A school administrator surveyed high school sophomores about their expectations for college attendance. One question asked was: "What do you think the chances are that you will graduate from college?" Their responses are shown below in the two-way table by gender.

Answer:

Length of Sarah rope    = 6 m

Length of Amanda's rope  = 4 m

Length of Mary's rope  = 7 m

Step-by-step explanation:

Let the length of Sarah rope = x

Length of Amanda's rope= x - 2

Length of Mary's rope = (x - 2 ) + 3 = x - 2 + 3 = x + 1

Length of rope = 17 m

x + x - 2 + x + 1 = 17

Combine like terms

x + x + x - 2 + 1 = 17

       3x  - 1 = 17

Add 1 to both sides

3x = 17 + 1

3x = 18

Divide both sides by 3

x = 18/3

x = 6

Length of Sarah rope = x  = 6 m

Length of Amanda's rope= x - 2 = 6 - 2 = 4 m

Length of Mary's rope =   x + 1 = 6 + 1 = 7 m

Answer:

145°

Step-by-step explanation:

180 - 35 = 145

145°

Based on the passage you provided, it seems like you are being asked to apply principles of logic and construct a truth table based on the premises and conclusion presented in the passage. To accomplish this, you need to follow the three steps outlined:

Step 1: Break the premises into several statements (usually denoted by p, q, r, etc.)

From the passage, we can identify the following statements:

- Statement 1: Water is fundamental for life and the environment.

- Statement 2: Water crisis is one of the most important challenges of the 21st century.

- Statement 3: Ensuring that we use water more wisely, more productively, and less profligately will be one of the defining challenges of this century.

- Statement 4: If all public services collaborate to address the water scarcity problem, then the governments will be able to provide a planning framework to manage water usage and boost awareness of the water crisis.

- Statement 5: There is a lack of planning frameworks or there are not enough campaigns to raise awareness of the water crisis.

- Statement 6: Therefore, there is no efficient collaboration among various public sectors to address the water shortage problem.

Step 2: Express the premises and conclusion symbolically.

Using the statements identified above, we can symbolically represent them as follows:

- p: Water is fundamental for life and the environment.

- q: Water crisis is one of the most important challenges of the 21st century.

- r: Ensuring that we use water more wisely, more productively, and less profligately will be one of the defining challenges of this century.

- s: All public services collaborate to address the water scarcity problem.

- t: Governments will be able to provide a planning framework to manage water usage and boost awareness of the water crisis.

- u: There is a lack of planning frameworks or there are not enough campaigns to raise awareness of the water crisis.

- v: There is no efficient collaboration among various public sectors to address the water shortage problem.

Step 3: Construct a truth table.

To construct a truth table, assign truth values (T or F) to each statement and evaluate the truth value of the conclusion based on the truth values of the premises

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Thus, the vertices of the larger square have the following coordinates: (-6, 7),  (1, 7),(1, 0), and  (-6 ,0).

The ratio of the scale of an original thing to a new object that is a representation of it but of a variable size is known as a scale factor (bigger or smaller).

The procedures below can be used to increase form A by a scale factor of 3.5 with the centre of enlargement at (8,-7).

Transform the square so that its origin is where the centre of enlargement is (0,0).

To do this, we deduct each vertex's coordinates from the centre of enlargement (8,-7):

A = (4 - 8, -3+ 7) = (-4, 4)

B = (6 -8, -3 + 7) = (-2, 4)

C = (6 - 8, -5 + 7) = (-2, 2)

D = (4 - 8, -5 + 7) = (-4, 2)

Multiply the coordinates of the each vertex by the scaling factor (3.5) to enlarge the translated square:

A = (-14, 14)

B = (-7, 14)

C = (-7, 7)

D = (-14, 7)

By adding those coordinates of the centre of the enlargement (8,-7) to each vertex, move the square from its larger state back to its original one:

A = (-14 + 8, 14-7) = (-6, 7)

B = (-7 + 8, 14-7) = (1, 7)

C = (-7 + 8, 7-7) = (1, 0)

D = (-14 + 8, 7-7) = (-6 ,0)

As a result, the vertices of the larger square have the following coordinates: (-6, 7),  (1, 7),(1, 0), and  (-6 ,0).

