Solve 3 and get 70 pts

the box plot shows the total amount of time, in minutes, the students of a class spend studying each day:

a box plot is titled daily study time and labeled time (min). the left most point on the number line is 40 and the right most point is 120. the box is labeled 57 on the left edge and 112 on the right edge. a vertical line is drawn inside the rectangle at the point 88. the whiskers are labeled as 43 and 116.

what information is provided by the box plot?

the lower quartile for the data
the number of students who provided information
the mean for the data
the number of students who studied for more than 112.5 minutes

question 5(multiple choice worth 3 points)

(08.05)theresa earned scores of 88 points, 84 points, 88 points, and 91 points on four tests. what is the lowest score she can get on the fifth test and still finish with an average score of 90 points?

96 points
97 points
98 points
99 points

question 6(multiple choice worth 3 points)

(08.05)some students reported how many pairs of shoes they have. the dot plot shows the data collected:

a dot plot is titled students pairs of shoes and labeled number of pairs. the values on the horizontal line are 1, 2, 3, 4, and 5. there is 1 dot above 1, 3 dots above 2, 5 dots above 3, 3 dots above 4, and 1 dot above 5.

what do the dots above the number 4 indicate?

there are exactly 3 students with less than 4 pairs of shoes.
there are exactly 4 students with less than 3 pairs of shoes.
there are exactly 4 students with 3 pairs of shoes.
there are exactly 3 students with 4 pairs of shoes.

Ques 1)

           The lower quartile for the data.

Ques 2)

             99 points

Ques 3)

 There are exactly 3 students with 4 pairs of shoes.

Ques 1)

Minimum value=40

Maximum value=120

First quartile or lower quartile (i.e. ) =57

Third quartile or upper quartile (i.e. )=112

Median (i.e. )=88

The information that is provided by the box plot is:

          The lower quartile for the data.

Ques 2)

The scored earned by Theresa in four test are:

88 points, 84 points, 88 points, and 91 points

Let 'x' be the point she earned in the fifth test.

Hence we need to find 'x' such that the average score is 90 points.

i.e.

Hence she scores 99 points in the fifth test.

Ques 3)

              Pair of shoes           Number of students

                       1                                   1

                       2                                  3

                       3                                   5

                       4                                   3

                        5                                   1    

Hence, the dots above the number 4 indicate that:

    There are exactly 3 students with 4 pairs of shoes.

1. f(x)=x²+10x+16

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(as, a> 0 the parabola is open upward), b=10. by putting the values.

-b/2a = -10/2(1) = -5

f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9

so, vertex = (-5, -9)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).

now find x-intercept put y=0 in the above equation. 0= x²+10x+16

x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

2. f(x)=−(x−3)(x+1)

by multiplying the factors, the general form is f(x)= -x²+2x+3.

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=2. by putting the values.

-b/2a = -2/2(-1) = 1

f(-b/2a)= f(1)=-(1)²+2(1)+3= 4

so, vertex = (1, 4)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).

now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.

-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

3. f(x)= −x²+4

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=0. by putting the values.

-b/2a = -0/2(-1) = 0

f(-b/2a)= f(0)= −(0)²+4 =4

so, vertex = (0, 4)

now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).

now find x-intercept put y=0 in the above equation. 0= −x²+4

−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

4. f(x)=2x²+16x+30

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(as, a> 0 the parabola is open upward), b=16. by putting the values.

-b/2a = -16/2(2) = -4

f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2

so, vertex = (-4, -2)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).

now find x-intercept put y=0 in the above equation. 0=2x²+16x+30

2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

5. y=(x+2)²+4

the general form of parabola is y=a(x-h)²+k , where vertex = (h,k)

if a> 0 parabola is opened upward.

if a< 0 parabola is opened downward.

compare the given equation with general form of parabola.

-h=2 ⇒h=-2

k=4

so, vertex= (-2, 4)

as, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.

hope this : )

the answer is 489

step-by-step explanation: