if the base area of hemisphere is 616cm sq . find circumference of the base

Answer:

the equations they're equal

Step-by-step explanation:

3.75 divided by 5 = 0.75

7.50 divided by 10 = 0.75

12.00 divided by 16 = 0.75

These two simultaneous equations are inconsistent. Then, If we draw the graph of these two equations, we get the lines representing the equations parallel to each other. So, there exists no solution.For this question, the option A and C are correct.

The given system of linear simultaneous equations is:

10x + 8y = 20 (1)

20x + 16y = 30 (2)

First, let's simplify these equations by dividing equation (1) by 10 and equation (2) by 20:

x + 0.8y = 2 (1)

x + 0.8y = 1.5 (2)

From the simplified system, it is evident that these two simultaneous equations are linearly dependent since both have the same coefficients for x and y, but different constant terms.

As a result, there is no unique solution (option B is incorrect). If we were to graph these two equations, the lines representing them would be parallel and not intersect (option C is correct), indicating that there are no solutions and making the system inconsistent (option A is correct).

Since the lines don't coincide (option D is incorrect) and there is a linear dependence between the equations, we can conclude that there are no infinite solutions for this system (option E is incorrect).

Therefore, the correct statements are A and C.

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Answer:

Step-by-step explanation:

700.5

The frequency of A allele after a single generation of mutation can be found as follows: Frequency of A allele after a single generationp(A) = p(A) x (1 - m) + q(a) x m

where,
m = mutation rate = 10^-6p(A) = frequency of A allele in initial generation = 0.75q(a) = frequency of a allele in initial generation = 0.25Thus,p(A) = 0.75 x (1 - 10^-6) + 0.25 x 10^-6 = 0.74999925

And the frequency of a allele will beq(a) = 1 - p(A) = 1 - 0.74999925 = 0.25000075

Therefore, the frequency of the A and a alleles in the next generation will beA: 0.74999925 and a: 0.25000075.

This is option D.

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Answer:

1296

Step-by-step explanation:

6^4

Step-by-step explanation:

1. 6s⁹ t³

2. y³ + 3y² + 3y + 1

hope it helps!

The scenario described here can be considered an experimental setup.

In this experiment, Kara is manipulating the independent variable, which is the presence or absence of ice cubes surrounding the smaller jars that hold the frogs. By placing ice cubes only in one set of jars and not in the other set, Kara is creating two different conditions: one with a cold environment (ice cubes surrounding the jar) and one without (no ice cubes surrounding the jar).

Kara's objective seems to be to observe the effect of the cold environment on the frogs, as she inserted a thermometer through a hole in the lid of each jar to monitor the temperature.

The setup allows for a comparison between the two groups of frogs: one group was exposed to the cold environment created by the ice cubes and the other group was exposed to a regular room temperature. By comparing the behavior, reactions, or physiological responses of the frogs in the two groups, Kara can draw conclusions about the potential impact of temperature on the frogs' well-being or behavior.

Therefore, this scenario represents an experimental study, as Kara is actively manipulating the independent variable and observing the effects on the dependent variable (the behavior or physiological response of the frogs) to draw conclusions.

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Answer:

C. I and III

Step-by-step explanation:

3(2x+8) = 6x + 24

Answer:

C

Step-by-step explanation:

Option 2 is 4(2x + 6) which is also equal to:

\(8x + 24\)

Distribute the 4 with the 2x + 6.

Option 3 is 3(2x+8) which is also equal to:

\(6x + 24\)

Distribute the 3 with the 2x + 8.

So, option 3 and option 1 are equivalent to each other.

we are given the following function:

We are asked to find:

This means the value of the function when x = -2, therefore, in the function where ever we find "x" we replace it with -2, like this:

Solving the operations:

Therefore, f(-2) = 11

The velocity of the top of the ladder is 20.62 feet per second.

We can use the Pythagorean theorem to relate the distance between the wall and the base of the ladder to the height of the ladder. Let h be the height of the ladder, then we have:

h² + 7² = 25²

h² = 576

h = 24 feet

We can then use the chain rule to find the velocity of the top of the ladder. Let v be the velocity of the base of the ladder, then we have:

h² + (dx/dt)² = 25²

2h (dh/dt) + 2(dx/dt)(d²x/dt²) = 0

Simplifying and plugging in h = 24 and dx/dt = -2, we get:

(24)(dh/dt) - 2(d²x/dt²) = 0

Solving for (d²x/dt²), we get:

(d²x/dt²) = (12)(dh/dt)

We can find (dh/dt) using the Pythagorean theorem and the fact that the ladder is sliding down the wall at a rate of 2 feet per second:

h² + (dx/dt)² = 25²

2h(dh/dt) + 2(dx/dt)(d²x/dt²) = 0

Substituting h = 24, dx/dt = -2, and solving for (dh/dt), we get:

(dh/dt) = -15/8

Finally, we can find (d²x/dt²) by plugging in (dh/dt) and solving:

(d²x/dt²) = (12)(dh/dt) = (12)(-15/8) = -45/2

Therefore, the velocity of the top of the ladder is 20.62 feet per second.

