When two sample means are significantly different
Group of answer choices

The pooled variance estimate should not be used

The difference is too great to attribute to chance

The corresponding population means are significantly different

The difference is of practical importance

Answers

Answer 1

When two sample means are significantly different, "the difference is too great to attribute to chance".

What is statistical significance?

The likelihood of finding a difference between two samples (such means or proportions) through pure chance is known as statistical significance. The likelihood of obtaining the observed difference if there were no actual difference between the associated population parameters is calculated to ascertain this. The difference is deemed statistically significant if the p-value is below a predetermined cutoff (often 0.05).

Significant difference between two sample means indicates that the likelihood of such a difference occurring by chance alone is low. If there is a true difference between the matching population means from which the samples were selected, it shows that the difference between the sample means is too large to be explained by chance.

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Related Questions

You can afford a $1000 per month mortgage payment. You've found a 30 year loan at 5.3% interest.
a) How big of a loan can you afford? (Round to the nearest cent, as needed.)
$
b) How much total money will you pay the loan company? (Round to the nearest cent, as needed.)
$
c) How much of that money is interest? (Round to the nearest cent, as needed.)

Answers

Answer:

a) To find out how big of a loan you can afford, we can use the formula for the monthly payment of a mortgage:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]

where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (which is the annual interest rate divided by 12), and n is the number of monthly payments (which is the number of years times 12).

In this case, we know that M = $1,000, i = 0.053/12, and n = 30 x 12 = 360. We want to solve for P, the principal we can afford.

Substituting these values into the formula, we get:

$1,000 = P [ 0.004416(1 + 0.004416)^360 ] / [ (1 + 0.004416)^360 - 1 ]

Simplifying and solving for P, we get:

P = $183,928.72

Therefore, you can afford a loan of approximately $183,928.72.

b) The total money paid to the loan company will be the monthly payment multiplied by the number of payments over the life of the loan. In this case, we have:

Total money paid = $1,000 x 360 = $360,000

Therefore, the total amount of money paid to the loan company will be $360,000.

c) To find out how much of that money is interest, we can subtract the principal from the total amount paid. In this case, we have:

Interest paid = Total money paid - Principal = $360,000 - $183,928.72 = $176,071.28

Therefore, the amount of money paid in interest will be $176,071.28.

1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping
and sprinkles. How many different sundaes can you make when you order one flavor of ice
cream, one topping and one color of sprinkles from the chart below? Show all possible
outcomes in a tree diagram.
Ice Cream
Chocolate
Vanilla
Strawberry
Topping
Fudge
Marshmallow
Sprinkles
Chocolate
Rainbow
a. How many sample spaces are there? HINT: How many possible combinations?
b. P (Chocolate, Fudge, Rainbow)

Answers

A. There are 9 sample spaces.

B.  The probability of choosing Chocolate, Fudge, and Rainbow is 1/9

What is meant by sample spaces?

In probability theory, a sample space is the set of all possible outcomes of a random experiment or process. It is used to define the space of events and calculate probabilities.

What is meant by probability?

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. It is calculated by dividing the number of favourable outcomes by the total number of possible outcomes.

According to the given information

A. There are 9 possible combinations (3 ice cream flavors x 3 toppings x 1 sprinkle color), so there are 9 sample spaces.

B.  The probability of choosing Chocolate, Fudge, and Rainbow is 1/9, assuming all combinations are equally likely.

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See the photo below

Answers

This problem involves integration and algebraic manipulation, and belongs to the subject of calculus. The solutions are:

[tex]A) $\int_{0}^{2} (f(x) + g(x)) dx = -3$[/tex]
[tex]B) $\int_{0}^{3} (f(x) - g(x)) dx = -4$[/tex]
[tex]C) $\int_{2}^{3} (3f(x) + g(x)) dx = -32$[/tex]


What is the explanation for the above response?

This is a problem that asks us to find the values of some definite integrals using given values of other definite integrals. We are given three definite integrals, and we are asked to compute three other integrals involving the same functions, using the given values.

The problem involves some algebraic manipulation and the use of the linearity of the integral.

It also involves finding the constant "a" that makes a definite integral equal to zero. The integral involves two functions, "f(x)" and "g(x)," whose definite integrals over certain intervals are also given.

See the attached for the full solution.

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Consider the verbal phrase.

Two and nineteen hundredths times a number g, plus fifty-nine hundredths

Part A

Enter an expression to represent the verbal phrase.

g +


Part B

Evaluate the expression when g = 3.
3.96
7.16
8.34
8.93

Answers

verbal phrase can be represented by 7.16.

What is the verbal phrase?

Part A:

The verbal phrase can be represented by the following expression:

[tex]2.19g + 0.59[/tex]

Here, "Two and nineteen hundredths times a number g" can be written as 2.19g, and "plus fifty-nine hundredths" can be written as [tex]0.59[/tex]  .

Part B:

To evaluate the expression when  [tex]g = 3[/tex], we substitute 3 for g in the expression and simplify:

[tex]2.19g + 0.59[/tex]

[tex]= 2.19(3) + 0.59 [\ Substitute g = 3][/tex]

[tex]= 6.57 + 0.59[/tex]

[tex]= 7.16[/tex]

Therefore, the correct answer is [tex]7.16.[/tex]

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The given question is incomplete. the complete question is given below:

Consider the verbal phrase.

Two and nineteen hundredths times a number g, plus fifty-nine hundredths

Part A

Enter an expression to represent the verbal phrase.

g +

Part B

Evaluate the expression when g = 3.

3.96

7.16

8.34

8.93

The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 35 minutes of calls is $16.83 and the monthly cost for 52 minutes is $18.87. What is the monthly cost for 39 minutes of calls?

Answers

Answer: We can use the two given points to find the equation of the line and then plug in 39 for the calling time to find the corresponding monthly cost.

Let x be the calling time (in minutes) and y be the monthly cost (in dollars). Then we have the following two points:

(x1, y1) = (35, 16.83)

(x2, y2) = (52, 18.87)

The slope of the line passing through these two points is:

m = (y2 - y1) / (x2 - x1) = (18.87 - 16.83) / (52 - 35) = 0.27

Using point-slope form with the first point, we get:

y - y1 = m(x - x1)

y - 16.83 = 0.27(x - 35)

Simplifying, we get:

y = 0.27x + 7.74

Therefore, the monthly cost for 39 minutes of calls is:

y = 0.27(39) + 7.74 = $18.21

Step-by-step explanation:

The diameter of a circle is 38 feet.what is the circles circumfrence. Use 3.14 for pi

Answers

Answer:

The circumference of the circle is 119.32 ft.

Step-by-step explanation:

The circumference of a circle can be solved through the formula:

C = πd

where d is the diameter

Given: d = 38 ft

π = 3.14

Solve:

C = πd

C = 3.14 (38 ft)

C = 119.32 ft

The base of the right prism shown is a right triangle.

1. Name two lines parallel to AD.
2. Name a line skew to DE.
3. State the number of base edges.
4. State the number of lateral faces.
5. Find the base area,
6. Find the lateral area.
7. Find the volume.

Answers

Two lines parallel to AD are BF and CE.

Two lines skew to DE are EF and DF.

The number of base edges is three: DE, EF, and DF.

The number of lateral faces is three: ABDF, BCEF, and ACDE.

The base area is 6 square units.

The lateral area is 72 square units.

The volume is 36 cubic units.

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

1. Name two lines parallel to AD.

BF, CE

2. Name a line skew to DE.

EF, DF

3. State the number of base edges.

DE, EF, DF

4. State the number of lateral faces.

3, Which are ABDF, BCEF, ACDE.

5. Find the base area,

the base of a prism is ΔDEF,

DE = AC = 3,

EF = BC = 4,

DF = 5

A = √(s(s-a)(s-b)(s-c))

s = (3 + 4 + 5)/2 = 6

A = √(s(s-a)(s-b)(s-c))

A = √(6(6-3)(6-4)(6-5))

A = √(6(3)(2)(1))

A = √36

A = 6

6. Find the lateral area.

the lateral area would be the sum of the area of the four rectangular faces.

A = lb

ABDF

A1 = 5* 6 = 30,

BCEF,

A2 =  4 * 6 = 24

ACDE

A3 = 3  *6 = 18

lateral area = 30 + 24 + 18

= 72

7. Find the volume.

The volume of a prism can be calculated by multiplying the area of the base by the height of the prism. Therefore, the formula for the volume of a prism is:

V = Bh

Where V is the volume, B is the area of the base, and h is the height of the prism.

V = 6 * 6 = 36

hence,

Two lines parallel to AD are BF and CE.

Two lines skew to DE are EF and DF.

The number of base edges is three: DE, EF, and DF.

The number of lateral faces is three: ABDF, BCEF, and ACDE.

The base area is 6 square units.

The lateral area is 72 square units.

The volume is 36 cubic units.

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Which geometric term describes ∠ T A G ?

Answers

Answer:

angle

Step-by-step explanation:

since there is a < sign, that makes it an angle. I'm not sure if that is the whole problem, or if It is missing a picture. Hope this helps!

Answer: i know it is acute

Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5 if-2.5 if-1.5 if -0.5 if 0.5 ≤x≤1.5
+
X
Ś

Answers

The required graph of the function given; h (x) has been attached.

Define a graph?

In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called vertices that are connected by edges, also called links or lines. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.

Here as per the question the graph of the function, h (x) has been attached.

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Complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B).

Answers

The truth table for (A ⋁ B) ⋀ ~(A ⋀ B) is:

A   B   (A ⋁ B) ⋀ ~(A ⋀ B)

0   0                0

0    1                0

1     0               0

1     1                0

The truth table is what?

A truth table is a table that displays all possible combinations of truth values (true or false) for one or more propositions or logical expressions, as well as the truth value of the resulting compound proposition or expression that is created by combining them using logical operators like AND, OR, NOT, IMPLIES, etc.

The columns of a truth table reflect the propositions or expressions themselves as well as the compound expressions created by applying logical operators to them. The rows of a truth table correspond to the various possible combinations of truth values for the propositions or expressions.

To complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B), we need to consider all possible combinations of truth values for A and B.

A   B   A ⋁ B   A ⋀ B   ~(A ⋀ B)   (A ⋁ B) ⋀ ~(A ⋀ B)

0   0      0            0             1                      0

0    1       1            0             1                      0

1    0       1            0             1                      0

1    1        1             1             0                     0

So, the only case where the expression is true is when both A and B are true, and for all other cases it is false.

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Given the expression 3x+2 evaluate the expression for the given values of x when x=(-2)

Answers

Answer:

...............................

Answer:

The answer is -4.

Explanation:

First, plug the value of x in.

3(-2)+2

Then, multiply 3 and -2 since they are next to each other and order of operations PEMDAS tells you to multiply first.

-6+2

Lastly, add -6 and 2 to get -4.

solve the equation
a) y''-2y'-3y= e^4x
b) y''+y'-2y=3x*e^x
c) y"-9y'+20y=(x^2)*(e^4x)

Answers

Answer:

a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:

r^2 - 2r - 3 = 0

Factoring, we get:

(r - 3)(r + 1) = 0

So the roots are r = 3 and r = -1.

The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:

y_h = c1e^3x + c2e^(-x)

To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = Ae^4x

Taking the first and second derivatives of y_p, we get:

y_p' = 4Ae^4x

y_p'' = 16Ae^4x

Substituting these into the original differential equation, we get:

16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x

Simplifying, we get:

5Ae^4x = e^4x

So:

A = 1/5

Therefore, the particular solution is:

y_p = (1/5)*e^4x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^3x + c2e^(-x) + (1/5)*e^4x

b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:

r^2 + r - 2 = 0

Factoring, we get:

(r + 2)(r - 1) = 0

So the roots are r = -2 and r = 1.

The general solution to the homogeneous equation y'' + y' - 2y = 0 is:

y_h = c1e^(-2x) + c2e^x

To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax + B)e^x

Taking the first and second derivatives of y_p, we get:

y_p' = Ae^x + (Ax + B)e^x

y_p'' = 2Ae^x + (Ax + B)e^x

Substituting these into the original differential equation, we get:

2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x

Simplifying, we get:

3Ae^x = 3xe^x

So:

A = 1

Therefore, the particular solution is:

y_p = (x + B)e^x

Taking the derivative of y_p, we get:

y_p' = (x + 2 + B)e^x

Substituting back into the original differential equation, we get:

(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x

Simplifying, we get:

-xe^x - Be^x = 0

So:

B = -x

Therefore, the particular solution is:

y_p = xe^x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^(-2x) + c2e^x + xe^x

c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:

r^2 - 9r + 20 = 0

Factoring, we get:

(r - 5)(r - 4) = 0

So the roots are r = 5 and r = 4.

The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:

y_h = c1e^4x + c2e^5x

To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax^2 + Bx + C)e^4x

Taking the first and second derivatives of y_p, we get:

y_p' = (2Ax + B)e^4x + 4Axe^4x

y_p'' = 2Ae^4x +

The line plot displays the number of roses purchased per day at a grocery store.

A horizontal line starting at 0 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 10. There are two dots above 1 and 4. There are three dots above 2 and 5. There are 4 dots above 3.

Which of the following is the best measure of variability for the data, and what is its value?

The IQR is the best measure of variability, and it equals 3.
The IQR is the best measure of variability, and it equals 9.
The range is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 9.

Answers

The range is the best measure of variability for this data, and its value is 4.

Which of the following is the best measure of variability for the data, and what is its value?

The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).

The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:

Range = Maximum value - Minimum value = 4 - 0 = 4

Therefore, the range is the best measure of variability for this data, and its value is 4.

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find the radius of a cylinder if the volume is 2,035.75 in^3 and the height is 3 times the radius. use the formula V= pi r^2h

Answers

The radius of the cylinder is approximately 6.75 inches.

How to calculate volume of cylinder?

We can use the formula for the volume of a cylinder to solve this problem:

[tex]V = \pi r^2h[/tex]

We know that the volume V is 2,035.75 [tex]in^3[/tex], and the height h is 3 times the radius r. So we can write:

[tex]V = \pi r^2(3r)[/tex]

Simplifying this expression, we get:

V = 3π[tex]r^3[/tex]

To solve for r, we can divide both sides of the equation by 3π[tex]r^2[/tex]:

V/(3π[tex]r^2[/tex]) = r

Substituting the given value for V, we have:

2,035.75/(3π[tex]r^2[/tex]) = r

Multiplying both sides by 3πr^2, we get:

2,035.75 = 3π[tex]r^3[/tex]

Dividing both sides by 3π, we have:

[tex]r^3[/tex] = 2,035.75 / (3π)

Taking the cube root of both sides, we get:

r = [tex](2,035.75 / (3\pi ))^{1/3[/tex]

Using a calculator, we find that:

r ≈ 6.75 inches

Therefore, The cylinder has a radius of about 6.75 inches.

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Write an equation for the polynomial graphed below

Answers

The polynomial in factor form is y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3).

How to derive the equation of the polynomial

In this problem we find a representation of polynomial set on Cartesian plane, whose expression is described by the following formula in factor form:

y(x) = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)

Where:

x - Independent variable.r₁, r₂, r₃, r₄ - Roots of the polynomial.a - Lead coefficient.y(x) - Dependent variable.

Then, by direct inspection we get the following information:

y(0) = - 3, r₁ = - 3, r₂ = - 1, r₃ = 2, r₄ = 3

First, determine the lead coefficient:

- 3 = a · (0 + 3) · (0 + 1) · (0 - 2) · (0 - 3)

- 3 = a · 3 · 1 · (- 2) · (- 3)

- 3 = 18 · a  

a = - 1 / 6

Second, write the complete expression:

y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3)

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7. A group of students wants to demonstrate that sunlight provides the energy for plants to grow. What is
the control group for the experiment?
A. Some plants will receive less water
B. Some plants will receive fertilizer
C. Some plants will receive no sunlight
D. Some plants will receive no water
I

Answers

The control group for the experiment would be option C: some plants will receive no sunlight.

What is control group for experiment ?

The control group in an experiment is the group that does not receive the treatment or intervention being tested, so that the effects of the treatment can be compared to a baseline or reference point. In this experiment, the treatment being tested is the provision of sunlight as an energy source for plant growth.

Therefore, the control group should not receive sunlight, so that the effects of sunlight can be compared to the baseline of plant growth without sunlight.

Therefore, the control group for the experiment would be option C: some plants will receive no sunlight.

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. Bert has a well-shuffled standard deck of 52 cards, from which he draws one card; Ernie has a 12-sided die, which he rolls at the same time Bert draws a card. Compute the probability that:

a. Bert gets a Jack and Ernie rolls a five.

b. Bert gets a heart and Ernie rolls a number less than six.

c. Bert gets a face card (Jack, Queen or King) and Ernie rolls an even number.

d. Bert gets a red card and Ernie rolls a fifteen.

e. Bert gets a card that is not a Jack and Ernie rolls a number that is not twelve.

Answers

Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.

What is probability, exactly?

The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.

Here,

a.

P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)

= (4/52) * (1/12)

= 1/78

b.

P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)

= (13/52) * (5/12)

= 65/624

c.

P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)

= (12/52) * (6/12)

= 1/4

d.

P(Bert gets a red card and Ernie rolls a fifteen) = 0

e.

Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:

A regular 52-card deck contains 48 cards that are not Jacks,

so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.

On a 12-sided dice with 11 possible outcomes,

Ernie rolls a non-12th-number (1, 2, 3, etc.).

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Given that sin 0 = 20/29 and that angle terminates in quadrant III, then what is the value of tan 0?

Answers

The value of Tanθ is 20/21.

What is Pythagorean Theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

Given: sinθ = -20/29 and that angle terminates in quadrant III.

We have to find the value of tanθ.

Using the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

Sinθ = Perpendicular/hypotenuse

Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.

Adjacent = - √Hypotenuse² - perpenducualr²

Replace the known values in the equation.

Adjacent = -√29² - (-20)²

Adjacent = -21

Find the value of tangent.

Tanθ = Perpendicular/base

Tanθ = -20/(-21)

Hence, the value of Tanθ is 20/21.

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The five number summary of a dataset was found to be:
45, 52, 56, 63, 66

An observation is considered an outlier if it is below:

An observation is considered an outlier if it is above:

Answers

An observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.

Identifying the outliers in the summary

To determine the outliers in a dataset using the five-number summary, we need to calculate the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).

IQR = Q3 - Q1

Where

Q1 = 52

Q3 = 63

So, we have

IQR = 63 - 52

IQR = 11

An observation is considered an outlier if it is:

Below Q1 - 1.5 × IQR

Above Q3 + 1.5 × IQR

Substituting the values, we get:

Below 52 - 1.5 × 11 = 35.5

Above 63 + 1.5 × 11 = 79.5

Therefore, an observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.

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Find each arc length. Round to the nearest tenth.




If FG = 27 yd, find the length of FED.


mFED= yards


(30 points) will give brainiest for effort

Answers

The length of arc FED is approximately 51.1 yards, rounded to the nearest tenth.

What is an arc length?

The length of a section of a circle's circumference is known as an arc length.

The radius of the circle and the angle the arc subtends at the centre of the circle are two variables that affect an arc's length.

To find the length of FED, we need to first find the measure of the arc EGD. Since a circle has 360 degrees, we can find the measure of arc EGD by subtracting the measures of arcs DGC, CGF, and FGE from 360:

m(EGD) = 360° - m(DGC) - m(CGF) - m(FGE)

m(EGD) = 360° - 80° - 47° - 90°

m(EGD) = 143°

The formula for arc length is:

Arc length = (central angle / 360) x (2πr)

We can use this information to find the radius of the circle:

FG = 2r

27 yd = 2r

r = 13.5 yd

Now we can use the formula for arc length to find the length of arc FED:

Arc length FED = ((∠FED) / 360) x (2πr)

We know that ∠(EGD) + ∠(FED) = 360, so we can solve for ∠(FED):

∠(FED) = 360° - ∠(EGD)

∠(FED) = 360° - 143°

∠(FED) = 217°

Plugging in the values, we get:

Arc length FED = (217° / 360) x (2π x 13.5 yd)

Arc length FED = (0.6028) x (84.78 yd)

Arc length FED = 51.11 yd

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What is the mean of the values in the stem-and-leaf plot?



Enter your answer in the box.

Answers

Answer:

mean = 24

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

the sum of the data set is

sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168

there is a count of 7 in the data set , then

mean = [tex]\frac{168}{7}[/tex] = 24

Write an equation in point-slope form. Part I: Create an equation of a line in point-slope form. Be sure to identify all parts of the equation before writing the equation. (3 points) Part II: Using the equation of the line you wrote in Part I, write an equation of a line that is perpendicular to this line. Show your work. (3 points)

Answers

The line's equation in point-slope form is shown here. Point (2, 5) is the given point on the line, and slope 2 is the given slope of the line. The slope of this line is -1/2, which is the negative reciprocal of the slope.

How do you formulate an equation in point-slope form?

A line's point slope form equation is [tex]y - y_1 = m(x - x_1)[/tex]. Consequently, y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.

We require a point on the line and the slope of the line in order to create a line equation in point-slope form. In point-slope form,

[tex]y - y1 = m(x - x1)[/tex]

As an illustration, suppose we want to formulate the equation of the line passing through the coordinates (2, 5) and having a slope of 2. The values can be entered into the point-slope form as follows:

y - 5 = 2(x - 2)Let's say the given line has the equation [tex]y - y1 = m(x - x1)[/tex], where (x1, y1) is a point on the line and m is the slope of the line.

we can use the given point (2, 5). Then we can plug in the values into the point-slope form:

[tex]y - 5 = (-1/2)(x - 2).[/tex]

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how am i supposed to prove that theyre collinear ​

Answers

Answer:

They are collinear if they are on the same line

PLSS HELP IMMEDIATELY

Answers

The continuous compounding rate earned by the investment is given as follows:

8.022%.

How to model continuous compounding?

The balance of an account after t years, using continuous compounding, is  modeled by the equation presented as follows:

A(t) = A(0)e^{kt}.

In which:

A(0) is the initial amount.k is the continuous compounding rates.

For this problem, the parameters are given as follows:

A(11) = 58, A(0) = 24, t = 11.

Hence the rate is obtained as follows:

24e^(11k) = 58

e^(11k) = 58/24

11k = ln(58/24)

k = ln(58/24)/11

k = 8.022%.

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La Suma delos cuadrados de dos números naturales consecutivos es 181 halla dichos numeros

Answers

The two consecutive natural numbers whose sum of squares is 181 are 9 and 10

Let's assume that the two consecutive natural numbers are x and x+1. Then, we can write an equation based on the given information:

x² + (x+1)² = 181

Expanding the equation:

x² + x² + 2x + 1 = 181

Combining like terms:

2x² + 2x - 180 = 0

Dividing both sides by 2:

x² + x - 90 = 0

Now, we can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 1, and c = -90

x = (-1 ± √(1 + 360)) / 2

x = (-1 ± √(361)) / 2

x = (-1 ± 19) / 2

We discard the negative value, as it does not correspond to a natural number:

x = 9

Therefore, the two consecutive natural numbers are 9 and 10, and their sum of squares is 81 + 100 = 181.

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Please help me solve and show my work

Answers

The degree measure of the angles are;

1. 5π/3 = 300°

2 3π/4 = 135°

3. 5π/6 = 150°

4. -3π/2 = 90°

What is degree and radian?

A degree is a unit of measurement which is used to measure circles, spheres, and angles while a radian is also a unit of measurement which is used to measure angles.

A circle has 360 degrees which are its full area while its radian is only half of it which is 180 degrees or one pi radian.

therefore π = 180°

1. 5π/ 3 = 5×180/3 = 300°

2. 3π/4 = 3× 180/4 = 540/4 = 135°

3. 5π/6 = 5×180/6 = 150°

4. - 3π/2 = -3 × 180/2 = -270° = 90°

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Find the final amount of a $750 investment after 15 years at 8% interest compounded semiannually, quarterly and daily.

Answers

With given compound interest, the final amount of the investment after 15 years at 8% interest compounded semiannually, quarterly and daily are $2,067.87, $2,094.28, and $2,101.62, respectively.

What is Compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit, or the interest earned on both the principal and any previously accrued interest. In other words, interest is computed not only on the original amount of money but also on any past interest gained. The interest generated on the cumulative interest can compound exponentially, resulting in enormous growth of an investment or loan sum over time. Compound interest is computed using a formula that takes the principle amount, interest rate, and compounding frequency into consideration.

Now,

To find the final amount of the investment, we can use the formula for compound interest:

A = P(1 + r/n)ⁿˣ

where:

A = final amount

P = principal (initial investment)

r = annual interest rate

n = times the interest is compounded per year

x = time in years

For semiannual compounding, n = 2 and x = 15:

A = 750(1 + 0.08/2)²*¹⁵= $2,067.87

For quarterly compounding, n = 4 and x = 15:

A = 750(1 + 0.08/4)⁴*¹⁵ = $2,094.28

For daily compounding, n = 365 (assuming no leap years) and x = 15:

A = 750(1 + 0.08/365)³⁶⁵*¹⁵ = $2,101.62

Therefore, the final amount of the investment after 15 years at 8% interest compounded semiannually, quarterly and daily are $2,067.87, $2,094.28, and $2,101.62, respectively.

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if k(x) =3x, then f'(x)=?​

Answers

If k(x) = 3x, then f(x) = 3x^2 + C, where C is a constant. Taking the derivative of f(x), we get:

f'(x) = d/dx (3x^2 + C)
= 6x

So, f'(x) = 6x.

0\left\{-10\le x\le10\right\}
Describe the transformations (vertical translation, horizontal translation, and dilation/reflection) from the parent function that happened to these formulas

Answers

The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.

What is Function?

A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).

The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).

Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.

To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:

g(x) = 0{-10≤x≤10}

Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].

However, if the formula is something like:

g(x) = 2 * 0{-10≤x+3≤10}

Then we can describe the transformations as follows:

Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.

Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.

Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.

To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.

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The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.

What is Function?

A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).

The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).

Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.

To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:

g(x) = 0{-10≤x≤10}

Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].

However, if the formula is something like:

g(x) = 2 * 0{-10≤x+3≤10}

Then we can describe the transformations as follows:

Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.

Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.

Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.

To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.

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PLEASE HELP

Find the Area

2cm

___cm^2

Answers

Answer:

3.14 cm^2

Step-by-step explanation:

1. Find radius:

If diameter is 2, divide it by 2 to get radius = 1

2. Find formula:

A=πr^2

3. Plug in:

A = π(1)^2

4. Solve (multiply):

A = π(1)^2:

3.14159265359

Or

3.14 cm^2

Answer:

3.14 cm^2

Step-by-step explanation:

A=[tex]\pi[/tex]r^2

r=2

2/2=1

A=[tex]\pi[/tex](1)^2

=[tex]\pi[/tex]1

≈3.14x1

≈3.14cm^2

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