find the number of terms in an AP whose first term is 5 common difference is 3 and the sum is 55

As y varies directly as (x−2)² and y = 5/3 when x = 4, then the equation for y in terms of x is y = (5/12)(x - 2)²

If the values of y varies directly as does of x, then there is a constant say "k" that is true for them, else y does not vary directly as x.

For y = 5/3 when = 4, we can solve for the constant k as follows:

5/3 = k(4 - 2)² {we simplify the expression in the bracket}

5/3 = k2²

5/3 = k4

k = 5/(3 × 4) {cross multiplication}

k = 5/12

Therefore, as y varies directly as (x−2)² and y = 5/3 when x = 4, the equation for y in terms of x is y = (5/12)(x - 2)²

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Given that, the function s(t) describes the motion of a particle along a line. s(t) = t³ − 13t² + 35t − 220

We need to find the time intervals in which the particle moves in the positive direction and the negative direction.

The given equation is s(t) = t³ − 13t² + 35t − 220

Taking the derivative,

v(t) = s'(t) = 3t² -26t + 35 = velocity at time t

s'(t) = 3t² -26t + 35 = 0

(3t -5)(t-7) = 0

t = 5/3 and 7 seconds

Therefore, the velocity > 0 when s'(t) > 0, when t>7 or t < 5/3 seconds

velocity <0 when 5/3 < t < 7 seconds

When moving in a positive direction, the intervals :-

(-∞, 5/3) ∪ (7, ∞)

When moving in a negative direction, the interval :-

(5/3, 7)

Hence, the time intervals are; positive direction (-∞, 5/3) ∪ (7, ∞) and negative direction (5/3, 7)

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The question was incomplete, so I solved for the question;

The function s(t) describes the motion of a particle along a line.

s(t) = t³ − 13t² + 35t − 220

(a) Find the velocity function v(t) of the particle at any time t ≥ 0.

(b) Identify the time interval(s) on which the particle is moving in a positive direction. (Enter your answer using interval notation.)

(c) Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.)

With a significance level of 0.05 (i.e., a confidence level of 95%), the confidence interval is calculated using the T function.

As a result, the range between 190,078.9152 and 209,921.0852 is represented by the confidence interval of 200,000 9921.0848.

Find the 0.025 critical value t* for 129 degrees of freedom in order to determine a 95% confidence interval for the mean based on the sample mean of 98.249 and sample standard deviation of 0.733. The critical value for 100 degrees of freedom is roughly 1.962.

Depending on the degree of confidence you want to have, choose the significance level. The two-tailed t table's =.05 corresponds to the most typical confidence level of 95%.

In the two-tailed t table, determine the critical value of t.

Add s/n to the crucial value of t.

Calculate the top limit of the confidence interval by adding this value to the mean, and the lower limit by deducting this value from the mean.

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Answer:

half a rotaoin

Step-by-step explanation:

think there is a crycle and you divide half and eat it and the secand half is 180 degree

Our point A(x,y) becomes A' when a point is rotated 180 degrees counterclockwise about the origin. All we actually do is turn both x and y negative.

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If PQ subtends angle at the circle's center, then let PQ be an arc with radius r and a center at O. Thus, the arc length of PQ is given by PQ = /360° (2r),  where is a degree.

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The length of b from the given triangle ABC is 4.1 inches.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in ΔABC, a = 6 inches, m∠A=121° and m∠B=36°.

Here, sin 121°/6=sin 36°/b

0.8571/6=0.5877/b

0.8571b=0.5877×6

0.8571b=3.5262

b=3.5262/0.8571

b=4.1 inches

Therefore, the length of b from the given triangle ABC is 4.1 inches.

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<1 = 45 degrees- are supplementary angles.

<2 = 95 degrees -  vertical angles.

<3 = 40 degrees because 1, 2, and 3 form a triangle.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

Using the provided figure, we can

Because <1 and the angle with a measure of 135 degrees are supplementary angles, m<1 = 45 degrees.

and, Because <2 and the angle measuring 95 degrees are vertical angles, m<2 = 95 degrees.

Also, Because 1, 2, and 3 make a triangle, m<3 = 40 degrees.

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Answer:

r = ±4.

