MATHEMATICS HIGH SCHOOL

a six-sided Fair die is rolled and a Fair coin is tossed. if event M represents getting an odd number on the die and event N represents landing tails on the coin, are these two events dependent or independent?

Answers

Answer 1

Answer: independent since the coin has no impact on the dice

Answer 2

Answer:

Step-by-step explanation:

Answer 1: The two events are Independent

Answer 2: In the given scenario, P(M and N) = P(M)*P(N)

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Find the solution of 3 times the square root of the quantity of x plus 5 equals negative 9, and determine if it is an extraneous solution.

Answers

Answer: x= 4 is an extraneous solution.

Step-by-step explanation:

Since we have given that

$3(√(x+5))=-9$

We need to find the extraneous solution.

So, our equation becomes,

$√(x+5)=(-9)/(3)\n\n√(x+5)=-3\n\n\text{On squaring both sides}\n\nx+55=(-3)^2\n\nx+5=9\n\nx=9-5\n\nx=4$

Now, we will check that x = 4 is an extraneous solution.

$3√(4+5)\neq -9\n\n3√(9)\neq -9\n\n3* 3\neq -9\n\n9\neq -9$

Hence, x= 4 is an extraneous solution.

The solution is $x=4$ .

If 1+9+8=1 what is 2+8+9?

Answers

One+Nine+Eight= ONE
Two+Eight+Nine= TEN

1+9+8=1
ONE+NINE+EIGHT=ONE

2+8+9=10
TWO+EIGHT+NINE=TEN

a train can travel 1230 miles in 5 hours. what is the unit rate that this train is traveling per hour? _____ miles per hour.

Answers

unit rate = 1230 miles / 5 hours = 246 miles per hour.

Solve 2(x−5)^1/3=−16

Answers

Answer:

x = − 19

Hope it helps

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A pizzeria makes brick-oven pizzas that are shaped like long rectangles with semi-circles at two ends. The pizzas come in three different sizes, which are measured by the longer side of each rectangle: 14 inches, 18 inches, and 29 inches. All of the pizzas are 10 inches wide, so the semi-circles at the ends have diameters of 10 inches, too. What is the area of each pizza? Use 3.14 for ? , and round your answers to the nearest tenth if necessary.

Answers

Answer:

Area of pizza whose longer side is of length is 14 inches = 218.5 $inches^(2)$

Area of pizza whose longer side of rectangle is 18 inches=258.5 $inches^(2)$

Area of pizza whose longer side is of length is 29 inches = 368.5 $inches^(2)$

Step-by-step explanation:

Given A pizzeria makes brick-oven pizzas that are shaped like long rectangles with semi-circles at two ends. The pizzas come in three different sizes, which are measured by the longer side of each rectangle: 14 inches, 18 inches, and 29 inches. All of the pizzas are 10 inches wide, so the semi-circles at the ends have diameters of 10 inches. we have to find the area of each pizza.

First, let us find the area of pizza whose longer side of rectangle is 14 inches

Area of 2 semicircles whose diameter is 10 inches

$=2((1)/(2)\pi r^(2))=\pi r^(2)=3.14* 5 * 5 = 78.5 inches^(2)$

Length = 14 inches

Breadth = 10 inches

Area of rectangle = $length * breadth$

= $14* 10=140 inches^(2)$

∴ Area of pizza whose longer side is of length is 14 inches = Area of rectangle + area of 2 semicircles

=140+78.5=218.5 $inches^(2)$

Now, let us find the area of pizza whose longer side of rectangle is 18 inches

Length = 18 inches

Breadth = 10 inches

Area of rectangle = $length * breadth$

= $18* 10=180 inches^(2)$

∴ Area of pizza whose longer side is of length is 18 inches = Area of rectangle + area of 2 semicircles

=180+78.5=258.5 $inches^(2)$

Now, let us find the area of pizza whose longer side of rectangle is 29 inches

Length =29 inches

Breadth = 10 inches

Area of rectangle = $length * breadth$

= $29* 10=290 inches^(2)$

∴ Area of pizza whose longer side is of length is 29 inches = Area of rectangle + area of 2 semicircles

=290+78.5=368.5 $inches^(2)$

Final answer:

To calculate the area of pizzas shaped like rectangles with semi-circular ends, we calculate the area of the rectangle and adjacent semi-circles separately then sum both. The rectangle's area is calculated as length times width while the semi-circle area is calculated as half of (pi*radius^2).

Explanation:

The area of a pizza that's shaped like a long rectangle with semi-circles at the ends can be calculated by first looking at the rectangle and then the semi-circles. For the rectangles, we use the formula for the area of a rectangle that is, length multiplied by width.

For the 14 inch pizza, the rectangle part:
Area = Length x Width = 14 x 10 = 140 square inches

The area of the semi-circle can be calculated as Area=1/2πr². The diameter is given as 10. So, the radius (r) will be half of the diameter, which is 5. Therefore, Area of each semi-circle = 1/2 x π x 5² = 1/2 x 3.14 x 25 = 39.25 square inches. The combined area of two such semi-circles will be = 39.25 x 2 = 78.5 square inches.

Adding the area for the rectangle and the semi-circles, the total area of each pizza will be 140 + 78.5 = 218.5 square inches.

Following these same steps, we can calculate the areas for the 18 inch and 29 inch pizzas.

Learn more about Area of a pizza here:

brainly.com/question/1329248

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Sydney is going to an amusement park. The price of admission into the park is $30, and once she is inside the park, she will have to pay $5 for every ride she rides on. How much money would Sydney have to pay in total if she goes on 15 rides? How much would she have to pay if she goes on r � r rides?

Answers

Answer:

105

Step-by-step explanation:

15×5=75

75+30=105

the answer is 105

Answer:

105

Step-by-step explanation:

15x5=75

105

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