If the total number of books checked out of the library at your high school is 14,400 and the student population is about 2400. how many books on average does each student have?

Using a system of equations, the numbers of each machine made are given as follows:

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows, considering the situation described:

The factory needs to make 54 tables each day, hence:

x + y + z = 54.

The number of dining tables made per day should equal the number of coffee tables, hence:

x = y.

Then, on the first equation:

2y + z = 54.

The number of coffee tables should be three more than the number of end tables, hence:

y = z + 3.

Replacing in the equation 2y + z = 54:

2(z + 3) + z = 54

3z = 48

z = 16.

Then:

The numbers of each machine made are given as follows:

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

When the function changes from increasing to decreasing, a local maximum occurs. The value of a = 5e.

A local maximum point on a function is a point (x, y) on the function's graph whose y coordinate is greater than all other y coordinates on the graph at "close to" points (x, y).

When the function changes from increasing to decreasing, a local maximum occurs. This means that the function's derivative will shift from positive to negative.

Let the function be [tex]&F(x)=a x e^{b x} \\[/tex]

[tex]&F '(x)=d / d x\left(a x e^{b x} ) \\[/tex]

[tex]&=a(d / d x)\left(x e^{b x}) \\[/tex]

simplifying the above equation, we get

[tex]&=a\left[\left(d / d x* x\right) e^{b x} +\left(x* d / d x* e^{b x} )\right] \\[/tex]

[tex]&=a\left[e^{b x} +b x e^{b x} \right] \\[/tex]

[tex]$&=a[1+b x] e^{b x}[/tex]

For critical points, set [tex]$f^{\prime}(x)=0$[/tex] and solve for x

[tex]&a[1+b x] e^{b x} =0 \\[/tex]

simplifying the above equation, we get

1 + bx = 0

bx = -1

x = -1/b

The value of x = -1/b

Given that f(x) has local max at 1/5, critical point x = 1/5 then

-1/5 = -1/b

Therefore, b = -5

[tex]&F(x)=a x e^{-5x}\\[/tex]

[tex]&F(1 / 5)=a / 5 e^{-1}\\[/tex]

1 = a/5e

Therefore, the value of a = 5e.

To learn more about local maximum, refer to:

https://brainly.com/question/27887497

#SPJ4

Exact Distance:   [tex]\sqrt{130}[/tex] units

Approximate Distance:  11.4018 units

===================================================

Explanation:

Use the distance formula to have the following steps

[tex](x_1,y_1) = (3,-2) \text{ and } (x_2, y_2) = (-4,7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-4))^2 + (-2-7)^2}\\\\d = \sqrt{(3+4)^2 + (-2-7)^2}\\\\d = \sqrt{(7)^2 + (-9)^2}\\\\d = \sqrt{49 + 81}\\\\d = \sqrt{130}\\\\d \approx 11.4018\\\\[/tex]

The exact distance is [tex]\sqrt{130}[/tex] units

This approximates to about 11.4018 units.

Answer:

Step-by-step explanation:

Let's open the brackets,

12z - 21 = -21 + 12z (distributive property)

12z - 12z = -21 + 21

0z = 0

z = 0

Answer:

The first and fourth statement.

Step-by-step explanation:

1. - 3 - 12/3 + 5

= - 3 - 4 + 5

= - 7 + 5

= - 2

- 2 < 0

4. 4 - 2 - 3/2

= 2 - 3 / 2

= 1 / 2

1 / 2 > 0

Hope this helped! ^^

Sidenote: If you need me to explain for 2, 3 and 5, comment below this and I'll explain.

The total number of notebooks on Sasha's notebook is 2c - 6.

Unitary method:

The unitary method is used to solve problems by first determining the value of a single unit and then multiplying that value by the required value.

So, this method is basically used to find the value of a unit and then the value of a required number of units.

Given,

Sasha has c green notebooks.

She has 6 fewer red notebooks then green notebooks.

So, here we need to find how many notebooks does Sasha have in all.

We know that.

Sasha has c green notebooks.

The number of red notebooks on her is  

=> c − 6.

Here Sasha has either green or red notebooks.

The total number of notebooks on Sasha's notebook is  

=> c + c − 6

=> 2c - 6

To know more about Unitary Method here.

https://brainly.com/question/3558587

#SPJ4

Answer:

$0.3

Step-by-step explanation:

Cost of one box in a set,

→ 67/15

→ 4.47 = $4.5

Cost of one box in another set,

→ 143/34

→ 4.205 = $4.2

The cost increase for each extra box,

→ 4.5 - 4.2

→ $0.3

Hence, the answer is $0.3.

