Calculus, I need help for these exercises

From density, the probability that X>1.6 or X<0.36 is 1 - (0.36 + 0.64) = 0.00.

Density in mathematics is a measure of how much of a certain quantity is contained within a given area or volume. It is defined as the ratio of the mass of the object to the volume of the object.

For example, the density of water is 1 gram per cubic centimeter (1 g/cm3). Density can be used to measure the concentration of a substance in a given area, such as the amount of salt in a given volume of water. Density can also help to identify different substances, such as air, oil, and water. It is an important concept in physics, chemistry, and engineering.

The probability that X>1.6 or X<0.36 is 0.00 because the density function is 0 for values outside the range from 0.36 to 1.6. The density function is a measure of how likely it is for a value of X to be within a certain range, and since the density of X is 0 for values outside the range, the probability of X being outside that range is also 0.

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Answer:

Step-by-step explanation:

Let's start by finding the total number of women in the company. We know that 40% of the employees are women, so if we let x be the total number of employees, we can write:

Number of women = 40% of x = 0.4x

Let's then use the given ratio to determine the number of single women in the company. If the ratio of single women to married women is 2:5, we can write:

Number of single women = (2/7) * Number of women = (2/7) * 0.4x = 0.114x

We are also given that there are 30 married women. Since the total number of women is 0.4x, we can write:

Number of married women = 30

0.6x = 30

x = 50

Therefore, there are a total of 50 employees in this company.

it takes 24 minutes for the rock climber to climb 288 feet.

How to determine?

The correct equation to represent this situation is:

$$\frac{720}{60}m=288$$

Here, we first convert the rate from feet per hour to feet per minute by dividing by 60. Then, we set up the equation where the product of the rate and the time in minutes equals the distance climbed.

Simplifying this equation, we get:

$$12m=288$$

Dividing both sides by 12, we get:

$$m=24$$

Therefore, it takes 24 minutes for the rock climber to climb 288 feet.

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The value of x is given as follows:

The angle measures are given as follows:

First we obtain the value of x, considering that the sum of the measures of the internal angles of a triangle is of 180º, hence:

4x - 16 + 9x - 26 + 2x + 12 = 180

15x = 210

x = 210/15

x = 14.

Hence the angle measures are given as follows:

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Answer:

E. none​

Step-by-step explanation:

Let's use algebra to solve the problem:

Let's start by defining some variables. We'll use T for Tim's current age, and M for Mary's current age.

According to the first sentence of the problem, "Tim's age was three-quarters of Mary's age 5 years ago." In other words, we can write:

T - 5 = (3/4)(M - 5)

We can simplify and rearrange this equation to get:

4T - 20 = 3M - 15

4T = 3M + 5

According to the second sentence of the problem, "Tim will be five-sixth of Mary's age in 3 years." In other words, we can write:

T + 3 = (5/6)(M + 3)

Again, we can simplify and rearrange this equation to get:

6T + 18 = 5M + 15

6T = 5M - 3

Now we have two equations with two variables (4T = 3M + 5 and 6T = 5M - 3). We can use these equations to solve for T and M.

Multiplying the first equation by 2, we get:

8T = 6M + 10

Multiplying the second equation by 3, we get:

18T = 15M - 9

We can now solve for M by subtracting the first equation from the second:

10T = 21

T = 2.1

Substituting this value of T into one of the equations (e.g. 4T = 3M + 5), we can solve for M:

4(2.1) = 3M + 5

M = 8.3

Therefore, Tim's current age is 2.1 years and Mary's current age is 8.3 years.

The sum of their ages right now is T + M = 2.1 + 8.3 = 10.4 years.

So the sum of Tim and Mary's ages right now is 10.4 years.

$5

$5 is the y intercept, so that would be the delivery fee. Also, each pizza costs $10

Answer:

$154.37

Step-by-step explanation:

$617.48 * 0.25 = $154.37

The price of shipping and handling is $154.37.

The perimeter of the triangle is 24 units.

what is perimeter ?

Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the length of all four sides, while the perimeter of a circle is the distance around the circle. Perimeter is typically measured in units such as centimeters, meters, feet, or miles.

Given by the question:

To find the perimeter of the triangle, we need to find the distance between each pair of vertices and then add them up.

Distance between (-4, -2) and (2, -2):

[tex]d = sqrt[(2-(-4))^2 + (-2-(-2))^2] = sqrt[6^2 + 0^2] = 6[/tex]

Distance between (2, -2) and (2, 6):

[tex]d = sqrt[(6-(-2))^2 + (2-2)^2] = sqrt[8^2] = 8[/tex]

Distance between (2, 6) and (-4, -2):

[tex]d = sqrt[(-4-2)^2 + (-2-6)^2] = sqrt[(-6)^2 + (-8)^2] = sqrt[36 + 64] = sqrt[100][/tex]= 10

Now we add up the distances:

Perimeter = 6 + 8 + 10 = 24

Therefore, the perimeter of the triangle is 24.

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The sum of interior angles of the polygon is 900 degrees.

A polygon is a two-dimensional geometric figure that has a finite number of sides. Therefore, a polygon is named according to the number of sides. For example we have triangles, hexagon, pentagon, quadrilaterals, heptagons, nonagon, decagons etc.

Therefore, the polygon in the diagram has seven sides. Hence its an heptagon.

The sum of interior angles of a heptagon can be found as follows:

sum of interior angles = 180(n - 2)

where

sum of interior angles = 180(7 - 2)

sum of interior angles = 180(5)

Therefore,

sum of interior angles = 900 degrees

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The sum of the interior angle of the polygon is 900^o.

A polygon is a plane shape which has three or more number of sides. The important thing about polygons is that they are named according to their number of sides. Some common examples are: trigon- 3 sides, pentagon- 5 sides, heptagon - 7 sides etc.

The sum of internal angles of a polygon = (n - 2)180

where n is the number of sides of the polygon

In the given diagram, the polygon has 7 sides, thus it is a heptagon. Thus n is 7, so that;

sum of internal angles of a heptagon = (n - 2)180        

                                            = (7 - 2)180

                                            = 5*180

                                            = 900

Therefore, the sum of the interior angles of the polygon is 900^o.

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A quadratic equation in standard form to represent the data in the table is as follows;

y = 0.5x² - 4x + 9

In order to determine a quadratic equation in standard form for the line of best fit that models the data points described above, we would use a scatter plot (graphing calculator).

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a quadratic equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the data set, a quadratic equation for the line of best fit is given by:

y = 0.5x² - 4x + 9

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Answer:

(0.0301, 0.1733)

Step-by-step explanation:

[tex]\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\\\CI_{98\%}=\biggr(\frac{287}{522}-\frac{233}{520}\biggr)\pm 2.326\sqrt{\frac{\frac{287}{522}(1-\frac{287}{522})}{522}+\frac{\frac{233}{520}(1-\frac{233}{520})}{520}}\\\\\\CI_{98\%}\approx\{0.0300,0.1734\}[/tex]

Hence, the best choice is (0.0301, 0.1733) which tells us that we are 98% confident that the difference between the two proportions of men and women who successfully found Egypt on the map when highlighted is between 0.0301 and 0.1733

The reflection of the vector v = [8, 5, 7] in the line L is [2/3, -67/3, 31/3].

Vector, in mathematics, a quantity that has both magnitude and direction. It is often represented by an arrow whose length is proportional to the magnitude of the quantity and whose direction is the same as that of the quantity.

The reflection of a vector v in a line L can be found by projecting v onto L and then doubling the projection.

To project v onto L, we need to find the projection of v onto a vector that lies on L. Let's call this vector a. We can find a by normalizing the vector [1, -2, 2] to get:

a = [1/3, -2/3, 2/3]

Now, the projection of v onto a is given by the dot product of v and a:

proj_v_a = (v . a) * a = [(81/3) + (5(-2/3)) + (7*2/3)] * [1/3, -2/3, 2/3]

= [13/3, -26/3, 26/3]

To find the reflection of v in L, we need to double the projection and subtract it from v:

ref_v_L = 2 * proj_v_a - v

= 2 * [13/3, -26/3, 26/3] - [8, 5, 7]

= [26/3, -52/3, 52/3] - [8, 5, 7]

= [2/3, -67/3, 31/3]

Therefore, the reflection of the vector v = [8, 5, 7] in the line L is [2/3, -67/3, 31/3].

