Alison is playing a video game. At the end of each level, the player is given either a bag of gold or a magic wand.

Alison says that the probability of getting a bag of gold is 30%. To test this, she plays the game 50 times and calculates the relative frequency of each outcome.
Outcome Bag of Gold Magic Wand
Relative frequency 0.32 0.68

Select from the drop-down menus to correctly complete each statement.

The relative frequency of getting a bag of gold is

30%.

Alison's claim about the theoretical probability is likely to be

.

Further, this means that the theoretical probability of getting a magic wand is most likely
.

A. The distance between the library and the park is equal to [tex]2\sqrt{10}[/tex] miles.

B. The distance between the park and the football field is [tex]2\sqrt{35}[/tex] miles.

Therefore, the correct answer option is D. [tex]2\sqrt{10}[/tex] miles and [tex]2\sqrt{35}[/tex] miles.

According to the geometric mean (leg) theorem, the length of the leg of a right-angled triangle is the geometric mean between its hypotenuse and the segment of the hypotenuse which is adjacent to that leg;

Hypotenuse/leg = leg/part or altitude/left = right/altitude

where;

left = 10 miles

right = 4 miles

Part A.

By applying geometric mean (leg) theorem, the distance between the library and the park (x) can be calculated as follows;

[tex]x^{2} =10 \times 4\\\\x=\sqrt{40} \\\\x=2\sqrt{10} \;miles.[/tex]

By applying geometric mean (leg) theorem, the distance between the park and the football field (y) can be calculated as follows;

(10 + 4)/y = y/10

14/y = y/10

[tex]y^2=\sqrt{140} \\\\y=2\sqrt{35}\;miles[/tex]

Answer:

5 pencils can be bought with 45 cents

Step-by-step explanation:

(180-30)/2 would be the equation and the answer is 150/2

The value of x (the perpendicular side) in the given right triangle is approximately 21.2137.

In a right triangle with a 45° angle, we can use the trigonometric function sine (sin) to find the value of the perpendicular side (x) when the hypotenuse is given.

sin(angle) = opposite / hypotenuse

Here the angle is 45°, and the hypotenuse is 30.

Therefore, we can write the equation as:

sin(45°) = x / 30

To solve for x, we can rearrange the equation:

x = sin(45°) × 30

Using the value of sin(45°) = 0.7071 (approximately), we can calculate x:

x = 0.7071 × 30

x = 21.2137

Therefore, the value of x (the perpendicular side) in the given right triangle is approximately 21.2137.

Learn more about Trigonometric functions here:

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Answer:

Step-by-step explanation:

Multiply the first bracket by 13

Multiply the second bracket by -4

13(6-x)-4(3x+12)=0

78-13x-12x-48=0

30-25x=0

-25x+30-30=0-30

-25x=-30

Divide by -25 for -25x and-30

x=30/25 reducing: 6/5= 1 1/5

Answer can be 30/25 or 6/5 or 1 1/5

Answer:

1:5.25

2:10.5

10:52.5

x:5.25x

Step-by-step explanation:

Basically, you do 42 divided by 8 to get the cost of $5.25 which is the cost of one ticket. Then you multiply that for each number of ticket.

Answer:

A) 5 + 2 =7 x 4= 28

B) 8

Step-by-step explanation:

A) 5 x 4 = 20 and 2 x 4 = 8 so you add 20 + 8 and you get 28

B)  so 5 x 4 is 20 and there is 8 left over and if you do 2 x 4 you get 8

To determine the number of egg salad sandwiches served, we set up an equation 5x + 2x = 28, where x is the number of egg salad sandwiches, and solve for x to find that 4 sandwiches were egg salad sandwiches.

To solve for the number of egg salad sandwiches served at the restaurant, we set up the following equation based on the proportion given: let x be the number of egg salad sandwiches, and 5 times x will be the number of tuna sandwiches since there are 5 tuna sandwiches for every 2 egg salad sandwiches.

The total number of sandwiches is 28, which gives us the following equation:

5x + 2x = 28

We then combine like terms:

7x = 28

Next, we divide both sides of the equation by 7 to solve for x:

x = 28 / 7

x = 4

This means that 4 sandwiches were egg salad sandwiches.

