a group of students played a game in which they earned points for answering questions correctly. the following dotplot shows the total number of points earned by each student.

The angle is changing at the rate  [tex]\frac{18}{\pi }[/tex] when a is 10m from the intersection and b is 20m from the intersection.

In this problem, all three variables (x, y & z) are changing with respect to time.

x = 20 and y = 10

[tex]\frac{dx}{dt} = -1[/tex]

[tex]\frac{dy}{dt} = 2[/tex]

[tex]tan[/tex](θ)=[tex]\frac{y}{x}[/tex]

take derivative :

[tex]tan[/tex] (θ) = [tex]\frac{y}{x}[/tex]

[tex]sec^{2}[/tex](θ) [tex]\frac{d\alpha }{dt}[/tex] = [tex]\frac{x\frac{dy}{dt} - y\frac{dy}{dt} }{x^{2} }[/tex]

Substitute the values :

[tex]sec^{2} \alpha (\frac{d\alpha }{dt} ) = \frac{20 . 2 - 10. (-1)}{20^{2} }[/tex]

solve the equation :

[tex]\frac{5}{4} (\frac{d\alpha }{dt} ) = \frac{20 . 2 - 10. (-1)}{20^{2} }[/tex]

[tex]\frac{5}{4} (\frac{d\alpha }{dt} ) = \frac{50}{400 }[/tex]

[tex](\frac{d\alpha }{dt} ) = \frac{50}{400 } * \frac{4}{5}[/tex]

[tex](\frac{d\alpha }{dt} ) = \frac{1}{10 }[/tex] radian/sec

[tex](\frac{d\alpha }{dt} ) = \frac{18}{\pi } degrees/sec[/tex]

This means that the angle is increasing as a gets closer to the intersection and b gets moves away from the intersection.

So, The angle is changing at the rate  [tex]\frac{18}{\pi }[/tex] when a is 10m from the intersection and b is 20m from the intersection.

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Let x be the number of miles the driver still has to travel.

The driver traveled 120 + 120/4 + 120/42/3 = 120 + 30 + 40 = 190 miles.

So the remaining distance is x + 190 = 55 + 1 2/3 * x

Multiplying both sides by 3/2 gives 3/2x + 3/2190 = 3/255 + 3/2*x + x

This simplifies to x = 190.

Therefore, the driver still has to travel 190 miles.

Answer:

130 feet

Step-by-step explanation:

Your have to find the perimeter. Perimeter of a shape is the distance around the shape

The value of a + c in the equation is -5

From the question, we have the following parameters that can be used in our computation:

y = ax² + 5x + c

x- intercepts at 1 and 3

This means that

When x = 1 and 3, the value of y is 0

So, we have

When x = 1:

a(1)² + 5(1) + c = 0

a + 5 + c = 0

a + c = -5

When x = 3:

a(3)² + 5(3) + c = 0

9a + 15 + c = 0

9a + c = -15

So, we have

a + c = -5

9a + c = -15

Hence, the value of a + c is -5

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[tex]Answer:\ \sqrt[12]{16^{11}}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\16^\frac{1}{4} *16^\frac{2}{3}=\\\\16^{\frac{1}{4} +\frac{2}{3} }=\\\\16^\frac{1*3+2*4}{4*3} =\\\\16^\frac{3+8}{12}= \\\\16^\frac{11}{12}= \\\\\sqrt[12]{16^{11}}[/tex]

Answer:

27.8miles

first we add 37 and 17=54

then multiple it with 20 and divide by 100 so we can change it to percent

so it will be 10.8 miles and then we add it with 17 miles =27.8 miles

The equation that represents one sixth of the number n is given as follows:

n/6.

The equation is a fraction of an amount. A fraction has the following format:

x/y.

In which:

One sixth is a fraction in which the numerator is one and the denominator is six, as follows:

1/6.

To obtain one six of a number n, the above fraction is multiplied by n, as follows:

n x 1/6.

When two fractions are multiplied, the numerators multiply themselves, as do the denominators, hence the product is given as follows:

n x 1/6 = n/6.

Hence the equation that represents one sixth of the number n is given as follows:

n/6.

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The equation that represents twenty-five is one-sixth of the number n is;

25 equals n over 6

We want to find the equation that represents twenty-five is one-sixth of the number n.

Now, to say that twenty-five is one-sixth of the number n simply means that twenty five is equal to one-sixth of the number n.

Expressing this algebraic statement as an algebraic expression gives us; 25 = ¹/₆n

So we can see that this represents the given algebraic statement and as such looking at the options, we can conclude that the correct one is Option A.

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Complete question is;

Which equation represents twenty-five is one-sixth of the number n?

25 equals n over 6

25 = 6n

6 = 25n

one sixth equals n over 25

The values of v and w are 12 and 20 respectively which makes ΔPQR ≅ ΔIJK (Congruent right triangles).

Two triangles are said to be congruent if their shape and size are the same. If two right triangles are said to be congruent, then they must have equal measures for their corresponding sides and angles.

The given two right triangles are congruent. I.e., ΔPQR ≅ ΔIJK

So, their corresponding sides QR = IJ and PR = IK, and the corresponding angle ∠Q = ∠J.

But we have QR = w - 1; IJ = 3w - 41; PR = 6v-12; IK = 5v

So, on equating them, we get

QR = IJ ⇒ w - 1 = 3w - 41

⇒ 3w - w = 41 - 1

⇒ 2w = 40

∴ w = 20

And

PR = IK ⇒ 6v-12 = 5v

⇒ 6v - 5v = 12

∴ v = 12

Thus, the value of v = 12 and w = 20.

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Answer:

  10 minutes

Step-by-step explanation:

You want to know how much longer 2/3 hour is than the sum of 1/5 hour and 3/10 hour.

Each fraction of an hour can be expressed in minutes:

The time difference of interest is ...

  (2/3 - 1/5 -3/10) h = (40 -12 -18) min = 10 min

Jacob spent 10 minutes more reading than doing housework.

Answer:

1. 6v+8

2.5x+6y

the amount of time taken by each of 10 students in a class to complete an exam is an example of quantitative data.

Quantitative data is numerical data which can be used to measure and quantify a certain phenomenon. In this example, the amount of time taken by each of the 10 students in a class to complete an exam is a numerical value, and it can be used to measure and quantify the performance of the students in the exam. Thus, this is an example of quantitative data.

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The tangential and normal components of the acceleration when s = 10 m is 40 m/s^2 and 8 m/s^2 respectively.

In the given question, a car is travelling along the road with a speed of 2s m/s, where s is in meters.

We have to determine the tangential and normal components of the acceleration when s = 10 m.

Speed (v) = 2s  

Motion is circular so, Radius of circle = 50m

Tangential acceleration = dv/dt

Tangential acceleration = d(2s) / dt

Tangential acceleration = 2(ds)/dt

Tangential acceleration = 2v

Tangential acceleration = 2(2s)

Tangential Acceleration = 4s

As given s = 10 m

Tangential acceleration = 4 x 10

Tangential acceleration  = 40 m/s^2

Normal acceleration = v^2/ r

Normal acceleration = 4s^2/r

Normal acceleration = {4 x 10^2}/50

Normal acceleration = {4 x 100}/50

Normal acceleration = 400/50

Normal acceleration = 8 m/s^2

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The complete question is:

A car is travelling along the road with a speed of 2s m/s, where s is in meters. Determine the tangential and normal components of the acceleration when s = 10 m. Treat the car as a particle

Answer:

Step-by-step explanation:

You want the number of months and the total amount paid when you pay off a credit card debt of $1367.90 with 9.5% APR at the rate of $400 each month.

The amount of the payment that goes to interest each month is the monthly rate (9.5%/12) multiplied by the remaining balance. The first month's interest is ...

  $1367.90 × 0.095/12 = $10.8292 ≈ $10.83 . . . . rounded to cents

Then the balance is reduced by ...

  $400 -10.83 = $389.17

so it becomes ...

  $1367.90 -389.17 = $978.73 . . . . . balance after first payment

These calculations are repeated for subsequent payments. It is convenient to let a spreadsheet do them. (It can round the interest for you.) The results are shown in the attachment.

The negative balance for month 4 reflects the overpayment that a payment of $400 would be. The actual month 4 payment is the previous balance ($191.12) together with the interest due on that ($1.51), so is $192.63.

The total repaid is the sum of interest charges ($24.73) and the initial balance ($1367.90). That is, you paid off the initial balance and the interest due.

You repaid a total of $1392.63 in 4 months.

__

Additional comment

The steps for computing the total repaid are ...

Note, there are formulas for the payoff time and the total repaid. However, they do not take into account rounding of intermediate values, and they presume the last payment is made partway through the month. In short, it only gives an approximation of the amount repaid.

By listing actual amounts, rounded to cents, the actual amount repaid can be figured with no error. A spreadsheet is very helpful for that.

The time is 8 seconds to reach the bottom of a 252-foot-long hill.

What is a quadratic equation?

Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

We have,

riding at a speed of 18mi/h when she starts down a long hill,

The distance she travels in feet can be modeled by d(t) = 4t² + 18t,

252 foot - long hill

I attempted the problem and I got 12.5 seconds.. but im not sure if im right

Use the quadratic formula to find t.

d(t) = 4t² + 18t,

d(t)=400

4t² + 18t =400

4t² + 18t -400=0          

2t²+9t-200=0          

x= 8; -25/2  

Hence, the time is 8 seconds to reach the bottom of a 252-foot-long hill.

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The rate of change of the height of the top of the ladder above the ground at the instant when the base of the ladder is 30 ft. from the base of the building is -3 ft./min.

The rate of change of the height of the top of the ladder above the ground at the instant when the base of the ladder is 30 ft. from the base of the building is -3 ft./min. This rate takes into account the fact that the ladder is slipping at a rate of 3 ft./min. As the base of the ladder is slipping away from the building, the top of the ladder is moving down, hence the negative rate of change. This rate of change will remain the same until the base of the ladder has slipped the full 50 ft. from the base of the building. At this point, the rate of the change of the height of the top of the ladder will be 0, since the ladder will no longer be slipping.

The rate of change can be calculated as follows:

Rate of change = Change in height / Change in time

Change in height = Initial height - Final height

Initial height = 50 ft.

Final height = 50 ft. - 30 ft. = 20 ft.

Change in time = 30 ft. / 3 ft./min. = 10 min.

Rate of change = (50 ft. - 20 ft.) / 10 min. = -3 ft./min.

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A line with a slope of 2 and a point at (4,3) satisfies the equation y = 2x - 5.

Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

In general, a straight line has the equation y = mx + c, where m denotes the gradient and y = c denotes the point at which the line intersects the y-axis. do s s., s. s s.. s... s.. A straight line with a gradient of m and an intercept of c on the y-axis has the equation y = mx + c.

Here,

given: slope of 2/3

the line that passes through the point (-3,4)

using formula

=>  y = mx + c.

=> (y-y') = m(x-x') + c

=> (y-4) = 2/3(x+3) + c

=> y = 2x - 5.

Thus equation comes out to be  y = 2x - 5..

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An output of a causal system is that whose inputs are just the past and the present. The outcome of a noncausal system depends on the upcoming inputs.

We will examine the connection between output as well as inputs to determine whether the provided system is causal or not.

Thus, there isn't a single example of an ontologically non-causal system, or one of a truly fundamental nature about which we can be sure, that we are aware of.

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Answer:

1. 80

2. runway 18

Step-by-step explanation:

The cost of the book before the sales tax is $31

From the question, we have the following parameters that can be used in our computation:

Sales tax = 5%

Cost of book = $32.55 after tax

The cost of the book before tax is calculated using the following equation

Cost of book after tax = Cost of book before tax * (1 + Sales tax)

Substitute the known values in the above equation, so, we have the following representation

32.55 = Cost of book before tax * (1 + 5%)

Evaluate the sum

So, we have the following representation

32.55 = Cost of book before tax * (1.05)

Divide both sides by 1.05

Cost of book before tax = 31

Hence, the cost is $31

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The probability that two or more of the events will occur is 0.683594.

The probability that two or more of the events will occur is equal to 1 minus the probability that none of the events will occur. Since the probability of each event occurring is 0.25, the probability that none of the events will occur is (1 - 0.25) * (1 - 0.25) * (1 - 0.25) * (1 - 0.25) = 0.316406. Therefore, the probability that two or more of the events will occur is 1 - 0.316406 = 0.683594.

Alternatively, you can find the probability that two or more of the events will occur by adding up the probabilities of each of the ways that two or more of the events can occur.

There are four ways that two events can occur (for example, event A and event B), six ways that three events can occur (for example, event A, event B, and event C), and four ways that all four events can occur.

Thus, the probability that two or more of the events will occur is (4 * 0.25 * 0.25) + (6 * 0.25 * 0.25 * 0.25) + (4 * 0.25 * 0.25 * 0.25 * 0.25) = 0.683594, which is the same result as before.

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Thee volume of the cone has a value of 1, 739. 60 cubic feet

The formula for calculating the volume of a cone is expressed as;

V = πr²h/3

Where;

From the information given, we have the values as;

Diameter = 19

But radius = Diameter/2

Now, radius = 18. 7/2 = 9.35 ft

Substitute the values into the formula

Volume = 3. 142( 9.35)² × 19/3

Find the value of the square

Volume = 3. 142(87. 42) × 6. 3

Multiply the values

Volume = 1, 739. 60 cubic feet

Hence, the value is 1, 739. 60 cubic feet

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By solving for the number of employees, there were 70 employees at the party.