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Answer:

Step-by-step explanation:

Let's assume that x is the number of boxes that the moving company moves in a certain amount of time (in hours). Then we can write the following equation to represent the relationship between the number of boxes moved and the time taken:

x = 50h

where h is the number of hours taken to move x number of boxes.

This equation means that the number of boxes moved, x, is equal to the product of 50 boxes per hour and the number of hours, h, taken to move those boxes.

For example, if the moving company moves 200 boxes, then we can find the time taken as:

200 = 50h

h = 200/50

h = 4

Therefore, the moving company takes 4 hours to move 200 boxes.

The solution is, y = 2x + 5+4 when graph would shift by 4 unit.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Given  : y = 2x + 5 .

To find :

If you wanted to shift the graph up what would be equation .

Solution : We have given that y = 2x + 5 .

BY the transformation rule ;

if f(x) +k then graph would shift up by k units .

Then to shift the graph of y = 2x + 5 up we need to add something in 5

Like   y = 2x + 5+4

Then graph would shift by 4 unit.

Therefore,   y = 2x + 5+4 graph would shift by 4 unit.

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SINE OF A TRIANGLE

16/34

The sine of an angle is the opposite divided by the hypotenuse,

In the given triangle, the opposite is the side facing the longest side(hypotenuse)

This will give us the answer 16/34

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The rock has an instantaneous velocity of 16 meters per second.

In this problem we need to determine the average velocity of the rock, represented by a secant line, and estimate its instantaneous velocity, represented by a tangent line. The average speed is defined by the following expression:

u = [y(t + Δt) - y(t)] / Δt

Where:

The instantaneous speed is the average speed when Δt ⇒ 0.

Part A

Case I

y(1) = 20 · 1 - 1.87 · 1²

y(1) = 20 - 1.87

y(1) = 18.13 m

y(2) = 20 · 2 - 1.87 · 2²

y(2) = 40 - 7.48

y(2) = 32.52 m

u = (32.52 m - 18.13 m) / 1 s

u = 14.39 m / s

Case II

y(1.1) = 20 · 1.1 - 1.87 · 1.1²

y(1.1) = 19.737 m

u = (19.737 m - 18.13 m) / 0.1 s

u = 16.07 m / s

Case III

y(1.01) = 20 · 1.01 - 1.87 · 1.01²

y(1.01) = 18.292 m

u = (18.292 m - 18.13 m) / 0.01 s

u = 16.2 m / s

Case IV

y(1.001) = 20 · 1.001 - 1.87 · 1.001²

y(1.001) = 18.146 m

u = (18.146 m - 18.13 m) / 0.001 s

u = 16 m / s

And the instantaneous velocity of the rock is approximately 16 meters per second.

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The rate of spreading in one year is approximately 0.00001 km/year.

To find the rate of spreading in one year, we need to divide the total distance of 927 km by the time it took to spread, which is 71 million years. However, it's important to convert the time unit from million years to years:

71 million years = 71,000,000 years

So, the rate of spreading in one year is:

927 km ÷ 71,000,000 years ≈ 0.00001307 km/year

Rounding to the nearest hundredth, we get:

0.00001307 km/year ≈ 0.00001 km/year

Therefore, the rate of spreading in one year is approximately 0.00001 km/year.

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Answer:

[tex]\frac{26}{3}[/tex]

Step-by-step explanation:

Decimal form would be 8.6

Answer:

v=0.32

Step-by-step explanation:

The graph provides a visual representation of the cost of book printing services for each bid, allowing Bruno to easily compare the two options.

To graph the linear equations, we will use the values in the table to plot points on the coordinate plane, and then connect the points to form lines.

