A printed poster is to have a total area of 528 square inches with top and bottom margins of 2 inches and side margins of 5 inches. What should be the dimensions of the poster so that the printed area be as large as possible?

There is a 16.7% chance or probability  of selecting three state flags without replacement, where all three flags have only two colors.

To calculate the probability of selecting three state flags with only two colors, we first need to determine how many state flags meet this criteria. Out of the 50 state flags in the United States, there are only three flags that have two colors - Maine, Maryland, and Missouri.
Now that we know there are only three possible flags to choose from, we can calculate the probability of selecting all three with only two colors.
When we randomly select the first flag, there are three possible flags to choose from. However, only one of them has only two colors. Therefore, the probability of selecting a flag with two colors on the first try is 1/3.
After the first flag is selected, there are only two flags left that meet the criteria. Therefore, the probability of selecting a second flag with two colors is 1/2.
Finally, after the second flag is selected, there is only one flag left that meets the criteria. Therefore, the probability of selecting the third flag with two colors is 1/1 (or simply 1).
To calculate the probability of all three events happening together (selecting three flags with only two colors), we need to multiply the probabilities of each event together.
Therefore, the probability of selecting three state flags without replacement, where all three flags have only two colors, is:
1/3 x 1/2 x 1/1 = 1/6 or approximately 0.167.
In simpler terms, there is a 16.7% chance of selecting three state flags without replacement, where all three flags have only two colors.

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Step-by-step explanation:

3y + 4) - (2y - 7)

=3y-2y-7+4

=y-3

Answer:

y+11

Step-by-step explanation:

Distribute and remove parentheses.

3y + 4 - 2y +7

Combine Like-Terms:

y + 11

Answer:

Q‘(3, -2) R‘(6,-8) S’(9,-2)

Step-by-step explanation:

Rule for reflection over the x-axis is (x,-y)

The coefficients for the half-range sine series of f(x) = cos(x) in the interval (0, 7).

an = (1/7) [(-1/2)cos((n+1)7)(n-1) - (1/2)cos((n-1)7)(n+1) - 1]

To obtain the half-range sine series of the function f(x) = cos(x) in the interval (0, 7), we first need to extend the function to an odd periodic function over the interval (-7, 7). Since f(x) = cos(x) is already an even function, we can extend it by making it periodic with a period of 14.

The extended odd periodic function, denoted as F(x), can be defined as follows:

F(x) = { cos(x) for -7 ≤ x ≤ 7

{ -cos(x) for -14 ≤ x < -7

Next, we need to express the function F(x) as a half-range sine series over the interval (0, 7). The half-range sine series expansion is given by:

F(x) = (a0/2) + Σ [an sin((nπx)/7)]

To find the coefficients an, we use the formula:

an = (2/7) ∫[0 to 7] F(x) sin((nπx)/7) dx

Let's calculate the coefficients:

a0 = (2/7) ∫[0 to 7] F(x) dx

Since F(x) = cos(x) for 0 ≤ x ≤ 7, the integral becomes:

a0 = (2/7) ∫[0 to 7] cos(x) dx

= (2/7) [sin(x)] [0 to 7]

= (2/7) (sin(7) - sin(0))

= (2/7) (sin(7))

an = (2/7) ∫[0 to 7] cos(x) sin((nπx)/7) dx

Using the product-to-sum identity, cos(x) sin((nπx)/7) can be expressed as [(1/2)sin((n+1)x) - (1/2)sin((n-1)x)]:

an = (1/7) ∫[0 to 7] [(1/2)sin((n+1)x) - (1/2)sin((n-1)x)] dx

= (1/7) [(1/2) ∫[0 to 7] sin((n+1)x) dx - (1/2) ∫[0 to 7] sin((n-1)x) dx]

The integral of sin(mx) over the interval (0, 7) can be evaluated as follows:

∫[0 to 7] sin(mx) dx = [-1/m cos(mx)] [0 to 7]

= [-1/m (cos(7m) - cos(0))]

= [-1/m (cos(7m) - 1)]

Substituting this back into the formula for an, we get:

an = (1/7) [(1/2) [-1/(n+1) (cos((n+1)7) - 1)] - (1/2) [-1/(n-1) (cos((n-1)7) - 1)]]

Simplifying the expression, we obtain the coefficients for the half-range sine series of f(x) = cos(x) in the interval (0, 7).

an = (1/7) [(-1/2)cos((n+1)7)(n-1) - (1/2)cos((n-1)7)(n+1) - 1]

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Answer:

See below

Step-by-step explanation:

1. (refresh if you cant see it)

\(F = \frac{9}{5}C+32\\\text{Bring variable C to left side}\\-\frac{9}{5}C=-F+32\\\text{Multiply by -1}\\\frac{9}{5}C=F-32\\\text{Multiply the equation by 5/9 to get C by itself}\\C = \frac{5}{9}(F-32)\)

2.

2(x + 3) = 20

Distribute.

2x + 6 = 20 \(\neq\) 2x + 3 = 20

Your answer is false.

3.

x \(\geq\) -2 because even though it includes the expression "x>5", those values are also above -2, including 5.

Answer: 0.9

Step-by-step explanation:

Sqrt 81 is 9

over 10 is 9/10

which is 0.9

Based on the definition of congruent triangles, we can state that: C. They are not congruent because only one pair of corresponding sides is congruent.

Congruent triangles refer to a pair of triangles that possess identical shape and size. If two triangles are congruent, it implies that their corresponding sides and angles are precisely equal.

The image that is attached below shows the diagram of triangles FGH and FJH. We see that only one pair of sides are congruent (FH = FH).

This is not enough to conclude that both triangles are congruent. Therefore, we can conclude that:

C. They are not congruent because only one pair of corresponding sides is congruent.

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Answer:

  x ≈ ±8.1

Step-by-step explanation:

  2x² -9 = 121 . . . . given

  2x² = 130 . . . . . . add 9

  x² = 65 . . . . . . . .divide by 2

  x = ±√65 . . . . . take the square root

  x ≈ ±8.1

log₂(7) + log₂(8) is equal to log₂(56).

Logarithmic is a mathematical concept that is used to describe the relationship between a number and its exponent. In particular, a logarithm is the power to which a base must be raised to produce a given number. For example, if we have a base of 2 and a number of 8, the logarithm (base 2) of 8 is 3, since 2 raised to the power of 3 equals 8.

Logarithmic functions are commonly used in mathematics, science, and engineering to describe exponential growth and decay, as well as to solve various types of equations. They are particularly useful in dealing with large numbers, as logarithms allow us to express very large or very small numbers in a more manageable way.

The logarithmic function is typically denoted as log(base a) x, where a is the base and x is the number whose logarithm is being taken. There are several different bases that are commonly used, including base 10 (common logarithm), base e (natural logarithm), and base 2 (binary logarithm). The properties of logarithmic functions, including rules for combining and simplifying logarithmic expressions, are well-defined and widely used in mathematics and other fields.

We can use the logarithmic rule that states that the sum of the logarithms of two numbers is equal to the logarithm of the product of the two numbers. That is,

log₂(7) + log₂(8) = log₂(7 × 8)

Now we can simplify the product of 7 and 8 to get:

log₂(7) + log₂(8) = log₂(56)

Therefore, log₂(7) + log₂(8) is equal to log₂(56).

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Answer:

-0.22222222222

Step-by-step explanation:

Answer:

-2/9

Step-by-step explanation:

6/9 - 8/9 = -2/9 or in decimal -0.22

 The sample we collect plays a cruciThe sample we collect can significantly affect our understanding of a population,

especially when it comes to making generalizations or drawing conclusions about the entire population based on the sample data. The key aspect in this regard is whether the sample is representative of the population.

A representative sample is one that accurately reflects the characteristics, diversity, and distribution of the population from which it is drawn. When our sample is representative, we can have greater confidence in generalizing the findings from the sample to the larger population. However, if our sample is not representative, our understanding of the population may be biased or limited.

In the provided example, the given data represents different age groups and their reported time spent with friends per day. If we were to collect a sample from this population, it would be crucial to ensure that the sample includes individuals from each age group in proportion to their representation in the population. This would help ensure that our sample accurately reflects the age distribution of the population.

If our sample is not representative, it may lead to inaccurate conclusions. For instance, if we only surveyed individuals from the age group 55-64 and ignored the other age groups, our understanding of the population's time spent with friends would be limited to that specific age group. We wouldn't be able to generalize our findings to the entire population because we would have missed important variations in behavior across other age groups.

To improve the representativeness of our sample, we could use random sampling techniques, such as simple random sampling or stratified sampling, to ensure that individuals from all age groups are included in the sample. By doing so, we can enhance our understanding of the population as a whole and make more accurate inferences.

In conclusion, the sample we collect plays a crucial role in shaping our understanding of a population. A representative sample enables us to make valid generalizations and draw reliable conclusions about the entire population. It ensures that the characteristics and diversity of the population are properly reflected in the sample, allowing for more accurate insights and informed decision-making.al role in shaping our understanding of a population

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Answer:

Correct Statement : The y- intercept of Function A is greater than the y- intercept of Function B

Answer:

a) 9

b)

\(1 \frac{1}{3} \)

c) 15

Step-by-step explanation:

The first step is to cancel out the fraction's denominator if possible.

a)

\(15 \times \frac{3}{5} \)

We can cancel the 5 out since 15 divided by 5 is 3. The answer that comes out is

\(3 \times \frac{3}{1} \)

Since 3/1 is 3, we can now simplify the values:

\(3 \times 3 = 9\)

b)

\(4 \times \frac{1}{3} \)

4 is indivisible by three and gives a non-whole value. This is not what we need here.

Instead we should do the division rule and find the remainder.

In this case, 4 divided by 3 gives 1 with a remainder of 1.

\(4 \times \frac{1}{3} = \frac{4}{3} \)

After we simplify the non-mixed fraction, we have to change it into a mixed fraction, which consists of a whole number and a fraction. We can split it into the following:

\( \frac{4}{3} = 1r1\)

The r1 is just the remainder of the fraction. Since we cannot remove 1 from the remainder, we add it back into the fraction's denominator of 3. This gives:

\( \frac{4}{3} = 1 + \frac{1}{3} = 1 \frac{1}{3} \)

c)

\( \frac{5}{2} \times 6\)

For this part, we can cancel out 2 since 6 is divisible by 2. This gives:

\( \frac{5}{1} \times 3\)

Since 5/1 is 5,

we can now solve part c:

\(5 \times 3 = 15\)

Answer:

Step-by-step explanation:

The volume of a cone is given by the formula ...

  V = 1/3πr²h

Filling in the given information, we can solve for the height.

  8792 mm³ = 1/3π(20 mm)²h

Dividing by the coefficient of h, we find the height to be ...

  h = 3(8792)/(3.14·400) mm = 21 mm

The height of the cone is 21 mm.

__

The slant height can be found using the Pythagorean theorem. It is the hypotenuse of a right triangle with legs equal to the radius (20 mm) and the height (21 mm).

  s² = (20 mm)² +(21 mm)²

__

  s² = (400 +441) mm² = 841 mm²

  s = √(841 mm²) = 29 mm

The ant crawls 29 mm to get from the base of the hill to the top.

The function f(x) = 2 - 8x is closest to the origin at the point (0.25, 1.5).

Let's calculate the distance using the formula d = sqrt(x^2 + y^2)

Substitute the value of y in terms of x in the above distance formula, we get d = sqrt[x^2 + (2 - 8x)^2]

Simplify this expression d = sqrt[x^2 + 4 - 32x + 64x^2]d = sqrt[65x^2 - 32x + 4]

To find the minimum value of d, we will find its derivative with respect to x

d' = (65x^2 - 32x + 4)^1/2 - (130x - 32)x / (2 * (65x^2 - 32x + 4)^1/2)

Equating the above derivative to 0 we get, 130x - 32 = 0x = 32/130 = 0.246

Let's find the corresponding y value using the function: f(x) = 2 - 8x

Substituting x = 0.246 we get y = f(0.246) = 1.508.

Thus the function f(x) = 2 - 8x is closest to the origin at the point (0.25, 1.5).

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is it factorization ...

Answer:

For two triangles to be congruent, SAS theorem requires two sides and the included angle of the first triangle to be congruent to the corresponding two sides and included angle of the second triangle. If the congruent angles are not between the corresponding congruent sides, then such triangles could be different.

hope that helps

Step-by-step explanation:

Answer:

associative property

Step-by-step explanation:

The value of x that will make the equation of the model true is: x = 5.8.

Create an equation using the model given, then isolate the variable in order to determine its value, which will make the equation true.

Given the model above, the following equation would be created below:

x + x + 9.4 = 21

Combine like terms

2x + 9.4 = 21

Subtract 9.4 from both sides

2x + 94 - 9.4 = 21 - 9.4 [subtraction property of equality]

2x = 11.6

Divide both sides by 2:

2x/2 = 11.6/2 [division property of equality]

x = 5.8

The value of x is: 5.8.

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Answer:

B

Step-by-step explanation:

It is B because every number, x, you plug in 5x-3, it is y.

Answer:

B

Step-by-step explanation:

If we plug in x = 5 because every chart has x = 5 as a different answer into the equation you will find it equals 22 and only B has 22 as the answer

Answer:

-5, 4                           10, 1

Step-by-step explanation:

Step-by-step explanation:

Original height is the initial value, burn down rate is 0.5 inches per hour

This would be represented by a function:

Ordered pairs:

If the rate at which the candle burned was 0.45 inches per hour instead of 0.5 inches per hour, the relation would still be a function. The output values would have same difference of 0.45 inches and the function would be:

Answer:

The Total Surface Area of cone is 264 cm²

Step-by-step explanation:

Radius (r) = 6 cm

Slant height (l) = 8 cm

To find TSA of cone

A = πr(l + r)

A = 22/7 × 6 × (8 + 6)

A = 22/7 × 6 × (14)

A = 22/7 × 84

A = 22 × 12

A = 264 cm²

Thus, The Total Surface Area of cone is 264 cm²

-TheUnknownScientist 72

Answer:

The mean weight of an adult is 66 kilograms with a variance of 144. If 123 adults are randomly selected, the sample mean would follow a normal distribution with a mean of 66 kilograms and a standard deviation of sqrt(144/123) = 3/sqrt(123) kilograms.

We can standardize the sample mean to find the probability that it would be greater than 66.7 kilograms. The standardized value for 66.7 is (66.7 - 66) / (3/sqrt(123)) = 2.3094.

Using a standard normal distribution table, we find that the probability of a standard normal variable being greater than 2.3094 is approximately 0.0104.

Therefore, the probability that the sample mean would be greater than 66.7 kilograms is approximately 0.0104, rounded to four decimal places.

Step-by-step explanation:

Answer:

Step-by-step explanation:

9x-1 + 5x-15 =180, 14x-16=180, x = 14

9x-1 + y-20 = 180, 126-1-20+y =180, y = 105

Answer:

-3/10

Step-by-step explanation:

-3/4 * 2/5 = (-3 * 2) / (4 * 5) = - 6/20 = -3/10

Answer:

-3/10

Step-by-step explanation:

reduce the numbers -3/2 x 1/5

multiply

Answer:

\(g(f(6))= 17\)

Step-by-step explanation:

\(g(f(6))= 3(2(6) - 5) - 4\)

\(3(12 - 5) - 4\)

\(3(7) - 4\)

\(21-4\)

\(g(f(6))= 17\)

Answer:

g(f(6)) = 17

Step-by-step explanation:

f(x) = 2x - 5

g(x) = 3x - 4,

g(f(6))

First find f(6) = 2*6 -5 = 12-5 = 7

Then find g(7) = 3*7 -4 = 21-4 = 17

g(f(6)) = 17

Answer:

44.92

Step-by-step explanation: