What is the answer 1/3 of 12 = 1/4

The better deal of the given pair is $31.05/1. The unit rate is $2.07.

The better deal is the deal that has the lower unit rate. Unit rate is the price per gallon. The unit rate can be determined by dividing the total cost by the total gallons bought.

Division is the operation that is used in mathematics to determine the quotient of two or more numbers. Division entails grouping a number into groups using another number. Other operations used in mathematics are addition, multiplication and subtraction.

Unit rate = total cost / number of gallons

$56 / 25 = $2.24

$31.05 / 15 = $2,07

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Answer: 192

Step-by-step explanation:

2×8=16

2×6=12

17×12=192

So, the answer is 192.

The probability value of (m, n) is (1, 2^1005).

Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.

We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.

Thus, the probability is:

P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004

We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.

Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|

where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.

By the inclusion-exclusion principle:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)

where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.

This simplifies to:

(1/2) ⋅ (2^1004 + (-1)^1005)

Thus, the probability is: P = (1/2^1004) ⋅ (1/2) ⋅ (2^1004 + (-1)^1005) = 1/2 + 1/2^1005. Hence, (m, n) = (1, 2^1005).

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Complete question:

If m/n is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with m and n being relatively prime positive integers. what is probability value of m and n?

The probability value of (m, n) is (1, 2^1005).This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.

We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.

Thus, the probability is:

P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004

We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.

Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|

where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.

By the inclusion-exclusion principle:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)

where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.

This simplifies to:

\((1/2) * (2^{1004} + (-1)^1005)\)

Thus, the probability is: P = \((1/2)^{1004}* (1/2) *(2^{1004} + (-1)^{1005}) = 1/2 + 1/2^{1005}.\)

Hence, (m, n) = (\(1, 2^{1005\)).

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Answer:

Slope: 1.75

Step-by-step explanation:

Slope = (3-10) / (0-4)

         = -7 / -4

         = 1.75

The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

9.4 cm to nearest tenth.

Step-by-step explanation:

Diagonal of the  6*2 base:

d^2 = 6^2 + 2^2 = 40

d = √40

So the required diagonal:

D^2 = (√40)^2+ 7^2

D^2 = 89

D = √89 = 9.434.

Answer:

15.1

Step-by-step explanation:

To find the length of the rectangular prism' diagonal, use the formula for the length of a diagonal of a right rectangular prism.

d=l2+w2+h2−−−−√

Substitute 7 for l, 6 for w, and 12 for h

Then simplify.

d=72+62+122−−−−√

=49+36+144−−−−√

=229−−−√≈15.1

Therefore, the length of the rectangular prism's diagonal is about 15.1cm.

The longest poster that can fit in the box must have dimensions of 10 inches (height) by 20 inches (length) by 12 inches (width).

To find the longest poster that can fit in the box, we need to determine the longest dimension of the box itself. Since the box is 10 inches high, the longest poster that can fit in the box must have a height of no more than 10 inches.

Now, we need to consider the other two dimensions of the box. The box is 20 inches long and 12 inches wide, so the longest poster that can fit in the box must have a length of no more than 20 inches and a width of no more than 12 inches.

As for why we can only fit one maximum-length poster in the box but we can fit multiple 22-inch posters in the same box, it's because the length and width of the box are larger than the length and width of the 22-inch poster.

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The marginal propensity to consume (MPC) for Australia in 2021, when total income (Y) is 10, is 0.3.

The consumption function for Australia in 2021 is given as C = 0.0052 + 0.3Y + 20, where C represents the total consumption and Y represents the total income. To calculate the MPC, we need to determine how much of an increase in income is consumed rather than saved. In this case, when Y = 10, we substitute the value into the consumption function:

C = 0.0052 + 0.3(10) + 20

C = 0.0052 + 3 + 20

C = 23.0052

Next, we calculate the consumption when income increases by a small amount, let's say ΔY. So, when Y increases to Y + ΔY, the consumption function becomes:

C' = 0.0052 + 0.3(Y + ΔY) + 20

C' = 0.0052 + 0.3Y + 0.3ΔY + 20

To find the MPC, we subtract the initial consumption (C) from the new consumption (C') and divide it by the change in income (ΔY):

MPC = (C' - C) / ΔY

MPC = (0.0052 + 0.3Y + 0.3ΔY + 20 - 23.0052) / ΔY

Simplifying the equation, we can cancel out the terms that don't involve ΔY:

MPC = (0.3ΔY) / ΔY

MPC = 0.3

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Answer:

4^3 - 25

Step-by-step explanation:

4^3 - 25 = 39

difference means subtract

Answer:

  \(\dfrac{887}{990}\)

Step-by-step explanation:

Multiply by 100, subtract the original and divide the result by 99.

  \(x=0.8\overline{95}\\100x=89.5\overline{95}\\100x-x=89.5\overline{95}-0.8\overline{95}=88.7\\99x=88.7\\\\x=\dfrac{88.7}{99}=\boxed{\dfrac{887}{990}}\)

Answer:

area = 288.62 mm²

Step-by-step explanation:

To find the area we divide the complex shape into simple shapes whose areas we can find.

There is a rectangle in the center.

There are 2 congruent triangles on the sides.

We have the lengths of 2 perpendicular sides of the triangles, so they are the base and height.

For the rectangle, we only have the width. We need to find the length.

The length of the rectangle is the hypotenuse of the triangles.

We use the Pythagorean theorem to find the length of the hypotenuse of the right triangle. That is the length of the rectangle.

a² + b² = c²

(10.4 mm)² + (15.3 mm)² = c²

c² = 342.25 mm²

c = 18.5 mm

area = area of triangles + area of rectangle

area = 2 × (1/2)bh + LW

area = 2 × (1/2) × 15.3 mm × 10.4 mm + 18.5 mm × 7 mm

area = 159.12 mm² + 129.5 mm²

area = 288.62 mm²

C is the correct answer.

The measure of the major arc JLK will be 206°. Then the correct option is B.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

The measure of the minor arc JK will be 154°.

Then the sum of the major arc and minor arc in a circle is 360°.

Then the major arc JLK will be given as,

JLK + JK = 360°

JLK + 154° = 360°

JLK = 206°

The measure of the major arc JLK will be 206°. Then the correct option is B.

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The answer is low using correlation.

What is correlation?

The terms "co" and "relation" are combined to form the word "correlation." Correlation is the relationship between any set of data when taken as a whole because the term "co" signifies together.

The correlation coefficient, which in statistics is a number between -1 and +1, measures the linear dependency of the collection of data.

It cannot capture nonlinear correlations between two variables and only assesses the magnitude and direction of the linear link between the two variables.

The difference between dependent and independent variables is not possible.

In the question, it is given that there is a high positive correlation between x and y, which means for every increase in x there is a corresponding increase in y

So if x is having low score, than y is also having low score

Hence the answer is low.

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1.62 is the volume (in cm3) of 2 troy ounces of pure gold .

What is full answer for density?

We determine the volume, V, corresponding to the given amount of gold. We do this by dividing the given mass, m, by the density, d, such that

               V = m/d

  m = 31.03 g

   d = 19.3 g/ml

We proceed with the solution

  V = m/d

     = 31.03/19.3

      ≈ 1.62 ml

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The standard deviation (σ) of this discrete random variable X is 6 dollars.

In Mathematics and statistics, an expected value is sometimes referred to as the long-term mean (average) of a discrete random variable, E(X) and it can be calculated by taking the weighted average of all the outcomes of the discrete random variable with respect to their probabilities.

In this context, we can logically deduce that the expected value (mean) is given by µₓ is equal to $6.

Based on the probability distribution table (see attachment), we would determine the variance of this discrete random variable X as follows;

Variance (X) = (-12 - 6)²(0.1) + (8 - 6)²(0.9)

Variance (X) = 36

Now, we can determine the standard deviation (σ) of this discrete random variable X is;

Variance (X) = σ²

σX = √36

σX = $6

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:

Side bc.

Step-by-step explanation:

Answer:

A- side AB

Step-by-step explanation:

Corresponding to line QR is BC and if u turn it anticlockwise the side is actually AB

I hope im right!!

The variable "middle" in a binary search algorithm represents the index or position of the element that is being compared in each iteration of the search process.

In a binary search, the algorithm repeatedly divides the search space in half by comparing the middle element with the target value. The "middle" variable keeps track of the index or position of the element that is considered as the midpoint of the current search range.

During each iteration, the algorithm compares the target value with the element at the middle position. If the target value is equal to the middle element, the search is successful, and the algorithm returns the index of the middle element. If the target value is less than the middle element, the search continues on the left half of the search range, excluding the middle element. If the target value is greater than the middle element, the search continues on the right half of the search range, again excluding the middle element.

The "middle" variable is crucial in the binary search algorithm as it helps determine the boundaries of the search range for each iteration. By updating the middle position based on the comparison results, the algorithm efficiently reduces the search space in each step, resulting in a significant improvement in the search time compared to linear search algorithms.

Thus, the "middle" variable in a binary search algorithm represents the index or position of the element that serves as the midpoint of the current search range, allowing for efficient and systematic exploration of the search space.

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The correct answer is D. $2.75 / $3.24

To determine how much you should expect to pay for gas in Philadelphia versus Cleveland, we need to compare the transportation expenses in both cities. Based on the given data, the transportation expenses are as follows:

Philadelphia: $117

Cleveland: $106

To calculate the expected gas prices, we need to consider the transportation expenses relative to the national average. The formula to find the expected gas price is:

Expected Gas Price = National Average * (Transportation Expense / National Average)

National Average for gas = $2.59

For Philadelphia:

Expected Gas Price in Philadelphia = $2.59 * ($117 / 92) ≈ $3.30

For Cleveland:

Expected Gas Price in Cleveland = $2.59 * ($106 / 78) ≈ $3.51

Comparing the expected gas prices, we find that:

A. $3.03 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

B. $1.95 / $2.59: This option does not match the expected gas prices in Philadelphia and Cleveland.

C. $2.34 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

D. $2.75 / $3.24: This option matches the expected gas prices in Philadelphia and Cleveland.

Therefore, the correct answer is:

D. $2.75 / $3.24

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The surface area of the rectangular prism is 88 square inches.

Given that:

Length, L = 6 inches

Width, W = 2 inches

Height, H = 4 inches

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

SA = 2(6 x 2 + 2 x 4 + 4 x 6)

SA = 2 (12 + 8 + 24)

SA = 2 x 44

SA = 88 square inches

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Answer:

x = -5

Step-by-step explanation:

each curve will get increasingly closer to -5 but never reach it

if you look at the function, f(x) = 3/(x+5),  x≠ -5 because then the denominator would be zero and that is never possible

The vertical asymptote of the function will  be \(x=-5\).

A vertical asymptote is a vertical line i.e. as approaches from either the positive or negative side, the function approaches infinity. Vertical asymptotes occur at the values where a rational function has a denominator of 0.

We have,

\(f(x)=\frac{3}{x} +5\)

So,

As the above definition says,

A Vertical asymptote of a function is a vertical line \(x=k\), where \(f(x)\) becomes unbounded.

So,

Vertical asymptote for given figure and given function is ,

\(x=-5\),

Hence we can say that the vertical asymptote of the function will  be \(x=-5\).

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The equation of the variable y in terms of x is y = -2x + 16

From the question, we have the following parameters that can be used in our computation:

(2, 12) and (6, 4)

A linear equation is represented as

y = mx + c

Substitute the given points in the above equation, so, we have the following representation

2m + c = 12

6m + c = 4

When the equations are subtracted, we have

-4m = 8

So, we have

m = -2

Next, we have

2(-2) + c = 12

Evaluate

c = 16

Recall that

y = mx + c

So, we have

y = -2x + 16

Hence, the variable y in terms of x is y = -2x + 16

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The missing value is 1/3 from the table that represents Judy's rate which is the correct answer that would be an option (C).

In mathematics, relations are used to describe the link between the components of two sets. They aid in mapping items from one set (known as the domain) to elements from another set (known as the range), resulting in ordered pairs of the form (input, output).

We have been given the rates of time taken by Judy and Sal to complete a puzzle.

Sal's rate is r, as we can see from the table. Judy is said to take 3 hours to solve a puzzle by herself. It barely takes them two hours to work with Sal.

Because Judy completes the task in three hours, the portion of the puzzle finished in one hour is 1/3.

Therefore, the missing value is 1/3 from the table that represents Judy's rate

Hence, the correct answer would be an option (C).

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Answer:

option D is correct

x=O and x=-8

The number of different spanning trees for each graph is: a) K3: 1, b) K4: 4, c) K2,2: 2 and d) C5: 5.

a) The complete graph K3 consists of 3 vertices, and in a spanning tree, we need to have exactly 3 vertices connected without forming any cycles. Therefore, K3 has only one possible spanning tree.

b) The complete graph K4 has 4 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. K4 can be thought of as a tree with 4 branches extending from a central vertex. Each branch can be connected to any of the other vertices. Hence, there are 4 possible spanning trees for K4.

c) The complete bipartite graph K2,2 consists of 4 vertices divided into two sets, each containing 2 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. Since there are only two possible edges between the two sets, there are only two possible spanning trees for K2,2.

d) The cycle graph C5 consists of 5 vertices arranged in a circular shape. To form a spanning tree, we need to connect all 5 vertices without creating any cycles. Removing any one of the edges from the cycle will result in a tree. Therefore, C5 has 5 different spanning trees.

Therefore, the number of different spanning trees for each graph is:

a) K3: 1

b) K4: 4

c) K2,2: 2

d) C5: 5  

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It is concluded that the alternative hypothesis H1: σ² < 100 is true.

The variance is the square of the standard deviation of a sample of observations. In order to test whether a given variance of the population is equal to a given value, we make use of the chi-square distribution.

Thus, let X be a random variable that has a normal distribution with mean μ and variance σ². The formula to calculate chi-square distribution is as follows:

chi-square (x²) = (n-1) * S² / σ²Where n = sample size, S² = sample variance, and σ² = population variance.

Now, let's perform a hypothesis test with the given data:

Null hypothesis:H0: σ² = 100

Alternative hypothesis:

H1: σ² < 100

The value of the test statistic is:chi-square (x²) = (n-1) * S² / σ²= (25-1) * 131.29 / 100= 33.82

The degrees of freedom (df) for the test is

:df = n - 1= 25 - 1= 24

The critical value for chi-square distribution at df = 24 and α = 0.01 is 9.7097.

Since the calculated test statistic (33.82) is greater than the critical value (9.7097), we reject the null hypothesis and conclude that there is evidence to suggest that the variance of the miles per gallon (mpg) is less than 100.

Therefore, it is concluded that the alternative hypothesis H1: σ² < 100 is true.

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Answer:

17.6

Step-by-step explanation:

Answer:

The given matrix equation can be written as:

[2 3; 2 1] * [x; y] = [20; 8]

Multiplying the matrices on the left side of the equation gives us the system of equations:

2x + 3y = 20 2x + y = 8

To solve for x and y using matrices, we can use the inverse matrix method. First, we need to find the inverse of the coefficient matrix [2 3; 2 1]. The inverse of a 2x2 matrix [a b; c d] can be calculated using the formula: (1/(ad-bc)) * [d -b; -c a].

Let’s apply this formula to our coefficient matrix:

The determinant of [2 3; 2 1] is (21) - (32) = -4. Since the determinant is not equal to zero, the inverse of the matrix exists and can be calculated as:

(1/(-4)) * [1 -3; -2 2] = [-1/4 3/4; 1/2 -1/2]

Now we can use this inverse matrix to solve for x and y. Multiplying both sides of our matrix equation by the inverse matrix gives us:

[-1/4 3/4; 1/2 -1/2] * [2x + 3y; 2x + y] = [-1/4 3/4; 1/2 -1/2] * [20; 8]

Solving this equation gives us:

[x; y] = [0; 20/3]

So, a t-shirt costs $0 and a notebook costs $20/3.