Test the series for convergence or divergence using the Alternating Series Test. 2 4 + 4 5 6 + 6 8 7 10 + 8 Identify bn.

The triangle that has the coordinates as A(0,-4) B(0,-9) C(-2,-5) is; A scalene Triangle

The formula for the distance between two coordinates is;

D = √[(y₂ - y₁)² + (x₂ - x₁)²]

Thus;

Distance AB = √[(-9 + 4)² + (0 - 0)²]

Distance AB = √25

Distance AB = 5

Distance BC = √[(-5 + 9)² + (-2 - 0)²]

Distance BC = √20

Distance CA = √[(-4 + 5)² + (-2 - 0)²]

Distance CA = √5

Since the three sides all have different lengths, then they the triangle is said to be a scalene triangle.

Read more about distance between coordinates at; https://brainly.com/question/7243416

#SPJ1

The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

We know,

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

we have,

∠DEC ≅ ∠BFC  Reason = All Right Angles with Equal dimensions are congruent.

∠C ≅ ∠C  Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.

Δ DEC ≅ Δ BFC  Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

 ≅   Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.

ABCD is a Rhombus Reason = Its sides are all congruent.

Learn more about Rhombus at;

brainly.com/question/20627264

#SPJ1

complete question:

Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

Viola needs to jump a distance of 0.04 m on her next attempt to increase her mean to 3.82 m

On average, she has jumped 3.80 m so far. Therefore, the sum of distances jumped so far by her is:

3.80 m × the total number of jumps taken so far.

On the next jump, she reaches 3.99 m. Therefore, after the next jump, the total distance jumped so far by her will be 3.80 m × total number of jumps taken so far + 3.99 m. The new mean is 3.81 m.

Therefore, (3.80 m × total number of jumps taken so far + 3.99 m)/(total number of jumps taken so far + 1) = 3.81.

The above equation can be simplified as 3.80 m × total number of jumps taken so far + 3.99 m = 3.81 m × (total number of jumps taken so far + 1).

This simplifies to 3.80 m × total number of jumps taken so far + 3.99 m = 3.81 m × total number of jumps taken so far + 3.81 m. Now, we need to solve the above equation to find out the distance she needs to jump on her next attempt to increase her mean to 3.82 m.

3.80 m × total number of jumps taken so far + 3.99 m = 3.81 m × total number of jumps taken so far + 3.81 m.

0.01 m = 0.01 m × total number of jumps taken so far.

1 = total number of jumps taken so far. Now, she needs to jump a distance of (3.82 m × (total number of jumps taken so far + 1)) - (3.80 m × total number of jumps taken so far)

= (3.82 m × (1 + 1)) - (3.80 m × 1)

= 3.82 m × 2 - 3.80 m

= 0.04 m

Therefore, she needs to jump a distance of 0.04 m on her next attempt to increase her mean to 3.82 m.

To learn more about mean and distance refer :

https://brainly.com/question/28448081

#SPJ11

Answer:98

Step-by-step explanation:

Answer:

14x7= 98

Step-by-step explanation:

for multiplication, think about if there are 9, 10 base blocks and 8, 1 base block

If two positive numbers are multiplied or divide then the result is always positive but if we take one positive and one negative number and then after multiply or divide we get always negative number.

What is Number system?

A system of writing to express the number with positive or negative sign is called number system.

Now, There are many applications for the use of positive and negative numbers to represent mathematical ideas.

⇒ Negative and positive numbers are used to describe the distance from a reference point.

⇒ If two positive numbers are multiplied or divide then the result is always positive but if we take one positive and one negative number and then after multiply or divide we get always negative number.

Learn more about the Negative and positive numbers visit:

https://brainly.com/question/17200227

#SPJ1

Answer:

?

Step-by-step explanation:

Answer: c

Step-by-step explanation:

A p e x

Using test statistic z, Typical parent would spend on their child's birthday gift is between $30.927 and $40.873.

In the given question we have to estimate how much a typical parent would spend on their child's birthday gift using a 98% confidence level.

Given in the question

Number of sample (n) = 29

Sample mean (X) = 35.9

Sample standard deviation (S) = 9.5

We need to calculate 98% confidence interval which can be calculated as

CI = X± \(t_{\alpha/2}\) * S/√n

Here confidence level CI = 0.98

Level of significance (\alpha) = 1-0.98=0.02

α/2 = 0.01

Degree of freedom (df) = n-1 = 29-1 = 28

from t table we found \(t_{\alpha/2}\) = 2.821

So 98% confidence interval is

CI = 35.9 ± 2.821* 9.5/√29

CI = 35.9± 2.821* 9.5/5.39

CI = 35.9± 2.821*1.763

CI = 35.9± 4.973

CI = (35.9-4.973, 35.9+4.973)

CI = (30.927, 40.873)

30.927 < μ < 40.873

So, Typical parent would spend on their child's birthday gift is between $30.927 and $40.873.

