A spinner numbered 1 to 8 is spun and a six-sided die is rolled. What is the probability of getting a multiple of 4 on the spinner and a multiple of 4 on the die?​

Answer:

\((5+3\sqrt{2} )^{2} =43+30\sqrt{2}\)  

≈85.43

Step-by-step explanation:

apply the binomial theorem to the square

\(=(5)^{2} +2(5)(3\sqrt{2} )+(3\sqrt{2} )^{2}\)

\(=25+30\sqrt{2} +18\\\)

\(=43+30\sqrt{2}\)

≈85.43

Hope this helps

Hello!

Here, we apply the algebraic identity :

\(\boxed {(a + b)^{2} = a^{2} + 2ab + b^{2}}\)

Let's solve!

⇒ (5 + 3√2)²

⇒ (5)² + 2(5)(3√2) + (3√2)²

⇒ 25 + 30√2 + 18

⇒ \(\boxed {43 + 30\sqrt{2}}\)

∴ The final answer will be 43 + 30√2.

2/3 of 35 is 23. Kofi is 23.

5.1489 is less than 5.2019

Therefore, the symbol between the two decimals would be less than symbol.

That is,

The symbol that would replace ? is <

The Expression x^2 - 6x + 9 when x = 2 + i   is -2i

To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:

(2 + i)^2 - 6(2 + i) + 9

Simplifying the first term, we get:

(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2

Since i^2 = -1, we can substitute that in and simplify further:

(2 + i)^2 = 4 + 4i - 1 = 3 + 4i

Now we substitute this into the original expression:

(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9

Simplifying further, we get:

= 3 + 4i - 12 - 6i + 9

= 0 - 2i

= -2i

Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.

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Answer: 1/5

Step-by-step explanation:

The number of pennies weighing as much s earth is  193 × 10²⁴

Index forms are described as described as those forms that are used to represent numbers that are too large or small in more proper ways.

Other names for index forms are scientific notation and standard forms.

Ratio is described as the comparison of numbers or variables on the basis of their size.

It shows how many times one number contains another.

From the information given, we have that;

The earth weighs = 5. 972 × 10 ²⁴ kilograms

The penny weighs = 3.1 × 10 ⁻³ kilograms

Divide the values

= 5. 972 × 10 ²⁴/3.1 × 10 ⁻³

= 1.93 × 10 ²⁶

= 193 × 10²⁴

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In 1 day, Candice and Porter will have collected 23 signatures each, using a system of equations.

Equations are mathematical statements that claim that two expressions are equal or equivalent.

Equality is depicted using the equation sign (=).

                                                                                   Candice   Porter

The number of signatures collected for nomination     21          18

Average collection of signatures per day                       2           5

Let the total signatures collected by Candice on day x = 21 + 2x

Let the total signatures collected by Porter on day x = 18 + 5x

The day the two candidates will have collected the same signatures is set as equality:

21 + 2x = 18 + 5x

21 - 18 = 5x - 2x

3 = 3x

x = 1

Check:

Total signatures collected by on day 1:

Candice = 21 + 2x = 21 + 2(1) = 23

Porter = 18 + 5x = 18 + 5(1) = 23

Thus, for Candice and Porter to have collected the same number of signatures, it will take them 1 day and each will have 23 signatures, using a system of equations.

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If each of X, Y, and N are positive integers, then the value of X+Y+N is 212.1

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

WE are given that A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses.

X = 7

Y = 10

If there are N packages (N ≥ 2) and the total value of them is $2021

X + Y = One packages

N packages = N(X + Y ) = 10 N

if each of X, Y, and N are positive integers, then;

10 N = 2021

N = 2021/10

N = 202.1

Therefore, X+Y+N = 10 + 202.1 = 212.1

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9514 1404 393

Answer:

Step-by-step explanation:

In your expression, you have ...

  a = 1

  b = 11

  c = 24

Then ac = (1)(24) = 24, and b = 11. The chart looks like the attached.

