Xavier has x dollars. This morning Alex had twice as much money as Xavier. After Alex spent three dollars on chips, he only had seven dollars left. How much money does Xavier have?

Eight people skiing downhill in a race can finish in 40,320 different orders.

Calculating probabilities for a set of possibilities keeping in account the order they are in is called permutation (\({n}_P_{r}\)).

If we overlook the order, it becomes a problem of combination (\({n}_C_{r}\)).

Permutation plays an important role in probability problems where the order of the possible outcomes is concerned. It does not allow repetition of outcomes.

Mathematically, permutation can be represented as:

\({n}_P_{r}=\frac{n!}{(n-r)!}\)

where 'n' represents the total objects/values/instances and 'r' represents our selected number of objects/values/instances.

In this case, we have total 8 drivers (n=8) and 8 positions we are selecting i.e. the order skiing people finish in (r=8);

\({n}_P_{r}=\frac{8!}{(8-8)!}=\frac{8!}{0!}=\frac{40320}{1}\)

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The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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The margin of error for this confidence interval is 3.8 grams, rounded to two decimal places.

The margin of error in a confidence interval is determined by half the width of the interval. In this case, the confidence interval is (2.3, 9.9) grams. To find the margin of error, we need to calculate half the width of the interval.

The width of the interval is found by subtracting the lower limit from the upper limit: 9.9 - 2.3 = 7.6 grams.

Since the confidence interval is symmetrical around the point estimate (which is the midpoint of the interval), the margin of error is half of the width: 7.6 / 2 = 3.8 grams.

Therefore, the margin of error for this confidence interval is 3.8 grams, rounded to two decimal places.

The margin of error represents the range within which the true population parameter is likely to fall. It indicates the level of uncertainty associated with the estimate and is influenced by the desired level of confidence. In this case, with a 99% confidence level, the margin of error is relatively large, suggesting a wider range of possible values for the average amount of salt consumed per day.

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Answer:

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Each figure adds four boxes to the bottom.

(1) The preceding figure, figure zero would have no rows of four and would thus just have two boxes.

(2) Each figure adds four boxes and started with two so

y(x)=4x+2

(3)

y(22)=4(22)+2

y(22)=88+2=90

Answer:

Volume = 7WH - (1/2)W^2H

Step-by-step explanation:

The base consists of the length (L) and the width (W).  It is rectangular, so the perimeter would be the sum of all four sides:

Perimeter = L + W + L +W,

or      Perimeter = 2L + 2W

We are told that 2L + 2W = 28cm     [The perimeter is 28 cm]

------

The volume of the box is given by:  

Volume = L*W*H     [Length x Width x Height]

=====

Let's rearrange the first equation and use it in the second:

2L + 2W = 28cm

2L = 28cm - 2W

L = (28cm - 2W)/2

L = (14 - W)

Now use this definition of L (14 - W) in the second equation:

Volume = L*W*H

Volume = (14 - W)/2)*W*H

Volume = (7-(1/2)W)*W*H

Volume = 7WH - (1/2)W^2H

This can also be written as:  Volume = WH(7 - (1/2)W)

If the series ∑an and ∑bn are both convergent series with positive terms, then the series ∑anbn is also convergent.

This can be proven using the Comparison Test for series convergence. Since an and bn are both positive terms, we can compare the series ∑anbn with the series ∑an∑bn.

If ∑an and ∑bn are both convergent, then their respective partial sums are bounded. Let's denote the partial sums of ∑an as Sn and the partial sums of ∑bn as Tn.

Then, we have:

0 ≤ Sn ≤ M1 for all n (Sn is bounded)

0 ≤ Tn ≤ M2 for all n (Tn is bounded)

Now, let's consider the partial sums of the series ∑an∑bn:

Pn = a1(T1) + a2(T2) + ... + an(Tn)

Since each term of the series ∑anbn is positive, we can see that each term of Pn is the product of a positive term from ∑an and a positive term from ∑bn.

Using the properties of the partial sums, we have:

0 ≤ Pn ≤ (M1)(Tn) ≤ (M1)(M2)

Hence, if ∑an and ∑bn are both convergent series with positive terms, then ∑anbn is also convergent.

Therefore, the given statement is True.

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Answer: A

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

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The simplified expression is given by (x² - 3x - 3) / ((x + 3)(x - 2)(x - 4)).

To simplify this expression, we need to find a common denominator for the two fractions and then combine them. To do this, we need to factor the denominators of both fractions.

Let's start with the first fraction's denominator:

x² + x - 6

We need to find two numbers that multiply to -6 and add to +1. These numbers are +3 and -2. Therefore, we can write:

x² + x - 6 = (x + 3)(x - 2)

Now let's factor the second fraction's denominator:

x² - 6x + 8

We need to find two numbers that multiply to 8 and add to -6. These numbers are -2 and -4. Therefore, we can write:

x² - 6x + 8 = (x - 2)(x - 4)

Now we can rewrite the original expression with a common denominator:

(x(x - 2) - (1)(x + 3)) / ((x + 3)(x - 2)(x - 4))

Next, we can simplify the numerator:

(x² - 2x - x - 3) / ((x + 3)(x - 2)(x - 4))

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

Finally, we can't simplify this expression any further. Therefore, the simplified expression is:

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

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Answer:

9.245 x 10^8

Step-by-step explanation:

To place a number into scientific notation count the number to decimal places there is between the original placement and the first single integer of the number

Answer:

100

Step-by-step explanation:

Multiply 10 by 10

Answer:

I think it is the last one .

Step-by-step explanation:

Hope this helps!

Sorry if I'm wrong.

Answer:

3/5

Step-by-step explanation:

Total= 2x + 2x + x= 5x

Total of Blue and yellow= 2x + x= 3x

So.. 3x/5x which is equivalent to 3/5

Answer: 600

Step-by-step explanation:

The solution of the given formula V = lwh for the variable w is V/lh.

According to the given question.

We have a formula.

V = lwh

Since, we have to solve this given formula V = lwh for the variable w.

Which means we have to write separate variable w to one side from the other variables which are in the given formua V = lwh .

Thereofre, the solution of the given formula V = lwh for the variable w is given by

V = lwh

⇒ V/l = wh      (dividing both the sides by l)

⇒ V/lh = w      (dividing both the side by h)

or w = V/lh

Hence, the solution of the given formula V = lwh for the variable w is V/lh.

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Answer:

5.86cm²

Step-by-step explanation:

Area of the shaded region = Area of the rectangle - Area of the circle

Area of rectangle = Length * Width

Area of rectangle = 3cm * 3cm

Area of rectangle = 9cm²

Area of the circle = πr²

Given radius r = 1cm

Area of the circle = 3.14(1)²

Area of the circle = 3.14cm²

Area of the shaded region = 9 - 3.14

Area of the shaded region = 5.86cm²

Answer:

5.86cm²

Step-by-step explanation:

Area of the shaded region = Area of the rectangle - Area of the circle

Area of rectangle = Length * Width

Area of rectangle = 3cm * 3cm

Area of rectangle = 9cm²

Area of the circle = πr²

Given radius r = 1cm

Area of the circle = 3.14(1)²

Area of the circle = 3.14cm²

Area of the shaded region = 9 - 3.14

Area of the shaded region = 5.86cm²

All veterinarians that responded to the questionnaire were included in the sample.

Complete Question : Veterinarians often use non-steroidal anti-inflammatory drugs to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the practice was in the United States. They obtained a list of all veterinarians treating large animals, including horses. They sent questionnaires to all the veterinarians on the list. Such a survey is called a census. The response rate was 40%. Which of the following statement is correct?

a. The sample consisted of all veterinarians on the list and therefore equaled the target population.

b. The sample consisted of all veterinarians who returned the questionnaire.

c. The sample consisted of all veterinarians who treat horses with NSAIDs.

d. None of the choices are correct.

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Factoring the sum or difference of cubes involves using specific formulas to simplify expressions.

The sum of cubes formula, a^3 + b^3 = (a + b)(a^2 - ab + b^2), and the difference of cubes formula, a^3 - b^3 = (a - b)(a^2 + ab + b^2), allow us to break down these expressions into more manageable factors.

To factor the sum or difference of cubes, you can use the following formulas:

Sum of Cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Cube difference: (a - b)(a - b)(a - b)(a - b)(a - b)

Sum of Cubes:

The sum of cubes formula states that the sum of two cubes, a^3 + b^3, can be factored into (a + b) multiplied by the quadratic expression a^2 - ab + b^2.

For example, let's factorize 8x^3 + 27:

We can identify a = 2x and b = 3, so using the sum of cubes formula:

8x^3 + 27 = (2x + 3)(4x^2 - 6x + 9)

Difference of Cubes:

The difference of cubes formula states that the difference between two cubes, a^3 - b^3, can be factored into (a - b) multiplied by the quadratic expression a^2 + ab + b^2.

For example, let's factorize 64y^3 - 125:

We can identify a = 4y and b = 5, so using the difference of cubes formula:

64y^3 - 125 = (4y - 5)(16y^2 + 20y + 25)

Factoring the sum or difference of cubes involves using specific formulas to simplify expressions. The sum of cubes formula, a^3 + b^3 = (a + b)(a^2 - ab + b^2), and the difference of cubes formula, a^3 - b^3 = (a - b)(a^2 + ab + b^2), allow us to break down these expressions into more manageable factors. Factoring such expressions can be useful in various algebraic calculations and simplifications.

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Answer:

-14°C

Step-by-step explanation:

Given that,

The mean temperature for the first 4 days in January was -4°C.

The mean temperature for the first 5 days in January was -6°C.

Mean = sum of observations/no. of observations

For first 4 days,

\(-4=\dfrac{S_4}{4}\\\\S_4=-16\ ...(1)\)

For first 5 days,

\(-6=\dfrac{S_4+T}{5}\\\\S_4+T=-30\ ..(2)\)

Let the temperature on 5th day is T. So,

Put S₄ = -16 in equation (2).

-16 + T = -30

T = -30+16

T = -14°C

So, the temperature on the 5th day is -14°C.

The solution:

Given:

Required:

Give the name of the given expression, and state the degree.

The given expression is a Polynomial (since it has 3 terms)

The degree is 4 because it has 4 as its highest power of the unknown)

Therefore, the correct answers are:

Name = polynomial

Degree = 4

The equivalent expressions are 7(2)^3x = 7(8)^x, 7(1/2)^x = 7(2)^-x, 7(4)^(3x + 1) = 7(2)^(6x + 2), 14(2)^x = 7(2)^(x + 1) and 14(2)^x = 14(4)^(x/2)

From the question, we have the following parameters that can be used in our computation:

The expressions on the left and those on the right

To do this, we solve the expressions on the left and look for a match

Using the above as a guide, we have the following:

(a) 7(2)^3x

Evaluate the exponent

7(2)^3x = 7(8)^x

(b) 7(1/2)^x

Apply the law of indices

7(1/2)^x = 7(2^-1)^x

So, we have

7(1/2)^x = 7(2)^-x

(c) 7(4)^(3x + 1)

Apply the law of indices

7(4)^(3x + 1) = 7(2^2)^(3x + 1)

So, we have

7(4)^(3x + 1) = 7(2)^(6x + 2)

(d) 14(2)^x and (e) 14(2)^x

Without solving them, we have

14(2)^x = 7(2)^(x + 1)

14(2)^x = 14(4)^(x/2)

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Answer:

The slope is -5/2 as a fraction

or -2.5 as a decimal.

Step-by-step explanation:

First we have to get it into this format y = mx + b

5x + 2y = 6 (subtract 5x on both sides)

2y = -5x + 6 (divide by 2 on both sides)

y = -5/2x + 3

The slope is -5/2 or -2.5

Hope this helps ya!!

Answer:

The area of sector is 4.71mi^2

Step-by-step explanation:

The area of the sector that Marla needs to remove is (3/2)π square feet.

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object. Area is measured in terms of standard areas. Therefore, they are relative to each other.

We normally use a square of unit length as its size. That unit can be 1 cm, 1 meter, etc.

Now when we want to find surface area of some object, then the value we get tells us that you can fit this many unit sided squares on that object's surface.

We are given that;

Central angle = 60°

The radius of the circle = 3 feet.

Now,

To find the area of the sector that Marla needs to remove, we can use the formula:

A = (θ/360)πr^2

where A is the area of the sector, θ is the central angle of the sector, r is the radius of the circle, and π is pi (approximately 3.14).

Plugging in the values we know, we get:

A = (60/360)π(3)^2 A

= (1/6)π(9) A

= (3/2)π

Therefore, the area of the fabric will be (3/2)π square feet.

