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

Answer:

[tex] x+2-2 <-5-2[/tex]

And after operate we got:

[tex] x <-7[/tex]

And then the solution would be [tex]x<-7[/tex]

Step-by-step explanation:

For this problem we have the following inequality:

[tex] x+2 <-5[/tex]

The first step would be subtract 2 from both sides of the equation and we got:

[tex] x+2-2 <-5-2[/tex]

And after operate we got:

[tex] x <-7[/tex]

And then the solution would be [tex]x<-7[/tex]

Answer:

[tex]\frac{9}{a - b}[/tex].

Step-by-step explanation:

a^2 - b^2 = 9

(a + b)(a - b) = 9

a + b = [tex]\frac{9}{a - b}[/tex].

ab = 3

a = 3/b

3/b + b = [tex]\frac{9}{\frac{3}{b} -b}[/tex]

3 + b^2 = [tex]\frac{9b}{\frac{3}{b}-\frac{b^2}{b} }[/tex]

3 + b^2 = [tex]\frac{9b}{\frac{3-b^2}{b} }[/tex]

3 + b^2 = [tex]9b * \frac{b}{-b^2 + 3}[/tex]

3 + b^2 = [tex]\frac{9b^2}{-b^2 + 3}[/tex]

(b^2 + 3)(-b^2 + 3) = 9b^2

-b^4 + 9 = 9b^2

b^4 + 9b^2 - 9 = 0

Let's say that b^2 = x

x^2 + 9x - 9 = 0

Hope this [somewhat] helps!

Answer:

Step-by-step explanation:

a²-b²=9

ab=3 then a=3/b

a²-b²=9

(a+b)(a-b)=9 ( the values has to b (3*3) or (9*1)

but since ab=3. so the value has to be (3*3)

(a+b)(a-b)=9

3*3=9

a+b=3

ab=3

Answer:

14%

Step-by-step explanation:

If the percentage of boys wearing polo shirts were boys, then the rest has to be girls. So 100%-80%=20%. However, we are not done here.

We have only figured out the percentage of girls out of the total number of people wearing polo shirts. We want to find the percentage of girls wearing polo shirts out of the whole school. To do that, we multiply 20% by 70%, since 20% of the polo shirt wearers were girls, and 70% of the entire student body is wearing a polo shirt.

Multiplying those two together gets you 14%.

Answer:

14%

Step-by-step explanation:

Answer:

x=46 degrees

Step-by-step explanation:

first find the size of the other angles(let call z and y)

the sum of a straight angle is 180:

180=130+z

z=180-130=50

y=180-96=84

sum of angles of triangle =180

x+y+z=180

50+84+x=180

x=180-134=46 degrees

Answer:

46°

Step-by-step explanation:

Angle of a line = 180°

To find the other side of 130°

The other side = 180° - 130° = 50°

To find the other side of 96°

The other side = 180° - 96° = 84°

To find x°

Total angle of a triangle = 180°

180° = x° + 50° + 84°

x° = 180° - 134°

x° = 46°

Answer:

18m square

Step-by-step explanation:

Formula for rectangular- based pyramid is L x W x H divided by 3

= 3 x 5 x 3.6 divided by 3 = 18

So you would need 18 m square for the sculpture

Hey there! I'm happy to help!

We know that the perimeter is 2L+2W. Le'ts plug in the values 3 and 5 from our ratio and see what our perimeter would be with that.

2(3)+2(5)

6+10

16

How can we get this 16 to 64?

64/16=4

So, we need to multiply this length and width by four to get 64 as our perimeter!

3*4=12

5*4=20

We can plug this into our perimeter equation

2(12)+2(20)

24+40

64

Therefore, our length is 12 and our width is 20.

Have a wonderful day! :D

Answer:

(5,-6)

Step-by-step explanation:

ONE WAY:

If [tex]f(x)=x^2-6x+3[/tex], then [tex]f(x-2)=(x-2)^2-6(x-2)+3[/tex].

Let's simplify that.

Distribute with [tex]-6(x-2)[/tex]:

[tex]f(x-2)=(x-2)^2-6x+12+3[/tex]

Combine the end like terms [tex]12+3[/tex]:

[tex]f(x-2)=(x-2)^2-6x+15[/tex]

Use [tex](x-b)^2=x^2-2bx+b^2[/tex] identity for [tex](x-2)^2[/tex]:

[tex]f(x-2)=x^2-4x+4-6x+15[/tex]

Combine like terms [tex]-4x-6x[/tex] and [tex]4+15[/tex]:

[tex]f(x-2)=x^2-10x+19[/tex]

We are given [tex]g(x)=f(x-2)[/tex].

So we have that [tex]g(x)=x^2-10x+19[/tex].

The vertex happens at [tex]x=\frac{-b}{2a}[/tex].

