Find the solution to the system of equations.

Answer:

the root is

\( \sqrt[2]{10.3923048} = 3.22370979\)

even tho I'm not sure

Step-by-step explanation:

h^2=135 h=√135

so the answer is 135

The surface area generated by revolving the curve y=f(x) on the interval [a,b] about the y-axis is given by the formula:

2π∫[a,b] f(x)√(1+(f'(x))^2) dx

To find the surface area generated by revolving the curve y=f(x) about the y-axis on the interval [a,b], we need to use the formula for the surface area of a surface of revolution.

This formula is derived by dividing the curve into small segments of length dx and approximating the surface area of each segment as a frustum of a cone. The formula for the surface area of a frustum of a cone is:

dA = 2πr √(dr^2 + dz^2)

where r is the radius of the circular cross-section of the frustum, and dz is the height of the frustum.

Using calculus, we can express r and dz in terms of x and dx. The radius of the circular cross-section of the frustum is equal to f(x), and the height of the frustum is equal to dx. Therefore, we have:

r = f(x)

dz = dx

Substituting these values into the formula for the surface area of a frustum of a cone, we get:

dA = 2πf(x) √(1 + (f'(x))^2) dx

To find the total surface area generated by revolving the curve y=f(x) on the interval [a,b] about the y-axis, we need to integrate dA from a to b:

A = ∫[a,b] dA

= ∫[a,b] 2πf(x) √(1 + (f'(x))^2) dx

This is the formula for the surface area generated by revolving the curve y=f(x) on the interval [a,b] about the y-axis.

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The given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) for all values of m, p, and v is equivalent to \(m^{8}p^{2}v^{12}\). Therefore, option D is the right choice for this question.

Monomials are algebraic expressions with single terms. They can be said to be specialized cases of polynomials.

We are given the algebraic expression - \(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

To simplify it we will use the rules of the indices as follows -

\(a^{m}.\ a^{n} = a^{m+n}\)

Now,

\(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

Segregating the like variables, we get,

= \((m^6.\ m^2) .\ (p^{-3}.\ p^{5}) .\ (v^{10}.\ v^{2})\)

by using the rules of indices, we will get,

= \((m^{6+2}) .\ (p^{-3+5}) .\ (v^{10+2})\)

= \((m^{8}) .\ (p^{2}) .\ (v^{12})\)

= \(m^{8}p^{2}v^{12}\)

Hence, the given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) is equivalent to \(m^{8}p^{2}v^{12}\).

Therefore, option D is the right choice for this question.

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Answer:

6%

Step-by-step explanation:

for this is divided the fee by the price of the item.

Answer:

It would be 2 (10)

Step-by-step explanation:

If you replace x with 10 then you have a multiplacation problem  and the output of the answer is 20

Answer:

heyyy

Step-by-step explanation:

The number "4" in the expression 4x - 5 represent the number of days Gerard worked.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Gerard worked the same number of hours, x, on Monday, Tuesday, and Wednesday, but on Thursday, he worked 5 hours less than the previous day.

The total number of hours Gerard worked can be found using the expression, 4x − 5

Hence:

The number "4" in the expression 4x - 5 represent the number of days Gerard worked which is Monday, Tuesday, and Wednesday and Thursday

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The probability of getting a head and a number greater than 5 i.e, independent events is 0.0833.

A coin is tossed and a die is rolled. These are two independent events. Two events are defined as independent if the outcome of one event has no effect on the outcome of another event. The probability is calculated by multiplying two independent probabilities together, i.e, P(A and B) = P(A) x P(B)

We have, Let us assume two independent events be ,

A : A coin is tossed and the head is thrown.

B : A die is rolled, and a number greater than 5 occurs.

Total possible outcomes when a coin tossed = 2 ={ H ,T }

Total possible outcomes when a die rolled = 6 = { 1,2,3,4,5,6} .

We have to determine probability of getting a head and a number greater

than 5.

Probability of getting the head on toss a coin, P(A) = 1/2

Probability of occuring a number greater than 5 on rolling a die = P(B) = 1/6

So, the probability of getting a head on coin and a number greater than 5 on die =P(A)×P(B)

=(1/2)× 1/6 = 1/12=0.0833

Hence, required probability is 0.0833.

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1. To find two starting terms for a Diginacci sequence such that the 2021st term is 11, we can work backward from the 2021st term to determine the preceding terms.

Let's denote the first term as a and the second term as b. We need to find the values of a and b that will result in the 2021st term being 11.

