What is the simplified answer to (2/3)^2 ?

The amount of pizza left for the other three classes is 1/2.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

The total number of pizzas ordered is 7.

The total number of pizzas eaten by the three classes is:

2 1/2 + 1 1/3 + 2 2/3

= (5/2) + (4/3) + (8/3)

= 15/6 + 8/6 + 16/6

= 39/6

= 6 3/6

= 6 1/2

Therefore, the amount of pizza left for the other three classes is:

7 - 6 1/2 = 1/2

So, there is half of a pizza left for the other three classes.

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The Lorenz curve is a graphical representation of income distribution in a country. The function f(x) measures the cumulative percentage of total income earned by the corresponding percentage of the population ranked by income.

Therefore, if the lowest 1/10 of the population earns 1/100 of the total income earned by everyone in the country, then f(1/10) would represent the cumulative percentage of total income earned by the bottom 10% of the population.

The Lorenz curve is a graphical representation of income distribution in a country. It measures the cumulative percentage of total income received by the cumulative percentage of the population.

In this case, if the lowest 1/10 of the population earns 1/100 of the total income, then f(1/10) represents the cumulative percentage of income earned by the lowest 10% of the population.

So, for this country, f(1/10) = 1/100. This means that the lowest 10% of the population earns 1% of the total income in the country.

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Step-by-step explanation:

x+y = 9     and   xy = 27     or   y = 27/x   sub this into the first equation

x + 27/x = 9

x^2 + 27= 9x

x^2 -9x + 27 = 0   Quadratic formula shows x = 9/2 +- 3 sqrt(3) i/ 2

so  x = 9/2 - 3 sqrt(3) / 2     y = 9/2 + 3 sqrt (3) i      ( or vica versa)

Answer:

No 1:85

no2:95

no3:96

no4 :78

no5:98

no6:100

no7:10999

no8:200

no9:48

no10:56

Step-by-step explanation:

distance = rate  X  time

    d         = 55 m/hr * 4 hr

     d = 220 miles

distance / time = rate

  220 miles / (3  2/3 hr ) =   60 m/hr

It is difficult to accurately predict the number of days a favorite radio or TV station will correctly forecast whether it will be cloudy over the next 30 days.

Forecasting weather accurately is a challenging task, and even the most advanced weather models are subject to errors. The accuracy of a station's forecasts depends on various factors such as the quality of their data sources, the skill and experience of their forecasters, and the complexity of the weather patterns in the region. Therefore, it is not possible to determine the exact number of days a station will make correct forecasts about whether it will be cloudy or not. However, it is important to note that modern weather forecasting has come a long way in recent years, and many stations now provide fairly accurate predictions. It is always a good idea to consult multiple sources and use personal judgment when making plans based on weather forecasts.

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Rectangle TUVY is dilated by a scale factor of 1/2 to form rectangle T’U’V’Y’.  The measure of side W’T’ is 15 units.

If rectangle TUVY is dilated by a scale factor of 1/2 to form rectangle T’U’V’Y’, the lengths of the corresponding sides are also scaled down by the same factor.

Given that side WT measures 30 units, we need to find the measure of side W’T’.

Since the scale factor is 1/2, we can calculate the length of W’T’ as follows:

W’T’ = (1/2) * WT

Substituting the given value:

W’T’ = (1/2) * 30

W’T’ = 15

Therefore, the measure of side W’T’ is 15 units.

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If the length of a rectangle is 7 centimeters less than five times its width, the dimensions of the rectangle are 2 cm × 3 cm.

Let x be the width of the rectangle in centimeters. Then, the length of the rectangle is 5x - 7 centimeters.

The formula for the area of a rectangle is A = lw, where A is the area, l is the length, and w is the width. In this case, we are given that the area is 6 square centimeters, so we can set up the equation:

6 = (5x - 7)x

Expanding the expression on the right side, we get:

6 = 5x² - 7x

Moving all terms to one side, we obtain:

5x² - 7x - 6 = 0

We can now solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 5, b = -7, and c = -6.

Plugging in these values, we get:

x = (7 ± √(7² - 4(5)(-6))) / 2(5)

x = (7 ± √(169)) / 10

x = (7 ± 13) / 10

The two possible values for x are x = 2 and x = -1/5. Since the width cannot be negative, we reject the negative solution and conclude that the width of the rectangle is 2 centimeters. Therefore, the length of the rectangle is 5(2) - 7 = 3 centimeters.

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Yes; using proportions, Andy is correct to believe that he has enough builders to finish this wall in less than 11 days.

Proportion refers to the ratio of one quantity or value compared to another.

Proportions are fractional values that are depicted in decimals, fractions, or percentages.

The number of builders that build Andy's wall in 15 days = 8

The number of days it would take 8 builders to finish the wall = 15 days

Proportionately, if 8 builders would take 15 days to build the wall, 11 builders would take 10.9 days (15 × 8) ÷11], which is approximately 11 days.

Thus, we can conclude that Andy is correct as 11 builders would take less than 11 days to finish the wall.

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Size, form, orientation, and location are the four fundamental geometric attributes that must be considered to define the geometry of a feature of a part.

Size refers to the dimensions of a feature or part, such as length, width, and height. These dimensions are typically specified in a drawing or model and must be precise to ensure that the part is manufactured to the correct size.

Form is the shape of a feature or part, including curves, angles, and other geometric features. Form must be accurately defined to ensure that the part is manufactured to the correct shape and that it will function as intended.

Orientation refers to the position of a feature or part in space. For example, a hole may need to be positioned at a specific angle relative to other features on the part. Orientation is critical to ensure that the part fits and functions correctly in the final assembly.

Location refers to the placement of a feature or part relative to other features on the part or relative to a specific reference point. The location of each feature on the part must be precisely defined to ensure that the part can be accurately manufactured and assembled.

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Based on the information we can infer that Sophie is a Savvy Shopper.

A "savvy shopper" is an informal term used to refer to a person who is an expert in finding and taking advantage of the best deals and promotions when shopping. Another outstanding characteristic of these people is that they plan their purchases in advance and take advantage of promotions and discounts.

According to the above, we can infer that if Sophie is a bargain shopper who collects coupons and plans her route to take advantage of sales. She is a savvy shopper.

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The prevalence of undernutrition among children aged 0-12 years in Refugee Camp X on January 1, 2011, was 57%. The incidence rate of measles among children during the same period was 51%.

The prevalence of undernutrition on January 1, 2011, can be calculated by dividing the number of children diagnosed with undernutrition (80) by the total number of children (140) and multiplying by 100. Therefore, (80/140) * 100 = 57%. This means that 57% of children in Refugee Camp X were diagnosed with undernutrition on January 1, 2011.

On January 31, 2011, there were no new additions or deaths among the children aged 0-12 years. Therefore, the total number of children remained the same at 140. Since the number of children with undernutrition did not change, the prevalence of undernutrition remained at 57%.

The incidence rate of undernutrition during the month of January 2011 can be calculated by dividing the number of new cases (20) by the total number of children at the beginning of the month (140) and multiplying by 100. So, (20/140) * 100 = 14%. This means that 14% of children developed undernutrition during January.

The incidence rate of measles during the month of January 2011 can be calculated by dividing the number of new measles cases (72) by the total number of children at the beginning of the month (140) and multiplying by 100. Thus, (72/140) * 100 = 51%. This indicates that 51% of children in Refugee Camp X developed measles during January 2011.

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Answer:

y = 4x + 10 y = 1 + 4^x

x y x y

0 10 0 2

1 14 1 5

2 18 2 17

3 22 3 65

4 26 4 257

Rate of change on [1, 3]:

For y = 4x + 10:

(22 - 14)/(3 - 1) = 8/2 = 4

For y = 1 + 4^x:

(65 - 5)/(3 - 1) = 60/2 = 30

The rate of change on [1, 3] is much greater on y = 1 + 4^x than on y = 4x + 10 because y = 1 + 4^x generally gives larger numbers than y = 4x + 10 as x gets larger.

Answer:

5/2 x 4 or 2.5 x 4 because they both equal the same thing so yeah and the second one because if u convert the fraction to decimal that’s what it equals bye have a great day please give brainliest I’m new to this app

Step-by-step explanation:

The relation ∼ on R × R, given by (x1,y1) ∼ (x2,y2) ⇔ (x1)²(y1)² = (x2)²(y2)², is an equivalence relation.

To show that the given relation is an equivalence relation, we need to prove that it satisfies the three conditions of reflexivity, symmetry, and transitivity.

Reflexivity: For any (x,y) in R × R, we have (x)²(y)² = (x)²(y)², which implies that (x,y) ∼ (x,y).

Symmetry: If (x1,y1) ∼ (x2,y2), then (x1)²(y1)² = (x2)²(y2)². This implies that (x2)²(y2)² = (x1)²(y1)², and hence (x2,y2) ∼ (x1,y1).

Transitivity: If (x1,y1) ∼ (x2,y2) and (x2,y2) ∼ (x3,y3), then (x1)²(y1)² = (x2)²(y2)² and (x2)²(y2)² = (x3)²(y3)². Multiplying these equations, we get (x1)²(y1)² = (x3)²(y3)², which implies that (x1,y1) ∼ (x3,y3).

Since the given relation satisfies all three conditions, it is an equivalence relation.

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The probability density function on [0 1] is 36, the correct option is C.

We are given that;

Function f(x) = ke-^(3x+2)

Now,

The function f(x) = ke^(-3x+2) is a probability density function on [0 1] if and only if the integral of f(x) from 0 to 1 is equal to 1.

∫(0 to 1) ke^(-3x+2) dx = -1/3ke^(-3x+2) from 0 to 1 = -1/3ke^-1 + 1/3ke^2

For f(x) to be a probability density function, the above expression must be equal to 1. Therefore,

-1/3ke^-1 + 1/3ke^2 = 1

Solving for k gives us k = 36

Therefore, by probability the answer will be 36.

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The minimum distance from the line x + 2y = 5 to the point (0, 0) is found to be √(5).

We can start by finding the equation of the perpendicular line that passes through the origin. The given line can be rewritten in slope-intercept form as y = (-1/2)x + 5/2. The slope of any line perpendicular to this line is the negative reciprocal, which is 2. So, the equation of the perpendicular line passing through the origin is y = 2x.

x + 2y = 5

y = 2x

Substituting y = 2x into the first equation gives,

x + 2(2x) = 5

5x = 5

x = 1

Substituting x = 1 into y = 2x gives,

y = 2(1)

y = 2

So, the intersection point is (1, 2). Now, the distance,

√[(1-0)² + (2-0)²] = √5

Therefore, the minimum distance from the line x + 2y = 5 to the point (0,0) is √5.

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Complete question - find the minimum distance from the line x + 2y = 5 to the point (0, 0). (hint : start by minimizing the square of the distance.)

Answer:

To simplify the given expression -2wx² (7w^5-3w³x² +8x^4), we can use the distributive property of multiplication over addition/subtraction. First, we can distribute -2wx² to each term inside the parentheses:-2wx² * 7w^5 = -14w^6x²-2wx² * (-3w³x²) = 6w³x^4-2wx² * 8x^4 = -16wx^6\

Now, we can combine these simplified terms by adding or subtracting them based on their exponents:-14w^6x² + 6w³x^4 - 16wx^6. This is the final simplified form of the given expression.

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The t-statistic distribution is similar to the normal distribution in shape, but it has heavier tails due to its smaller sample size and greater variability. This means that the t-statistic distribution has more extreme values (both positive and negative) than the normal distribution.

The shape of the t-statistic distribution, compared to the normal distribution, can be described as having thicker tails and a more peaked center. This means that the t-distribution has a higher probability of extreme values than the normal distribution. As the sample size increases, the t-distribution approaches the normal distribution in shape.

The t-statistic distribution is a probability distribution used in hypothesis testing when the sample size is small and the population standard deviation is unknown. It is a family of continuous probability distributions that depend on the sample size and the degrees of freedom.

The t-distribution is similar in shape to the standard normal distribution, but it has heavier tails and is more spread out. The shape of the t-distribution changes as the degrees of freedom change. As the sample size increases, the t-distribution approaches the standard normal distribution.

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The directional derivative of the function f(x,y) in the direction of a at the point p0 is given by the dot product of the gradient of f at p0 and the unit vector in the direction of a.

Therefore, to find the derivative of f(x,y) at p0 in the direction of a, we first need to find the gradient vector of f at p0 and then compute the dot product of that gradient vector with the unit vector in the direction of a.