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Answer (x + 7) • (x + 2) • (x - 3) • (x - 6)

The 95% confidence interval for the difference in population proportions of students who were consuming protein-rich food in 2000 and 2010 is (-0.111, -0.029).

What is confidence interval?

In statistics a confidence interval, usually refers to the probability that a population parameter may fall between a set of values for a certain proportion of times. The often use confidence intervals that contain either 95% or 99% of expected observations.

For constructing a 95% confidence interval for the difference in population proportions of students who were consuming protein-rich food in 2000 and 2010, can be determined by using the formula:

\(( p_{1} -p_{2} ) + z^{*} \sqrt{\frac{p_{1}(1-p_{1} ) }{n_{1} } +\frac{p_{2}(1-p_{2}) }{n_{2} }\)

and \(( p_{1} -p_{2} ) - z^{*} \sqrt{\frac{p_{1}(1-p_{1} ) }{n_{1} } +\frac{p_{2}(1-p_{2}) }{n_{2} }\)

where:

p₁ and p₂ implies that the sample proportions of students consuming protein-rich food in 2000 and 2010, respectively.

n₁ and n₂ = the sample sizes of the two years.

\(z^{*}\) is the critical value of the standard normal distribution corresponding to a 95% confidence level, which is  equals to 1.96.

Using the given data, we have:

p₁ = 0.75, n₁ = 700

p₂ = 0.82, n₂ = 850

Substituting these values into two formulae, we get:

\(( 0.75 -0.82) + 1.96\sqrt{\frac{0.75(1-0.75 ) }{700 } +\frac{0.82(1-0.82) }{850 }\)

\(( 0.75 -0.82) - 1.96\sqrt{\frac{0.75(1-0.75 ) }{700 } +\frac{0.82(1-0.82) }{850 }\)

Solving the above two expressions, we get:

-0.07 ± 0.041

Hence, rounded to three decimal places, the lower bound is -0.111 and the upper bound is -0.029.

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Answer:

B

Step-by-step explanation:

Answer:

$110

Step-by-step explanation:

APEX

The link between xn+1 and xn for all n ∈ N is xn+1 = 2xn - xn-1. The link between yn+1 and yn is yn+1 = 2yn - yn-1. The link between xn and x0 is xn = 2x0 - xn-1. The link between yn and y0 is yn = 2yn - yn-1.

The explicit formula for x1n, x2n, and x3n is as follows:

x1n = 2x10 - x1(n-1)

x2n = 2x20 - x2(n-1)

x3n = 2x30 - x3(n-1)

The sheep can jump to infinity in a bounded space of the plane if and only if the initial positions of M1, M2, and M3 form an equilateral triangle.

The link between xn+1 and xn can be found by considering the symmetry of the leapfrog game. When M1 jumps over M2, the new position of M1 is the mirror image of its previous position with respect to M2. This means that the x-coordinate of M1 will be the same as the x-coordinate of M2, but the y-coordinate will be the negative of the y-coordinate of M2.

The link between yn+1 and yn can be found by considering the symmetry of the leapfrog game. When M2 jumps over M3, the new position of M2 is the mirror image of its previous position with respect to M3. This means that the y-coordinate of M2 will be the same as the y-coordinate of M3, but the x-coordinate will be the negative of the x-coordinate of M3.

The explicit formula for x1n, x2n, and x3n can be found by using the recursive formulas for xn+1 and xn.

The condition for the sheep to jump to infinity in a bounded space of the plane can be found by considering the distance between the sheep. If the initial positions of M1, M2, and M3 form an equilateral triangle, then the distance between the sheep will remain constant. This means that the sheep will continue to jump forever, and they will never reach the boundary of the space.

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Answer:

121.5

Step-by-step explanation:

1.5 x 9 x 9 (the equation for volume (minus the 1/2 inch that Isaac's grandmother said to leave out) = 121.5

Answer:

Graph y=0.4x−3.6.

Slope: 0.4

y-intercept: (0,−3.6)

x    y  

0  −3.6

9    0

Graph AB.

Slope: 0

y-intercept: (0,0)

Plot each graph on the same coordinate system.

y=0.4x−3.6

AB

Step-by-step explanation: