find the partial sum s, of the arithmetic sequence that satisfies the given conditions.

The correct answer is a)True  c)True The order of the cyclic group is determined by the number of elements in the group, whereas the order

a. True. If a nonempty subset H of a group G is closed under the binary operation of G, contains the identity element of G, and contains the inverse of each of its elements, then H is a subgroup of G.

c. A is true but B is false. Every cyclic group is indeed abelian, but the order of the cyclic group is not necessarily the same as the order of its generator. The order of the cyclic group is determined by the number of elements in the group, whereas the order of the generator refers to the smallest positive exponent that generates all elements of the group.

a. Zero has no inverse. In the set of real numbers under the usual multiplication operation, the element zero does not have a multiplicative inverse. Every nonzero real number has an inverse, but zero itself does not. In a group, every element should have an inverse, so the set of all real numbers under multiplication does not form a group.

Learn more about abelion groups here:

https://brainly.com/question/30454143

#SPJ11

Answer:true

Step-by-step explanation:

Answer:

The expression that equivalent to (g - f)(3) is 6(3) - 4 + 3² ⇒ C

Step-by-step explanation:

Let us solve the question

∵ f(x) = 4 - x²

∵ g(x) = 6x

→ Find at first (g - f)(x) by subtracting f(x) from g(x)

∵ (g - f)(x) = 6x - (4 - x²)

→ Remember (-)(+) = (-) and (-)(-) = (+)

∴ (g - f)(x) = 6x - 4 + x²

→ Substitute x by 3 to find (g - f)(3)

∵ (g - f)(3) = 6(3) - 4 + (3)²

∴ (g - f)(3) = 6(3) - 4 + 3²

The expression that equivalent to (g - f)(3) is 6(3) - 4 + 3²

Obtaining data with a small p-value would be strong evidence against the null hypothesis. Correct option is 3).

In hypothesis testing, the null hypothesis assumes that there is no significant difference or relationship between variables, while the alternative hypothesis suggests otherwise. To determine whether to reject the null hypothesis, we calculate a p-value, which represents the probability of observing the data or more extreme results if the null hypothesis were true.

A small p-value indicates that the observed data is unlikely to occur under the null hypothesis, providing strong evidence against it. Therefore, obtaining data with a small p-value (option 3) would be considered strong evidence against the null hypothesis.

On the other hand, a large p-value (option 4) would suggest that the observed data is likely to occur even if the null hypothesis were true. This would not provide strong evidence against the null hypothesis, as it suggests that the data is consistent with the null hypothesis.

Using a small level of significance (option 1) or a large level of significance (option 2) refers to the predetermined threshold at which we decide to reject or fail to reject the null hypothesis. While the choice of significance level affects the decision-making process, it does not directly indicate evidence against the null hypothesis like the p-value does.

Learn more about  p-value here:

https://brainly.com/question/30461126

#SPJ11

The general form of an equation of a circle with center at (a, b) and radius of length m is x² + y² - 2ax - 2by + (a² + b² - m²) = 0.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

Standard form of a circle is given by the equation,

(x - h)² + (y - k)² = r²

where, (h, k) is the center of the circle and r is the radius of the circle.

Here center is given as (a, b).

Radius is given as m.

Substituting,

(x - a)² + (y - b)² = m²

x² - 2ax + a² + y² - 2by + b² = m²

x² + y² - 2ax - 2by + (a² + b²) = m²

x² + y² - 2ax - 2by + (a² + b² - m²) = 0

Hence the required equation is, x² + y² - 2ax - 2by + (a² + b² - m²) = 0.

Learn more about General Form of Circle here :

https://brainly.com/question/10618691

#SPJ7

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

Since we are to find the probability that 2 randomly selected points from Q,R,S,T and W are non-collinear

Non collinear points are points that doesn't lie on the same straight line. From the diagram given, the two point that are non colliear are (QR, QS, QT and QW making 4 2random non collinear points. Hence out expected number of outcome is 4.

For the total possible outcome, we are to find the number of ways we can randomly select two points from the 5 points given and this can be done using the combination rule.

This can therefore be done in 5C2 number of ways.

5C2 = 5!/(5-2)!2!

5C2 = 5!/3!2!

5C2 = 5*4*3*2*1/3*2*2

5C2 = 5*2

5C2 = 10 different ways

Hence the total possible outcome is 10

Therefore, the probability that 2 randomly selected points from Q,R,S,T and W are noncollinear will be 4/10 = 2/5

Answer:

y= 6/5x-10

Step-by-step explanation:

The coefficient of determination, denoted by R^2, is a measure of how well the regression model fits the data. It represents the proportion of the total variation in the dependent variable (sales dollars) that is explained by the independent variable (number of contacts).

In this case, we can use the formula:

R^2 = SS_regression / SS_total

where SS_regression is the sum of squares of the regression (13,591.17) and SS_total is the total sum of squares (14,249.12).

Thus,

R^2 = 13,591.17 / 14,249.12

R^2 = 0.953

Therefore, the coefficient of determination is 0.953 or 95.3%. This means that 95.3% of the variation in sales dollars can be explained by the number of contacts made by the salesperson, and the remaining 4.7% is due to other factors not included in the model.

To know more about coefficient of determination visit:

https://brainly.com/question/28975079

#SPJ11

The correct option is for the value of c,  such that f(c) is the average value of the function on the interval [0, 2], is D.

The average value of a function on an interval [a, b] is given by:

R = (f(b) - f(a))/(b - a)

Here the interval is [0, 2], then:

f(2) = √(2 + 2) = 2

f(0) = √(0 + 2) = √2

Then here we need to solve the equation:

√(c + 2) = (f(2) - f(0))/(2 - 0)

√(c + 2) = (2 + √2)/2

Solving this for c, we will get:

c = [ (2 + √2)/2]² - 2

c = 0.9

Them tjhe correct option is D.

Learn more about average value:

https://brainly.com/question/130657

#SPJ1

The length of the third side of the triangle with a perimeter of 7x + 8 is 2x + 3

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

A triangle is a polygon that has three sides. The perimeter of a triangle is the sum of all the three sides.

Hence:

Perimeter of triangle = side 1 + side 2 + side 3

A triangle has a perimeter of 7x + 8. the first side of the triangle has a length of 3x, and the second side has a length of 2x − 5.

Hence:

Perimeter of triangle = side 1 + side 2 + side 3

7x + 8 = 3x + (2x - 5) + side 3

7x + 8 = (5x - 5) + side 3

side 3 = 7x + 8 - (5x - 5)

side 3 = 2x + 13

The length of the third side is 2x + 3

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

Step-by-step explanation:

The probability P(Z>1.28) represents the area under the standard normal distribution curve to the right of the z-score 1.28.

Using a standard normal distribution table or a calculator, we find that the area to the right of 1.28 is approximately 0.1003.

Therefore, the answer is closest to option (b) 0.10. there is a 10% chance of obtaining a value above 1.28 in a standard normal distribution.

know more about normal distribution: brainly.com/question/15103234

#SPJ11

Answer: yes

Step-by-step explanation:

Answer:

there wont be a fraction the sweets are gone

Step-by-step explanation:

she got fat

Answer:

9.00-3.29= 5.71 meters rope remaining

The area of each parallelogram or triangle is 24 cm²,22.5 cm², 98 ft²,48 cm², 90 m², and  30 in² respectively.

In this skills practice problem, we are asked to find the perimeter and area of each parallelogram or triangle, based on their given dimensions. Let's start by defining the formulas for calculating the perimeter and area of each shape:

Perimeter of a parallelogram = 2 x (length + width)

Area of a parallelogram = base x height

Perimeter of a triangle = sum of the lengths of its sides

Area of a triangle = 1/2 x base x height

Now, let's apply these formulas to each shape:

Parallelogram with length 6 cm and width 4 cm:

Perimeter = 2 x (6 + 4) = 20 cm

Area = 6 x 4 = 24 cm²

Triangle with base 9 cm and height 5 cm:

Perimeter = 9 + 8 + 7 = 24 cm

Area = 1/2 x 9 x 5 = 22.5 cm²

Parallelogram with length 14 ft and width 7 ft:

Perimeter = 2 x (14 + 7) = 42 ft

Area = 14 x 7 = 98 ft²

Triangle with base 12 cm and height 8 cm:

Perimeter = 12 + 8 + 10 = 30 cm

Area = 1/2 x 12 x 8 = 48 cm²

Parallelogram with length 18 m and width 5 m:

Perimeter = 2 x (18 + 5) = 46 m

Area = 18 x 5 = 90 m²

For more questions like Triangle click the link below:

https://brainly.com/question/2773823

#SPJ11Triangle with base 6 in and height 10 in:

Perimeter = 6 + 8 + 10 = 24 in

Area = 1/2 x 6 x 10 = 30 in²

Therefore, we have calculated the perimeter and area of each given parallelogram or triangle.

For more questions like Triangle click the link below:

https://brainly.com/question/2773823

#SPJ11

Answer:

i think its b but im not sure

Step-by-step explanation:

The components of the vector:

a)  P1 to P2 are (-1, 3).

b) P1 to P2 are (-7, 2).

c)  P1 to P2 are (-3, 6, 1).

(a) Given points P1(3, 5) and P2(2, 8), we can find the components of the vector by subtracting the corresponding coordinates:

P2 - P1 = (2 - 3, 8 - 5) = (-1, 3)

So, the components of the vector from P1 to P2 are (-1, 3).

(b) Given points P1(7, -2) and P2(0, 0), the components of the vector from P1 to P2 are:

P2 - P1 = (0 - 7, 0 - (-2)) = (-7, 2)

The components of the vector from P1 to P2 are (-7, 2).

(c) Given points P1(5, -2, 1) and P2(2, 4, 2), the components of the vector from P1 to P2 are:

P2 - P1 = (2 - 5, 4 - (-2), 2 - 1) = (-3, 6, 1)

The components of the vector from P1 to P2 are (-3, 6, 1).

Learn more about vector here:

https://brainly.com/question/24256726

#SPJ11

Answer:

3rd option is your answer.....

The value of the expression 9(4 + 9) using the distributive property is 117.

To evaluate the expression 9(4 + 9) using the distributive property, we need to distribute the 9 to both terms inside the parentheses.

First, we distribute the 9 to the term 4:

9 * 4 = 36

Next, we distribute the 9 to the term 9:

9 * 9 = 81

Now, we can rewrite the expression with the distributed values:

9(4 + 9) = 9 * 4 + 9 * 9

Substituting the distributed values:

= 36 + 81

Finally, we can perform the addition:

= 117

Therefore, the value of the expression 9(4 + 9) using the distributive property is 117.

for such more question on distributive property

https://brainly.com/question/29667212

#SPJ8

Step-by-step explanation:

student

whole number between 4 and 8 is 5,6 and7

and between 12 and 16 is 13,14 and 15

Answer:

a) 5,6,7

b) 13,14,15

Step-by-step explanation:

Check the picture below.

\(\textit{area of a circular ring}\\\\ A=\pi (R^2-r^2) ~~ \begin{cases} R=\stackrel{larger}{radius}\\ r=\stackrel{smaller}{radius}\\[-0.5em] \hrulefill\\ R=10.5\\ r=7 \end{cases}\implies \begin{array}{llll} A=\pi (10.5^2 - 7^2)\implies A=61.25\pi \\\\\\ A\approx 192.42~m^2 \end{array}\)

The area of the circle r = 18 sinθ as an integral in polar coordinates is 81π.

We must evaluate the integral of the function r = 18sinθ with respect to θ in order to determine the circle's area in polar coordinates, where r stands for the radius and θ for the angle.

The whole revolution of the circle should be covered by the limits of integration for θ. Our bounds of integration will be 0 to 2π(or 0 to 360 degrees), which is the range of a whole revolution.

The following is the formula for the area in polar coordinates:

A = (1/2)\(\int[a, b] r^2 d\theta\)

A = 0 and b = 2 in this instance. The radius at every given angle is represented by the function r = 18sinθ, which must be squared to get r².

We can now determine the area:

A = (1/2) \(\int[0, 2\pi] (18sin\theta)^2 d\theta\)

Simplifying the integrand:

A = (1/2) \(\int[0, 2\pi] 324sin^2\theta d\theta\)

Using the trigonometric identity sin²θ = (1/2)(1 - cos2θ):

A = (1/2) \(\int[0, 2\pi] 324(1/2)(1 - cos2\theta) d\theta\)

A = (1/4) \(\int[0, 2\pi] (162 - 162cos2\theta) d\theta\)

Integrating term by term:

A = (1/4) [162θ - 81sin2θ] evaluated from 0 to 2π

Plugging in the limits:

A = (1/4) [(162(2π) - 81sin(4π)) - (162(0) - 81sin(0))]

Simplifying further:

A = (1/4) [324π - 0 - 0 - 0]

A = (1/4) (324π)

Finally, we can calculate the area:

A = 81π

Therefore, the area of the circle r = 18sinθ in polar coordinates is 81π square units.

To learn more about polar coordinates link is here

brainly.com/question/31904915

#SPJ4

Answer:

Khalid’s rate is ___140_ miles per hour. Jesse’s rate is _150___ miles per hour. So, _Jesse’s___ train traveled at a faster speed.

Step-by-step explanation:

The general equation of a straight line is

y = mx + b

for y = 150x

We have the slope as 150

This is 150 miles/hour

This relates to Jesse’s train speed

for Khalid, we have his own speed obtainable from the graph

The speed is simply the slope of the graph

We proceed to select two points from the graph and find the slope

The points are; ((1,140) and (4,560)

Mathematically, the slope will be;

m = (y2-y1)/(x2-x1)

m = (560-140)/(4-1) = 420/3 = 140 miles per hour

By answering the given question, we may state that Hence, the first-time interest home buyer's mortgage brokerage fees would be $1,653.45.

Divide the principal by the interest rate, the length of time, and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This method makes it easiest to calculate interest. The most typical technique to figure out interest is as a portion of the principal sum. He will only pay his share of the 100% interest, for example, if he borrows $100 from a friend and agrees to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an annual percentage of the loan total. The interest on the loan is this percentage.

In order to determine the mortgage brokerage fees, we must first determine 1.05% of the funded amount and then add the $300 flat charge.

The formula for 1.05% of $128,900 is as follows:

1.05/100 x $128,900 = $1,353.45

The following would be the mortgage brokerage fees:

$1,353.45 + $300 = $1,653.45

Hence, the first-time home buyer's mortgage brokerage fees would be $1,653.45.

To know more about interest visit:

https://brainly.com/question/28792777

#SPJ1

The dimensions of the box that minimize total cost are height h =3.17m, width, w and length, l=9.52m  are equal to  .

Let h is the height of the box.

Given Volume of the box is 216 m³  with no top.

And the cost of the bottom is 40USD/m².

For the sides, it is 30USD/m².

The bottom of the box is square, so l = w.

So Volume

\(V=hl^{2}\)

\(216=hl^{2}\)

\(h=\frac{216}{l^{2} }\)

Now Surface Area of the box without a top is

S = 4hl + l²

So,

cost = 4 × 30hl +40l²

cost = 120 hl + 40 l²

Putting h ,

cost = 120 × \((\frac{216}{l^{2} })l + 40l^{2}\)

cost = \(\frac{25960}{l^{2} }+40l^{2}\)

To find minimum cost, derivate the  by using the calculator at

\(l=3\sqrt[3]{4}\)

l=4.762203 m

\(h=\frac{216}{4.762203^{2} }\)

h = 9.5244069354 m

Hence the dimensions of the box are

l=w

 =9.52 m

and height ,h=3.17 m  

Know more about the volume of the box here:

brainly.com/question/11168779

#SPJ4

Answer:

- 3/8

Step-by-step explanation:

y = 1/2x - 3/4

(1/2)(-3/4) = - 3/8

Answer:

81, 64, 47, 30, 13, -4

Answer:

The next two numbers are 13 and -4.

Step-by-step explanation:

We are subtracting 17 each time.

30 - 17 = 13

13 - 17 = -4