What is the equation of the line that is parallel to the
given line and passes through the point (-2, 2)?
O y=1/5x+4
Oy= 1/5x+12/5
O y = -5x + 4
O y=-5x +12/5

Answer:

30°

Step-by-step explanation:

it is the alternating angle.

(a) The value of c is determined to be 0.5. (b) The probability that X is greater than 1 is approximately 0.269. (c) The probability that X is less than 0.5 given that X is less than 1.0 is approximately 0.368.

(a) To find the value of c, we integrate the given density function over its entire range and set it equal to 1. The integral of f(x) from 0 to infinity should equal 1:

∫[0,∞] c(e^(-2x) - e^(-3x)) dx = 1.

Evaluating this integral gives us:

[-0.5e^(-2x) + (1/3)e^(-3x)] from 0 to ∞ = 1.

As x approaches infinity, both terms in the brackets go to 0, so we are left with:

0 - (-0.5) = 1,

0.5 = 1.

Therefore, the value of c is 0.5.

(b) To compute P(X > 1), we integrate the density function from 1 to infinity:

P(X > 1) = ∫[1,∞] 0.5(e^(-2x) - e^(-3x)) dx.

Evaluating this integral gives us approximately 0.269.

Therefore, the probability that X is greater than 1 is approximately 0.269.

(c) To calculate P(X < 0.5 | X < 1.0), we need to find the conditional probability that X is less than 0.5 given that it is already known to be less than 1.0. This can be found using the conditional probability formula:

P(X < 0.5 | X < 1.0) = P(X < 0.5 and X < 1.0) / P(X < 1.0).

The probability that X is less than 0.5 and X is less than 1.0 is the same as the probability that X is less than 0.5 alone, as X cannot be less than both 0.5 and 1.0 simultaneously. Therefore, P(X < 0.5 | X < 1.0) = P(X < 0.5).

Integrating the density function from 0 to 0.5 gives us approximately 0.368.

Therefore, the probability that X is less than 0.5 given that X is less than 1.0 is approximately 0.368.

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Answer: X=18

Step by Step:

2−10+x=6−8+12

Step 1: Simplify both sides of the equation.

2−10+x=6−8+12

2+−10+x=6+−8+12

(x)+(2+−10)=(6+−8+12)(Combine Like Terms)

x+−8=10

x−8=10

Step 2: Add 8 to both sides.

x−8+8=10+8

x=18

Answer:

\(x = 18\)

Step-by-step explanation:

\(2 - 10 + x = 6 - 8 + 12 \\ - 8 + x = - 2 + 12 \\ - 8 + x = 10 \\ x = 10 + 8 \\ x = 18\)

If f: rn → rm is a linear map, then its derivative is simply the map itself. This is because a linear map is a function that preserves vector addition and scalar multiplication.

In other words, if we take two vectors in the domain and add them together, and then apply the linear map, it is the same as applying the linear map to each vector separately and then adding the results. Similarly, if we multiply a vector in the domain by a scalar and then apply the linear map, it is the same as multiplying the result of applying the linear map to the original vector by the same scalar.
Formally, we can express this idea using the concept of a Jacobian matrix. The Jacobian matrix of a function describes the rate at which the function changes near a particular point. For a linear map, the Jacobian matrix is simply the matrix that represents the map. This means that the derivative of f is the matrix A such that f(x) = Ax for all x in rn.
To see why this makes sense, consider the simplest case of a linear map from R1 to R1, given by f(x) = ax, where a is a constant. The derivative of this function is f'(x) = a, which is just the constant coefficient of the linear map. More generally, the derivative of a linear map f: rn → rm is the matrix A such that f(x) = Ax for all x in rn.

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Answer:

There are 7,344,000 seconds until the swim team meet.

Step-by-step explanation:

First we have to figure out how many seconds in a day.

There are 86,400 seconds in a day.

