Roger completed a probability experiment with a coin. He flipped the coin 32 times, and it landed on tails eight times. He looked at the results of his experiment to determine the ratio of heads outcomes to tails outcomes.
The ratio of heads to tails in simplified form is
to
.

The simplified expression of the given expression is given by 3√(27x¹²) is 3x⁴.

From the rule exponent we know that the exponents follow the below rules,

aˣ⁺ʸ = (aˣ)*(aʸ)

(aˣ)ʸ = aˣʸ

aˣ⁻ʸ = (aˣ)/(aʸ)

The given expression is,

3√(27x¹²) that is in words "Cube root of 27x¹²"

Now we know that, 3³ = 27 and we can write from exponent formula that,

x¹² = (x⁴)³ [As 4*3 = 12]

So, now simplifying the given expression we get,

3√(3³(x⁴)³) = 3√((3x⁴)³) = 3x⁴ [Omitting the exponent 3 and cube root]

Hence the simplified expression of the given expression is given by 3√(27x¹²) is 3x⁴.

To know more about exponent here

https://brainly.com/question/11975096

#SPJ1

The measurements which is best estimate is given as 6m, 100grams, 2L.

Measurement is the process of quantifying a physical property of an object or phenomenon, typically by comparing it to a standard unit of measurement. This allows for precise and objective description and comparison of different quantities.

An estimate is an approximate calculation or judgment of the value, amount, size, or cost of something, based on available information and assumptions. It is often used when precise measurements or exact values are not available or practical. Estimates can be useful in planning, budgeting, and decision-making, but they should be used with caution and updated as more accurate information becomes available.

a) The best estimate for the height of a lamp post would be 6 meters (6m).

b) The best estimate for the mass of a pear would be 100 grams (100g).

c) The best estimate for the amount of water in a filled kettle would be 2 litres (2L).

Learn more about measurement here:

https://brainly.com/question/4725561

#SPJ1

The probability that Jennifer selects a blue cube is 1/4 or 25%.

The probability that Jennifer selects a blue cube can be found by dividing the number of blue cubes by the total number of cubes:

P(selecting a blue cube) = number of blue cubes / total number of cubes

We are given that there are 5 blue cubes out of a total of 20 cubes:

P(selecting a blue cube) = 5/20

Simplifying this fraction by dividing both the numerator and denominator by 5, we get:

P(selecting a blue cube) = 1/4

Therefore, the probability that Jennifer selects a blue cube is 1/4 or 25%.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ1

Answer:

200

Step-by-step explanation:

Perimeter of parallelogram = 2(b + c)

b = 48

c = 52

Let's solve

2(48 + 52) = 200

So, the perimeter of the parallelogram is 200

Using the volume of the room we know that the area of the floor is 139 m² respectively.

A cuboid is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces.

Cuboid is short for "like a cube".

A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.

A cuboid's volume is calculated by summing its length, breadth, and height.

So, let the values be:

Breadth = b

Length = 2b

Height = 2b/3

The volume of the cuboid:

V=whl

Insert values:
V=whl

972=b*2b*2b/3

972*3=b*2b*2b

2,916=b*2b*2b

2,916=5b³

b³=2916/5

b³=583.2

b=³√583.2

b=8.35 m

Now, l = 2b ⇒ 2(8.35) = 16.7 m

Now, the area of the floor is: l * b

= 16.7 * 8.35

= 139.445 m²

Rounding off: 139 m²

Therefore, using the volume of the room we know that the area of the floor is 139 m² respectively.

Know more about volume here:

https://brainly.com/question/29568631

#SPJ1

Answer:

There is 1 solution to the equation 7m = 49.