A number raised to a power represents a product where the same number is used as a repeated factor. The number is called the base and the power is given by the exponent. The base is the repeated factor and the exponent counts the number of factors. An exponent is that we are dealing with products and multiplication.

In the expression bn, b is the base and n is the exponent.

The Power Rule for Exponents: (am)n = am*n.

To raise a number with an exponent to a power, multiply the exponent times the power.

Negative Exponent Rule: x–n = 1/xn.

Invert the base to change a negative exponent into a positive.

Zero Exponent Rule: x0 = 1, for .

Any non-zero number raised to the zeroth power is 1.

For more information about Exponents

visit  brainly.com/question/13669161

#SPJ9

Answer:

A blank one

Step-by-step explanation:

There's no picture

Answer:

Sussy

Step-by-step explanation:

1. There is nothing

2. Imposters are barely visible.

3. Your welcome

Weight of pet & age of pet  are   the two categories that would yield quantitative data.

What foundation does qualitative data have?

Which two sorts of quantitative data are there?

Weight of pet & age of pet  are   the two categories that would yield quantitative data because both quantity can measured or counted.

Learn more about quantitative data

brainly.com/question/14810759

#SPJ4

Based on the solution below, the number of people Deb can invite in order to spend a total of $65 is 5 people.

Given:

blank x + 2x + blank = 65 ............................... (1)

Where:

x = Number of people Deb can invite

First blank with x variable = 5; since Deb must pay an additional $5 for each person in the group

Second blank without x variable = 30; since Deb $30 to reserve a private karaoke room

Substituting the relevant values into equation (1) and solving for x, we have:

5x + 2x + 30 = 65

7x = 65 - 30

7x = 35

x = 35 / 7

x = 5

Learn more about the equation here: https://brainly.com/question/14686792.

#SPJ1

Answer:

x = 9/11

Step-by-step explanation:

distribute the 2:

6x - 4 + 5x - 3 + 2

combine like terms:

11x - 7 = 2

add 7 to both sides:

11x = 9

divide by 11 to isolate x:

x = 9/11

Step-by-step explanation:

Distribute 2 to 3x-2

[tex]6x - 4 + 5x - 3 = 2[/tex]

Them combined like terms

[tex]11x - 7 = 2[/tex]

Then add 7 to both sides

[tex]11x = 9[/tex]

Then divide by 11 and get

[tex] \frac{9}{11} [/tex]

(a) Differentiate [tex]s(t)[/tex] to get the velocity.

[tex]s(t) = \cos(t^2 - 1)[/tex]

Use the chain rule.

[tex]u = t^2 - 1 \implies \dfrac{du}{dt} = 2t[/tex]

[tex]s(u) = \cos(u) \implies \dfrac{ds}{du} = -\sin(u)[/tex]

[tex]\implies \dfrac{ds}{dt} = \dfrac{ds}{du} \dfrac{du}{dt} = \boxed{-2t\sin(t^2-1)}[/tex]

(b) Evaluate the derivative from (a) at [tex]t=0[/tex].

[tex]\dfrac{ds}{dt}\bigg|_{t=0} = -2\cdot0\cdot\sin(0^2-1) = \boxed{0}[/tex]

(c) The object is stationary when the derivative is zero. This happens for

[tex]-2t \sin(t^2 - 1) = 0[/tex]

[tex]-2t = 0 \text{ or } \sin(t^2 - 1) = 0[/tex]

[tex]t = 0 \text{ or } t^2 - 1 = n\pi[/tex]

(where [tex]n[/tex] is any integer)

[tex]t = 0 \text{ or } t = \pm\sqrt{n\pi + 1}[/tex]

We omit the first case. In the second case, we must have [tex]n\ge0[/tex] for the square root to be defined. Then in the given interval, we have two solutions when [tex]n=\in\{0,1\}[/tex], so the times are

[tex]t_1 = \sqrt{1} = \boxed{1}[/tex]

[tex]t_2 = \boxed{\sqrt{\pi + 1}} \approx 2.035[/tex]

(d) A picture is worth a thousand words. See the attached plot. If you're looking for a verbal description, you can list as many features of the plot as are relevant, such as

• intercepts (solve [tex]s(t)=0[/tex] to find [tex]t[/tex]-intercepts and evaluate [tex]s(0)[/tex] to find the [tex]s[/tex]-intercept)

• intervals where [tex]s(t)[/tex] is increasing or decreasing (first derivative test)

• intervals where [tex]s(t)[/tex] is concave upward or concave downward (second derivative test; at the same time you can determine any local extrema of [tex]s(t)[/tex], which you can see in the plot agrees with the critical points found in (c))

The volume of the box in terms of x will be :   [tex]\frac{50x-x^{3} }{2} cm^{3}[/tex]

We know, Total surface area of a cuboid is: 2(l*b + b*h + h*l)

and it is given that TSA is 100cm^2, the length of the base which is in a square shape is x. So, length l = breadth b = x, and taking height h = y

We need to find out the value of y for finding out the volume of the box.