Working backward, we know that the 2021st term (which is 11) is the sum of the digits of the previous two terms. Let's denote the (2020)th term as x and the (2019)th term as y. Therefore, we have:

11 = x + y

2. To find a suitable pair of x and y, we can iterate through possible values. Since the first two terms can be any positive whole numbers, we have some flexibility in choosing them.

For example, let's try a = 1 and b = 1:

Term 1: 1

Term 2: 1

Term 3: 2

Term 4: 1

Term 5: 3

Term 6: 4

Term 7: 7

Term 8: 11

The 8th term is 11, which matches our target. Therefore, if we start with a = 1 and b = 1, the 2021st term will indeed be 11.

To find a Diginacci sequence that has no term equal to 11, we need to ensure that none of the subsequent terms sum up to 11.

One way to achieve this is to start with two terms that are relatively large and have no digits summing up to 11. Let's try a = 99 and b = 100:

Term 1: 99

Term 2: 100

Term 3: 19 (9 + 9)

Term 4: 10 (1 + 0)

Term 5: 1

Term 6: 1

Term 7: 2

Term 8: 3

Term 9: 5

Term 10: 8

Term 11: 13

Term 12: 12

Term 13: 7

Term 14: 10

...

By starting with a = 99 and b = 100, the Diginacci sequence continues without reaching the value 11. The terms keep changing without summing up to 11, as seen in the subsequent terms above.

Thus, this particular Diginacci sequence starting with a = 99 and b = 100 does not have any term equal to 11.

The probability that the jury makes the correct decision is 0.9999

This is a binomial distribution problem where the event of interest is a juror making a correct decision (voting guilty) and the number of trials is 12 (the number of jurors).

The probability of a single juror making the correct decision is 0.80. Therefore, the probability of a single juror making the incorrect decision (voting not guilty) is 1 - 0.80 = 0.20.

To calculate the probability that at least 10 out of 12 jurors make the correct decision (voting guilty) if the defendant is guilty, we can use the binomial distribution formula:

P(X ≥ 10) = 1 - P(X < 10)

where X is the number of jurors who make the correct decision.

Since the probability of a single juror making the correct decision is 0.80, we can use the binomial probability formula to calculate the probability of X jurors making the correct decision

P(X = x) = (12 choose x) * 0.80^x * 0.20^(12-x)

where (12 choose x) is the number of ways to choose x jurors out of 12.

Using this formula, we can calculate the probability of fewer than 10 jurors making the correct decision:

P(X < 10) = P(X = 0) + P(X = 1) + ... + P(X = 9)

We can use a calculator or software to calculate this probability:

P(X < 10) = 0.00000436

Therefore, the probability of at least 10 out of 12 jurors making the correct decision if the defendant is guilty is:

P(X ≥ 10) = 1 - P(X < 10) = 1 - 0.00000436 = 0.99999564

Rounding to four decimal places, the probability is 0.9999.

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Given:

The figure of a triangle.

The perimeter of the triangle ABC is 31.

To find:

The value of x in the given triangle.

Solution:

Three sides of the triangle ABC are AB, BC, AC are their measures are \(3b-4,2b+1,b+10\) respectively.

The perimeter of the triangle ABC is 31.

\(AB+BC+AC=31\)

\((3b-4)+(2b+1)+(b+10)=31\)

\(6b+7=31\)

Subtract 7 from both sides.

\(6b=31-7\)

\(6b=24\)

\(b=\dfrac{24}{6}\)

\(b=4\)

Now, the measures of the sides are:

\(AB=3b-4\)

\(AB=3(4)-4\)

\(AB=12-4\)

\(AB=8\)

\(BC=2b+1\)

\(BC=2(4)+1\)

\(BC=8+1\)

\(BC=9\)

And,

\(AC=b+10\)

\(AC=4+10\)

\(AC=14\)

Using the law of cosines, we get

\(\cos A=\dfrac{b^2+c^2-a^2}{2bc}\)

\(\cos A=\dfrac{(AC)^2+(AB)^2-(BC)^2}{2(AC)(AB)}\)

\(\cos A=\dfrac{(14)^2+(8)^2-(9)^2}{2(14)(8)}\)

\(\cos A=\dfrac{179}{224}\)

Using calculator, we get

\(\cos A=0.7991\)

\(A=\cos ^{-1}(0.7991)\)

\(x=36.9558^\circ\)

\(x\approx 37.0^\circ\)

Therefore, the value of x is 37.0 degrees.

The equilibrium quantity is approximately 10,664 units and the equilibrium price is approximately $4.953.

To find the equilibrium quantity and price, we need to solve the system of equations:

2x + 7p - 56 = 0

3x - 11p + 45 = 0

We can use any method to solve this system, such as substitution or elimination. Let's use the substitution method.

