Expand and evaluate the series.

∑6n=13n
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a) On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6)  best represents the data.

This is because the data represents a set of paired values, with the months as the independent variable (x) and the average maximum monthly temperature as the dependent variable (y). A scatter plot is the appropriate graph for displaying this type of data.

Option a shows the correct placement of the data points on a scatter plot, with the x-axis representing the months and the y-axis representing the average maximum monthly temperature. The points are clearly organized in a sequence from January to December, with an upward trend in temperature from the winter months to the summer months, followed by a gradual decrease in temperature in the fall and winter months.

Option b has the correct range of temperatures, but the points are not arranged in a logical sequence and are scattered randomly across the graph. Option c also has a similar issue with random placement of points and does not reflect the actual values in the data set. Option d only has three points and does not represent the complete data set.

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Answer:

[tex]a_{n}[/tex] = 5n + 20

Step-by-step explanation:

there is a common difference between consecutive terms in the sequence

30 - 25 = 35 - 30 = 5

this indicates the sequence is arithmetic with explicit formula

[tex]a_{n}[/tex] = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 25 and d = 5 , then

[tex]a_{n}[/tex] = 25 + 5(n - 1) = 25 + 5n - 5 = 5n + 20

Answer:

a³ = -357911/5832.

Step-by-step explanation:

We can use the given equation to find the value of n, and then use it to find the value of a³.

a¹ = 13 and a = ⁿ⁻¹ - 4

Substituting the value of a in terms of n in the first equation, we get:

ⁿ⁻¹ - 4 = 13

ⁿ⁻¹ = 13 + 4

ⁿ⁻¹ = 17

ⁿ = 18

Now, substituting the value of n in the equation a = ⁿ⁻¹ - 4, we get:

a = 18⁻¹ - 4

a = 1/18 - 4

a = -71/18

Finally, to find a³, we can cube the value of a:

a³ = (-71/18)³

a³ = -357911/5832

Therefore, a³ = -357911/5832.

Answer: 10/40 or 1/4

Step-by-step explanation:

Add up all the amount of rolls, so 10+6+4+8+6+6=40

then add the probability of rolling a 3 or 6 = 10

divide that quantity out of the whole

answer is 10/40 and simplified is 1/4

hope it helps

Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

Step-by-step explanation:

If sin is neg AND tan is neg     then cos is positive

   (because tan = sin/cos)

this occurs in Q IV

Answer:

6

Step-by-step explanation:

this is if you meant: Jasmine sold 5 cherry pies and 12 lemonade how much more did Jasmine sell of lemonade than cherry pies

Answer:

If the diameter of the circle increases to 60 inches, the new area would be approximately 2700 square inches.

The cord will begin to stretch after approximately 1.46 seconds.

h(t) = -16t^2 + V0t + h0

149 = h0 - h(t)

Substituting h0 = 241 and h(t) = -16t^2 + V0t into this equation, we get:

149 = 241 - (-16t^2 + V0t)

we get:

16t^2 - V0t - 92 = 0

4(16)(-92) / (2(16)

t = sqrt(1856) / 32

Using a calculator, we get:

t ≈ 1.46 seconds

Therefore, the cord will begin to stretch after approximately 1.46 seconds.

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Answer:

13 + 8 + 13 + (1/2)(8π) = 34 + 4π feet

= 46.57 feet

Answer:

x = 12

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{x}{24}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = 24 ( divide both sides by 2 )

x = 12

Answer:

36

Step-by-step explanation

6x6

Answer:  -5, 3

Step-by-step explanation:

Equation:

x² + 2x -15 = 0   The equation is already set =0   so you will factor.

To factor, find 2 numbers that multiply to the last term (-15) but add up to the middle term (+2).  Be careful with signs,  signs matter

+5 and -3 multiply to -15 but add up to the +2    so these are your factored numbers

put it in factored form

(x+5)(x-3)=0         set each parenthesis =0 to solve for x

x+5 =  0                    x-3=0

x= -5        and           x=3

Note that the sequence of transformations that will move ABC onto DEF is; "The translation (x,y)->(x+7,y), followed by a dilation by a scale factor of 2 centered at the origin." *Option C)

A transformation is a mathematical function that repositions points in one-, two-, three-, or any other n-dimensional space.

A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer. Such a dilatation is a resemblance of space in Euclidean space.

