A coin is tossed at the same time a die is rolled. Are the
events independent or dependent? Why?
A. The events are dependent. There is no way the outcome
of the coin toss can affect the rolling of the die and vice
versa.
B. The events are dependent. The number rolled on the die
can be affected by what is flipped on the coin.
C. The events are independent. There is no way the
outcome of the coin toss can affect the rolling of the die and
vice versa,
D. The events are independent. The number rolled on the die
can be affected by what is flipped on the coin.

Answer:

There are 20 football players

The center-radius form of the circle equation is in the format

(x – h)²+ (y – k)² = r²

with the center being at the point (h, k) and the radius being "r"

So, just plug in the (-5,3) and you get:

(x+5)²+(y-3)²=16

For this case we have that by definition of logarithmic properties that, the expression

[tex]log_ {b} (a) = c[/tex] is equivalent to:

[tex]b ^ c = a[/tex]

Then, we have the following expression:

[tex]log_ {7} () = - 3[/tex]

It can be equivalent to:

[tex]7 ^ {- 3} =[/tex]

Answer:

The correct option is option A

[tex]7 ^ {-3}[/tex]

Answer:

d o the formula Ltimes W divided by 2

Step-by-step explanation:

Answer:

Area of triangle = 44.104 cm²

Step-by-step explanation:

Formula:-

Area of triangle = bh/2

where b - Base  and h - Height

To find the height of triangle

Let h be the height of triangle then we can write,

Sin 63 = h/11

h = 11 * sin 63 = 11 * 0.891 = 9.801 cm

To find the area of triangle

Area = bh/2

 = (9 * 9.801)/2 = 44.104  cm²

Answer:

The answer is B.

Step-by-step explanation:

If you look at all four circles, you can clearly tell that B has the least amount of blue shaded in.

Answer:

Step-by-step explanation:

[tex]V_p=4\\\\\text{Calculate the volume of a cube:}\\\\V_{c}=\left(\dfrac{1}{3}\right)^3=\dfrac{1}{27}\\\\\text{Calculate how many times the volume of the prism is greater}\\\text{than the volume of the cube:}\\\\\dfrac{V_p}{V_c}=\dfrac{4}{\frac{1}{27}}=4\cdot27=108[/tex]

The most efficient way is the 1st option

because all you have to do is add -3y on both sides to isolate x

If you used any other variables, you would have to use division which are extra steps

Answer:

Hence, the correct option is A) The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.

Step-by-step explanation:

Consider the provided system of equation.

x - 3y = 1  and  7x + 2y = 7

Let first solve the second equation.

[tex]7x + 2y = 7[/tex]

Step 1:

Divide both the sides by 7.

[tex]x + \frac{2y}{7} = 1[/tex]

Step 2:

[tex]x = 1- \frac{2y}{7} [/tex]

It took 2 steps to isolate the the variable x.

Now again consider the system of equation.

But this time we will solve the first equation.

[tex]x - 3y = 1[/tex]

Step 1:

[tex]x = 1 + 3y[/tex]

it took only 1 step to isolate the variable as the variable x in the first equation has a coefficient of one.

Hence, the correct option is A) The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.

Step 2: -26.7 · -3

When you divide with a fraction, it's helpful to multiple by the reciprocal of the fraction .

This step instead multiplied by the negative reciprocal .

Therefore, the correct answer would be -80.1 instead of 80.1

The error was made in step 2.

.

Convert the tax rate from a percent to a decimal number by moving the decimal point 2 places to the left.

8.8% = 0.088

Now multiply the price of the item by the tax rate:

63 x 0.088 = 5.544

Now round that to the nearest cent = $5.54

Answer:

$5.54

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

11+11+6+6+5=39

ANSWER

44 inches

EXPLANATION

The perimeter is the distance around the figure.

The unknown vertical height of the shape is 11-6=5 in.

The unknown horizontal width of the shape is 11-6=5 in.

Adding all the distance gives the perimeter.

The perimeter is

[tex]11 + 6 + 5 + 5 + 6 + 11 = 44in.[/tex]

Therefore the perimeter of the shape is 44 inches.