From the first equation, we can solve for x in terms of p:

2x = 56 - 7p

x = (56 - 7p)/2

Substituting this expression for x into the second equation, we get:

3((56 - 7p)/2) - 11p + 45 = 0

Simplifying the equation:

168 - 21p - 22p + 45 = 0

-43p + 213 = 0

-43p = -213

p = 213/43 ≈ 4.953

Now, we can substitute this value of p back into the first equation to find x:

2x + 7(4.953) - 56 = 0

2x + 34.671 - 56 = 0

2x = 21.329

x = 10.664

Therefore, the equilibrium quantity is approximately 10,664 units and the equilibrium price is approximately $4.953.

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First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

Answer: (5,7)

Step-by-step explanation:

We want to find the image of a point after a given translation.

The image of the point (-5, 2) under the translation T(3, -4) is the point (-2, -2)

First, we can define how a general translation T(a, b) affects a general point (x, y).

It will add a units to the x-value and b units to the y-value, then we have:

T(a,b)[(x, y)] = (x + a, y + b).

Now we just need to apply the translation:

T(3, -4) to the point (-5, 2)

It gives:

T(3, -4)[(-5, 2)] = (-5 + 3, 2 + (-4)) = (-2, -2)

So the image of the point (-5, 2) under the translation T(3, -4) is the point (-2, -2)

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The equation that represents the scatterplot is: y = -0.8x + 30

From the scatterplot, we see that when x = 25, y = 10

Option A: The equation is given as:

y = -0.8x + 30

At x = 25, we have:

y = -0.8(25) + 30

y = -20 + 30

y = 10

Option B: The equation is given as:

y = -1.5x + 50

At x = 25, we have:

y = -1.5(25) + 30

y = -37.5 + 30

y = -7.5

Option C: The equation is given as:

y = -2.8x + 73

At x = 25, we have:

y = -2.8(25) + 73

y = -70 + 73

y = 3

Option D: The equation is given as:

y = -3.5x + 82

At x = 25, we have:

y = -3.5(25) + 82

y = -87.5 + 82

y = -5.5

Thus, only option A is correct

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Answer:

The range will be (-∞,∞)

Step-by-step explanation:

Since there is no number that can make this function undefined or limited to a certain set of values,  the range shall be infinite.

The forecaster (or the software) must set three parameters using Winter's exponential smoothing. (Option 4)

Winter's exponential smoothing is a method for forecasting in which the forecast for the next period is weighted more heavily based on the data that was recorded in previous periods.

The formula for Winter's exponential smoothing includes three parameters: alpha, beta, and gamma. Parameters in Winter's exponential smoothing:

alpha: The degree of smoothing that is applied to the level of the series. The alpha value will vary between 0 and 1.

beta: The degree of smoothing applied to the trend of the series. The beta value will vary between 0 and 1.

gamma: The degree of smoothing applied to the seasonal component of the series. The gamma value will vary between 0 and 1.

Hence, the forecaster (or the software) must set three parameters using Winter's exponential smoothing.

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The expected time (also known as the expected value or the mean) Is approximately 12.5 days.

The expected time for an activity is the average time it is likely to take, taking into account its optimistic, most likely, and pessimistic estimates. The three-point estimate formula is used to calculate the expected time by weighting the most likely estimate four times as much as the optimistic and pessimistic estimates. In this case, the optimistic time is 15 days, the most likely time is 18 days, and the pessimistic time is 27 days. By plugging these values into the formula, the expected time is calculated to be 12.5 days. This means that, on average, the activity is likely to take 12.5 days to complete.

The expected time (also known as the expected value or the mean) can be calculated using the three-point estimate formula, which is:

Expected time = (Optimistic time + 4 * Most likely time + Pessimistic time) / 6

Plugging in the values, we get:

Expected time = (15 + 4 * 18 + 27) / 6 = (75) / 6 = 12.5

So the expected time for this activity is 12.5 days.

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Answer:

See explanation below.

the numbers are 27 and 36

or

the numbers are 4 and 13

Step-by-step explanation:

Let the numbers be x and y.

"the difference between two positive numbers is 9"

y - x = 9

One of your statements is:

"one number is three times less than four times the other"

Are you sure the first word times belongs there?

