A class rolls a number cube 100 times and records the results. Use these results to predict about how many times the class will roll the number 4 in 1,000 trials. The class will roll the number 4 about times.

Answer:

The golf ball was in the air for 4 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

We have to find the amount of time it takes for the ball to hit the ground. We have that:

[tex]d(t) = -2t^2 + 7t + 4[/tex]

Which is a quadratic equation with [tex]a = -2, b = 7, c = 4[/tex].

How long is the golf ball in the air?

We have to find t for which [tex]d(t) = 0[/tex]

So

[tex]-2t^2 + 7t + 4 = 0[/tex]

[tex]\Delta = b^{2} - 4ac = (7)^2 - 4(-2)(4) = 81[/tex]

[tex]t_{1} = \frac{-7 + \sqrt{81}}{2*(-2)} = -0.5[/tex]

[tex]t_{2} = \frac{-7 - \sqrt{81}}{2*(-2)} = 4[/tex]

Time is a positive measure, so t = 4.

The golf ball was in the air for 4 seconds.

Answer:

y - 10 = -1/2(x + 4)

General Formulas and Concepts:

Algebra I

Coordinates (x, y)

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify variables

m = -1/2

Point (-4, 10) → x₁ = -4, y₁ = 10

Step 2: Find

Answer: [tex]y=-\frac{1}{2} x+8[/tex]

Step-by-step explanation:

An equation of a line can be in slope intercept form which is y=mx+b

m is the slope, b is the y intercept, x it the x coordinate, and y is the y coordinate. Since we know the slope is -1/2 and we know a x coordinate is -4 and a y coordinate is 10 we can sub them in and solve for the value of b.

[tex]y=mx+b\\10=(-\frac{1}{2})(-4)+b\\10=2+b\\10-2=2+b-2\\8=b[/tex]

The value of b is 8. We can now sub it in for our equation of the line. This time with x and y as variables.

y=-1/2x+8

Answer:

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

Answer:

24 + y = 41

y = 17

Step-by-step explanation:

24 + y = 41

y + 24 = 41

y + 24 - 24 = 41 - 24

y = 17

Answer:

101 =x

Step-by-step explanation:

The measure of the exterior angle is equal to the sum of the opposite interior angles

143 = 42+x

Subtract 42 from each side

143-42 = 42+x-42

101 =x

Answer:

x = 101 degrees

Step-by-step explanation:

The sum of the external angle and its adjacent is 180 degrees

143 + y = 180

y = 37 degrees

The sum of the inner angles of a triangle is 180 degrees

37 + 42 + x = 180

79 + x = 180

x = 101 degrees

Answer:

65x + 115 = 180

65x = 65

_______

65

x = 1

Answer:

the answer is b because -(-6) becomes 6 and 6 is greater than 3

Answer: B.

Step-by-step explanation: A. 45 is not less than or equal to 18. I got 45 because 2 negatives make a positive and I got 18 because it was in absolute value bars making it positive. B. 6 is greater than -3. I got 6 because it is in an absolute value bar. C. 32 is not less 28. I used the same steps I used on the others. D. 9 is not greater than or equal to 10.

C = 25 deg

a ≈ 10.72 ft

b ≈ 11.83 ft

Answer:

C = 25

a = 10.72

b = 11.83

Step-by-step explanation:

C:

Solve; 180 - (90 + 65)

a:

Tan(65) = a/5

Tan(65) * 5 = a

10.72 = a

b:

Cos(65) = 5/b

Cos(65) * b = 5

b = 5 / Cos(65)

b = 11.83

Hope this helps!

Answer:

The probability is [tex]\frac{24}{70}[/tex].

Step-by-step explanation:

topping options available: four vegetables, two meats, and two cheeses

Number of topping on one pizza = 4

Getting two vegetables = (4 C 2)

Getting one meat = (2 C 1)

Getting one cheese = (2 C 1)

Choosing 4 toppings out of 8 = (8 C 4)

probability that the pizza is ordered with exactly two vegetables, one meat, and one cheese

[tex]\frac{(4C2)\times (2C1)\times (2C1)}{(8C4)}\\\\\frac{6\times 2\times 2}{70}\\\\\frac{24}{70}[/tex]

9514 1404 393

Answer:

  x = 8/7

Step-by-step explanation:

The only real zero of this linear function is the value of x that makes y=0:

  0 = -7x +8

  7x = 8 . . . . . . add 7x

  x = 8/7 . . . . . .divide by 7

Answer:

how old are you gghhjjzetstu9u

Answer:

4 ft

Step-by-step explanation:

let's find radius first

radius=diameter/2

=6/2

=3 ft

radii=3 ft

Now by using pythagoras theorem

a^2 + b^2 = c^2

3^2 + 3^2 =AB^2

9+9=AB^2

18=AB^2

[tex]\sqrt{18}[/tex] AB

4.24 =AB

4 ft =AB (after converting to nearest foot)

Answer:

22°

63°

m<H=22°

m<G=63°

Problem 1

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

Work Shown:

For any triangle, the three angles always add to 180

For any isosceles triangle, the base angles are congruent. The base angles are opposite the congruent sides. We see that angle O = angle H.

