What is the value of a + bc when a = 7, b = 4, and c = 2 ?

Mode: Separate multiple are 17, 23, and 25.

The mean age is 22.4 years old, to the nearest tenth.

The range of ages is 13 years.

Here is a dot plot for the given data set:

16 ●●

17 ●●●

19 ●

20 ●

21 ●●●

23 ●●●

24 ●

25 ●●●●

27 ●

29 ●●

Mode: The mode is the most common value in the data set. In this case, there are multiple values that occur with the same frequency, so there are multiple modes: 17, 23, and 25.

Mean: The mean is the sum of all the values divided by the total number of values. We can add up all the ages and divide by 21 (the number of contestants) to get:

(20 + 23 + 25 + 24 + 16 + 19 + 21 + 29 + 29 + 21 + 17 + 25 + 25 + 17 + 23 + 27 + 23 + 17 + 16 + 21 + 16) / 21 = 22.4

Median: The median is the middle value when the data set is arranged in order. We can arrange the ages in ascending order:

16, 16, 17, 17, 19, 20, 21, 21, 23, 23, 23, 24, 25, 25, 25, 27, 29, 29

The median is the middle value, which is 23.

Range: The range is the difference between the largest and smallest values in the data set.

The largest value is 29 and the smallest value is 16, so the range is:

29 - 16 = 1

For similar question on median.

https://brainly.com/question/2217700

#SPJ11

Question

Create a Dot Plot on your paper for the data set, then find the mode, mean, median, and range.

The ages of the top two finishers for "American Idol" (Seasons 1-11) are listed below.

20, 23, 25, 24, 16, 19, 21, 29, 29, 21, 17, 25, 25, 17, 23, 27, 23, 17, 16, 21, 16

Create a Dot Plot on your paper for the data set

Find the following:

Mode: Separate multiple answers with a comma. Mean to nearest tenth: Median: Range:

The function that represent the function g(x) is g(x) = f(x) + 4.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

The graph of the function f(x) is given.

We know that, a linear function in slope intercept form can be represented as, y = mx + d, where m is slope and d is the y intercept.

y intercept is the y coordinate of the point where the line touches with the Y axis. At this point x coordinate is 0.

From the graph, we have f(x) = y = -1 when x = 0.

So y intercept, d = -1

Take two points from the graph (1, 0) and (0, -1).

Slope, m = (-1 - 0) / (0 - 1) = -1 / -1 = 1

f(x) can be represented in slope intercept form as f(x) = x - 1

We have a second function g(x) from the transformation of f(x).

y intercept of g(x) = 3

f(x) + 4 = x - 1 + 4 = x + 3 which can be g(X), since y intercept is 3.

Hence g(x) = f(x) + 4 is the function that represents the transformation of f(x) with y intercept 3.

Learn more about Slope here :

https://brainly.com/question/19131126

#SPJ1

The triangle which could be drawn as per the given description is only option b. isosceles triangle with measure 20° and 80°.

An acute triangle with sides measuring 7, 4, and 2

In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side .

According to the Pythagorean Theorem.

Here, 7² is greater than (4² + 2²).

So this is not possible.

An isosceles triangle with angles measuring 20° and 80°

In an isosceles triangle, two angles are equal, so if two angle measures 20° and 80°,

Then the third angle measures is

180° - 20° - 80°= 80°

Two angles are congruent implies two sides are congruent.

It is possible to form isosceles triangle.

An obtuse triangle with sides measuring 5, 10, and 15

In an obtuse triangle, the longest side is opposite the largest angle.

Sum of squares of two shorter sides is less than square of longest side according to Pythagorean Theorem.

However, 15²is greater than (5²+ 10²),

so this is not possible.

A scalene triangle with angles measuring 110° and 35°

The sum of the angles of any triangle is 180°,

so the third angle must measure

180° - 110° - 35° = 35°.

Two angles are congruent so it is isosceles triangle.

It is not possible to form scalene triangle.

Therefore, the triangle possible to draw as per the given condition is only option b. isosceles triangle with measure 20° and 80°.

Learn more about triangle here

brainly.com/question/15833022

#SPJ1

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:Your answer would be -8 x - 17 y

Step-by-step explanation: x - 9 x would be - 8 x

                                               You would have to distribute the negative in the problem -(9 x- 8 y) which would make it -9 x +8 y and 9 y + 8 y is 17 y so there fore the answer is -8 x - 17 y

Answer:

B) \(4i\sqrt{2}\)

Step-by-step explanation:

\(\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}\)

Answer:

60

Step-by-step explanation:

ratio: 12/6 =1/2 x/30=1/2 x=60

The solution of the system is then given by:

x = t[1 -1 1 0.5 0.5 0.33] + s[0 -2 1 1 -2 1]

This is the general solution of the system in the form of a sum of scalar multiples of fixed column vectors.

The system of linear equations can be written in matrix form as:

[1 0 1 2 1 3 | 1]

[2 1 2 4 0 10| 5]

[3 1 3 6 6 15| 8]

where the augmented matrix is [A | B].

To solve the system using the method of specifying appropriate free variables, we first convert the coefficient matrix into reduced row echelon form using Gaussian elimination.

In reduced row echelon form, the first non-zero element of each row (known as the leading entry) is 1, and the leading entries of lower rows are to the right of the leading entries of higher rows.

Applying Gaussian elimination to the coefficient matrix, we get:

[1 0 1 2 1 3 | 1]

[0 1 0 2 -2 7| 0]

[0 0 0 0 0 0| 0]

We can see that there are two non-zero rows, indicating that the system has two independent equations.

We can choose two of the variables to be free variables, and express the other variables in terms of the free ones.

Let's choose x1 and x3 as the free variables.

We can find x2 as follows:

x2 = -x1 - 2x3 + 7

And we can find x4, x5 and x6 as follows:

x4 = (1 - x1 - x3)/2

x5 = 1 - x1 - 2x3 + 2x4

x6 = (1 - x1 - x3 - 2x4)/3

So the general solution of the system can be expressed as a sum of scalar multiples of fixed column vectors:

x1 = t

x2 = -t - 2s + 7

x3 = s

x4 = (1 - t - s)/2

x5 = 1 - t - 2s + (1 - t - s)/2

x6 = (1 - t - s)/3

where t and s are scalars.

For more questions on Gaussian elimination to the coefficient matrix

https://brainly.com/question/28681914

#SPJ4

There a rule for logarithms:

         \(\log_n(a^m) = m \cdot \log_n(a)\)

So when you're working with \(\log_5(a^3)\), we can use that rule to rewrite this as
        \(\log_5(a^3) = 3 \cdot \log_5(a)\)

And since the first part tells us (on paper) that \(\log_5(a) = 2\), then we can say
        \(\log_5(a^3) = 3 \cdot \log_5(a) = 3 \cdot 2 = 6\)

Answer:

3m − 5

Step-by-step explanation:

Answer:

3m - 5

Step-by-step explanation:

Answer:

166

Step-by-step explanation:

multiply the 6 by 2 and then multiply 13 by 10

to get 166

Answer:

k = 77

Step-by-step explanation:

\(\frac{k}{11} =7\\\\\rightarrow 11 * 7 = 77\\\rightarrow 77 \div 11 = 7\)

Answer:

k = 77

Step-by-step explanation:

The question in equation form is :

\(\frac{k}{11} =7\)

Now we multiply both sides by 11 to solve for k :

k = 7×11

k = 77

Hope this helped and brainliest please

Answer:

Step-by-step explanation:

3. The volume of the new gumball machine is of 861.75 in³.

4. This is a real solution, as it is a positive number.

The volume of the old machine was of:

5575 in.³

(as stated in the problem)

The volume of the new machine is obtained as follows:

532 in.³ less than 1/4 of the volume of the globe of the giant gumball machine.

One fourth of the volume of the old machine is obtained as follows:

1/4 x 5575 in³ = 1393.75 in³.

532 in.³ less than that is obtained as follows:

1393.75 - 532 = 861.75 in³.

An extraneous volume is a negative value to the volume, as the volume cannot be negative. Since the number is positive, it represents a real solution.

More can be learned about volumes at https://brainly.com/question/463363

#SPJ1

The values of f(4) , f(0) and f(-5) are 16/7, -12 and -7/11 respectively.

We are given the function:-

f(x) = (x + 12)/(2x - 1)

We have to find the values of  f(4) , f(0) and f(-5).

Putting x = 4 in the given function, we can write,

f(4) = (4+12)/(2*4-1) = 16/7

Putting x = 0 in the given function, we can write,

f(0) = (0 + 12)/(2*0 - 1) = 12/(-1) = -12

Putting x = -5 in the given function, we can write,

f(-5) = (-5 + 12)/(2*(-5) - 1) = 7/(-10-1) = 7/(-11) = -7/11

To learn more about function, here:-

https://brainly.com/question/12431044

#SPJ1

#CarryOnLearning

Answer:

1.) False

The product \(\bold{\frac{5}{2}}\)(\(\bold{\frac{4}{25}}\)) will give the unit price of one kilogram of rice.

2.) False

Emily paid less than $1.50 per kilogram of rice.

3.) True

If Emily has $1.00 \:to\: spend\: on\: rice, she\: can\: get \(\frac{4}{10}\)$ of a kilogram of rice.

#CarryOnLearning

Answer:

z = 30

Step-by-step explanation:

All angles of a triangle add up to 180:

z + 120 + 30 = 180

z + 150 = 180

z = 180 - 150

z = 30

Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

For more such questions on linear regression line:

https://brainly.com/question/30401933

#SPJ8

Answer:

Step-by-step explanation:

4w + 2L = 670

2w + L = 335

L = 335 - 2w

Area A(w) = w(335 - 2w)

max occurs at the average of the solutions.

solutions are w=0 and w = 167.5

the average is 83.75

83.75 * (335 - 2 * 83.75) = 14028.125

The observation of the pattern is discussed below.

When we calculate the squares of the numbers from 1 to 10 and observe the digits at the one's place of each square, we notice a pattern:

1²=1

2²=4

3²=9

4²=16

5²=25

6²=36

7²=49

8²=64

9²=81

10²=100

If we focus on the digits at the one's place, we can see that they form a repeating pattern: 1, 4, 9, 6, 5, 6, 9, 4, 1, 0. This pattern repeats itself as we calculate the squares of higher numbers.

This observation is known as the "digit at one's place pattern" or the "units digit pattern." It occurs because the square of any number depends only on the digit at the one's place of that number. Hence, when we square numbers that have the same digit at the one's place, we get the same digit at the one's place in the result.

Learn more about Sequence here:

https://brainly.com/question/30262438

#SPJ1

Answer:

x + 1.4x = 180

2.4x = 180

x = 75, so 1.4(75) = 105

Answer:

9.75

1 1/2+5=6 1/2

6 1/2=6 2/4=6.50

16.25-6.50=9.75

Answer:

Step-by-step explanation:

y - 4 = 7(x - 1)

y - 4 = 7x - 7

y = 7x - 3

Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

Answer:

I think its 10

Step-by-step explanation:

the numbers go down by 10

\(~~~~~~~\dfrac{x(x-2)}{(x+3)(x-5)}=0\\\\\\\implies x(x-2) = 0\\\\\\\implies x = 0,~ x =2\\\\\text{The zeroes are}~ 0~ \text{and}~ 2.\)

Answer:

62 %

Step-by-step explanation:

186   out of 300

186/300 = .62    this represents 62%

Answer:

9 inches

Step-by-step explanation:

Area of rectangle= length ×width

Let the length of the rectangle be x inches.

Width of rectangle= (x +2) inches

since the width is 2 more than the length.

63= x(x+2)

63= x(x) +2x

Bringing constant to one side,

x² +2x -63= 0

(x +9)(x-7) = 0 (factorise)

x+9= 0 or x-7= 0

x= -9 or x= 7

(reject)

width of rectangle

= 7+2

= 9 inches

*We reject x= -9 since the length of the rectangle cannot be a negative number.