For Bid 7:

X y

0 5

3 50

5 80

7 110

10 155

For Bid 8:

X y

0 40

3 70

5 90

7 110

10 140

We can now plot these points on the coordinate plane and connect them to form two lines. Hence we obtain  Graph of Bid 7 and Bid 8

The x-axis represents the number of books, and the y-axis represents the cost. The title of the graph is "Comparison of Bids for Book Printing Services." We can see that Bid 7 is represented by the blue line, while Bid 8 is represented by the orange line.

To create the legend, we can add a key that explains which line represents which bid. For example, we could add a note at the bottom of the graph that says "Blue line: Bid 7, Orange line: Bid 8."

Overall, the graph provides a visual representation of the cost of book printing services for each bid, allowing Bruno to easily compare the two options.

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The appropriate hypotheses for the researcher are: Null hypothesis: p <= 0.5 and Alternative hypothesis: p > 0.5.

In statistics, a hypothesis is an assumption or proposition about a population parameter, based on sample data. A hypothesis is a statement that is tested to determine whether it is true or false. It is an important component of statistical inference, which involves drawing conclusions about a population based on a sample of data. There are two types of hypotheses in statistics: the null hypothesis and the alternative hypothesis. The null hypothesis is the hypothesis that is tested against the alternative hypothesis. It is usually a statement of "no effect" or "no difference" between two groups or conditions. The alternative hypothesis is the hypothesis that is accepted if the null hypothesis is rejected. It is usually a statement of an effect or difference between two groups or conditions.

Here,

The null hypothesis states that the proportion of households in the city that gave a charitable donation in the past year is less than or equal to 50 percent. The alternative hypothesis states that the proportion of households that gave a charitable donation is greater than 50 percent. The researcher will test these hypotheses using the sample data to determine whether there is convincing statistical evidence to support the alternative hypothesis.

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Let's start by finding the amount that Alex earns per hour before overtime. We know that he works 40 hours, so if we let his hourly pay be x, then his total pay before overtime can be expressed as 40x.

Since Alex gets 50% more than his usual pay for overtime, his overtime pay per hour would be 1.5x, or his usual pay plus 50% of his usual pay. This means that for the 6 hours of overtime he worked, he would earn a total of 6 * 1.5x = 9x.

Now we can write an expression for Alex's total pay, including overtime:

Total pay = 40x + 9x

Simplifying this expression, we get:

Total pay = 49x

So Alex's total pay, including overtime, is 49 times his hourly pay.

The dimensions of the rectangle after dilation by a sclae factor of 3 is,

Length = 15 inches

Breadth = 27 inches.

A dilation is a transformation that produces an image of a different size but with a similar overall shape to the original.

A dilation that enlarges an image is called an enlargement, and a dilation that shrinks an image is called a reduction.

The scale factor, which is employed to enlarge a mathematical entity, will determine the size of the image (compared to the original object). When the absolute value of the scaling factor is greater than 1, an expansion occurs.

The given rectangle dimension is :

width= 5 inches and

length= 9 inches.

When the sides of a rectangle are multiplied by a scale factor of 3, the rectangle is said to be dilated by that factor.

So, the width of rectangle is after dilation is 5×3 = 15  inches

So, the length of rectangle is after dilation is 9×3 = 27 inches

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Therefore, there is a 1/20 chance of getting a red marble out of a container containing 3 red, 2 black, and 5 yellow marbles when rolling a 4 on a cube.

By reducing the number of positive outcomes even by total number of potential outcomes, probability—the chance that a will occur—is determined. The most basic illustration is a coin toss. There are simply two results when users flip a coin: either it shows up heads or tails.

Given that there is only one possible method to roll a 4 out of six equally probable outcomes, the chance of rolling a 4 on a standard six-sided die is 1/6. (rolling a 1, 2, 3, 4, 5, or 6).