Compare [tex]x^2-10x+19[/tex] to [tex]ax^2+bx+c[/tex] to determine [tex]a,b,\text{ and } c[/tex].

[tex]a=1[/tex]

[tex]b=-10[/tex]

[tex]c=19[/tex]

Let's plug it in.

[tex]\frac{-b}{2a}[/tex]

[tex]\frac{-(-10)}{2(1)}[/tex]

[tex]\frac{10}{2}[/tex]

[tex]5[/tex]

So the [tex]x-[/tex] coordinate is 5.

Let's find the corresponding [tex]y-[/tex] coordinate by evaluating our expression named [tex]g[/tex] at [tex]x=5[/tex]:

[tex]5^2-10(5)+19[/tex]

[tex]25-50+19[/tex]

[tex]-25+19[/tex]

[tex]-6[/tex]

So the ordered pair of the vertex is (5,-6).

ANOTHER WAY:

The vertex form of a quadratic is [tex]a(x-h)^2+k[/tex] where the vertex is [tex](h,k)[/tex].

Let's put [tex]f[/tex] into this form.

We are given [tex]f(x)=x^2-6x+3[/tex].

We will need to complete the square.

I like to use the identity [tex]x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2[/tex].

So If you add something in, you will have to take it out (and vice versa).

[tex]x^2-6x+3[/tex]

[tex]x^2-6x+(\frac{6}{2})^2+3-(\frac{6}{2})^2[/tex]

[tex](x+\frac{-6}{2})^2+3-3^2[/tex]

[tex](x+-3)^2+3-9[/tex]

[tex](x-3)^2+-6[/tex]

So we have in vertex form [tex]f[/tex] is:

[tex]f(x)=(x-3)^2+-6[/tex].

The vertex is (3,-6).

So if we are dealing with the function [tex]g(x)=f(x-2)[/tex].

This means we are going to move the vertex of [tex]f[/tex] right 2 units to figure out the vertex of [tex]g[/tex] which puts us at (3+2,-6)=(5,-6).

The [tex]y-[/tex] coordinate was not effected here because we were only moving horizontally not up/down.

Answer:

The equation for renting a car is ;

y = 3.5x + 220

where y is the rental cost and x is the number of miles driven

The cost of rising 388 miles is $1,578

Step-by-step explanation:

88 miles cost $428 while 158 miles cost 673, now we want to create an equation that represents renting a car from Hertz

We can make this in form of a plot with us having 2 data points here.

let the value y represent the cost of driving and x represent the number of miles driven.

So the kind of relationship we want to establish is a linear one that looks like ;

y = mx + c

Now let’s calculate the slope m with the two data points

The two points are; (88,428) and (158,673)

So the slope would be; (673-428)/(158-88) = 245/70 = 3.5

So what is left is the y intercept. To find this , we can make use of any of the two data points

Let’s say (88,428) in this case , so we have

528 = 88(3.5) + c

c = 528-88(3.5) = 528 - 308 = 220

So this means that our equation takes the form;

y = 3.5x + 220

where y represents the cost of traveling and x represents the number of miles driven

Now to the second part of the question, we want to know the cost of driving 388 miles

Just substitute the value 388 into the equation

y = 3.5(388) + 220

y = 1358+ 220 = $1,578

Answer:

The answer to your question is -5

Step-by-step explanation:

Data

            [tex]\frac{3}{2}x - \frac{7}{2} = 5x + 14[/tex]

Process

1.- Subtract 5x in both sides

            [tex]\frac{3}{2} x - \frac{7}{2} - 5x = 5x -5x + 14[/tex]

2.- Simplify

           [tex]- \frac{7}{2} x - \frac{7}{2} = 14[/tex]

3.- Add 7/2 in both sides

           [tex]-\frac{7}{2} x = 14 + \frac{7}{2}[/tex]

4.- Simplify

           - [tex]\frac{7}{2} x = \frac{35}{2}[/tex]

5.- Solve for x

               x = [tex]\frac{35}{2} / - \frac{7}{2}[/tex]

6.- Simplify

               x = -5

Answer: x = -3.71

Step-by-step explanation:

3/2*-7/2=5x+14

-4.55=5x+14

Subtract 14

-18.55=5x

Divide by 5

x = -3.71

Hope it helps <3

Answer:

[tex]f(x) = (x+1)^2 +2[/tex]

Step-by-step explanation:

Well you complete the square and get,

[tex]x^2 + 2x + 1 ^2 - 1^2 +3[/tex]

Then you use the binomial formula to get,

(x + 1)^2 + 2

Thus,

f(x) = x^2 + 2x + 3 is f(x) = (x + 1)^2 + 2.

