how to solve a sequence

The solution to the inequality 1 + 3r > 10 is r > 3.

This means that any value of r greater than 3 will satisfy the inequality.

To solve the inequality 1 + 3r > 10, we need to isolate the variable r on one side of the inequality sign.

Let's begin by subtracting 1 from both sides of the inequality:

1 + 3r - 1 > 10 - 1

This simplifies to:

3r > 9

Next, we can divide both sides of the inequality by 3 to solve for r:

(3r)/3 > 9/3

This simplifies to:

r > 3

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we are allowed to change the vertical axis on a line chart.

suppose we have a large range of value needed to plot along the vertical and horizontal axis, but the current line chart cannot meet this demand. in such cases, we can customize the scales to provide more vertical and horizontal spaces.

dramatic slopes are the steep slopes of a straight line calculated by vertical and horizontal coordinate of two points laying on it. By changing the vertical axis as well as the horizontal axis we can plot a graph of a straight line more properly and finally more dramatic slope is visible there.

hence, we can change the scale values on a line chart to meet the requirement of the plot.

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Answer:  Each lemon costs 75 cents

Step-by-step explanation:

If you divide 8 from 6 then the answer is .75 and that is your answer.

Solution

Red = 10

Green= 4

Blue = 8

Total = 22

P ( red and green ) = P ( red ) X P(green )

P(red) = number of red balls / total number of balls

P(red) = 10/22

P(green) = 4/22

NOTE : The use of 'AND ' in probability simply means multiplying the probabilities

Answer:9/41

SOH = opposite over hypotenuse

Step-by-step explanation:

i need points

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Answer:

  96°

Step-by-step explanation:

You want the value of angle C in the diagram with two parallel lines and a triangle between them.

The sum of angles in a triangle is 180°, so the missing angle in the triangle is ...

  180° -60° -24° = 96°

Angle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:

  C = 96°

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The number of sodas sold at the baseball game was 119, while the number of hot dogs sold was 72.

Let's assume the number of sodas sold as 'x' and the number of hot dogs sold as 'y'.

According to the problem, the total number of sodas and hot dogs sold is 191, so we can write the equation:

x + y = 191   ...(1)

The problem also states that the number of hot dogs sold was 47 less than the number of sodas sold. Mathematically, we can express this as:

y = x - 47   ...(2)

To find the values of x and y, we can solve the system of equations (1) and (2). Substituting equation (2) into equation (1), we have:

x + (x - 47) = 191

Simplifying the equation:

2x - 47 = 191

2x = 191 + 47

2x = 238

Dividing both sides by 2:

x = 238/2

x = 119

Substituting the value of x back into equation (2):

y = 119 - 47

y = 72

As a result, the total amount of sodas sold is 119, and the total amount of hot dogs sold is 72.

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9514 1404 393

Answer:

  (4, -1)

Step-by-step explanation:

The orthocenter is the intersection of altitudes. Each altitude is the line through a vertex and perpendicular to the opposite side of the triangle.

It is useful to plot the points on a graph. This shows you segment KM is a horizontal line, so one altitude line is x=4, the vertical line through point L.

The graph also shows you segment KL has a rise of 8 for a run of 2, so a slope of rise/run = 8/2 = 4. Then the altitude perpendicular to that side will have slope -1/4 (the opposite reciprocal of 4), and will go through point M(8, -2). In point-slope form, the equation of the altitude through M can be written ...

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

  y +2 = -1/4(x -8)

We want to find the y-coordinate of the point of intersection of this line with the line x=4. We can substitute x=4 and solve for y.

  y +2 = -1/4(4 -8) . . . . . . substitute x=4

  y = 1 -2 . . . . . . . . . . simplify and subtract 2

  y = -1

The orthocenter for the given triangle has coordinates (4, -1).

The partial sum of the sequence {2, 3, 5, 8, 13, ...} for the first 8 terms is 761/2.

