what is the probability that at least two of the six members of a family are not born in the fall? assume that all seasons have the same probability of containing the birthday of a person selected randomly.

Answer:

x∈ [1; +∞)

Step-by-step explanation:

First write down the whole inequality:

1 - 3x ≤ -2 ﹤ 3x + 5

Then it can be seen that there are two separate inequalities here, so we have a system of inequalities:

{1 - 3x ≤ -2,

{3x + 5 ﹥ -2;

we express x from both inequalities:

From the first one:

-3x ≤ -2 - 1

-3x ≤ -3 / : (-3)

x ≥ 1

From the second one:

3x ﹥ -2 - 5

3x ﹥ -7 / : 3

[tex]x﹥ - \frac{7}{3} [/tex]

[tex]x﹥ - 2 \frac{1}{3} [/tex]

So, now that we have expressed x from both inequalities, we can write down the general range of x values for them (as you can see in the picture, the answer is the common values of x for both inequalities, both red and green colors):

x∈ [1; +∞)

Answer:

Step-by-step explanation:

error = 16 - 15 = 1 fluid ounce

percent error [tex]=\frac{1}{16} \times 100=\frac{100}{16}=6.25 \%[/tex]

Step-by-step explanation:

Find length b by using the Pythagorean theorem for right triangles

17^2 = 8^2 + b^2

b = 15

the area = L x W = 15 X 8 = 120 cm^2

Answer:

120

Step-by-step explanation:

Find out B- 17 squared- 8 squared ( square root) = 15

b = 15

8 X 15 = 120

we used the method of pythagoros - a squared + b squared = c squared

Have a nice day !

Answer:

Step-by-step explanation:

Step 1: Find the TV price:

£1200×(100%+20%)= £1440

Step 2: Find the final price Harry have to pay:

since he deposited £300 so the ammout he have to pay is:

£1440 - £300 = £1140

Step 3: Find the monthly payment

in this case he pays equally every month so we take the ammount he has to pay devided by 10 months

£1140÷10=£114

Conclusion: He has to pay £114 every month

It will take 32 hours for the water level to drop 2 feet.The rate of leaking is 0.40 cubic feet per minute.

To calculate how many hours it will take for the water level to drop 2 feet, we can use the following formula:Time (in hours) = Volume of water (in cubic feet) ÷ Rate of leaking (in cubic feet per minute)In this case, the volume of water is equal to the volume of the pool, which can be calculated using the formula V = l × w × h, where l is the length of the pool, w is the width of the pool, and h is the height of the pool. In this case, l = 24, w = 8, and h = 4, so the volume of the pool is V = (24)(8)(4) = 768 cubic feet.The rate of leaking is 0.40 cubic feet per minute.Therefore, the time (in hours) it will take for the water level to drop 2 feet is equal toTime (in hours) = 768 cubic feet ÷ 0.40 cubic feet per minute Time (in hours) = 1920 minutes Time (in hours) = 32 hoursTherefore, it will take 32 hours for the water level to drop 2 feet.

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The value of the addition of the two composite function is (x - 6) + √(x + 7).

A function in mathematics is a relationship between a set of possible outputs (the range) and a set of inputs (the domain), with the assets that each input is connected to exactly one output. By carrying out operations like addition, subtraction, multiplication, division, and composition with other functions, functions can be changed. By summing the results of the two functions f(x) and g(x), we may add them. In a similar manner, we may combine two functions, f(x) and g(x), by inserting the output of g(x) into f(x).

Given that f(x) = x - 6 and g(x) = √(x + 7).

The composite function (f + g)(x) is given as:

(f + g)(x) = f(x) + g(x)

= (x - 6) + √(x + 7)

Hence, the value of the addition of the two composite function is (x - 6) + √(x + 7).

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-1

To use regrouping to solve, we need to add and subtract the numbers in the expression, taking care to keep track of any negative signs.

10 - 1 - 1 - 6 - ² - 2

= 10 - (1 + 1) - 6 - ² - 2 [Group the first two numbers together and add them]

= 10 - 2 - 6 - ² - 2 [Simplify the first three terms]

= (10 - 2) - 6 - ² - 2 [Group the first two terms together and subtract them]

= 8 - 6 - ² - 2 [Simplify the first two terms]

= 2 - ² - 2 [Simplify the first two terms]

= -1 [Simplify the expression by subtracting ² and 2 from -1]

Therefore, the final answer is -1.

Answer:

A) 6; B) 29∘; C) 29∘; D) 151∘

Step-by-step explanation:

A) Since ∠3 = ∠5 (opposite angles), we can make an equation:

5x - 1 = 3x + 11

5x - 3x = 11 + 1

2x = 12 / : 2

x = 6

B) ∠3 = 5x - 1 (x = 6)

∠3 = 5 × 6 - 1 = 29∘

C) ∠3 = ∠1 = 29∘ (cross angles)

D) ∠2 = 180∘ - ∠1 = 180∘ - 29∘ = 151∘

The probability of a person being randomly choosing having waiting time greater than 4.25 is 0.2917 or 29.17%.

To answer this question we need to know about-

Probability is the measure of the likelihood of an event to happen. The probability value ranges between 0 and 1.

When the probability value is 0, it means that the event is impossible to happen.

When the probability value is 1, it means that the event is certain to happen.

Uniform distribution is when the values of a probability distribution are spread uniformly across the interval, it is called a Uniform distribution

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes.

The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is found as follows:

Let X = Waiting time of a randomly selected passenger P(X > 4.25) = ?

Now we have to use the uniform distribution formula to find the probability:

P(C< X >D)=C-D/B-A

where C = lower value of the selected interval

           D= upper value of the selected interval

           B= highest value of the selected interval

           A= lowest value of the selected interval

putting above values in the formula -

P(X > 4.25) = 6 - 4.25/6-0= 0.2917

Hence the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.2917.

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Answer:

Step-by-step explanation:

the answer is 785.51

After re-financeing his home loan, Garrets mortage payment is 30 percent less that it used to be the value of Garretts monthly payment now is 2191.

A hypothec loan, also known as a mortgage loan, is a type of loan that is commonly used by real estate purchasers to secure funds for the purchase of property, or by property owners seeking to obtain funds for any purpose, while simultaneously placing a lien on the property being mortgaged. In essence, a mortgage can be described as a situation where a borrower provides collateral in exchange for a loan.

we need to find how much is Garretts monthly payment now:

therefore first we need to find 30% of 3130 that is,

30 x 3130/100 = 939

now we need to subtract this value from the originally mortgage amount

therefore, 3130 - 939 = 2191

therefore, the value of Garretts monthly payment now is 2191.

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The correct option - d. control.  After identifying the variables that are independent and dependent in an experiment, we can decide what to do with the remaining variables. We are diminishing "control" if we keep everything else constant.

Something kept constant or constrained in a research study is referred to as a control variable. Although not being relevant to the study's goals, this variable is controlled since it could have an impact on the results.

Thus, after identifying the variables that are independent and dependent in an experiment, we can decide what to do with the remaining variables. We are diminishing "control" if we keep everything else constant.

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Answer:

1536 in^3.

Step-by-step explanation:

Volume = 1/3 * area of base * height

             = 1/3 * 256 * 18

             = 1536 in^3.

Answer:

(a) To determine the linear function that predicts the number of calculators sold at a given price, we need to find the equation of the line that passes through the points (98, 11,000) and (93, 13,150).First, we can find the slope of the line using the formula:slope = (change in y) / (change in x)slope = (13,150 - 11,000) / (93 - 98)slope = -430 per 1 dollar decrease in price(Note that we can interpret the negative slope as an inverse relationship between price and quantity demanded. As price decreases, the quantity demanded increases.)Next, we can use the point-slope form of a line to find the equation of the line:y - y1 = m(x - x1)where y1 = 11,000, x1 = 98, and m = -430.y - 11,000 = -430(x - 98)Simplifying and solving for y, we get:y = -430x + 51,340Therefore, the linear function that predicts the number of calculators sold at a given price is:y = -430x + 51,340(b) To predict the number of calculators that would be sold each week at a price of $73, we can substitute x = 73 into the linear function we found in part (a):y = -430(73) + 51,340y = 18,140Therefore, we predict that 18,140 calculators would be sold each week at a price of $73.

Answer:

B. 4/9

Step-by-step explanation:

We can simplify the given expression by finding a common denominator for 18 and 12. The least common multiple of 18 and 12 is 36.

Multiplying the first fraction 5/18 by 2/2 (which equals 1) to get a denominator of 36:

5/18 = 5/18 x 2/2 = 10/36

Multiplying the second fraction 2/12 by 3/3 (which equals 1) to get a denominator of 36:

2/12 = 2/12 x 3/3 = 6/36

Now we can add the two fractions with the same denominator:

10/36 + 6/36 = 16/36

We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 4:

16/36 = 4/9

Therefore, the solution is B) 4/9.

Answer:

the answer for the question is b) 4/9

The coaster starts at a height of 250, then drops down to 0 at x=500, and then rises back up to a height of 250. The bump is located at x=500 and is the highest point on the coaster.

y = -0.0005(x-500)² + 250

The coaster starts at the highest point (y=250) when x=0 and then drops down to x=500 by following the equation y=ax(x-1000). To create the bump, we need to make the coaster rise before it falls, so we use a quadratic equation that has a vertex at x=500 and y=250 (the initial height).

The equation y = -0.0005(x-500)² + 250 is a downward-facing quadratic equation with a maximum value of y=250 at x=500. This means that as the coaster approaches x=500, it starts to rise, and then falls down again. The coefficient -0.0005 controls the steepness of the coaster's drop and the height of the bump.

Here's a graph of the coaster:

         ^

       260|                               *

          |                          *    

          |                     *  

          |                *    

          |            *  

 height   |        *      

          |     *          

          |  *            

        0 +--------------->

            0      500    1000   x-axis

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Answer:

Step-by-step explanation:

35.5

The x-intercepts of the function are x₁ = 1, x₂ = 6.

Any equation of the form [tex]\rm ax\²+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

To find the zeros, we need to solve the equation f(x) = 0. We can use the quadratic formula for this, which is given by:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c.

[tex]x = (-(-21) \pm \sqrt{((-21)^2 - 4(3)(18))) / 2(3)}\\\\x = (21 \pm\sqrt{(441 - 216)) / 6}\\\\x = (21 \pm\sqrt{(225)) / 6}\\\\x_1 = 1 \ \rm and \ x_2 = 6[/tex]

Therefore, the zeros of the function f(x) are x₁ = 1 and x₂ = 6.

To find the x-intercepts, we need to plot the graph of the function and look for the points where the graph intersects the x-axis. We can start by plotting a few points to get a rough idea of the shape of the graph:

When x = 0, f(x) = 1

When x = 1, f(x) = 0

When x = 2, f(x) = 0

When x = 3, f(x) = 0

When x = 4, f(x) = 6

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Answer:

700 cm

Step-by-step explanation:

Mutiply the value by 100.

The solution curve represents a spiral that converges towards the origin.

(a) To classify the behavior of the system, we can use the (A,T) chart. Here, A is the sum of the elements in each row of the system matrix and T is the sum of the absolute values of the off-diagonal elements.

The system matrix for this scenario is:

[ 0   1 ]

[-1   1 ]

So, A = 1 for both rows, and T = 1 (absolute value of the off-diagonal element).

Using the (A,T) chart, we can see that the system is a focus.

(b) To find the eigenvalues and eigenvectors of the system, we need to solve the characteristic equation:

| 0-lambda  1       |   |u|    |0|

| -1        1-lambda| [tex]\times[/tex] |v| =  |0|

Expanding the determinant, we get:[tex]\lambda^2[/tex] -[tex]\lambda[/tex] + 1 = 0

Solving for lambda using the quadratic formula, we get:[tex]\lambda[/tex] = (1 +/- sqrt(3)i) / 2

So, the eigenvalues are complex conjugates with a real part of 1/2. The eigenvectors can be found by solving the system of linear equations:(0 - lambda)u + v = 0

(-1)u + (1 - lambda)v = 0

For lambda = (1 + sqrt(3)i) / 2, we get:u = [1, -1 + sqrt(3)i]

For lambda = (1 - sqrt(3)i) / 2, we get:u = [1, -1 - sqrt(3)i]

(c) To sketch the solution curve that starts at R(0) = 1, J(0) = 1, we can use the eigenvectors and eigenvalues. The general solution for the system can be written as:[x(t), y(t)] = [tex]c_1 \times u_1 \times e^(l \ambda1 \times t) + c2 \times u2 \times e^(\lambda2 \times t)[/tex]

where c1 and c2 are constants determined by the initial conditions, u1 and u2 are the eigenvectors, and lambda1 and lambda2 are the eigenvalues.

Plugging in the values, we get:

[tex][x(t), y(t)] = c_1 \times [1, -1 +\ sqrt(3)i] \times e^{((1 + \sqrt(3)i)t} / 2) + c_2\times [1, -1 - \sqrt(3)i] \times e^{((1 - \sqrt(3)i)t} / 2)[/tex]

Using the initial condition R(0) = 1, J(0) = 1, we get:

[tex]c_1 + c_2 = 1[/tex]

(-1 + sqrt(3)i)c1 + (-1 - sqrt(3)i)c2 = 1

Solving for [tex]c_1[/tex] and [tex]c_2[/tex], we get:

[tex]c_1[/tex] = (1 + sqrt(3)i) / (2[tex]\times[/tex] sqrt(3)i)

[tex]c_2[/tex]= (1 - sqrt(3)i) / (2 [tex]\times[/tex] sqrt(3)i)

Plugging in these values, we get:

[x(t), y(t)] = [1, 0] [tex]\times[/tex] e^((1 + sqrt(3)i)t / 2) + [0, 1] [tex]\times[/tex]  e^((1 - sqrt(3)i)t / 2)

This solution curve represents a spiral that converges towards the origin.

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The translation of circle A to circle B is achieved using the translation rule

The scale factor of Circle A to Circle B is 2

In geometry, translation refers to a transformation that moves an object in a straight line without changing its size, shape, or orientation.

This movement is done by sliding the object along a line, which is called the axis of the translation.

The scale factor is solved by comparing the diameter

Circle A has diameter of 2 units

Circle B has diameter of 4 units

let the scale factor be k

diameter of circle A * k = diameter of circle B

2 * k = 4

k = 4 / 2

k = 2

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Answer:

(3x^3)(8x + 1)

= (3x^3)(8x) + (3x^3)(1)

= 24x^4 + 3x^3

= 3x^3(8x + 1) + 24x^2 - 24x^2 + 3x^3

= 3x^3(8x + 1) - 24x^2 + 3x^3

= 24x^4 - 24x^2 + 3x^3

= 3x^3 + (-24x^2 + 24x^4)

Step-by-step explanation:

The equation to determine the original price per pound is 3(x + 0.75) = 5.88, where x is original price per pound. so, the original price is  $1.21.

Let x be the original price per pound of apples.

When the price increased, the new price became x + 0.75.

Sam bought 3 pounds of apples at the new price for a total of $5.88. This can be expressed as:

3(x + 0.75) = 5.88

Expanding the left side of the equation, we get:

3x + 2.25 = 5.88

Subtracting 2.25 from both sides, we get:

3x = 3.63

Dividing by 3, we get:

x = 1.21

Therefore, the original price per pound of apples was $1.21.

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The area of the equilateral triangle with a side length of 8 cm is 16√(3) cm².

To find the altitude of an equilateral triangle with a side length of 8 cm, we can use the Pythagorean theorem.

The Pythagorean theorem is states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In these triangles, the side opposite the 60-degree angle is half the length of the hypotenuse, which is 8 cm. Using the Pythagorean theorem, we can find that the length of the altitude is:

Altitude = √(8² - (4²)) = √(48) = 4√(3)

Now that we know the altitude, we can plug it into the formula for the area of a triangle:

Area = (base x height) / 2 = (8 x 4√(3)) / 2 = 16√(3) cm²

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The products of 2.1.1 x(x-1) 2.1.2 (-3)(x² + 3x + 9) is -3x² - 9x - 27

2.1.1 x(x-1) can be simplified using the distributive property of multiplication:

x(x-1) = xx - x1 = x^2 - x

2.1.1 x(x-1):

Expanding the expression x(x-1) using the distributive property:

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

Therefore, the product of 2.1.1 is:

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

2.1.2 (-3)(x² + 3x + 9):

Expanding the expression (-3)(x² + 3x + 9) using the distributive property:

(-3)(x² + 3x + 9) = -3x² - 9x - 27

Therefore, the product of 2.1.2 is:

(-3)(x² + 3x + 9) = -3x² - 9x - 27

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(a) The discriminant is positive (25)

(b) The quadratic equation has two zeros.

(c) The type of the zeros is real and distinct.

The given quadratic equation is: x² - 7x + 6 = 0

To find the discriminant, we use the formula:

Discriminant = b² - 4ac

Here, a = 1, b = -7, and c = 6.

So, the discriminant is:

b² - 4ac = (-7)² - 4(1)(6) = 49 - 24 = 25

Therefore, the discriminant is 25.

To determine the number of zeros, we use the discriminant as follows:

Here, the discriminant is positive (25), so the quadratic equation has two real and distinct roots.

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The required answers are Part A: Domain: {n | n is a positive integer}, Part B: 12, Part C: 0.98 cm/day.

Part A:

To plot the growth function f(n), we need to consider a reasonable domain that includes all relevant values of n. Since we are dealing with the growth of a plant, the domain should only include positive integers, as it does not make sense to talk about fractional or negative days. Therefore, a reasonable domain to plot the growth function would be:

Domain: {n | n is a positive integer}

Part B:

The y-intercept of the graph of the function f(n) is the value of f(0), which can be found by substituting n = 0 into the equation:

[tex]$f(0) = 12(1.03)^0 = 12(1) = 12[/tex]

Therefore, the y-intercept of the graph represents the initial height of the plant, which is 12 cm.

Part C:

The average rate of change of the function f(n) from n = 3 to n = 10 can be found using the formula:

Average rate of change = (f(10) - f(3))/(10 - 3)

We can evaluate f(10) and f(3) using the given equation:

f(10) = 12(1.03)^10 ≈ 18.27

f(3) = 12(1.03)^3 ≈ 13.41

Substituting these values into the formula, we get:

[tex]$Average rate change=\frac{(f(10) - f(3))}{10-3} \approx0.98[/tex]

Therefore, the average rate of change of the function f(n) from n = 3 to n = 10 is approximately 0.98 cm/day. This represents the average daily growth rate of the plant during this period.

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Answer: 0.000012

Step-by-step explanation: The exponent is -5, making it 10 to the power of negative 5. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 5 times

1.2 -> 0.000012