Hope this helps :)

Answer:

20

Step-by-step explanation:

let the number be n then twice the number is 2n and half the number is [tex]\frac{1}{2}[/tex] n

Then the difference is

2n - [tex]\frac{1}{2}[/tex] n = 30 ( multiply through by 2 to clear the fraction )

4n - n = 60, that is

3n = 60 ( divide both sides by 3 )

n = 20

Answer:

Height of flagpole before it fell = 5.15 m

Step-by-step explanation:

Given:

Height of remain pole (p) = 1.7 m

Distance from base (b) = 3 m

Find:

Height of flagpole before it fell

Computation:

Using Pythagorean theorem

H = √ p² + b

Length of broken part = √ 1.7² + 3²

Length of broken part = √ 2.89 + 9

Length of broken part = √ 11.89

Length of broken part = 3.45 (Approx)

Height of flagpole before it fell = Length of broken part + Height of remain pole

Height of flagpole before it fell = 3.45 + 1.7

Height of flagpole before it fell = 5.15 m

Answer:

Period : 2π

Maximum: 2

Minimum: -4

y-intercept: (0,-1)

Amplitude: 3

When does the max occur: x=π/2

When does the min occur: x =3π/2

Equation of Axis: y = -1

Answer:

Step-by-step explanation:

In a right triangle, the sides forming the right angle also determine the angle opposite one of the sides.

Tan(29) =26/x                Multiply both sides by x

x tan(29) = 26                 Divide by tan(29)

x = 26/tan(29)                Find tan(29)

x = 26/0.5543                Divide

x= 46.9

Answer:

d. (4) + (-5)

Step-by-step explanation:

We know that 4 is the positive value and 5 is the negative value, therefore if to be able to rewrite in it we will almost make a sum of these values without changing the meaning of each one of the values, therefore:

(+4) + (-5)

Which means that the correct option is the last option, that is, d. (4) + (-5). Furthermore, the representation is correct because the resulting arrow is the one corresponding to -1.

ok                                                         its 11 sqrt 6                                    

because if sqrt 6 is x, and 5x +6x=11x

so its 11 sqrt 6              

Answer:

  -0.0062 and 27.5

Step-by-step explanation:

You can write the equation of the line using the 2-point form:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

The given values of the variables are ...

  (h, T) = (10000, -34.5) and (15000, -65.5)

Putting these into the formula, we have ...

  T = (-65.5 -(-34.5))/(15000 -10000)(h -10000) +(-34.5)

  T = -31/5000(h -10000) -34.5

  T = -0.0062h +62 -34.5

  T = -0.0062h +27.5

The appropriate choice is ...

  -0.0062 and 27.5

Answer:

If the question is saying that length is 7x, then the answer (width) is x-2

Answer:

  identity element property

Step-by-step explanation:

June's value did not change, so the value she added was the additive identity element: 0.

She made use of the identity element property of addition, which says that adding the identity element does not change the value.

Answer:

43cm

Step-by-step explanation:

Given

Length of Log = 291cm

First Piece = 67cm

Second Piece = 181cm

Required

Determine the length of the third piece

Given that the log was cut into three;

this implies that;

Length of Log = First Piece + Second Piece + Third Piece

Substitute values for first piece, second piece and length of log;

[tex]291 = 67 + 181 + Third\ Piece[/tex]

[tex]291 = 248 + Third\ Piece[/tex]

Subtract both sides by 248

[tex]291 - 248 = 248 - 248 + Third\ Piece[/tex]

[tex]43 = Third\ Piece[/tex]

[tex]Third\ Piece = 43[/tex]

Hence, the length of the third piece is 43cm

Answer:

[tex](x-7)^2+(y-3)^2=7^2[/tex]

Step-by-step explanation:

[tex](x-h)^{2}+(y-k)^{2}=r^{2}\\[/tex]

Thus,

[tex](x-7)^2+(y-3)^2=7^2[/tex]

Answer:

4 batches

Step-by-step explanation:

1/3=2/6, 2/3=4/6

Answer:

  16 hours

Step-by-step explanation:

In the time it took Ruth to plant 5 bulbs, Terry planted 3 bulbs. So, Terry did 3/8 of the work of planting 8 bulbs in that time.

We expect that Terry alone would take 8/3 of the time that it took when working together with Ruth.

  (8/3)×(6 hours) = 16 hours . . . . . . for Terry to do the job alone

Answer:

33m 40cm.

Step-by-step explanation:

One side of the shed measures 8 meters and 35 centimetres, which is 800 + 35 = 835 centimetres.

Since the shed is a square, all side lengths are 835 centimetres long. So, the perimeter is 835 * 4 = 3,340 centimetres. That means that the perimeter is 33 meters and 40 centimetres.

Hope this helps!

Answer:

a. 15/23

b. 13/27

c. 400g

Step-by-step explanation:

a. When the denominators are the same, you can just sum the numerators.

Which becomes, 13+2=15--> 15/23

b. Same, when the denominator is the same, you can just minus the numerators. Which becomes, 25-12=13--> 13/27

c. 1kg=1000g. 1000/5=200✖️2=400

Answer:

3x^2 -4

Step-by-step explanation:

f(x) = 2x^2 +3

g(x) = x^2 -7

(f+g) (x) =  2x^2 +3 +  x^2 -7

 Combine like terms

            = 3x^2 -4

Answer:

[tex]\boxed{3x^2-4}[/tex]

Step-by-step explanation:

[tex](f+g)(x)[/tex]

Rewrite.

[tex]f(x)+g(x)[/tex]

[tex](2x^2 +3)+(x^2-7)[/tex]

Combine like terms and simplify.

[tex](2x^2 +x^2 )+(3-7)[/tex]

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

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

Answer:

140°

Step-by-step explanation:

Every triangles angles when combined equals 180°

In an isosceles triangle there are 2 acute angles and one obtuse angles.

It was given that the base angle/acute angle is 20°

This brings us to our equation. 20° + 20° + x = 180°

20 + 20 = 40

40 + x = 180

Now we solve algebraically:

180-40= 140

Therefore the answer is x = 140°

I hope this helps!

Answer:

Step-by-step explanation:

Given the coordinates P(-2, -3). Q(2, - 6). R(6. - 3). S(2, 1), to determine the type of shape the quadrilateral is, we need to find the measure of the sides. To get the measure of each sides, we will take the distance between the adjacent coordinates using the formula to formula for calculating the distance between two points as shown;

D = √(x₂-x₁)²-(y₂-y₁)²

For the side PQ with the coordinate P(-2, -3). Q(2, - 6)

PQ = √(2-(-2))²-(-6-(-3))²

PQ = √(2+2)²-(-6+3)²

PQ = √4²-(-3)²

PQ = √16-9

PQ = √7

For the side QR with the coordinate Q(2, - 6) and R(6, -3)

QR = √(6-2))²-(-3-(-6))²

QR = √(4)²-(3)²

QR = √16-9

QR = √7

For the side RS with the coordinate R(6. - 3) and S(2, 1)

RS = √(2-6)²-(1-(-3))²

RS = √(-4)²-(1+3)²

RS = √16-(4)²

RS = √16-16

RS = 0

For the side PS with the coordinate P(-2, -3) and S(2, 1)

PS = √(2-(-2))²-(1-(-3))²

PS = √(4)²-(1+3)²

PS = √16-(4)²

PS = √16-16

PS = 0

For the quadrilateral to be a rectangle, then two of its sides must be equal and parallel to each other. A rectangle is a plane shape that has two of its adjacent sides equal and parallel to each other. Since two of he sides are equal i.e RS = PS and PQ = QR then the quadrilateral PQRS is a rectangle. Both rhombus and square has all of its sides equal thereby making them wrong.

Answer:

9 terms

Step-by-step explanation:

Given:  

1, 8, 28, 56, ..., 1

Required

Determine the number of sequence

To determine the number of sequence, we need to understand how the sequence are generated

The sequence are generated using

[tex]\left[\begin{array}{c}n&&r\end{array}\right] = \frac{n!}{(n-r)!r!}[/tex]

Where n = 8 and r = 0,1....8

When r = 0

[tex]\left[\begin{array}{c}8&&0\end{array}\right] = \frac{8!}{(8-0)!0!} = \frac{8!}{8!0!} = 1[/tex]

When r = 1

[tex]\left[\begin{array}{c}8&&1\end{array}\right] = \frac{8!}{(8-1)!1!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8[/tex]

When r = 2

[tex]\left[\begin{array}{c}8&&2\end{array}\right] = \frac{8!}{(8-2)!2!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} =2 8[/tex]

When r = 3

[tex]\left[\begin{array}{c}8&&3\end{array}\right] = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56[/tex]

When r = 4

[tex]\left[\begin{array}{c}8&&4\end{array}\right] = \frac{8!}{(8-4)!4!} = \frac{8!}{4!3!} = \frac{8 * 7 * 6 * 5 * 4!}{4! *4*3* 2 *1} = \frac{8 * 7 * 6*5}{4*3 *2 *1} = 70[/tex]

When r = 5

[tex]\left[\begin{array}{c}8&&5\end{array}\right] = \frac{8!}{(8-5)!5!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56[/tex]

When r = 6

[tex]\left[\begin{array}{c}8&&6\end{array}\right] = \frac{8!}{(8-6)!6!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} = 28[/tex]

When r = 7

[tex]\left[\begin{array}{c}8&&7\end{array}\right] = \frac{8!}{(8-7)!7!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8[/tex]

When r = 8

[tex]\left[\begin{array}{c}8&&8\end{array}\right] = \frac{8!}{(8-8)!8!} = \frac{8!}{8!0!} = 1[/tex]

The full sequence is: 1,8,28,56,70,56,28,8,1

And the number of terms is 9