Then we multiply the seconds in one day by the number of days:

86,400 x 85 = 7,344,000

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The height of the machine piston after 10 seconds is 2. 5m . Option B

Given the function;

y = 4.4 sin (0.4x -1.7) +2.3,

Where;

Given x as 10 seconds

y = 4. 4 sin ( 0.4(10) - 1. 7) + 2. 3

y = 4. 4 sin ( 4 - 1. 7) + 2. 3

y = 4. 4 sin (2. 3) + 2. 3

y = 4. 4(0. 04013) + 2. 3

y = 2. 47

y = 2. 5 meters in the nearest tenth

Thus, the height of the machine piston after 10 seconds is 2. 5m . Option B

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Answer:

D. 5.6 m

Step-by-step explanation:

Use your context clues.

All the other answers had O, like an X, so I put D, which was correct. *Wink*

Answer:

a) yes

b) yes

c) no

d) yes

Step-by-step explanation:

-2 + 5 = 3

5-2 = 3

-2 - (-5) = -2 + 5 = 3

-2 - 5 = -7

5 + (-2) = 5-2 = 3

Using concept of linear inequality, number of least deliveries is 30 and value of freight is $60000.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given charge of $70 per delivery and A charge of 6.5% of the total value of the freight for each delivery and least amount is $102,000.

Let only one delivery is possible per day and no. of deliveries=n

amount of each freight=x

Therefore,

Linear inequality will be n(6.5/100**x+70)>102000

So least values of n and x will be

n=30 and x=$60000

Hence,

          number of least deliveries is 30 and value of freight is $60000.

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The correlation coefficient of the data-set would decrease inserting the 70-year-old male with a finishing time of 35 minutes into the data-set.

A correlation coefficient is a statistical measure that indicates the strength and direction of a linear relationship between two variables.

The coefficients can range from -1 to +1, with -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation.

From the image given at the end of the answer, we have that the point (70, 35) is far from the cluster of points in the scatter plot, hence the correlation coefficient would decrease.

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Answer:

7 + 5(7) + 8(4) – 2 g

Step-by-step explanation:

163.79 students were surveyed.

The survey asked randomly selected students whether they preferred vanilla ice cream or chocolate ice cream. 58% of the students said they preferred vanilla ice cream, with a 5% margin of error. To calculate the total number of students surveyed, we can use the following formula:

Number of Students Surveyed = (100 - Margin of Error) ÷ (Percentage that Prefer Vanilla/100)

In this case, we get:

Number of Students Surveyed = (100 - 5) ÷ (58/100)

Number of Students Surveyed = 95 ÷ 0.58

Number of Students Surveyed = 163.79

Therefore, 163.79 students were surveyed.

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If abcde is a regular pentagon, the smallest rotation about e which maps a to d is 144 degrees.

Using the fact that a regular pentagon has rotational symmetry of order 5. This means that if we rotate the pentagon by 72 degrees around its center, it will appear the same as it did before the rotation.

To map a to d, we need to rotate the pentagon by some angle around point e. Since e is the center of rotation, we need to find an angle that is a multiple of 72 degrees.

To determine the smallest angle of rotation, we need to find the number of 72 degree rotations that take us from a to d.

Starting from a, we can count the number of 72 degree rotations we need to make to reach d. We see that we need to make two 72 degree rotations in a counterclockwise direction.

Therefore, smallest rotation about e that maps a to d is a 144 degree counterclockwise rotation.

We can visualize this by drawing a regular pentagon and marking the point a and d on it. Then, we draw a line segment from a to d and a line segment from e to the midpoint of segment ad.

The angle between these two line segments is 144 degrees.

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If person saves 12.5% of his income how much does he spend in a month if his monthly income is Rs 10,000 then he spends 8750 of his monthly income.

percentage, a relative value indicating hundredth parts of any quantity.

Given that a person saves 12.5% of his income.

The monthly income of the person is 10000.

We need to find how much he spend in a month.

Convert 12.5 % to the decimal value by dividing 12.5 by 100.

12.5/100=0.125

Now multiply 0.125 with 10000

0.125×10000

1250

Subtract 1250 from 10000

10000-1250

8750

Hence, person spends 8750  of his monthly income.

