The response to a question has three alternatives: A,B , and C. A sample of 120 responses provides 54 A ,24 B, and 42C . Show the frequency and relative frequency distributions (use 2 decimal for the relative frequency column)
Class Frequency Relative Frequency
A
B
C

Answer:

A

Step-by-step explanation:

As x gets larger, the y-values became more and more negative. This means that as x approach infinity, y approaches negative infinity.

On the other side, as x gets smaller, the y-value also gets more and more negative. This means as x approaches negative infinity, y also approaches negative infinity.

This is shown in answer option A.

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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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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The algebraic expression is 2 + y.

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,

Sum of 2 and y

This can be written as,

2 + y

Thus,

The expression is 2 + y.

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The probability of randomly drawing a vowel is 2/7, option C is correct.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given a set of cards spell P, E, R, C, E, N, T, S

total cards = 8

so total outcome = 8

to find  the probability of randomly drawing a vowel,

set contains 2 vowels,

a favorable outcome for vowel = 2

probability =  favorable outcome/total outcome

P(vowel) = 2/7

Hence option C is correct.

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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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Just put your name on the check's back to complete a blank endorsement. The teller at the bank will ask if you want to cash it or deposit it after you arrive.

The three types of endorsements available for checks are blank, special, and restriction. When the payee signs their name on the check's top back, it becomes a blank endorsement.

To accomplish this, you just sign the check on the back and inform the bank teller whether you want to deposit it into a certain account or cash it. When depositing a check using mobile deposit or an ATM, a blank endorsement is also acceptable.

To be accepted for deposit, a check needs to have an endorsement on the back. Therefore, always add your signature to the document right before bringing it to the bank in the place provided next to the X.

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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

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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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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Answer: 7

Step-by-step explanation:

Combine like terms

7^15/7/^14 = 7

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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The cost to rent each chair and table is $7.2 and $6.6 respectively.

Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables that satisfies all such equations. This implies that the simultaneous equations have a common solution.

Let chairs = c

Let tables = t

5c + 3t = 36 --- 1

2c + 6t = 54 --- 2

From equation 2

2c + 6t = 54

c = 27 - 3t

Substitute c in equation 1

5(27 - 3t) = 36

135 - 15t = 36

135 - 36 = 15t

t = 99/15

t = $6.6

c = 27 - 3(6.6)

c = 27 - 19.8

c = $7.2

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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 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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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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The length of side x obtained using trigonometric ratios is 5 units

Trigonometric ratios are expressions that indicate the relationship between the lengths of two of the sides of a right triangle and the interior angles of the right triangle.

The specified triangle is a right triangle, therefore, if the interior angles, and the length of one of the sides is known, the lengths of the other sides can be found.

The right triangle is a 30°-60°-90° right triangle

The length of the hypotenuse side = 10

The length of the leg with measurement x, can therefore, be found using trigonometric ratios follows;

sin(θ) = Opposite/Hypotenuse

sin(30°) = x/10

Therefore; x = 10 × sin(30°)

x = 10 × 0.5 = 5

The length of the side x in the right triangle is 5 units

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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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Corn's market value  in 5 days will  be 64273.95.

What is exponential decay function?

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

The form of the general exponential decay is:

f(x) = A*(r)ˣ

r is rate

A=initial value

Exponential decay:

y=a(1-r)ᵗ

a= initial value, r in decimal = 0.07, t = 5 days

y= 92389 (1-0.07)⁵

y=  92389(0.93)⁵

y= 64273.95

Corn's market value  in 5 days will  be 64273.95

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The remaining ratios for the angle are:

sin θ = 2/√7

cos θ = √3 /√7

tan θ = 2/√3

sec θ = √7 /√3

cot θ = √3 /2

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. Trigonometry is used to determine the lengths of the sides of a triangle when one or more angles and/or the lengths of one or more sides are known.

The remaining ratios are as follows

csc θ = √7 /2

Since sin θ = 1/cscθ

sin θ = 2/√7

Remember: sin θ= opposite/hypotenuse  = 2/(√7)

adjacent =  √((√7)² - 2²) = √3

cos θ = √3 /√7   (adjacent/hypotenuse)

tan θ = 2/√3  (opposite/adjacent)

sec θ = 1/cos θ

sec θ = √7 /√3

cot θ = 1/tan θ

cot θ = √3 /2

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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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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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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.

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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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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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 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 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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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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