Simplify the following expressions. Type out and label your answers for A and B.

Using the combination formula, the probability that a person with one combination of five numbers will win is:

[tex]\frac{1}{1,221,759}[/tex]

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

For this problem, 5 numbers are taken from a set of 45, hence the number of combinations is:

[tex]C_{45,5} = \frac{45!}{5!40!} = 1,221,759[/tex]

Hence the probability is:

[tex]\frac{1}{1,221,759}[/tex]

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The dilation by a scale factor of 2 of the points A(2, 3), B(5, 4), C(3, 6) gives;

a. A'(4, 6), B'(10, 8), C'(6, 12)

b. A'(-2, -2), B'(4, 0), C'(0, 4)

c. The transformation that would carry dilation 1 onto dilation 2 is T(-6, -8)

d. The proportion of the side length of Dilation 1 and Dilation 2 is 1:1

The general formula for finding the coordinates of the image of a point following a dilation is presented as follows;

[tex]D _{(a , \: b)k}(x, \: y) = (a + k \times (x - a) , \: b+ k \times (y - b))[/tex]

Where;

(a, b) = The center of dilation

k = The scale factor of dilation

(x, y) = The coordinate of the pre-image

The given points are;

A(2, 3), B(5, 4), C(3, 6)

a. The scale factor of dilation = 2

The center of dilation = The origin (0, 0)

Therefore;

[tex]D _{(0 , \: 0)2}(2, \: 3) = (0 + 2 \times (2 - 0) , \: 0+ 2 \times (3 - 0)) = (4, \:6)[/tex]

Therefore dilation about the origin, with a scale factor of 2 gives;

Similarly

b. With the center of dilation at (6, 8), we have;

[tex]D _{(6 , \: 8)2}(2, \: 3) = (6 + 2 \times (2 - 6) , \: 8+ 2 \times (3 - 8)) = (-2, \:-2)[/tex]

[tex]D _{(6 , \: 8)2}(5, \: 4) = (6 + 2 \times (5 - 6) , \: 8+ 2 \times (4 - 8)) = (4, \:0)[/tex]

[tex]D _{(6 , \: 8)2}(3, \: 6) = \mathbf{(6 + 2 \times (3 - 6) , \: 8+ 2 \times (6 - 8))} = (0, \:4)[/tex]

c. The difference between the coordinates of the points on dilation 1 and 2 is a shift left 6 places and a shift downwards 8 places

Using notation, we have;

The area of the images of dilation 1 and 2 are equal given that the scale factor is the same.

d. From the above calculation, given that the difference between pre-image point and the center is multiplied by the scale factor followed by the addition of the x and y-values, the lengths of the sides of dilation 1 and 2 are the same, such that we have;

Given that the side lengths are the same, by AAA congruency postulate, we have;

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Answer:

The angle measures are the same.

Step-by-step explanation:

The width of his patio is 19.5 feet based on the information about the area given.

Area = Length × Width

175.5 = 19.5 × w

Width = 175.5/19.5

Width = 9 feet

The width of his patio is 19.5 feet.

The number of blocks that were used will be:

= 175.5/(1.5 × 1.5)

= 175.5/2.25

= 78 blocks

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Complete question

Gavin made the patio area out of square block that are 1.5 by 1.5 feet. The area of the patio is 175.5 ft² and the length is 19.5ft.

a. Determine the width of his patio.

b. Determine the number of blocks Gavin used to make his patio.

Answer:

21+21+7+7+7+7+8+8+8+8+9+9

Step-by-step explanation:

amswer is 120

Answer:

Step-by-step explanation:

21+2=42.There are four sevens-which is  7x4=28.There are four eights meaning it is 8x4=32+28=60+42=102+(9+9)=102+18=120

The graph that is used to represent this probability distribution is the graph of b.

In mathematics and the field of statistics, the probability is used tp denote likelihood of an event occurring.

The sample space is given as

S = {GGG, GGO, GOG, OGG, GOO, OGO, OOG, OOO}.

X=0, the Probability of having Orange(O), in GGG  is given to be 1/8

X=1, we have to get the probability, in G G O , GOG,and O G G, this gives a total of 3 =  3/8

X=2, Probability of Orange O, in GOO , OGO, oog =   3/8

X=3, Probability of Orange O in all is also given as 1. Hence the probability is = 1/8

A spinner has two equal sections, one green and one orange. The spinner is spun three times, resulting in the sample space S = {GGG, GGO, GOG, OGG, GOO, OGO, OOG, OOO}. If the random variable X represents the number of times orange, O, is spun, which graph represents the probability distribution?

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Answer:

y = 33.6

Step-by-step explanation:

1/2 y + 3.2 = 20     subtract 3.2 from both sides of the equation

1/2y = 16.8              multiply both sides by 2

y = 33.6

The jo's drink have stronger pineapple taste.

Given that fruit punch calls for 333 liters of orange juice and 222 liters of pineapple juice and Jo creates a drink by mixing 444 liters of orange juice with 333 liters of pineapple juice.

In the Recipe for fruit punch calls

The Number of liters of orange juice = 333.

The Number of liters of pineapple juice = 222.

Thus, Total number of liters of juice = 222+333= 555 liters

Now, % of pineapple juice in fruit punch is

P₁=(222/555)×100

P₁=0.4×100

P₁=40%

Further, % of orange juice in fruit punch is

O₁=(333/555)×100

O₁=0.6×100

O₁=60%

In Jo's drink

The Number of liters of orange juice = 444.

The Number of liters of pineapple juice = 333.

Thus, Total number of liters of juice = 444+333= 777 liters

Now, % of pineapple juice in jo's drink is

P₂=(333/777)×100

P₂=0.43×100

P₂=43%

Further, % of orange juice in jo's drink is

O₂=(444/777)×100

O₂=0.57×100

O₂=57%

Hence, the taste of both drinks was not the same, jo's drink will have a stronger pineapple taste and jo's drink will have a lesser orange taste.

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Helen needs a replacement ball bearing whose radius is 5.99mm

A sphere is a perfectly round geometrical 3-dimensional object. It can be characterized as the set of all points located distance r (radius) away from a given point (center). It is perfectly symmetrical, and has no edges or vertices.

The formula of surface area of the sphere is [tex]4\pi r^{2}[/tex] where r represents radius

Given:  Surface area of ball  = 452.16[tex]mm^{2}[/tex]

Using formula we get,

[tex]4\pi r^{2}[/tex] = 452.16[tex]mm^{2}[/tex]

r^2 = 452.16/4[tex]\pi[/tex]

r = 5.99 mm

Thus Helen needs a replacement ball bearing whose radius is 5.99mm

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Answer:

t = 3/2

Step-by-step explanation:

Instead of randomly guessing values of "t" that will satisfy the equation, you can easily find the correct value by solving the equation in terms of "t". In other words, you can set the equation equal to "t" to find the final answer.

(-2/3)t - 2 = -3                             <----- Original equation

(-2/3)t = -1                                   <----- Add 2 to both sides

t = 3/2                                        <----- Divide both sides by -2/3

You can check this value by plugging it into "t" and determining whether both sides of the equations will be equal.

(-2/3)t - 2 = -3                            <----- Original equation

(-2/3)(3/2) - 2 = -3                      <----- Plug 3/2 into "t"

-6/6 - 2 = -3                               <----- Multiply -2/3 and 3/2

-1 - 2 = -3                                    <----- Simplify -6/6

-3 = -3                                        <----- Subtract

The value of f left parenthesis 3 right parenthesis is 45.

According to the statement

We have given that the F(x) = 5(x)^2

and we have to find the value when Sophia have a 3 right parenthesis.

So, Parenthesis are used in mathematical expressions to denote modifications to normal order of operations.

And now we have to find the value for 3 right parenthesis

And for this purpose we have to put the value X= 3 in the f(x) then

F(x) = 5(x)^2

F(3) = 5(3)^2

F(3) = 5*9

F(3) = 45.

here the value of 3 right parenthesis is 45.

So, The value of f left parenthesis 3 right parenthesis is 45.

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The midpoints of A(-3,-9) and B (-8,-2) is the coordinate points (-5.5, -3.5)

Coordinate points are written in the form (x, y). The midpoint of two points (x1, y1) and (x2, y2) is expressed as:

M(x, y) ={(x1+x2)/2, (y1+y2)/2}

Given the following coordinates A(-3,-9) and B (-8,-2)

M(x, y) = {(-3+(-8))/2, (-9-(-2))/2}

M(x, y) = {(-3-8)/2, (-9+2)/2}

M(x, y) = (-11/2, -7/2)

M(x, y) = (-5.5, -3.5)

Hence the midpoints of A(-3,-9) and B (-8,-2) is the coordinate points (-5.5, -3.5)

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Here,

y=mx+c

the slope of the line 6x+4y= -16 is -20.

if the two lines are perpendicular, the slope of 1st line * slope of second line=-1

the slope of the 2nd line is -1/2

y-y1=m(x-x1)

y-13=-1/2(x- -18)

when you solve, you get the equation of the line as 2y+x=50

In basic geometry, if two geometry objects intersect at right angles (90 degrees or π / 2 radians), they are vertical.

If two lines intersect at right angles, the line is perpendicular to another line. Explicitly (1) if two lines intersect, the first line is perpendicular to the second line. (2) At the intersection, the straight line angle on one side of the first line is cut by the second line into two congruent angles. Verticality can be shown as symmetric. That is, if the first line is perpendicular to the second line, then the second line is also perpendicular to the first line. Therefore, two straight lines can be said to be perpendicular (to each other) without specifying the order.

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The given statements:

1) ΔQRS ≅ ΔSTU (according to the ASA axiom)

2) The congruent ∠S: ∠RSQ ≅ ∠UST (Vertical angles)

The ASA axiom states that "two triangles are said to be congruent if two pairs of corresponding angles and the sides between these angles are equal".

It is given that,

S is the midpoint of QT.

So, SQ ≅ ST <S>

Since ∠S is at the intersection of two transversal lines, ∠RSQ ≅ ∠UST <A>.  This is beacuse they are vertically opposite.

And QT is the transverse line for the parallel lines, QR║UT. So, the alternate angles(interior) are congruent. I.e., ∠SQR ≅ ∠UTS <A>.

From this, the given triangles have two equal corresponding angles and congruent sides in between them.

So, ΔQRS ≅ ΔSTU according to ASA axiom.

Therefore, ΔQRS ≅ ΔSTU and ∠RSQ ≅ ∠UST.

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Answer:

original price $75

discount $18.75

sale price $56.25

Step-by-step explanation:

I found a pair of dress pants for $75.

Since the discount is 25%, then the discount is

25% of $75 = 0.25 × $75 = $18.75

The sale price is the original price, $75, minus the discount, $18.75.

$75 - $18.75 = $56.25

The area of the wings of the model is 100000 square centimeters

The given parameters are:

Scale factor, k = 1/2

Actual area of wings, A = 40 square meters

The model area is calculated as

Model area = Actual area * k^2

This gives

Model area = 40 * (1/2)^2

Evaluate

Model area = 10 square meters

Convert square meters to square centimeters

Model area = 10 * 10000 square centimeters

Evaluate

Model area = 100000 square centimeters

Hence, the area of the wings of the model is 100000 square centimeters

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The service area of the cylinder is 42[tex]\pi[/tex] square fts.

Two parallel bases joined by a curving surface make up the three-dimensional solid known as a cylinder.

Typically, the bases are shaped like circles. The height "h" of the cylinder stands for the perpendicular distance between the bases, while "r" stands for the cylinder's radius.

The uses of cylinder are-

Total surface area of the cylinder formula:

It is the sum of the base surface area and the lateral surface area;

Total area = base area + lateral area , or

Total area = 2 π r² + (2 π r) h , or

Total area = 2 π r (r + h)

Calculation for the total area of the cylinder;

Base diameter is 6 ft

Radius is 6/2 = 3 ft

Height is 4 ft

Total area = 2[tex]\pi[/tex]3(3 + 4)

                 = 6[tex]\pi[/tex]×7

                 = 42[tex]\pi[/tex]

Therefore, the total surface area of the cylinder is 42[tex]\pi[/tex] square fts.

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Answer:

7.6

Step-by-step explanation:

mean = [weights] / amount of weights

m = 10 + 7 + 6 + 10 + 13 + 10 / 6

m = 46 / 6

m = 7.66666666 (recurring)

m = 7.6

The total amount that roland paid for the ticket is $27.60

Given that the price of an all-access ticket to the fair is $42.99 before tax. Roland bought the all-access ticket for 40% off.

We need to calculate the total amount paid by the roland

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100

The price after 40% off -

= 42.99*60% = $25.794

Sales tax on 25.794

= 25.794*7% = $1.80558

Total amount Paid for the ticket

= 1.80558 + 25.794 = $27.59958

= $27.60

Hence the total amount paid by roland is $27.60

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Answer:

Line LM

Step-by-step explanation:

Answer:

A line is a straight path on a plane that extends forever in both directions with no endpoints.

The answer will be lineLM

Answer:

screenshot attached of graph

Step-by-step explanation:

The polynomial function in standard form that has the zeros listed. i and -i is  x² +1 = 0.

A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions.

The values of x that fulfil the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.

Calculation for the polynomial function-

The general two degree/quadratic equation is given by-

ax² + bx + c = 0

Where a ≠ 0

If the two roots of the equation are x1 and x2.

Then the relation between roots and coefficients of the polynomial are -

         x1 + x2 = (-b)/a

        x1.x2 = c/a

From the above two relation the general equation can be written as-

x² -(x1 - x2)x + x1.x2 = 0

Lets say x1 = i and x2 = -i

Substitute the values of x1 and x2 in the general equation

x² -(i - i)x + (i).(-i) = 0

x² - i ² = 0

x² + 1 = 0

Therefore, the polynomial function in standard form that has the zeros listed. i and -i is x² + 1 = 0.

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Answer:

Step-by-step explanation:

Answer:

65.4 cm²

Step-by-step explanation:

The volume of a cuboid is calculated by multiplying the length, base, and height together. Since a cube has equal sides, the formula for the volume of a cuboid can be simplified as shown below.

Volume of cube

= side ×side ×side

= side³

Given that the volume is 36 cm³, let's find the length of each side.

side³= 36

Cube root both sides:

side=[tex]\sqrt[3]{36}[/tex]

Total surface area of a cube is the sum of the surface areas of its 6 identical square faces.

Area of a square

= side ×side

= side²

Surface area of 1 face= [tex](\sqrt[3]{36})^2[/tex]

Total surface area

= [tex]6(\sqrt[3]{36} )^2[/tex]

= 65.416 (5 s.f.)

= 65.4 cm² (nearest tenth)

Additional:

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Answer:

d. 90

Step-by-step explanation:

z = (x - mean)/SD = (15 - 18)/5.4 = - 3/5.4 = -0.55555555... ≈

≈ -0.56

remember the z-table represents the rounded values.

the z-table at -0.56 gives us the p-value of 0.28774.

that is the probability to the left of 15 pounds, so, the probability to have lost 15 pounds or less.

to have lost at least 15 pounds, we have to get the right side of 15 pounds in the bell curve.

and that is 1 - 0.28774 = 0.71226

so, the probability to have lost at least 15 pounds is therefore 0.71226.

how many people are that ?

well, there were in total 128 people (with the total probability of 1 representing everything).

the number of people that lost at least 15 pounds are the proportionate share of 0.71226 of 1 (the whole) :

128 × 0.71226 = 91.16928...

so, the closest answer option is d. 90

Answer:

D

Step-by-step explanation:

You are looking for what you would need to cancel the yards in 800 yards.

800 yards (1 mile/ 1760 yards).  You have yards in the numerator of your original measurement.  You will cross cancel out the yard on the the top and the yards on the bottom.

The expression has been dragged the correct location on the table.

It should be noted that an exponential expression simply means a way to write Lowe's in short form.

In this case, the expression has been dragged the correct location on the table.

This is attached below.

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Answer:

Step-by-step explanation:

20% of a number is 17 . find the number

divide 17 by 20 and you find 1%, multiply by 100 and you get 100%

x = 17 : 20 * 100

x = 0.85 * 100

x = 85

Answer:

D

Step-by-step explanation:

simplified is 1 1/2, 1.5 or 3/2

Answer:

Step-by-step explanation:

John has $1.25

James has $1.75

i think

Answer:

$1.00

Step-by-step explanation:

James has $0.50 more than John.

When they put their money together, they have a combined total of $2.50.

[tex]2.50-0.50=2.00[/tex]
[tex]2.00\div2=1.00[/tex]
[tex]1.00+1.50=2.50[/tex]
[tex]=2.50[/tex]

John has one dollar.

Hope this helps.

Answer:

Yes

Step-by-step explanation: The answer is Side Angle Side (SAS)