A number cube is tossed 60 times.


Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8

Determine the experimental probability of landing on a number greater than 4.
17 over 60
18 over 60
24 over 60
42 over 60

A dog in an open field runs 12.0 m east and then 29.0 m in a direction 51.0 west of north, 69.50 south of east or 20.50 east of south must the dog then run to end up 10.0m south of her original starting point.

A dog in an open field runs 12.0 m east and then 27.0 m in a direction 54.0 degree west of north.

The dog's displacement vector is d(1) = [tex]12 \hat{i} + 29 [-sin51^{o} \hat{i} + cos51^{o} \hat{j}][/tex]

Thus, d(1) = [tex]12 \hat{i} + (-22.5 ) \hat{i} + (18.2) \hat{j}[/tex]

d(1) = [tex]-10.5 \hat{i} + 18.2 \hat{j}[/tex]

The dog's overall displacement is then

P = -10[tex]\hat{j}[/tex] - d(1)

P = [tex]-10 \hat{j} - [-10.5 \hat{i} + 18.2 \hat{j}][/tex]

P = [tex]10.5 \hat{i} - 28.2 \hat{j}[/tex]

The dog's direction is

θ = [tex]tan^{-1}[/tex][(28.2/10.5)]

θ = 69.50 south of east or 20.50 east of south

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If 18 is the quotient of a number and 6, the value of the unknown number is 108.

Given the statement in the question;

18 is the quotient of a number and 6

Let the unknown number be represented by 'x'.

The quotient of a number and 6 the same as x / 6

Hence

18 = x / 6

Solve for x

Cross multiply the equation

18 × 6 = x

x = 18 × 6

Multiply 18 and 6

x = 108

Therefore, the value of x is 108.

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The decimal inch scale is based on tenths and hundredths of an inch. This scale is a common unit of measurement used for industrial, mechanical, and construction purposes.

The formula for a decimal inch is 1 inch = 0.1 decimal inch. This means that every 0.1 decimal inch is equal to 1 inch. To calculate a decimal inch, simply divide the number of inches by 10. The decimal inch scale is based on tenths and hundredths of an inch. This scale is a common unit of measurement used for industrial, mechanical, and construction purposes. For example, if you have a measurement of 6 inches, the decimal inch measurement would be 0.6. You can also convert decimal inches to inches by multiplying the decimal number by 10. For example, if you have a measurement of 0.6 decimal inches, the inch measurement would be 6 inches.

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The equation of the trend line to estimate the​ hiker's elevation after 165 minutes is 2291.3 feet.

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

Given that,

The equation of a trend line for the​ hiker's elevation is y = 9.82x + 671​.

We have to determine,

The equation of the trend line to estimate the​ hiker's elevation after 165 minutes.

According to the question,

The equation of a trend line for the​ hiker's elevation is y = 9.82x + 671​.

Where, x represents the number of minutes and y represents the​ hiker's elevation in feet.

To find the trend line to estimate the​ hiker's elevation after 165 minutes, substitute the value of x = 165 minute in the given equation.

Hence, The equation of the trend line to estimate the​ hiker's elevation after 165 minutes is 2291.3 feet.

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The radical form of a number involves a square root. The number under the square root is a natural number or real number.

What is a radical?

The square root or nth root is represented by the symbol. Expression with a square root is referred to as a radical expression. Radicand: A value or phrase contained within the radical symbol. An equation with radical expressions and variables as radicands is referred to as a radical equation.

The term "simplest radical form" refers to an algebraic expression's or number's most basic radical form. If the number or algebraic expression under the radical has no factors that are perfect nth powers, then the radical is said to be in its simplest radical form.

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Answer: n/a

Step-by-step explanation:

there are no numerical values given to derive an answer from.

to find the mean, take the sum of all numbers and divide it by the number of added numbers.

for the standard deviation, subtract every data point from the mean and square it. add all of those together and divide it by the number of data points. then find the square root of that number

Answer:A(-5,4),B(-5,6),C(-7,6),D(-7,4)

Step-by-step explanation:If you draw a big enough graph it is easy to do.

The Mean Value Theorem guarantees that the values of c for f(x)=x^3+x^2-4x+2 on the interval [1,3] are [7,9].

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

f(c)=f'(b)-f'(a)/(b-a)

f(x)=x^3+x^2−4x+2

f'(x)=3x²+2x-4

x=-1, 3

f'(-1)=3-2-4

=-3

f'(3)=27+6-4

=29

f(c)=29+3/3+1

=32/4

f(c)=8

=[7,9]

The values of c guaranteed by the Mean Value Theorem for f(x)=x^3+x^2−4x+2 on the interval [−1,3] is [7,9].

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The volume of the given object would be the addition of the volume of the cone and the volume of the rectangular prism = 3,648 in³.

The volume of cone = v = πr²h/3

where π = 3

r = 8/2 = 4ft

h = 12ft

Volume = 3× 4² × 12/3

= 576/3 = 192ft³

The volume of the rectangular prism = l×w×h

where;

l = 7ft

w = 2ft

h = 8ft

volume = 7×2×8 = 112ft³

Therefore the volume of the object = 192+112 = 304ft³

To convert to inches the following is carried out;

1 ft = 12 inches

304 ft = 304× 12 = 3,648 in³

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the speed from kilometers per year to kilometers per hour 4.3x107 km/hr, the distance of 4.4 light years to kilometers.

1. First, convert the distance of 4.4 light years to kilometers.

1 light year = 9.46x1012 km

4.4 light years = 4.1x1013 km

2. Next, divide the distance by the time to calculate the speed:

Speed = Distance/Time

Speed = 4.1x1013 km/110 years

Speed = 3.7x1011 km/year

3. Finally, convert the speed from kilometers per year to kilometers per hour:

1 year = 8760 hours

Speed = 3.7x1011 km/8760 hours

Speed = 4.3x107 km/hr

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When graphing "AND" inequalites, shading looks like Shading that always connects the 2 dots.

An algebraic statement that connects two values that are not equal is referred to as an inequality in mathematics. Inequality signals state that one of the two variables on either side of the inequality could be greater than, greater than or equal to, less than, or less than or equal to another value.

If a linear inequality has a sign that is either (less than) or, you will shade below the boundary line (less than or equal to). In a linear inequality, if the sign is > (greater than) or, you will shade above the boundary line (more than or equal to).

Follow these steps:

Rearrange the equation so "y" is on the left and everything else on the right.

Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)

Shade above the line for a "greater than" (y> or y≥)

or below the line for a "less than" (y< or y≤).

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Step-by-step explanation:

Is power of mind is truee

The concept of the power of the mind is a widely debated topic, with varying opinions and perspectives. Some people believe in the power of positive thinking and visualization to achieve goals and create positive changes in one's life. Others may be more skeptical and question the scientific evidence supporting these ideas. Ultimately, whether or not the power of the mind is "true" is subjective and depends on one's personal beliefs and experiences.

The number of ways the elevator buttons can be lighted is (m)(m-1)(m-2)...(m-n+1).

What is Permutations?

The mathematical notion of permutation describes the placement of things in a particular order. It is a method of determining how many unique configurations there are for a given set of objects.

If there are n persons in the elevator, and each one presses a button for a floor between 1 and m, what would happen? (inclusive). The number of permutations of m things taken n at a time, indicated as P, determines the number of ways the elevator buttons can be lit if no two individuals hit the same floor button and each person pushes a different floor button (m, n).

[tex]The formula for permutations is: P(m, n) = m! / (m - n)!.Therefore, the number of ways the elevator buttons can be lighted is:P(m, n) = m! / (m - n)! = m! / (m - n)! = m! / (m - n)! = m! / (m - n)! = (m)(m-1)(m-2)...(m-n+1).[/tex]

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The number of ways the elevator buttons can be lighted is [tex]m(m-1)(m-2)...(m-n+1)[/tex].

What are Permutations?

The placing of things in a specific order is described by the mathematical concept of permutation. It is a technique for figuring out how many different arrangements of a group of things there are.

It would be inclusive if there were n people in the elevator and each one pressed a button for a floor between 1 and m. If no two people press the same floor button and everyone presses a separate floor button, the number of P permutations of m items taken n at a time defines how many ways the elevator buttons can be lit (m, n).

The formula for permutations is:

[tex]P(m,n)=m(m-1)(m-2)...(m-n+1)[/tex]

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Answer: B. x=6 only

Explanation: A fast way to check these kind of multiple choice questions is to just plug in one of the values into the equation and see if it works. For example you can put (6^2)-(12×6)+36 and it would equal 0 making the equation true. All other options wouldn't have equaled 0 so it would make x=6 the only right option.

If gasoline costs $1.95 per gallon $0.52 is its cost per liter?

One gallon of gasoline costs $1.95. To find the cost per liter, we need to convert gallons to liters. The conversion factor between gallons and liters is 1 gallon = 3.78541 liters.

So, to convert gallons to liters, we multiply the number of gallons by 3.78541.

In this case, the cost of one gallon of gasoline is $1.95. To find the cost per liter, we need to convert $1.95 from dollars per gallon to dollars per liter.

To do this, we divide $1.95 by the conversion factor between gallons and liters:

$1.95 / 3.78541

= $0.52/liter.

Therefore, the cost of one liter of gasoline is $0.52.

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Taking LCM and comparing the values we see that: 39/57 > 38/57. Hence, option C is the correct statement.

In mathematics, the value that is equally divided by the two supplied numbers is known as the LCM of any two. Least Common Multiple is its full name. Another name for it is the Least Common Divisor (LCD).

When the fractions' denominators differ, LCM can also be used to add or subtract any 2 fractions. LCM is used to make the denominators common when doing any arithmetic operations using fractions, such as addition and subtraction.

The two values are:

13/ 19 and 2/3

Taking LCM we have:

13(3)/ 19(3) and 2(19) / 3(19)

39/ 57 and 38/57

Hence, comparing the values we see that:

39/57 > 38/57

Option C is the correct answer.

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There are 3 ordered pairs of the places jimmy visits in the order he visits them.

An ordered pair is a pair that is formed by two elements and are separated by a comma and written inside the parenthesis.

An example of ordered pair is (x,y).

where x is called the first element and y is called the second element of the ordered pair.

If we consider 2 order pairs the first-order pair is not equal to the second-order pair.

Example: (x,y) [tex]\neq[/tex] (y,x)

Now as per the diagram, jimmy has started at home next he walks to the horse which is the intersection of (1,1) points.

After then he walks 3 units up which is (1,3) which reaches the horse barn from that point he is supposed to move  4 units right and reached (5,6)  At the Storage barn.

so the order pairs are:

(1,1) - At the house

(1,3) - At the horse barn

(5,6) - At the Storage barn

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The required length of the arc of the circle is  approximately 13.08 cm.

In mathematics, an arc is defined as a portion of the boundary of a circle or a curve. It can also be referred to as an open curve. The boundary of a circle is the perimeter or the distance around a circle, also known as the circumference.

The length of an arc of a circle is given by the formula:

L = θ * r / 180 * π

Where θ is the central angle in radians, r is the radius, and π is pi.

In your case, the radius of the circle is 6, and the central angle is 126°, so we need to first convert 126° to radians:

θ = 126° * π / 180 = 2.18 radians

Substituting the values in the formula, we get:

L = θ * r / 180 * π = 2.18 * 6 / 180 * π = 2.18 * 6 / π = 13.08 cm

So the length of the arc of the circle with radius 6 and central angle 126° is approximately 13.08 cm.

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Since the sum is given to be equal to 9, then the exact value of c must be equal to 9/1.

The given equation is ∑ n = 0 c n 1 = 9. This means that the sum of all of the terms beginning at n = 0 and continuing for infinity is equal to 9. Therefore, the exact value of c must be equal to 9/1. In other words, c must have a value of 9 in order for the given equation to be true. As such, the exact value of c is 9/1. Since the sum is given to be equal to 9, then the exact value of c must be equal to 9/1.

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Using inequality views, the compound inequality is given by:

50 ≤ P ≤ 90

            a ≤ x ≤ b

                                          50 ≤ P ≤ 90

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If angle b is five times the size of angle c, the equation can be used to find the measure of angle is 5x+x=90°.

because complementary angles complete each other to 90 degrees.

These angles b and c add up to 90° because they are complementary.

Let's say angle C is named x.

angle b is five times the size of angle c, this can be written: 5x

Complementary angles add up 90°, so angle B add angle C equal 90°

the equation to find the measure of angle C is 5x+x = 90°.

Types of angles are one of the materials in mathematics that you always encounter at every level of education. Learning about angles is very important, because angles are always present in everyday life and need to be identified.

An angle is a shape formed by two rays having an endpoint at one point. In angles, terms such as the leg of the angle, vertex, and area of the angle are also found.

The legs of the angle are the lines forming the angle. The vertex is the point where the two legs of the angle intersect, and the area of the angle is the area bounded by the two legs of the angle.

Your question is incomplete but most probably your full question was:

Only Interaction Angle B and angle C are complementary: If angle B is five times the size of angle C which equation can be used to find the measure of angle C?

5x+x=180

5x = 180

5x+x=9

5x = 90

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The required 84% of the people attending the basketball game supported the home team.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

To find the percentage of people who supported the home team, we need to calculate the proportion of people supporting the home team and convert it to a percentage.

The total number of people attending the game is,
2940 + 560 = 3500.

The proportion of people supporting the home team is,
= 2940 / 3500
= 0.84.

