If 4 1/2 = 2, 8 1/3 = 2, and 16 1/4 = 2, then for what value of x would x 1/5 = 2?

2
4
24
32

The polynomial in standard form from the given options is [tex]x^4y^2 + 4x^3y + 10x[/tex], as it orders the terms by degree in descending order, first by the degree of x and then y.

The term standard form in mathematics, especially in relation to polynomials, refers to a way of writing the polynomial so that the terms are ordered by their degree in descending order. More specifically, for a polynomial in two variables, x and y, the standard form would have the terms arranged first by the degree of x, then y, from highest to lowest.

Looking at the options provided in the question, the polynomial that is written in standard form would have the highest degree term first, and so on. The polynomial [tex]x^4y^2 + 4x^3y + 10x[/tex] follows this convention, with the terms ordered by decreasing powers of x first and y second. Therefore, this is the polynomial written in standard form.

Note that while the other options are all polynomials, they do not follow the standard form convention as closely as the correct option provided.

Q +N =27

Q=27-N

0.25Q + 0.05N =3.75

0.25(27-N) + 0.05 =3.75

6.75-0.25N+0.05N=3.75

6.75-0.2N=3.75

-0.2N=-3

N=-3/-0.2 = 15

15 nickels

27-15 = 12

12 quarters

15x0.05 = 0.75

12 x 0.25 = 3.00

3.00 + 0.75 = 3.75

 12 quarters & 15 nickels

The value of x for the circle is 25.8. The correct option from the following is (D).

Simple closed shapes include circles. It is the collection of all points in a plane that are a certain distance from the center. A segment is a section of a straight line that has every point on the line that lies in its middle and is enclosed by two clearly defined endpoints.

The products of two secant lines that cross one another outside of a circle are equal.

The value of x is:

5(x+5) = 7(15+7)

5x + 25 = 7 × 22

5x + 25 = 154

5x = 154 - 25

5x = 129

x = 129/5

x = 25.8

Hence, the value of x is 25.8.

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In this case, the Poisson distribution is the best one to use. The formula for Poisson distribution is given as:

P[x] = e^-m * m^x / x! 

Where,

m = mean number of typographical errors = 6

x = sample value

A. The probability of exactly 4 errors are found on a page is:

P[4] = e^(-6) * 6^4/4!

P[4] = 0.1339

B. The probability that at most 4 errors will be the summation of x = 0 to 4:

P[0] = e^(-6) * 6^0/0! = 2.479 E -3

P[1] = e^(-6) * 6^1/1! = 0.01487

P[2] = e^(-6) * 6^2/2! = 0.04462

P[3] = e^(-6) * 6^3/3! = 0.08924

Therefore summing up all including the P[4] in A gives:

P[at most 4] = 0.2851

C. The probability that more than 4 would be the complement of answer in B.

P[more than 4] = 1 - P[at most 4]

P[more than 4] = 1 - 0.2851

P[more than 4] = 0.7149

Answer:

V = 9025.8 cm3

Step-by-step explanation:

Using the Poisson distribution formula, substitute the given mean and the number of occurrences into the formula to find the probability. Hence P(4; 8)= e^-8 * 8^4 / 4!. The answer will be in decimal form, signifying the probability.

The probability in a Poisson distribution that an event happens exactly k times when the mean occurrence rate (μ or Lambda) is given is determined using the following formula:

P(k; μ) = (e^-μ * μ^k) / k!

Where e is Euler's number (approximately equal to 2.71828), k is the number of occurrences (in this case, it is 4) and μ is the mean number of occurrences (in this case, it is 8).

Applying the values into the formula, we have:

P(4;8) = (e^-8 * 8^4) / 4!

You can calculate the above expression using a calculator to find the probability. Remember, the answer will be in decimal form, representing the probability of the event occurring 4 times when the average rate of occurrence is 8.

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The surface area of a regular pentagonal prism can be found by calculating the area of the pentagonal bases and the area of the rectangular sides and then summing those areas together.

Calculating the Surface Area of a Regular Pentagonal Prism

To find the surface area of a regular pentagonal prism with given dimensions, we need to calculate the area of two components: the area of the pentagonal bases and the area of the rectangular sides (also called the lateral faces). We are given that the side length (s) of the pentagon is 8 units, the prism's altitude (h), or height, is 20 units, and the apothem (a) is approximately 5.5 units.

Firstly, the area of a pentagon (Apentagon) is calculated using the formula Apentagon = ½ * perimeter * apothem, where the perimeter (P) of a regular pentagon is the side length multiplied by 5. Thus, the area of one pentagonal base is ½ * 5 * 8 * 5.5. Next, to find the entire area of the two pentagonal bases, we multiply this result by 2.

