For a one-tailed test (lower tail) with 22 degrees of freedom at 95% confidence, the value of t =

O -1.383

O 1.383

O -1.717

O -1.721

Answer:

Step-by-step explanation:

Approximately 234.33 seconds for a radio signal to travel from Earth to a space station on Mars.

To calculate the time required for a radio signal to travel from Earth to Mars, we need to divide the distance between Earth and Mars by the speed of light.

Given:

Distance between Earth and Mars = 7.03x10⁷ km

Speed of light = 3x10⁸ m/s

First, we need to convert the distance from kilometres to meters:

Distance between Earth and Mars = 7.03x10⁷ km = 7.03x10⁷ x 1000 m = 7.03x10¹⁰ m

Calculate the time using the formula:

Time = Distance / Speed

Time = 7.03x10¹⁰ m / 3x10⁸ m/s

Time = 7.03x10¹⁰ / 3x10⁸

Time = 234.33 seconds

Therefore, it would take approximately 234.33 seconds for a radio signal to travel from Earth to a space station on Mars.

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If Cara spends $2,000 a month, then she spends on $250 clothing

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

Clothing = 1/8

Total amount = $2000

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

Clothing = 1/8 of total amount

So, we have

Clothing = 1/8 of 2000

Evaluate the product

Clothing = 250

Hence, she spends on $250 clothing

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Question

Cara spent 1/3 of his monthly salary on rent, 1/4 on food, 1/6 on travelling and 1/8 on clothes.

If Cara spends $2,000 a month, how much does she spend on clothing?

Step-by-step explanation:

\(\bf a=2\cdot (1+2+3....224)+225\)

\(\bf a=2\cdot \big[(1+224)\cdot 224 : 2\big]+225\)

\(\bf a=2\cdot \big(225\cdot 224 : 2\big)+225\)

\(\bf a=2\cdot \big(225\cdot 112\big)+225\)

\(\bf a=2\cdot 25200+225\)

\(\bf a=50400+225\)

\(\bf a=50625\)

\(\red{\boxed{\bf a=225^{2} \implies ~patrat ~perfect}}\)

\(\bf \sqrt{a}=\sqrt{225^{2}} \implies \purple{\boxed{\bf a = 225}}\)

The solution to the recurrence relation an = 6an-1 - 8an-2 for n ≥ 2, with initial conditions a0 = 4 and a1 = 10, is an = 3(-2)^n - 4(-4)^n.

To solve the given recurrence relation, we start by finding the characteristic equation associated with it. The characteristic equation is obtained by substituting the general form an = r^n into the recurrence relation, where r is a constant.

Using the given recurrence relation an = 6an-1 - 8an-2, we substitute an = r^n:

r^n = 6r^(n-1) - 8r^(n-2).

Dividing both sides by r^(n-2), we get:

r^2 = 6r - 8.

Simplifying the equation, we have:

r^2 - 6r + 8 = 0.

Solving the quadratic equation, we find two distinct roots: r1 = 4 and r2 = 2.

The general solution to the recurrence relation is of the form:

an = A(4^n) + B(2^n),

where A and B are constants determined by the initial conditions. Plugging in the initial conditions a0 = 4 and a1 = 10, we can solve for A and B to obtain the specific solution.

Substituting n = 0 and n = 1, we have:

a0 = A(4^0) + B(2^0) = A + B = 4,

a1 = A(4^1) + B(2^1) = 4A + 2B = 10.

Solving these equations, we find A = 3 and B = -2.

Therefore, the solution to the recurrence relation is:

an = 3(-2)^n - 4(4)^n.

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Answer:

181.58 pics per month

Step-by-step explanation:

divide 1150 by 6.33

1150/6.33=181.58

It is called the y-coordinate

The point itself is called a coordinate, vertically, the vertical component of the coordinate is called the y-coordinate, while horizontally, the horizontal component of the coordinate is called the x-coordinate.

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The required time is mathematically given as

t-150 minutes.

This is further explained below.

We know that the volume of the prism is given by.

\(\text{Volume}=\text{(Base Area)}\times\text{height}\)

\(\text{Base Area}=\dfrac{1}{2}\times(1.4+0.6)\times2\)

\(\text{Base Area}=2\ \text{m}^2\)

Now,

\(\text{Volume}=2\times1=2\ \text{m}^3\)

Given that there is a twenty percent drop in the level of the pond during the first thirty minutes.

Because of this, the volume increases.

\(\text{Volume}=2\times0.8=1.6\ \text{m}^3\)

Now, the rate of emptying the tank is,

\(=\dfrac{2-1.6}{30} =\dfrac{1}{75} \ \text{m}^3/ \text{min}\)

In conclusion, We also know that,

$$

\(\text{time}=\dfrac{\text{volume}}{\text{rate}}\)

\(\text{time}=\dfrac{2}{\frac{1}{75} } =150 \ \text{min}\)

Therefore, Colin must wait for the pond to drain for a total of 150 minutes.

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The number of students in the entire class is 40.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

From the information given, when eating in the cafeteria at school, 65%, or 26, of the students in the class ate pizza.

