what is the probability that when a pair of dice are rolled, either (at least) one dice shows a 5, or that the dice sum to 8?

The confidence interval gets broader as the confidence level rises because the error bound rises as well. The confidence interval gets narrower as the confidence level is reduced since the error bound is also reduced.

This can be the reason why  you might want to increase the confidence level, even though it means that precision is lost and the interval widens.

We must widen the distance in order to obtain greater trust. The multiplier, which rises with confidence level, shows this clearly. The width of confidence intervals will rise when sample size is increased.

An unknown population parameter's likely range of values is known as a confidence interval. A certain proportion of the confidence intervals will include the population mean if you repeatedly take random samples. The confidence level is expressed as this percentage.

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The number of students who passed only physics is 6, the number of students who passed only geography is 2, and the number of students who passed only history is 5.

First, let's represent the number of students who passed each subject with the variables P, G, and H. Then, we can represent the number of students who passed multiple subjects with the variables PG, PH, and GH.

We are given the following information:

39 students passed physics (P)

36 students passed geography (G)

40 students passed history (H)

22 students passed both physics and history (PH)

21 students passed both physics and geography (PG)

23 students passed both geography and history (GH)

10 students passed all three subjects (PHG)

We can set up the following equations to represent these relationships:

P = 39

G = 36

H = 40

PH = 22

PG = 21

GH = 23

PHG = 10

We can use these equations to solve for the number of students who passed only physics (P - PH - PG + PHG), only geography (G - GH - PG + PHG), and only history (H - PH - GH + PHG).

So, the number of students who passed only physics is:

P - PH - PG + PHG = 39 - 22 - 21 + 10 = 6

The number of students who passed only geography is:

G - GH - PG + PHG = 36 - 23 - 21 + 10 = 2

The number of students who passed only history is:

H - PH - GH + PHG = 40 - 22 - 23 + 10 = 5

Thus, there are 6 students who passed only physics, 2 students who passed only geography, and 5 students who passed only history.

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Answer:

A) The equation y = 2x represents a proportional relationship. This is because the values of y are directly proportional to the values of x. In other words, as x increases, y also increases by the same factor. This is the definition of a proportional relationship.

B) The unit rate of change for this situation is 2 hot dogs per minute. This is because the equation y = 2x represents a linear relationship, where the rate of change (the slope) is constant. The unit rate of change is the slope of the line, which in this case is 2. This means that for every 1 minute that passes, Peter eats 2 hot dogs.

The system of equations that could be used to solve the problem are;

400a + 1000p = 8800

a + p = 13

Where a is associate and p is partner

Let the variables be defined as:

Associate is denoted by a

Partner is denoted by p

We are told that the daily rate charged to the client for each associate is $400 and the daily rate for each partner is $1000. Thus, the equations are:

400a + 1000p = 8800   -----(1)

a + p = 13   ------(2)

Make a the subject in eq 2 to get;

a = 13 - p   -----(3)

Put 13 - p for a in eq 1 to get;

400(13 - p) + 1000p = 8800

5200 - 400p + 1000p = 8800

5200 + 600p = 8800

5200 + 600p = 8800

600p = 3600

p = 6 partners

a = 13 - p

a = 13 - 6

a = 7 associates

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The following complex number (1-i)³ in a+ bi form is -2+4i

In mathematics, a complex number is a part of a number system that includes an element with the symbol I often known as the imaginary unit, and extends the real numbers. Complex numbers satisfy the equation that any complex number can be represented as a + bi, where a and b are real numbers. Rene Descartes referred to me as an imaginary number because no real number can satisfy the aforementioned equation. A and b are referred to as the real and imaginary parts, respectively, of the complex number a+bi. Complex numbers are accepted in the mathematical sciences as being just as "real" as real numbers despite the historical appellation "imaginary."

(1-i)³

=1³-i³-3(1)(i)(1-i)

=1+i-3(1-i)

=1+i-3+3i

=-2+4i

Therefore, the following complex number (1-i)³ in a+ bi form is -2+4i.

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Answer:

5/ Slope is 0

6/ Slope is 4/1

7/ Slope is -4/2 = -2

8/ Slope is undefined

Step-by-step explanation:

5/ Slope is 0 when it goes straight to the right

6/ We see that the y goes up 4, x over 1, so the slope is 4/1

7/ We see that the y goes down by 4, and x over by 2, so the slope is -2

8/ Slope is undefined when it goes straight up!

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The range of possible lengths for the third side is  [46.13,57.27] .

What is pythagoras theorem?

The Pythagorean theorem or Pythagoras' theorem could be a elementary relation in parabolic geometry between the 3 sides of a trigon.