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Answer:

Yes

Step-by-step explanation:

\(6^{2}\) + \(8^{2}\) = \(10^{2}\)

36 + 64 = 100

The Pythagorean theorem is true.

x= -21 / 40

I hope it will help you

Answer: -4

There are rules, just follow the rules

6 students can be seated in a row of 6 chairs in 121 ways.

Given,

Number of students = 6

Number of chairs = 6

We have to find the number of ways the students can be seated in a row.

Here,

Jack insists on sitting in the first chair.

So, 1 way of sitting for jack.

Next,

5 students and 5 chairs are there.

So they can sit in;

5! = 120 ways

Therefore,

Total number of way of sitting is 120 + 1 = 121 ways.

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So, the value of r, the exponent of c, is 2, and the value of s, the exponent of d, is 4/3.

To simplify the expression \((c^6d^4)^{(1/3)}\), we can apply the exponent rule for raising a power to another power.

According to the rule, when we raise a power to another power, we multiply the exponents. In this case, we have \((c^6d^4)\) raised to the power of 1/3, which means we need to multiply the exponents by 1/3.

For c, the exponent becomes: 6 * (1/3) = 2

For d, the exponent becomes: 4 * (1/3) = 4/3

Therefore, the expression \((c^6d^4)^{(1/3)}\) simplifies to \(c^2d^{(4/3)}\)

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Answer:

12 Minutes

Step-by-step explanation:

60 minutes in fifths

60 ÷ 5

Answer:

12 min

Step-by-step explanation:

60= 1hr

60/5=12

Answer:

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

Step 1: Subtract 3x from both sides.

x+4−3x=3x−6−3x

−2x+4=−6

Step 2: Subtract 4 from both sides.

−2x+4−4=−6−4

−2x=−10

Step 3: Divide both sides by -2.

−2x /−2 = −10 /−2

x = 5

Answer:

C

Step-by-step explanation:

There are 3 pairs of corresponding sides with proportional lengths.

2 is a function h that multiplies a number x by 3.

The problem can be solved by following the given steps:

Step 1: Multiply a number x by 3.

Step 2: Subtract the cube of x from the result of step 1.

Step 3: Divide the result of step 2 by your age.

We can express this problem as an equation using function notation.

Let h(x) be the function that multiplies a number x by 3, then subtracts the cube of x, and divides the result by your age.

Then, we have:

\(h(x) =\frac{ (3x-x^3)}{a}\)

Where a represents your age.

We can substitute any value of x and a into this equation to find the result.

For example, if x = 2 and a = 20, then

\(h(2) = \frac{(3(2) - (2^3))}{20h(2)}\)

\(h(2) = \frac{(6 - 8)}{20h(2)}\)

\(h(2) = \frac{-2}{20h(2)}\)

\(h(2) = -0.1\)

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Answer:

10

Step-by-step explanation:

20/2=10

Answer:

10

Step-by-step explanation:

20÷2=10

twenty divided by two is ten

Cladograms are considered to be hypotheses because they depict possible evolutionary relationships variable between organisms based on their shared characteristics.

Cladograms are diagrams that depict the evolutionary relationships between organisms based on shared characteristics. They are used to illustrate the evolutionary history of organisms and to show how different species are related to each other. Cladograms are considered to be hypotheses because they are used to make inferences about evolutionary relationships and are based on the assumption that organisms with similar characteristics are more closely related. Cladograms are used to reconstruct the phylogeny of organisms and to identify new species or recent evolutionary changes. Cladograms provide a visual representation of how organisms are related and can be used to make predictions about how organisms may have evolved in the past and how they may continue to evolve in the future.

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The total mass of the lamina is 32π units, the moment about the x-axis is (32/5), the moment about the y-axis is 0, the center of mass is (0, 1/(5π)), and the moment of inertia about the origin is (64/7)π.