The numbers on the side have a sum equal to the bottom number (11) and a produce equal to the top number (24). These are the constants in the binomial factors, so the factored form is ...

  (x +8)(x +3) . . . . equivalent factored form

The value of ac is

✔ 24

.

The value of b is

✔ 11

.

The equivalent factored form of the polynomial is

✔ (x + 3)(x + 8)

.

Answer :

\(\boxed{\textsf {The red area is the required answer . }}\)

Step-by-step explanation:

A linear inequality in two variables is given to us and we need to plot it's graph .So the the given inequality is ,

\(\sf\implies y \geq- \dfrac{1}{5}x +5 \)

So firstly let's simplify out the inequality for easy plotting of the graph .

\(\sf\implies y \geq- \dfrac{1}{5}x +5 \\\\\sf\implies y \geq \dfrac{-x+5(-5)}{5}\\\\\sf\implies y \geq \dfrac{-x-25}{5}\\\\\sf\implies y \geq -(1)\dfrac{x+25}{5}\)

Now let's put some values of x to get values of y .

• Firstly put x = 0 then we get , y is greater than or equal to 0+5/5 (-1) = 5/5(-1) = -1 . Hence we get y ≥ (-1) .

• Secondly put x = 1 , then we get , y is greater than or equal to 1+5/5(-1)=6/5(-1) = -6/5 . Hence we get y ≥ -6/5 .

• Thirdly put x = -1 , then we get y is greater than or equal to -1+5/5(-1) = -4/5 . Hence we get y ≥ -4/5

• Fourthly put x = (-5) , then we get y is greater than or equal to -5+5/5(-1) = 0 .Hence we get y ≥ 0 .

With reference to these let's plot a graph . For the graph kindly refer to the attachment :) .

Here in the graph the red area shows the possible values of x and y .

Answer:

For cobalt-60, which has a half-life of 5.27 years, 50% remains after 5.27 years (one half-life), 25% remains after 10.54 years (two half-lives), 12.5% remains after 15.81 years (three half-lives), and so on.

Step-by-step explanation:

You can figue out the rest.

The solutions of the system of inequalities are:

(0, 3)

(6, 2)

Here we have the graph of a system of inequalities, the solutions are all the points on the area where the two shaded regions intercept (it would be on the purple area).

And we can see that one line is solid, the points on that line are solutions, the other line is dashed, the points on that line are not solutions.

Then the points that are solutions are:

(0, 3)

(6, 2)

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Answer:4$

Step-by-step explanation:

Answer:

The posters will be 1 foot away from each other

Step-by-step explanation:

The equation is right

The medians are about the same.

Option C is the correct answer.

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

Movie theater 1.

From the box plot given,

The median is 995.

Movie theater 2.

From the box plot given,

The median is 995.

Thus,

The median in both the box plot is the same.

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Answer:

x = 5

Step-by-step explanation:

assuming you mean the slope of the line id undefined and passes through (5, 0 )

A line with an undefined slope is a vertical line parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (5, 0 ) with x- coordinate 5 , then

x = 5 ← equation of line

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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If the ball rebounds 2/4 of its original height.

The ball rebound 1 ft on its 5th bounce.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

We are assuming that the ball rebounds 2/4 of its original height.

Now,

Original height = 32 ft

1st  bounce.

= 2/4 x 32

= 16 ft

2nd bound.

= 2/4 x 16

= 8 ft

3rd bound.

= 2/4 x 8

= 4 ft

4th bound.

= 2/4 x 4

= 2 ft

5th bound.

= 2/4 x 2

= 1 ft

Thus,

The ball rebound 1 ft on its 5th bounce.

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The average confidence interval, according to our 80% level of confidence, falls between 31.54 and 35.86 minutes for the total population.

You only have a 5% probability of making a mistake with a 95% confidence interval. You have a 10% probability of being mistaken when the confidence interval is 90%. The difference between a 95 percent and 99 percent confidence interval is the width of the interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

Confidence intervals include details about the range in which the true value is likely to fall, as well as the kind and magnitude of the effect that has been proved. Conclusions concerning the can be made as a result of this.