Answer: -125p12z18u3

Reason:

Square negative five twice, so: -5 x -5 x -5 = -125

The first squaring is -5 x -5, which is 25. The second squaring is 25 x (-5), which is - 125.

When it comes to the letters, they act like they are being multiplied.

(p4)3 = p12

(z6)3 = z18

(u)3 = u3

So the answer is -125p12z18u3.

Hope this helps! :)

First you have to know the "power rule." This is when there is an exponent outside the parentheses and some/all of the variables/numbers in the parentheses have exponents as well. What you do is multiply the outer exponent with each of the exponents inside the parentheses.

[tex]((-5)^{1*3} p^{4*3} z^{6*3} u^{1*3} )[/tex]

[tex](-5)^{3}p^{12}z^{18}u^{3}[/tex]

[tex]-125p^{12}z^{18}u^{3}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Explanation:

5x+5x=10x

Answer is 10x( D).

The expression (5x + 5x) is equivalent to....

10x

The answer would be D

Hope this helps!

Answer: 150 degrees

Reason: Vertically opposite angles are similar

(When two straight lines form an X when crossing over one another, an angle and the angle on the opposite side of the X are the same)

The measure of angle 8 is 150 degrees.

Opposite angles are angles that are found opposite each other. They are formed when two lines intersect. The value of a pair of opposite angles is equal.

It is given that angle 5 is equal to 150 degrees.

The image is also provided.

We can see that angles 5 and 8 are opposite angles.

We know that opposite angles have equal measures.

This means that the measure of angle 8 is the same as angle 5.

The measure of angle 5 is 150 degrees. Therefore, the measure of angle 8 is also 150 degrees.

We have found that the measure of angle 8 is the same as angle 5 which is 150 degrees since they are opposite angles.

Therefore, we have found that the measure of angle 8 is 150 degrees.

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Answer:

B

Step-by-step explanation:

You may have a different calculator than me, but what I did is I pressed the statistics button on my calculator, then I went to the option that said "Edit" which brought me to a table where I could type the given values in. Then I pressed the statistics button again but this time I went to the page that said "CALC" and I scrolled down to the option that said "LinReg(ax+b), then I went all the way down to where it says "Calculate" and I pressed the enter button. And then it told me what the slope and y-intercept values are for the line of regression (a is the slope, and b is the y-intercept or starting value).

Answer:

it is y=-8.583x+475.215

Step-by-step explanation:

Answer:

Because the answer is found as

5/2(s) - 5/2(s) = 0,

S can actually be anything since the above results to 0(s)=0 and anything multiplied by 0 just gives you 0 Hence, the value of S can be anything

Answer:

5/2(s) - 5/2(s) = 0

Step-by-step explanation:

[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{31em}{0.25pt}\\\\ h(x)=x^2+x-6 \qquad \begin{cases} x_1=0\\ x_2=3 \end{cases}\implies \cfrac{h(3)-h(0)}{3-0} \\\\\\ \cfrac{(3^2+3-6)~~-~~(0^2+0-6)}{3}\implies \cfrac{(6)-(-6)}{3} \\\\\\ \cfrac{6+6}{3}\implies \cfrac{12}{3}\implies 4[/tex]

Answer:

8n

Step-by-step explanation:

8 and n are factors of the product 8·n.

A correct option is option (a).

The functions factor is used to encode a vector as a factor (the terms ‘category’ and ‘enumerated type’ are also used for factors). If the argument ordered is TRUE, the factor levels are assumed to be ordered. For compatibility with S, there is also a function ordered.

