Three changes that have happened to the environment

Answer: variability between means increases relative to the variability within groups

Step-by-step explanation:

The formula to calculate F-ratio : variance between groups divided by variance within groups

Here, F-ratio \(\propto\) is proportional to variance between groups but inversely proportional to variance within groups .

So, F-ratio increases when variability between means increases relative to the variability within groups.

Answer:

b) \(4a^{2} b^{2} c^3[\sqrt[3]{b} ]}\)

Step-by-step explanation:

For the network, the minimum value for x4 is 0, and there is no maximum value for x4, as it can go to infinity.

(a) To set up the system of equations that describe the traffic flow, we can use the principle of conservation of flow. This means that the total inflow into a junction must equal the total outflow.

Let x1, x2, x3, and x4 represent the flows in the network. Based on the given information, we can set up the following system of equations:

1. Junction A: x1 = x2 + x3
2. Junction B: x2 = x4
3. Junction C: x3 = x4

(b) Now we need to determine the flows x1, x2, and x3 if x4 = 100. We can use the equations from part (a) and substitute the value of x4:

1. Junction B: x2 = x4 = 100
2. Junction C: x3 = x4 = 100

Now we can substitute these values into the equation for Junction A:
x1 = x2 + x3 = 100 + 100 = 200

So, the flows are x1 = 200, x2 = 100, and x3 = 100.

(c) To determine the maximum and minimum values for x4, we need to consider the constraints that all flows are nonnegative:

x1 >= 0, x2 >= 0, x3 >= 0, x4 >= 0

Using the equations from part (a), we have:

1. x1 = x2 + x3
2. x2 = x4
3. x3 = x4

There is no upper limit on x4 since it only states that flows are nonnegative. So, x4 can go to infinity.

For the minimum value of x4,

if x4 = 0,

then

x2 = x4 = 0 and x3 = x4 = 0.

This will make x1 = x2 + x3 = 0 + 0 = 0, which satisfies the nonnegative constraint.

Therefore, the minimum value for x4 is 0, and there is no maximum value for x4, as it can go to infinity.

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Answer:

1100 square inches

Step-by-step explanation:

Formula: LxW

Smallest rectangles area: 5*20=100= 1 rectangle

there are 2 smal  rectangles so= 100*2=200

Medium rectangles area: 5*30=150

There are 2 so= 150*2= 300

Biggest rectangle: 30*20= 600

Total Area: 200+300+600= 1100 square inches

Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

Answer: The first option:

x ≤ -2  and 2x ≥ 6

Step-by-step explanation:

A compound inequality will have no solution if the inequalities are contradictory.

An example of this would be:

x > 3 and x < 1

There is no value of x that is at the same time larger than 3, and smaller than 1.

Now, let's analyze the options.

1) x ≤ -2  and 2x ≥ 6

This has no solution, because if x ≥ -2, the maximum value that x can take is x = -2

Replacing that in the other inequality we get:

2*(-2) > 6

-4 > 6

This is false, then this compound inequality has no solution.

2) x ≤ -1  and 5*x < 5

This ineqalty has infinite solutions, one can be x = -2

-2 ≤ -1 and 5*(-2) < 5

are both true.

3) x ≤ -1 and 3x ≥ -3

A solution for this can be x = -1

-1 ≤ -1  is true

3*(-1) ≥ -3

-3 ≥ -3 is true.

Then we have at least one solution here.

4) x ≤ -2  and 4x ≤ -8

Here we have infinite solutions, one can be x = -10

-10 ≤ - 2 is true

4*(-10) ≤ -8

-40 ≤ - 8 is also true.

Then the only option that has no solutions is the first one.

