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3 years ago

A teacher will pick 1 student at random from 20 for the lead in a play. What is the probability of a student, Jo, of winning?

Mathematics

1 answer:

Eduardwww [97]3 years ago

5 0

Answer:

5% chance

Step-by-step explanation:

devide how many students the teacher will choose from the amount of students there is to choose from:

1 / 20 = 0.05

then multiply by 100 to get the amount expressed in percentage:

.05 * 100 = 5%

the result:

Jo has 5% chance of winning.

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Given f (x) = -3x - 1, solve for x when f (x) = -4

Aleks [24]

Answer:
11
Explanation:
f(x) = -3x - 1 when f(x) = -4
f(x) = -4 * -3 -1 = 12 - 1 = 11

8 0

3 years ago

If you know the measure of the vertex angle of an isosceles triangle, how do you find out the measure of the base angles?

Irina-Kira [14]

Answer:

Step-by-step explanation:

An isosceles triangle has 2 sides that are the same length. Let's say that our triangle has the 2 sides measuring the same and the base is a different length. The vertex angle is the top angle. By the definition of an isosceles triangle, since the 2 sides measure the same length, then the angles across from those sides have the same degree measure. If we know the measure of the vertex angle, then we have

180 = vertex angle - base angle - base angle

but since the base angles are the same and we have 2 of them, then

180 = vertex angle - 2 base angles

For example, if the vertex angle measures 80 degrees, then 180 - 80 = 100. That 100 has to be split in half for each of the base angles which are the same as each other. So the vertex angle is 80 and each base is 50.

6 0

3 years ago

Circle P is described by the equation (x−1)2+(y+6)2=9 and circle Q is described by the equation (x+4)2+(y+14)2=4. Select from th

xeze [42]

Answer:

(a) Circle Q is 9.4 units to the center of circle P

(b) Circle Q has a smaller radius

Step-by-step explanation:

Given

$P:(x - 1)^2 + (y + 6)^2 = 9$

$Q:(x + 4)^2 + (y + 14)^2 = 4$

Solving (a): The distance between both

The equation of a circle is:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$Center: (h,k)$

$Radius:r$

P and Q can be rewritten as:

$P:(x - 1)^2 + (y + 6)^2 = 3^2$

$Q:(x + 4)^2 + (y + 14)^2 = 2^2$

So, for P:

$Center = (1,-6)$

$r = 3$

For Q:

$Center = (-4,-14)$

$r = 2$

The distance between them is:

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

Where:

$Center = (1,-6)$ --- $(x_1,y_1)$

$Center = (-4,-14)$ --- $(x_2,y_2)$

So:

$d = \sqrt{(1 - -4)^2 + (-6 - -14)^2$

$d = \sqrt{(5)^2 + (8)^2$

$d = \sqrt{25 + 64$

$d = \sqrt{89$

$d = 9.4$

Solving (b): The radius;

In (a), we have:

$r = 3$ --- circle P

$r = 2$ --- circle Q

By comparison

$2 < 3$

<em>Hence, circle Q has a smaller radius</em>

4 0

3 years ago

The perimeter of a triangle is 41 inches. The three sides of the triangle are all differnt lenghts. The longest side is 10 less

erma4kov [3.2K]

Answer:

$Longest\ side=20\ inches\\\\Middle\ side=15\ inches\\\\Shortest\ side=6\ inches$

Step-by-step explanation:

Let be "x" the lenght of the longest side, "y" the lenght of the middle side and "z" the lenght of the shortest side.

The perimeter is:

$41=x+y+z$ [Equation 1]

We know that the longest side is 10 less than twice the middle side length. This can be expressed as:

$x=2y-10$ [Equation 2]

And the middle side length is three less than three times the shortest side length. This is:

$y=3z-3$ [Equation 3]

The steps are:

- Solve for "z" from the third equation:

$y=3z-3\\\\y+3=3z$

$z=\frac{y+3}{3}$ [Equation 4]

- Substitute [Equation 4] into [Equation 1]

- Substitute [Equation 2] into [Equation 1]

Then:

$41=(2y-10)+y+(\frac{y+3}{3})$

- Solve for "y":

$41=2y-10+y+\frac{y+3}{3}\\\\41=2y-10+y+\frac{y}{3}+1\\\\41=\frac{10}{3}y-9\\\\41+9=\frac{10}{3}y\\\\\frac{50*3}{10}=y\\\\y=\frac{150}{10}\\\\y=15$

- Substitute this value into [Equation 2] and into [Equation 4]:

$x=2(15)-10\\\\x=20$

$z=\frac{(15)+3}{3}\\\\z=6$

4 0

4 years ago

Suppose You want to but three loaves of bread that cost $1.50 each and a jar of grape jelly that costs $4.A jar of Peanut Butter

Cloud [144]

You want 3 loaves of bread, at $1.50 a piece and a jar of jelly, at $4. So set up the equation 3(1.5)+1(4). You don't want peanut butter so that's unnecessary information. Your total is $8.50, so subtract that from 10, you get 1.5. You will have $1.50 left over.

4 0

4 years ago

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