Tom keeps all of his marbles in a bag. 5 red marbles. 4 blue marbles. and three yellow are in the bag. if he randomly chooses one marble what is the probability it is blue?

Answer:

208

Step-by-step explanation:

There are 5 weekdays in a week and 2 weekend days. Since there are 4 weeks, multiply 5 times 4 to get 20 weekdays/month, and 2 times 4 to get 8 weekend days/month. 20 times 8 (the hours she sleeps) is 160 hours, and 8 times 6 is 48 hours. Put together, you get 208 total hours.

Answer:

300 miles

Step-by-step explanation:

125 ÷ 2.5 = 50 miles per hour

50 x 6 = 300 miles

Answer:

u will multiply -x by the big bracket and rhen start cancelling and factor it by common numbers

Answer:

(x + 3)(- x² - 3x + 1)

Step-by-step explanation:

Given

(x + 3) - x(x² + 6x + 9) ← factor is a perfect square

= (x + 3) - x(x + 3)² ← factor out (x + 3) from each term

= (x + 3)(1 - x(x + 3))

= (x + 3)(1 - x² - 3x)

= (x + 3)(- x² - 3x + 1)

Answer:

C. $20.00

Step-by-step explanation:

First, you need to calculate the unit price (per pound). $6.00/3lbs = $2.00/lb. Now, you multiply the unit price by the new amount.  $2.00x10lbs = $20.00

Answer:

it is c  i think

Step-by-step explanation:

Answer:

2y to the negative 3rd power is -2000

Step-by-step explanation:

Answer:

2 over y^3

Step-by-step explanation:

Answer:

4 gifts

Step-by-step explanation:

4÷4=0

so you get each other a gift so there none to spare

Answer:

12 gifts

Step-by-step explanation:

If there are 4 people, and each person brings a gift for each of the other three people, that means that there are 12 gifts at the party. Let's say there are four people: A, B, C, and D. Person A would have to bring 3 gifts to give  B, C, and D. Similarly, B would bring a gift each for A, C, D. C would bring a gift for A, B, D. Lastly, D would bring a gift for A, B, and C. Each person brings three gifts to give to the other three people at the party, and 3*4 people is 12. I hope that makes sense.

Answer:

Step-by-step explanation:

Use Pythagorean theorem to find the length of the square.

Length of the square = a

a² +a² = diagonal²

2a² = 12²

2a² = 144

a² = 144 ÷ 2

a² = 72

\(a =\sqrt{72}\\\\ = \sqrt{2*2*2*3*3}\\\\ = 2*3\sqrt{2}\\\\a = 6\sqrt{2}\\\\\\\\Perimeter= 4a\\\\ = 4*6\sqrt{2}\\\\= 24\sqrt{2} cm\)

The best possible prediction of obtaining a three during the die roll is 1 time .

The probability of an event is the ratio of the required outcome to the total possible outcome.

Mathematically,

Probability = required outcome / Total possible outcome

Here ,

required outcome = Number of 3's on a die = 1

total possible outcome = number of sides on a die= 6

P(obtaining a 3 ) = 1/6

After 6 rolls ; (6 × 1/6) = 1

The best prediction for the number of times a 3 can be obtained after 6 rolls is 1

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\(\frac{2a}{3} +13, \:a=15\)

Step 1: Substitute \(a\) for 15

\(\frac{2(15)}{3} +13\)

Step 2: Solve

15 × 2 = 30

\(\frac{30}{3} +13\)

30 ÷ 3 = 10

\(10 +13\)

10 + 13 = 23

The evaluation of the expression is 23.

The given equation is 2x³+11x²−9x−18=0 and the value of x is to be found out.Factoring is a very useful method of solving cubic equations. One factor can always be found out by putting x=1,2,3, etc. in the equation and finding out whether it is satisfied or not.

If we put x = 1, then the left-hand side is equal to 2 + 11 − 9 − 18 = −14. Thus, x = 1 is not a root of the equation. If we put x = 2, then the left-hand side is equal to 16 + 44 − 18 − 18 = 24. Thus, x = 2 is a root of the equation.

The factor theorem states that if (x − a) is a factor of the polynomial p(x), then p(a) = 0. Using this theorem, we can divide the polynomial 2x³+11x²−9x−18 by (x − 2) and obtain a quadratic equation.

Long Division :

           2x² + 15x + 9
      ________________________
  x - 2 |  2x³ + 11x² - 9x - 18
           2x³ - 4x²
           __________
                 15x² - 9x
                 15x² - 30x
                 ___________
                            21x - 18
                            21x - 42
                            _______
                                     24
The factorization of 2x³+11x²−9x−18 is given by (x−2)(2x²+15x+9). Now, we need to solve the quadratic equation 2x²+15x+9=0.

2x²+15x+9=0
We can use the quadratic formula to solve for x.

x = (-b ± sqrt(b² - 4ac)) / 2a, where a = 2, b = 15, and c = 9.
x = (-15 ± sqrt(15² - 4(2)(9))) / 4
x = (-15 ± sqrt(177)) / 4
x = (-15 + sqrt(177)) / 4, or x = (-15 − sqrt(177)) / 4

Thus, the roots of the cubic equation 2x³+11x²−9x−18=0 are x=2, x=(-15 + sqrt(177)) / 4, and x = (-15 − sqrt(177)) / 4.

The possible rational roots of the cubic function are ±1, ±2, ±3, ±6, ±9 and ±18 and the roots of the equation are x = -1, x = 3/2 and x = -6

To find the roots of the equation 2x³ + 11x² - 9x - 18 = 0, we can use various methods such as factoring, synthetic division, or numerical methods. In this case, let's use the Rational Root Theorem and synthetic division to determine the roots.

The Rational Root Theorem states that if a rational number p/q is a root of the equation, where p is a factor of the constant term and q is a factor of the leading coefficient, then p/q is a possible root.

The constant term of the equation is -18, and its factors are ±1, ±2, ±3, ±6, ±9, and ±18. The leading coefficient is 2, which only has factors of ±1 and ±2. Therefore, the possible rational roots are:

±1, ±2, ±3, ±6, ±9 and ±18

The roots of the original equation 2x³ + 11x² - 9x - 18 = 0 are:

x = -1, x = 3/2 and x = -6

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The relation ⊂ (subset) can be considered as a binary relation between sets, and it is a partial order on the power set P(S) of an arbitrary nonempty set S. However, it is not a total order.

A partial order is a binary relation that satisfies three properties: reflexivity, antisymmetry, and transitivity. Let's analyze whether ⊂ satisfies these properties for the power set P(S).

Reflexivity: For any set A, A is a subset of itself (A⊂A) holds true. Therefore, ⊂ is reflexive.

Antisymmetry: If A⊂B and B⊂A, then A and B must be equal sets. In other words, if two sets are subsets of each other, they must be the same set. This property is satisfied, and ⊂ is antisymmetric.

Transitivity: If A⊂B and B⊂C, then A⊂C. If one set is a subset of another set, and the other set is a subset of a third set, then the first set is also a subset of the third set. This property is satisfied, and ⊂ is transitive.

Therefore, ⊂ satisfies the properties of reflexivity, antisymmetry, and transitivity, making it a partial order on P(S).However, ⊂ is not a total order because it does not satisfy the total ordering property. In a total order, for any two distinct elements, one must be greater than or equal to the other. In the case of ⊂, there are sets A and B that are not subsets of each other (neither A⊂B nor B⊂A). Therefore, it is not a total order.

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Given:

The base of an isosceles triangle is 16 cm long.

The equal sides are each 22 cm long.

To find:

The height of the triangle.

Solution:

We know that the altitude of an isosceles triangle divides the base into two equal parts as shown in the below figure.

According to the Pythagoras theorem:

\(Hypotenuse^2=Perpendicular^2+Base^2\)

Using Pythagoras theorem, we get

\(22^2=h^2+8^2\)

\(484=h^2+64\)

\(484-64=h^2\)

\(420=h^2\)

Taking square root on both sides, we get

\(\sqrt{420}=h\)                  (Because side cannot be negative)

\(2\sqrt{105}=h\)

Therefore, the height of the isosceles triangle is \(2\sqrt{105}\) cm. Approximate height is 20.49 cm.

Answer:

14

Step-by-step explanation:

you substitute a with 3. so 2x2x2=8. then you do 8+6=14

The required statements and reasons to prove that DE is equal to CE is explained.

The triangle congruence theorem is a theorem that can be used to prove that two or more triangles are the same, considering the corresponding properties of the triangles. The properties are length of the sides, and measure of internal angles.

The statements and reasons to prove that DE is equal to CE are explained below using the triangle congruence theorem.

         STATEMENT                            REASON

1. AD = BC                                          Given

2. <BCD = <ADC                                Given

3. DC = DC                                         Reflexive property

4. ΔADC ≅ ΔBCD                              SAS

5. <EDC ≅ <ECD                                CPCTC

6. AC = BD                                          Definition of diagonal

7. DE = CE                                           Congruent sides of isosceles triangle

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He would pay $14.48

To get this answer you would need to multiply $2.73 by 24 and subtract by $80.

The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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Work Shown:

n = number of sides

c = central angle

c = 360/n

c = 360/10

c = 36

This formula applies to regular polygons only (all sides must be the same length; all angles must be the same).

Answer:

9,000 m2

Step-by-step explanation:

If the longer rope has three times the length of the shorter rope, the perimeter and the sides of the triangle formed by the longer rope are three times the perimeter and sides of the triangle formed by the smaller rope.

The area of an equilateral triangle is:

\(Area = \frac{side^{2} * \sqrt{3}}{4}\)

So, if the side is three times bigger, the area will be 9 times bigger (3^2).

The area of the small triangle is 1000 m2, so the area of the bigger triangle is 9 * 1,000 = 9,000 m2

Answer:

B.) 13

C.) 0.6

Step-by-step explanation:

The order of operations to evaluate these expressions is as follows:

Parentheses

Exponents

Multiplication/Division

Addition/Subtraction

So, for B.)

\(9^\frac{1}{2}+\sqrt{25}-8\div2+3^2\)

This can be rewritten as
\(9^\frac{1}{2}+25^\frac{1}{2}-8\div2+3^2\)

Since there are no parentheses, evaluate the exponents first:

\(3+5-8\div2+9\)

Next, there are no multiplication steps, but there is one division:

\(3+5-4+9\)

To finish, evaluate from left to right:

\(3+5-4+9\\8-4+9\\4+9\\13\)

Follow the same pattern for C.)

\((\frac{1}{2})(\frac{3}{5})(2^3-6)\)

This expression can be rewritten as

\((1\div2)(3\div5)(2^3-6)\)

First, evaluate the expressions in the individual parentheses, keeping in mind the expression \((2^3-6)\) must be evaluated following the same pattern (evaluate the exponent before subtracting six):

\((.5)(.6)(8-6)\\(.5)(.6)(2)\)

To finish, evaluate from left to right:

\((.3)(2)\\.6\)

Hope that helps!

Answer:

$47.50

Step-by-step explanation:

75 times 30 is 2,250, so then we put back the decimal and its 22.50, add that to 25.00, your answer is 47.50

True

Step-by-step explanation:

explanation is written inside the attachment

Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

Answer:

39.3

Step-by-step explanation:

81.6 - 3 = 78.6

78.6 ÷ 2 = 39.3

Answer:

mean: 68

median: 76.5

mode: 23, 95

range: 93

Step-by-step explanation:

Put numbers in order:

17, 23, 23, 64, 67, 86, 95, 95, 100, 110

mean: sum of the terms / number of terms

sum of the terms: 17 + 23 + 23 + 64 + 67 + 86 + 95 + 95 + 100 + 110 = 680

number of terms: 10

680 / 10 = 68

median: number of terms / 2

10 / 2 = 5, 5th number on the list

17, 23, 23, 64, 67, 86, 95, 95, 100, 110

between 67 and 86 since its an even number data set

67 + 86 / 2 = 76.5

mode: the most occurring number

17, 23, 23, 64, 67, 86, 95, 95, 100, 110

- 17, 64, 67, 86, 100, 110 has 1 each

- 23 has 2

- 95 has 2

23 and 95 have the same reoccurring amount

range: max - min numbers

17, 23, 23, 64, 67, 86, 95, 95, 100, 110

110 - 17 = 93

NO outliers

Hope this helps you a little more for your last day of finishing hmw :)

Let me know if you need anymore help !

OR have questions

Answer:

Options (B), (D) and (E)

Step-by-step explanation:

In the figure attached, a triangle has been given with interior angles x, y and z and exterior angle as w.

By the exterior angle theorem,

"Exterior angle formed by extending one side of a triangle is equal to the opposite two interior angles."

Therefore, x° + y° = w°

Since measure of angle w is equal to the sum of two angles x and y,

So, w° > x°

Similarly, w° > y°

Therefore, Options (B), (D) and (E) are the correct options.

The number of prime factors of 3×5×7+7 is 3.

To find the number of prime factors, we need to calculate the given expression:

3×5×7+7 = 105+7 = 112.

The number 112 can be factored as 2^4 × 7.

In the first step, we factor out the common prime factor of 7 from both terms in the expression. This gives us 7(3×5+1). Next, we simplify the expression within the parentheses to get 7(15+1). This further simplifies to 7×16 = 112.

So, the prime factorization of 112 is 2^4 × 7. The prime factors are 2 and 7. Therefore, the number of prime factors of 3×5×7+7 is 3.

In summary, the expression 3×5×7+7 simplifies to 112, which has three prime factors: 2, 2, and 7. The factor of 2 appears four times in the prime factorization, but we count each unique prime factor only once. Thus, the number of prime factors is 3.

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The statement is true. The timing of observations is crucial for time series data, while it is not significant for cross-sectional data.

For time series data sets, the time at which each observation is made is crucial. Time series data involves collecting observations over a specific time period, where the order and timing of the observations hold significance. Time series data allows for the analysis of trends, patterns, and changes over time.

On the other hand, for cross-sectional data, the time at which each observation is made is not important. Cross-sectional data involves collecting observations at a single point in time, capturing a snapshot of different entities or individuals at that particular moment. The focus is on comparing different entities or variables, rather than analyzing changes over time.

Therefore, the statement is true. The timing of observations is crucial for time series data, while it is not significant for cross-sectional data.

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It would take approximately 4.77 seconds for a rider to travel from the bottom of the Ferris wheel to a point 10 vertical feet above the bottom.

To find the time it takes for a rider to travel from the bottom of the Ferris wheel to a point 10 vertical feet above the bottom, we can use the concept of arc length and angular velocity.

The arc length formula for a circle is given by:

s = rθ

Where:

s is the arc length,

r is the radius of the circle,

θ is the central angle (in radians).

In this case, we want to find the time it takes to travel a vertical distance of 10 feet, which corresponds to an arc length of 10 feet on the Ferris wheel.

Given that the radius of the wheel is 20 feet and it completes one revolution (2π radians) per minute, we can set up the following equation:

10 = 20θ

To find θ, we can rearrange the equation:

θ = 10 / 20

θ = 0.5 radians

Now, we need to convert the time from minutes to seconds. Since the wheel revolves at a rate of one revolution per minute, we know that in one minute, there are 60 seconds. Therefore, one revolution takes 60 seconds.

To find the time it takes for the rider to travel from the bottom to the desired point, we can calculate the proportion of the central angle (θ) to a full revolution (2π radians) and then multiply it by the time for one revolution (60 seconds).

t = (θ / (2π)) * 60

Plugging in the value for θ, we have:

t = (0.5 / (2π)) * 60

Calculating this expression gives us:

t ≈ 4.77 seconds

Therefore, it would take approximately 4.77 seconds for a rider to travel from the bottom of the Ferris wheel to a point 10 vertical feet above the bottom.

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The equation of the sequence:f(n) = -1/16n³ + 3/8n² - 11/48n + 1/2

The sequence is given as 3 2 , − 4 4 , 5 8 , − 6 16 , 7 32.

Let us examine the sequence to see if there is a pattern.

To begin, let us look at the first terms in each fraction:

3, -4, 5, -6, 7

The first differences of these terms is -7, 9, -11, 13

The second differences is 16, -20, 24.

The third differences is -36, 44.

If we examine the third differences, we can notice that the third differences are constant and equal to -36.

So the degree of the polynomial that generates the sequence is three or less.

To determine the equation that generates the sequence, we'll use the following method:

Since the sequence has degree 3 or less, we can use the general form:

f(n) = an³ + bn² + cn + d

We can use four points from the sequence to get four equations to solve for a, b, c, and d:

Let n = 1: f(1) = a + b + c + d

= 3/2

Let n = 2: f(2) = 8a + 4b + 2c + d

= -4/4

Let n = 3: f(3) = 27a + 9b + 3c + d

= 5/8

Let n = 4: f(4) = 64a + 16b + 4c + d

= -6/16

Solving these equations will give us the equation of the sequence:

f(n) = -1/16n³ + 3/8n² - 11/48n + 1/2

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AS per the unitary method, the number of freshmen majoring in chemistry are 162.

Unitary method:

Unitary method defied as a process of finding the value of a single unit, and based on the known values.

Given,

In a certain​ country, 9/50 of college freshmen major in chemistry. A community college in a region of the country has a freshman enrollment of approximately 900 students.

Here we need to find the the number of freshmen majoring in chemistry.

As per the concept of unitary method, let us consider x be the number of freshmen majoring in chemistry.

So, we know that, 9/50 of college freshmen major in chemistry.

The total number of students in the community colleges is 900.

Therefore, the number of freshmen in it is calculated as

x = 900 x 9/50

x = 18 x 9

x = 162

Therefore, there are 162 freshmen in chemistry.

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