To learn more about test statistic z link is here

brainly.com/question/3006526

#SPJ4

Answer:  

5× 10 to the power -5

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

The total length of craft wire used by Samantha is 10x + 9

What is the scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Let's call the length of the smaller quadrilateral's 6-centimeter side "x".

Then the length of the corresponding side in the larger quadrilateral would be 6+3=9 centimeters, since the scale factor is 3.

To find the total length of craft wire used, we need to add up the lengths of all the sides in both quadrilaterals.

The smaller quadrilateral has four sides, each with a length of x.

The larger quadrilateral also has four sides, but only one of them has a different length (9 cm), while the other three sides are simply 3 times longer than the corresponding sides in the smaller quadrilateral.

So the total length of craft wire used by Samantha is:

4x + 9 + 3x + 3x + 3x

Simplifying this expression, we get:

10x + 9

Hence,  the total length of craft wire used by Samantha is:

10x + 9

To learn more about scale factor visit:

https://brainly.com/question/29967135

#SPJ4

Answer:

There’s a pretty possible chance this is right 20%

Step-by-step explanation:

Answer:

Tamanna scored more.

Step-by-step explanation:

Bhaskar scored -60, 20 and 0. His total score is therefore:

-60 + 20 + 0 = -40

Tamanna scored 20, 0, 60. His total score is therefore:

20 + 0 + 60 = 80

Therefore, Tamanna scored more.

The p-value for 2.03 is 0.0212.

The p-value for 1.50 is 0.0668.

The p-value for 1.20 is 0.1151.

The p-value for 2.76 is 0.0029.

To calculate the p-values for the given critical values, we need to refer to a standard normal distribution graph or a z-table. This table provides the probabilities associated with different z-scores (standardized scores). The z-score represents the number of standard deviations a data point is away from the mean.

a. Critical value: 2.03

To find the p-value for the critical value of 2.03, we look at the standard normal distribution graph or z-table. Locate the value of 2.03 on the graph and find the corresponding area under the curve. This means that if the null hypothesis is true, there is a 0.0212 probability of obtaining a test statistic as extreme as 2.03 or more extreme.

b. Critical value: 1.50

Similarly, we locate the value of 1.50 on the standard normal distribution graph and find the corresponding area. This implies that if the null hypothesis is true, there is a 0.0668 probability of obtaining a test statistic as extreme as 1.50 or more extreme.

c. Critical value: 1.20

Again, we locate the value of 1.20 on the standard normal distribution graph and find the corresponding area. This means that if the null hypothesis is true, there is a 0.1151 probability of obtaining a test statistic as extreme as 1.20 or more extreme.

d. Critical value: 2.76

Locating the value of 2.76 on the standard normal distribution graph, we find the corresponding area.  This indicates that if the null hypothesis is true, there is a 0.0029 probability of obtaining a test statistic as extreme as 2.76 or more extreme.

To know more about p-value here

https://brainly.com/question/30078820

#SPJ4

Answer:

y=3/5x + 1

Step-by-step explanation:

It says to translate UP 5 units, meaning the constant of -4 is the one being affected. The translation of 5 units is +5 on the graph, so -4+5=1. Everything else should be the same if i'm correct so y=3/5x + 1 is the answer

Answer:

Domain: {-10, -8, -6, -4}

Range: {-5, -4, -3, -2}

Step-by-step explanation:

The domain is a set of all the x's. Here you were given points and the first number in the parenthesis is the x in (x, y). Sometimes they will give you a table or a graph. But domain is all the x's gathered together. I put them in order from small to big to be neat. There aren't any repeats here, but if there ever are repeats you don't have to list them multiple times, just once.

The range is all the y's in the points (x, y) its the second number. Gather all the y's in a set, that is the range.

Answer:

The domain is 15 ≤ x ≤ 25

Step-by-step explanation:

The given parameters are;

The number of hours Miguel works each week = Between 15 and 25 hours

The amount he is paid per hour = $12

Therefore, we have;

The domain is all real numbers, 'x', such that 15 ≤ x ≤ 25

The amount Miguel makes each week, 'y' is between; 12 × 15 ≤ A ≤ 12 × 25

Therefore the range is 180 ≤ y ≤ 300.

The correct formula for the general term of the arithmetic sequence representing the cost of the venue hire and catering for n guests is 1950 + 100n.

To find the formula for the general term of the arithmetic sequence representing the cost of the venue hire and catering for n guests, we can analyze the given information.