Let the total number of people be illustrated as x.

This will be:

65% × x = 26

0.65x = 26

Divide

x = 26/0.65

x = 50

The total students is 40.

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The percent the students estimate's off is mathematically given as

y=40%

Question Parameters:

A student has a container with a volume of 0.5% liter. She estimates the volume to be 0.7 liter.

Generally the equation for the Percentage is  is mathematically given as

0.5+x=0.7

Therefore

x=0.2

Hence

y=0.3/0.5*100/1

y=40%

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Answer:

2.5

Step-by-step explanation:

\(h(t)=213 \\ \\ \implies -16t^2 +126t=213 \\ \\ 16t^2-126t+213=0 \\ \\ t=\frac{-(-126) \pm \sqrt{(-126)^2-4(16)(213)}}{2(16)} \\ \\ t \approx 2.46, 5.42\)

If we consider the graph, since height can't be negative, we only consider the first root.

Answer:

00059 or .0006

Step-by-step explanation:

You are trying to find what won't be in the water because there are many combinations so you use a complement formula.

1-0.79=0.29

Use the left over percentage in an equation to determine the probability.

The exponent 6 comes from the number of locations.

Answer:

A NOT C

Step-by-step explanation:

JKHMDSVCJDSAHVCDSVCJDSHG

Applying the altitude theorem and the Pythagorean theorem, the length of line segment BC to the nearest tenth is: C. 31.2 units

Recall:

First find DC using the altitude theorem:

x = DC

y = 5 units

h = 12 units

12 = √(5×DC)

12² = 5(DC)

144/5 = DC

DC = 28.8

Considering right triangle BDC, use Pythagorean theorem to find BC:

BC = √(DC²+BD²)

BC = √(28.8²+12²)

BC = 31.2 units

In summary, applying the altitude theorem and the Pythagorean theorem, the length of line segment BC to the nearest tenth is: C. 31.2 units

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Answer:

5

Step-by-step explanation:

5x 5 = 25

25-1= 24

24+3=27

27+27=54

Answer:

54

Step-by-step

5x 5 = 25

25-1= 24

24+3=27

27+27=54

On a circle with a radius of 4 and center at (0, 0), to find the x and y coordinates at an angle of 180 degrees (or π in radian measure), we can use the trigonometric functions.

At 180 degrees, the x-coordinate will be 0, as it lies on the y-axis. The y-coordinate can be found by using the sine function.  Using the equation y = r * sin(θ), where r is the radius and θ is the angle in radians, we can substitute the values. In this case, r is 4 and θ is π (since 180 degrees equals π radians).

Therefore, the x-coordinate is 0 and the y-coordinate is 4 * sin(π) = 0. So, the x-coordinate is 0 and the y-coordinate is also 0.
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To calculate the probability of obtaining 2 defective watches in a sample of 3 from a lot of 30 watches with a 20% defective rate, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = (n C k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k successes (in this case, 2 defectives),

n is the sample size (3),

k is the number of successes (2),

p is the probability of success (defective rate, 20% or 0.2), and

(1 - p) is the probability of failure (1 - 0.2 = 0.8).

Using these values, we can calculate the probability as follows:

P(X = 2) = (3 C 2) * (0.2)^2 * (0.8)^(3 - 2)

(3 C 2) represents the number of ways to choose 2 out of 3 watches, which is calculated as 3! / (2! * (3 - 2)!), which simplifies to 3.

P(X = 2) = 3 * (0.2)^2 * (0.8)^(3 - 2)

      = 3 * 0.04 * 0.8

      = 0.096

Therefore, the probability that a sample of 3 watches from the lot of 30 watches contains 2 defectives is 0.096 or 9.6%.

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Answer:

x = 24

Step-by-step explanation:

x/4 + 10 =16

      -10    -10

x/4 = 6

*4     *4

x=24

hope this helps! :)

Answer:

x=4.5

Step-by-step explanation:

Isolate the variable by dividing by each side by factors that don't contain the variable.

The probabilities are given as follows:

(a) an even number as the sum: 1/2.

(b) a total of at least 10: 1/6.

(c) same number on both dice i.e. a doublet: 1/6.

(d) a multiple of 3 as the sum: 1/3.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The 36 total outcomes when a pair of dice are thrown are given as follows:

The sum follows the pattern even, odd, ..., even, so there are 18 even sums and 18 odd sums, hence the probability of an even sum is given as follows:

p = 18/36 = 1/2.

There are six outcomes with a sum of at least 10, hence the probability is of:

p = 6/36 = 1/6.

There are six doblets, (1,1), (2,2), ..., (6,6), ..., hence the probability is given as follows:

p = 6/36 = 1/6.

There are 12 outcomes in which the sum is a multiple of 3, hence the probability is given as follows:

p = 12/36

p = 1/3.