The sequence given is a Fibonacci sequence, where each term is the sum of the previous two terms. To find the partial sum for the first 8 terms, we can use the formula for the sum of a finite geometric series:

Sₙ = a(1 - rⁿ)/(1 - r),

where Sₙ is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 2, r = 3/2 (since each term is 1.5 times the previous term), and n = 8. Plugging these values into the formula, we get:

S₈ = 2(1 - (3/2)⁸)/(1 - (3/2))

Simplifying the expression, we get:

S₈ = 761/2

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H =20

G = 8 mor than I

the measure of H is 28 because it says that g is 8 more so that means I can be 0 and that means G is 8 and then H is 20. therefore solving your answer

What is the frequency of the graph of y=2 sin(1/2x)?​

Remember that

The frequency of a trigonometric function is the number of cycles it completes in a given interval

so

using a graphing tool

see the attached figure to better understand the prioblem

give me a minute to draw the function

the frequency of this graph is 4pi

The equation of the ellipse is \((x - 3)^2 / 16 + (y - 3)^2 / 64 = 1.\)

To determine the equation of the ellipse, we need to find its major and minor axes, as well as the distance from each focus to the center.

Given that the foci of the ellipse are located at (3, 1) and (3, 5), we can determine that the center of the ellipse is at the midpoint between these two foci, which is (3, 3).

The endpoints of the minor axis are (7, -2) and (-1, -2), which tells us that the length of the minor axis is 7 - (-1) = 8 units.

Now, let's calculate the distance from the center to one of the foci. Using the distance formula, we have:

sqrt((3 - 3)^2 + (3 - 1)^2) = sqrt(0 + 4) = 2.

Since the foci are vertically aligned, the major axis is vertical. Therefore, the length of the major axis is twice the distance from the center to one of the foci, which gives us 2 \(\times\) 2 = 4 units.

Using the standard form of the equation for an ellipse centered at (h, k), with a horizontal major axis of length 2a and a vertical minor axis of length 2b, the equation is:

\((x - 3)^2 / 4^2 + (y - 3)^2 / 8^2 = 1.\)

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The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).

To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2  from the y-coordinates of each vertex:

N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)

M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)

O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)

Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)

So the reflected vertices are:

The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have  a y-coordinate of -6.

The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so  one need to move down 3 units to have a y-coordinate of -5.

The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so  one need to move down 5 units to have  a y-coordinate of -7.

So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)

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Answer:

---------------------

Given triangle MNO with vertices:

It is reflected in line y = - 2.

This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.

Since y = - 2 is the line of symmetry,  it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.

Using midpoint equation, find the y-coordinates.

So the coordinates of the image are:

This is matching the option D.

See attached for visual representation of the problem.

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

Minimum height is 7.25ft and maximum height is 7.75ft

Step-by-step explanation:

You measured to the nearest half foot, so the greatest possible error is 0.25 foot.

Minimum height= measured value-possible error= 7.5-0.25= 7.25ft

Maximum height= measured value+possible error= 7.5+0.25= 7.75ft

The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

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Answer:

answer is D

Step-by-step explanation:

(2^3)^-2= 2^(3)*(-2)
             = 2^-6
             = 1/2^6
             = 1/64

     

The expressions (a), (d), (e) and (f) have values less 1.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Solving each expression :-

1) 4¹¹ / 4¹⁴        

= 4¹¹ × 4⁻¹⁴

= (4)¹¹⁻¹⁴

= 4⁻³

= 1 / 4³

2) (3⁵)² / 3⁸

= 3¹⁰ / 3⁸

= 3¹⁰⁻⁸

= 3²

= 9

3) 4⁻¹ × 4⁵

= 4⁻¹⁺5

= 4⁴

= 64

4) (2³)⁻²

= 2⁻⁶

= 1 / 2⁶

5) (5⁴)² x 5⁻¹¹

= 5⁸ x 5⁻¹¹

= 5⁻³

= 1 / 5³

6) (6⁻⁴ x 6⁶) / 6³

= 6² / 6³

= 1 / 6

Hence, the expressions (a), (d), (e) and (f) have values less 1.

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According to the information, the vertex at the top left of the parallelogram is (4, 8.25). Thus, the other two vertices of the parallelogram are (2, 5), (9, 5), (7, 8), and (4, 8.25).