Note that translation takes B(0,0) to B'(7, 0),
Takes A(0, 4) to A'(7, 0) and C (3, 0) to C' (10, 0)

when you multiply the new points by the scale factor of 2, you'd get the new  figure when the coordinates are graphed.

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Answer:

  D.  Dilation by 2, translation right by 7.

Step-by-step explanation:

You want to know the sequence of transformations that maps ∆ABC to ∆DEF.

Segment DE is 8 units long, and located at x=7. Segment AB is 4 units long and located at x=0.

The scale factor is the ratio of segment lengths:

  DE/AB = 8/4 = 2

Triangle DEF is dilated by a factor of 2 (eliminates B).

Triangle DEF is oriented the same way as triangle ABC, so there is no reflection involved (eliminates A). As we noted, segment DE is 7 units to the right of segment AB, so a translation of x ⇒ x+7 is involved.

The translation must occur after the dilation about the origin (eliminates C). If it were to occur first, the translation would be multiplied by the scale factor, so that DE would end up at x=14.

The required sequence of transformations is ...

  D. A dilation by a scale factor of 2, centered at the origin, followed by the translation (x, y) ⇒ (x+7, y).

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Answer:

c

Step-by-step explanation:

The 99% confidence interval for the population proportion p is (0.776, 0.824).

To find the 99% confidence interval for a proportion, we can use the formula:

CI = p^ ± z*(SE)

where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.

For a 99% confidence interval, the critical value z is 2.576.

Substituting the given values into the formula, we have:

CI = 0.80 ± 2.576*(0.03/√200)

Simplifying this expression, we have:

CI = 0.80 ± 0.024

This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.

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Answer:

  -9 11/12

Step-by-step explanation:

You want the product of 2 5/6 and -3 2/4.

The product of mixed numbers is often most easily computed by rewriting them to improper fractions.

  (2 5/6)(-3 2/4) = (17/6)(-7/2) = -(17·7)/(6·2) = -119/12

  = -(108/12 +11/12)

  = -9 11/12

__

Additional comment

Your calculator can probably help you with this.

<95141404393>

Answer:

Step-by-step explanation:

a. Using Cramer's Rule:The system of equations can be written in matrix form as:Copy code| 7 -8 5 | | x | | 5 | | -4 5 -3 | x | y | = |-3 | | 1 -1 1 | | z | | 0 |The determinant of the coefficients matrix is:scssCopy code| 7 -8  5 | | -4  5 -3 | | 1 -1  1 | = 7(5)(1) + (-8)(-3)(1) + 5(-4)(-1) - 1(-3)(7) - 1(5)(-8) - (-1)(-3)(5) = 70To find x, we replace the x-coefficients with the constants and solve for x:scssCopy code| 5 -8  5 | | -3  5 -3 | | 0 -1  1 | x = | 7 -8  5 | | -4  5 -3 | | 1 -1  1 | = (5(5)(1) + (-8)(-3)(1) + 5(-3)(-1) - 1(-3)(5) - 1(5)(-8) - 0(-1)(-4))/70 = 9/14To find y, we replace the y-coefficients with the constants and solve for y:scssCopy code| 7  5  5 | | -4 -3 -3 | | 1  0  1 | y = | 7 -8  5 | | -4  5 -3 | | 1 -1  1 | = (7(-3)(1) + (-8)(-3)(1) + 5(0)(-1) - 1(5)(-3) - 0(-8)(-4) - 1(-1)(-4))/70 = -1/14To find z, we replace the z-coefficients with the constants and solve for z:scssCopy code| 7 -8  5 | | -4  5 -3 | | 5 -1  0 | z = | 7 -8  5 | | -4  5 -3 | | 1 -1  1 | = (7(5)(0) + (-8)(-3)(1) + 5(-1)(-1) - (-1)(5)(5) - 1(5)(-8) - 0(-1)(-4))/70 = -12/35Therefore, the solution to the system of equations is x = 9/14, y = -1/14, z = -12/35.b. Using Inverse Method:The system of equations can be written in matrix form as:Copy code| 7 -8 5 | | x | | 5 | | -4 5 -3 | x | y | = |-3 | | 1 -1 1 | | z | | 0 |The coefficients matrix is:Copy code| 7 -8 5 | | -4 5 -3 | | 1 -1 1

The graph that best shows `y=x^2` translated `2` units down is graph d

From the question, we have the following parameters that can be used in our computation:

y = x^2

When the function y=x^2` is translated `2` units down, we do the following

We subtract 2 from the function equation

So, we have

y = x^2 - 2

This means that the translated function is 2 units below the function y = x^2

From the list of options, this is represented with graph (d)

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Answer: A

Step-by-step explanation:

To simplify 3w-4-w-9, we need to combine the like terms (terms that have the same variable and exponent).