Main Body:

To find range of possible lengths for the third side , we will use Pythagoras theorem : a²+b² = c²

given =   24 ft , 52 ft​

24² =576

52² =2704

2704+576=3280

√3280 =57.27

AND

52² = 24²+b²

b²= 2704-576

b=√2128

b = 46.13

range of possible lengths for the third side is [46.13,57.27]

Hence the range of third side is found out.

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(3, 11) is the coordinate of the point that is most likely an outlier

How to draw a scatter diagram?

A scatter diagram is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data

Given: The Age and Value as shown in the question

Age (years)        4   6    5   4   2   8  3   3  5   7    1    5

Value (£ 000's) 46 37 52 60 74 21 65 11 67 27 86 40

The values of Age against Value will then be plotted on a scatter plot as shown in the image attached. Note that Age will be on the horizontal while Value will be on the vertical.

Therefore, the coordinate of the point that is most likely an outlier is (3, 11). This is because it is too far from the line

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Answer:

Step-by-step explanation:

perp. -1/5

y - 6 = -1/5(x + 3)

y - 6 = -1/5x - 3/5

y - 30/5 = -1/5x - 3/5

y = -1/5x + 27/5

parallel: 5

y - 6 = 5(x + 3)

y - 6 = 5x + 15

y = 5x + 21

The volume of the cube with a mass of 20 grams and a density of 6 g/cm³ is 3.33 cm³

From the question, we are to determine the volume of the given cube

From the given information,

The mass of the cube is 20 grams

and

The density of the cube is 6 g/cm³

From the formula,

Density = Mass / Volume

Then, we can write that

Volume = Mass / Density

Thus,

The volume of the cube is

Volume = 20/6

Volume = 3.33 cm³

Hence, the volume is 3.33 cm³

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Answer:

9

Step-by-step explanation:

Because it is multiplication, the parenthesis are not important. It is the equivalent of 3*9*8 = 8*3*n. From here, you can tell that the 9 is missing.

Answer:

The two numbers are 44 as the smaller number and 89 as the larger number.

Step-by-step explanation:

Hope it helps!

Let's call the larger number x, and the smaller number y. We know that y is one more than half of x, so we can write y = x/2 + 1. We also know that the sum of the two numbers is 133, so we can write x + y = 133. We can use these two equations to solve for the values of x and y. Substituting the first equation into the second, we get:

x + (x/2 + 1) = 133

Combining like terms, we get:

1.5x + 1 = 133

Subtracting 1 from both sides, we get:

1.5x = 132

Dividing both sides by 1.5, we get:

x = 88

Substituting this value for x in the first equation, we get:

y = 88/2 + 1 = 44 + 1 = 45

Therefore, the two numbers are 88 and 45, and we can check our solution by verifying that the sum of these numbers is indeed 133.

x + y = 88 + 45 = 133

This confirms that our solution is correct.

The solution is h⁴ for the equation h⁻⁵ / h⁻⁹.

Given equation,

h⁻⁵ / h⁻⁹

We know that ,

According to law of exponents ,

xᵃ / xᵇ = xᵃ⁻ᵇ

So here

h⁻⁵ / h⁻⁹ = h⁻⁵ ⁺⁹

= h⁴

Therefore the solution of the equation h⁻⁵ / h⁻⁹ is h⁴.

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Answer: 356 mil

Step-by-step explanation:

Answer:

Each tube will contain 15.7 millimeters

Step-by-step explanation:

Since  235.5 milliliters of water is to be shared among 15 test tubes then the amount of water in each test tube is:

[tex]\frac{235.5}{15} \\\\= 15.7[/tex]

Thus each tube will contain 15.7 millimeters

Answer:

1) 3/4 x 7/6
2) 21/24
3) 7/8

Step-by-step explanation:

1) KCF, Keep change flip. 3/4 stays the same, division sign changes into multiplication, and 6/7 changes into its reciprocal.
2) Multiply numerator by numerator and denominator by denominator
3) Find their greatest common factor (GCF) and divide the numerator and denominator by it. There's your simplified answer.

Answer:

7/8

Step-by-step explanation:

Divide 3/4 with 6/7

3

4

÷

6

7

is

7

8

.

Steps for dividing fractions

Find the reciprocal of the divisor

Reciprocal of

6

7

:

7

6

Now, multiply it with the dividend

So,

3

4

÷

6

7

=

3

4

×

7

6

=

3 × 7

4 × 6

=

21

24

After reducing the fraction, the answer is

7/8

Answer:

6p+3q

Step-by-step explanation:

1.5(4p+2q)

Distribute property

1.5(4p)+1.5(2q)

6p+1.5(2q)

6p+3q

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Answer:

3 x (2p+q)

Step-by-step explanation:

STEP 1:

                3

Simplify   —

                 2

The equation at the end of step 1:

 3

 — • (4p + 2q)

 2

STEP 2:

Pulling out like terms

3.1     Pull out like factors :

  4p + 2q  =   2 • (2p + q)

Final result :

 3 • (2p + q)

The answer to this question would be (B)

Answer: csc^2x+sec^2x=1

Step-by-step explanation:

The Tangents of the three circles  passing though point P and A are attached below

2.

The circle is inscribed in the triangle and is the largest circle which will fit within the triangle. The line from each triangle vertex to the center of the circle bisects each angle of the triangle

What is a tangent ?

A tangent in geometry is a line that originates at an outside point and travels through a curve's Centre. When you ride a bicycle, every point on the wheel's circumference forms a tangent with the road, providing a practical illustration of a tangent. Let's use an illustration to better grasp what a tangent is. The arc S and point P outside of S are depicted in the following figure. S has been reached via a tangent from P. This serves as an illustration of a tangent.

Two crucial characteristics of the tangent are:

A tangent only hits a curve once.

A line that never reaches the inside of the circle is known as a tangent.

At the point of tangency, the tangent makes a right angle contact with the circle's radius.

A tangent to the circle also has mathematical theorems linked with it, which are needed when doing important computations in geometry in addition to the qualities mentioned above. Let's go into further depth on a couple tangents to circle theorems.

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1) We can explain why the area is πr² by assuming the figure as a rectangle, 2) Diameter = 24.20 cm, Area = 452.91 cm² and 3) the area of the table is 1074.66 in²

The circle is a 2D geometrical figure, with no side or angle, and is made a collection of points.

Given that, 1) a circle with circumferences = 2πr and radius = r, 2) a circle having circumferences = 76 cm and 3) Jada is painting a table having diameter 37 in.

1) Assume the figure as a rectangle, (refer to attached figure)

We get, the length of it is πr and width is r.

And the area of a rectangle is = the Product of length and width.

So, we can conclude that the area of this rectangle is = πr×r = πr²

Therefore, by assuming the figure as a rectangle, we can explain why the area of a circle is πr²

2) circumferences = 2πr

2πr = 76

πr = 38

r = 38/3.14  (π ≈ 3.14)

r = 12.01 cm

Diameter = 2r

D = 2x12.01 = 24.20 cm

Area = πr²

= 3.14x12.01²

= 452.91 cm²

3) Diameter = 37 in

r = 37/2 = 18.5 in

Area = πr²

= 3.14x18.5²

= 1074.66 in²

Therefore, the area of the table is 1074.66 in²

Hence, the answers are 1) We can explain why the area is πr² by assuming the figure as a rectangle, 2) Diameter = 24.20 cm, Area = 452.91 cm² and 3) the area of the table is 1074.66 in²

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Answer:

a = 84°

b = 21°

c = 48°

Step-by-step explanation:

Step 1.)

The first step is recognizing the angle of 75° is sticking out from a straight-line, PQ. That straight-line represents an angle of 180°

180°-75° = 105 = a° + b°

Step 2.)

We also know that the line RS is 180°. Therefore, it must be true that

75° + 4b° + b° = 180°

or simply

5b + 75 = 180°

Now solve for b. Subtract both sides by 75 and divide the right side by 5

5b = 105°

b = 21°

4b° = 4 x b = 4 x 21° = 84° = 4b°

Step 3)

Since we know that a + b = 105°, we use substitution to get:

a + 21° = 105

Now subtract both sides by 21

a = 84°

Now let's double check if a + b + 75 = 180

84 + 21 + 75 = 180 [check]

Step 4.)

Since we know that PQ is a straight-line that is 180°, we can say:

180° = 4b° + 2c°

Now substitute 4b with 84°

180° = 84° + 2c

Now solve by subtracting 84 from 180 and divide by 2, if needed.

96° = 2c°

48° = c°

Now double check

96° + 84° = 180° [check]

Therefore:

a = 84°

b = 21°

c = 48°

Hope that helps.

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Answer:

Picture 1:

Step 1- Given

Step 2- Addition Property of Equality

Step 3- Division Property of Equality

Picture 2:

Step 1- Given

Step 2- Combine Like Terms

Step 3- Subtraction Property of Equality

Picture 3:

Step 1- Given

Step 2- Distributive Property

Step 3- Combine Like Terms

Step 4- Division Property of Equality

Picture 4:

Step 1- Given

Step 2- Distributive Property

Step 3- Combine Like Terms

Step 4- Addition Property of Order

Step 5- Division Property of Order

Picture 5:

Step 1- Given

Step 2- Distributive Property

Step 3- Subtraction Property of Order

Step 4- Addition Property of Order

Step 5- Combine Like Terms

Step 6- Division Property of Order

Hope this helps :)

Step-by-step explanation:

The solution to the given system of linear equations is x = 2, y = 6.

From the question, we are to solve the given system of linear equations

The given system of linear equations is

-x +5y = 28

x+3y=20

To solve the equation, add the equations

  -x +5y = 28

+  x + 3y=20

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

8y = 48

Divide both sides by 8

8y/8 =48/8

y = 6

Substitute the value of y into the second equation

x+3y=20

x + 3(6) = 20

x + 18 = 20

x = 20 - 18

x = 2

Hence, the solution is x = 2, y = 6

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Answer:

  p = 8

Step-by-step explanation:

Given 4 equations in 4 unknown values, you want to find the value of p.

Substituting for c in the second equation, we have ...

  ts = (t +s) +t -s

  ts = 2t . . . . . . simplify

  s = 2 . . . . . . . divide by 2

Substituting for c and s in the third equation, we have ...

  3(t +2) = t +10·2

  2t = 14 . . . . . . . . . subtract t+6

  t = 7

Substituting for c, t, s in the equation for p gives ...

  p = ((t +s) +t)/s = (2·7 +2)/2 = 8

The value of p is 8.

__

Additional comment

The variable values are (c, p, s, t) = (9, 8, 2, 7).

The correct option is B in the given Temperature problem by Calculation T ≈ 26.4 + (20 - 8.8) × (28.8 - 26.4) / (11.1 - 8.8) ≈ 27.7 degrees Celsius,

T ≈ 55 + (20 - 10) × (60 - 55) / (20 - 10) ≈ 60 degrees Celsius

According to the given information:

For the first question, we need to compare the rate of change of temperature with respect to rotation speed for both engines. We can do this by calculating the difference in temperature for a change in rotation speed of 111 cycles per second for both engines.

For the first engine, the temperature increased by:

31.2 - 28.8 = 2.4 degrees Celsius

For the second engine, the temperature increased by:

60 - 50 = 10 degrees Celsius

Since the temperature increase for the second engine is greater, we can conclude that the second engine's temperature increased more for each increase of 111 cycles per second. Therefore, the answer is (B) The second engine.

For the second question, we can use linear interpolation to estimate the temperature of each engine at 20 cycles per second.

For the first engine, we can use the two closest data points (8.8 and 11.1 cycles per second) to estimate the temperature at 20 cycles per second:

T ≈ 26.4 + (20 - 8.8) × (28.8 - 26.4) / (11.1 - 8.8) ≈ 27.7 degrees Celsius

For the second engine, we can use the same method with the two closest data points (10 and 20 cycles per second):

T ≈ 55 + (20 - 10) × (60 - 55) / (20 - 10) ≈ 60 degrees Celsius

Therefore, we can conclude that the second engine was hotter when it rotated at 20 cycles per second. The answer is (B) The second engine.

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The variables in an experiment that tests the distance honey flows at different temperatures is the distance honey flows is the dependent variable and temperature is the independent variable .

Given :

In the experiment " Temperature" is dependent variable and the distance honey flows is independent variable.

What is independent variable ?

It is the factor that one can purposely control or change to observe its effect , is called independent variable.

What is dependent variable ?

It respond to the change in the independent variable , is called dependent variable.

Hence temperature is dependent and distance honey flow is independent variable.

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Answer:

This is a solution to the linear inequality.

Step-by-step explanation:

(-8, 9)

x + y ≤ 4

-8 + 9 ≤ 4

1 ≤ 4

This is a solution to the linear inequality.

Answer:

Step-by-step explanation:

According to the graph that I graphed online, the point (-8,9) is a solution to the linear inequality. To find out that, (-8,9) is a solution you have to look if that point is shaded if it is shaded then it is a solution to the inequality.

(-8 is the x variable and 9 is the y variable, to find out if that is a point you look for the -8 in the graph but you would look down on the the x side and then you go up looking for a 9.)

Answer:

[tex]x = 9[/tex]

Step-by-step explanation:

[tex] \frac{12}{x} = \frac{8}{6} \\ 12 = \frac{8x}{6} \\ 12 \times 6 = 8x \\ \frac{72}{8} = x \\ 9 = x[/tex]

Check

[tex] \frac{12}{x} = \frac{8}{6} \\ \\ \frac{12}{9} = \frac{8}{6} \\ \\ 1.333 = 1.333[/tex]

The system has no solution.

The solution to the system would be the intersection point of the two lines.  Since these lines don't appear to intersect, there's no solution.

The equation of the transformed function is g(x) = x + 4

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

f(x) = x

g(x) = translation 4 units up of f(x) = x

The above equations implies that, we have the transformation to be:

Translation 4 units up of f(x)

Mathematically, this can be represented as

g(x) = f(x) + 4

Substitute the known values in the above equation, so, we have the following representation

g(x) = x + 4

Hence, the transformed function si g(x) = x + 4

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