Putting these values in the formula for TSA,

             => 2(x*x + x*y + x*y) = 100

             => 2(x^2 + 2xy) = 100    =>  y = (50-x^2)/2x

Put this value of y in the formula for volume.

The volume of Cuboid is : l*b*h

            =>  x*x*{(50-x^2)/2}       =>  x^2{(50-x^2)/2x}

             =>   (50x - x^3)/2

Hence, the volume for the box is   [tex]\frac{50x-x^{3} }{2} cm^{3}[/tex]

To know more about Volume of Cuboid, Click here :

https://brainly.com/question/22694657

#SPJ4

so a lot of detachment is really just a former way of saying, like if then so it's if you pass a final, then you pass the class. You passed the final.

Therefore you pass the class, right? So it's the law of attachment basically says, Okay, if U then D and we're just told that U is true.

Answer:212

Step-by-step explanation: 36 plus 36 40 plus 40 29 plus 29 19 plus ten then add the sums then u get 212

Answer:

no

Step-by-step explanation:

y = 9 + 2 is 11 not 7

We get that the solution for the equation 4 x² - 7 x = 3 x + 24 as 4 or 3 / 2.

We are given an equation:

4 x² - 7 x = 3 x + 24

We need to solve it for x.

4 x² - 7 x - 3 x = 24

4 x ² - 10 x = 24

4 x ² - 10 x - 24 = 0

4 x² - 16 x + 6 x - 24 = 0

4 x( x - 4) + 6( x - 4) = 0

(x - 4)(4 x + 6) = 0

Solving for x, we get that:

x = 4 or x = 6 / 4 = 3 / 2.

Therefore, we get that the solution for the equation 4 x² - 7 x = 3 x + 24 as 4 or 3 / 2.

Learn more about equation here:

https://brainly.com/question/1214333

#SPJ9

Using it's concept, the probabilities are given as follows:
A. 1/4.B. 11/16.C. 0.What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.In this problem, the number of marbles is given by:7 + 5 + 4 = 16.Then:For item a, 4 are red, hence the probability is 4/16 = 1/4.For item b, 4 are red and 7 are green, hence the probability is 11/16.For item c, there are no orange marbles, hence the probability is of 0.

A point is the solution of the inequality expression given as: -2x + 3y > 1 - 5x + 6y is (0, -2/3)

The inequality expression is given as:

-2x + 3y > 1 - 5x + 6y

Collect the like terms in the above expression

So, we have:

3y - 6y > 1 + 2x - 5x

Evaluate the like terms in the above expression

So, we have:

-3y > 1 - 3x

Divide both sides by -3

y < -1/3 + x

Let x = 0

So, we have

y < -1/3

This means that a point in the solution is

(x, y) = (0, < -1/3)

-2/3 < -1/3

So, we have

(x, y) = (0, -2/3)

Hence, a point is the solution of the inequality expression given as: -2x + 3y > 1 - 5x + 6y is (0, -2/3)

Read more about inequality at:

https://brainly.com/question/24372553

#SPJ1

z + 16.2 ≤ 30

z ≤ 13.8

Step-by-step explanation:

I assume these are all angles.

4x is the arc angle (at the center of the circle) between the 2 endpoints of the short triangle side (baseline).

the trials itself is isoceles, so both legs have the same length, bedclothes the arc angles between their endpoints are equal.

now, when we move the reference point of an arc angle back, back, back to the circle arc, the angle is cut in half.

so, the inner top angle of the triangle is therefore 4x/2 = 2x.

because of the isoceles nature, the second triangle inner angle at the baseline is also x.

the sum of the triangle angles is therefore

2x + x + x = 4x

and we know the sum of all angles in a triangle is always 180°.

so,

4x = 180

x = 180/4 = 45°

4x is then again 180°, and 2× 8y are then the remaining 180° of the full circle 360°.

2× 8y = 180

8y = 90

y = 90/8 = 11.25

x = 45

y = 11.25

The approximate standard deviation of the sampling distribution of the proportion is 3.8%.

A standard deviation (or) is a measure of how widely distributed the data is in reference to the mean.

A low standard deviation indicates that data is clustered around the mean, whereas a high standard deviation implies that data is more spread out.

