Calculate the density of benzene if 0.10L has a mass of 36.4g.

Answer:

1 and 5

Step-by-step explanation:

So basically corresponding angles are the angles which lie on the same line of the transversal

And also one of them will be an interior angle and the other a exterior angle

Answer:

D

Step-by-step explanation:

The limit is finite and non-zero, the series Σ((-1)^(11n - 3))/(10n + 3) is divergent by the nth term test.

To test the convergence or divergence of the series Σ((-1)^(11n - 3))/(10n + 3) from n = 1 to infinity, we need to find the limit of the expression (11n - 3)/(10n + 3) as n approaches infinity.

To determine the highest power of n in the fraction, we can observe the exponents of n in the numerator and denominator. In this case, the highest power of n is n^1.

Let's calculate the limit:

lim(n→∞) [(11n - 3)/(10n + 3)]

To find the limit, we can divide the numerator and denominator by n:

lim(n→∞) [(11 - 3/n)/(10 + 3/n)]

As n approaches infinity, the terms with 3/n become negligible, and we are left with:

lim(n→∞) [11/10]

The limit evaluates to 11/10, which is a finite value.

Since the limit is finite and non-zero, the series Σ((-1)^(11n - 3))/(10n + 3) is divergent by the nth term test.

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Answer:

\( \frac{ {x} + 9}{x - 4} \)

Step-by-step explanation:

\( \frac{ {x}^{2} + 5x - 36}{ {x}^{2} - 16} \\ \\ = \frac{ {x}^{2} + 9x - 4x- 36}{ {x}^{2} - {(4)}^{2} } \\ \\ = \frac{ x({x} + 9) - 4(x + 9)}{ (x + 4)(x - 4) } \\ \\ = \frac{ ({x} + 9) \cancel{(x - 4)}}{ \cancel{(x + 4)}(x - 4) } \\ \\ = \frac{ {x} + 9}{x - 4} \)

The probability of no Hispanic being selected is 0.0496 (rounded to four decimal places).

Probability is a branch of mathematics that deals with the study of random events or experiments, and the likelihood or chance of their occurrence. It is a measure of the degree of certainty or uncertainty of an event, expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event is certain to occur.

We can model the number of Hispanics selected as jurors with a binomial distribution, where n=8 is the number of trials (selecting jurors), and \($p=0.44$\) is the probability of success (selecting a Hispanic juror).

The probability of selecting no Hispanic jurors is given by:

\($P(X=0) = \binom{8}{0}(0.44)^0(1-0.44)^8 \approx 0.0496$\)

So the probability of no Hispanic being selected is 0.0496 (rounded to four decimal places).

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The probability of no Hispanic being selected is 0.0496 (rounded to four decimal places).

Probability is a branch of mathematics that deals with the study of random events or experiments, and the likelihood or chance of their occurrence. It is a measure of the degree of certainty or uncertainty of an event, expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event is certain to occur.

We can model the number of Hispanics selected as jurors with a binomial distribution, where n=8 is the number of trials (selecting jurors), and \($p=0.44$\) is the probability of success (selecting a Hispanic juror).

The probability of selecting no Hispanic jurors is given by:

\($P(X=0) = \binom{8}{0}(0.44)^0(1-0.44)^8 \approx 0.0496$\)

So the probability of no Hispanic being selected is 0.0496 (rounded to four decimal places).

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Answer:

a. See attachment 2

b. Scale factor is 1/4

Step-by-step explanation:

See attachment 1 for complete question

Given

Original

\(Height = 5\)

\(Width = 10\)

\(Center = 4\)

Scaled Copy

\(Height = 1.25\)

\(Width = 2.5\)

\(Center = 1\)

Solving (a): Corresponding Points & Sides

The corresponding points of the original copy to the scaled copy can be gotten by writing out the measurements as : (x,y)

Where x represents the original and y represents the scaled copy

Taking the height as a point

We have:

\(Height: (5,1.25)\)

This will be represented as a dot or point.

A dot at the tip of the line representing height in the original and scaled copy can be colored green

And the width and center as sides

We have:

\(Width: (10,2.5)\)

\(Center = (4,1)\)

These will be represented by lines

For width:

Two lines representing width in the original and scaled copy respectively can be colored yellow

For center:

Two lines representing center in the original and scaled copy respectively can be colored red

See attachment

Solving (b): The scale factor

To solve for the scale factor, we simply divide the measurement of the scaled copy by the original copy

Recall that:

\(Height: (5,1.25)\)  ,  \(Width: (10,2.5)\)   and   \(Center = (4,1)\)

Using Height:

\(Scale\ Factor = \frac{1.25}{5}\)

This gives:

\(Scale\ Factor = \frac{1}{4}\)

For width:

\(Scale\ Factor = \frac{2.5}{10}\)

This gives:

\(Scale\ Factor = \frac{1}{4}\)

For the center:

\(Scale\ Factor = \frac{1}{4}\)

Hence, the scale factor is 1/4

In the given research hypothesis that proposes that consuming low carbohydrate diets results in increased weight loss, the dependent variable will be the average number of pounds lost per person.

