Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.

Answer:

3x-14xy+13y+4

Step-by-step explanation:

3x – 10xy + 13y – 4xy + 2x2

= 3x-14xy+13y+4

Simplification of the expression  [tex]3x - 10xy + 13y - 4xy + 2x^{2}[/tex]  is  [tex]3x - 14xy + 13y + 2x^{2}[/tex] .

Given expression is  [tex]3x - 10xy + 13y - 4xy + 2x^{2}[/tex]

Grouping the like terms from the expression, results -

= [tex]3x - (10xy - 4xy) + 13y + 2x^{2}[/tex]

Simplification of the expression is -

= [tex]3x - 14xy + 13y + 2x^{2}[/tex]

Thus, simplification of the expression  [tex]3x - 10xy + 13y - 4xy + 2x^{2}[/tex]  is  [tex]3x - 14xy + 13y + 2x^{2}[/tex] .

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Answer:

Part 1) [tex]A=96\ cm^{2}[/tex]

part 2) [tex]A=40.8\ ft^{2}[/tex]

Step-by-step explanation:

Part 1)

we know that

The area of a trapezoid is equal to

[tex]A=(1/2)[b1+b2]h[/tex]

In this problem we have

[tex]b1=12\ cm[/tex]

[tex]b2=6+12+2=20\ cm[/tex]

[tex]h=6\ cm[/tex] ----> perpendicular distance between the two bases

substitute

[tex]A=(1/2)[12+20](6)[/tex]

[tex]A=96\ cm^{2}[/tex]

Part 2)

we know that

The area of a kite is equal to

[tex]A=(1/2)[D1*D2][/tex]

we have

[tex]D1=10.2\ ft[/tex]

[tex]D2=8\ ft[/tex]

substitute

[tex]A=(1/2)[10.2*8][/tex]

[tex]A=40.8\ ft^{2}[/tex]

Answer:

25) 96 cm²

26)  40.8 ft ²

Step-by-step explanation:

25) To find the area of trapezoid

Area of trapezoid = h(a + b)/2

Here a = 6 + 12 + 2 = 20 cm

b = 12 cm and h = 6

Area =  h(a + b)/2

 = 6(20 + 12)/2

 = 96 cm²

26) To find the area of kite

Area of kite = pq/2

Where p and q are the two diagonals

Here p = 10.2 ft and q = 8 ft

Area = pq/2

 = (10.2 * 8)/2 = 40.8 ft²

Answer:

SAS

Step-by-step explanation:

we know that

Triangles are congruent by SAS, if any pair of corresponding sides and their included angles are equal in both triangles

so

In this problem

we have that

the pair of corresponding sides AB with DC and AD with DA and their included angles  ∠ BAD with ∠CDA are equal

therefore

Triangle ABD is congruent with triangle DCA by SAS congruency theorem

Answer:

sas

Step-by-step explanation:

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Answer:

[tex]\displaystyle \boxed{-\frac{1}{2}}[/tex]

Step-by-step explanation:

Slope formula:

     ↓

[tex]\displaystyle \frac{Y_2-Y_1}{X_2-X_1}[/tex]

[tex]\displaystyle Y_2=5\\\displaystyle Y_1=3\\\displaystyle X_2=(-2)\\\displaystyle X_1=2\\[/tex]

[tex]\displaystyle \frac{5-3}{(-2)-2}=\frac{2}{-4}=\frac{2\div2}{-4\div2}=\frac{1}{-2}=-\frac{1}{2}[/tex]

Therefore the slope is -1/2.

-1/2 is the correct answer.

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Answer:

5/6 is larger

Step-by-step explanation:

5/6 * (6/6) = 30/36

30/36 > 29/36

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Answer:

1. trapezoid

A quadrilateral with at least one pair of parallel sides.  

2. bases of a trapezoid

The parallel sides

3. legs of a trapezoid  

The nonparallel sides.  

4. median of a trapezoid  

The segment connecting the midpoints of the legs.  

5. isosceles trapezoid

A trapezoid with legs of the same length.

Answer:

A trapezoid is defined as a quadrilateral with at least one pair of parallel sides, when the trapezoid as equal legs, it's called an isosceles trapezoid.

The bases of a trapezoid are the pair of parallel sides, both of them are called base, the longer one is the major base, and the shorter one is the minor base.

The legs of a trapezoid are the nonparallel sides, because if they were parallel, that wouldn't be a trapezoid, it would be another quadrilateral.

The median of a trapezoid is a segment that connects the midpoints of the legs. Remember that medians are always line that intercept midpoints.

As we said before, an isosceles trapezoid are those which have legs with equal legs. The name isosceles refers to equality.

Therefore, the right matches are

1. Trapezoid: A quadrilateral with at least one pair of parallel sides.  

2. Bases of a trapezoid: The parallel sides.

3. Legs of a trapezoid: The nonparallel sides.  

4. Median of a trapezoid: The segment connecting the midpoints of the legs.  

5. Isosceles trapezoid: A trapezoid with legs of the same length.

Answer:x^1/2

Step-by-step explanation:

x^1/6*3=

x^3/6=

x^1/2

Answer:

Line segment TU is parallel to line segment RS because 32/36 = 40/45.

Step-by-step explanation:

The line segment TU is parallel to the line segment RS because 32 / 36 is equal to 40 / 45.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The converse theorem states that if TU || RS, then the ratio of the corresponding sides will be constant.

32 / 36 = 40 / 45 = 8 / 9 = constant

The line segment TU is parallel to the line segment RS because 32 / 36 is equal to 40 / 45.

Then the correct option is A.

The graph is given below.

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Answer:

d

Step-by-step explanation:

Answer:

(3a2 + 3a2) + [–5ab + (–8ab)] + [b2 + (–2b2)]

Step-by-step explanation:

Answer: c. (3a^2+3a^2)+[-5ab+(-8ab)]+[b^2+(-2b^2)]

for the second part: =a. 6a^2-13ab-b^2

Step-by-step explanation:

i did it

ANSWER

GCF=4

EXPLANATION

The given monomials are:

[tex]8m = {2}^{3} m[/tex]

[tex]36 {m}^{3} = {2}^{2} \times {3}^{2} {m}^{3} [/tex]

[tex]12 = {2}^{2} \times 3[/tex]

The greatest common factor is the product of all the least powers of the common factors.

We can see that:

[tex] {2}^{2} [/tex]

is the common to all the factors.

Therefore the greatest common factor is

[tex] {2}^{2} = 4[/tex]

Answer: [tex]GCF=4[/tex]

Step-by-step explanation:

To find the Greatest Common Factor (GCF) of 8m, 36m³, and 12, you need to descompose them into their prime factors. Then:

[tex]8m=2*2*2*m=2^3*m\\\\36m^3=2*2*3*3*m^3=2^2*3^2*m^3\\\\12=2*2*3=2^2*3[/tex]

You can observe that the common factor with the lowest exponent is the following:

[tex]2^2[/tex]

Therefore,  the Greatest Common Factor (GCF) of 8m, 36m³, and 12 is:

[tex]GCF=2^2\\GCF=4[/tex]

Answer:

the second one

Step-by-step explanation:

Answer:

the second one

Step-by-step explanation:

the one that says +14

Answer:

86%

Step-by-step explanation:

64.97/ 75 = 0.8662...

0.8662 x 100 = 86%

but it weighted so:

0.8662 x actual weighted % =  % got out of weighted %

example:

Test is Weighted 25% out of 100%

0.8662 x 25% = 21 %

this case you got 21% out of 25% for the test

The midpoint of the line segment with endpoints (-2, 5) and (4, -9) is found using the midpoint formula and is (1, -2).

To find the midpoint of the line segment whose endpoints are (-2, 5) and (4, -9), you use the midpoint formula, which is derived from finding the average of the x-coordinates and the y-coordinates of the endpoints respectively.

The midpoint formula is:

( (x1 + x2) / 2, (y1 + y2) / 2 )

Plugging in our given endpoints (-2, 5) and (4, -9) into the formula, it becomes:

( (-2 + 4) / 2, (5 + (-9)) / 2 )

This simplifies to:

( 2 / 2, -4 / 2 )

And finally:

( 1, -2 )

Therefore, the midpoint of the line segment is at coordinates (1, -2).

Answer:

LCM = 30

Step-by-step explanation:

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Answer:

Third length =

12-7 = 5

12+7 = 19

Third length can be only in this range

5Means the third length must be greater than 5 and less than 19.

Step-by-step explanation:

The y-intercept of a line that has a slope of –3 and passes through point (–5, 4) is -11.

The slope-intercept of a line is

[tex](y-y_{1})=m(x-x_{1})[/tex]

Here, [tex](x_{1},y_{1})[/tex] is the point through which the line passes and 'm' is the slope of the line.

Given, the line has a slope of –3 and passes through point (–5, 4).

Therefore, [tex](y-4)=-3[x-(-5)][/tex]

⇒ [tex](y-4)= -3(x+5)[/tex]

⇒ [tex](y-4)= -3x-15[/tex]

⇒ [tex]3x+y = -11[/tex]

⇒ [tex]y = -3x-11[/tex]

Comparing it with the standard form of equation, we get:

the y-intercept of the required line is -11.

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Answer:

C) a+3

Step-by-step explanation:

We are given the following data:

Tom's Age:  10  11  12  a

Kim's Age:   13  14  15  

We have to evaluate Kim's age when Tom's age is a.

We have to build a relationship between Tim's age and Kim's age. If we look at their ages carefully we can see a pattern and their relation can be described as:

[tex]\text{Kim's age = Tim's age + 3}[/tex]

Thus, when Tim's age is a, we can compute Kim's age as:

[tex]\text{Kim's age = a + 3}[/tex]

Answer:

answer is A

Step-by-step explanation:

The formula for circumference of a circle using diameter is pi times "d". "d" means diameter. 3.14 x 16= 50.24

C = pi•d

C = 3.14(16)

C = 50.24 inches

Answer:

y+5=-1/2(x+3)

Step-by-step explanation:

as perpendicular,

compare that given eqn with y-y1=m(x-x1),

m1=2

then,

perpendicular case,

m1×m2=-1

m2=-1/2

now,

as the eqn passes through point (-3,-5),

we know,

y-y1=m(x-x1)

then putting value,

y+5=-1/2(x+3)

Answer:

y + 5 = - [tex]\frac{1}{2}[/tex](x + 3)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line.

y - 4 = 2(x - 6) is in this form with slope m = 2

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]

Hence the equation passing through (- 3, - 5) is

y - (- 5) = - [tex]\frac{1}2}[/tex] (x - (- 3)), that is

y + 5 = - [tex]\frac{1}{2}[/tex](x + 3) ← equation of perpendicular line

Answer:

Option D is correct.

Step-by-step explanation:

The length of 2 sides of triangle are given i.e 10 cm and 16 cm.

We need to find the range of the values of length of the third side.

Sum of 2 sides of triangle is greater than the 3rd side

so, 10+16 = 26

So, the length of third side should be less than 26

and we know that the length of third side should be greater than the absolute difference of other two sides

16-10 = 6

So, the length of third side should be greater than 6

Combining both we get 6<x<26

Hence Option D is correct.

The range of possible values for the third side of the triangle is 6 < x < 26

10 + 16 = 26 cm

Difference = 16 cm - 10cm

= 6 cm

Therefore, the range of value of the third side is x is greater than 6cm less than 26cm

6 < x < 26

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Answer:

iii) P=65h

iv) P=70h

Step-by-step explanation:

Payment of First day = $300

Number of hours = 5

Payment per hour = $60

Payment of First day = $240

Number of hours = 4

Payment per hour = $60

Payment of First day = $360

Number of hours = 6

Payment per hour = $60

Hence the rate of Payment for an hour is $60

Hence the rates

P=65h

and

P=70h

are more than the rate of payment made to labor.

Answer:

295.01

Step-by-step explanation:

Use A = Pe^(rt)

$294.88 is the worth of the investment after 4 years.

percentage, a relative value indicating hundredth parts of any quantity.

Given that  $190 is invested at an interest rate of 11% per year and compounded continuously.

We need to find the worth of the investment after 4 years.

[tex]A=Pe^{rt}[/tex]

A is the final amount

p is the principal amount

r is the rate of interest

t is the time.

[tex]A=190e^{0.11(4)}[/tex]

[tex]A=190e^{0.44}[/tex]

A=190×1.552

A=294.88

Hence, $294.88 is the worth of the investment after 4 years.

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Answer:1/2

Step-by-step explanation:

the slope of a line in an equation comes before x

since we know parallel lines have the same slope it is 1/2

Final answer:

Maggie needs to practice at least 1.5 hours on each of the two remaining days.

Explanation:

To determine the minimum number of hours Maggie needs to practice on each of the two remaining days, we can set up an inequality based on the given information. Maggie needs to spend at least six hours each week practicing the piano, and she has already practiced three hours. Let's let x represent the number of hours she needs to practice on each of the remaining two days. The inequality can be written as:

3 + 2x ≥ 6

Solving for x, we subtract 3 from both sides of the inequality:

2x ≥ 3

Then, we divide both sides by 2 to solve for x:

x ≥ 1.5

Therefore, Maggie needs to practice at least 1.5 hours on each of the two remaining days.

Maggie must practice for at least [tex]$\dfrac{3}{2}$[/tex] hours each of the last two days.

Let x equal the number of hours Maggie practices each of the last two days. Since she Needs to practice at least 6 hours per week, and she already practiced 3 hours this week, she must practice for at least 6 - 3 = 3 more hours.

Splitting this time evenly between the two days means she practices x hours each day.

This can be expressed in the following inequality: [tex]$x + x \geq 3$[/tex] which combines the information about the minimum number of hours needed and the fact that she splits the remaining time evenly.

Simplifying the left side of the inequality gives [tex]$2x \geq 3$[/tex]. Dividing both sides by 2 gives [tex]$x \geq \dfrac{3}{2}$[/tex].

Thus, Maggie must practice for at least [tex]$\dfrac{3}{2}$[/tex] hours each of the last two days.

The answer to your question is 0.55555555555

Solution: You simply divide 5 by 9 to get your whole number. In other words, 5/9 =0.55555555555

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The fraction 5/9 cannot be converted into a whole number because it results in a decimal number (approximately 0.55) upon division.

In Mathematics, we have different types of numbers - whole numbers, fractions, decimals, etc. Here, you are asked to convert a fraction 5/9 into a whole number. However, it's essential to understand, that 5/9 cannot be converted into a whole number because it is less than 1.

For general understanding, a whole number can only be a non-negative number without any fractional or decimal parts, such as 0, 1, 2, 3, 4, and so forth. A fraction like 5/9 implies division, and when you divide 5 by 9, you get a decimal number (approximately 0.55), which is not a whole number.

Thus, the fraction 5/9 cannot be precisely converted into a whole number without rounding it off.

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Answer:

C

Step-by-step explanation:

To evaluate (f ￮ g)(x)

Substitute x = g(x) into f(x)

f(x² + 14) = x² + 14 - 14 = x² → C

The value of (fog)(x) = x^2. So, option C is correct.

The functions f(x) and g(x) are composite functions then,

(fog)(x) = f(g(x)).

Given that,

f(x) = x - 14

g(x) = [tex]x^2+14[/tex]

Then,

(fog)(x) = f(g(x))

           = ([tex]x^2+14[/tex]) - 14

           = x² + 14 - 14

           = x²

Therefore, the value of (fog)(x) = x².

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there were D. 1163 books left on the shelves or in circulation.

///////////////////////////////////////////////////////////////////////////

let us count the number of books that are NOT on the shelves now.

1st step: 32 + 24 = 56

2nd step: the total number of books minus the amount of books that are damaged or out:  1,219 - 56 = 1163

Answer:

C. 1,163

Step-by-step explanation:

Total books = books on shelves + books lost + books out for repair

What do we know

1219 =  books on shelves + 32 + 24

1219 = books on selves + 56

Subtract 56 from each side

1219-56 = books on shelves - 56

1163 = books on shelves

Answer:

[tex]\displaystyle 64 = y[/tex]

Step-by-step explanation:

[tex]\displaystyle y = 8[3] + 40; y = 24 + 40; 64 = 24 + 40[/tex]

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Answer:

1. C. Jana

2. I. Matthew and Jake