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Answer:

33.5%

Step-by-step explanation:

The general form of an exponential equation showing decay is;

A = I(1-r)^t

The percentage part is 1-r

Equate this to what we have in the question

1-r = 0.665

r = 1-0.665

r = 0.335

This in percentage is 33.5%

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

I really like cake and made a cake not to long ago.

Divide each term in the bracket by 4:

=  

3

x

−

2

Explanation:

Multiplying by  

1

4

is the same as dividing by 4. - You are finding a quarter of something.

To find a quarter of the bracket, divide each coefficient by 4.

You will get two unlike terms so you will not be able to simplify them.

This is the reason why you cannot simplify inside the original bracket either.

Step-by-step explanation:

Answer:

612 pi m^3

Step-by-step explanation:

Volume of the cylinder = 576 pi m^3

volume of the cone = (radius^2 x pi x height)/3 = (6^2 x pi x 3)/3 = 36 pi m^3

total  volume = 576 pi + 36 pi = 612 pi m^3

Approximating 7,123,456 by rounding to the nearest million will be 7,000,000.

Anything similar to something else but not precisely the same is called an approximation. By rounding, a number can be roughly estimated. By rounding the values in a computation before carrying out the procedures, an estimated result can be obtained.

If you want to round to one or two decimal places, look at the digit immediately following the decimal point. To the right of the necessary place value digit, draw a vertical line. Observe the following digit. Increase the preceding digit by one if the following digit is 5 or higher.

Therefore, approximating 7,123,456 by rounding to the nearest million will be 7,000,000.

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To have a margin of error of 7% with a 95% confidence level, approximately 8 people should be included in the survey.

To determine the sample size needed for a survey with a 95% confidence level and a margin of error of 7%, we can use the formula:

\(n = (Z * Standard deviation / E)^2\)

where:

n = sample size

Z = z-score corresponding to the desired confidence level (in this case, 95% confidence level corresponds to Z = 1.96)

σ = standard deviation (unknown, we'll assume 0.5 for a conservative estimate)

E = margin of error (0.07 or 7% in this case)

Substituting the given values into the formula, we have:

n = \((1.96 * 0.5 / 0.07)^2\)

Simplifying:

n = \(2.8^2\)

n = 7.84

Therefore, to have a margin of error of 7% with a 95% confidence level, approximately 8 people should be included in the survey. However, since sample sizes must be whole numbers, rounding up to the nearest whole number, we would need at least 8 people in the survey.

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For an acute angle, if the opposite side is known, the opposite side is known and the adjacent side is unknown. If the adjacent side is known, the adjacent side is known and the opposite side is unknown. For a right angle, the lengths of the adjacent and opposite sides can be determined, while the hypotenuse is unknown.

The known side and unknown side in a right triangle can be determined by using the known angle.

If the known angle is the acute angle and we know the length of the side opposite to it, then the opposite side is known and the adjacent side is unknown. The hypotenuse can also be determined using the Pythagorean theorem.

If the known angle is the acute angle and we know the length of the side adjacent to it, then the adjacent side is known and the opposite side is unknown. The hypotenuse can be determined using the Pythagorean theorem.

If the known angle is the right angle (90 degrees), then the lengths of the two sides adjacent and opposite to it can be determined. The hypotenuse is unknown.

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Answer:

n=0

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

The equation that results from translating (j(x) = |x|  right 8 units and up 6 units is:

j(x) = |x - 8| + 6

To translate the function (j(x) = |x| right 8 units and up 6 units, we need to modify the expression inside the absolute value function.

The translation right 8 units means we need to replace x with (x - 8).

The translation up 6 units means we need to add 6 to the entire expression.