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Answer: 16in or 7040 ft

Step-by-step explanation: 5+5+3+3=16

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

The weighted mean of the comparison is in the order  P1<P2<P3.

The weighted mean is a type of mean that is calculated by multiplying the weight (or probability) associated with a particular event or outcome with its associated quantitative outcome and then summing all the products together.

Weighted mean for P1 = ((700*10.4%) + (12000*-29.7%) + (600*37.20%) + (4400*7.5%) + (250*6.3%)) / (700+12000+600+4400+250) = -16%

Weighted mean for P2 = ((6000*10.4%) + (9000*-29.7%) + (4500*37.20%) + (2000*7.5%) + (1100*6.3%)) / (6000+9000+4500+2000+1100) = -1%

Weighted mean for P3 = ((3500*10.4%) + (5500*-29.7%) + (5750*37.20%) + (1500*7.5%) + (4500*6.3%)) / (3500+5500+5750+1500+4500) = 6%

So, P1<P2<P3.

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Complete question:

Calculate the weighted mean of the rors for each portfolio. based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst?

a) The coefficient of variation (CV) for speed can be calculated using the formula CV = (σ / μ) * 100, where σ is the standard deviation and μ is the mean.

CV for speed = (2.76 / 69.16) * 100 ≈ 4.0 to tenths.

b) The coefficient of variation (CV) for height can be calculated using the same formula.

CV for height = (157.70 / 177.80) * 100 ≈ 88.7 to tenths.

c) To determine which set of data has greater variation, we compare the coefficients of variation. Since the CV for height (88.7) is greater than the CV for speed (4.0), it means that the height data has a greater variation compared to the speed data.

To compare the variation between the two sets of data, we can calculate the coefficient of variation (CV). The CV is a relative measure of variation that allows us to compare the dispersion of data with different units or scales. It is calculated by dividing the standard deviation by the mean and multiplying by 100 to express it as a percentage.

In the first set of data (speed), the standard deviation is the square root of the variance, which is √2.76. To calculate the CV, we divide √2.76 by the mean speed of 69.16 and multiply by 100. This will give us the CV for speed, expressed to the nearest tenth.

In the second set of data (height), we follow the same process. The standard deviation is √157.70, and we divide it by the mean height of 177.80 and multiply by 100 to calculate the CV for height.

After calculating the CV for both speed and height, we can compare the values. The variable with the greater CV has a higher relative variation. Therefore, the variable with the greater CV indicates greater variation.

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In mathematics, sequences refer to a set of numbers or objects arranged in a definite order according to specific rules. The nth term of a sequence is a formula that enables us to determine the value of any term in the sequence using the position of that term within the sequence.In order to find the nth term rule for a sequence, we first need to understand the sequence's pattern. Here is how we can find the nth term rule for a sequence:

Step 1: Determine the sequence's first term and the common difference between terms.

Step 2: Subtract the first term from the second term to determine the common difference between terms. For example, if the first two terms are 3 and 7, the common difference is 7 - 3 = 4.

Step 3: Use the formula "nth term = a + (n-1)d" to find the nth term, where a is the first term and d is the common difference between terms. For example, if the first term is 3 and the common difference is 4, the nth term rule is given by "nth term = 3 + (n-1)4".

In conclusion, finding the nth term rule for a sequence requires identifying the pattern in the sequence and determining the first term and the common difference between terms. We can then use the formula "nth term = a + (n-1)d" to find the value of any term in the sequence using its position within the sequence.