An equation is a mathematical statement that shows that two expressions are equal. An equation typically consists of two sides, with an equals sign (=) in between.

A linear equation is an equation in which the highest power of the variable is 1. In other words, a linear equation is an equation that can be written in the form:

ax + b = 0

where a and b are constants and x is the variable.

To find out how many employees attended the party, you can set up the following equation:

Number of employees * $30 per employee = $1000 for space + $850 for food + $250 for decorations

You can then solve for the number of employees by dividing both sides of the equation by $30 per employee:

Number of employees = ($1000 for space + $850 for food + $250 for decorations) / $30 per employee

= $2100 / $30

= 70 employees

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The 12-foot ribbon is cut into pieces three-quarters of a foot long, then 16 pieces can be made.

What is a three-quarter length?

The fraction 3/4 or three-quarters means 3 parts out of 4. The upper number, 3, is called the numerator and the lower number, 4, is the denominator.

We have a 12-foot ribbon and you are making a cut into pieces three-quarters  (3/4-foot)  of a foot long sections, and you want to know many times you can do that here.

So, the number of pieces = (Length of the ribbon  ÷ Length of each piece)

You just need to take 12 and divide it by 3/4, to see how many sections you can have.

12 ÷ 3/4

Change division to multiplication by taking the reciprocal (the flipping) of the second number:

= (12 * 4) / 3

= 48/3

= 16

To multiply fractions, multiply straight across on top and straight across on bottom:

Hence, the 12-foot ribbon is cut into pieces three-quarters of a foot long, then 16 pieces can be made.

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(a) The net force acting on this object at t = 1 s is 88 N.

(b) The net force acting on this object at t = 4 s is 0 N.

(c) The net force acting on this object at t = 7 s is -13.2 N.

In the given question, the velocity graph of a 2.2 kg object as it moves along the x-axis.

The given mass = 2.2

a) We have to find the net force acting on this object at t = 1 s.

At t=1 s

Slope of a graph = acceleration

Acceleration = slope

Acceleration = 12/3

Acceleration = 4 m/s^2

Net force, F = m*a

F = 22*4

F = 88 N

So the net force is 88 N.

b) We have to find the net force acting on this object at t = 4 s.

At t = 4 s

Acceleration, a=slope of graph

a = ( 12 - 12) /(3 - 0)

a = 0 m/s^2

The net force , F = m * a

F = 2.2 * 0 = 0 N

c) We have to find the net force acting on this object at t = 7 s.

At t = 7 s

Acceleration, a = ( 0 - 12 ) / (8 - 6)

a = - 6 m/s^2

The net force, F = m * a

F = 2.2 * (-6)

F = -13.2 N

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The complete question is:

The figure(figure 1) shows the velocity graph of a 2.2 kg object as it moves along the x-axis.

(a) What is the net force acting on this object at t = 1 s.

(b) What is the net force acting on this object at t = 4 s.

(c) What is the net force acting on this object at t = 7 s.

Answer: The median of the shoe sizes is 6.5. If a shoe size of 4 is added to the data, the median will not change because it is based on the middle value in the data set and the addition of a value of 4 will not affect the middle value.

Step-by-step explanation:

The item Marco will buy more between frozen yogurt and frozen custard given his budget and cost of each item is frozen yogurt.

Hence, a 3-ounce cup of frozen yogurt cost less than a 3-ounce cup of frozen custard.

Therefore, Marco will buy more frozen yogurt than frozen custard because of the cheap price.

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Answer:

Dilation

Step-by-step explanation:

The  a'b'c'    figure is larger than the original a b c

To solve this equation, you can use the property of equality, which states that whatever you do to one side of the equation, you must also do to the other side.

To isolate the variable "y," you can divide both sides of the equation by 4:

4y / 4 = 164 / 4

This simplifies to:

y = 41

Therefore, y equals 41.

Answer:

[tex] \sf \: a) \: 41[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of y.

The equation is,

→ 4y = 164

Then the value of y will be,

→ 4y = 164

→ y = 164/4

→ [ y = 41 ]

Hence, the value of y is 41.

Step-by-step explanation:

a/b × c/d = (a×b)/(c×d)

so,

-4/9 × 11/12 = (-4×11) / (9×12) = -44/108 = -11/27