3w - w = 2w

-4 - (-9) = -4 + 9 = 5

So,

3w - 4 - w - 9 = 2w - 13

Therefore, the expression 3w-4-w-9 is equivalent to 2w-13, which is option A.

With a market yield to maturity of 5.33%, the amount that would be received for a R 1,000 par value zero coupon bond that matures in five years, but sold today will be R747.26.

To calculate the price you will receive for your zero coupon bond, we can use the formula:

P = F / (1 + r)^n

where:

In this case, the par value is R1,000, the yield to maturity is 5.33%, or 0.0533 as a decimal, and the number of years to maturity is 5.

Therefore, you can expect to receive approximately R747.26 for your R1,000 par value zero coupon bond when the market yield to maturity is 5.33%.

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If the Raj’s bathtub is draining at rate of 1.5 gallons of water per-minute, then the range will be (c) all real numbers such that 0 ≤ y ≤ 40.

The "Range" of function is defined as the set of all possible "output-values'.

The amount of water remaining in the bathtub is decreasing as it drains, so the range of the function is bounded below by 0 (because we cannot have negative water in the bathtub) and above by 40 (the initial amount of water in the bathtub).

Looking at the given values of y, we can see that the value of "y" lies between 0 and 40.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining.

   x          y

   0         40

  0.5     39.25

    1        38.5  

   1.5       37.75

What is the range of this function?

(a) all real numbers such that y ≤ 40

(b) all real numbers such that y ≥ 0

(c) all real numbers such that 0 ≤ y ≤ 40

(d) all real numbers such that 37.75 ≤ y ≤ 40.

Answer:

Step-by-step explanation:

Distance between 2Points XY=Distance between 2 points YZ=7.615

Distance between 2 points ZX=5.6568

Hence it is an isosceles triangle

2401/16 square inches

Step-by-step explanation:

Given:

The quilt made by Spencer had a 7×7 array of different color square patches such that each patch is  in long.

To find: the area of the whole quilt

Solution:

Side of each quilt =

Quilt is in the form of a square such that area of square is given by

Therefore, area of quilt =   square inches

i Got u Bro!

Obtuse scalene triangle.

Sides: a = 34   b = 9.922   c = 27.442

Area: T = 112.86

Perimeter: p = 71.364

Semiperimeter: s = 35.682

Angle ∠ A = α = 124° = 2.164 rad

Angle ∠ B = β = 14° = 0.244 rad

Angle ∠ C = γ = 42° = 0.733 rad

Height: ha = 6.639

Height: hb = 22.75

Height: hc = 8.225

Median: ma = 11.694

Median: mb = 30.495

Median: mc = 20.951

Inradius: r = 3.163

Circumradius: R = 20.506

Vertex coordinates: A[27.442; 0] B[0; 0] C[32.99; 8.225]

Centroid: CG[20.144; 2.742]

Coordinates of the circumscribed circle: U[13.721; 15.239]

Coordinates of the inscribed circle: I[25.76; 3.163]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 56° = 2.164 rad

∠ B' = β' = 166° = 0.244 rad

∠ C' = γ' = 138° = 0.733 rad

The coordinates of the fourth vortex of the rectangular piece of material drawn by Freddy would be  (4. 6, - 3 ).

Rectangles are quadrilaterals which have two sets of parallel lines. This means that two sets of sides are equal which are the opposite ones. This means that when plotted on a coordinate plane, of the four points, the x - values should repeat twice and the y - values should repeat twice as well.

They would do so by alternating with each other. This means that in a rectangle with (-2, -3), (- 2 . 3, 1 . 6), ( 4 . 6 , 1. 6 ), the fourth vertex would be the two x and y values that are yet to repeat which would be:

( 4. 6, - 3 ).

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Answer:

Area of shaded region:

12r^2 - (2(2r^2) + 2πr^2) =

12r^2 - 4r^2 - 2πr^2 =

(2r^2)(4 - π)

Probability of point chosen in shaded region:

(2r^2)(4 - π)/(12r^2) = (4 - π)/6 = .143 = 14.3%