Answer:

C

Step-by-step explanation:

There is a right triangle formed by the slant height, h and the radius

Use Pythagoras' theorem to solve for h

With radius = 8 ft ( half the diameter ) , slant height is hypotenuse

h² = 17² - 8² = 289 - 64 = 225

Take the square root of both sides

h = [tex]\sqrt{225}[/tex] = 15 → C

Answer:

The correct choice is A.

Step-by-step explanation:

The axis of symmetry of the function is given by

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

If the axis of symmetry is -1 then the relation between the 'a' and 'b' value for all the function that has an axis of symmetry to be -1, is

[tex]b=2a[/tex]

A. [tex]y=4x^2-8x+1[/tex]

We can see that

[tex]-8\ne 2(4)[/tex]

hence this function does not have an AOS of x=-1

The correct choice is A.

B. [tex]y=x^2+2x-6[/tex]

[tex]2\ne 2(1)[/tex], hence this function has an axis of symmetry of x=-1.

C. [tex]y=3x^2+6x[/tex]

[tex]6=2(3)[/tex]

This also has AOS x=-1

D. [tex]y=-x^2-2x+3[/tex]

[tex]-2=2(-1)[/tex]

AOS is x=-1

Answer:

X - 90 degrees

Y - 43 degrees

Step-by-step explanation: When you fold over the triangle to reflect you get 47 degrees as angle C. Then, because X is a perfect right angle it is 90 degrees. Then you add 47 and 90 and get 137, then subtract that from 180 because all the angles within a triangle should eqaul up to 180 degrees.

Answer:

Step-by-step explanation:

Step 1: Additive inverse

Step 2: Additive identity

Step 3: Addition property of equality

22 is D

Answer:

-4, -1, 3, 5, 6

Step-by-step explanation:

Answer:

-4, -1, 3, 5, 6

Step-by-step explanation:

The domain is always on the left side. That was the trick I learned to remember. When you plot the numbers you would have them lined as X,Y. X,Y is equal to Domain, Range. I hope this helps!

80 minutes past the hour

Answer:

4.7840 square yards

Step-by-step explanation:

1 square meters equals 1.19599 square yards.

This is the formula for area conversion from square meters to yards and vice versa.

We are required to determine how many square yards are in 4 square meters.

Using the above conversion we have;

1 square meters = 1.19599 square yards

4 square meters = ?

We simply cross multiply;

4*1.19599 square yards = 4.7840 square yards

ANSWER

The correct answer is C

EXPLANATION

The given inequality is:

[tex]2x - 8 \: < \: 7[/tex]

Group the constant terms on the right hand side to get;

[tex]2x \: < \: 7 + 8[/tex]

Simplify the right hand side

[tex]2x \: < \: 15[/tex]

Divide both sides by 2

[tex]x \: < \: \frac{15}{2} [/tex]

{x|x<15/2}

The correct answer is C

Answer:

[tex]\large\boxed{\left\{x\ |\ x<\dfrac{15}{2}\right\}}[/tex]

Step-by-step explanation:

[tex]2x-8<7\qquad\text{add 8 to both sides}\\\\2x-8+8<7+8\\\\2x<15\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}<\dfrac{15}{2}\\\\x<\dfrac{15}{2}[/tex]

Answer:

is the fourth one

Step-by-step explanation:

just replace x with the numbers given

and then work it out.

y=x-5

y=1-5=-4

y=2-5=-3

and so on

hope this helps

For this case we have a function of the form [tex]y = f (x)[/tex]where:

[tex]f (x) = x-5[/tex]

We must find the values of "y" when [tex]x = 1,2,3,4[/tex]

Then, keeping in mind that different signs are subtracted and the sign of the major is placed:

Answer:

Option D

The answers are:

[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]

To calculate the speed of the cars, we need to write two equations in order to create a relation between the two speeds and be able to calculate one in function of the other.

