Ninety members of a gym were asked whether or not they use a treadmill when they exercise and whether or not they lift weights when they exercise.

The results of the poll are as follows:
14 members do not use a treadmill or lift weights
31 members use a treadmill but do not lift weights
28 members lift weights but do not use a treadmill
17 members use a treadmill and lift weights
Which two-way table represents the information found in the poll?

Step-by-step explanation:

13^2 + x^2 = 17^2

169 + x^2 = 289

289 - 169 = 120

x^2 = 120

[tex] \sqrt{120} = 10.9544511501[/tex]

x = 11.0

A quadratic equation is in the form of ax²+bx+c. It took 3seconds for the golf ball to reach the green.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

A.) The time that the ball takes to reach the green can be found by equation the equation against zero. As the ball will have 0 height when it will be on the green,

t²+4t-21=0

t²+7t-3t-21=0

t(t+7)-3(t+7)=0

(t+7)(t-3)=0

t = -7, 3

Hence, it took 3seconds for the golf ball to reach the green.

B.) Since the time can not be negative the second value is wrong.

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Answer:

30 degrees

Explanation:

Let the ratio's be in x, 2x, 3x

Total Interior Angle of a triangle sum ups to 180°

The smallest angle which is x is 30°

The wheat production of both farms will approach a stable amount as the years pass.

An exponential function is one that is steadily increasing or decreasing. We can see that in this case there is a positive sign indicating an increase.

Thus, from the graph, we can see that, the wheat production of both farms will approach a stable amount as the years pass.

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Answer:

4 ounces

Step-by-step explanation:

Answer:

1 stick butter is equivalent to __4___ ounces.

Step-by-step explanation:

1 stick of butter is equal to 4 ounces

Answer:

$122.88

Step-by-step explanation:

the phone decreases by 20% each year , that is

(100 - 20)% = 80% = [tex]\frac{80}{100}[/tex] = 0.8

the phone reduces by a factor of 0.8 each year , then after 4 years

value = $300 × [tex](0.8)^{4}[/tex] = $122.88

Answer:

2 - 9 - 36

= - 43

Step-by-step explanation:

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Answer:

11 students are present and 9 are absent.

The expression that is equivalent to √10 / (4√8) is given as √5 / 8

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

√10 / (4√8)

Simplifying:

= √10 / (4√(4 * 2))

= √10 / (8√2)

= √5 / 8

The expression that is equivalent to √10 / (4√8) is given as √5 / 8

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The number of players in the team would be 15 which can bring to the tournament.

A soccer squad collected $1511 to attend a competition. They spent $933.50 on a bus rental and $38.50 for each player on food.

A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

Let the number of players would be x

As per the given information, the required solution would be as:

Total budget = (per player meal)(x players) + bus rent

1511 = 38.50x + 933.50

Rearrange the terms and solve for x

1511 - 933.50 = 38.50x

577.50 = 38.50 x

Divide both sides by 38.50 into above equation,

x = 15

Therefore, the number of players in the team would be 15 which can bring to the tournament.

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Answer:

The roots are 0.5 and 4.

Step-by-step explanation:

-2x^2+9x=4

Rearrange:

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

x = [-b +/- √(b)^2 - 4ac)] / 2a

Using this quadratic formula the solution is:

x = [-9 +/- √(9)^2 - 4*(-2)*(-4)] / (2*-2)

   = (-9 +/- √49) / -4

   = 9/4 +/- (-7/4)

   = 9/4 - 7/4 = 0.5

and 9/4 + 7/4 = 4

Answer:

36

Step-by-step explanation:

[tex]\angle AOC[/tex] is made up of s + r, and since r is [tex]\frac{3}{5}[/tex] of [tex]\angle AOC[/tex] we know r must be the remaining [tex]\frac{2}{5}[/tex] of [tex]\angle AOC[/tex].

We can solve for [tex]\angle AOC[/tex] by using this equation:

[tex]\frac{2}{5}\angle AOC = 24\\(\frac{2}{5}\angle AOC)\frac{5}{2} = (24)\frac{5}{2}\\ \boxed{\angle AOC = 60}[/tex]

1. 2 fifths of  [tex]\angle AOC[/tex] is 24

2. multiply both sides by [tex]\frac{5}{2}[/tex] to isolate [tex]\angle AOC[/tex]

3. [tex]\angle AOC[/tex] is 60°

We can now solve for r

[tex]r = \frac{3}{5}\angle AOC\\r = \frac{3}{5}(60)\\\boxed{r = 36}[/tex]

1. the equation the problem gave us

2. substitute [tex]\angle AOC[/tex] for 60 (we solved for it before)

3. [tex]r[/tex] is 36°

Answer:

f(x) + g(x) = 3x - 2 + 2x + 1

(f + g)(x) = 5x - 1

Answer:

7/23

Step-by-step explanation:

Each answer is 1.5/23 less than the previous

17/46  - 1.5/23 =   17/46 - 3/46 = 14/46 = 7/23

A fraction is a way to describe a part of a whole. The number of hours that Mr Mason painted each day is 1.625  hours.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The total number of hours that Mr Mason took to paint the fence is 6 2/4 hours, while the number of days taken by him is 4 hours. Therefore, the number of hours for which Mr Mason painted each day can be written as,

= (6 ²/₄)/4

= (26/4)/4

= 26/16

= 1.625 hours a day

Hence, the number of hours that Mr Mason painted each day is 1.625  hours.

