A wooden peg game in the shape of a triangular prism is 2 inches tall. The triangle has a base of 12 inches and a height of 9 inches. Find the volume of the game.

To honor 50 years of business, All Strikes Bowling is having an anniversary special. The game he can bowl is 25.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

To honor 50 years of business, All Strikes Bowling is having an anniversary special.

Shoes rent for $1.25 and each game is $0.75. If Charlie has $20 and needs shoes.

Charlie can bowl 25 games.

= 20 - 1.25

= 18.75

So, he can bowl game

= 18.75/ 0.75

= 25 games

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As hamster wheel is circular so for revolution we will find the circumference.

Diameter of the Hamster wheel = 8.5 in

One revolution of the wheel = circumference of the wheel

Circumference = π × d

π = 3.14 and d = 8.5

So, Circumference = 3.14 × 8.5

Circumference = 26.69 in

So in one revolution the hamster wheel travels a distance of 26.69 in

The correct option is B. 81 mm, 7 mm, 72 mm could be the lengths of the sides of a triangle.

To determine if a set of numbers could be the lengths of the sides of a triangle, the Triangle Inequality Theorem must be satisfied. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's apply this theorem to each set of numbers:

A. 81 mm, 7 mm, 6 mm

- The sum of the two smallest sides is 81 + 6 = 87 mm, which is greater than the third side, 7 mm. However, the sum of the two smallest sides, 7 + 6 = 13 mm, is not greater than the largest side, 81 mm. Therefore, these lengths cannot form a triangle.

B. 81 mm, 7 mm, 72 mm

- The sum of the two smallest sides is 7 + 72 = 79 mm, which is greater than the third side, 81 mm. This set satisfies the Triangle Inequality Theorem.

C. 81 mm, 7 mm, 88 mm

- The sum of the two smallest sides is 81 + 7 = 88 mm, which is equal to the third side, 88 mm. According to the Triangle Inequality Theorem, the sum must be strictly greater than the third side, so these lengths cannot form a triangle.

D. 81 mm, 7 mm, 77 mm

- The sum of the two smallest sides is 7 + 77 = 84 mm, which is greater than the third side, 81 mm. However, the sum of the two smallest sides, 81 + 7 = 88 mm, is not greater than the third side, 77 mm. Therefore, these lengths cannot form a triangle.

Based on the Triangle Inequality Theorem, the only set of lengths that can form a triangle is option B: 81 mm, 7 mm, 72 mm.

Answer:

30 bags

Step-by-step explanation:

Nc + Nd = 50

5Nc + 3Nd = 190

Multiply by -5 becomes:

-5Nc - 5Nd = -250

5Nc + 3Nd = 190

Equals:

-2Nd= -60

simplify:

-2Nd/-2 and -60/-2 = Nd= 30 bags

In this detailed answer, the probabilities of drawing two coins from Kevin's pocket - with 6 nickels and 4 dimes - are explained. The probabilities of both coins being nickels and dimes are 0 due to the lack of replacement, while the probability of one nickel and one dime is 4/15.

To calculate the probabilities of drawing coins from Kevin's pocket, where he has 6 nickels and 4 dimes:

Probability both coins are nickels: Since each draw affects the remaining number of nickels and dimes, the probability is 0.

Probability both coins are dimes: Similarly, as the draws are not independent, the probability here is also 0.

Probability of one nickel and one dime: Since Kevin has 6 nickels and 4 dimes, the probability of drawing a nickel first is 6/10 (6 nickels out of 10 coins) and drawing a dime second is 4/9 (4 dimes remaining out of 9 coins), which equals 24/90 or 4/15.

Answer:

Option A  [tex]\frac{4}{30}=0.13333...=0.1\bar3[/tex]

Step-by-step explanation:

Given : Expression [tex]\frac{4}{30}[/tex]

To find : What is the decimal equivalent of the fraction?