Answer:

The probability of landing on 8 twice is 1/64

Step-by-step explanation:

If you spin the spinner once, there are 8 possibilities each time (1-8). The possibility of landing on the number 8 is 1 of these 8 possibilities. Its probability is therefore 1/8

Each spin is independent. In other words, the spins do not affect each other. The number you land on during the first spin does not impact the second spin's number. The probability of landing on 8 the second time is the same as the first time: 1/8

Because the two events are independent, we find the probability of them both occurring by multiplying them together.

1/8 times 1/8= 1/64

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Answer:

answer is D prettyy sure

In order for Janet's investment to increase to $10,000 in five years at a 4% yearly interest rate compounded monthly, she needs to put aside about $8,079.90 now.

For instance, if you put $1,000 in a bank account that offers 1% yearly interest, after a year you would have received $10 in interest. Compound interest allowed you to make 1 percent on $1,010 in Year Two, which amounted to $10.10 in interest payments for the year.

We can use the formula for compound interest to find how much Janet needs to invest now:

\(A=P\left(1+\frac{r}{n}\right)^{n t}\)

where:

A = the amount of money after the specified time period

P = the principal (the amount of money Janet needs to invest now)

r = the annual interest rate (4% = 0.04)

n = the number of times the interest is compounded per year (12, since it is compounded monthly)

t = the time period, in years (5)

Plugging in the values we get:

10,000 = P(1 + 0.04/12)⁽¹²*⁵⁾

Solving for P, we get:

P = 10,000 / (1 + 0.04/12)⁽¹²*⁵⁾

P ≈ $8,079.90

Therefore, Janet needs to invest about $8,079.90 now to grow to $10,000 in 5 years at a 4% annual interest rate compounded monthly.

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Answer:

The probability of flipping a coin three times and getting 3 tails is 1/8.

Step-by-step explanation:

Answer:

c=16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

c = r+6

If r = 10 then,

c = 10+6

c = 16

The type of variable that represents the names of the automobile manufacturers would be the categorical variable.

A variable is defined as the quantity that may change within the context of a mathematical problem, research work or an experiment.

There are various types of variables that include the following:

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Answer:

The sale price is $7.00

Step-by-step explanation:

Answer:

-50

Step-by-step explanation:

I am going to rewrite it to make it look cleaner.

15y - 4x.

x = 5 and y = -2

15(-2) - 4(5) = -30 - 20 = -50

Answer:

=10

Step-by-step explanation:

Evaluate for x=5,y=2

(−4)(5)+(15)(2)

(−4)(5)+(15)(2)

=10

An inequality that can be written in the form ax + by < c (where a and b are not both zero) is called a linear inequality in two variables.

An inequality that represents a line in a two-dimensional coordinate system is referred to as a linear inequality. The set of points that satisfies the inequality is a half-plane bounded by a line that may be dashed or solid.

In contrast to a linear equation, which represents a line, a linear inequality represents a half-plane. The points on one side of the line, rather than the points on the line, are solutions to the inequality.

The method of shading is used to graph a linear inequality in two variables. First, graph the boundary line, which is usually represented by a solid or dashed line, and then select a test point on one side of the line. Shaded regions of the half-plane containing the test point satisfy the inequality.

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\( \frac{1}{2}\)will be the answer.

Step-by-step explanation:-

If the altitude to the hypotenuse of a right-angled triangle bisects the hypotenuse, then we can know that the triangle is Isosceles right triangle. (AB=AC)

Make AB=AC=2, so,

BC=\( \sqrt{ {2}^{2} + {2}^{2} } \)= \( \sqrt{4 + 4} \)= \( \sqrt{8} \)

Prime factorizing, we get,

BC = \( \sqrt{2 \times 2 \times 2} \)

Take two 2's outside by taking common because of "square" root,

⇢BC = \(2 \sqrt{2} \)

BD = DC = \( \sqrt{2} \),

AD = \( \sqrt{AB^{2} - BD^{2} } \)= \( \sqrt{4 - 2} \)= \( \sqrt{2} \)

So, AD=BD=CD= \( \frac{1}{2}\)BC

∴⇢\( \frac{AD}{BC} = \frac{1}{2} \)

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Answer:

As x approaches 6:

\( \frac{6 - x}{ {x}^{2} - 36 } = - \frac{x - 6}{(x - 6)(x + 6)} = - \frac{1}{x + 6} = - \frac{1}{6 + 6} = - \frac{1}{12} \)

The limit of the given function as x approaches 6 is -1/12. This is achieved by factoring and revising the original function, and then substituting into the revised function.

The student is asking for the limit of the function (6-x) / (x²-36) as x approaches 6. In mathematics, this is a problem of calculus and specifically involves limits. Let's solve this by first factoring the denominator to get (6-x) / ((x-6)(x+6))

By realizing we can revise the numerator as -(x-6), we make it obvious that the limit can be directly computed by substituting x=6 after canceling out the (x-6) terms. The result is -1/12, therefore the limit of the function as x approaches 6 is -1/12.

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Answer:

1:3

2:2

Step-by-step explanation:

Answer:

Step-by-step explanation:

All the other answers are wrong.

The points are reflected across the x-axis.

Here is why:

Correct choice is D.

Answer:

Total amount = $150160.24

Step-by-step explanation:

The amount deposit by the Bob annually (annuity) = $900

Number of years for which annuity made = 12 years

Inerest rate = 7.6% or 0.076

After 35 years the amount grows at the rate of 7.6% till the age of 65, the total number of years = 30 years.

Now we have to find the total amount after 65 years.

Total amount = annuity [((1+r)^n – 1) / r] × (1+r)^n

Total amount = 900[((1+ 0.076)^12 – 1) / 0.076] × (1+ 0.076)^30

Total amount = $150160.24

The number of silver coins Lily initially had is 28.

A ratio is described as a comparing two quantities with the same unit to determine the amount of each quantity is existent in the other. Ratios are divided into two types.

Now according to the question;

Let 'x' be the share of silver coin of Lily.

Let 'y' be the share of silver coin of Nada.

Lily and Nada share silver coins in the ratio 7:3

Thus, x/y = 7/3

Cross-multiplying

3x = 7y (equation 1)

Now, if Lily gives 3 silver coins to Nada, the ratio becomes 5:3.

(x - 3)/(y + 3) = 5/3

cross multiplying;

3x - 9 = 5y + 15

Simplifying;

3x  = 5y + 24 (equation 2)

Comparing equation 1 and 2.

7y = 5y + 24

2y = 24

y = 12 (Nada's share)

Substitute the value of y in equation 1;

3x = 7y

3x = 7×12

x = 28

Therefore, the initial share if Lily was 28.

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\(\huge \bf༆ Answer ༄\)

The given number in standard form is ~

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:3.75 \times 10 {}^{8} \)

Step-by-step explanation:

step 1. (a + b)(a - b) = a^2 - ab + ab - b^2 = a^2 - b^2.

step 2. this is always a binomial and never a trinomial and hence never a perfect square trinomual.

step 3. answer: never.

From the figure, the total number of students is

The number 15 is common in spanish, chemistry and math.

Hence, the number of students studying spanish, chemistry and math, n=15.

Therefore, the probability of surveying a student that is in math Spanish and chemistry is,

Therefore, the

Answer:

The last one is an easy way to tell that the slope is not -2 1/5 because it is positive

Step-by-step explanation:

When a line goes up from left to right, it's positive. If it goes down from left to right, it's negative.

The flow coefficient for the valve is 44.3 gpm/psi. The valve gain is 2215 gpm/%CO. The transfer function of the valve is G(s) = 2215 / (1 + 10s).