We are given two data points: the cost for 50 guests, which is $6,950, and the cost for 100 guests, which is $11,950. We can observe that the difference between these two costs is $11,950 - $6,950 = $5,000.

Since the cost forms an arithmetic sequence, the difference between consecutive terms will remain constant. In this case, the difference is $5,000.

Now, we need to find the initial term of the sequence. By examining the cost for 50 guests, we notice that the difference between the cost for 50 guests and the initial term is $6,950 - $5,000 = $1,950.

Putting it all together, we have the formula for the general term of the arithmetic sequence: initial term + (difference × (n - 1)).

Plugging in the values, the formula becomes: 1,950 + (5,000 × (n - 1)) = 1,950 + 5,000n - 5,000 = 5,000n - 3,050. Simplifying further, we get the final formula: 5,000n - 3,050.

To learn more about arithmetic sequence

https://brainly.com/question/6561461

#SPJ8

Answer: $108

Step-by-step explanation:

what is 144 / 4 ? 36 = one meal ticket

what is 36 x 3 ? 108

each game ticket costs 108 dollars

Answer:

26

Step-by-step explanation:

The Pythagorean Theorem states that a² + b² = c²

so, c = √(a² + b²)

10² + 24² = 676

√676 = 26

The amplitude of the function f(x) = sin(5x) is 1

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

f(x) = sin(5x)

A sinusoidal function is represented as

f(x) = Asin(B(x + C)) + D

Where

Amplitude = A

Period = 2π/B

So, we have

A = 1

Period = 2π/5

Evaluate

A = 1

Period = 2π/5

Hence, the amplitude is 1

Read more about sinusoidal function at

brainly.com/question/21286958

#SPJ1

A sequence is arithmetic sequence when the first differences are all the same non-zero number.

An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a defined number. The common difference of the series, which is a constant value, is the same for all following pairs of terms.

As a result, a sequence can be said to be arithmetic if its first differences all contain the same non-zero value. For instance, the arithmetic sequence 3, 6, 9, 12, 15,... has a common difference of 3.

To know more about Arithmetic sequence, visit,

https://brainly.com/question/6561461

#SPJ4

Answer:

p = - 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, - 3) and (x₂, y₂ ) = (3, 7)

m = \(\frac{7-(-3)}{3-(-1)}\) = \(\frac{7+3}{3+1}\) = \(\frac{10}{4}\) = \(\frac{5}{2}\)

Parallel lines have equal slopes

Calculate the slope of the other 2 points and equate to \(\frac{5}{2}\)

with (x₁, y₁ ) = (3, p) and (x₂, y₂ ) = (7, - 4p)

m = \(\frac{-4p-p}{7-3}\) = \(\frac{-5p}{4}\) = \(\frac{5}{2}\) ( cross- multiply )

- 10p = 20 ( divide both sides by - 10 )

p = - 2

Step-by-step explanation:

Let the 2 numbers be X and Y

X+Y=88

X-Y=60

______

2X. = 148. X=74

Put the value of X to find Y

74+Y=88

74-Y = 60 :. Y = 14

=>X=74

=>Y=14

To evaluate c ∇f · dr, we need to first find the gradient vector ∇f and the differential vector dr.

Since the function f is not given, we cannot find ∇f explicitly. However, we know that ∇f points in the direction of greatest increase of f, and that its magnitude is the rate of change of f in that direction. Therefore, we can make an educated guess about the form of ∇f based on the information given.

The function f could be any function, but let's assume that it is a function of two variables x and y. Then, we have:

∇f = (∂f/∂x, ∂f/∂y)

where ∂f/∂x is the partial derivative of f with respect to x, and ∂f/∂y is the partial derivative of f with respect to y.

Now, let's find the differential vector dr. The parameterization of c is given by:

x = t^2 + 1

y = t^3 + t

0 ≤ t ≤ 1

Taking the differentials of x and y, we get:

dx = 2t dt

dy = 3t^2 + 1 dt

Therefore, the differential vector dr is given by:

dr = (dx, dy) = (2t dt, 3t^2 + 1 dt)

Now, we can evaluate c ∇f · dr as follows:

c ∇f · dr = (c1 ∂f/∂x + c2 ∂f/∂y) (dx/dt, dy/dt)

where c1 and c2 are the coefficients of x and y in the parameterization of c, respectively. In this case, we have:

c1 = 2t

c2 = 3t^2 + 1

Substituting these values, we get:

c ∇f · dr = (2t ∂f/∂x + (3t^2 + 1) ∂f/∂y) (2t dt, 3t^2 + 1 dt)

Now, we need to make an educated guess about the form of f based on the information given. We know that f is a function of x and y, and we could assume that it is a polynomial of some degree. Let's assume that:

f(x, y) = ax^2 + by^3 + cxy + d

where a, b, c, and d are constants to be determined. Then, we have:

∂f/∂x = 2ax + cy

∂f/∂y = 3by^2 + cx

Substituting these values, we get:

c ∇f · dr = [(4at^3 + c(3t^2 + 1)t) dt] + [(9bt^4 + c(2t)(t^3 + t)) dt]

Integrating with respect to t from 0 to 1, we get:

c ∇f · dr = [(4a/4 + c/2) - (a/2)] + [(9b/5 + c/2) - (9b/5)]

Simplifying, we get:

c ∇f · dr = -a/2 + 2c/5

Therefore, the value of c ∇f · dr depends on the constants a and c, which we cannot determine without more information about the function f.

The value of c where c has parametric equations x = t2 + 1, y = t3 + t, 0 t 1. is  c ∇f · dr=  [(2t^5 + 2t^3)(∂f/∂x) + (9t^7 + 3t^5)(∂f/∂y)] dt.

We have the following information:

c(t) = (t^2 + 1)i + (t^3 + t)j, 0 ≤ t ≤ 1

f(x, y) is a scalar function of two variables

We need to find c ∇f · dr.

We start by finding the gradient of f:

∇f = (∂f/∂x)i + (∂f/∂y)j

Then, we evaluate ∇f at the point (x, y) = (t^2 + 1, t^3 + t):

∇f(x, y) = (∂f/∂x)(t^2 + 1)i + (∂f/∂y)(t^3 + t)j

Next, we need to find the differential vector dr = dx i + dy j:

dx = dx/dt dt = 2t dt

dy = dy/dt dt = (3t^2 + 1) dt

dr = (2t)i + (3t^2 + 1)j dt

Now, we can evaluate c ∇f · dr:

c ∇f · dr = [c(t^2 + 1)i + c(t^3 + t)j] · [(∂f/∂x)(2t)i + (∂f/∂y)(3t^2 + 1)j] dt

= [c(t^2 + 1)(∂f/∂x)(2t) + c(t^3 + t)(∂f/∂y)(3t^2 + 1)] dt

= [(t^2 + 1)(2t^3 + 2t)(∂f/∂x) + (t^3 + t)(9t^4 + 3t^2)(∂f/∂y)] dt

Therefore, c ∇f · dr = [(2t^5 + 2t^3)(∂f/∂x) + (9t^7 + 3t^5)(∂f/∂y)] dt.

Learn more about parametic equation at https://brainly.com/question/24097871

#SPJ11

Answer:x=3 , y=-5 OR (3,-5)

Step-by-step explanation:

Answer:

10 water and 4 cheese sticks

Step-by-step explanation:

water

5 10 15 20 25 30 35 40 45 50<--

cheese sticks

12 24 38 50<--

Answers:

Slope = 3/4

y intercept = -1/2

================================================

Explanation:

The form y = mx+b is known as slope intercept form

m is the slope and b is the y intercept

Comparing y = (3/4)x - 1/2 to y = mx+b, we see that

m = 3/4

b = -1/2

Step-by-step explanation:

Given

To Prove

\(\dfrac{3\sin x}{1-\cos x}=3\csc x+3\cot x\)

Take the Left side of equation and rationalize

\(\Rightarrow \dfrac{3\sin x}{1-\cos x}\times \dfrac{1+\cos x}{1+\cos x}\\\\\Rightarrow \dfrac{3\sin (1+\cos x)}{1-\cos^2 x}\\\\\Rightarrow \dfrac{3\sin (1+\cos x)}{\sin^2 x}\\\\\Rightarrow \dfrac{3\sin x}{\sin ^2x}+\dfrac{3\sin x\cos x}{\sin^2 x}\\\\\Rightarrow \dfrac{3}{\sin x}+\dfrac{3\cos x}{\sin x}\\\\\Rightarrow 3\csc x+3\cot x\)

Left side is equal to right side

Hence, proved

Answer:

\(y=3x+6\)

Step-by-step explanation:

In order to create an equation in slope-intercept form, we need to first find the slope of the line. In order to do this, we use the equation:

\(\frac{y2-y1}{x2-x1} =m\)

Plug your two coordinates into this equation:

\(\frac{(3--3)}{(-1--3)} = \frac{6}{2} = 3\)

Now, you can add the slope to the slope-intercept formula. We still need to find b, though.

\(y=3x+b\)

Choose one coordinate you were given and plug in x and y.

\(3=3(-1)+b\\3=-3+b\\6=b\)

Hence, your equation is:

\(y=3x+6\)