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To calculate the line integral of the given vector field, we will use the formula of line integral. For the given function, the formula will be:∫CF.v dlWhere v = (x²+2yz)i + y²j and dl = dx i + dy j + dz kTherefore,∫CF.(x²+2yz) dx + y² dy … (1)Here, C is the curve from point (0,0,0) to (1,1,1) along the given route, that is, (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1).∴

The above line integral is the required value. So, we need to evaluate this integral. To calculate the line integral of the given vector field, we will use the formula of line integral. For the given function, the formula will be:

∫CF.v dl

Where

v = (x²+2yz)i + y²j

and

dl = dx i + dy j + dz k

Therefore,

∫CF.(x²+2yz) dx + y² dy … (1)

Here, C is the curve from point (0,0,0) to (1,1,1) along the given route, that is, (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1).∴ The above line integral is the required value. So, we need to evaluate this integral.The integral is a line integral of a vector field, with the curve path of integration is given by C as follows: C: (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1)In other words, we need to evaluate the integral of the dot product of the vector field v with the differential of the curve:

∫CF.v dl...

where

v = (x²+2yz)i + y²j

and

dl = dx i + dy j + dz k

We must split the curve C into three distinct segments before we can start evaluating the integral. The segments will be from (0,0,0) to (1,0,0), from (1,0,0) to (1,1,0), and from (1,1,0) to (1,1,1).Let's start with the first segment, from (0,0,0) to (1,0,0). We can set x = t, y = 0, z = 0, with t varying from 0 to 1, to parametrize this segment. Then dx = dt, dy = 0, dz = 0. We have:∫(0,0,0)to(1,0,0)

vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(t²+0)dt + 0 + 0= [t³/3]0to1= 1/3

Now, let's evaluate the second segment, from (1,0,0) to (1,1,0). We can set x = 1, y = t, z = 0, with t varying from 0 to 1, to parametrize this segment. Then dx = 0, dy = dt, dz = 0. We have:

∫(1,0,0)to(1,1,0)vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(1²+0)dx + t²dy + 0dz= 1∫0to1(t²)dt= [t³/3]0to1= 1/3

Finally, let's evaluate the third segment, from (1,1,0) to (1,1,1). We can set x = 1, y = 1, z = t, with t varying from 0 to 1, to parametrize this segment. Then dx = 0, dy = 0, dz = dt. We have:

∫(1,1,0)to(1,1,1)vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(1²+2(1)(t))dx + 1²dy + 0dz= ∫0to1(1+2t)dt + 1(0to1)+ 0= [t²+t]0to1+ 1= 3/2

Therefore, the line integral is the sum of the integrals along the three segments:

∫CF.v dl= 1/3+ 1/3+ 3/2= 2

Thus, the value of the line integral of the given function v = x²+2yzi + y²j from (0,0,0) the point (1,1,1) by the route (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1) is equal to 2.

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Answer: 20+3 per person

Step-by-step explanation:

Answer:

The watch is cheaper in Geneva, Switzerland by a value of £20

Step-by-step explanation:

To get the city in which the watch is cheaper, what we need to do is to express the price of the watch in the same currency.

Since pounds is also used in the b part of the question, it would be easier working with it.

In Geneva, the price of the watch is 193.75 CHF

from our conversion formula;

£1 = 1.55 CHF

£x = 193.75 CHF

We cross multiply to get the value of x

(193.75 * 1)/1.55

= 193.75/1.55 = £125

We can see that the watch costs less in Geneva and higher in Manchester

By how much is it cheaper?

We can calculate this by subtracting the value in Geneva from the value in Manchester

That would be 145-125 = £20 cheaper

Answer:

After making the deposit, he/she still has a bank account of -4 dollars.

Step-by-step explanation:

Answer:

In math, a unit fraction can be defined as a fraction whose numerator is 1. It represents 1 shaded part of all the equal parts of the whole.

Step-by-step explanation:

Answer:

6.25 hours

Step-by-step explanation:

pages per hour

pages/hour

90/2.5 = 36

36 pages per hour

225 / 36 = 6.25 hours

Answer:

6.25 hours

Step-by-step explanation:

2 and half hours = 2.5 hours

Proportions:

90 pages  ⇔  2.5 hours

225 pages  ⇔  E hours

E = 225*2.5/90

E = 6.25 hours

6.25 hours = 6 and 1 quarter hours

The decimal equivalent of 3/4 is: B. .75.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole numerical value. This ultimately implies that, a fraction is simply a part of a whole numerical value.

We know that multiplying a number by 1 produces the same number. This ultimately implies that, we would multiply the given fraction by 10/10:

3/4 × 10/10

30/4 × 1/10

30/4 = 7.5

Decimal equivalent = 7.5 × 1/10

Decimal equivalent = 0.75.

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Complete Question:

The decimal equivalent of 3/4 is?

.30 .75 .80 .90 none of these

Step-by-step explanation:

z = 32°

then

53 + 32 + y = 180 °   ( a straight line )

y = 95°

Answer:

7

Step-by-step explanation:

Answer:

(1)[ -3+2i-2(24)-8i ]

(2)[ -51-6i ]

Step-by-step explanation:

Throw the given equation into a calculator and simplify it. Answer #1 is simply a different/more complicated form of answer #2.