The factor of [tex]8n[/tex] is,

[tex]8\times n[/tex]

We cannot find the factor [tex]8-n[/tex] and [tex]8+n[/tex]

And the factor of [tex]\frac{8}{n}[/tex] is [tex]\frac{8}{n} =8\times \frac{1}{n}[/tex]

Learn more about the topic factor:

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Answer:

(f * g)(2) =  -11√2 +66

Step-by-step explanation:

Points to remember

Let f(x) and g(x) be the two functions, then (f * g) can be written as,

(f * g) = [f(x)][g(x)]

To find the value of (f * g)(2)

we have,

f(x) = -5x - 1 and g(x) =√x - 6

f(2) = -5*2 - 1 = -11

g(2) = √x - 6 = √2 - 6

(f * g)(2) = [f(2)][g(2)]

 = -11 (√2 - 6)

= -11√2 +66

Therefore (f * g)(2) =  -11√2 +66

Answer:

420

Step-by-step explanation:

420 I think that’s what you wanna

The last digit of 73 factorial (73!) is 0 because any factorial of a number greater than 4 ends in 0 due to the multiplication with 2 and 5.

The last digit in a factor of an integer is dependent upon the pattern of the last digits in its individual factors. We know that factorial of any number greater than 4 ends in 0 because factorial operation involves multiplication by 2 and 5. Since 2 and 5 are factors of any number greater than 4, and the multiplying them results in 10, the final digit will always be 0.

In our case, the student wants to find out the last digit in 73!, which is far greater than 4. So, the last digit of 73! is 0.

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Answer:

45 years

Step-by-step explanation:

First, lets break the problem down, step-by-step.

Jeremy's age can be represented using the varibale, j.

His father's age is 53, or 11 less than j squared.

Jeremy's father's age can be represented using the following equation:

j^2 - 11 = 53

Now, solve for j.

j^2 - 11 = 53

j^2 = 64

j = 8

That means Jeremy is 8 years old. Now, find the difference between his age and his father's age.

53 - 8 = 45.

So, Jeremy's father is 45 years older than his son.

I hope this helps! :)

To find how many years older Jeremy’s father is than Jeremy, we determined that Jeremy is 8 years old and his father is 45 years older than him. We did this by solving the equation derived from the problem statement. Thus, Jeremy's father is 45 years older than Jeremy.

To solve the problem, let's denote Jeremy's age by x. According to the problem, Jeremy’s father’s age is 11 less than Jeremy’s age squared. The given information states that Jeremy’s father is 53 years old.

We can write this as an equation:

[tex]x^2 - 11 = 53[/tex]

[tex]x^2 = 53 + 11[/tex]

[tex]x^2 = 64[/tex]

Taking the square root of both sides, we get:

x = 8

So, Jeremy is 8 years old. Now, to determine how many years older Jeremy’s father is than Jeremy:

53 (father's age) - 8 (Jeremy's age) = 45

Thus, Jeremy’s father is 45 years older than Jeremy.

Answer:

2 quart ///////////////////// I think

[tex]\bf \cfrac{1}{x-10}\div\cfrac{9x}{x^2-9x-10}\implies \cfrac{1}{x-10}\cdot \cfrac{x^2-9x-10}{9x} \\\\\\ \cfrac{1}{\begin{matrix} x-10 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot \cfrac{\begin{matrix} (x-10) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+1)}{9x}\implies \cfrac{x+1}{9x}[/tex]

The answer is:

She will need 9 tins to cover all the panels.

To find how many tins will she need to cover the 30 panels for her allotment and her garden, we need to calculate the total area of the panels and then, calculate how many tins will she need knowing that each liter of tin, covers 12 square meters.

We are given the dimensions of the panels:

[tex]Long=1.8m\\Hight=2m[/tex]

Now, calculating the area of one (1) panel, we have:

[tex]Area=long*height=1.8m*2m=3.6m^{2}[/tex]

So , the total area of all 30 panels is:

[tex]TotalArea=30*3.6m^{2}=108m^{2}[/tex]

Then, calculating how many tins will she need to paint all the panels, we have:

[tex]NeededTins=\frac{TotalArea}{AreaToCoverWithOneTin}\\\\NeededTins=\frac{108m^{2}}{12m^{2} }=9[/tex]

Hence, we have that she will need 9 tins to cover all the panels.

Have a nice day!

To treat 30 panels, Nancy will need 9 tins of wood preservative.