What is the dependent variable?The dependent variable is defined as the variable that is affected by the independent variable or experimental conditions. In other words, it is the variable whose changes are observed and measured based on the changes in the independent variable. In this given research hypothesis, the independent variable is the carbohydrate content of the diet, i.e. low-carb diet and high-carb diet.The dependent variable will be the average number of pounds lost per person, which is being compared between the two groups of people following low-carb and high-carb diets.

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Answer:

None of the given points satisfy the inequality 2x - 3y < 1.

Step-by-step explanation:

To determine which points satisfy the inequality 2x - 3y < 1, we can substitute the coordinates of each point into the inequality and check if the inequality holds true.

Let's consider the given points:

Point A: (1, 0)

2(1) - 3(0) < 1

2 - 0 < 1

2 < 1 (False)

Point B: (-1, -1)

2(-1) - 3(-1) < 1

-2 + 3 < 1

1 < 1 (False)

Point C: (3, -2)

2(3) - 3(-2) < 1

6 + 6 < 1

12 < 1 (False)

None of the given points satisfy the inequality 2x - 3y < 1.

Therefore, none of the points A, B, or C satisfy the inequality.

Answer:

3

Step-by-step explanation:

If 6 numbers have a mean value of 10, it means that the sum of the numbers divided 6 is equal to 10. This can be expressed as:

x÷6=10

x=60

The new number added will be the 7th number and now the mean is 9. You have to ask what number divided by 7 is equal to 9? This can be expressed as:

y÷7=9

y=63

63-60=3

So the new number added is 3

Answer:

3

Step-by-step explanation:

Mean is calculated as

mean = \(\frac{sum}{count}\)

Given the mean of 6 numbers is 10, then

\(\frac{sum}{6}\) = 10 ( multiply both sides by 6 )

sum = 60

When another number x is added then count is 7

\(\frac{60+x}{7}\) = 9 ( multiply both sides by 7 )

60 + x = 63 ( subtract 60 from both sides )

x = 3 ← the number added

On solving the provided question, we can say that by equation

30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

x = amount (ton) of vegetables sold on day one; y = amount (ton) of vegetables sold on day two. Z = the amount of vegetables sold on the third day (in tons).

\(x=y-3\\z=(5/9)*(x+y)\\x+y+z=98\\x+y+[(5/9)*(x+y)]=98\\ 9x+9y+5x+5y=882\\14x+14y=882\\x=y-3\\14x+14y=882\)

solution

\(x=30\\y=33\\x+y+z=98---- > z=98-(x+y)---- > z=98-63--- > 35\)

30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.

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The prefix for one million in the metric system is "mega-". The prefix "mega-" is derived from the Greek word "megas" which means large. It is used to denote a factor of one million, or 10^6.

To illustrate, let's consider the metric unit of length, the meter. If we add the prefix "mega-" to meter, we get the unit "megameter" (Mm). One megameter is equal to one million meters.

Similarly, if we consider the metric unit of grams, the prefix "mega-" can be added to form the unit "megagram" (Mg). One megagram is equal to one million grams.

In summary, the prefix for one million in the metric system is "mega-". It is used to denote a factor of 10^6 and can be added to various metric units to represent quantities of one million, such as megameter (Mm) or megagram (Mg).

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The slope of that line through the origin that divides the region bounded is 1.0315