O+H+T = 180

H+H+T = 180

2H+T = 180

2H+22 = 180

2H = 180 - 22

2H = 158

H = 158/2

H = 79

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

Problem 2

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

Work Shown:

We'll use the same ideas as problem 1.

In this case, angle O = angle D = 63 since they are the base angles opposite the congruent sides.

D+G+O = 180

63+G+63 = 180

G+126 = 180

G = 180-126

G = 54

Answer:

Hi, there the answer is

These are the equations with exactly one solution

-5x + 12 = –12x – 12

-5x + 12 = 5x + 12

-5x + 12 = 5x – 5

Hope This Helps :)

Step-by-step explanation:

First degree equations

A first degree equation has the form

ax + b = 0

There are some special cases where the equation can have one, infinitely many or no solution

If , the equation has exactly one solution

If a=0 and b=0 the equation has infinitely many solutions, because it doesn't matter the value of x, it will always be true that 0=0

If a=0 and  the equation has no solution, because it will be equivalent to b=0 and we are saying it's not true. No matter what x is, it's a false statement.

We have been given some equations, we only need to put them in standard form

-5x + 12 = –12x – 12

Rearranging

7x + 24 = 0

It has exactly one solution because a is not zero

.......................

-5x + 12 = 5x + 12

Rearranging

-10x + 0 = 0

It has exactly one solution because a is not zero

.......................

-5x + 12 = 5x – 5

Rearranging

-10x + 17 = 0

It has exactly one solution because a is not zero

.......................

-5x + 12 = -5x – 12

Rearranging

0x + 24 = 0

It has no solution, no matter what the value of x is, it's impossible that 24=0

Answer: These are the equations with exactly one solution

-5x + 12 = –12x – 12

-5x + 12 = 5x + 12

-5x + 12 = 5x – 5

Answer:

A. 1/2 cups

Step-by-step explanation:

13/15 is close to 1

1/5 is a small amount

9/20 is just over 1/2

5/11 is just under 1/2

7/15 is just under 1/2

Estimate: 1 + 1/2 + 1/2 + 1/2 + a little = 2 1/2

He needs 3 cups, so he needs another 1/2 cup.

Answer: A. 1/2 cups

Answer:

it a 1/2

Step-by-step explanation:

Hope this help!!!

Have a nice day!!!

Answer:

Step-by-step explanation:

Given that:

[tex]y^2 (y^2-4) = x^2(x^2 -5)[/tex]

at point (0, -2)

[tex]\implies y^4 -4y^2 = x^4 -5x^2[/tex]

Taking the differential from the equation above with respect to x;

[tex]4y^3 \dfrac{dy}{dx}-8y \dfrac{dy}{dx}= 4x^3 -10x[/tex]

Collect like terms

[tex](4y^3 -8y)\dfrac{dy}{dx}= 4x^3 -10x[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]

Hence, the slope of the tangent line m can be said to be:

[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]

At point (0,-2)

[tex]\dfrac{dy}{dx}= \dfrac{4(0)^3 -10(0)}{4(-2)^3-8-(2)}[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{0 -0}{4(-8)+16}[/tex]

[tex]\dfrac{dy}{dx}= 0[/tex]

m = 0

So, we now have the equation of the tangent line with slope m = 0 moving through the point (x, y) = (0, -2) to be:

(y - y₁ = m(x - x₁))

y + 2 = 0(x - 0)

y + 2 = 0

y = -2

Answer:

27.3

Step-by-step explanation:

27.3

Answer:

Plays a musical instrument

Top left

Plays a sport: 0.46

Plays a musical instrument

Top right

Does not Play a sport: 0.54

Does not play a musical instrument

Bottom Left

Plays a sport: 0.73

Does not play a musical instrument

Bottom right

Does not Play a sport: 0.27

Step-by-step explanation:

I hope this helps you! :D

Answer:

First find the SA of the triangular figure

4 x 3 = 12 cm^2 (the triangles on the sides)

2 x 3 = 6 cm^2 (the back square)

2 x 5 = 10 cm^2 (the slanted square)

*I'm not sure if this question includes the bottom of the triangle but here it is anyways

4 x 2 = 8 cm^2

Including the bottom the SA of the triangular figure is:

12 + 6 + 10 + 8 = 36 cm^2

Find the SA of the rectangular shape

4 x 2 = 8 cm^2 (the bottom square)

2 x 6 = 12 x 2 = 24 cm^2 (the sides)

4 x 6 = 24 x 2 = 48 cm^2 (the front and back)

Add them up

8 + 24 + 48 = 80 cm^2

If you wanted to find the SA of the whole figure it would be:

12 + 6 + 10 + 8 + 24 + 48 = 108 cm^2

Hope this helps!