If so, then the second equation below is correct.

y = 4x/3

y = x + 9

y = 4x/3

4x/3 = x + 9

4x = 3x + 27

x = 27

y = x + 9

y = 27 + 9

y = 36

Answer: the numbers are 27 and 36

If the second statement is really:

"one number is three less than four times the other number"

without the first word "times"

then the second equation is

y = 4x - 3

The equations are:

y - x = 9

y = 4x - 3

4x - 3 - x = 9

3x = 12

x = 4

y - 4 = 9

y = 13

Answer: the numbers are 4 and 13

The weight of gold in a bar of gold and silver can be determined by comparing the weight loss of gold and silver when weighed in water. Given that 10 kg of silver loses 1 kg when weighed in water and 19 kg of gold loses 1 kg, we can calculate the weight of gold in the bar. The weight of gold in the bar is 95 kg.

When weighed in water, 10 kg of silver loses 1 kg, which means the weight of silver in water is 99 kg - 10 kg = 89 kg. By subtracting the weight loss (1 kg) from the weight of silver in water, we find the weight of silver in air as 10 kg + 1 kg = 11 kg.

To calculate the weight of gold in water, we subtract the weight loss (1 kg) from the weight of silver in water: 89 kg - 1 kg = 88 kg.

Next, to determine the weight of gold in air, we subtract the weight of silver in air (11 kg) from the total weight of the bar in air (106 kg): 106 kg - 11 kg = 95 kg.

Therefore, the weight of gold in the bar is 95 kg.

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Answer:

Equation: 154 = 158n - 132 n = 11/6

Step-by-step explanation:

Let's start by converting this into an equation. Some keywords to look for are "is" which means an equal sign (=), "product" which is multiplication (*), and "decreased" which means a minus sign (-):

So this is our equation: 154 = 158n - 132

Now we have to solve for n:

First, we add 132 to both sides to isolate the n more:

286 = 158n

Then to completely isolate the n, we divide both sides by 158

286

------    =     n

156

n = 11/6, final answer.

Solution:

Let the two integers be x and y;

Thus;

CORRECT OPTION: B

a) The probability that he receives no job offers is given as follows: 0.0001.

b) The probability that he receives at least one job offer is given as follows: 0.9999.

c) The expected number of job offers is given as follows: 5.6.

The mass probability formula for the number of successes x in n trials is defined by the equation presented as follows:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters, along with their meaning, are presented as follows:

The parameter values for this problem are given as follows:

n = 8, p = 0.7.

Hence the expected value is given as follows:

E(X) = np = 8 x 0.7 = 5.6.

The probability of no offers is:

\(P(X = 0) = (1 - 0.7)^8 = 0.0001\)

Hence the probability of at least one job offer is given as follows:

1 - P(X = 0) = 1 - 0.0001 = 0.9999.

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Answer:

I think the answer would be -1/2 or D.

Step-by-step explanation:

Use this formula for calculating slope : y2-y1 / x2 - x1                                                            

1. label the pairs, 1 and 2

(-6, 1)  - ( x1, y1 )          or        (4,-4) - (x1, y1)

(4,-4) - ( x2, y2)                      (-6,1) - (x2, y2)  

(the order does not matter)

2. Than plug in your numbers

y2-y1 / x2 -x1                 y2-y1 / x2 -x1

-4 - 1 / 4 - (-6)        or        1 - (-4) / -6 - 4

= -5/10 or -1/2               = - 5/-10 or -1/2

im only in eight grade so i did my best explaining , and this hope it helps :)

It is not necessarily true that either [a] = [0] or [b] = [0] when [a],[b] ∈ z6 and [a]·[b] = [0].

This is because in z6, there are other pairs of elements that multiply to [0] besides [0] and any other element. For example, [2]·[3] = [6] = [0] in z6, but neither [2] nor [3] are equal to [0].

However, if [a],[b] ∈ z7 and [a]·[b] = [0], then it is necessarily true that either [a] = [0] or [b] = [0]. This is because z7 is a field, meaning that it has no zero divisors (elements that multiply to [0] besides [0] itself). Therefore, the only way for [a]·[b] = [0] in z7 is if either [a] or [b] are equal to [0].

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Answer:

$72693.9

Step-by-step explanation:

To get this answer you need to use the compound interest formula, which will be A=P(1+r/n)^n(t). P=59,000 r=11%=0.11 n=1 (annually) t=2 years. From there you should be able to figure the rest out and get the answer. Hope this helps!

Answer: y=3x-3

Step-by-step explanation: Formula: y=mx+b The slope is m which is 3, rise over run, and b is the y-intercept which is -3.

Answer:

y=3x+-3

Step-by-step explanation:

the slope is 3/1 which is 3.

the y intercept is the point at which theine crosses te y axis so it's-3

y=mx+b

y=3x+-3