The cylindrical jar above has a height of 12 centimeters and a radius of 4 centimeters. The jar contains 20 spherical marbles. Each marble has a radius of 0.8 centimeters. Which of the following represents the amount of space in the jar that is not occupied by marbles?

There are 700 students were enrolled at Valley View Middle School before the increase.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

The number of students at Valley View Middle School increased by 10%, to 770 total students.

Now,

Since, The number of students at Valley View Middle School increased by 10%,

And, The number student after the increase = 770

So, We can formulate;

The number of students before the increased is calculated as;

= 770 / (1 + 10%)

= 770 / 1.1

= 700

Thus, There are 700 students were enrolled at Valley View Middle School before the increase.

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The amount of an investment of $5,000 at an interest rate of 4.5% compounded monthly for 10 years will be $7,847, rounded to the nearest whole dollar.

To determine the amount of an investment that starts at $5,000, with an interest rate of 4.5% compounded monthly for 10 years, we use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

Plugging the values into the formula:

A = 5000(1 + 0.045/12)^(12*10)

A = 5000(1 + 0.00375)^(120)

A = 5000(1.00375)^(120)

A = 5000 * 1.569463137

A = $7,847 (rounded to the nearest whole dollar)

The amount of the investment after 10 years, compounded monthly at 4.5% interest, will be $7,847.

The solutions of the equation [tex]-x^2+4x=x-4[/tex] is:

               x= -1 and x=4

The solution of the graphs of the equation is equal to the x-value of the point of intersection of the graph of two functions i.e. the function on the left side of the equality on the right side of the equality.

Here, the expression is:

[tex]-x^2+4x=x-4[/tex]

Hence, we will see at which point the graph  of:

[tex]y=-x^2+4x[/tex]

and [tex]y=x-4[/tex] meet.

The point of intersection of the graph is: (-1,-5) and (4,0).

Hence, the solution of the graph is: x= -1 and x=4

20 books / 5 months = 4 books per month

4 books  * 7 months = 28 books total

Answer:the answer would be c which is 146

Step-by-step explanation:

Answer:

  12 inches

Step-by-step explanation:

15 - 3 = 12

The board is 12 inches long.

_____

A measuring tape is like a number line. To find the distance between two numbers on the number line, you subtract the smaller one from the larger one. The tape measure works the same way. Subtract the number at one end of the board from the number at the other end of the board to find the length of the board.

To calculate the rate at which the water level drops, use the formula dh/dt = dV/dt / (25Ï) and the given drainage rate of 250 liters per minute. The resulting rate is -0.01/Ï meters per minute, which represents the speed of the water level decreasing.

To determine the rate at which the water level inside the cylindrical tank drops, we use the given volume formula of the cylinder, V = 25Ï h, where V is volume in cubic meters, h is height in meters, and Ï is the constant pi (approximately 3.14159).

Draining the tank at a rate of 250 liters per minute corresponds to a volume rate of 0.25 cubic meters per minute (since 1 cubic meter equals 1000 liters). Using the formula dV/dt = 25Ï dh/dt, we want to find the rate dh/dt at which the height of the water decreases.

Rearranging for dh/dt gives us dh/dt = dV/dt / (25Ï). Substituting the known rate of volume change, dV/dt = -0.25 m³/min (negative because the volume is decreasing), we get dh/dt = -0.25 / (25Ï), which simplifies to dh/dt = -0.01 / Ï meters per minute. Therefore, the rate at which the water level drops is -0.01/Ï meters per minute.

The total costs t of the eggs is the dependent variable.

Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on other.

Thus if variable is taking its values independently of any visible direct cause, then that variable is called independent variable.

The variables that take their values based on some other variables' values are called dependent variables.

Given that the number of eggs e in the carton and the total costs t of the eggs.

Here, we know the number of eggs, e, to know how much it costs.

Hence, it is the dependent variable.

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8-3 = 5

7-2 = 5

 so the answer would be A

You need to represent the number of males in terms of females.

Since you know the number of males relative to females, it makes sense to represent the number of females as a variable, let's say f.

So then the number of males is f+240 and we know that the number of males plus the number of females is 2500. Knowing this, we can write an equation: f+(f+240)=2500. I put the number of males in brackets there just to make it easy to recognize.

This equation can be condensed into 2f+240=2500 and then solved:

2f=2500−240
f=2500−2402
f=1130

Then, we know the number of females, and we can solve for the number of males from here using our male formula: males=f+240. You should then get 1370 as the number of males.

Checking this answer, we see that 1130 + 1370 does equal 2500.

Answer:

Emanuel made huis mistake in first step and step 1 is incorrect.

Step-by-step explanation:

The given expression is

[tex](\frac{3}{5})(\frac{4}{9})(-\frac{1}{2})[/tex]

It can be written as

[tex]\frac{3}{5})(\frac{4}{9})(\frac{-1}{2}[/tex]

Step 1: [tex](\frac{(3)(4)(-1)}{(5)(9)(2)})[/tex]

Emanuel used negative sign with both numbers 1 and 2. Therefore the first step of Emanuel is incorrect.

Step 2: [tex]\frac{-12}{90}[/tex]

Step 3: [tex]\frac{-2}{15}[/tex]

Therefore Emanuel made huis mistake in first step and step 1 is incorrect.

The value of x is 75.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

6 consecutive integers are x − 2, x − 1, x, x + 1, x + 2, x + 3

Now, the integers add up to 447.

So, x-2 + x-1 + x+ x +1 + x+2 + x+3= 447

6x -3 + 6 = 447

6x = 450

x= 75

Hence, the value of x is 75.

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Final answer:

Two events A and B are considered independent if the probability of A given B (P(A|B)) is equal to the probability of A, and the probability of B given A (P(B|A)) is equal to the probability of B. In this case, events a and b are not independent.

Explanation:

Two events A and B are considered independent if the probability of A given B (P(A|B)) is equal to the probability of A, and the probability of B given A (P(B|A)) is equal to the probability of B.

In this case, if p(a|b) = 0.35, p(b) = 0.75, and p(a) = 0.44, we can determine if events a and b are independent by comparing the given probabilities.

To check if events a and b are independent, we need to find p(a|b) and compare it to p(a), and find p(b|a) and compare it to p(b).

p(a|b) = 0.35 means that the probability of event a occurring given that event b has occurred is 0.35. Since p(a|b) is not equal to p(a), events a and b are not independent.

Answer:   C.  ΔSQR

Step-by-step explanation:

In [tex]\triangle{STR}[/tex] and [tex]\triangle{SQR}[/tex], we have

[tex]\angle{TSR}\cong\angle{OSR}\\\\\angle{STR}\cong\angle{QRS}=90^{\circ}[/tex]

By AA- similarity postulate , we get

[tex]\triangle{STR}\sim\triangle{SQR}[/tex]

Answer:

P=2(l+w)

Step-by-step explanation:

It is given that perimeter, P, of a rectangle is the sum of twice the length and twice the width.

Let length of rectangle is l and width of the rectangle is w.

Perimeter = 2 × Length + 2 × Width

[tex]P=2\times l+2\times w[/tex]

[tex]P=2l+2w[/tex]

Taking out common factors.

[tex]P=2(l+w)[/tex]

[Note: (l+l)+(w+w) units is also true but according to the statement only option 1 is true]

Therefore, the correct option is 1.