The following formula can be used to determine the likelihood of drawing a red marble from a container containing 3 red, 2 black, and 5 yellow marbles:

P(red) = number of red marbles / total number of marbles

So in this case:

P(red) = 3 / (3 + 2 + 5) = 3/10

To find the probability of both events occurring (rolling a 4 and pulling a red marble), we can multiply the probabilities of each event:

P(rolling a 4 and pulling a red marble) = P(rolling a 4) * P(red)

P(rolling a 4 and pulling a red marble) = (1/6) * (3/10)

P(rolling a 4 and pulling a red marble) = 1/20

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We can write the given limits as -

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is the graph of the function f(x) as shown in the image.

We can write the limits as -

{ 1 } -

[tex]$ \lim_{x \to 2^{-} } f(x)[/tex] = 0

{ 2 } -

[tex]$ \lim_{x \to 2^{+} } f(x)[/tex] = -1

{ 3 } -

[tex]$ \lim_{x \to 2 } f(x)[/tex] = -1

Therefore, we can write the given limits as -

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So, in response to the above question, we can state thatThe equilibrium interest rate is 5.0% as a result (determined by equation adding $50 in interest to a $1000 bond over a year). The right response is thus 5.3%.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

We must locate the point at which the supply and demand for bonds are equal in order to determine the equilibrium interest rate. To do this, we may solve for Q by setting the demand and supply equations to equal values.

1000 - 0.5Q = 450 + 5Q

5.5Q = 550

Q = 100

We can calculate the equilibrium price (interest rate) by putting Q=100 into either the demand or supply equations now that we are aware of the quantities that are requested and supplied at equilibrium:

P = 1000 - 0.5Q = 1000 - 0.5(100) = $950

The equilibrium interest rate is 5.0% as a result (determined by adding $50 in interest to a $1000 bond over a year).

The right response is thus 5.3%.

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The difference in population proportions of students who wish to study science in college between the two schools has a standard error for a confidence interval of about 0.0165.

One of the mathematical methods used in statistics to calculate variability is the standard error. It is referred to as SE. The standard deviation of a sample distribution serves as the standard error of a statistic or estimate of a parameter. It can be characterized as a projection of that standard deviation.

The standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college can be calculated as:

SE = sqrt{ [p1(1-p1)/n1] + [p2(1-p2)/n2] }

where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

For School G, p1 = 108/185 = 0.5838, and n1 = 185.

For School H, p2 = 92/165 = 0.5576, and n2 = 165.

Substituting these values into the formula, we get:

SE = sqrt{ [0.5838(1-0.5838)/185] + [0.5576(1-0.5576)/165] }

SE = sqrt{ [0.2365/185] + [0.2436/165] }

SE = sqrt{ 0.000125 + 0.000147 }

SE = sqrt{ 0.000272 }

SE = 0.0165

Therefore, the standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college is approximately 0.0165.

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Answer:

there are 720 ways to arrange the 7 friends around the circular table at the wedding reception

Step-by-step explanation:

The number of ways to arrange n distinct objects in a circle is (n-1)!, since there are n ways to choose the starting point, and then (n-1)! ways to arrange the remaining objects in a circle.

In this case, we have 7 friends seated around a circular table, so the number of ways to arrange them is:

(7-1)! = 6! = 720

Therefore, there are 720 ways to arrange the 7 friends around the circular table at the wedding reception.

Answer:

720

Step-by-step explanation:

(7-1)! = 6! = 720

The rabbit could be at any of these 8 points: 3, 5, 7, 9, 11, 13, 15, or 17.

A number line is a pictorial representation of numbers on a straight line. In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.

here, we have,

to get the possible positions of the rabbit

The rabbit could be numerous positions, given that each jump can be either positive or negative.

The possible positions are solved as follows

The rabbit is at 10 + 4 + 2 + 1 = 17

The rabbit is at 10 + 4 - 2 + 1 = 13

The rabbit is at 10 - 4 + 2 + 1 = 9

The rabbit is at 10 - 4 - 2 + 1 = 5

The rabbit is at 10 + 4 + 2 - 1 = 15

The rabbit is at 10 + 4 - 2 - 1 = 11

The rabbit is at 10 - 4 + 2 - 1 = 7

The rabbit is at 10 - 4 - 2 - 1 = 3

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