Solution :

Step 1 - Write the fraction

[tex]\frac{4}{30}[/tex]

Step 2 - Divide the numerator by denominator,

[tex]\frac{4}{30}=0.13333...[/tex]

or [tex]\frac{4}{30}=0.13333...=0.1\bar3[/tex]

Therefore, Option A is correct.

the ship would travel approximately 9685.82 miles from Iceland to Antarctica.

To convert the angle from degrees to radians, we use the conversion factor[tex]\( \pi \)[/tex]radians = 180 degrees.

[tex]\[ \text{Angle in radians} = \frac{\text{Angle in degrees} \times \pi}{180} \][/tex]

In this case, the angle in degrees is 140 degrees:

[tex]\[ \text{Angle in radians} = \frac{140 \times \pi}{180} \]\[ \text{Angle in radians} = \frac{140}{180} \times \pi \]\[ \text{Angle in radians} = \frac{7}{9} \pi \][/tex]

Next, we'll find how far the ship would travel using Earth's radius. The distance traveled on a circle is given by the formula:

[tex]\[ \text{Distance} = \text{radius} \times \text{angle in radians} \][/tex]

Given Earth's radius as 3960 miles and the angle in radians as [tex]\( \frac{7}{9} \pi \)[/tex], we can calculate the distance:

[tex]\[ \text{Distance} = 3960 \times \frac{7}{9} \pi \]\[ \text{Distance} = 3080 \pi \]\[ \text{Distance} \approx 9685.82 \text{ miles} \][/tex]

So, the ship would travel approximately 9685.82 miles from Iceland to Antarctica.

Answer:

Step-by-step explanation:

Alright, lets get started.

The given expression is :

[tex]2x^3+10x^2+4x+20[/tex]

taking 2 common factor

[tex]2(x^3+5x^2+2x+10)[/tex]

[tex]2(x^3+2x+5x^2+10)[/tex]

[tex]2[(x+5)(x^2+2)][/tex]

So, the correct answer is option B :    answer

Hope it will help :)

Answer:

P(red or blue) = 5/18 + 6/18 = 11/18

The equation that represents each mixed number as a sum of whole numbers and unit fractions of [tex]4\frac{1}{4}[/tex] is  [tex]4\frac{1}{4}[/tex] = 4 + 1/4.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

We have the mixed fraction,

[tex]4\frac{1}{4}[/tex].

Converting the mixed fraction to an improper fraction,

[tex]4\frac{1}{4}[/tex] = 17/4

We need to write it as a sum of whole numbers and unit fractions:

So, it becomes,

[tex]4\frac{1}{4}[/tex] = 4 + 1/4

[tex]4\frac{1}{4}[/tex] = (16 + 1)/4

[tex]4\frac{1}{4}[/tex] = 17/4

Therefore, [tex]4\frac{1}{4}[/tex] = 4 + 1/4 is the required equation.

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Therefore, an organic cleaner is not as effective as a non-organic cleaner in killing germs that cause colds and the flu.

The radius of the penny is 9.54 millimeters.

The circumference means the length of the literal line that surrounds and forms a circle.

The formula for the circumference of the circle is given by

[tex]circumference = 2\pi r[/tex]

Where,

r is the radius

and π = 3.14

A radius is a straight line from the center of a circle to the circumference of a circle.

According to the given question.

We have a penny whose circumference is 59.69 millimeters.

Let r be the radius of the penny and 2πr be the circumference of the penny.

Since we know that, the shape of the penny is circular.

Therefore,

The radius, r of the penny is given by

[tex]2\pi r= 59.69[/tex]

[tex]\implies r = \frac{59.69}{2\pi }[/tex]

[tex]\implies r = \frac{59.69}{2(3.14)}[/tex]

[tex]\implies r = \frac{59.69}{6.28}[/tex]

[tex]\implies r = 9.54\ millimeters[/tex]

Hence, the radius of the penny is 9.54 millimeters.

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