A class consists of 6 girls and 10 boys. if a committee of 3 is chosen at random from the class, find the probability th

Answer:

So, if coach Stevens places as sprinkler of maximum distance 50 ft, he won't be able to cover the entire infield.

Step-by-step explanation:

Consider the infield as a polygon ABCDE.

It is given that each side AB, BC, CD, and DA is of length 90ft. It is also given that the infield is a perfect square.

Thus, the area of the square ABCD = 8100 ft.

Now consider the triangle BCD. Because of symmetry, the area of this triangle equals half the area of the square. Again, because of symmetry, the length of the base BD equals twice the length of the height EC.  

Thus from to the formula of area of the triangle:

base × height = 4050 base × height = 8100 2(height) × height= 8100 height63.64 ft

Answer:

Therefore, the correct option is: (C.) [tex]\( f(x) = 2 \cdot 4^x \)[/tex]

Explanation:

To determine the exponential function that passes through the given points, we can use the general form of an exponential function:

[tex]\[ f(x) = a \cdot b^x \][/tex]

Where:

[tex]\( a \)[/tex] is the initial value or the value of the function when [tex]\( x = 0 \).[/tex]

[tex]\( b \)[/tex] is the base of the exponential function.

Given the points [tex]\((1, 8)\) and \((4, 512)\)[/tex], we can substitute these coordinates into the general form and solve for [tex]\( a \) and \( b \).[/tex]

Using the point [tex]\((1, 8)\):[/tex]

[tex]\[ 8 = a \cdot b^1 \][/tex]

[tex]\[ 8 = a \cdot b \][/tex]

Using the point [tex]\((4, 512)\):[/tex]

[tex]\[ 512 = a \cdot b^4 \][/tex]

We can divide the equation obtained from the second point by the equation obtained from the first point to eliminate [tex]\( a \)[/tex] and solve for [tex]\( b \):[/tex]

[tex]\[ \frac{512}{8} = \frac{a \cdot b^4}{a \cdot b} \][/tex]

[tex]\[ 64 = b^3 \][/tex]

Taking the cube root of both sides:

[tex]\[ b = 4 \][/tex]

Now that we have found the value of [tex]\( b \)[/tex], we can substitute it back into one of the equations to find \( a \). Let's use the first point [tex]\((1, 8)\):[/tex]

[tex]\[ 8 = a \cdot 4 \][/tex]

[tex]\[ a = 2 \][/tex]

So, the exponential function that passes through the points [tex]\((1, 8)\) and \((4, 512)\)[/tex] is:

[tex]\[ f(x) = 2 \cdot 4^x \][/tex]

4.2 Adding up the two equivalent fractions 

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(x+5) - (10 * 7) / 7 = x - 65 / 7

Equation at the end of step 4:

x - 65 / 7 > 0

Step 5: 5.1 Multiply both sides by 7

Final answer:

To solve an equation by factoring, find the factors, set them equal to zero, and solve for the variable.

Explanation:

To solve an equation by factoring, you need to find the factors of the equation and set each factor equal to zero. Then, solve each equation separately to find the values of the unknown variable. Let's take an example:

If we have the equation [tex]x^2 - 5x + 6 = 0[/tex]:

This method of factoring and setting each factor equal to zero is a systematic approach to solving quadratic equations, providing a structured way to identify the solutions for the unknown variable. The application of this technique is fundamental in algebra, enabling the efficient determination of roots in quadratic expressions and contributing to a comprehensive understanding of solving equations.

There are 1000 three digit locker combinations are possible if the digits are able to repeat.

The correct option is B.

If the digits are able to repeat, there are 10 options for each digit (0-9) in a three-digit combination.

Since each digit can be chosen independently, the total number of different three-digit combinations is given by:

Number of combinations

= Number of options for the first digit x Number of options for the second digit x Number of options for the third digit

Number of combinations = 10 x 10 x 10 = 1000

Learn more about Combination here:

https://brainly.com/question/13058214

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Answer:

never

Step-by-step explanation:

In a 30 - 60 - 90 degree triangle , the common ratio is

1  : [tex]\sqrt{3}[/tex] : 2

Shorter leg that is opposite to 30 degree = 1

Longer leg that is opposite to 60 degree = [tex]\sqrt{3}[/tex]

Hypotenuse is opposite to 90 degree = 2

Shorter leg is half the length of the hypotenuse as per the ratio

Long leg is never the half of the hypotenuse

Answer:

The correct option is (A) i.e. cylinder.

Step-by-step explanation:NET BANGERZ

parallelogram

DH = FH

3x -3 = x + 7

2x = 10

 x = 5

Answer

All equation has always even numbers of imaginary roots because they always come in pairs. Therefore there must be either 2 imaginary roots, or zero. 

To determine the types of roots, we could try synthetic division by some of the factors of the number -32. The simplest factors are +1 or -1. Using this, we can quickly show that (x + 1) is a factor, and leaving (x² + 4x - 32) as the remainder. This remainder equation then factorises to (x - 4) (x + 8). 

So to conclude there are three real zeros which are:

x = -1

x = 4

x = -8

Answer:

y = 3/7 x - 12/7

Step-by-step explanation:

The slope is (0+3)/(4+3) = 3/7

So, now you have a point and a slope, so use the point-slope form. That gives you

y-0 = 3/7 (x-4)

Now just rearrange to slope-intercept form.

y = 3/7 x - 12/7