Step-by-step explanation:

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. To write the equation 2r^2 - 32 in this form, you can subtract 32 from both sides to get 2r^2 - 32 = -32, and then divide both sides by 2 to get r^2 - 16 = -16. Finally, you can add 16 to both sides to get r^2 = 0, which is the standard form of a quadratic equation.

So, the equation 2r^2 - 32 = 0 can be written as the quadratic equation r^2 = 16, which has two real roots, r = ±4.

The number of tiles that will fit along the edge of the square mosaic is 28 tiles.

The concept used here is finding the square root of an area to determine the length of a side of a square and then using simple division to determine the number of tiles that will fit along the edge of the square. This involves using the formulas for finding the area of a square and the perimeter of a square.

To determine the number of 2 in x 2 in tiles that will fit along the edge of a square mosaic, you need to determine the length of one side of the square mosaic. You can do this by finding the square root of the total area:

sqrt(196) = 14

So one side of the square mosaic is 14 inches. The perimeter of the square is 4 * 14 = 56 inches.

Since each tile is 2 inches wide, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.

Thus, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.

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The number of tiles that will fit along the edge of the square mosaic is 28 tiles.

The concept used here is finding the square root of an area to determine the length of a side of a square and then using simple division to determine the number of tiles that will fit along the edge of the square. This involves using the formulas for finding the area of a square and the perimeter of a square.

To determine the number of 2 in x 2 in tiles that will fit along the edge of a square mosaic, you need to determine the length of one side of the square mosaic. You can do this by finding the square root of the total area:

sqrt(196) = 14

So one side of the square mosaic is 14 inches. The perimeter of the square is 4 * 14 = 56 inches.

Since each tile is 2 inches wide, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.

Thus, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.

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Answer:

Solution

or, 11°=90° {being complementary angle}

or,90°-11°

79°

Answer is 79°

When rotated about it’s center, a regular heptagon has 5 rotational symmetries. In addition to rotational symmetry, a regular heptagon has 7 lines of reflectional symmetry.

The number of times an object is precisely the same as the original object during a full 360° revolution is known as rotational symmetry, a sort of symmetry. It can be found in various geometrical objects as rhombuses, squares,

A sort of symmetry that pertains to reflections is called reflection symmetry. Line symmetry and mirror symmetry are other names for reflection symmetry. If a figure has at least one line dividing it into two halves, one half is said to be the mirror image of the other half.

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Answer:

-7.925

Step-by-step explanation:

The statement Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2) is correct.

The probability that an event will occur is equal to the ratio of positive outcomes to all outcomes, according to the probability formula. The proportion of positive outcomes to overall outcomes, or P(E), determines the likelihood that an event will occur.

Given three softball players discussed their batting averages after a game.

Probability

Player 1 is seven elevenths = 7/11

P(Player 1) = 0.636

Player 2 is six ninths = 6/9

P(Player 2) = 0.666

Player 3 is = five sevenths = 5/7

P(Player 3) = 0.714

so the probability of P(Player 3) > P(Player 2) > P(Player 1).

so Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2).

Hence option D is correct.

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Answer: 0.8  miles

Step-by-step explanation:

The equation to illustrate this will be 600 + 28m m.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this situation, the owners of a recreation area are filling a small pond with water and they are adding water at a rate of 28 liters per minute. There are 600 liters in the pond to start.

The equation to illustrate this will be:

= 600 + (28 × m)

= 600 + 28m

m = number of minutes.

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Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 28 liters per minute. There are 600 liters in the pond to start. Write the equation to illustrate this.

The rocket peaks at 5000 meters above sea-level.

The height of the rocket as a function of time is given by h(t) = -5t^2 + 1000t. To find the peak, we need to find the maximum height, which can be done by taking the derivative of the function and setting it equal to zero:

h'(t) = -10t + 1000

h'(t) = 0 => t = 100

So the rocket peaks at t = 100 seconds, and to find the height at this time, we plug t = 100 into the original function:

h(100) = -5 * 100^2 + 1000 * 100 = -50000 + 10000 = 5000

Therefore, The rocket peaks at 5000 meters above sea-level.

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The rocket peaks at 5000 meters above sea-level.

The height of the rocket as a function of time is given by h(t) = -5t^2 + 1000t. To find the peak, we need to find the maximum height, which can be done by taking the derivative of the function and setting it equal to zero:

h'(t) = -10t + 1000

h'(t) = 0 => t = 100

So the rocket peaks at t = 100 seconds, and to find the height at this time, we plug t = 100 into the original function:

h(100) = -5 * 100^2 + 1000 * 100 = -50000 + 10000 = 5000

Therefore, The rocket peaks at 5000 meters above sea-level.

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A segment that connects the vertex of a triangle with the opposite side so it makes a 90-degree angle is called Altitude.

In geometry, Altitude is used to describe the height of a polygon, triangle, or other two-dimensional shapes. The altitude of a figure is a line segment perpendicular to the base and passes through the vertex of the constitution. It is used to calculate the area of the figure and to determine the lengths of the sides and angles.

In three-dimensional figures, the altitude can also refer to the distance between the highest and lowest points of the constitution. The concept of altitude is widely used in mathematics, particularly in geometry, trigonometry, and related fields.

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Complete Question:

A line that connects the vertex of a triangle with the opposite side so it makes a 90 degree angle_____.

the boundary condition at a perfectly insulated surface is expressed mathematically as (0) -k = 0 depending on the physical characteristics of the surface.

A boundary condition is a mathematical expression that describes the behavior of a physical system at its boundaries, such as a surface.

Mathematically, a perfectly insulated surface is represented as an isothermal surface, meaning that the temperature is constant across the surface.

This is described by the equation (0) = 0, where эт represents the rate of heat transfer at the surface.

In other words, a perfectly insulated surface does not allow heat to flow through it.

This equation shows that the heat transfer is in the opposite direction of the temperature gradient at the surface.

Finally, the boundary condition at a perfectly insulated surface can also be expressed as эт (0,) -k = 0, which means that the heat transfer at the surface is equal to zero and there is no net heat transfer at the surface.

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The standard deviation of the sample mean decreases as the sample size increases. This is because the larger the sample size, the more accurately it reflects the population mean.

The standard deviation of the sample mean is a measure of how close the sample mean is to the population mean. The sample mean is an estimate of the population mean, and the standard deviation of the sample mean is a measure of how accurate that estimate is. When the sample size is increased, the sample mean becomes a more accurate estimate of the population mean, thus the standard deviation of the sample mean decreases. This is because the larger the sample size, the more accurately it reflects the population mean, and the closer the sample mean is to the population mean, the lower the standard deviation of the sample mean. The decrease in the standard deviation of the sample mean as the sample size increases is called the law of large numbers.

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Answer:

150000

Step-by-step explanation:

Slope=0.500/2.000=0.250

-6/1 = 6.00000

6/4 = 3/2 = 150000

Answer:

ABD =30 +45

ABD=75

75°is the answer

The number of solutions to the system of linear equations shown on the graph is given as follows:

D. One solution at (2, −3).

The number of solutions of the system of equations is given by the number of times which the two functions intersect.

From the image given at the end of the answer, the two functions intersect once, at x = 2 and y = -3, hence the correct option is given by option D.

The graph is given by the image presented at the end of the answer.

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The graph of function f is shown. If g(x) = -2f(x), which graph is the graph of function g is show on the attachment

Note that the new function, g(x), provides a value for y that is -2 times the value returned by f(x).  That means that for the same value of x, the resulting value of g(x) will be -2 times that provided by f(x).

See the attached image.  The table shows how the values of y change for each value of x used in the respective function.  Plot those new values to produce the graph.

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The final value of z = xy will be 1.05 times the original value.

The formula for calculating the growth rate of z = xy is z’/z = (x’/x)+(y’/y). The prime symbol (‘) denotes the rate of growth. In this case we can substitute the given rates of growth of x and y: x’/x = 2% and y’/y = 3%. By substituting these values into the formula we can calculate the rate of growth of z. z’/z = (2% + 3%) = 5%.

Therefore z = xy will grow approximately by 5%. To calculate the exact change in z, we can use the formula for compound growth: z’ = z (1 + r/100)^t, where r is the rate of growth and t is the number of time periods. In this case, r = 5% and t = 1 (as the growth rate is per period). Therefore, z’ = z (1 + 5/100)^1 = z (1.05) = z * 1.05. This means that the final value of z = xy will be 1.05 times the original value.