The total area of 30 panels:

Each panel is 1.8m * 2m = 3.6m²

Total area for 30 panels = 30 panels * 3.6m²/panel = 108m²

Calculate the number of tins needed:

1 litre of preservative covers 12m²

Number of tins needed = Total area / Area covered by 1 tin = 108m² / 12m² = 9 tins

I guess it’s the second one because only in the second the x value is giving the respective y value

Step-by-step explanation:

8*8=64

4S=64

S=16

white = 6S = 96 ft²

Blue = 6S = 96 ft²

Turkeyy :))

The area of the figure will be 96 square feet.  Then the correct option is A.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A composite figure has three congruent triangles removed from it.

Then the area of the figure will be

Area = 3 x area of square + 3 x area of triangle

Area = 3 x 8 x 8 - 3 x 1/2 x 8 x 8

Area = 192 - 96

Area = 96 square feet

The area of the figure will be 96 square feet.

Then the correct option is A.

More about the geometry link is given below.

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Answer:

It's x = -4 ,  2.

Step-by-step explanation:

x^2 + 2x - 8 = 0

The left side will factor to the form (x + a)(x + b).

We need 2 numbers  (a and b)  whose  product = -8 and whose sum = +2.

These  are a = 4 and b = -2,  so the factors are

(x + 4)(x - 2) = 0

Now either x + 4 = 0 or x - 2 = 0,

giving x = -4, x = 2 (answer).

Answer:

-2 , 4

Step-by-step explanation:

Their are 4 ways you can solve this but I am going to factorise to solve

x² + 2x − 8 = 0

Factors = 4 , -2

Sum = 2

Product = -8

x ( x + 4 ) - 2 ( x + 4 ) = 0

( x - 2 ) ( x + 4 ) = 0

x = - 2 , 4

Answer:

A

Step-by-step explanation:

If you reflect figure P over the x-axis, it will be below the axis, below where figure P is. Then you need to move it 7 units right.

Answer: A

Answer:15 pi

Step-by-step explanation:

The scope is 10(r)*2*pi

XPY is 3 quarters of the slope, which equals to 0.75*20*pi=15pi

Final answer:

The volume of Kathy's stacks is 24 cm³ greater than Marco's stacks. Each cube has a volume of 8 cm³, and after multiplying by the number of cubes each person has and subtracting, we find the difference in volume.

Explanation:

To calculate how much greater the volume of Kathy's stack of cubes is compared to Marco's, we need to determine the volume of both sets of cubes and then subtract the smaller volume from the larger one. Each cube has a volume of 2 cm × 2 cm × 2 cm, which equals 8 cm³.

Kathy has 8 cubes, so her total volume is:

8 cubes × 8 cm³ per cube = 64 cm³.

Marco has 5 cubes, so his total volume is:

5 cubes × 8 cm³ per cube = 40 cm³.

To find out how much greater Kathy's volume is:

Kathy's volume – Marco's volume = 64 cm³ – 40 cm³ = 24 cm³.

Therefore, the volume of Kathy's stacks is 24 cm³ greater than Marco's stacks.

the 0 are 2, 3 and -6. ....

Answer:

Given function,

[tex]f(x)=(x^4-16)(x^2+3x-18)[/tex]

[tex]=((x^2)^2-(4)^2)(x^2+(6-3)x-18)[/tex]

[tex]=(x^2-4)(x^2+4)(x^2+6x-3x-18)[/tex]

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

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

For zeros of function f(x),

f(x) = 0

[tex]\implies (x-2)(x+2)(x+2i)(x-2i)(x-3)(x+6)=0[/tex]

By zero product property,

We get,

x = 2, -2, -2i, 2i, 3, -6

Hence, the real roots of f(x) are 2, -2, 3, -6.

Also, the roots lie at the point where a function intersects the x-axis.

Hence, the positions of the roots of f(x) in the graph are ,

(2, 0), (-2, 0), (3, 0) and (-6, 0)

Answer:

Step-by-step explanation:

|a| = a for a ≥ 0

|a| = -a for a < 0

therefore

|-4.5| = -(-4.5) = 4.5

Answer:

4.5

Step-by-step explanation:

usually if you are finding absolute value for a negative number, it is usually the opposite of that negative number.

If I am trying to find absolute value for -7 it would be 7.

hope my handwriting is readable.

using pythagoras theorem the height ladder reaches above the wall can be found as in picture the answer would be 12ft