y = 5x - 3x2

5x - 3x2 = 0

x(5 - 3x) = 0

x = 0 , x = 5/3

Area under y = 5x - 3x2 is A = [0 to 5/3] 5x - 3x2 dx

A = [0 to 5/3] 5x2/2 - 3x3/3

A = [0 to 5/3] 5x2/2 - x3

A = 5(5/3)2/2 - (5/3)3 = 125/54

line passing through origin is in the form of y = mx

==> mx = 5x - 3x2

==> 3x2 + mx - 5x = 0

==> 3x2 + x(m -5) = 0

==> x(3x + (m -5)) = 0

==> x = 0 , x = (5 -m)/3

Area under y = 5x - 3x2 and y = mx is (125/54)/2 = 125/108

==> ?[0 to (5 -m)/3] 5x - 3x2 -mx dx = 125/108

==> ?[0 to (5 -m)/3] (5 - m)x - 3x2 dx = 125/108

==> [0 to (5 -m)/3] (5 - m)x2/2 - x3 = 125/108

==> (5 - m)[(5 -m)/3]2/2 - ((5 -m)/3)3 = 125/108

==> (5 -m)3/18 - (5 -m)3/27 = 125/108

==> (5 -m)3/54 = 125/108

==> (5 -m)3 = 125/2

==> (5 -m) = 3.9685

==> m = 5 - 3.9685

==> m = 1.0315

Hence slope of line = 1.0315

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The complete question is given below

There is a line through the origin that divides the region bounded by the parabola y=5x−3x^2 and the x-axis into two regions with equal area. What is the slope of that line?

Answer:3

Step-by-step explanation:

Just count from -1 to positive 2 the dot doesn’t move

Answer:

-\(\frac{5}{7}\)

Step-by-step explanation:

Slope = \(\frac{rise}{run}\)

          = \(\frac{6-11}{5-(-2)}\)

          = \(\frac{6-11}{5+2}\)

          = \(\frac{-5}{7}\)

          = -\(\frac{5}{7}\)

Answer:

To calculate the slope, you can first substract the points to get the vector that join both, you may do it like this:

(-2, 11) - (5,6) = (-2 - 5, 11 - 6) = (-7, 5)

To get the slope when you get the vector (x,y), you will have to divide y be x:

5/-7

So the slope is 5/-7, \(-\frac{5}{7}\)

y = -1/3x + 1

y = -2x - 3

We can compare the equations to the graphs and see which graph represents the intersection point of the two equations.

The first equation, y = -1/3x + 1, has a negative slope (-1/3) and a y-intercept of 1.

The second equation, y = -2x - 3, also has a negative slope (-2) and a y-intercept of -3.

Based on the slopes and y-intercepts, we can identify the correct graph by finding the point where the two lines intersect.

Unfortunately, since the graphs are not provided, I am unable to determine which specific graph shows the solution to the system of linear equations. I recommend referring to the graph representation of the equations and identifying the intersection point to determine the correct graph.

Step-by-step explanation:

3/4 of 12

3/4 × 12 = 9

6/7 of 49

6/7 × 49 = 42

2/3 × 27 = 18

3/8 x 16 = 6

t is the number of years since the initial count of 5,400 birds is \(N(t) = 5,400 * e^{(-0.03*t)}\)

A function is a rule that assigns to each input value, or argument, a unique output value. The input values are typically drawn from a set called the domain of the function, while the output values are typically drawn from a set called the range of the function.

Functions are often represented using algebraic expressions, such as.

by the question.

Let's call the initial number of birds "N" and the percentage decrease per year "r". The formula for exponential decay is:

\(N(t) = N₀ * e^{(-r*t2)}\)

where:

N(t) is the number of birds at time t.

N₀ is the initial number of birds.

e is the mathematical constant e (approximately 2.71828)

r is the annual decay rate (as a decimal)

t is the time elapsed (in years)

In this case, N₀ = 5,400 and r = 0.03 (since the birds are decreasing by 3% per year).

So, the exponential function that models this situation is:

\(N(t) = 5,400 * e^{(-0.03*t)}\)

\(N(t) = 5,400 * e^{(-0.03*t)}\)

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The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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The volume of oil exiting the pipe is approximately 100 cu in/hr, 2,400 cu in/day, and 1.39 cu ft/day when converting cu in/day to cubic feet per day.



To calculate the volume of oil exiting the pipe every hour, you would need to know the flow rate of the oil in cubic inches per hour. Let's assume the flow rate is 100 cubic inches per hour.To find the volume of oil exiting the pipe every day, you would multiply the flow rate by the number of hours in a day. There are 24 hours in a day, so the volume of oil exiting the pipe every day would be 100 cubic inches per hour multiplied by 24 hours, which equals 2,400 cubic inches per day.

To convert the volume from cubic inches per day to cubic feet per day, you would need to divide the volume in cubic inches by the number of cubic inches in a cubic foot. There are 1,728 cubic inches in a cubic foot. So, dividing 2,400 cubic inches per day by 1,728 cubic inches per cubic foot, we get approximately 1.39 cubic feet per day.

Therefore, the volume of oil exiting the pipe is approximately 100 cubic inches per hour, 2,400 cubic inches per day, and 1.39 cubic feet per day.

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Answer:

$19

Step-by-step explanation:

Answer:

Step-by-step explanation:

76

The height of the water balloon at 2 seconds is -36.3 feet.