So, let be the first car speed "x" and the second car speed "y", writing the equations we have:

For the first car:

[tex]x_{FirstCar}=x_o+v*t[/tex]

For the second car:

We know that the speed of the second car travels 14 mph faster than the first car, so:

[tex]x_{SecondCar}=x_o+(v+14mph)*t[/tex]

Now, we already know that both cars met after 2 hours and 45 minutes, and the distance between A and B is 264 miles,  so, we can calculate the relative speed between both carsby the following way:

If the cars are moving towards each other the relative speed will be:

[tex]RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph[/tex]

So , since we know that they covered a combined distance equal to 264 miles in 2 hours + 45 minutes, we  have:

[tex]2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours[/tex]

Writing the equation:

[tex]264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph[/tex]

We have, the speed of the first car is equal to 41 mph.

Now, for the second car we have that:

[tex]SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph[/tex]

So,  the speed of the second car is equal to 55 mph.

Hence, the answers are:

[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]

Have a nice day!

Answer:

1 + 1.58i , 1 - 1.58i

Step-by-step explanation:

2x^2=4x-7

2x^2 - 4x + 7 = 0

x = [-(-4) +/- sqrt((-4)^2 - 4 * 2 * 7 )] / 2*2

= [ 4 +/- sqrt (16 - 56)] / 4

= [4 +/- sqrt (-40) ] / 4

= 1 +/- 6.32i / 4

= 1 + 1.58i  and 1 - 1.58i  (answer).

Answer:

[tex]\boxed{x = 1 \pm i\sqrt{\frac{5}{ 2}} }\\[/tex]

Step-by-step explanation:

2x² = 4x - 7

2x² - 4x + 7 =0

a = 2; b = -4; c = 7

[tex]y =\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]

[tex]=\frac{4\pm\sqrt{(-2)^2-4\times2\times7}}{2\times2}\\[/tex]

[tex]= 1 \pm\frac{\sqrt{16-56}}{4}\\[/tex]

[tex]= 1 \pm\frac{\sqrt{-40}}{4}\\[/tex]

[tex]= 1 \pm\frac{2i\sqrt{10}}{4}\\[/tex]

[tex]= 1 \pm\frac{i\sqrt{10}}{2}\\[/tex]

[tex]= 1 \pm i\sqrt{\frac{10}{4}}\\[/tex]

[tex]\boxed{= 1 \pm i\sqrt{\frac{5}{ 2}} }\\[/tex]

The graph of y = 2x² - 4x + 7 has a minimum at (1, 5). It never touches the x-axis, so both roots are imaginary.

[tex]\bf \stackrel{\textit{dot product}}{<a,b>\cdot <c,d>}\implies (a\cdot c)+(b\cdot d) \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} u=&2i+3j\\ v=&-6i-5j \end{cases}\implies \begin{cases} <2,3>\\ <-6,-5> \end{cases} \\\\\\ <2,3>\cdot <-6,-5>\implies (2\cdot -6)+(3\cdot -5)\implies -27[/tex]

Answer:

a. equivalent

b. not equivalent

c. equivalent

d. equivalent

Step-by-step explanation:

a. 3x +7x = (3+7)x = 10x . . . equivalent to 10x

__

b. 5x -10x = (5 -10)x = -5x . . . not equivalent to 5x

__

c. 4(1 +2x) -3x = 4·1 +4·2x -3x = 4 +(8 -3)x = 4 +5x = 5x +4 . . . equivalent to 5x +4

__

d. 5 -3(2 -4x) = 5 -3·2 -3(-4x) = 5 -6 +12x = -1 +12x . . . equivalent to -1 +12x

Answer:

Look to the attached graph

Step-by-step explanation:

* Lets revise how to graph the quadratic function

- Find the vertex of it

- Find the y-intercept

- Find the x-intercept

∵ f(x) = (x - 5)² + 1 ⇒ the completing square form

- The completing square form for any quadratic is

 ( x - h)² + k, where h and k are the coordinate of the vertex point

* Lets compare the two forms

∵ (x - h)² + k = (x - 5)² + 1

∴ h = 5 and k = 1

∴ The vertex of the parabola is (5 , 1)

- To find the x-intercept put f(x) = 0

∵ (x - 5)² + 1 = 0 ⇒ subtract 1 from both sides

∴ (x - 5)² = -1 ⇒ the square can not give -ve number

∴ The parabola does not intersect the x-axis

- To find the y-intercept put x = 0

∵ f(0) = (0 - 5)² + 1 = 25 + 1 = 26

∴ The parabola intersects the y-axis at point (0 , 26)

- The parabola is opened upward because the coefficient of x² is +ve

* Now lets graph it

- Look to the attached graph

The answer is -9

Answer:

The missing value is -9

Step-by-step explanation:

-9+6 is -3.