To find the vertex of the parallelogram we can use the point-slope form of a line: y - y1 = m(x - x1), where,

For the side sloping up from left to right, we can use the point (2, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:

Simplifying, we get:

To find the point where this line intersects the top side of the parallelogram, we can use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (2, 5) is 5 units away from the intersection point in the x-direction, so we can add 5 to the x-coordinate to find the intersection point. Plugging in x = 7 into the equation above, we get:

Therefore, the vertex at the top right of the parallelogram is (7, 8).

For the side sloping down from left to right, we can use the point (9, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:

Simplifying, we get:

To find the point where this line intersects the top side of the parallelogram, we can again use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (9, 5) is 5 units away from the intersection point in the x-direction, so we can subtract 5 from the x-coordinate to find the intersection point. Plugging in x = 4 into the equation above, we get:

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Answer:

After calculating values from test statics we come to know that value of if null hypothesis is true then it will rejected

As critical values of z is ±1.96 after apply the test statics formula , we get the value of z that is - 4.50 As we consider the equation that

H₀ > z

Apply test statistic we fine the true value . So there is sufficient evidence to reject the claim.

Step-by-step explanation:

critical values z₀ = ±1.96; standardized test statistic z ≅ -4.50;

reject H₀

There is sufficient evidence to reject the claim.

Step-by-step explanation: This equation is prime.

The greatest positive acceleration occurs at the midpoint of the interval, when the particle is changing velocity most rapidly.

What is velocity?

Velocity is a measure of the rate of change of an object's position over a period of time. It is a vector quantity, which means it has both magnitude (or size) and direction. Velocity is usually expressed in terms of distance traveled per unit of time, such as meters per second (m/s). Velocity can be determined by dividing the distance traveled by the time taken. For example, if an object travels 20 meters in 5 seconds, its velocity would be 4 m/s. Velocity can also be calculated by taking the derivative of the object's position with respect to time.

The particle will achieve its greatest positive acceleration at the midpoint of the interval, at t = b/2.

This is because the acceleration is greatest when the velocity is changing most rapidly.

At the beginning of the interval, the particle has zero velocity, so it has no acceleration.

At the end of the interval, the particle has reached its maximum velocity, and the rate of change of velocity is zero, so it has no acceleration. Therefore, the greatest positive acceleration occurs at the midpoint of the interval, when the particle is changing velocity most rapidly.

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Based on the cross-price elasticity of Demand, we can conclude that good X and good Y are substitutes.

Let's calculate the cross-price elasticity of demand using the given information:

a. Find the percentage change in quantity demanded of good Y:

Percentage Change in Quantity Demanded of Good Y = (New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded * 100

Percentage Change in Quantity Demanded of Good Y = (6250 - 5000) / 5000 * 100 = 25%

b. Find the percentage change in the price of good X:

Percentage Change in Price of Good X = (New Price - Initial Price) / Initial Price * 100

Percentage Change in Price of Good X = (5 - 4) / 4 * 100 = 25%

Now, we can calculate the cross-price elasticity of demand:

Cross-Price Elasticity of Demand = Percentage Change in Quantity Demanded of Good Y / Percentage Change in Price of Good X

Cross-Price Elasticity of Demand = 25% / 25% = 1

b. Based on the calculated cross-price elasticity of demand, we can determine the types of goods:

If the cross-price elasticity of demand is positive (as in this case, where it is 1), it indicates that the two goods are substitutes. This means that when the price of good X increases, the quantity demanded of good Y also increases, suggesting that consumers view these goods as alternatives to each other.

Therefore, based on the cross-price elasticity of demand, we can conclude that good X and good Y are substitutes.

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Answer:

Step-by-step explanation:

Answer:

Transcribed image text: The graph of a quadratic function with vertex (0, -1) is shown in the figure below. Find the range and the domain. 10 1 Write your answers as inequalities, using x or y as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) range: 0 <D > OSO (b) domšin: ] DED olo

Step-by-step explanation:

pls points

Answer:

D =  - 2 < x < 2

R =  - 3 < y < 10

Step-by-step explanation:

domain is all the x-values of the function, range is all the y values of the function, you can use the < sign as long as u start with the lowest number and end with the highest of those values

Answer:

the answer is x over -2 × 14

Answer:-2,2 -7,7 -14,14 0,0

Step-by-step explanation:im not really good at this but i tried and i oped it worked

Answer:

Step-by-step explanation:

Find the coordinates:

Correct choice is A