a bag contains $10$ red marbles and $6$ blue marbles. three marbles are selected at random and without replacement. what is the probability that one marble is red and two are blue? express your answer as a common fraction.

The equation for getting the number of digits in a square root is (n + 1) / 2.

Given,

The number of digits in perfect square of a number = n

n is an odd number.

We have to find the number of digits in it’s square root.

Let’s check ,

If n is taken as 3, the smallest odd number,

Take a perfect square of 3 digits.

Let’s take 100.

Square root of 100 is 10 and has 2 digits.

That is, (3 + 1) / 2 = 4/2 = 2

Now, perfect square with 5 digits.

10000 and its square root is 100 which has 3 digits.

Here, we can get as:

(5 + 1) / 2 = 6/2 = 3

So, in case of n, we can write it as:

(n + 1) / 2 = number of digits in square root

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Given:

The equation is

\(-12+8y+12=7x\)

To find:

The constant of direct variation if the given equation represents direct variation.

Solution:

If y is directly proportional to x, then

\(y\propto x\)

\(y=kx\)            ...(i)

Where, k is the constant of proportionality.

We have,

\(-12+8y+12=7x\)

\(8y=7x\)

\(y=\dfrac{7}{8}x\)          ...(ii)

At x=0,

\(y=\dfrac{7}{8}(0)\)

\(y=0\)

The equation (ii) passes through (0,0). So, it represents a proportional relationship.

On comparing (i) and (ii), we get

\(k=\dfrac{7}{8}\)

Therefore, the constant of proportionality is \(k=\dfrac{7}{8}\).

Step-by-step explanation:

\(16 {x}^{2} - 25 = 0 \\ 16 {x}^{2} = 0 + 25 \\ 16 {x}^{2} = 25 \\ {x}^{2} = \frac{25}{16} \\ x = \sqrt{ \frac{25}{16} } \\ = 1.25 \: or \frac{5}{4} \: or1 \frac{1}{4} \)

Do note that this question might have two answers as Square roots will actually give you a positive and negative solution. Clarify with your teacher about this.

Answer:

x=0.09765625 or rounded up as 0.1

Step-by-step explanation:

first you have to add 25 to the 0 and subtract it from the sid it is on. making it look like this

16x²=25

256x=25

now divide both sides by 256 and you get

x=0.09765625 or rounded up as 0.1

Answer:

\(\left \{ {{a_1=1} \atop {a_n=a_{n-1}-5}} \right.\)

Step-by-step explanation:

The recursive formula of an arithmetic sequence is\(\left \{ {{a_1=x} \atop {a_n=a_{n-1}+d}} \right.\). Plugging in each value (\(a_1 = 1, d=-5\)) gives us the recursive formula  \(\left \{ {{a_1=1} \atop {a_n=a_{n-1}-5}} \right.\).

Answer:

5(5r - 6)

Step-by-step explanation:

25r - 30

we can factor out a 5 since 25 and 30 are both multiples of 5

so we get 5(5r - 6)

hope this helps!

ps i love ur pfp

The equation of the parabola in vertex form that passes through the points (-2, 4) and (1, 0):

y = -2(x + 1)^2 + 2

The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the vertex is (-1, 2), so we can write the equation as y = -2(x + 1)^2 + 2.

To find the vertex of the parabola, we can take the average of the x-coordinates of the two points, and then take the average of the y-coordinates of the two points. The average of the x-coordinates is (-2 + 1)/2 = -0.5, and the average of the y-coordinates is (4 + 0)/2 = 2. Therefore, the vertex is (-0.5, 2).

Once we know the vertex, we can find the value of a by substituting the vertex coordinates into the vertex form of the parabola. Substituting (-0.5, 2) into the equation y = a(x - h)^2 + k, we get 2 = a(-0.5 - (-1))^2 + 2. Simplifying, we get 2 = a(0.25) + 2. Solving for a, we get a = -2.

Plugging in a = -2 into the vertex form of the parabola, we get y = -2(x + 1)^2 + 2. This is the equation of the parabola in vertex form.

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The equation of the parabola in vertex form that passes through the points (-2, 4) and (1, 0):

y = -2(x + 1)^2 + 2

The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the vertex is (-1, 2), so we can write the equation as y = -2(x + 1)^2 + 2.

To find the vertex of the parabola, we can take the average of the x-coordinates of the two points, and then take the average of the y-coordinates of the two points. The average of the x-coordinates is (-2 + 1)/2 = -0.5, and the average of the y-coordinates is (4 + 0)/2 = 2. Therefore, the vertex is (-0.5, 2).

Once we know the vertex, we can find the value of a by substituting the vertex coordinates into the vertex form of the parabola. Substituting (-0.5, 2) into the equation y = a(x - h)^2 + k, we get 2 = a(-0.5 - (-1))^2 + 2. Simplifying, we get 2 = a(0.25) + 2. Solving for a, we get a = -2.

Plugging in a = -2 into the vertex form of the parabola, we get y = -2(x + 1)^2 + 2. This is the equation of the parabola in vertex form.

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Answer:

Question=Q

Q2=18.9

Q3=26.7

Q4=24.8

Q5=35.6

Here are some answers

Remember if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² - b²)

if leg b is unknown, then. b = √(c² - a²)

for hypotenuse c missing, the formula is. c = √(a² + b²)

Have a wonderful day!

we have proven that the average degree in a tree is always less than 2.

To prove that the average degree in a tree is always less than 2, we need to first understand what a tree is. A tree is an undirected graph that is connected and acyclic, meaning it does not contain any cycles. Each node in a tree has exactly one parent, except for the root node, which has no parent. The degree of a node in a tree is the number of edges that are connected to it. For the root node, its degree is equal to the number of edges that are connected to its children.

Now, let's consider a tree with n vertices. The total number of edges in a tree is always n-1, since each node except the root node has exactly one incoming edge, and the root node has no incoming edges. Therefore, the sum of the degrees of all the nodes in a tree with n vertices is equal to 2(n-1), since each edge is counted twice, once for each of the nodes it connects.

If we let d_i denote the degree of the i-th node in the tree, then the average degree of the tree can be expressed as:

(1/n) * sum(d_i) = (1/n) * 2(n-1)

Simplifying the right-hand side, we get:

(1/n) * 2(n-1) = 2 - (2/n)

As n approaches infinity, the average degree approaches 2, but for any finite value of n, the average degree is always less than 2. Therefore, we have proven that the average degree in a tree is always less than 2.

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The angle of elevation of the sun is decreasing at a rate of  \(0.25 rad/hr\) then the shadow is increasing at the rate = \(100ft/hr\)

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

The angle of elevation of the sun is decreasing at a rate = \(0.25 rad/hr\)

The height of the building = \(400 ft-tall\)

We need to find the rate at which the shadow is increasing

d/dθ = 1/4 rad/hr at θ = π/4  

So,

We can write,

\(\frac{400}{x}\) = tan θ

x = 400/ tan θ

Upon derivation with t

\(\frac{dx}{dt}\) = 400 sec²θ/tan ²θ dθ/dt

at θ = π/4 and dθ/dt  = \(0.25 rad/hr\)

\(\frac{dx}{dt}\) = \(400 (2*3) * 0.25\)

\(\frac{dx}{dt}\) = \(100ft/hr\)

Therefore,  

The angle of elevation of the sun is decreasing at a rate of  \(0.25 rad/hr\) then the shadow is increasing at the rate = \(100ft/hr\)

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Answer:

9.277

Step-by-step explanation:

It is an irrational number.

Explanation

Since area is length squared, length of a side of a rug is simply the square root of 86.

The square root of 86 is a rational number if 86 is a perfect square. It is an irrational number if it is not a perfect square. Since 86 is not a perfect square, it is an irrational number.

Hope this answer will help!

Since it is difficult to evaluate this integral exactly, use technology to approximate it. After calculation, the length is approximately 3.9205 (rounded to four decimal places).

To find the length of the function y =\(2x^(3/2)/3 - x^(1/2)/2\) over the interval [1, 4], you need to evaluate the integral of the square root of [1 + (y')^2] with respect to x, where y' is the derivative of y with respect to x.

First, find the derivative y':
y'(x) = d(2x^(3/2)/3 - x^(1/2)/2)/dx = x^(1/2) - 1/(4x^(1/2))

Now, find (y')^2:
\((y')^2 = (x^(1/2) - 1/(4x^(1/2)))^2\)
Next, find the square root of [1 + (y')^2]:
\(√[1 + (y')^2] = √[1 + (x^(1/2) - 1/(4x^(1/2)))^2]\)

Finally, evaluate the integral:
Length = \(∫(√[1 + (y')^2]) dx\) from x = 1 to x = 4

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Answer:

It's incorrect. there is no such thing as 120%

Step-by-step explanation:

No step problem

The common ratio only applies to the first portion of the sequence: 2, -4, 8, -16, 32, -64. For this portion, the common ratio is -2.

The given sequence is 2, -4, 8, -16, 32, -64, -2, -6, 6, 2. To determine the common ratio between successive terms in the sequence, we need to examine the ratio between each term and its preceding term.

In the sequence, each term is obtained by multiplying the preceding term by -2. The sequence alternates between positive and negative terms. From 2 to -4, we have -4/2 = -2 as the common ratio.

Similarly, from -4 to 8, we have 8/-4 = -2 as the common ratio. This pattern continues for all successive terms: the ratio between each term and its preceding term is -2.

However, it's important to note that the sequence provided seems to have a break after the term -64, and then continues with a different set of numbers: -2, -6, 6, 2.

Therefore, the common ratio only applies to the first portion of the sequence: 2, -4, 8, -16, 32, -64. For this portion, the common ratio is -2.

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Answer:

vertex is (6, -11)

Step-by-step explanation:

Given equation
f(x) = x² - 12x + 25

is that of an upward-facing parabola(since the coefficient of x² is positive).

The vertex will be at a minimum and its x-coordinate can be found by finding the first derivative of f(x), setting it equal to zero and solving for x

f'(x) = d/dx(x² - 12x + 25)

= 2x - 12

f'(x) = 0 ==> 2x - 12 = 0

2x = 12

x = 6

Substitute x = 6 in f(x) to get

f(6) = 6² - 12(6) + 25

= 36 - 72 + 25

= -11

So the vertex is at (6, -11)

The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12

An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.

To evaluate the integral:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)

We can integrate each term of the polynomial separately using the power rule of integration, which states that:

\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)

where C is the constant of integration.

So, we have:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)

Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):

\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)

Simplifying:

\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)

\($ = -\frac{1}{12} $\)

Therefore,

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)

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The ratio of basketballs to baseballs is 5 : 4 means out of 9 balls there are 5 basketballs and 4 baseballs.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

Written as quantity₁ ∝ quantity₂ or quantity₁ = kquantity₂

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

quantity₁ ∝ 1/quantity₂.

quantity₁ = K.1/quantity₂.

Given, The ratio of basketballs to baseballs is 5 : 4.

this means out of 9 balls there is 5 basketballs and 4 baseballs.

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Answer:

(B) -8

Step-by-step explanation:

Given the 2-column table below:

\(\left|\begin{array}{c|c}x&y\\--&--\\-3&14\\-1&10\\1&6\\4&0\\8&?\\10&-12\end{array}\right|\)

Taking the pair (-3,14) and (-1,10)

\(Slope, m=\dfrac{10-14}{-1-(-3)} =\dfrac{-4}{2} =-2\)

Taking the pair (1,6) and (4,0)

Slope, \(m=\dfrac{0-6}{4-1} =\dfrac{-6}{3} =-2\)

Since the slope is constant, the table represents a linear function whose slope is -2. Therefore:

Taking the pair (8,y) and (4,0)

Slope, \(m=\dfrac{0-y}{4-8} =-2\)

\(\dfrac{-y}{-4} =-2\\y=-2*4=-8\)

Therefore, the value of ? on the y-column is -8.

Answer:

-8

Step-by-step explanation:

In order to calculate the maximum loan amount the Rosens can afford, we can use the 28% rule of thumb..Down Payment + Points = 15% Down Payment + 3 Points Down Payment + Points = 15% x 113,500 + 3 Points

In order to calculate the maximum loan amount the Rosens can afford, we can use the 28% rule of thumb. This rule states that the total monthly mortgage payment (principal, interest, taxes, and insurance) should not exceed 28% of the Rosens’ adjusted monthly income. The adjusted monthly income is calculated by subtracting the total monthly payments for their car, boat, and furniture from their gross monthly income To calculate the maximum loan amount, we can use the following formula :Maximum Loan Amount = (Adjusted Monthly Income x 28%) - (Monthly Property Tax + Monthly Home Insurance)For the Rosens, the adjusted monthly income is 4750 - 420 = 4330. The maximum loan amount is then calculated as follows: Maximum Loan Amount = (4330 x 0.28) - (1200/12 + 320/12)Maximum Loan Amount = 1208 - 200 Maximum Loan Amount = 1008.The maximum loan amount the Rosens can receive is then calculated by subtracting the down payment and points from the maximum loan amount .Down Payment + Points = 15% Down Payment + 3 Points Down Payment + Points = 15% x 113,500 + 3 Points.

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Answer: 18

Step-by-step explanation:

Answer: $6085.15

Step-by-step explanation:

Substituting into the exponential decay formula yields \(9250(1-0.051)^8 \approx \$6085.15\).

f(x+h) = 2(x+h)^2 - 7(x+h) + 9

f(x+h) - f(x) = 4xh + 2h^2 - 7h.

hf(x+h) - f(x) = 2hx^2 + 4hx^2 + 2h^3 - 7hx - 7h^2 + 9h - 2x^2 + 7x - 9.

f(x+h) = 2(x+h)^2 - 7(x+h) + 9

Simplifying this expression, we get:

f(x+h) = 2(x^2 + 2xh + h^2) - 7x - 7h + 9

= 2x^2 + 4xh + 2h^2 - 7x - 7h + 9

So, f(x+h) = 2x^2 + 4xh + 2h^2 - 7x - 7h + 9.

f(x+h) - f(x), we subtract the value of f(x) from f(x+h):

f(x+h) - f(x) = (2x^2 + 4xh + 2h^2 - 7x - 7h + 9) - (2x^2 - 7x + 9)

f(x+h) - f(x) = 2x^2 + 4xh + 2h^2 - 7x - 7h + 9 - 2x^2 + 7x - 9

= 4xh + 2h^2 - 7h

So, f(x+h) - f(x) = 4xh + 2h^2 - 7h.

hf(x+h) - f(x), we multiply f(x+h) by h and subtract f(x) from the result:

hf(x+h) - f(x) = h(2x^2 + 4xh + 2h^2 - 7x - 7h + 9) - (2x^2 - 7x + 9)

Expanding and simplifying this expression, we get:

hf(x+h) - f(x) = 2hx^2 + 4hx^2 + 2h^3 - 7hx - 7h^2 + 9h - 2x^2 + 7x - 9

So, hf(x+h) - f(x) = 2hx^2 + 4hx^2 + 2h^3 - 7hx - 7h^2 + 9h - 2x^2 + 7x - 9.

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Drawing a 10 from the bag      unlikely

Rolling a number less than 5   Likely

Drawing a red marble             equally likely and unlikely

Here is the completed frequency table:

Number       frequency

1                       9

2                    12

3                    10

4                    8

5                    5

6                     6

Hiro's prediction is likely.

Probability determines the odds that a random event would happen. If the probability value is 0.5, it is equally likely and unlikely that the event would happen. If it is less than 0.5, it is unlikely that the event would happen. If it is greater than 0.5, it is likely that the event would happen.

Probability of drawing a 10 = number of 10s in the bag / total number in the bag = 1/100 = 0.01

It is unlikely that you would draw a 10.

Probability of rolling a number less than 5 = numbers that are less than 5 / total number of sides =  4/6 = 0.67

It is likely that a number less than 5 would be rolled.

Probability of drawing a red marble = total number of red marbles / total number of marbles = 8 / 16 = 0.5

It is equally likely and unlikely that a red marble would be picked

In order to determine the frequency, if the denominator of the relative frequency of the number is equal to 50, then the numerator is equal to the frequency. In the case where the denominator is less than 50, divide 50 by the number, multiply the quotient by the numerator in order to determine the frequency.

The frequency of 2 = (50 / 25) x 6 = 12

Number       frequency

1                       9

2                    (6 x 2) 12

3                    (1 x 10) 10

4                    (4 x 2) = 8

5                    (1 x 5) 5

6                     (3 x 2) 6

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Answer:

X - 24 = 29

X = 29 + 24

X = 53 degrees

Answer:

3x=96

Step-by-step explanation:

From the information given, you can write the following:

a+x=96 (1)

a=2x (2)

where a is the number of CDs that Sue has and x is the number of CDs that Gwen has.

You can replace 2 in 1 and you would have the following:

2x+x=96

3x=96

From this, you can isolate x to find its value:

x=96/3

x=32

According to this, the equation that could be used to find the number of CDs, x, that Gwen has is: 3x=96.

Answer:

-2

Step-by-step explanation:

\(y = - 2x\)

the line is going down meaning its a negative and to find the slope do rise over run

Answer:

30 hours

Step-by-step explanation:

so i did 396.10/ 17, and i got 23.3 then u divide his hourly pay by 699.00 and u got 30

The class intervals appropriate to use in creating a histogram of the data are 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130. The correct option is B.

A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.

The width of the intervals must be equal. This means that the difference between the lower bound and the upper bound must be equal. Also, the upper bound of the preceding interval must be the same as the lower bound of the next interval.

This means that the intervals must be overlapping. Of all the options, it is 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130 that satisfy both conditions.

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Answer:first option

Step-by-step explanation:

Answer:

it is 2mm long

Step-by-step explanation:

16x0.125=2 so it is 2mm long