25 POINTS!! Which of the following shows the number 10,000 written as a number having just three significant digits?

A. 1.000 x 10 to the 4rd power
B. 1.00 x 10 to the 4th power
C. 1.0 x 10 to the 4th power
D. 1 x 10 to the 4th power

(a) Let "X" be the random variable that represents the time in minutes required to assemble the product.

(b) The random variable may assume the values in the interval (0, ∞).

(c) The random variable "X" is continuous in nature.

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Answer: k = √27-i

Step-by-step explanation:

$6273.04 have to deposit at the end of each of the next 5 years to fund this liability

PV of Annuity = P*[1-{\({1+i}^{n}\)}]/i

Where, P = Annuity = 12000, i = Interest Rate = 0.08, n = Number of Periods = 4

PV at 6 years from today = 12000*[1-{(1+0.08)^-4}]/0.08 = 12000*0.26497/0.08 = $39745.52

PV at 5 years from today = PV at 6 years from today/[1+Interest Rate] = 39745.52/[1+0.08] = $36801.41

FV of Annuity = P*[{\(1+i^{n}\)}-1]/i

Where, FV = 36801.41, i = Interest Rate = 0.08, n = Number of Periods = 5

Therefore,

36801.41 = P*[{(1+0.08)^5}-1]/0.08

2944.1127 = P*0.469328

Therefore, Amount to be deposited =

                                 P = 2944.1127/0.469328 = $6273.04

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Answer:

logx+log(x +1)= log6

Step-by-step explanation:

Please find attached photograph for your answer.

We are asked to find out whether the given lengths correspond to a right-angled triangle.

Recall that a right-angled triangle must satisfy the Pythagorean theorem.

Let us substitute the given values into the above formula

As you can see, the Pythagorean theorem is satisfied.

Therefore, the given lengths form a right triangle.

The pairs of lines are classified as: perpendicular, parallel, neither, neither.

The slopes of the first pair of lines differ, making them neither parallel nor perpendicular. The slopes of the first and second lines are 1/2 and -2, respectively.

The second set of lines is perpendicular because the slopes of the first line, which is -3, and the second line, which is 1/3, are the opposites of each other.

The third set of lines have varying slopes and are neither equal nor perpendicular. The slopes of the two lines are -2/3 for the first line and 6/4 for the second, which reduces to 3/2.

To classify each pair of lines as parallel, perpendicular, or neither, we need to compare their slopes.

2y = x and y = -2x + 6

The first equation can be written in slope-intercept form as y = (1/2)x, which means its slope is 1/2. The second equation can be written in slope-intercept form as y = -2x + 6, which means its slope is -2. Since the slopes are negative reciprocals of each other, these lines are perpendicular.

y + 3x = 1 and 2y = -6(x - 1)

The first equation can be written in slope-intercept form as y = -3x + 1, which means its slope is -3. The second equation can be written in slope-intercept form as y = -3x + 3, which means its slope is also -3. Since the slopes are the same, these lines are parallel.

3y + 2x = -3 and 4y = 6x + 12

The first equation can be written in slope-intercept form as y = (-2/3)x - 1, which means its slope is -2/3. The second equation can be written in slope-intercept form as y = (3/2)x + 3, which means its slope is 3/2. Since the slopes are not equal and not negative reciprocals of each other, these lines are neither parallel nor perpendicular.

y + 2 = 5x and 5y - x = -2

The first equation can be written in slope-intercept form as y = 5x - 2, which means its slope is 5. The second equation can be written in slope-intercept form as y = (1/5)x - 2/5, which means its slope is 1/5. Since the slopes are not equal and not negative reciprocals of each other, these lines are neither parallel nor perpendicular.

Therefore, the pairs of lines are classified as follows:

perpendicular

parallel

neither

neither

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The conditional using the hypothesis of the first conditional and the conclusion of the third conditional is: "If the hypothesis of the first conditional is true, then the conclusion of the third conditional is true."

In logic, a conditional statement consists of a hypothesis and a conclusion. The conditional statement asserts that if the hypothesis is true, then the conclusion must also be true. In this case, we are asked to construct a conditional statement using the hypothesis of the first conditional and the conclusion of the third conditional.

To determine the truth value of this conditional, we need to evaluate the validity of both the hypothesis and the conclusion. If the hypothesis of the first conditional is true and the conclusion of the third conditional is true, then the conditional statement would be true. However, if either the hypothesis or the conclusion is false, then the conditional statement would be false.

Without specific details about the hypotheses and conclusions involved, it is not possible to determine the truth value of this conditional statement. The truth value depends on the specific content and logical coherence of the statements being used.

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Answer:

GUESS: 55ft

Step-by-step explanation:

55 ft is my guess, not 100 percent sure but the math i did was 50% of 110

Answer:

84 ft

Step-by-step explanation:

The ground and the two ropes form a right triangle.

For the 50-deg angle, the height, h, is the opposite leg. The hypotenuse is the 110-ft side.

sin A = opp/hyp

sin 50° = h/110

h = 110 sin 50°

h = 84

Answer: 84 ft

The probability of the binomial distribution:

R

Copy code

sum(dbinom(0:15, size = 60, prob = 1/6))

To estimate the probability of rolling 15 or fewer sixes when rolling a die 60 times, we can use a normal approximation.

In this case, we can assume that rolling a six follows a binomial distribution with parameters n = 60 (number of trials) and p = 1/6 (probability of success, which is rolling a six).

To estimate the probability using a normal approximation, we need to calculate the mean (μ) and standard deviation (σ) of the binomial distribution and then use these values to approximate the probability using a normal distribution.

The mean of a binomial distribution is given by μ = n * p, and the standard deviation is given by σ = √(n * p * (1 - p)).

For this problem, we have n = 60 and p = 1/6. Therefore, μ = 60 * (1/6) = 10 and σ = √(60 * (1/6) * (1 - 1/6)) ≈ 2.5819.

To estimate the probability using the normal approximation, we can use the cumulative distribution function (CDF) of the normal distribution. We want to find P(X ≤ 15), where X is the number of sixes rolled.

Using R, we can calculate this probability using the pnorm() function with the parameters mean = μ and sd = σ:

pnorm(15, mean = 10, sd = 2.5819)

The true probability can be found by using the dbinom() function, which directly calculates the probability of the binomial distribution:

R

Copy code

sum(dbinom(0:15, size = 60, prob = 1/6))

By comparing the estimated probability using the normal approximation with the true probability calculated using the binomial distribution, we can assess the accuracy of the approximation.

Please note that the values obtained will depend on the specific version of R and its packages used, as well as the specific implementation details.

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The probability that a student selected randomly will have black or blond hair is 7/20.

Here, we are given that there is a group of 120 students. Further-

Number of students with black hair = 7

Number of students with blond hair = 35

Number of students with red hair = 12

Thus, the number of students with brown hair will be-

120 - 7 - 35 - 12

= 120 - 54

= 66

Now, the probability that a student selected randomly will have black or blond hair will be-

Number of students with black or blond hair/ total number of students

= (7 + 35)/ 120

= 42/ 120

= 7/ 20

Thus, the probability that a student selected randomly will have black or blond hair is 7/20.

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There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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Answer: -6r + 6

Hope this helps :)

Answer:

-6r + 6

Step-by-step explanation:

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ÷)

Answer:

-6

Step-by-step explanation:

From the given information, the probability of getting at least one head in two coin tosses is 3/4 or 0.75.

A coin toss is a random event in which a coin is flipped and the outcome is either heads or tails. The outcome of a coin toss is not dependent on any previous tosses, and each toss is considered to be independent of the others.

The probability of getting at least one head in two coin tosses can be calculated as follows:

There are four possible outcomes when tossing two coins: HH, HT, TH, and TT, where H represents heads and T represents tails. Out of these four outcomes, three have at least one head (HH, HT, TH), and only one has no heads (TT).

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A rational expression is a fraction with one or more variables in the numerator or denominator. To find the restricted values of x, we need to look for values of x that make the denominator of the fraction equal to zero. This is because division by zero is undefined in mathematics.

If the denominator of the rational expression is a polynomial, then we can set it equal to zero and solve for x to find the restricted values. However, if the denominator contains a square root or other non-polynomial terms, we may need to use algebraic manipulation to simplify the expression before we can identify the restricted values.

In order to determine the restricted values of x for a rational expression, we must look for values of x that make the denominator equal to zero. If the denominator is a polynomial, we can solve for x by setting it equal to zero and finding the roots. However, if the denominator contains non-polynomial terms, we may need to simplify the expression using algebraic manipulation before we can identify the restricted values. If there are no values of x that make the denominator equal to zero, then there are no restrictions on x.

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Answer:

It will take 1.6 hours for the two trains to be 336 miles apart.

Step by step explanation:

Given that:

Speed of eastbound train = 95 miles per hour

Speed of westbound train = 115 miles per hour

Combined speed = 95+115 = 210 miles

Distance = 336 miles

\(Speed = \frac{Distance}{Time}\\\\210 = \frac{336}{Time}\\\\Time = \frac{336}{210}\\\\Time = 1.6\ hours\)

Hence,

It will take 1.6 hours for the two trains to be 336 miles apart.

Answer:

42

Step-by-step explanation:

758 divided by 18 is 42.1 I just rounded down to 42

Answer:

42 pieces

Step-by-step explanation:

758/18 = 42.1 repeating

42 is the maximum amount of pieces

Answer:

-6

Step-by-step explanation:

-3-3=-6

Step-by-step explanation:

-3-|-3|

-3+3

0

-×-=+

hope that helps

The term 3x² in the quotient is the result of dividing 3\(x^{4}\) by x²

On dividing 3x^4 by x² we get the following by the long division method

x² | 3x^4 | 3x² --------> quotient

    -(3x^4)

    ______

         0

Thus the quotient is 3x² as mentioned in the question and the remainder is 0. Long division is a method to find out the quotient and remainders on dividing number, algebraic expression by another. As shown above, on the right-hand side we get the quotient and at the bottom, the remainder is obtained.

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Answer:

10 <√111 <11

Step-by-step explanation:

10 <√111 <11

Place given number between two consecutive integers: 10 <√111 <11

Answer: 10 <√111 <11

Answer:

112cm^2

Step-by-step explanation:

A=2(wl+hl+hw)=2·(2·8+4·8+4·2)=112

Answer: B. 64 cm³

Step-by-step explanation:

Let's lenth of the object set is a, width - b and height - h

Thus,

V=abh

a=8 cm   b=2 cm    h=4 cm

Hence,

V=8*2*4

V=64 cm³

Answer:

Option c.

Step-by-step explanation:

It is given that the piecewise function represents the Social Security taxes for 2009.

\(Tax=\begin{cases}0.062x & \text{ when } 0< x < 106,800 \\ \$6,621.60 & \text{ when } x > 106,800 \end{cases}\)

We need to find Rachel's security tax if she earned $102,000 in 2009.

Since 102,000 lies in \(0<x<106,800\), therefore

\(Tax=0.062x\)

Put x=102000.

\(Tax=0.062(102000)\)

\(Tax=6324\)

So, the Social  Security tax is $6324.

Therefore, the correct option is c.

Answer:These words are point, line and plane, and are referred to as the "three undefined terms of geometry".

The completing the square method is a method for solving a quadratic equation in the form of ax2 + bx + c = 0.

To solve a quadratic equation by completing the square, the equation must first be written in the form of ax2 + bx = -c. The next step is to add (b/2)2 to both sides of the equation. This will give the equation (ax2 + bx + (b/2)2 = -c + (b/2)2. Then, factor the left side of the equation as a perfect square. The equation should now be in the form of (x + (b/2a))2 = -c + (b/2)2 + (b/2a)2. The final step is to take the square root of both sides of the equation, resulting in x = -(b/2a) ± √(-c + (b/2)2 + (b/2a)2). This is the solution to the quadratic equation.

For example, consider the equation 2x2 + 8x = -4.

2x2 + 8x + (8/2)2 = -4 + (8/2)2

(2x + 4)2 = -4 + 16

2x + 4 = ±√20

x = -4 ± √20/2

Therefore, the solutions to the equation are x = -4 ± √5.

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The degree measure of < A is approximately 16 degrees when rounded to the nearest whole degree, the angle A is 90 degrees.

Given that AB = 24, BC = 7, and AC = 25, the degree measure of angle A has to be determined.

According to the Pythagorean theorem,

\(AB^2 + BC^2 = AC^224^2 + 7^2 = 25^2\)

=> 576 + 49 = 625

=> 625 = 625

Using the cosine law, we can rearrange the formula to find cos(C).

\(cos(C) = (a^2 + b^2 - c^2) / 2ab\)

Substitutes the specified value.

\(cos(C) = (24^2 + 7^2 - 25^2) / (2 * 24 * 7)\)

cos(C) = (576 + 49 - 625) / (336)

cos(C) = 0 / 336

cos(C) = 0

cos(C) = 0, which means that angle C is right (90 degrees). In a triangle, the angles sum to 180 degrees, so angle A is

Angle A = 180 degrees - 90 degrees

Angle A = 90 degrees

Therefore, the triangle is a right-angled triangle at B since the Pythagorean theorem has been satisfied.

Then, sin(A) = BC/ACsin(A) = 7/25

=> 0.28 (approx)A = \(sin^{-1(0.28)\)

=> 16 degrees (approx)

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There are no real solutions to the equation 0 = x² + 5, and the graph of y = x² + 5 does not intersect the x-axis.

To find the solutions of 0 = x² + 5, we need to find the values of x that make the equation true. One way to do this is by solving the equation algebraically using methods like factoring, completing the square, or using the quadratic formula.

We cannot use the graph of y = x² + 5 directly to find the solutions of 0 = x² + 5, since the graph shows the values of y that correspond to different values of x, not the values of x that satisfy the equation 0 = x² + 5. However, we can use the graph to help us visualize the solution to the equation.

Since 0 = x² + 5 is equivalent to x² = -5, we know that the solutions to the equation must be imaginary numbers, since the square of any real number is always non-negative. Therefore, there are no real solutions to the equation 0 = x² + 5, and the graph of y = x² + 5 does not intersect the x-axis.

In summary, we cannot use the graph of y = x² + 5 directly to find the solutions of 0 = x² + 5, but we can use the graph to see that the equation has no real solutions.

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Answer:

y=2/3x-6

Step-by-step explanation:

rise over run

starts at -6

The required equation of the line is y = 2x/3 - 6

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

Given that The graph of a linear equation passes through (0, -6) and (9,0).

We know that the equation of line passing through two point is;

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Therefore, y+6 = 6/9(x-0)

y = 2x/3 - 6

Hence, the required equation of the line is y = 2x/3 - 6

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Answer:

The main reason for the large population growth in Texas between 1850 and 1860 was __________.

a.

a large increase in the birth rate

b.

a large decrease in the death rate

c.

settlers moving in from other places

d.

all of the above

Please select the best answer from the choices provided

A

B

C

D

Step-by-step explanation: