An English teacher wants to know the
mean number of words students included
in recent essays. He randomly chooses
20 essays submitted by 180 students. He
records the word count of each one. His
data are shown below.

The magnitude of their sum is 6 units

The formula for calculating the resultant vector is given as:

From the given figure, the resultant is calculated as:

[tex]V=\sqrt{[(4cos45)+(2sin45)]^2+((4sin45)+2cos45)^2} \\V=\sqrt{[2\sqrt{2}+\sqrt{2}]^2 +[2\sqrt{2}+\sqrt{2}}]^2\\V=\sqrt{18+18} \\V= 6 units[/tex]

Hence the magnitude of their sum is 6 units

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Answer:

E. 1 nickel

Step-by-step explanation:

2 ten cent= 20 cent

a quarter is 25 cent

25-20=5

a nickel is 5 cent

Answer:

E.) nickle (5 cents)

Step-by-step explanation:

You give 25 cents (value of a quarter)

2 ten-cent candies is equal to 20 cents:

[tex]2*10=20\\10+10=20[/tex]

Find the difference between what you paid and the actual amount:

[tex]25-20=5[/tex]

You paid an extra 5 cents. Find the answer that has the same value as 5 cents:

A. ) 1 dime

This is wrong because a dime is worth 10 cents, not 5

B.) 1 nickel 2 pennies

this is wrong because a nickle is worth 5 cents and a penny is worthy 1 cent. Add the values, and the change would be 7 cents.

C.) 2 dimes

This is wrong because a dime is worth 10 cents, so 2 dimes would be 20 cents.

D.) 2 nickles

This is wrong because a nickle is worth 5 cents, so 2 nickles would be 10 cents.

E.) 1 nickle

This is correct because a nickle is worth 5 cents, the exact change you should receive.

:Done

Answer:

20

Step-by-step explanation:

A square has four sides and if the perimeter is 80 then you divide the perimeter by four to find the length of each side

Answer:

The length of the arc is 221π/18 ft or 38.55 ft

Step-by-step explanation:

Given

Subtended angle, θ = 17π/18

Radius, r = 13 ft

Required

Length of the arc.

When an angle is given in radians, the length of the arc is calculated using the formula below

Length = rθ

By substituting

Length = 13 * 17π/18

Length = 221π/18

The answer can be left in this form.

But for simplification purpose, I'll solve further.

Taking π as 3.14

Length = 221 * 3.14/18

Length = 693.94/18

Length = 38.552222

Length = 38.55 ft (Approximated).

Hence, the length of the arc is 221π/18 ft or 38.55 ft

Answer: each triangle is 1/3 of the whole

Step-by-step explanation: If you add an upside down triangle to the two triangles below you would get the whole.

three triangles make that whole so one third of the whole is only one of the triangles.

(hope this helps)

Answer:

it is the blue box (not teal)

64 x 7/4 is less than 64 because 7/4 > 1

Hope this helps :)

Answer:

False

Step-by-step explanation:

Please have a look at the attached photo

As we know the shapes of the horizontal cross-sections of the cylinder  are circles congruent with the circle at the base and at the top of the cylinder because they are parallel to each other.

Answer

12 (5 - 3)

Step-by-step explanation:

The greatest common factor is the largest number that will divide both numbers evenly. As an example, 6 is a common factor because it divides both 60 and 36. However, it is not the greatest common factor.

If I break 60 into it's prime factors, I would get 2 * 2 * 3 * 5.

If I break 36 into it's prime factors, I would get 2 * 2 * 3 * 3.

The two number have the factors, 2, 2, and 3 in common.

The greatest common factor is then: 2 * 2 * 3, or 12.

The expression can be factored as:  12 ( 5 - 3)

To factor the expression 60 - 36, we need to find the GCF of the numbers. The GCF is 12, so the factored form is 24.

To factor the expression using the Greatest Common Factor (GCF) 60 - 36, we need to find the largest number that evenly divides both 60 and 36. The GCF of 60 and 36 is 12.

Therefore, we can rewrite the expression as 12 * (5 - 3). Simplifying further, we get 12 * 2 = 24.

