You and two friends (Adam and Alana) will only play a game if it is fair for all three of you. The game your friend has proposed is to roll two number cubes (numbered 1-6) and find the sum. If the sum. If the sum is from 1-4 you get the point, 5-8 Adam gets the point, and 9-12 Alana gets the point.

1 gallon = 231 cubic inches

7cm = 2.75591 inches ( round to 2.76 )

10 x 10 x 2.76 = 276 cubic inches

there will be more than enough room for the gallon of paint

276-231 = 45 cubic inches of space left over

13 hearts

 a 13/52 probability.

that reduces to a 1/4 probability of getting a heart

Answer: The second statement is true. It is a reduction because 0 < n < 1.

Step-by-step explanation:

Given: A triangle is dilated by a scale factor of n = 1/3 .

as n is less than 1 but greater than 0.

A dilation is a rigid transformation that forms an image that is the same shape as of the original figure, but with a different size.  A dilation transform a figure by scalar factor 'n' about the center of dilation is a fixed point in the plane which never change.

A dilation that forms a larger image is known as enlargement.  A dilation that forms a smaller image is known as reduction.

• If n is greater than 1, then the image is an enlargement.

• If n is between 0 and 1, then the image is a reduction .

• If n is 1, the figure and then the image are exactly same.

Answer:

2nd statement

Step-by-step explanation:

7/10-1/5 = 7/10-2/10 = 5/10 = 1/2

 so 280 pennies fills 1/2 of her piggy bank

 so 280*2 = 560

her piggy bank can hold 560 pennies

Please see attached document for the graphs:

The functions with the given graphs can't be solutions of the differential equation dy dt = et(y − 1)2.

(a) won’t work, since it has negative slope on portions of its solutions. The slope, e t (y − 1)2 , is a nonnegative function.

(b) won’t work, since it has positive slope at y = 1, where the slope must be flat.

Functions with given graphs cannot be solutions to the differential equation dy / dt = e^t(y-1)^2 because their graphs don't satisfy the conditions imposed by the equation, such as non-oscillatory behavior and non-linear variation with time.

The question pertains to why certain functions represented by their graphs cannot be solutions to the differential equation dy / dt = et(y-1)2. The explanation lies in the structure of the given differential equation and the properties of function graphs.

Equation dy / dt = et(y-1)2 is a non-linear first order differential equation. To be a solution to this equation, a function's graph must satisfy certain conditions imposed by the equation. However, if certain function graphs represent an undefined curve or if their graphs demonstrate oscillatory behavior, they do not satisfy these criteria.

For instance, the differential equation demands non-oscillatory behavior as seen in the general solution provided in the reference: Yn(x) = Ce-Bx +De+Bx. This form describes a gradual attenuation of y(x), i.e., it does not oscillate. Similarly, if a graph represents a function that varies non-linearly with time (like In[A] vs. Time), it does not represent a solution to the differential equation as well.

Thus, the inability of certain function graphs to satisfy the conditions required by the given differential equation is the reason they cannot be its solutions.

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Answer: [tex]250\ m[/tex]

Step-by-step explanation:

Assuming that:

[tex]1\ m=3.3\ ft[/tex]

We can make the conversion from feet per second to meters per second with this procedure:

[tex](165\ \frac{ft}{s})(\frac{1\ m}{3.3\ ft})=50\ \frac{m}{s}[/tex]

Let be "x" the amount of meters the parachutist will fall during 5 seconds of free fall

Knowing that in 1 second the parachutist falls 50 meters, we can calculate "x" by solving the following multiplication:

[tex]x=(50\ \frac{m}{s})(5\ s)\\\\x=250\ m[/tex]

The parachutist's rate of free fall is 165 feet per second, which is equivalent to 50 meters per second. The parachutist will fall approximately 250 meters during 5 seconds of free fall.

To convert the rate of 165 feet per second to meters per second, we need to use the conversion factor of 1 meter equals 3.3 feet. So, the rate in meters per second is 165 feet per second divided by 3.3 feet per meter, which equals 50 meters per second.

To find how many meters the parachutist will fall during 5 seconds of free fall, we can multiply the rate of 50 meters per second by the time of 5 seconds. This gives us 250 meters of free fall during 5 seconds.

Final answer:

The expression 2(f^4)^2 f^3 divided by 6f^9 simplifies to 1/3 f^2, after applying the properties of exponents and dividing coefficients.

Explanation:

To simplify the expression 2(f^4)^2 f^3 divided by 6f^9, we need to use the properties of exponents. First, we simplify (f^4)^2 by multiplying the exponents, which gives us f^8.

Then, we multiply f^8 by f^3 to get f^11. Next, we divide our new expression 2f^11 by 6f^9. This can be done by dividing the coefficients (2 divided by 6) and subtracting the exponents of f (11 minus 9), resulting in f^2 over 3, or 1/3 f^2.

Final answer:

The probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%, calculated using the Central Limit Theorem to find the standard error and z-scores.

Explanation:

To calculate the probability that the sample mean diameter of the tennis balls is between 2.62 and 2.64 inches, we can use the Central Limit Theorem since we are dealing with a sample of tennis balls rather than just one. The Central Limit Theorem tells us that the sampling distribution of the sample mean will be normally distributed with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is called the standard error (SE).

Given that the population mean (μ) is 2.63 inches, the population standard deviation (σ) is 0.03 inch, and the sample size (n) is 9, we first calculate the standard error (SE) as follows:

SE = σ / √n = 0.03 / √9 = 0.03 / 3 = 0.01 inch.

Next, we convert the sample mean range (2.62, 2.64) to z-scores, which are measures of how many standard deviations an element is from the mean.

Z for 2.62 = (2.62 - μ) / SE = (2.62 - 2.63) / 0.01 = -0.01 / 0.01 = -1
Z for 2.64 = (2.64 - μ) / SE = (2.64 - 2.63) / 0.01 = 0.01 / 0.01 = 1

Using a standard normal distribution table or calculator, we find the probabilities corresponding to these z-scores. The probability of a z-score being between -1 and 1 is approximately 0.6827 (68.27%).

Therefore, the probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%.

Answer:

Glide reflection

Step-by-step explanation:

A glide reflection is a composition of a translation and a reflection across a line parallel to the direction of translation. A glide reflection requires a translation on a figure, which is then reflected over a line. This is a symmetry operation that requires a translation rule and a line to reflect over. A common example of this are footsteps in the sand.

Answer: 40 inches squared

Step-by-step explanation:

1. first, you multiply, do 5*16 what does that give you? (80)

2. then, divide your answer by 2 what do you get? (40)

3. lastly, it should look like this: 5*16=(answer)/2=(answer)

hope this helps

Answer:

May be !

i> Q = 7P

ii> when p =5 then from above eqn we can find Q = 7p and = 7×5=35

iii> from eqn i we can write p = Q/7 So when Q=42 then P=Q/7=42/7=6

volume = pi x r^2 x h

3.14 x 4 x 14^2 = 2461.76 cubic feet

Fixed the typo I had in my answer.

Answer:

So volume of the swimming pool is 2461.76 feet³.

Step-by-step explanation:

The Darnells are having a swimming pool installed.

The pool has a radius of 14 feet and height of 4 feet.

Since pool is in the form of a cylinder so volume of cylinder

= πr²h

= π (14)² × 4

= (3.14) (196) × 4

= 2461.76 cubic feet.

So volume of the swimming pool is 2461.76 feet³.

Answer: Weight of the oil is 672.74 grams.

Step-by-step explanation:

Since we have given that

Radius of cylinder = 5 cm

Height of cylinder = 10 cm

Volume of cylinder would be

[tex]\pi r^2h\\\\=3.14\times 5\times 5\times 10\\\\=785\ cm^3[/tex]

Weight of 10W-40 oil = 0.857 grams per cubic cm

So, Weight of the oil in the can would be

Volume × Weight per cm³

[tex]=785.71\times 0.857\\\\=672.74\ grams[/tex]

Hence, Weight of the oil is 672.74 grams.