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Answer:

1/16

Step-by-step explanation:

To find probiblity all you have to do is divide the number of events by the number of possible outcomes

There are 16 possible outcomes

and there is only 1` way that the student can get all 4 questions right

so the answer is: 1/16

Answer:

1/16

Step-by-step explanation:

Number of possible outcomes = 16

Only one set will be the correct option

P(getting all four questions correct) = 1/16

A group should consist of 13 people in order to ensure that at least two of the group members have birthdays that are in the same month.

Given:

This problem is an example of pigeonhole principle which states that If n+ 1 objects are placed into n boxes, then some box contains at least 2 objects.

Here no. of months in a year are boxes n = 12.

Therefore number of objects( people) = n+1= 13.

Then, at least two people  in the group whose birthdays fall in the same month.

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To find the maximum amount of money that an attorney can receive for different jury award sizes, we need to apply the given percentages based on the specified ranges.

To calculate the maximum amount an attorney can receive for a given jury award, we need to determine the applicable percentages for each range. For a jury award of $250,000, the first $150,000 is subject to a 40% percentage, which amounts to $60,000. The remaining $100,000 falls into the next range and is subject to a 33.3% percentage, resulting in $33,300. Adding these amounts together, the maximum amount the attorney can receive is $60,000 + $33,300 = $93,300.

Similarly, for a jury award of $350,000, the attorney can receive $60,000 + $50,000 (33.3% of $150,000) + $20,000 (30% of $200,000) = $130,000.

For a jury award of $560,000, the attorney can receive $60,000 + $50,000 + $60,000 (30% of $200,000) + $48,000 (24% of $200,000) + $32,000 (24% of $60,000) = $204,000.

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The response variable in this experiment is the scores on the midterm exam. The response variable is the one that is measured or observed to determine whether it has been affected by the explanatory variable.

The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.

The explanatory variable in this experiment is the type of music played in the background during the exam. The explanatory variable is the one that is deliberately manipulated or changed by the researcher in order to observe its effect on the response variable. In this case, the researcher wanted to investigate whether the type of music played during the exam would have an effect on the students' performance, so they manipulated the type of music and observed its effect on the exam scores.

The response variable in this experiment is the scores on the midterm exam. The response variable is the one that is measured or observed to determine whether it has been affected by the explanatory variable. In this case, the researcher measured the exam scores of the two groups to see if there was a difference between the group that listened to Dave Matthews Band and the group that listened to Death Cab for Cutie.

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Answer:  \(\frac{28}{27}\) or \(1\frac{1}{27}\)

Step-by-step explanation:

\(\frac{7}{9} /\frac{6}{8} = \frac{7}{9}(\frac{8}{6})\)

\(\frac{7}{9} (\frac{8}{6} ) = \frac{28}{27}\)

\(\frac{28}{27} = 1 \frac{1}{27}\)

Answer:

$18.48

Step-by-step explanation:

To find a percentage you just multiply the amount x the percentage in decimal form.

17 x 0.087 = 1.479 tax

Then you add that number too the original total.

17+1.479 = 18.479

Then you round to the nearest cent.

18.48

Total:

$18.48

Answer:

10

Step-by-step explanation:

Pythagorean theorem

c² = a² + b²

26² = a² + 24²

a² = 26² - 24² = 100

a = √(100) = 10

The length of unknown leg will be a = 10 units

The steps are as follow:

(hypotenuse)^2 = (Side)^2 + (Side)^2

(26)^2 = (24)^2 + (a)^2

676 = 576 + (a)^2

(a)^2 = 676 - 576

(a)^2 = 100

a = 10 units

So the length of unknown leg will be a = 10 units

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Gauss-Jordan elimination is a method used to solve a system of linear equations by reducing the augmented matrix of the system to a reduced row-echelon form through a series of elementary row operations.

The process involves manipulating the rows of the augmented matrix to obtain a triangular matrix, where all entries below the diagonal are zero. This is achieved by applying elementary row operations such as adding a multiple of one row to another row or multiplying a row by a scalar.

Once the augmented matrix is in triangular form, further elementary row operations are used to eliminate the nonzero entries above the diagonal. This results in the augmented matrix being in reduced row-echelon form, where the pivot elements are all equal to 1 and the columns corresponding to the pivot elements are linearly independent.

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The function that represents the given equation is:

f(x) = 3x + 8

The equation is -12x + 4y = 32. To solve for y as a function of x, we need to isolate y on one side of the equation.

Adding 12x to both sides, we get 4y = 12x + 32.

To solve for y, we divide both sides of the equation by 4. This gives us y = 3x + 8.

Hence, the function that expresses y as a function of x is:

f(x) = 3x + 8.

Using this function, we can determine the value of y corresponding to any given x value. For example, if we substitute x = 5 into the function, we have f(5) = 3(5) + 8 = 15 + 8 = 23. Therefore, when x is 5, y is 23 according to the function f(x) = 3x + 8.

In summary, the function f(x) = 3x + 8 represents the relationship between x and y in the given equation, allowing us to calculate the corresponding y value for any given x value.

Therefore, the function that represents the given equation is:

f(x) = 3x + 8

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Answer:

Janelle can ride her bike at a rate of 9.32 miles per hour

Step-by-step explanation:

15 kilometers is 9.32 miles