The area of each of the rectangular sides can be found by multiplying the side length by the prism's altitude. Since there are 5 identical rectangular sides in a regular pentagonal prism, their total area is 5 * 8 * 20.

Adding these two results together gives us the total surface area of the prism. So, the formula for the surface area is Total Surface Area = (2 * ½ * 5 * 8 * 5.5) + (5 * 8 * 20).

Answer:

in other words b

Step-by-step explanation:

The total distance Preston covered on his camel safari is 9 km, and his displacement is 6.71 km toward the northeast.

Determining Distance and Displacement

To answer the student's question about Preston's journey during his camel safari, we need to consider the definitions of distance and displacement.

Distance is the total length of the path traveled regardless of direction. In Preston's case, he traveled 5 km north, then 3 km east, and then 1 km north again. Therefore, the total distance covered is the sum of these individual distances

Displacement, on the other hand, measures the change in position from the starting point to the final point and is direction-dependent. It is a vector quantity with both magnitude and direction. To find the displacement, we can represent Preston's movement on a coordinate system with north being the positive y-direction and east being the positive x-direction.

From the starting point, moving 5 km north and then 1 km north results in a total of 6 km in the positive y-direction.

The magnitude of the displacement can be calculated using the Pythagorean theorem:

√((6 km)² + (3 km)²) = √(36 km² + 9 km²) = √(45 km²) = 6.71 km (rounded to two decimal places)The direction of the displacement would be to the northeast. Therefore, Preston's displacement is 6.71 km toward the northeast.

Answer:  Equation relating C to S   : [tex]C=6500+250S[/tex]

The total cost to transport 19 tons of sugar is $11, 250.

Step-by-step explanation:

Given : It will cost $6500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported.

Total cost =  $6500 + $250 x (amount of sugar transported ( in tons))

Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported.

Then, the equation relating C to S  would be : [tex]C=6500+250S[/tex]

When S= 19 , we get

[tex]C=6500+250(19)=6500+4750= 11250[/tex]

Hence, the total cost to transport 19 tons of sugar would be $11, 250.

An equation that relates Cost to the amount of sugar S

C = 6500 + 250S

The total cost is $1120

C = total cost

C = 6500 + 250(19)

Total cost = 6500 + 4750

= 11250

Therefore the total cost of transporting the 19 tons of sugar is $11250

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divide the base by the sin of the opposite angle

 base = 2

opposite angle = 30 degrees

2/sin(30) = 4

 x = 4

Final answer:

The probability is approximately 0.267.

Explanation:

To find the approximate probability that the mean salary of the 100 players exceeded $4.0 million, we can use the Central Limit Theorem and the Z-score formula. The Z-score formula is:

Z = (x - μ) / (σ / sqrt(n))

where x is the value we want to find the probability for (in this case $4.0 million), μ is the mean of the population ($3.26 million), σ is the standard deviation of the population ($1.2 million), and n is the sample size (100).

We calculate the Z-score as follows:

Z = (4.0 - 3.26) / (1.2 / sqrt(100)) = 0.617

We then use a Z-table or a calculator to find the probability corresponding to a Z-score of 0.617. The probability is approximately 0.267.

The solution is: Jiri is 20 years old.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Pamela is 13 years older than Jiri so:

p=j+13

Then you are told that the sum of their ages is 53 so:

p+j=53

We already know from the first statement that p=j+13, this makes p+j=53 become:

(j+13)+j=53  so we combine the two j's on the left side

2j+13=53  subtract 13 from both sides

2j=40  divide both sides by 2

j=20

So Jiri is 20 years old.

Hence, The solution is: Jiri is 20 years old.

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To find the equivalent expression, multiply the first fraction by y and the second fraction by x. Simplify the expression by combining like terms.

To find the expression equivalent to the given complex fraction, we can simplify it step by step. First, multiply the numerator and denominator of the first fraction (2/x) by y, and multiply the numerator and denominator of the second fraction (-5/y) by x. This gives us (2y)/(xy) - (4x)/(-5x). Next, simplify the expression by combining like terms. The final equivalent expression is (2y - 4x)/(xy + 5x).

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 lower box = x

 upper box = y

x+y=137

x=137-y

12.50x + 10y=1502.50

12.50(137-y) + 10y=1502.50

1712.5-12.50y+10y=1502.50

1712.5-2.50y=1502.50

-2.5y=-210

y=-210/-2.50 = 84

y = 84

x=137-84=53

53 lower box tickets

84 upper box tickets