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Answer:

[tex]\sqrt{\frac{x}{2} }[/tex]

Key:

• [tex]\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{x}}{\sqrt{2}}\\[/tex]

[tex]\frac{\sqrt{x}}{\sqrt{2}}=\sqrt{\frac{x}{2}}\\[/tex]

[tex]=\sqrt{\frac{x}{2}}[/tex]

Answer:

see the attachment photo!

Answer:

A = l x b

Step-by-step explanation:

Area = length x breath

So find the area and length and work it out by dividing area by length.

Answer: [tex]18^{\circ}[/tex]

Step-by-step explanation:

In triangle RUV, angle RUV is a right angle (and thus measures 90 degrees), and angle RVU measures 72 degrees.

Since angles in a triangle add to 180 degrees, angle VRU measures

Answer:

S=6a^2

S=6×2^2

S=6×4=24

The right answer is C

Answer:

24 units²

Explanation:

The surface area of cube is 6(side)²

Here given:

a = 2

The surface area:

= 6(2)^2

= 6(4)

= 24

Answer:

  2,592,100 m³

Step-by-step explanation:

The volume of the pyramid can be found by using the given dimensions in the formula for the volume of a square pyramid.

__

  V = 1/3s²h

where s is the side length of the square base, and h is the height.

Using the given dimensions, s = 230 m, h = 147 m, we find the volume to be ...

  V = 1/3(230 m)²(147 m) = 2,592,100 m³

The volume of the pyramid is 2,592,100 cubic meters.

First of all we will understand the question!!

The question is saying that you are given a function and you have to find the value of x which will give the maximum profit... Lets solve it by finding the extrema using the vertex

[tex] \rm \: p(x) = - 5 {x}^{2} + 30x + 8[/tex]

[tex] \rm \: p(x) = { - 5x}^{2} + 30x + 8 \\ \rm \: a = - 5 \: and \: b \: = 30[/tex]

[tex] \rm \: x = \frac{30}{ 2 \times (- 5)} [/tex]

[tex] \rm \: x = 3[/tex]

Answer:

[tex]\textsf{Length}=0.8x^2-0.7x+0.7\quad \sf units[/tex]

Step-by-step explanation:

Area of a rectangle = width × length

Therefore, to find the length of the rectangle, we need to divide the area by the width.

Using long division:

[tex]\large\begin{array}{r}0.8x^2-0.7x+0.7\phantom{)} \\x+0.5{\overline{\smash{\big)}\,0.8x^3-0.3x^2+0.35x+0.35\phantom{)}}}\\-~\phantom{(}\underline{(0.8x^3+0.4x^2)\phantom{-b))))))))))))))}}\\0-0.7x^2+0.35x+0.35\phantom{)}\\ \underline{-~\phantom{()}(-0.7x^2-0.35x)\phantom{-b)))))}}\\ 0.7x+0.35\phantom{)}\\\underline{-~\phantom{()}(0.7x-0.35)}\\ 0\phantom{)}\end{array}[/tex]

Therefore, the length of the rectangle is:

[tex]0.8x^2-0.7x+0.7[/tex]

========================================================

Reason:

Ari hasn't considered the case of "red and yellow" which is almost identical to "yellow and red".

It helps to lay out a two by two table. Along the rows and columns, you'll have "red" and "yellow". See below.

Then inside the table are the list of all outcomes in the form (x,y) where x is the horizontal component along the columns, and y is the vertical component along the rows.

Example: if x = red and y = red, then we have the outcome (x,y) = (red, red)

As the table shows, we have 4 outcomes. Therefore the probability of getting two yellows is 1/4

Technically the (red, yellow) = (yellow, red) since ultimately order doesn't matter in this case. For some probability problems, order will matter. But again, order doesn't matter here and it means that we can treat these two situations the same. So I can see why Ari thinks there are only three outcomes.

--------------------------------

Here's another way to look at it:

The probability of landing on yellow is 1/2 assuming red and yellow are equally likely.

This means the probability of two yellow in a row is (1/2)*(1/2) = 1/4

Each is spin is independent of any other.

Answer: =-6d+10d^2

Step-by-step explanation:

Answer:

  D.  10 square units

Step-by-step explanation:

The area of a triangle is given by the formula ...

  A = 1/2bh

__

This triangle has a base of 4 units and a height of 5 units. (These dimensions can be counted from the graph, or found by subtracting coordinate values.) Its area is ...

  A = 1/2(4 units)(5 units) = 10 square units

_____

Additional comment

The first two coordinates lie on the line x=0. The length of that segment is the difference of the y-values: 4 -(-1) = 5.

The first and last coordinates lie on the line y=-1. The length of that segment is the difference of the x-values: 4 -0 = 4.

Answer:

x < -4

Step-by-step explanation:

-7x>28

7x<-28

x<-4

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The statement which is true is the airplane reaches its maximum height of 81 feet in 12 seconds.

Since the height of the plane is a function given by a parabola, we need to know the equation of a parabola in vertex form

The equation of a parabola with vertex (h,k) is given by y = a(x - h) + k

Since the height (in feet) of the airplane as a function of time (in seconds after the timer was started) is given by the equation h(t) = −(t − 12) + 81

So, the statement which is true is the airplane reaches its maximum height of 81 feet in 12 seconds.

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