So the equation that results from translating (j(x) = |x|  right 8 units and up 6 units is:

j(x) = |x - 8| + 6

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The amount each paid was (1.3h + 2.6)

Here, we want to get the amount paid by the two given the tip percentage

From the question, Harriet's cost was h

She paid or added a 30% tip

Mathematically, that would be;

Lucy had a dinner that cost an extra 4

The amount she would be paying is $(h+4)

We proceed to find the 30% tip and add

That would be;

The total cost of the bill is thus;

To find the individual amount paid, we divide this value by 2, which is;

Answer:

Ans: Rs 181.44.

Step-by-step explanation:

A condition that is impossible to satisfy has no solution.

Mathematics can be a powerful tool for solving many problems, but there are some issues that can't be solved.

In particular, any condition that is impossible to satisfy, such as the logical statement ‘this statement is false’, has no solution in mathematics. This is because the statement can’t be proven true or false, and so it can’t be solved.

An unsolvable condition is one that cannot be solved using any combination of logical and mathematical steps.

This means that no matter how much time and effort is put in, a solution to the problem cannot be discovered.

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The 95% confidence interval for the true proportion of tails in the population is (0.510, 0.572). This means that we are 95% confident that the true proportion of tails in the population is between 51.0% and 57.2%.

To find a 95% confidence interval for the true proportion of tails in the population, we can use the following formula:

\(CI = p + z\times (\sqrt{(p\times (1-p)/n))}\)

Where:

p = the proportion of tails in the sample (541/1000 = 0.541)

z = the z-score associated with a 95% confidence level (1.96, since the distribution is approximately normal for large sample sizes)

n = the sample size (1000)

Substituting the values we have:

\(CI = 0.541 + 1.96\times (\sqrt{(0.541\times (1-0.541)/1000))}\)

Simplifying:

CI = 0.541 ± 0.031

Therefore, the 95% confidence interval for the true proportion of tails in the population is (0.510, 0.572). This means that we are 95% confident that the true proportion of tails in the population is between 51.0% and 57.2%.

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The required formula to calculate exterior angle and an interior angle are  360°/n and (n-2) * 180°/n.

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which meaning numerous) and gon (means sides). To create a closed figure, a minimum of three line segments must be connected end to end.

The measure of an exterior angle of a regular polygon with n sides is given by 360°/n. The measure of an interior angle of a regular polygon with n sides is given by (n-2) * 180°/n.

So if you provide the number of sides of the polygon, I can give you the measures of the exterior and interior angles rounded to the nearest tenth if necessary.

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Torsion refers to the twisting of a structural member due to the application of torque. Pure torsion occurs when a structural member is subjected to torsional loading only. It is analyzed using assumptions such as linear elasticity, circular cross-sections, and small deformations. The torsion equation relates the applied torque, the polar moment of inertia, and the twist angle of the member. However, this formula has limitations in cases of non-circular cross-sections, material non-linearity, and large deformations.

Torsion is the deformation that occurs in a structural member when torque is applied, causing it to twist. In pure torsion, the member experiences torsional loading without any other external forces or moments acting on it. This idealized scenario allows for simplified analysis and calculations. The assumptions made in pure torsion analysis include linear elasticity, which assumes the material behaves elastically, circular cross-sections, which simplifies the geometry, and small deformations, where the twist angle remains small enough for linear relationships to hold.

To analyze pure torsion, engineers use the torsion equation, also known as the Saint-Venant's torsion equation. This equation relates the applied torque (T), the polar moment of inertia (J), and the twist angle (θ) of the member. The torsion equation is given as T = G * J * (dθ/dr), where G is the shear modulus of elasticity, J is the polar moment of inertia of the cross-section, and (dθ/dr) represents the rate of twist along the length of the member.

However, the torsion equation has its limitations. It assumes circular cross-sections, which may not accurately represent the geometry of some structural members. Non-circular cross-sections require more complex calculations using numerical methods or specialized formulas. Additionally, the torsion equation assumes linear elasticity, disregarding material non-linearity, such as plastic deformation. It also assumes small deformations, neglecting cases where the twist angle becomes significant, requiring the consideration of non-linear relationships. Therefore, in practical applications involving non-circular cross-sections, material non-linearity, or large deformations, more advanced analysis techniques and formulas must be employed.

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