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Answer:

1000

Step-by-step explanation:

10³

= 1000

Answer:

10 * 10 * 10

Step-by-step explanation:

Cubing a number just means you are multiplying that number 3 times to itself. Since we have 10^3, we multiply 10 to itself three times.

Best of Luck!

The area of the composite figure is 23.98 m²

Composite figure are made of up of two dimensional figures which might include rectangle, triangle etc.

The above composite figure is made up of a sector of a circle and a rectangle. The area of the composite figure is the sum of the whole areas.

Therefore,

area of the composite figure = area of the sector + area of rectangle

Therefore,

area of the sector = ∅ / 360 × πr²

where

r = radius = 5.5 / 2 = 2.75

area of the sector = 30 / 360 × 3.14 × 2.75²

area of the sector = 712.3875 / 360

area of the sector = 1.97885416667

area of the sector = 1.98 m²

area of the rectangle = lw

where

l = length

w = width

area of the rectangle = 4 × 5.5

area of the rectangle = 22 m²

Therefore,

area of the composite figure = 1.98 + 22 = 23.98 m²

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The amount of cups of lemonade sold by Abbie is 6 x 8 = a.

Hence, option A is correct.

Use the concept of multiplication defined as:

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that,

Number of lemonade cups sold by Lust = 8

Number of lemonade cups sold by Abbie =  6 times of lust

Let 'a' represents the number of cups sold by Abbie,

Therefore,

6 x 8 = a

Hence,

The correct expression is 6 x 8 = a which is option A.

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The complete question is:

Luct sold 8 cups of lemonade Abbie sold 6 times as many cups of lemonade. Which equation helps us find how many cups Abbie sold if the number of cups sold by Abbie is 'a'.

A. 6x8 = a

B. 8xa = 6

C. 6xa = 8

Answer: x = -5

Step-by-step explanation:

g(x) = -3x + 1

g(x) = 16

This means that -3x + 1 = 16

Solving this equation, x = -5

Answer:    It's not entirely clear what is being asked for in the given question, as it is not clear what the numbers represent or what operation is being performed. If you could provide more information or context, I would be happy to try and help you.

Step-by-step explanation:

Answer:

Dollars per passenger would be $252.
The maximum revenue is $63,404.

Step-by-step explanation:

Let's define the number of passengers above 212 as x.

The revenue function is given by R(x) = (212 + x)(292 - x).

We can expand and simplify the revenue function:

\(R(x) = 212 * 292 + 212 * (-x) + x * 292 + x * (-x)\)

= \(61804 - 212x + 292x - x^2\)

= \(-x^2 + 80x + 61804\)

The revenue function is a quadratic function in the form\(R(x) = -x^2 + 80x + 61804\), representing a downward-opening parabola.

To find the x-coordinate of the vertex (which gives the number of passengers for maximum revenue), use the formula \(x = -b/2a\), where \(a = -1\) and \(b = 80\).

\(x=\frac{-80}{2*(-1)}\)

\(= \frac{80}{2}\)

\(= 40\)

Therefore, the number of passengers above 212 for maximum revenue is 40.

Substitute x = 40 into the revenue function to find the maximum revenue:

\(R(x) = -(40)^2 + 80(40) + 61804\)

\(= -1600 + 3200 + 61804\)

\(= 61804 + 1600\)

\(= 63404\)

Hence, the maximum revenue is $63,404.

To determine the fare per passenger, subtract x from the base fare of $292:

Fare per passenger = Base fare - x

\(= 292 - 40\)

\(= 252\) Dollars per passenger.

Answer:

\(\sqrt{207}\)

Step-by-step explanation:

Use the right triangle formula c^2=a^2+b^2

C is the number of the hypothenuse while b and c are the 2 others.

16^2=7^2+a^2

256=49+a^2

now solve for the equation.

a^2=207

now take the square root of both.

a=\(\sqrt[2]{207}\)