To solve for m, we can divide both sides of the equation by 7:

7m / 7 = 49 / 7

m = 7

Therefore, there is only 1 solution to the equation 7m = 49.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

using the sine ratio in the right triangle

sin73° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{20}{x}[/tex] ( multiply both sides by x )

x × sin73° = 20 ( divide both sides by sin73° )

x = [tex]\frac{20}{sin73}[/tex] ≈ 20.9 ( to the nearest tenth )

The solution is :

A) Median: 7

Mode: 8

Range: 5

B) Tyler is wrong, the greater the MAD value, the greater the variability

A) Given the data set: 4,6,6,7,7,8,8,8,9

The median is 7 (the middle point in the ordered list)

The mode is 8 (the most repeated number)

The range is 5 (the difference between the highest and lowest values)

B) Tyler is wrong, the greater the MAD value, the greater the variability.

To learn more on median click:

brainly.com/question/20425811

#SPJ1

complete question:

A fitness instructor tested the arm strength of members of a fitness dass to compare their scores to the national average. The test rated members on a scale from 1, the weakest, to 10, the strongest. The scores of 9 members are shown in the data set below. 4,6,6,7,7,8,8,8,9 Part A What is the value of each measure? Answers: Median: Mode: Range: Part B The mean absolute deviation (MAD) value of the data set is about 1.1. Tyler says that the lower the MAD value, the greater the variability. Is Tyler correct? Explain.

Answer: P*0.06*(50/360) = 11900

Step-by-step explanation: good luck

Answer:

  1428000

Step-by-step explanation:

You want the principal that would result in interest of 11900 at a rate of 6% for a period of 50 days.

Ordinary interest is calculated on the basis of 360 days per year. The fraction of a year represented by 50 days is 50/360, so the interest formula tells us ...

  I = Prt . . . . . . . where P is the principal at rate r for t years

  11900 = P·0.06·(50/360)

  P = 11900/(0.06·50/360) = 1428000

The principal amount is 1428000.

The surface area of the figure shown is,

⇒ 204 cm²

We have o given that;

Upper cube has side = 3 cm

And, Lower cube has side = 5 cm

We know that;

Surface area of cube = 6a²

Hence,

The surface area of the figure shown is,

⇒ 6 × 3² + 6× 5²

⇒ 6 × 9 + 6 × 25

⇒ 54 + 150

⇒ 204 cm²

Thus, The surface area of the figure shown is,

⇒ 204 cm²

Learn more about the cuboid visit:

https://brainly.com/question/26403859

#SPJ1

Answer:

- 6 > - 8

 8 > 5

- 1 < 0

Step-by-step explanation:

The probabiltiy that when a marble is chosen from the bag at random then choosen marble is blue is 1/2.

Given that the bag has 6 red marble and 6 blue marbles. Now, a marble is chosen from the bag at random. Therefore, the probabiltiy that choosen marble is blue is:

Probability(Blue Marble)

= Number of blue marbles / Total number of marbles in the bag

= 6/ 12

= 1/ 2

Hence, the probability is 1/2.

Learn more about the Proabability here:
https://brainly.com/question/30034780

#SPJ1

The complete question must be:

A bag with 6 red marbles has 6 blue marbles. A marble is chosen from the bag at random. What is the probability that it is blue? Write your answer as a fraction in simplest form.

Using both hoses at the same time, it would take 10 minutes to fill up the kiddie pool. The correct option is B).

Let's call the time it takes to fill up the pool using the back hose alone "B". From the problem, we know that B = 30 minutes. We also know that the front hose fills the pool in half the time of the back hose, so the time it takes to fill up the pool using the front hose alone is 1/2 B = 15 minutes.

Now let's use the formula for "combined work" to find out how long it will take to fill the pool using both hoses at the same time. The formula is

Combined time = (time for hose A * time for hose B) / (time for hose A + time for hose B)

Let's let "A" represent the time it takes to fill up the pool using both hoses at the same time. We know that the combined time is the time it takes to fill up the pool, so A is what we're looking for.

Using the formula, we get

A = (30 * 15) / (30 + 15)

A = 10 minutes

Therefore, it will take 10 minutes to fill up the pool using both hoses at the same time. The correct answer is B.

To know more about time:

https://brainly.com/question/15764331

#SPJ1

Step-by-step explanation:

fourth one

.

..

.

....

.

.

..

The overall free throw success rate in the entire game is 25%

A rate is a ratio that compares two different quantities which have different units.

Success rate of free = number of free throw made ÷ total number of free throws × 100

In the first half,

represent the total free throw by x

40 = 2/x × 100

40x = 200

x = 200/20

x = 5

In the second half;

20 = 3/x × 100

20x = 300

x = 300/20

x = 15

Therefore the total success rate of free throw = total number of free throw made ÷ total number of free throws × 100

= (3+2)/(15+5)

= 5/20 × 100

= 25%

learn more about rate from

https://brainly.com/question/119866

#SPJ1

Step-by-step explanation:

INVERSE variation means that   y = k/x

when x =3    y = 10

 10 = k/3    shows the proportionality constant k = 30

y = 30 / x       now when x = 5      y = 6

The statement which is true about the minimum values of the two quadratic functions presented in the question is f(x) and g(x) have the same minimum value. Therefore, the correct option is option C.

When  [tex]tan(\theta) = 1[/tex] , the value of  [tex]sin(\theta)[/tex] in quadrant III is [tex]\frac{-1}{\sqrt{2} }[/tex]. Therefore the correct option is option B.

First picture

Finding the vertex of each function, to determine the minimum values of functions. The vertex of a quadratic function in the form [tex]f(x) = ax^{2} +bx + c[/tex] can be find by the coordinates [tex](\frac{-b}{\ 2a} , f(\frac{-b}{\ 2a} ))[/tex].

For function [tex]f(x) = x^{2} +4x - 4[/tex], a = 1, b = 4. Substituting these values in vertex formula,

[tex]x = \frac{-b}{\ 2a} = \frac{-4}{\ (2\ *\ 1)} = -2[/tex]

Finding the value of f(-2):

[tex]f(-2) = (-2)^{2} + 4(-2) - 4[/tex]

= 4 - 8 - 4

= -8

So the vertex of f(x) is (-2, -8), and the minimum value is -8.

For function g(x)

From the values, the minimum value of g(x) is -8, which occurs when x = 0.

Comparing the minimum values of f(x) and g(x),

Minimum value of f(x) is -8

Minimum value of g(x) is -8

Therefore, the correct answer is: C. f(x) and g(x) have the same minimum value.

Second picture

In Quadrant III, x-coordinate and y-coordinate both are negative.

[tex]tan(\theta) = \frac{sin(\theta)}{cos(\theta)} = 1[/tex]

Since, [tex]cos(\theta)[/tex] is negative and [tex]tan(\theta) = 1[/tex], using the Pythagorean identity to find [tex]cos(\theta)[/tex],

[tex]cos^2(\theta) = \frac{1 }{(1 + tan^2(\theta))}[/tex]

[tex]cos^2(\theta) = \frac{1}{(1 + 1)}[/tex]

[tex]cos^2(\theta) = \frac{1}{2}[/tex]

[tex]cos(\theta) = \sqrt{\frac{1}{2} }[/tex]

[tex]cos(theta) = -\frac{\ 1}{\sqrt{2} }[/tex]

⇒ [tex]sin(\theta) = tan(\theta) * cos(\theta)[/tex]

[tex]sin(\theta) = 1 * (-\frac{1}{\sqrt{2} } )[/tex]

[tex]sin(\theta) = -\frac{\ 1}{\sqrt{2} }[/tex]

Therefore, in Quadrant III, [tex]sin(\theta) = -\frac{\ 1}{\sqrt{2} }[/tex]

Know more about quadratic functions and trigonometric identities,

https://brainly.com/question/29129656

#SPJ1

Answer:

nonlinear

Step-by-step explanation:

It is nonlinear (NOT a straight line).  It is a open-up parabola with a vertex at (0, 8)

Answer:

Step-by-step explanation:

A sequence is a list of things in which repeats are permitted and order is important. The last term of the missing pattern is 57.

What is a sequence?

A sequence is a list of things in which repeats are permitted and order is important. It has members, just like a set. The length of the sequence is defined by the number of items.

In the given sequence, the difference between the first two-term is 4, while in the next two-term is 16(4²), Therefore, in the next two-term, the difference between the two terms will be equal to 64(4³).

Therefore, the last term will be,

Hence, the last term of the missing pattern is 57.

1. The measure of <POQ  = π/3.

2. (-0.5, 0.87) and (0.5, -0.87) are on circle.

3. R is on the positive y axis.

We have,

The arc PQ has a length of 5.

1. Circumference of circle

C = 2πr

C = 2π(1)

and, Arc length = [tex]\theta[/tex] /360 x 2πr =π/3

[tex]\theta[/tex] = π/3

So, the measure of <POQ  = π/3

2. Q has approximate coordinates (0.5, 0.87)

Then (-0.5, 0.87) and (0.5, -0.87) are on circle.

3. <POR = π/2

x = r cos π/2 = 0, y= r sin π/2= 1

Thus, R is on the positive y axis.

Learn more about Arc length here:

https://brainly.com/question/16403495

#SPJ1

The decimal that represents the amount of pine and spruce trees in Hidden Forest is

If 50% of the trees in Hidden Forest are spruce,

10% are maple, and

25% are oak, then

the remaining percentage must be pine trees.

To find the percentage of pine trees, we solve as below

100% - 50% - 10% - 25% = 15%

Therefore, 15% of the trees in Hidden Forest are pine trees.

To write a decimal that represents the amount of pine and spruce trees, we can add the percentage of spruce trees and pine trees together and convert it to a decimal:

50% + 15% = 65%

Converting 65% to a decimal, we get:

0.65

Learn more about decimal at

https://brainly.com/question/1827193

#SPJ1

Justin's pack was lighter than Sue's pack.

Therefore, the answer is B. Justin.

Answer:

Step-by-step explanation:

To find the missing values, we can use the ROI formula:

ROI = Margin x Turnover

We are given that ROI is 70%. We can use this to solve for the missing values:

Margin x Turnover = 70%

We can rearrange this equation to solve for Margin:

Margin = ROI / Turnover

To find Turnover, we can use the formula:

Turnover = Sales / Average Operating Assets

Plugging in the given values, we get:

Turnover = $300,000 / $187,500 = 1.6

Now we can solve for Margin:

Margin = 70% / 1.6 = 43.75%

Therefore, the closest option is B) 40%.

a) The graph shows the mean and the values at ±1, ±2, and ±3 standard deviations from the mean.

b) -0.1213

c) 0.0653

d) 0.0171

e) EOC

Given that;

The EOC exams are normally distributed with a mean of 702.19 and a standard deviation of 35.81. A score of 700 is needed to earn 3 points.

Now, We can formulate;

a) The graph shows the mean and the values at ±1, ±2, and ±3 standard deviations from the mean. Each mark differs from the one below by the value of the standard deviation, 36.18. The central mark is the mean, 704.39.

b) As you know, the z-score is computed from ...

 z = (x -µ)/σ

 z = (700 -704.39)/36.18

 z = -0.1213

c) Same formula, different numbers.

 z = (22 -21.65)/5.36

 z = 0.0653

d) Likewise, ...

 z = (530 -528)/117

 z = 0.0171

e) EOC would be the easiest. The required score has the lowest z-value, so the applicant only needs to do better than a smaller number of peers.

Actually, the answer to this depends on why the thresholds vary. If we assume that the threshold on each test is set appropriate to the desired knowledge and ability, the test-taker would find his knowledge and ability allows him to do better on the ACT than on the other tests.

On the other hand, if the scores are representative of test taker populations all with the same knowledge and ability, less of that knowledge is required to achieve the necessary score on the EOC.