Now, as per the questions;

Whenever the population size is so very large, the PQ/N factor approaches zero, and the standard deviation equation becomes:

σp = √( PQ/n)

We don't know how so many listeners this same radio station has in this case, but we can assume it's a large number.

P = probability of listening at work, is 14% or 0.14

Q = probability of not listening at work, is (100- 14)% = 86% = 0.86

N = sample size, is 85

The sample standard deviation is then

σp = √(14×.86/85)

σp = 0.0376

σp = 3.8% (approximately)

Therefore, the approximate vale of the standard deviation is found to be 3.8 %.

To know more about the standard deviation, here

https://brainly.com/question/12402189

#SPJ4

The correct question is-

If 14% of the listeners of a radio station listen to it while they are at work, what is the approximate standard deviation of the sampling distribution of the proportion for samples of size 85?

Answer:

5 year

3 inches every year 48 minus 32 equals 16 3 Inches divided into 16 equal 5.333333 round it equals 5 years y = 5 years

Answer:

x = 1 and x = -3.5

Step-by-step explanation:

y = -2x² -5x + 2

-2x² -5x + 2 = -5

which means y = -5

Draw the line on y = -5 like the green line in the attached file

and see where this line intersects with the graph

the values are:

x = 1 and x = -3.5

Answer:

Draw a line at y = -5.

x ≈ -3.5

x ≈ 1

Step-by-step explanation:

Given equation:

[tex]y = -2x^2 - 5x + 2[/tex]

This is the equation of the graphed parabola.

To solve the equation  [tex]-2x^2 - 5x + 2 = -5[/tex]  draw a line at y = -5 and find the points of intersection of the two graphed equations.

From inspection of the graph, the x-values of the points of intersection are:

Solving algebraically

Add 5 to both sides of the equation:

[tex]\implies -2x^2-5x+2+5=-5+5[/tex]

[tex]\implies -2x^2-5x+7=0[/tex]

Factor out -1 from the left side:

[tex]\implies -1(2x^2+5x-7)=0[/tex]

Divide both sides by -1:

[tex]\implies 2x^2+5x-7=0[/tex]

Find two numbers that multiply to -14 and sum to 5:  7 and -2

Rewrite b as the sum of these two numbers:

[tex]\implies 2x^2+7x-2x-7=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(2x+7)-1(2x+7)=0[/tex]

Factor out the common term (2x + 7):

[tex]\implies (x-1)(2x+7)=0[/tex]

Apply the zero-product property:

[tex](x-1)=0 \implies x=1[/tex]

[tex](2x+7)=0 \implies x=-\dfrac{7}{2}=-3.5[/tex]

The relative frequency are

i) Pilot error = 15.9 percent

ii)   Human Error =3.8 percent

iii)   Weather = 19.3 percent

iv)  Mechanical problem = 42 percent

v)  Sabotage = 19.2 percent

The formula for the relative frequency is = f/n

                             Where, f = the number of times the data occurred in an observation

                                           n = total number of observations.

If we have to convert it into percentage form we will multiply it by 100

Thus we have been given that

       Crashes due to pilot error = 260

       Crashes due to other human error = 62

       Crashes due to weather = 315

      Crashes due to mechanical problem = 682

       Crashes due to sabotage = 313

Total number of errors occurred = 260+62+315+682+313

                                                           = 1632

Hence, the relative frequency are

 i) Pilot error = 260/1632 * 100 = 15.9 percent

 ii) Human Error = 62/1632 * 100 =3.8 percent

iii)  Weather = 315/1632 * 100 = 19.3 percent

iv) Mechanical problem = 686/1632 * 100 = 42 percent

v) Sabotage = 313/1632 * 100 = 19.2 percent

Learn more about relative frequency here : https://brainly.com/question/15164292

#SPJ9

Answer:

45 $

Step-by-step explanation:

20 x 2 = 40

40 + 5 = 45

The distance from the left side of the stage to the first trap door is 24 3/4.

given;

total lenght of the stage is 76 feet.

Anna is 26 feet high on a rock-climbing.

here we have to substract 76-26 1/2.

   =76-26 1/2

  =49 1/2/2

  =24 3/4

Distance is a scalar quantity. The distance of an object can be defined as the complete path travelled by an object. For example. if a car travels east for 5 km and takes a turn to travel north for another 8 km, the total distance travelled by car shall be 13 km.the space between the two points are called distance

Distance is a scalar quantity. The distance of an object can be defined as the complete path travelled by an object. For example. if a car travels east for 5 km and takes a turn to travel north for another 8 km, the total distance travelled by car shall be 13 km..

to know more about distance;

visit;https://brainly.com/question/4710186

#SPJ9