To convert this proportion to a percentage, we multiply it by 100:

= 0.84 × 100 = 84%

Thus, 84% of the people attending the basketball game supported the home team.

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5 flight attendants are required.

The number of flight attendants required on an aircraft is determined by regulatory agencies such as the Federal Aviation Administration (FAA) in the United States and the European Aviation Safety Agency (EASA) in Europe.

The number of flight attendants depends on several factors, including the type of aircraft, the number of passenger seats, the length of the flight, and the number of passenger exits.

The number of flight attendants required can be determined by the following formula:

The minimum number of flight attendants = (N / 50) + 1 where N is the number of passenger seats.

So, for an aircraft with 275 seats and 249 passengers:

(249 / 50) + 1

= 5 flight attendants are required.

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A. the value of x = 6.5( nearest tenth)

B. the value of x = 8.0 ( nearest tenth)

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Sin(tetha) = opp/hypotenuse

cos (tetha) = adj/hyp

tan (tetha) = opp/adj

in the first figure,

Tan22 = x/16

x =tan 22 × 16

x = 6.5(nearest tenth)

in the second figure,

sin42 =x/12

x = sin42× 12

x = 8.0 ( nearest tenth)

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Answer:v = ωr

v = speed in miles per hour (mph)

is the angle's speed in radians per hour.

r is the radius in miles.

(2400-rpm/60 minutes) =

(two radians per rev) Equals __ radians per hour

r=16 inches/2 = (8 inches)

(1/5280 miles/ft) (1/12 feet/in) = ______ miles

v = r = _ miles per hour

Step-by-step explanation:

v = ωr

v = speed in miles per hour (mph)

is the angle's speed in radians per hour.

r is the radius in miles.

(2400-rpm/60 minutes) =

(two radians per rev) Equals __ radians per hour

r=16 inches/2 = (8 inches)

(1/5280 miles/ft) (1/12 feet/in) = ______ miles

v = r = _ miles per hour

The number of cans are 9 and number of frozen food is 4.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, Jayden bought cans of soup and frozen dinners. Each can of soup has 200 mg of sodium and each frozen dinner has 650 mg of sodium. Jayden purchased a total of 13 cans of soup and frozen dinners which collectively contain 4400 mg of sodium.

Let she bought x cans and y frozen food.

Therefore, establishing the equations,

x + y = 13

y = 13-x...(i)

200x + 650y = 4400...(ii)

Put eq(i) in eq(ii)

200x + 650(13-x) = 4400

200x + 8450 - 650x = 4400

450x = 4050

x = 9

Put x = 9 in eq(I)

y = 13-9

y = 4

Hence, the number of cans are 9 and number of frozen food is 4.

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The length of the photo is shorter by 11/16 inches.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Top cutoff length = 5/16 inch

Bottom cutoff length = 3/8 inch

Now,

The length of the photo is shorter by:

= 5/16 + 3/8

= (5 + 6) / 16

= 11/16 inch

Thus,

The photo is shorter by 11/16 inches.

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Answer: 7

Step-by-step explanation:

Combine like terms

7^15/7/^14 = 7

The ratio of action videos to adventure videos is 14:21.

This question uses the concept of ratios, which is a comparison of two or more values. Ratios are used to compare quantities in a variety of situations.

Count the number of action videos and the number of adventure videos. In this example, there are 14 action videos and 21 adventure videos.

Create a ratio by writing the number of action videos first, followed by a colon, followed by the number of adventure videos. In this example, the ratio is 14:21.

Simplify the ratio if needed. In this example, the ratio is already in its simplest form.

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A general solution to the system Ax = 0 in parametric vector form is given by:

X = X_2 * [1 0 1 0 0] + X_3 * [0 1 0 1 0]

The matrix [2 -1 -4 2 6 -3] can be row-reduced to the row-echelon form [2 -1 -4 0 6 -9], which has a pivot in the first, second and fourth columns. This implies that the columns with zero entries in the row-echelon form correspond to free variables in the solution.

Since there are two free variables in the row-echelon form, the solution to the homogeneous linear system Ax = 0 will be in the form of a parametric vector, where X_2 and X_3 are the free variables and X_1, X_4, and X_5 are expressed in terms of X_2 and X_3.

A general solution to the system Ax = 0 in parametric vector form is given by:

X = X_2 * [1 0 1 0 0] + X_3 * [0 1 0 1 0]

where X_2 and X_3 are arbitrary constants. This represents a two-dimensional subspace in R^5, which consists of all linear combinations of the two linearly independent vectors [1 0 1 0 0] and [0 1 0 1 0].

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