In a survey at a local university 32% of students say they get less than the recommended eight hours of sleep per night. In a group of 3330 students how many would you expect to get 8 or more hours?

Here,

the initial point of vector u(x1,y1)=(-7,2)

the final point of vector u (x2,y2)=(11,5)

so the component of vector u(x,y)=(x2,y2)-(x1,y1)

=(11+7,5-2)=(18,3)

according to the question, the magnitude of vector is thrice the magnitute of vector u and is opposite ot the ditecrion of vector u.

so the component of vector v is -3(x,y)

=-3(18,3)=(-54,-9)

Answer:

y ≈ - 3.8

Step-by-step explanation:

Given the 2 equations

5x + 2y = 21 → (1)

- 2x + 6y = - 34 → (2)

To eliminate the terms in x , multiply (1) by 2 and (2) by 5

10x + 4y = 42 → (3)

- 10x + 30y = - 170 → (4)

Add (3) and (4) term by term

(10x - 10x) + (4y + 30y) = (42 - 170)

34y = - 128 ( divide both sides by 34 )

y ≈ - 3.8 ( to the nearest tenth )

Answer:

20,944 years

Step-by-step explanation:

The formula you use for this type of decay problem is the one that uses the decay constant as opposed to the half life in years.  We are given the k value of .00012.  If we don't know how much carbon was in the bones when the person was alive, it would be safer to say that when he was alive he had 100% of his carbon.  What's left then is 8.1%.  Because the 8.1% is left over from 100% after t years, we don't need to worry about converting that percent into a decimal.  We can use the 8.1.  Here's the formula:

[tex]N(t)=N_{0} e^{-kt}[/tex]

where N(t) is the amount left over after the decay occurs, [tex]N_{0}[/tex] is the initial amount, -k is the constant of decay (it's negative cuz decay is a taking away from as opposed to a giving to) and t is the time in years.  Filling in accordingly,

[tex]8.1=100e^{-.00012t}[/tex]

Begin by dividing the 100 on both sides to get

[tex].081=e^{-.00012t}[/tex]

Now take the natural log of both sides.  Since the base of a natual log is e, natural logs and e "undo" each other, much like taking the square root of a squared number.

ln(.081)= -.00012t

Take the natual log of .081 on your calculator to get

-2.513306124 = -.00012t

Now divide both sides by -.00012 to get t = 20,944 years

Answer:

4 hours

Step-by-step explanation:

0:8

6:12

12:16

18:20

24:24

Answer: 4 hours

Step-by-step explanation:

Answer:

Pemdas

Step-by-step explanation:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

You go from left to right and solve in the order called Pemdas.

To use a system of equations to find the solution algebraically, follow these steps: identify the unknowns and knowns, write down the equations, solve for one variable, substitute the expression into the other equation(s), solve for the remaining variables, and check your answer(s) for reasonableness.

1. Identify the unknowns and knowns.

2. Write down the equations that represent the given information.

3. Solve one of the equations for one variable in terms of the other.

4. Substitute this expression into the other equation(s), replacing the variable.

5. Solve the resulting equation(s) to find the value(s) of the remaining variable(s).

6. Check your answer(s) to ensure they make sense in the context of the problem.

Answer:

1.29 s

Step-by-step explanation:

h = -490t² + 1260t

810 = -490t² + 1260t

490t² - 1260t + 810 = 0

49t² - 126t + 81 = 0

(7t - 9)² = 0

7t - 9 = 0

t = 9/7

t ≈ 1.29

To find the time when the rocket is at a height of 810 cm, set the equation -490t^2 + 1260t equal to 810 and solve for t using the quadratic formula. The quadratic formula will give two solutions: choose the positive solution as we cannot have negative time.

We are given the equation h=-490t^2+1260t to represent the height of the rocket. We're also told that the height h is 810 cm and we are asked to solve for time t when this is the case.

To find the time when the rocket's height is 810 cm, we can first set the equation equal to 810: -490t^2 + 1260t = 810.

We can then simplify that to -490t^2 + 1260t - 810 = 0 and solve for t using the quadratic formula t = [-b ± sqrt(b² - 4ac)] / 2a, where a = -490, b = 1260 and c = -810.

This will give us the two points in time at which the rocket is at a height of 810 cm. Remember, the negative solution is likely extraneous as we cannot have negative time, so you should consider only the positive solution.

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Answer:

Step-by-step explanation:

If the sides form a right triangle, the sum of the squares of the shorter two sides will equal the square of the longest side.

1. 10.5^2 + 20.8^2 = 23.3^2 . . . . . true algebraic statement; right triangle

__

2. 6^2 +20.1^2 = 440.01 ≠ 22.9^2 = 524.41 . . . . . this is an obtuse triangle

Answer:

The jar of jelly that costs $2.32 for 16 ounces is the better buy, because the unit rate is less

Step-by-step explanation:

step 1

Find the units rate

One jar of jelly costs $2.32 for 16 ounces

so

The unit rate is equal to [tex]\frac{2.32}{16}= 0.145\frac{\$}{ounce}[/tex]

Another jar costs $2.03 for 13 ounces

so

The unit rate is equal to [tex]\frac{2.03}{13}= 0.156\frac{\$}{ounce}[/tex]

step 2

Compare the unit rates

[tex]0.145\frac{\$}{ounce} < 0.156\frac{\$}{ounce}[/tex]

therefore

The jar of jelly that costs $2.32 for 16 ounces is the better buy, because the unit rate is less

The jelly that costs $2.32 for 16 ounces is the better buy. The unit rate for this jar of jelly is $0.145 or approximately $0.15 per ounce. The unit rate for the second jar of jelly is $0.156 or approximately $0.16 per ounce

Answer:

  3/4

Step-by-step explanation:

1/2 the deck is red cards.

1/4 of the deck is spades.

There are no spades that are red cards, so the probability of drawing a red card or a spade at random from a well-shuffled deck is ...

  1/2 + 1/4 = 3/4

Answer:

  D.  The graph of g(x) is shifted 2 units up.

Step-by-step explanation:

Adding 2 to the y-coordinate of a point shifts it up by 2 units.

___

The graph of f(x) is all points (x, f(x)). When you add 2 to f(x), you make the graph of g(x) be all points (x, g(x)) = (x, f(x)+2). That is all of the points on the original graph are shifted up by 2 units.

Answer:

[tex]200in^3[/tex]

Step-by-step explanation:

To solve this, we are using the formula for the volume of a rectangular prism:

[tex]V=whl[/tex]

where

[tex]w[/tex] is the width of the base

[tex]l[/tex] is the length of the base

[tex]h[/tex] is the height of the prism

We know from our problem that the height is 10 inches. The length of the base is 6 inches. The width of the base is 5 inches.

Replacing values

[tex]V=(5in)(10in)(6in)[/tex]

[tex]V=300in^3[/tex]

Now, to find 2/3 of that volume, we just need to multiply it by 2/3

[tex]\frac{2}{3} V=\frac{2}{3} 300in^3[/tex]

[tex]\frac{2}{3} V=200in^3[/tex]

We can conclude that 2/3 of the volume of the vase is 200 cubic inches.

Answer:

y = 3 • ± √2 = ± 4.2426

Step-by-step explanation:

2y2 -  36  = 0  

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  2y2 - 36  =   2 • (y2 - 18)  

Trying to factor as a Difference of Squares :

3.2      Factoring:  y2 - 18  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =  

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.  

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 18 is not a square !!  

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step  3  :

 2 • (y2 - 18)  = 0  

Step  4  :

Equations which are never true :

4.1      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.2      Solve  :    y2-18 = 0  

Add  18  to both sides of the equation :  

                     y2 = 18  

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     y  =  ± √ 18  

Can  √ 18 be simplified ?

Yes!   The prime factorization of  18   is

  2•3•3  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 18   =  √ 2•3•3   =

               ±  3 • √ 2  

The equation has two real solutions  

These solutions are  y = 3 • ± √2 = ± 4.2426

Answer:

It is 15.

Step-by-step explanation:

The answer is:

The correct option is:

A. $0.49

From the statement, we know that the iHome is used on average three hours a day, and we are asked to find the cost for a week, so first, we need to calculate the total hours that the iHome is used for, and then, calculate the kilowatt-hour consumption rate.

[tex]TotalTime_{week}=3\frac{hours}{day} *7days=21hours[/tex]

[tex]TotalEnergyConsumption_{week}=180watt*21hours=3780watt.hour[/tex]

Now, we must remember that:

[tex]1Kilowatt=1000watts[/tex]

So,

[tex]3780watts=3780watts.hour*\frac{1KiloWatt}{1000watts}=3.78KiloWatt.hour[/tex]

Then, calculating the cost, we have:

[tex]TotalCost_{week}=0.13\frac{dollar}{killowat.hour}*3.78killowat.hour=0.49(dollar)[/tex]

Hence, we have that the correct option is:

A. $0.49

Have a nice day!

