic inches.

Therefore, the volume of the cube is 343 cubic inches. In a cube, all sides, angles, and faces are congruent, making it a regular polyhedron with 6 square faces.

Complete Question:

A cube that has side lengths measuring 7 inches.

The statements that are true about the intersecting rays are

A) m∠3 = m∠1

B) m∠2 = 60°

D) m∠3 = 120°

Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees.

Perpendicular lines are two straight lines that intersect and form right angles. When two perpendicular lines intersect, they form four right angles.

When lines intersect, two angle relationships are formed:

Opposite angles are congruent

Adjacent angles are supplementary

Given data ,

Let the two intersecting lines be m and n

Now , the angles formed are shown in the diagram

where the measure of ∠1 = ∠3 ( Opposite angles are congruent )

Now , the measure of ∠2 = 180° - ( 65° + 55° ) ( angles in a triangle = 180° )

The measure of ∠2 = 60°

So , the measure of ∠3 = 180° - ∠2 ( Adjacent angles are supplementary = 180° )

And , the measure of ∠3 = 120°

Hence , the angles in the intersecting lines are solved

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The two numbers are 33 and 14, where 33 is the larger number and 14 is the smaller number that is 19 less than the larger number. Their sum equals 47.

Finding Two Numbers Based on Sum and Difference

The problem given states that the sum of two numbers is 47, and that the smaller number is 19 less than the larger number. To solve this, let's denote the larger number as x and the smaller number as x - 19. The equation representing their sum is:

x + (x - 19) = 47

Combining like terms, we get:

2x - 19 = 47

Adding 19 to both sides gives:

2x = 66

Dividing both sides by 2, we get:

x = 33

So the larger number is 33. Now we can find the smaller number:

33 - 19 = 14

Therefore, the two numbers are 33 and 14.

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The scale of the drawing is [tex]\( \boxed{1 : 0.4} \).[/tex]

To find the scale of the drawing, we need to determine the ratio between the length in the drawing and the actual length.

Let x  be the scale of the drawing.

According to the given information, the length of the plane in the drawing is 35 centimeters, and the actual length of the plane is 87.5 feet.

So, we can set up the proportion:

[tex]\[\frac{\text{Length in drawing}}{\text{Actual length}} = \frac{35}{87.5} = x\][/tex]

To find x , we solve for it:

[tex]\[x = \frac{35}{87.5} = 0.4\][/tex]

The scale of the drawing is [tex]\( \boxed{1 : 0.4} \).[/tex]

The probability of drawing a red marble is 1/8.

The correct option is C.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

We have,

Total marbles = 24

White marble = 6

Blue marble = 8

Black marble = 7

Red marble = 3

So, the probability of drawing a red marble

= 3 / 24

= 1/8

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Answer:

  multiply the others by n

Step-by-step explanation:

If you want to keep the same ratio, you must multiply all of the numbers by n.

A ratio of 1 : 1 will remain 1 : 1 if all the numbers are multiplied by n:

  1 : 1 = n : n

_____

Comment on alternate interpretation of the question

There are occasions for multiplying the ratio by n:

  x/n = 1/2

To solve this for x, we multiply the ratio (1/2) by n. This multiplies the numerator, but does not change the denominator.

  x = n(1/2) = n/2

To find the largest number in a stem-and-leaf plot, identify the row with the highest stem and the largest leaf in that row.

The largest number in a set represented by a stem-and-leaf plot can be determined by locating the highest stem value and the largest leaf value attached to it. In a scenario where the stem represents units of 100,000 and the leaf represents units of 10,000, as with the example regarding U.S. cities' populations, you would look for the row with the highest stem number and the highest leaf number within that row to find the largest value. For instance, with a stem of 4 and a leaf of 9, one would interpret the largest number as 490,000.

When constructing a stemplot, each data point's stem is written in a vertical column with the leaves arranged to the right. Negative numbers are handled with negative stems, and the leaves are rounded to represent two significant digits. This method creates a clear visual of data distribution, showing values, potential outliers, and general trends.

Answer:

1- The average rate of change of f(x) is greater than the average rate of change of g(x).

5- The average rate of change of f(x) is -0.1, and the average rate of change of g(x) is -0.25.

Step-by-step explanation:

average rate of change of a function h(x) in the interval [a, b] is computed as follows:

average rate of change = h(b) - h(a)/(b - a)

So, for f(x) (see table):

average rate of change = f(10) - f(4)/(10 - 4) = (0.4 - 1)/(10 - 4) = -0.1

And for g(x) (see figure):

average rate of change = g(10) - g(4)/(10 - 4) = (1 - 2.5)/(10 - 4) = -0.25