Answer:

maybe if u translate it in English

Step-by-step explanation:

it wouldv been helpful if u mind?

Answer:

87

Step-by-step explanation:

Answer:

11 is the answer.....

Step-by-step explanation:

6x-15+39+90 = 180

9514 1404 393

Answer:

  x = 63

Step-by-step explanation:

The base angles of each isosceles triangle are equal, so we can write the sum of the four angles in the quadrilateral as ...

  72° +(72° +x°) +x° +90° = 360° . . . . . clockwise from upper left

  2x = 126 . . . . . . . . . divide by °, subtract 234

  x = 63 . . . . . . . . . . . divide by 2

Answer:

LA = 2πrh

Step-by-step explanation:

The lateral surface area is the area of all the sides of a 3-dimensional object excluding its base and top.

The lateral area of a cylinder is the area of its surfaces excluding the area of its base and top

LA = 2πrh

Answer:

after 10 months

Step-by-step explanation:

Let x be the number of months and y be the amount they still owe.

Sin Ian borrows $1000 from his parents, then the y-intercept b= 1000 since he owes $1000 when x = 0. He pays them back $60 each month The slope is then m = -60 . Substituting in b = 1000 and m = -60 into the slope-intercept form of a line then gives y= mx + b=-60x +1000.

Sin Ken borrows $600 from his parents, then the y-intercept b = 600 since he owes $600 When x= 0. He pays them back $20 per month so the amount he owes decreases $20 each month. The slope is then m = -20 . Substituting in

b= 600 and m = -20 into the slope-intercept form then gives y = mx +b = -20x + 600.

They will owe the same amount when they have the same y-coordinate. Therefore -60x+ 1000= y= -20x+600. Solve this equation for x:

-60x+ 1000 = -20x+ 600

1000 = 40x+ 600

400 = 40x

10=x

They will then owe the same amount after 10 months.

Answer:

[tex]14 + x \leqslant 26 \\ x \leqslant 26 - 14 \\ { \tt{x \leqslant 12}}[/tex]

Answer:

In 25 years I will have $ 27,137.65. Therefore, I will earn $17,137.65 interest.

Step-by-step explanation:

Given that I deposit $ 10,000 in an account earning 4% interest compounded monthly, to determine how much will you have in the account in 25 years and how much interest will I earn, the following calculation must be performed:

10,000 x (1 + 0.04 / 12) ^ 25x12 = X

10,000 x (1 + 0.00333) ^ 300 = X

10,000 x 2.7137 = X

27,137.65 = X

Therefore, in 25 years I will have $ 27,137.65. Therefore, I will earn $17,137.65 interest.

Answer:  -2

This is because (-2)^5 = -32. Applying the fifth root to both sides lets us say [tex]-2 = \sqrt[5]{-32}[/tex]

There are four other roots but they are complex. Effectively, we are solving the equation [tex]x^5 + 32 = 0[/tex]

Answer:

Profit % on skates = 8.7 %

Step-by-step explanation:

Step 1 : Find cost price of skates

Cost price of helmet = £45

Let cost price of skate be = x

Selling price = £224

Cost price = (x + 45)

Total profit % = 40%

[tex]Profit \% = \frac{Selling \ price - cost \ price }{Cost \ price} \times 100[/tex]

[tex]\frac{40}{100} = \frac{224 - (x + 45)}{(x + 45)}\\\\40(x+ 45) = 100(224 - (x +45))\\\\40(x + 45) = 22400 - 100(x + 45)\\\\40(x +45) + 100(x+ 45) = 22400\\\\140(x + 25) = 22400\\\\x + 45 = \frac{22400}{140}\\\\x = 160 - 45 = \£ \ 115[/tex]

Total cost price = 45 + 115 = £160

Step 2 : Selling price of Helmet

Cost price of Helmet = £45

Let selling price of helmet be = y

Profit % of helmet = 120 %

[tex]Profit \% = \frac{selling \ price - cost \ price}{cost \ price}[/tex]

[tex]\frac{120}{100} = \frac{y -45}{45}\\\\\frac{120 \times 45}{100} = y -45\\\\54 = y - 45\\\\99 = y[/tex]

Step 3 : Selling price of skates

Total selling = selling price of helmet + selling price of skates

224 = 99 + selling price of skates

224 - 99 = selling price of skates

125 = selling price of skates

Step 4 : Profit percentage on skates

Cost price of skate = £ 115

Selling price of skate = £ 125

[tex]Profit \% \ on \ skates = \frac{selling\ price- cost \ price }{cost \ price} \times 100[/tex]

                           [tex]= \frac{125-115}{115} \times 100\\\\=\frac{10}{115} \times 100\\\\= 8.7 \%[/tex]

Answer:

what is the question?

Step-by-step explanation:

answer the question