The lengths of the legs of a similar triangle to the one Juan drew, which has leg lengths 6cm and 8cm, could be 12 cm and 16 cm because the sides of similar triangles are proportional.

Juan's right triangle has leg lengths of 6 centimeters and 8 centimeters. To find a similar right triangle, we need ratios of corresponding sides to be equivalent or proportional. As these are right triangles, we can use the Pythagorean theorem which states that a² + b² = c². If the original triangle has sides 6 cm and 8 cm, then triangle with proportional sides could have sides that are multiple of these dimensions, such as 12 cm (which is 6cm x 2) and 16 cm (which is 8cm x 2). So, one example of a similar triangle could have leg lengths of 12 cm and 16 cm.

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Answer:

B. 28.26

Step-by-step explanation:

First you have to find the circumference:

R²= 3²=9

Then you multiply your circumference by 3.14 to get you answer:

9·3.14=28.26

Answer: 4.10s

t=2Vi*sin(theta)/g

Vi=initial velocity=35m/s

g=9.8m/s^2

t=2*35*sin(35)/9.8=4.10s

Answer:

4.1 seconds to the nearest tenth.

Step-by-step explanation:

The vertical component of the velocity = 35 sin 4.935 m/s.

The relation between the height (h) of the projectile and time is given by:

h = ut + 1/2 g^2   where u = initial velocity, t = the time and g = acceleration due to gravity which we can take to be 9.8 m/s/s. When the projectile hits the ground h = 0 .

So we have h = 35sin35 t - 4.9t^2 = 0

t(35sin35 - 4.9t) = 0

4.9t = 35 sin35

t = 35 sin 35 / 4.9

=  4.097 seconds

Answer:

D. 272 poles

Explanation:

We are given that:

The top layer has 20 poles, the next down one has 24 poles and the third one has 28 poles

We can note that each layer has 4 poles more that the one above it

Based on this, we can get the number of poles in each layer as follows:

Top layer has 20 poles

Second one has 20 + 4 = 24 poles

Third one has 24 + 4 = 28 poles

Fourth one has 28 + 4 = 32 poles

Fifth one has 32 + 4 = 36 poles

Sixth one has 36 + 4 = 40 poles

Seventh one has 40 + 4 = 44 poles

Eighth one has 44 + 4 = 48 poles

Now, we can get the total number of poles by adding the poles in all layers

This is done as follows:

Total number of poles = 20 + 24 + 28 + 32 + 36 + 40 + 44 + 48

Total number of poles = 272 poles

Hope this helps :)

Answer:

exponential; y = 89 • 0.62^x

Step-by-step explanation:

Answer:

Option B exponential y = 89 · 0.62x

Step-by-step explanation:

The table shows the estimated number of deer living in a forest over a five year period.

Year            Number of deers

0                     89

1                      55

2                     34

3                     21

4                     13

Now we have to find the model representing this situation. Difference in number of deer, in the forest.

We can see there is a common ratio between each successive term r = [tex]\frac{55}{89}[/tex] = 0.618

r = [tex]\frac{34}{55}[/tex] = 0.618

so it can be represented by an exponential model.

[tex]y=a (r) ^{x}[/tex]

[tex]y=89(62) ^{x}[/tex]

Option B is the answer.

there is 6 chickens and 16 rabbits, need the work tho?

6 chickens 16 rabbits

Answer:

[tex]\boxed{\text{Year 17}}[/tex]

Step-by-step explanation:

[tex]a(t) = 100e^{0.024t}[/tex]

Data:

a(t) = 150

a(0) = 100

Calculations :

[tex]\begin{array}{rcll}150 & = & 100e^{0.024t} & \\\\1.50 & = & e^{0.024t} & \text{Divided each side by 100}\\0.4055 & = & 0.024t & \text{Took the ln of each side}\\t & \approx & \mathbf{17} & \text{Divided each side by 0.024}\\\end{array}[/tex]

[tex]\text{The consumer price index will be 50 \% higher in } \boxed{\textbf{year 17}}[/tex]

Answer:

The average rate of change is : [tex]6.3[/tex]

Step-by-step explanation:

The number of car owners is modeled by the function;

[tex]f(t)=1.1t^2-2.5t+1.5[/tex], where t is the different number of years.