To find the gradient vector of f at p0, we first compute the partial derivatives of f with respect to x and y:

fx(x,y) = y

fy(x,y) = x - 6y

Then, we evaluate these partial derivatives at the point p0=(-7,0) to obtain:

fx(-7,0) = 0

fy(-7,0) = -7

Therefore, the gradient vector of f at p0 is:

∇f(-7,0) = (0, -7)

To find the unit vector in the direction of a, we first need to normalize a by dividing it by its magnitude:

|a| = sqrt(1^2 + 2^2) = sqrt(5)

a_hat = (1/sqrt(5), 2/sqrt(5))

Then, the derivative of f at p0 in the direction of a is given by:

Daf(-7,0) = ∇f(-7,0) · a_hat

         = (0, -7) · (1/sqrt(5), 2/sqrt(5))

         = -14/sqrt(5)

Therefore, the derivative of f(x,y) at p0=(-7,0) in the direction of a=(1,2) is -14/sqrt(5).

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The design parameters for the rapid-mix system are Number of tanks= 1, Water power input = 11.9 kW, Tank dimensions: depth = 2 m, width = 4.62 m, Diameter of the impeller is 1.2 m and Rotational speed of impeller is  50 rpm.

To design the rapid-mix system, we can use the following equations:

Number of tanks: n = Q t / V

where Q = flow rate = 0.168 m^3/s

t = detention time = 5 s

V = volume of one tank = [tex](depth)^{2}[/tex] × width

Water power input: P = ρ Q [tex]G^{2}[/tex] B / NP

where ρ = density of water = 1000 kg/[tex]m^{3}[/tex]

G = velocity gradient = 700 [tex]s^{-1}[/tex]

B = shape factor = 3/2

NP = power number = 5.7

Tank dimensions: depth = width / 2

Diameter of the impeller: D = 0.35 × width

Rotational speed of impeller: N = (P / 2π) × (NP / ρ [tex]D^{5}[/tex])

Using the above equations, we can solve for the design parameters as follows:

Volume of one tank:

V = Q t / n = (0.168)(5) / 1 = 0.84[tex]m^{3}[/tex]

Tank dimensions:

width = [tex](V/Depth^{2} )^{1/3}[/tex] = [tex](0.84/Depth^{2} )^{1/3}[/tex]

depth = width / 2

To find the width and depth of the tank, we need to try different values of depth and calculate the corresponding width using the above equation. We can start with a depth of 1 m and iterate until we get a width that is close to a square plan (i.e., width ≈  [tex](depth)^{2}[/tex] ). For example, if we try a depth of 1 m, we get:

width = [tex](0.84/1^{2} )^{1/3}[/tex] ≈ 0.96 m

This is not close to a square plan, so we can try a larger depth, say 2 m:

width = [tex](0.84/2^{2} )^{1/3}[/tex] ≈ 1.21 m

This is closer to a square plan, so we can use a depth of 2 m and a width of 4.62 m.

Number of tanks:

n = Q t / V = (0.168)(5) / 0.84 ≈ 1.0

We can use one tank for this design.

Diameter of the impeller:

D = 0.35 × width = 0.35 × 4.62 m ≈ 1.62 m

We can choose the impeller diameter of 1.2 m from the available options.

Water power input:

P = ρ Q [tex]G^{2}[/tex] B / NP = (1000)(0.168)[tex]700^{2}[/tex](3/2) / 5.7 ≈ 11.9 kW

Rotational speed of impeller:

N = (P / 2π) × (NP / ρ [tex]D^{5}[/tex]) = (11.9 kW / (2π)) × (5.7 / (1000)[tex]1.2^{5}[/tex] ≈ 50 rpm

Therefore, the design parameters for the rapid-mix system are:

Number of tanks: 1

Water power input: 11.9 kW

Tank dimensions: depth = 2 m, width = 4.62 m

Diameter of the impeller: 1.2 m

Rotational speed of impeller: 50 rpm

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Answer:

A. This data set has two modes. Both 3 and 4 are the modes of the data set.

Step-by-step explanation:

The mode is a statistical measure that represents the most frequently occurring value in a data set. In the given data set, 1 appears once, 2 appears once, 3 appears three times, 4 appears three times, 5 appears once, and 7 appears once. Since both 3 and 4 appear three times, the data set has two modes, which are 3 and 4. Therefore, the correct answer is A: "This data set has two modes. Both 3 and 4 are the modes of the data set." Option B is incorrect because the mode cannot be calculated by taking the average of the values that appear most frequently, and option C is incorrect because the data set does have modes.

Given a time impact of 3 months and a likelihood of 0.40, the risk consequence time (rt) is calculated to be 1.2 months is False

The formula for calculating Risk Consequence Time (RCT) is:

RCT = Time Impact x Likelihood

Using the values given in the question:

RCT = 3 months x 0.40 = 1.2 months

Therefore, the calculated RCT is 1.2 months, which is the same as the value given in the question. So the statement is true.

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The number of dots that should be place above the 3 in the dot plot is: 4 dots

A dot plot is one that is used to represent any data in the form of dots or small circles. It is similar to a simplified histogram or a bar graph as the height of the bar formed with dots represents the numerical value of each variable. Dot plots are thus used to represent small amounts of data. For example, a dot plot can be used to collect the vaccination report of newborns in an area, which is represented in the following table.

Now, from the given table, we see the pea pods and the number of peas they have.

Now, from the table, only one Pea pod has 2 peas and that's why we have one dot above 2.

However, we can see that 4 pea pods have 4 number of peas and as such we will have 4 dots above 3.

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The factored function is given as follows:

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (x^2 + 6x - 4)(x^2 - 4x + 8)[/tex]

The function for this problem is defined as follows:

[tex]y = x^4 + 2x^3 - 20x^2 + 64x - 32[/tex]

The zeros are given as follows:

Hence the function is factored as follows:

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (ax^2 + bx + c)(x - 2 + 2i)(x - 2 - 2i)[/tex]

(we have the multiplication of two second degree polynomials resulting in a fourth degree polynomial, we must obtain the other second degree polynomial).

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (ax^2 + bx + c)(x^2 - 4x + 8)[/tex]

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = ax^4 + (-4 + b)x^3 + \cdots + 8c[/tex]

(it is not necessary to make the calculations in the middle of the function as they are not needed to obtain the constants).

Hence the value of a is given as follows:

a = 1.

The value of b is given as follows:

-4 + b = 2

b = 6.

The value of c is given as follows:

8c = -32

c = -4.

Hence the factored expression is of:

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (x^2 + 6x - 4)(x^2 - 4x + 8)[/tex]

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The sampling distribution for random samples of 30 students is most likely to follow a normal distribution.

This is based on the central limit theorem, which states that as sample size increases, the sampling distribution of the mean tends to approach a normal distribution, regardless of the shape of the population distribution.

The normal distribution is characterized by a symmetrical bell-shaped curve and is commonly used in statistical analysis to model a wide range of natural phenomena, including measurement errors, human traits, and physical properties. It is also widely used in inferential statistics to estimate population parameters, such as means and variances, from sample statistics.

Therefore, in the absence of information about the population distribution, a normal distribution is a reasonable assumption for the sampling distribution of random samples of 30 students.

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The sampling distribution for random samples of 30 students is most likely to follow a normal distribution.

This is based on the central limit theorem, which states that as sample size increases, the sampling distribution of the mean tends to approach a normal distribution, regardless of the shape of the population distribution.

The normal distribution is characterized by a symmetrical bell-shaped curve and is commonly used in statistical analysis to model a wide range of natural phenomena, including measurement errors, human traits, and physical properties. It is also widely used in inferential statistics to estimate population parameters, such as means and variances, from sample statistics.

Therefore, in the absence of information about the population distribution, a normal distribution is a reasonable assumption for the sampling distribution of random samples of 30 students.

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Answer:

Step-by-step explanation:

Answer: 0.6

Any other answer would be too far away

If it takes 5 seconds to travel and you hear it in 3, then 3/5 equals 0.6

Answer:

0.6 miles

Step-by-step explanation:

5 sec is to 1 mile as 3 sec is to x miles

5/1 = 3/x

5x = 3

x = 3/5 = 0.6

Answer: 0.6 miles

The association of the graph scatterplot is a negative nonlinear association

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be scattered and they do not follow a particular direction

Also, we can see that

As the x values change, the y values do not follow a pattern

This represents a nonlinear association.

Hence, the association is a negative nonlinear association

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The correct answer is D. The flux of F across C is the sum of the components of F orthogonal or normal to C at each point of C.

The flux of a two-dimensional vector field F across a smooth oriented curve C represents the amount of the field that passes through the curve. In this context, the correct answer is: D. The flux of F across C is the sum of the components of F orthogonal or normal to C at each point of C. This means that the flux is calculated by considering the components of the vector field that are perpendicular to the curve at each point along C. By summing these orthogonal components, we can determine the overall quantity of the field that passes through the curve.

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