certain game, a fair die is rolled and a player gains 20 points If the die shows a If the die does not show a 6the player loses 3 points die were to be rolled 100 times, what would be the expected total gain or loss for the player?

The height attained is 1290 feet

The time taken to reach the ground is 9s

The velocity on reaching the ground is  288 m/s.

We know that we can be able to handle the problems that we have here by the use of the equations of motion and that is what we shall do in the problems that follow.

h = ut - 1/2gt^2

h = height

u = initial velocity

g = acceleration due to gravity

t = time

Thus;

h = (18 * 5) - 1/2 * (-32) * 5^2

h =90 + 400

h = 490 feet

Thus the height after five seconds is 490 feet + 800 feet = 1290 feet

Using h = ut + 1/2gt^2

h = 1290 feet

u = 0 m/s when dropped

1290=  + 1/2 * (32) *t^2

1290 = 16t^2

Thus

t = 9s

The velocity when it hits the ground is;

v = u + gt

u = 0 m/s when dropped

v = 32 * 9

v = 288 m/s

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Answer:

y = [tex]\frac{-3}{8}[/tex]x - [tex]\frac{57}{8}[/tex]

Step-by-step explanation:

a perpendicular slope is the opposite reciprocal.  The slope will be [tex]\frac{-3}{8}[/tex]

Two write the equation, you need the slope and the y-intercept.  We have the slope ([tex]\frac{-3}{8}[/tex]).  We know need to find the y-intercept.

We will use the m or slope of [tex]\frac{-3}{8}[/tex], x value of -3 from the point (-3,-6)and the y value of -6 from the point (-3,-6)

y = mx + b

-6 = [tex]\frac{-3}{8}[/tex]([tex]\frac{-3}{1)}[/tex]) + b

-6 = [tex]\frac{9}{8}[/tex] + b  Subtract [tex]\frac{9}{8}[/tex] from both sides

[tex]\frac{-6}{1 }[/tex] - [tex]\frac{9}{8}[/tex] = [tex]\frac{9}{8}[/tex] - [tex]\frac{9}{8}[/tex] + b  Use the common denominator of 8

[tex]\frac{-48}{8}[/tex] - [tex]\frac{9}{8}[/tex] = b

[tex]\frac{-57}{8}[/tex] = b

y = [tex]\frac{-3}{8}[/tex]x - [tex]\frac{57}{8}[/tex]

Michel-Eugène Chevreul found that the greatest intensity came from placing complementary colors next to each other. The Option C is correct.

Chevreul made great contributions to the field of color theory as he made key findings was that placing complementary colors next to each other creates the greatest intensity.

These colors are opposite to each other on the color wheel such as red & green, blue & orange or yellow &  purple. When these color are placed next to each other, these colors create a visual contrast that makes them appear brighter and more intense.

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Answer:

To find how far above the water the lip balm will be after 3 seconds, we need to evaluate the polynomial -16t² + 220 when t = 3.

Substituting t = 3 into the polynomial, we get:

-16(3²) + 220 = -16(9) + 220 = -144 + 220 = 76

Therefore, after 3 seconds, the height of the lip balm above the water will be 76 feet.

The volume of the cylinder is 238. 7m³

The formula that is used for calculating the cross-sectional area of a cylinder is expressed with the equation;

A = πr²

Such that;

From the information given, we have that;

17 = 3.14 × r²

Divide the values

r² = 5. 414

Find square root

r = 2.33 m

The volume of a cylinder is given as;

Volume = πr²h

Substitute the values

Volume = 3.14 × 2.33² × 14

Multiply the values

Volume = 238. 7m³

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The interest earned and the future value of an annuity with monthly payments of $200 for two years that pays 6% interest per year compounded monthly is $25.43 and $225.43

Principal,P = $200

Time, t = 6%

Number of periods, n = 12

Interest rate, r = 6%

= 6/100

= 0.06 rate per year,

FV = P(1 + r/n)^nt

FV = 200.00(1 + 0.06/12)^(12)(2)

FV = 200.00(1 + 0.005)^(24)

FV = $225.43

Therefore,

Principal = $200.00

Interest = $25.43

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Answer:

12/2

Step-by-step explanation:

(x - h)^2 + (y - k)^2 = r^2

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

Comparing this to the given equation, we see that the center of the circle is (-10,0) and the radius is sqrt(9) = 3.

The diameter of the circle is twice the radius, so:

diameter = 2(radius) = 2(3) = 6

Therefore, the diameter of the circle is 6.

We can write this in simplified, rationalized form as:

diameter = 6 = 6/1 = 12/2

Answer:

∠ C = 84°

Step-by-step explanation:

A quadrilateral inscribed in a circle is a cyclic quadrilateral.

the opposite angles sum to 180° , that is

∠ A + ∠ C = 180 , then

x² + 60 + 8x + 36 = 180

x² + 8x + 96 = 180 ( subtract 180 from both sides )

x² + 8x - 84 = 0 ← in standard form

(x + 14)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x + 14 = 0 ⇒ x = - 14

x - 6 = 0 ⇒ x = 6

x > 0 , then x = 6 , so

∠ C = 8x + 36 = 8(6) + 36 = 48 + 36 = 84°

Answer:

  9

Step-by-step explanation:

You want the number of non-congruent rectangles that can be drawn on a 4 × 4 geoboard.

A rectangle will have right-angle corners and opposite sides the same length. The attachment shows the 9 rectangles we believe exhaust the possibilities for a grid of 4 dots by 4 dots.

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Answer:

Step-by-step explanation:

The solution for y in the given equation x + 3y = 6 and 2x - y = 10 is 2/7.

The line that has the slope with the greatest value is determined as the: A. Blue line.

The slope of a line is the change in y over the change in x, which can also be calculated as:

Slope (m) = rise / run = y2 - y1 / x2 - x1.

Also, the steeper the slope, the greater the value of the slope that you will get, while the more gentle the slope, the smaller the value of the slope of the line we would get.

Out of the three lines shown in the graph, the steepest is the blue line, this means that it has the greatest slope value.

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A) The best graphical representatiοn tο display the data wοuld be a histοgram.

B) The resulting histοgram shοuld shοw the distributiοn οf the grades and allοw fοr easy cοmparisοn οf the frequency οf grades in different ranges.

A) The best graphical representatiοn tο display the data wοuld be a histοgram. This is because a histοgram is a bar graph-like representatiοn οf data that grοups a range οf values intο intervals called bins οr classes. The height οf each bar represents the frequency οr number οf data pοints that fall within that bin οr class. A histοgram is an apprοpriate display fοr the data because it shοws the distributiοn οf the grades and allοws fοr easy cοmparisοn οf the frequency οf grades in different ranges.

Part B: Tο create a histοgram οf the data, the steps are as follows:

Step 1: Chοοse a title fοr the histοgram, such as "Distributiοn οf 7th Grade Math Exam Grades".

Step 2: Determine the range οf the data by finding the minimum and maximum values. In this case, the minimum grade is 61 and the maximum grade is 98.

Step 3: Divide the range intο a suitable number οf bins οr classes. A cοmmοn rule οf thumb is tο use between 5 and 20 bins, depending οn the range and distributiοn οf the data. Fοr this data, we can use 10 bins, with a bin width οf 3 (rοunded up frοm 2.9).

Step 4: Label the x-axis with the range οf grades, and label the y-axis with the frequency οr number οf grades.

Step 5: Draw the histοgram by drawing a bar fοr each bin, with the height οf the bar representing the frequency οf grades in that bin. Fοr example, the first bin wοuld be fοr grades between 60 and 62, the secοnd bin wοuld be fοr grades between 63 and 65, and sο οn. Cοunt the number οf grades that fall within each bin, and draw a bar with that height οn the y-axis.

Therefοre, The resulting histοgram shοuld shοw the distributiοn οf the grades and allοw fοr easy cοmparisοn οf the frequency οf grades in different ranges.

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The value of P(A∩B) rounding to the nearest thousandth, if necessary is:  0.086

The parameters given are:

P(A) = 0.12

P(B) = 0.3

P(A ∪ B) = 0.334

We want to find the probability P(A∩B)

The P(A∪B) probability formula is given as:

P(A∪B) = P(A) + P(B) - P(A∩B)

where:

P(A) is Probability of event A happening

P(B) is Probability of event B happening

P(A∩B) is Probability of happening of both A and B.

Thus:

0.334 = 0.12 + 0.3 - P(A∩B)

P(A∩B) = 0.12 + 0.3 - 0.334

P(A∩B) = 0.086

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Answer:

The pattern of association between time and distance is positive and linear.

The composite figure has an area of 142 square yards

The composite figure has one square, right triangle, two rectangles

Area of square = side × side

=8×8

=64 yards

Area of triangle =1/2×8×6

=24 square yards

Area of 1st rectangle = 3×6

=18 square yards

Area of 2 nd rectangle = 9×4

=36 square yards

Total area is sum of square, rectangles and triangle

total area = 64+24+18+36

=142 square yards

Hence, the composite figure has an area of 142 square yards

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The bearing of the cruise ship displacement from its initial position is 15.06°, which makes the second option correct

Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.

We will get a right triangle from travels of the ship, such that we can call the initial position A, the point after 8 miles B and the point after 30 miles C

angle B = 30° + 60° = 90°

AB = 8

BC = 30

by Pythagoras rule;

AC = √(8² + 30²) = 31.04

using sine rule;

30/sinA = 31.04/sin90

A = sin⁻¹[(30 × sin90)/31.04]

A = 75.06°

bearing from initial position = (30° + 75.06°) - 90°

bearing from initial position = 105.06 - 90°

bearing from initial position = 15.06°

Therefore, the bearing of the cruise ship displacement from its initial position is 15.06°

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The graph that represents f(2x) is given by option B.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The parent function in this problem is given as follows:

f(x) = x².

For the transformation, we want the numeric value of the function at x = 2x, hence:

f(2x) = [2x]²

f(2x) = 4x².

Which is given by option b, representing an horizontal compression by a factor of 1/4 = vertical stretch by a factor of 4 of the graph of the parent function y = x².

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The sum of 3√5 and 4√25 is an irrational number.

First, simplify the expressions inside the square roots:

3√5 = 3√(5×1) = 3√5

4√25 = 4√(25×1) = 4×5 = 20

Now, we add them together:

3√5 + 4√25 = 3√5 + 20

This is the simplest form since 20 is already a rational number and we cannot simplify the square root of 5 any further.

To determine whether the result is rational or irrational.

Since 3√5 is irrational and cannot be simplified any further, the expression as a whole is also irrational.

Therefore, the sum of 3√5 and 4√25 is an irrational number.

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Answer:

w=0,

w=-7

Step-by-step explanation:

The missing angle C of the given triangle using law of cosine is: 62.1°

The Law of Cosines is defined as a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.

Numerically, the Law of Cosines can be communicated as:

c² = a² + b² - 2abcos(C),

where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.

Thus:

90² = 55² + 50² - 2(55 * 50)cos(C),

2575 = 5500 cos C

2575/5500 = cos C

cos C = 0.4682

C = cos⁻¹0.4682

C = 62.1°

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1) Matrices that have determinants are square matrices

2) Due to the inverse matrix's calculation utilizing a matrix's determinant, the determinant and the inverse matrix are connected.

3) The determinant affects whether a matrix has an inverse.

A matrix is a collection of numbers that have been sorted into rows and columns to create a rectangular array. The elements, or entries, of the matrix are the integers.

If and only if the determinant of a square matrix A is nonzero, the matrix has an inverse. The matrix A is referred to as singular and devoid of an inverse if its determinant is zero.

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The value of P in the equation (10011 base 2 + P + 11100 base 2 + 101 base 2 = 1001111 base 2) is 11011 base 2.

The value of P in the equation is found as follows from the given equation:

10011 base 2 + P + 11100 base 2 + 101 base 2 = 1001111 base 2

Hence;

P = 1001111 base 2 - (10011 base 2 + 11100 base 2 + 101 base 2)

Summing the values in the bracket: 10011 + 11100 + 101 = 110100

Then the value of  P will be:

P = 1001111 base 2 - 110100 base 2

P = 11011 base 2

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The value of x measure as 90 degree. the solution would be sinx = 1.

Since it is known that Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

WE are given the trigonometric functions as;

(sin2x)/(cosx)=2 for 0≤x≤2π

We know that sin 2x = 2 sinx cosx

Therefore,

(sin2x)/(cosx)=2

(2 sinx cosx)/(cosx)=2

sinx = 2/2

sinx = 1

Thus sin 90 = 1

x = 90 degree

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The value of X, given the matrices, can be found to be X = [ [ 4 ], [-1.5 ] ].

We are told that the value of X can be found to be :
2X + A = B

Solving this would give:
X = (B - A) / 2

We can then apply this to the matrices to give:
B - A = [ [ 11 - 3 ], [1 - 4 ] ]

B - A =  [[ 8 ],  [ -3 ] ]

X = [ [ 8 / 2 ], [ -3/2 ] ]

X = [ [ 4 ], [-1.5 ] ]

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The most likely number of minutes of usage recorded by Jason is A . approximately 50.

We can see that initially, the temperature of the electronic system began to increase as the time increased. It then began to decrease from the 20 minute and ketp decreasing till the 40th minute.

Assuming that the temperature keeps decreasing, it would mean that at 50 minutes, the temperature would be more than the temperature at 40 minutes and so would most likely be 48 degrees.

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Answer:

n = -6

Step-by-step explanation:

We can allow n to represent the unknown number.

Now, we can set the two expressions equal to each other to find the number, n:

[tex]2n-1=4n+11\\2n=4n+12\\-2n=12\\n=-6[/tex]

Finally, we can check if the number fits the equation and the verbal expression by plugging in -6 for n:

Algebraically:

2(-6) - 1 = 4(-6) + 11

-12 - 1 = -24 + 11

-13 = -13

Verbally:

Two times the number -6 is -12 and 1 less than - 12 is -13

Four times the number -6 is -24 and 11 more than this is -13

Answer: x= -6

Step-by-step explanation:

Each word in a word problem translates to a mathematical symbol

> 1 less than =>  - 1

> two times a number => 2x

put that together 1 less than two times a number means:

2x-1

> is => =

> 11 more  => 11+

> four times the number  => 4x

put it all together

2x-1=11+4x     bring all like terms to each side

-2x = 12         solve for x

x= -6

The expected number of people over 70 years old in that country in 2050 is given as follows:

D) 5.40 million.

The expected number of people over 70 years old in that country in 2050 is obtained applying the proportions in the context of the problem.

The expected population of that country in 2050 is given as follows:

180 million.

Hence the expected population of the country over 70 years old, equivalent to a percentage of 3%, is obtained as follows:

0.03 x 180 million = 5.4 million.

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The solutions to the expressions are (m-8)² = m² - 16m + 64 and 2m²-16m + m²-8m+161 = 3m²- 24m + 161

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

(m-8)²

Expand

So, we have

m² - 16m + 64

Next, we have

2m²-16m + m²-8m+161

Evaluate the like terms

3m²- 24m + 161

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