Answer:

Mitch bought 5 buckets of wings

Step-by-step explanation:

y=# of wings

X= # of pizza

X+Y=13

X = 13 - Y

11.75X + 19.95Y = 193.75

11.75(13 - Y) + 19.95Y = 193.75

152.75 - 11.75Y + 19.95Y = 193.75

152.75 + 8.2Y = 193.75

8.2Y = 41

Y = 5

Mitch bought 5 buckets of wings

Mitch bought 5 buckets of wings for his Super Bowl party, which was determined by solving a system of equations using the given information about the total number of items purchased and the total cost.

To determine how many buckets of wings Mitch bought for his Super Bowl party, let's define a system of equations based on the information given:

Let's say p represents the number of pizzas, and w represents the number of buckets of wings. We are told that Mitch bought a total of 13 items, which gives us the equation:
p + w = 13.

We are also told that he spent a total of $193.75, with pizzas costing $11.75 each and buckets of wings costing $19.95 each. This gives us the second equation:
11.75p + 19.95w = 193.75.

To solve the system of equations, we can use substitution or elimination. One way is to solve the first equation for p (p = 13 - w) and substitute that into the second equation, leading to:
11.75(13 - w) + 19.95w = 193.75.

Simplifying the equation will allow us to find the value for w. The simplified equation is:
152.75 + 8.2w = 193.75

Subtracting 152.75 from both sides gives us
8.2w = 41,
and dividing both sides by 8.2 yields
w = 5.

Therefore, Mitch bought 5 buckets of wings for the party.

The sum of the measures of the interior angles of a triangle is 180˚. Example 3: In NMQ. ∆.

For this case, we have given an ABC triangle with internal angles α,β,γ. By definition, the sum of the internal angles must be 180 degrees.

That is to say:

α+β+γ=180

This can be demonstrated according to the fifth postulate of Euclid. From there we have to draw a parallel to one of the sides, by the vertex opposite him, the interior angles of the left side add two right angles.

Answer:

180 degrees

Answer:

x = - 7, x = 5

Step-by-step explanation:

To find the zeros equate f(x) to zero, that is

x² + 2x - 35 = 0

To factorise the quadratic

Consider the factors of the constant term (- 35) which sum to give the coefficient of the x- term (+ 2)

The factors are + 7 and - 5, since

7 × - 5 = 35 and 7 - 5 = + 2, hence

(x + 7)(x - 5) = 0

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x - 5 = 0 ⇒ x = 5

ANSWER

[tex]x = - 7 \: or \: x = 5[/tex]

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 2x - 35[/tex]

To find the zeros, we equate the function to zero.

[tex] {x}^{2} + 2x - 35 = 0[/tex]

Split the middle term to obtain,

[tex]{x}^{2} + 7x - 5x- 35 = 0[/tex]

Factor by grouping:

[tex]{x}(x + 7) - 5(x + 7)= 0[/tex]

[tex](x + 7)(x - 5) = 0[/tex]

[tex](x + 7) = 0 \: or \: (x - 5) = 0[/tex]

.

[tex]x = - 7 \: or \: x = 5[/tex]

The approximate probability that both you and your friend will choose chocolate ice cream from seven different flavors is 1/49, or approximately 0.020408.

We are looking to find the probability that both you and your friend choose chocolate ice cream from a selection of 7 different flavors. Since the choice of ice cream is independent for each person, we can calculate the probability of both events occurring by multiplying the probability of each event occurring individually.

The probability that one person chooses chocolate ice cream is 1 out of 7, or approximately 0.142857. To find the probability that both you and your friend choose chocolate ice cream, we multiply the individual probabilities:

Probability of you choosing chocolate: 1/7

Probability of your friend choosing chocolate: 1/7

Combined probability: 1/7 x 1/7 = 1/49

Therefore, the approximate probability that both you and your friend choose chocolate ice cream is 1/49, or approximately 0.020408.