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At the specified values of the independent variables the function is a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33 b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10 c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

Given that the function is:

f(x) = 5x + 7

To evaluate the function at the specified values substitute the value in x:

a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33

b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10

c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52

Hence, at the specified values of the independent variables the function is a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33 b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10 c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52.

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All three students could be correct if they recorded the mass of the 20 bags of rice in different units. For example, one student could have recorded the mass in kilograms, another student could have recorded the mass in pounds, and the third student could have recorded the mass in ounces.

In order for all three students to be correct, they would have to be recording the mass of the 20 bags of rice in different units. For example, one student could have recorded the mass in kilograms, another student could have recorded the mass in pounds, and the third student could have recorded the mass in ounces. This would explain why each student has a different answer, as they are all measuring the mass in different units. The only way to ensure accuracy would be to measure the mass in the same unit of measurement, so that all students have the same answer.

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The values of the trigonometric functions of t are Sin(t)=0.2, Cos(t) = -5/12, Csc(t) = 5,Sec(t) = -12/5, Cot(t) = -5/12 and  the radius r of the circle if an arc of length 20 m on the circle subtends a central angle of 5π/7 rad is 8.86 m

To find the values of the trigonometric functions of t, the tan(t) value was used to calculate the sin(t) value by using the relationship sin²(t) + cos²(t) = 1. The other trigonometric functions were calculated by using the relationship among the trigonometric functions.

Sin(t) = √(1 - (tan(t))^2) = √(1 - (-12/5)^2) = √(1 - 144/25) = √(25/25 - 144/25)   = √(1/25) = 0.2

Csc(t)= 1/0.2= 5

The radius of the circle was then determined by using the arc length and the angle subtended at the center. The arc length was divided by the subtended angle to find the radius. The result was rounded off to two decimal places.

Radius r = (20m)/(5π/7)   = (20m*7)/(5π)   = 28/π = 8.86 m

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The probabilities from least to greatest are P(8), P(>4), P(odd) and P(prime).

What is probability?

Calculating probability is a method of determining how likely something is to occur. The probability scale runs from 0 to 1, where 0 denotes impossible and 1 denotes certainty.

We are given that a single die is rolled 100 times.

So, the outcomes can be {1,2,3,4,5,6}

Now,

P(odd) = Probability of odd numbers

Odd numbers are 1, 3 and 5

So, P(odd) = 3/6 = 1/2

P(>4) = Probability of numbers greater than 4

Numbers greater than 4 are 5 and 6

So, P(>4) = 2/6 = 1/3

P(prime) = Probability of prime numbers

Prime numbers are 1, 2, 3 and 5

So, P(prime) = 4/6 = 2/3

P(8) = Probability of number 8

In a dice, the maximum number is 6

So, P(8) = 0

Hence, the probabilities from least to greatest are P(8), P(>4), P(odd) and P(prime).

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The graph of the model is illustrated below and  the resistance when x = 85 is 1.12

The resistance of a conductor (such as a wire) is a measure of the opposition it presents to the flow of electric current. The resistance of a wire is dependent on various factors such as its length, cross-sectional area, and material. In this case, we are looking at the resistance of 1000 feet of solid copper wire, where the diameter of the wire is given in mils (0.001 inches).

The resistance of the wire can be approximated using the mathematical model:

=> y = 10,770/x² - 0.375,

where x is the diameter of the wire in mils and y is the resistance in ohms. The model is valid for values of x ranging from 5 to 100.

To complete the table, you need to plug in different values of x into the model and solve for y. For example, when x = 10,

=> y = 10,770/(10²) - 0.375 = 106.975 ohms.

The graph of the model can then be plotted by plotting the points (x,y) from the table and connecting them with a smooth curve. The graph can be used to estimate the resistance of the wire when x = 85.5 mils by finding the y-coordinate of the corresponding point on the graph.

Finally, you can use the model to algebraically confirm the estimate you found from the graph by plugging in the value x = 85.5 into the model and solving for y then we get the value as 1.12. This should give you the same answer as you found from the graph.

In conclusion, the resistance of a wire can be estimated using the mathematical model and can be used to make predictions about the resistance for different wire diameters.

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