The average rate of change  of f(t)  from t=3 to t=5 is simply the slope of the secant line connecting:

(3, f(3)) and (5,f(5))

Which is given by:

[tex]\frac{f(5)-f(3)}{5-3}[/tex]

Now, we substitute t=3 into the function to get;

[tex]f(3)=1.1(3)^2-2.5(3)+1.5[/tex]

[tex]f(3)=3.9[/tex]

We substitute t=5 into the function to get;

[tex]f(5)=1.1(5)^2-2.5(5)+1.5[/tex]

[tex]f(5)=16.5[/tex]

Therefore the average rate of change is : [tex]\frac{14.5-3.9}{2}=6.3[/tex]

Answer: brianna rode for 54 minutes and maddie rode for 108 minutes.

Step-by-step explanation:

let the time for which brianna rode be = x

(since maddie rode twice as brianna then,)

let the time for which maddie rode be = 2x

(together they rode for 162 minutes. so,)

x + 2x = 162

3x = 162

x = 162/3

=>x = 54

=>2x = 54*2 = 108

hope it helps

Answer:

[tex]2\sqrt[4]{5}[/tex]

Step-by-step explanation:

First, you calculate the quotient which is [tex]\sqrt[4]{80}[/tex]

Then you simplify the radical which is [tex]2\sqrt[4]{5}[/tex]

Inputting this in a calculator will give you 2.99 which is also correct.

Final answer:

The car's average rate during the second part of the trip is 65 miles per hour, which is calculated by dividing the remaining distance of 390 miles by the remaining travel time of 6 hours.

Explanation:

We need to find the average rate of the car during the second part of the trip. We know the total distance of the trip is 520 miles and the total time for the trip is 8 hours. Since the first part of the trip was at 65 miles per hour for 2 hours, the car would have covered 130 miles (65 miles/hour * 2 hours).

We subtract the distance covered in the first part of the trip from the total distance to find the distance covered during the second part of the trip: 520 miles - 130 miles = 390 miles. The remaining time for the second part of the trip is 8 hours - 2 hours = 6 hours.

To find the average speed during the second part of the trip, we divide the remaining distance by the remaining time:
Average rate = Distance / Time = 390 miles / 6 hours = 65 miles per hour.

Answer:

240.3

Step-by-step explanation:

       Tan(31) = y/400ft

400 tan (31) = y

                 y = 240,3

Answer:

6 y² - 20 y + 6

Step-by-step explanation:

Multiply step by step the terms inside the brackets:

3y * y

3y * -3

-1 * y

-1 * -3

add those up to get 3y² - 10 y + 3

multiply all terms of the result by 2

Answer:

6y^2 - 20y + 6.

Step-by-step explanation:

2(3y − 1)(y − 3)

= 2 [ 3y(y - 3) - 1(y - 3)]

= 2 (3y^2 - 9y - y + 3)

= 2(3y^2 - 10y + 3)

= 6y^2 - 20y + 6.

Answer:

The altitude of the climber is 1.40 miles

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle BCD

tan(22°)=h/(x-0.5)

h=tan(22°)*(x-0.5) ----> equation A

In the right triangle ACD

tan(15°)=h/x

h=tan(15°)*(x) ----> equation B

Equate equation A and equation B and solve for x

tan(22°)*(x-0.5)=tan(15°)*(x)

tan(22°)*x-tan(22°)*0.5=tan(15°)*x

x[tan(22°)-tan(15°)]=tan(22°)*0.5

x=tan(22°)*0.5/[tan(22°)-tan(15°)]

x=1.48 miles

Find the value oh h

h=tan(15°)*(1.48)=0.40 miles

therefore

The altitude of the climber is equal to

0.40+1=1.40 miles

Answer:

Step-by-step explanation:

Just solved a similar problem and figured it out, the angle of elevation is somewhat unintuitive as the angle of the second search team needs to be flipped. The diagram should look more like this:
This isn't an explanation of the math but more of a visualization for those that just needed the 2D representation. The real answer would be 1.081 miles (:

Answer:

Step 1: Multiply 1x5 Step 2: Multiply 2x3 Step 3: Add the two products

d=v*t

d=distance

v=velocity(speed)

t=time

distance is equal to the product of velocity and time, equation form;

d=vt

Any questions please feel free to ask. Thanks!

The answer would be D, where all of the given x values touch the x axis

Answer: D)

Step-by-step explanation:

The equation is: (x - 2)(x - 1)(x + 4) = 0

We can find the x-intercepts by Applying the Zero Product Property:

x - 2 = 0           x - 1 = 0             x + 4 = 0

x = 2                 x = 1                   x = -4

Which graph shows the curve crossing the x-axis at these points?  D