Learn more about the standard deviation visit:

https://brainly.com/question/475676

#SPJ1

Complete question is,

In order to graduate from Ohio, you need to earn 3 points on an Algebra EOC or score remediation

scores on the ACT and SAT math exams. The EOC exams are normally distributed with a mean of 704.39

and a standard deviation of 36.18. A score of 700 is needed to earn 3 points.

the values of each standard deviation above and below the mean, and make sure to add in the value

of the mean. Answers only are fine.

free

(Graph below)

b. What would be the z-score for a 700 on the EOC? Show work.

C. You can also earn math credit by scoring a remediation free score on the ACT. ACT tests have a mean

value of 21.65 and a standard deviation of 5.36. What would be a Z-score for a 22 on the ACT? Show work.

d. You can also earn math credit by scoring a remediation free score on the SAT. SAT tests have a mean value

of 528 and a standard deviation of 117. What would be a z-score for a 530 on the SAT? Show work.

e. Of the three testing options, which would be statistically easier to earn? Circle the answer and explain

your reasoning. EOC ACT SAT​

Using a trigonometric relation we can see that the value of the missing side is x = 3.9

We can use the trigonometric relation:

cos(75°) = adjacent cathetus/hypotenuse

Where the adjacent cathetus is x, and the hypotenuse measures 15 units, then we can replace these values to get.

cos(75°) =x/15

Solving this for x we get.

15*cos(75°) =x

3.9 = x

So the correct option is D, the length of the missing side is 3.9 units.

Learn more about right triangles at:

https://brainly.com/question/2217700

#SPJ1

The surface area of the table top that is not covered by the mirror in the form of algebraic expressions is [tex]5x^2 - 17x +6\,\,m^2[/tex] .

The length of the table top = 5x - 2 m.

The width of the table not covered by mirror is x-3 m.

The surface area of the table top not covered by the mirror is

[tex]$(5x-2)(x-3) = 5x^2 -15x -2x +6 \,\,m^2[/tex]

[tex]$=5x^2 -17x +6\,\, m^2[/tex] in the form of algebraic expressions.

Surface area of cylinder of radius r and height h = [tex]2\pi r^2 + 2\pi rh[/tex]

Surface area of a cuboid of side length a = [tex]6a^2[/tex]

Outside area for a sphere of radius r = [tex]4\pi r^2[/tex]

Surface area of a regular tetrahedron of edge length a = [tex]\sqrt{3}\,a^2[/tex]

Surface area of a right angled cone of base radius r, and lateral height l = [tex]\pi r^2 + \pi r l[/tex]

To know more about surface area, visit:

https://brainly.com/question/29298005

#SPJ1

The value of angle x include the following: A. 34.5°

In Mathematics and Geometry, the theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants, the value of m∠x can be calculated as follows:

m∠x = 1/2(126 - 57)

m∠x = 1/2(69)

m∠x = 34.5 degrees.

Read more on intersecting secants here: https://brainly.com/question/31049910

#SPJ1

Answer:

The answer is: y ≤ (2/3)x - 1/2

Step-by-step explanation:

Add 2y to both sides of the inequality:

2/3x ≥ 1 + 2y

Subtract 1 from both sides of the inequality:

2/3x - 1 ≥ 2y

Divide both sides by 2 to isolate y:

y ≤ 1/2(2/3x - 1)

This gives you the inequality in slope-intercept form, y ≤ (2/3)x - 1/2, where the slope is 2/3 and the y-intercept is -1/2.

To graph the boundary line, plot the y-intercept at (0, -1/2) and then use the slope to find another point. For example, if you move up 2 units and to the right 3 units from the y-intercept, you'll arrive at the point (3, 1/2). Connect these two points with a straight line to graph the boundary line.

Finally, to shade the region of the coordinate plane that satisfies the inequality, test any point above or below the boundary line to see if it's a solution to the inequality. If the point satisfies the inequality, shade the region that it's in. If it doesn't, shade the opposite region.