Calculating the flow coefficient for the valve

The flow coefficient for the valve is calculated as follows:

Cv = Qmax / (ΔP * K)

where:

Cv is the flow coefficient for the valve

Qmax is the maximum flow rate

ΔP is the pressure drop

K is the valve constant

The maximum flow rate is given as 1000 gpm/psi. The pressure drop is calculated as follows:

ΔP = 115 psig - 70 psig = 45 psig

The valve constant is calculated as follows:

K = 1830 kg/m³ * 9.81 m/s² / 45 psig * 6.24 x 10^4 L/m³ * psi

= 0.226 L/s/psi

Therefore, the flow coefficient for the valve is calculated as follows:

Cv = 1000 gpm/psi / (45 psig * 0.226 L/s/psi) = 44.3 gpm/psi

Calculating the valve gain in gpm/%CO

The valve gain in gpm/%CO is calculated as follows:

G = Cv * Rangeability

where:

G is the valve gain in gpm/%CO

Cv is the flow coefficient for the valve

Rangeability is the ratio of the maximum flow rate to the minimum flow rate

The rangeability is given as 50.

Therefore, the valve gain in gpm/%CO is calculated as follows:

G = 44.3 gpm/psi * 50 = 2215 gpm/%CO

Illustration of the transfer function of the valve

The transfer function of the valve in terms of block diagram if the time constant of valve actuator is 10s is as follows:

G(s) = 2215 / (1 + 10s)

where:

G(s) is the transfer function of the valve

s is the Laplace variable

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There are 144 combinations of 1 entree, 2 vegetables, and 1 dessert that can be selected from 4 entrees, 6 vegetables, and 6 desserts.

To determine the number of combinations, we multiply the number of options for each category.

For the entree, we have 4 options to choose from.

For the vegetables, we need to select 2 out of 6, which can be done in 6 choose 2 ways.

This is calculated as 6! / (2!(6-2)!), which simplifies to

6! / (2!4!)

Similarly, for the dessert, we have 6 options to choose from.

To calculate 6 choose 2, we can use the formula for combinations:

n choose r = n! / (r!(n-r)!).

Plugging in the values, we have

6! / (2!4!) = (6 × 5 × 4 × 3 × 2 × 1) / [(2 × 1) × (4 × 3 × 2 × 1)] = 15.

Therefore, we have 4 options for the entree, 15 options for the vegetables, and 6 options for the dessert.

Multiplying these numbers together, we get 4 × 15 × 6 = 144.

Therefore, there are 144 possible combinations of 1 entree, 2 vegetables, and 1 dessert, given the options of 4 entrees, 6 vegetables, and 6 desserts.

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Answer:

Let 2n = the first of three consecutive even numbers, where n is an integer.

Let 2n + 2 = the second of three consecutive even numbers, and

Let 2n + 4 = the third of three consecutive even numbers.

We're given that "sum of three consecutive even numbers is 552." We can translate this English sentence mathematically into the following equation to be solved for n:

2n + (2n + 2) + (2n + 4) = 552

Removing the parentheses, we have:

2n + 2n + 2 + 2n + 4 = 552

Now, by the Commutative Law of Addition, i.e., a + b = b + a, we have on the left side of the equation:

2n + 2n + 2n + 2 + 4 = 552

Now, collecting like-terms on the left, we get:

6n + 6 = 552

To solve for the variable n, We now begin isolating n on the left side by subtracting 6 from both sides as follows:

6n + 6 - 6 = 552 - 6

6n + 0 = 546

6n = 546

Now, divide both sides by 6 to finally solve for n:

(6n)/6 = 546/6

(6/6)n = 546/6

(1)n = 91

n = 91

Therefore, the first of three consecutive even numbers, 2n, is:

2n = 2(91)

= 182

The second of three consecutive even numbers is:

2n + 2 = 2(91) + 2

= 182 + 2

= 184

The third of three consecutive even numbers is:

2n + 4 = 2(91) + 4

= 182 + 4

= 186

CHECK:

2n + (2n + 2) + (2n + 4) = 552

182 + 184 + 186 = 552

552 = 552

Therefore, the desired and first of three consecutive even numbers is indeed 2n = 182.