So, the factored form of 60 - 36 is 24.

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Answer:

more likely she draws 2 face cards

Step-by-step explanation:

there is a 50% chance of drawing a black card because there are 26/52 black cards but there aee only 12/52 face cards

The value of x of the missing angles is: 45

How to find the missing angle?

A linear pair of angles is a pair of adjacent angles formed when two lines intersect. The two angles of a linear pair are always supplementary, which means their measures add up to 180 degrees.

Some properties of linear pairs of angles include:

The angles in a linear pair are adjacent.

Their non-common arms are opposite rays and form a straight line.

They together form a straight angle.

Two angles forming a linear pair have a common vertex and a common arm. Their non-common sides are opposite rays that form a line.

Thus:

3x + x = 180

4x = 180

x = 180/4

x = 45

Answer:

Second graph

Step-by-step explanation:

In the second graph we can see how the rate of collection decreases steadily at 0 < x < 7.5; at x = 7.5 it becomes constant; and later in the day, there were two short periods (about x = 12.5 and x = 22.5) where the rate of collection has two peaks.

Answer:

54.3m

Step-by-step explanation:

h = distance above sea level

d = distance he can sea above sea level

d = 3.57h

h = 15.21m

d = ?

d = 3.57 × 15.21

d = 54.2997m approximately 54.3m

The person can see up to a distance of 54.3m

Answer:

d = 7.5

Step-by-step explanation:

d = 3.57[tex]\sqrt{h}[/tex]

= 3.57[tex]\sqrt{4.41}[/tex]

= 3.57( 2.1)

= 7.497

d = 7.5!

Answer:

yes I agree with teacher

Step-by-step explanation:

I I think this because 1 people that have a phone and a computer are the highest group and two becauseit seems that most of the class has a phone it also seems that most of the class has a computer

Answer: -8

Step-by-step explanation:

Answer:

x = -8

Step-by-step explanation:

If you multiply -8 by 5 you get -40. Then if you add 65 to -40 you get 25.

Hope this helps.

Answer:

5 is indeed correct

Step-by-step explanation:

The smallest value of x will be 5 that will make the original inequality true.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The solution to an inequality is,

⇒ 5 ≤ x < 9.

Now,

Since, The solution to an inequality is,

⇒ 5 ≤ x < 9.

Hence, The value of x = { 5, 6, 7, 8 }

Thus, The smallest value of x = 5

Therefore, The smallest value of x will be 5 that will make the original inequality true.

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Answer:

On a coordinate plane, a line goes through (0, 3) and (2, 4) and another line goes through (0, 3) and (0.75, 0).

This answer almost coincide with option C. I suppose there was a mistype.

Step-by-step explanation:

The system of equations is formed by:

–x + 2y = 6

4x + y = 3

In the picture attached, the solution set is shown.

The first equation goes through (0, 3) and (2, 4), as can be checked by:

–(0) + 2(3) = 6

–(2) + 2(4) = 6

The second goes through (0, 3) and (0.75, 0), as can be checked by:

4(0) + (3) = 3

4(0.75) + (0) = 3

On a coordinate plane, a line goes through (-6, 0) and (0, 3) and another line goes through (0.75, 0) and (0, 3).

Given :

The system of equation -- (-x + 2y = 6) and (4x + y = 3)

The following steps can be used in order to determine the graph represents the solution set to this system of equations:

Step 1 - Write the given system of equations.

-x + 2y = 6        --- (1)

4x + y = 3         --- (2)

Step 2 - The x-intercept of equation (1) is:

-x + 0 = 6

x = -6

Step 3 - The y-intercept of equation (1) is:

0 + 2y = 6

y = 3

Step 4 - The x-intercept of equation (2) is:

4x + 0 = 3

x = 3/4

Step 5 - The y-intercept of equation (2) is:

0 + y = 3

y = 3

On a coordinate plane, a line goes through (-6, 0) and (0, 3) and another line goes through (0.75, 0) and (0, 3).

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Answer:

a: 5

b: -3

c: -1

d: 1

Step-by-step explanation:

Given the matrix:

A = [4   12

       1   10]

its determinant is: 4*10 - 1*12 = 28

the inverse of A is:

1/28*[10  -12

        -1    4]    

[10/28  -12/28

-1/28    4/28]    

A^-1 = [5/14  -3/7

          -1/28  1/7]

a: 5

b: -3

c: -1

d: 1

Given the matrix:

A = [4   12

      1   10]

its determinant is: 4(10) - 1(12) = 28

Now

the inverse of A is:

1 ÷ 28 × [10  -12

       -1    4]    

[10 ÷ 28  -12 ÷ 28

-1 ÷ 28    4 ÷ 28]    

A^-1 = [5÷  14  -3 ÷ 7

         -1÷  28  1 ÷  7]

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Answer:

speed of commuter bus: 32 km

speed of passenger car  : 48 mph

Step-by-step explanation:

We will use the concept of speed distance and time.

where time = distance / speed

____________________________________________________

Let the speed of commuter bus be x mph

Given that passenger car travels 16 mph faster than commuter bus.

Speed of passenger car if speed of commuter bus is x mph (x+16)mph

Distance traveled by commuter bus  = 56 miles

Time taken by commuter bus  to travel 56 miles = 56/X   (1)

Distance traveled by passenger car  = 84 miles

Time taken by passenger car to travel 84 miles = 84/(X+16)   (2)

__________________________________________

It is given that time taken by both bus and car is same

so equating equation  1 and 2

we have

56/X = 84/(X+16)   (by cross multiplication we have)

=> 56(X+16)  = 84*X

=> 56X + 896 = 84X

=> 896 = 84X - 56 X

=> 896 = 28X

=> X = 896/28 =  32.

Therefore , speed of commuter bus is x mph or 32 km

speed of passenger car  is x+16 mph = (32+16) mph = 48 mph

Final answer:

The passenger car travels at 48 mph, while the commuter bus travels at 32 mph, derived from the fact that they travel the same time but different distances.

Explanation:

To find the speeds of the passenger car and the commuter bus, we can use the formula for distance (distance = speed × time). Since both the bus and the car travel for the same amount of time, we can set up an equation to solve for their speeds based on the distances they travel.

Let x be the speed of the commuter bus in mph. Consequently, the speed of the passenger car would be x + 16 mph. According to the information given:

The bus travels 56 miles.

The car travels 84 miles.

Since they travel for the same time t, we have:

Bus: 56 miles = x × t

Car: 84 miles = (x + 16 mph) × t

Dividing the mileage of the car by the bus gives us:

[tex]\(\frac{84}{56} = \frac{(x + 16)t}{xt}\)[/tex]

[tex]\(1.5 = \frac{x + 16}{x}\)[/tex]

Multiplying by x to get rid of the fraction and then solving for x provides:

1.5x = x + 16

0.5x = 16

x = 32 mph

This means the bus travels at 32 mph and the passenger car travels at:

32 mph + 16 mph = 48 mph

Therefore, the speed of the passenger car is 48 mph and the speed of the commuter bus is 32 mph.

Answer:

12x² - 2x - 30

Step-by-step explanation:

(3x - 5)(4x + 6)

12x² + 18x - 20x - 30

12x² - 2x - 30

The Multiplication of the binomials (3x - 5) and (4x + 6) will be 12x² - 2x - 30. Then the correct option is D.

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

The binomails are given below.

(3x - 5) and (4x + 6)

Multiply the binomials (3x - 5) and (4x + 6), then we have

⇒ (3x - 5) · (4x + 6)

⇒ 3x · (4x + 6) - 5 · (4x + 6)

⇒ 12x² + 18x - 20x - 30

⇒ 12x² - 2x - 30

The Multiplication of the binomials (3x - 5) and (4x + 6) will be 12x² - 2x - 30. Then the correct option is D.

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Answer:

8^1

Step-by-step explanation:

Answer:

1) 3 and 4

2) B

Step-by-step explanation:

sorry if i am wrong

Answer:

the model for the height, h, of the chair at a function of time is [tex]y = -20 \times sin (\frac{2\pi }{15} \times t + \frac{\pi }{2} ) + 26[/tex]

Step-by-step explanation:

To answer the question, we note that the height of the Ferris will varies proportionately to the angle of rotation, hence we can model the height according to he sine function as follows;

y = a·sin(b·x+c) + d

Where: a = Amplitude = Maximum displacement = r = 20 ft

or [tex]a = \frac{maximum - minimum}{2} = \frac{44 - 4}{2} = 20 \, ft[/tex]

The period,  [tex]\frac{2\pi }{b}[/tex] = Time for one complete revolution, for a Ferris wheel making 4 revolutions per minute, we have

Period = 1 minute/4 = 15 seconds

Therefore,  [tex]\frac{2\pi }{b}[/tex] = 15 seconds or [tex](b =\frac{2\pi }{15})[/tex]

d = the vertical shift is given by minimum + amplitude or maximum - amplitude = 6 + 20 = 26 ft

c = Phase shift since we want the chair to be at the minimum at t = 0 we put c = π/2

x = Independent variable, which in the case of the question is time, t

Therefore, the model for the height, h, of the chair at a function of time is as follows

[tex]y = -20 \times sin (\frac{2\pi }{15} \times t + \frac{\pi }{2} ) + 26[/tex]

i.e. y = -20×sin(2π/15 + π/2) + 26.

Final answer:

To model the height of the chair as a function of time on a Ferris wheel, use the equation h(t) = 20 × cos((8π/60)t) + 6, where t is in seconds and h(t) is in feet.

Explanation:

To write a model for the height, h, of the chair as a function of time, t, for a Ferris wheel with a radius of 20 feet and a rotation rate of 4 revolutions per minute, we must consider the motion of the wheel. Since the Ferris wheel completes one rotation in 15 seconds (60 seconds/4 minutes), the chair's height above the ground will depend on the cosine of the angular position of the chair. Including the initial condition of the chair being 6 feet above the ground at its lowest point, the mathematical model will be:

h(t) = 20 × cos(ωt + ϕ) + 6

where angular velocity ω is calculated from the rotation rate (4 revolutions per minute) and phase shift ϕ accounts for the initial position. Since t = 0 corresponds to the lowest point, ϕ is 0 degrees or 0 radians (cos(0) = 1). The angular velocity in radians per second is:

ω = 2π × rotation rate = 2π × 4 / 60 = 8π/60 rad/s

Thus, the final equation for the height of the chair as a function of time is:

h(t) = 20 × cos((8π/60)t) + 6

where t is in seconds and h(t) is in feet.

Answer:

Mr. Prieto can buy 6 pizzas

Step-by-step explanation:

Cost of 5 soda's = 5 * 2  = $ 10

Remaining amount with him after buying 5 soda's= 94 - 10 = $ 84

Number of pizza's = Remaining amount/cost of 1 pizza

[tex]=\frac{84}{14}[/tex]

=  6 pizzas

Answer:

he can buy 6 pizzas

Step-by-step explanation:

5 x 2 = 10

94-10 = 84

84 divided by 14 = 6

he can buy 6 pizzas.

Answer:

B) x = 1/4y²

Step-by-step explanation:

I graphed x = 1/4y² below and it matched the graph that you gave.

Answer:

y= (0.25)1/x-4 +3

Step-by-step explanation:

You just multiply the compression by mx. then you would add the translation (-4 since it goes to the right). and +3 since it moves up on the y axis

Answer:

The graph of g(x) = (x + 2)2 is a translation of the

graph of f(x) ✔ left by 2 units.

The graph of h(x) = (x − 3)2 is a translation of the

graph of f(x) ✔ right by 3 units.

100% Correct

Step-by-step explanation:

Answer: 64 years old

Step-by-step explanation:You subtract 2082 by 2018 to get the sum of 64

Answer:

64/63

Step-by-step explanation:

It depends on what day it is in 2082 however the calculation should be simple...

2082-2018=64

If it is before September 12th in 2082, then they would be 63 because their 64th birthday would be on September 12th!

Hope this helps!