To find the total mass, we need to integrate the density function over the given region

m = ∬ρ(x,y) dA

where ρ(x,y) = 2(x^2+y^2) and the region is x^2+y^2 ≤ 16 in the first quadrant. Using polar coordinates, we have

m = \(\int\limits^0_\(pi /2\) \(\int\limits^0_4\) 2r^2 r dr dθ

= 2 \(\int\limits^0_\(pi /2\) [r^4/2]₀^4 dθ

= 2 \(\int\limits^0_\(pi /2\) 32 dθ

= 32π

So the total mass is 32π.

To find the moment about the x-axis, we need to integrate the product of the density function and the distance from the x-axis

Mx = ∬ρ(x,y) y dA

Using polar coordinates, we have

Mx = \(\int\limits^0_\(pi /2\)\(\int\limits^0_4\)2r^4 sinθ dr dθ

= 2\(\int\limits^0_\(pi /2\) [r^5/5]₀^4 sinθ dθ

= (32/5) \(\int\limits^0_\(pi /2\) sinθ dθ

= (32/5)

So the moment about the x-axis is (32/5).

To find the moment about the y-axis, we need to integrate the product of the density function and the distance from the y-axis

My = ∬ρ(x,y) x dA

Using polar coordinates, we have

My =\(\int\limits^0_\(pi /2\) \(\int\limits^0_4\) 2r^4 cosθ dr dθ

= 2 \(\int\limits^0_\(pi /2\) [r^5/5]₀^4 cosθ dθ

= 0

Since the region is symmetric with respect to the y-axis, the moment about the y-axis is zero.

To find the center of mass (X, Y), we need to use the following formulas

X = (My)/m

Y = (Mx)/m

From part B, Mx = (32/5), and from part A, m = 32π. Therefore:

Y = (Mx)/m = (32/5)/(32π) = 1/(5π)

From part C, My = 0. Therefore, X = 0. So the center of mass is located at (0, 1/(5π)).

To find the moment of inertia about the origin, we need to integrate the product of the density function and the distance squared from the origin

I = ∬ρ(x,y) (x^2+y^2) dA

Using polar coordinates, we have

I = \(\int\limits^0_\(pi /2\) \(\int\limits^0_4\) 2r^4 r^2 dr dθ

= 2\(\int\limits^0_\(pi /2\) [r^7/7]₀^4 dθ

= (128/7) ∫₀^(π/2) dθ

= (64/7)π

So the moment of inertia about the origin is (64/7)π.

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Answer:

100,000 days

Step-by-step explanation:

1,000,000 / 10 = 100,000 days.

Answer:

\( \displaystyle a) \: {x}^{ \circ} = 21.8 ^{ \circ} \)

Step-by-step explanation:

we are given opposite and adjacent

we want to figure out x°

remember that,

\( \displaystyle \: \tan( \theta) = \frac{opp}{adj} \)

where our opp is 5 and adj is 12.5

let \(\theta\) be x°

so

\( \displaystyle \: \tan( {x}^{ \circ} ) = \frac{5}{12.5} \)

\( \displaystyle \: {x}^{ \circ} = \arctan \left( \frac{5}{12.5} \right)\)

by using calculator

\( \displaystyle \: {x}^{ \circ} = 21.8\)

hence,

our answer is a

For breakfast, you have had 1/2 a serving of cereal and 1/4 cup of raisins, which count as one serving of fruit.

For breakfast, you have had one serving of cereal and one serving of fruit. In general, one serving of cereal is considered to be one cup, while one serving of fruit is considered to be one half cup. Therefore, in your bowl of oatmeal, you would have had two servings of cereal, and in your quarter cup of raisins, you would have had one serving of fruit. For lunch, you have had one serving of fruit in your glass of orange juice.

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Answer:

Step-by-step explanation:

Outlier

Answer:

Step-by-step explanation:

4 x 14= 56

The value of mean, variance and covariance matrix is illustrated in following solution as

\(V(\frac{X}{X'} )=\left[\begin{array}{ccc}\frac{1}{12} &\frac{1}{12} \\\frac{1}{12} &\frac{4}{45} \\\end{array}\right]\)

The mean vector consists of the means of each variable and the variance-covariance matrix consists of the variances of the variables along the main diagonal and the covariances between each pair of variables in the other matrix positions. with \bar{x} and \bar{y} denoting the means of X and Y, respectively.