To find an equation representing the height of the water balloon at time T seconds, we can use the equation of motion for an object in free fall:

h = h₀ + v₀t + (1/2)gt²

Where:

h is the height of the object at time T

h₀ is the initial height (12 feet in this case)

v₀ is the initial velocity (which we need to determine)

t is the time elapsed (T seconds in this case)

g is the acceleration due to gravity (approximately 32.2 ft/s²)

Since the water balloon reaches a maximum height of 37 feet after 1.25 seconds, we can use this information to find the initial velocity. At the maximum height, the vertical velocity becomes zero (the balloon momentarily stops before falling back down). So, we can set v = 0 and t = 1.25 seconds in the equation to find v₀:

0 = v₀ + gt

0 = v₀ + (32.2 ft/s²)(1.25 s)

0 = v₀ + 40.25 ft/s

Solving for v₀:

v₀ = -40.25 ft/s

Now we have the initial velocity. We can substitute the values into the equation:

h = 12 + (-40.25)T + (1/2)(32.2)(T²)

To find the height of the balloon at 2 seconds (T = 2), we can plug in T = 2 into the equation:

h = 12 + (-40.25)(2) + (1/2)(32.2)(2²)

h = 12 - 80.5 + (1/2)(32.2)(4)

h = 12 - 80.5 + 16.1

h = -52.4 + 16.1

h = -36.3

Therefore, the height of the water balloon at 2 seconds is -36.3 feet.

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Problem N 7

Part A

Find out the measure of angle QRS

we have that

m by form a linear pair

m given

mmm

Part B

Find out the measure of angle Q

we have that

145=y+4y -----> by exterior angle theorem

solve for y

145=5y

y=29

Find out the measure of angle Q

mtherefore

To determine the number of ways the ant can move to the bottom left corner of the 4x6 checkerboard in exactly 10 moves, we can approach this problem using combinatorics and counting techniques.

Let's represent the ant's movements as a sequence of "U" (up), "D" (down), "L" (left), and "R" (right) corresponding to the directions the ant can move. Since the ant needs to reach the bottom left corner in exactly 10 moves, the sequence will consist of 10 characters.

Now, let's count the number of valid sequences. To reach the bottom left corner, the ant needs to move down six times and left four times. Therefore, we need to find the number of different arrangements of six "D" and four "L" in the sequence of 10 moves.

This can be calculated using combinations (binomial coefficients). The formula for combinations is:

C(n, k) = n! / (k! * (n - k)!)

In this case, we need to calculate C(10, 4) since we are selecting 4 positions for "L" from a total of 10 positions.

C(10, 4) = 10! / (4! * (10 - 4)!)

        = 10! / (4! * 6!)

        = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)

        = 210

Therefore, there are 210 different ways the ant can move to the bottom left corner of the 4x6 checkerboard in exactly 10 moves.

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Answer:

Point form:

(2, 9)

Equation form:

x = 2,y = 9

Step-by-step explanation:

The measure of the differences of all observations from the mean, expressed as a single number is called the "standard deviation". It is a commonly used measure of the amount of variability or dispersion within a set of data.

The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences between each observation and the mean.

It is expressed in the same units as the data itself, and provides a way to understand how spread out the data is from the average or mean value.

A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.

The standard deviation can be used to compare the variability of different sets of data, and can also be used in statistical tests to determine if the difference between two sets of data is statistically significant.

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a. The equilibrium interest rate,  is determined by the risk-free interest rate, the probability of repayment, and the cost of default.

b. The probability of the government repaying its loan can be calculated using the loan repayment threshold and the distribution of the output.

c. If the interest rate, r, is equal to or greater than the equilibrium interest rate, the borrowing country would default.

a. To find the equilibrium interest rate,  we need to consider the risk-free interest rate, the probability of repayment, and the cost of default. The equilibrium interest rate is given by the formula: r = r + (c/p), where r is the risk-free interest rate, c is the cost of default, and p is the probability of repayment.

b. The probability that the government will repay its loan can be calculated by determining the percentage of the output distribution that exceeds the loan repayment threshold. Since 0.5 of the output is required to repay the loan, we need to calculate the probability that the output exceeds L/0.5.

c. If the interest rate, r, is equal to or greater than the equilibrium interest rate, the borrowing country would default. This can be proven by comparing the repayment threshold (L/0.5) with the loan repayment amount (L + Lr). If the repayment threshold is greater than the loan repayment amount, the borrowing country would default.

Calculations and further details would be required to provide specific numerical answers for each part of the question.

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