Solve the system by substitution.

A rectangular region is removed from another rectangular region to create the shaded region shown below. Find the area of the sh

Simora [160]

Answer:

wgtvwthrr

Step-by-step explanation:

3 0

3 years ago

Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given freque

maw [93]

Answer:

The number of individuals included in the summary is 146.

Step-by-step explanation:

The frequency distribution table provided is as follows:

Class Intervals Frequency

100 - 199 24

200 - 299 90

300 - 399 27

400 - 499 1

500 - 599 4

The lower class limit it the smallest value of each class interval.

Lower class limit = {100, 200, 300, 400, 500}

The upper class limit it the highest value of each class interval.

Upper class limit = {199, 299, 399, 499, 599}

The lower class boundaries are the lower class limits decreased by 0.5 and the upper class boundaries are the upper class limits increased by 0.5.

Class boundaries:

99.5 - 199.5

199.5 - 299.5

299.5 - 399.5

399.5 - 499.5

499.5 - 599.5

The class width is the difference between the class boundaries of each class.

Class width = 199.5 - 99.5 = 100

So, the class width is 100.

The midpoints of a class is the average value of the boundaries of a class.

$\text{Midpoint}_{100-199}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\$

$=\frac{99.5+199.5}{2}\\\\=149.5$

$\text{Midpoint}_{200-299}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\$

$=\frac{199.5+299.5}{2}\\\\=249.5$

$\text{Midpoint}_{300-399}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\$

$=\frac{299.5+399.5}{2}\\\\=349.5$

$\text{Midpoint}_{400-499}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\$

$=\frac{399.5+499.5}{2}\\\\=449.5$

$\text{Midpoint}_{500-599}=\frac{\text{Lower class boundary} + \text{Upper class boundary}}{2}\\$

$=\frac{499.5+599.5}{2}\\\\=549.5$

The number of individuals included in the summary is the sum of all frequencies.

$\text{Number of Individuals}=24 + 90 + 27 + 1 + 4=146$

Thus, the number of individuals included in the summary is 146.

3 0

3 years ago

Read 2 more answers

ich sequence of transformations would result in a figure that is similar, but not congruent, to the original figure? Select all

n200080 [17]

Translations, reflections, and rotations always result in a figure that is congruent. Only dilations with a scale factor other than 1 will give a similar, but not congruent, figure.

The 1st and 4th selections apply.

6 0

3 years ago

f(x) = −16x2 + 24x + 16 Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points) WILL GIVE BRAINLIEST

castortr0y [4]

Answer:

Step-by-step explanation:

f(x) = −16x2 + 24x + 16 = 0 can be reduced to -2x^2 + 3x + 2 = 0 and then to 2x^2 - 3x - 2 = 0. Solve this for x using the quadratic formula:

The discriminant is b^2 - 4ac = (-3)^2 - 4(2)(-2) = 9 + 16 = 25.

Therefore the roots are:

-(-3) ± √25 3 ± 5

x = ----------------- = ------------ => x = 2 and x = -1/2

2(2) 4

The x-intercepts are points: (2, 0) and (-1/2, 0)

Because the coefficient of the x^2 term is negative, this graph opens down and the vertex represents a maximum.

To graph this function, find and plot the vertex. It is exactly halfway between the x-intercepts, that is, at x = 1 1/4, for which the y value is 21:

vertex and maximum at (5/4, 21)

Finally, find the y-intercept. Let x = 0; we find that y = 16. The y-intercept is 0, 16)

We now have four points on the graph and know where the maximum is. Plot this max (5/4, 21) and the x-intercepts (2, 0) and (-1/2, 0), and finally the y-intercept. Draw a smooth curve through these points, remembering that the graph is symmetrical about the axis of symmetry x = 5/4.

3 0

3 years ago

Amanda worked the entire summer before her freshman year of college. She saved $2000. She withdraws $150 per week for expenses.

ivolga24 [154]

Answer:

12 weeks.

Step-by-step explanation:

Amanda starts with $2000 and is getting $150 per week which means that we can make the expression:

$2000-150n=200$

The expression is equal to 200 because is the limit where we can arrive to avoid the fee, then the n is the number of weeks that we are looking for:

$150n=2000-200\\n=\frac{1800}{200}\\n=12$

n=12 weeks

3 0

3 years ago