Mean and variance is a measure of central dispersion. Mean is the average of given set of numbers. The average of the squared difference from the mean is the variance. Central dispersion tells us how the data that we are taking for observation are scattered and distributed.

To find the mean, variance and covariance matrix of a random vector

\(\left[\begin{array}{ccc}X\\X'\\\end{array}\right]\) X~ U(0,1)

\(E(X')=\int\limits^1_0 {r} \, dr = \frac{1}{r+1}\)

where, r = 1 , 2, 3...

Now,

\(E(X) = \frac{1}{2}\\ \\E(X^2) = \frac{1}{3}\\ \\E(X^3) =\frac{1}{4}\\\)

\(E(X^4)=\frac{1}{5}\)

So, cov(X , X') =

\(E(X^3)-E(X).E(X')\\\\=\frac{1}{4} -\frac{1}{2}.\frac{1}{3}\\ \\ =\frac{1}{12}\)

\(Var(X) = E(X^4) -E'(X')\\\\\frac{1}{5}-\frac{1}{9}\\ \\ \frac{4}{45}\)

Hence,

\(V(\frac{X}{X'} )=\left[\begin{array}{ccc}\frac{1}{12} &\frac{1}{12} \\\frac{1}{12} &\frac{4}{45} \\\end{array}\right]\)

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The given question is incomplete, complete question is:

suppose y follows a γ(α, β) distribution. find the mean and variance covariance matrix of the random vector x x2 , where x

The circumference of circle of radius 70 cm is 440 \(cm^{2}\).

According to the question,

We have the following information:

Radius of the circle = 70 cm

(Diameter is twice that of its radius..)

We know that the following formula is used to find the circumference of circle:

Circumference of circle = 2πr

(More to know: the formula to find the area of circle is π\(r^{2}\).)

(More to know: there are two values of π. One is 3.14 and one is 22/7.)

Circumference of circle = 2*(22/7)*70

Circumference of circle = 440 \(cm^{2}\)

Hence, the circumference of the circle of radius 70 cm is 440 \(cm^{2}\).

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Answer:

d line 1 and 3

Step-by-step explanation:

Answer:

It's 8.275. Hope that helped...

Answer:

y=70 x=20

Step-by-step explanation:

Answer:

The x-intercept is found by finding the value of x when y = 0, (x, 0), and the y-intercept is found by finding the value of y when x = 0, (0, y).

Step-by-step explanation:

x y = x + 2 Ordered pair

0 0 + 2 = 2 (0, 2)

1 1 + 2 = 3 (1, 3)

2 2 + 2 = 4 (2, 4)

this is probably not right but i gave an an example

:)

Answer:

C.

Step-by-step explanation:

By definition, the x-coordinate of the terminal point is equal to cos t and the y-coordinate is equal to sin t. This allows us to easily find the values of sin t and cos t. To find tan t, we use the formula tan t = sin t / cos t, which we can substitute with our previously found values for sin t and cos t.

First need to understand what is meant by the terms "terminal point" and "unit circle". The unit circle is a circle with a radius of 1, centered at the origin of the coordinate plane. The terminal point is the point where the circle intersects with a line that starts at the origin and passes through an angle t measured in radians.
To find sin t and cos t, we need to look at the coordinates of the terminal point. Let's call the x-coordinate of the terminal point x' and the y-coordinate y'. By definition, x' = cos t and y' = sin t. Therefore, sin t = y' and cos t = x'.
To find tan t, we use the formula tan t = sin t / cos t. Substituting in our values for sin t and cos t, we get:
tan t = y' / x'
So, to summarize:
- sin t = y'
- cos t = x'
- tan t = y' / x'
In summary, we can use the unit circle to determine the values of sin t, cos t, and tan t for any angle t measured in radians. The terminal point on the unit circle is the point where the circle intersects with a line passing through the origin at angle t.

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