Find the area under the curve y = 2 x^-3 from x = 6 to x = t and evaluate it for t = 10 , t = 100 . Then find the total area under this curve for x ≥ 6 .
(a) t = 10
(b) t = 100
(c) Total area

Answer:10.24

Step-by-step explanation: Since the triangles are similar, then

r/3x2= 4x48/1x4,

r=3.2x4.48=10.24

Answer:

x=5/4 or x=5/9

pls mark me brainliest

Answer:

x=5/4 (for the first x),x=5/9 (for the second x)

Jana, because she has the highest ratio since 8/10 is greater than 9/12.

A ratio is a comparison of two numbers or quantities expressed in relation to each other. It represents the relative size or magnitude of one quantity with respect to another. Ratios are typically written as a fraction, with the first number being the numerator and the second number being the denominator, and can also be expressed as a decimal or percentage.

Batting average is a statistical measure used in baseball to evaluate a player's performance at the plate. It is calculated as the ratio of a player's total number of hits to their total number of at-bats (the number of times they attempt to hit the ball).

In the given question,

A higher batting average indicates a better performance, since it means the player is successfully hitting the ball more often.

In this case, we are given the number of hits and attempts for two players, Jana and Tasha. To compare their batting averages, we need to calculate the ratio of their hits to their attempts.

Jana has hit the ball 8 times out of 10 attempts, so her batting average is 8/10 = 0.8.

Tasha has hit the ball 9 times out of 12 attempts, so her batting average is 9/12 = 0.75.

To determine which player has the better batting average, we compare their ratios. Since 0.8 is greater than 0.75, Jana has the higher ratio and therefore the better batting average.

So, the answer is Jana, because she has the highest ratio (8/10 = 0.8), which means she has the better batting average compared to Tasha (9/12 = 0.75).

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According to the figure showing 2020 GDP for selected countries, America’s GDP is 21.43% which is 7.19% larger than China’s GDP which is 14.24%.

A country's economic output is measured by its gross domestic product (GDP). GDP is estimated by totaling all the commodities and services produced in a nation within a predetermined time frame, typically a year. In 2020, America’s GDP was 21.43% of the total GDP of selected countries. This is 7.19% larger than China’s GDP which was 14.24% of the total GDP of selected countries.

We must use exchange rates to convert GDPs to a common currency in order to compare GDPs across nations. Once the GDPs are expressed in a similar currency, we can compare the GDP per capita of each nation by dividing the GDP by the population. Large GDPs are common in countries with big populations, although GDP is not always a reliable measure of a country's wealth. GDP per capita is a better metric.

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Complete question is:

According to the figure showing 2020 GDP for selected countries, how much larger (in percentage terms) is America's GDP than:

The G D Ps are as follow: United states, 21.43; China, 14.24; Japan, 5.08; Germany, 3.86; India, 3.87; Great Britain, 2.83; Russia, 1.70; Mexico, 1.27; Sweden, 0.53; Greece, 0.21; Haiti, 0.08.

Round your responses to the nearest whole number.

1. Russia?

______ % larger

2. Germany?

______ % larger

Answer:

Step-by-step explanation:

[tex]90 \% \text{ of }600=\frac{90}{100}\times600[/tex]

                  [tex]=90 \times 6[/tex]

                  [tex]=540[/tex]

So 540 students passed the exam.

Answer:

  D.  87

Step-by-step explanation:

You want to know the measure of the angle opposite the longest side in a triangle with side lengths 13, 16, and 20 inches.

The angle x is opposite the side of length 20 inches in this triangle, which is the longest side. That tells you x is the largest angle.

The largest angle in any triangle is never less than 60°. This eliminates all answer choices except the last one:

  x = 87

If you want to go to the trouble to solve the triangle, the law of cosines is helpful. For sides a, b, c and angle C, it tells you ...

  c² = a² +b² -2ab·cos(C)

Solving for the angle, we have ...

  C = arccos((a² +b² -c²)/(2ab))

  C = arccos((13² +16² -20²)/(2·13·16)) = arccos(25/416) ≈ 86.55°

  x ≈ 87

the rectangle has a surface area of 11/6 square inches and perimeter is 23/3 inches.

We must multiply the length by the width of the rectangle to determine its area. Applying the provided metrics, we have:

Area is equal to the product of length and width.

Area is equal to (11/3) x (1/2) inches.

11/6 square inches is the area.

As a result, the rectangle has a surface area of 11/6 square inches.

The lengths of all four sides must be added up in order to determine the rectangle's perimeter. Applying the provided metrics, we have:

Perimeter equals 2 (length plus width).

Perimeter equals 2 (3 2/3 inches plus 1 inch).

perimeter equals two (11/33 inch plus 1/2 inch).

P = 2 (or 23/6 inches)

Diameter is 23 3/8 inches.

As a result, the rectangle's perimeter is 23/3 inches.

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To catch the top 1% of all cars on the freeway, the speed of the car needs to be greater than 99 mph. This is because 99 mph is three standard deviations above the mean, which would put it in the top 1% of speeds.

The question asks for the z-scores and probabilities of cars going 60 mph and 86 mph on the freeway. It also asks for the speed at which the highway patrol woman needs to catch the top 1% of cars.

Let xx be the speed for a randomly selected car on the freeway, with a mean of 66 mph and standard deviation of 10 mph.

The z-score for a car that is caught going 60 mph is -2.0000. This means that the car is two standard deviations below the mean. The probability of randomly choosing a car on the freeway and it going below 60 mph is 0.0228.

The z-score for a car that is caught going 86 mph is 2.0000. This means that the car is two standard deviations above the mean. The probability of randomly choosing a car on the freeway and it going above 86 mph is 0.0228.

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The point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

What is Segment?

In geometry, a segment is a part of a line that has two endpoints. It can be thought of as a portion of a straight line that is bounded by two distinct points, called endpoints. A segment has a length, which is the distance between its endpoints. It is usually denoted by a line segment between its two endpoints, such as AB, where A and B are the endpoints. A segment is different from a line, which extends infinitely in both directions, while a segment has a finite length between its two endpoints.

To find the point that partitions segment AB in a 1:4 ratio, we need to use the midpoint formula to find the coordinates of the point that is one-fourth of the distance from point A to point B. The midpoint formula is:

((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the segment.

So, let's first find the coordinates of the midpoint of segment AB:

Midpoint = ((-3 + 7)/2, (2 - 10)/2)

= (2, -4)

Now, to find the point that partitions segment AB in a 1:4 ratio, we need to find the coordinates of a point that is one-fourth of the distance from point A to the midpoint. We can use the midpoint formula again, this time using point A and the midpoint:

((x1 + x2)/2, (y1 + y2)/2) = ((-3 + 2)/2, (2 - 4)/2)

= (-1/2, -1)

So, the point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

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Statement (b) and (c) are true about the situation.

Using standardized instruments or units, measurements are the process of figuring out the size, quantity, or degree of anything.

Using the given function, h(t) = -5t^2 + 10t + 3, we can determine the true statements about the situation:

a. False: The diver begins at h(0) = 3 meters above the water, not 5 meters.

b. True: The diver begins at h(0) = 3 meters above the water.

c. True: The function has one zero that makes sense.

To find it, we set h(t) = 0 and solve for t:  -5t² + 10t + 3 = 0

Using the quadratic formula, we find that: t ≈ 2.161

This means that the diver reaches a height of zero after 2.161 seconds.

d. False: As we found in part (c), the function has only one zero.

e. False: The graph of the function does not start at the origin.

f. False: The diver begins at 3 meters above the water, not at the same height as the water level.

Therefore, statement (b) and (c) are true about the situation.

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Complete question-

Using proportions, the real height of the telephone mast is estimated to be 9 meters.

A proportion is a fraction of a total amount, and equations are constructed using these fractions and estimates to find the desired measures in the problem using basic arithmetic operations like multiplication and division. Because the telephone box and the mast are similar figures in this problem, their side lengths are proportional.

The following proportional relationship is established as a result:

x / 1.5 cm = 10.8 cm / 1.8 cm.

The relationship's left side can be simplified as follows:

6 = x / 1.5 cm.

The estimate is then calculated using cross multiplication, as shown below:

6 x 1.5 cm = 9.5 cm².

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By answering the question the answer is Therefore, landscapers should equation use 35 gallons of an 80% pesticide solution.

In mathematics, an equation is a statement that two expressions are equal. The equation consists of her two sides divided by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of solving an equation is to find the values ​​of the variables to make the equation true. Simple or complex equations, regular or nonlinear, and equations involving one or more factors are all possible. For example, the expression "[tex]x2 + 2x - 3 = 0\\[/tex]" squares the variable x. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.  

Let's say a landscaper needs to use x gallons of an 80% pesticide solution.

The amount of pesticide for an 80% solution is 0.8 x gallons and the amount of pesticide for a 30% solution is 0.3 (35) = 10.5 gallons.

After mixing the two solutions, the total amount of pesticides in the mixture is 0.8 x + 10.5 gallons and the total volume of the mixture is x + 35 gallons.

Since we need a 55% pesticide solution, we can set the following formula:

[tex]0.8x10.5 0.55(x+35)0.8x10.5 0.55x+19.250.25x = 8.75x = 35[/tex]

Therefore, landscapers should use 35 gallons of an 80% pesticide solution.

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The vectors in set (c) span R3.Answer: (a) The vectors span R3, (b) The vectors do not span R3, (c) The vectors span R3.

To solve this problem, you need to determine if the given sets of vectors spanR3 or not. You may use Octave for your calculations.Here are the sets of vectors: (a) S1 = { [1; 0; 0], [0; 2; 1], [1; 0; 3] }(b) S2 = { [1; 1; 0], [3; 0; 0] }(c) S3 = { [1; 0; 1], [3; 1; 0], [-1; 0; 0], [2; 1; 5] }To determine whether the vectors in the given sets span R3, you can place the vectors in a matrix as column vectors and compute the rank of the matrix. If the rank is 3, then the vectors span R3. Otherwise, they do not.

(a) S1 = { [1; 0; 0], [0; 2; 1], [1; 0; 3] }R1 = [1 0 1; 0 2 0; 0 1 3]rank(R1) = 3The rank of R1 is 3, so the vectors in set (a) span R3.

(b) S2 = { [1; 1; 0], [3; 0; 0] }R2 = [1 3; 1 0; 0 0]rank(R2) = 2The rank of R2 is 2, so the vectors in set (b) do not span R3.

(c) S3 = { [1; 0; 1], [3; 1; 0], [-1; 0; 0], [2; 1; 5] }R3 = [1 3 -1 2; 0 1 0 1; 1 0 0 5]rank(R3) = 3The rank of R3 is 3, so the vectors in set (c) span R3.Answer: (a) The vectors span R3, (b) The vectors do not span R3, (c) The vectors span R3.

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The 68th percentile on the standard normal curve corresponds to the mean value of the data set. This statement is false.

The 68th percentile on the standard normal curve corresponds to one standard deviation away from the mean. In other words, approximately 68% of the data falls within one standard deviation of the mean on the standard normal distribution. This is a property of the normal distribution, which is a continuous probability distribution commonly used in statistics.

To clarify, the mean value of a data set is the arithmetic average of all the values in the data set. It is not directly related to the 68th percentile on the standard normal curve. The mean is a measure of central tendency and is influenced by all the data values, while the percentile is a measure of relative position in the distribution of data.

Therefore, it is important to understand the difference between percentiles and measures of central tendencies, such as mean, median, and mode, when analyzing data using statistical techniques.

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The test is one-tailed to the right due to the Alternate hypothesis.

In a hypothesis test, a Null hypothesis (H0) is a statement of "no effect" or "no difference," whereas the Alternate hypothesis (HA) is a statement of "some effect" or "some difference." Here are the correct null and alternative hypotheses for the given scenario: Null hypothesis: H0: μ = 71, Alternative hypothesis: HA: μ > 71 (One-tailed test) we have a one-tailed hypothesis test since the research hypothesis is directed. In a one-tailed test, we're looking for a difference in one direction only. In this case, Dr Carl thinks that there has been an improvement, so the alternative hypothesis reflects this. Therefore, the test is one-tailed to the right.

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Equation can also be used to calculate how many novels Deon needs to read in a certain amount of months. For example, if the number of months is 4, then Deon needs to read 8 novels.

An equation is a statement that expresses the relationship between two or more mathematical expressions. It is typically written in the form of an equality, such as "2x + 3 = 7", where "2x + 3" is the left-hand side and "7" is the right-hand side. Equations are used to model real-world problems and can be solved to determine the value of the unknowns within the equation.

The equation above shows that the number of novels Deon needs to read in a certain amount of months is twice the number of months. This can be graphically represented by a straight line, with a slope of 2, that passes through the origin on the graph. The graph below illustrates this equation. The x-axis represents the number of months (M) and the y-axis represents the number of novels (N). As the number of months increases, the number of novels Deon needs to read also increases, at a rate of 2 novels per month.


This equation can also be used to calculate how many novels Deon needs to read in a certain amount of months. For example, if the number of months is 4, then Deon needs to read 8 novels.

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Step-by-step explanation:

(a) To factorize 25t² - 4, we can use the difference of squares formula:

a² - b² = (a + b)(a - b)

In this case, a = 5t and b = 2. So we have:

25t² - 4 = (5t + 2)(5t - 2)

Therefore, 25t² - 4 can be factorized as (5t + 2)(5t - 2).

(b) To factorize x² - 6x - 3xy + 18y, we can group the terms:

(x² - 3xy) - (6x - 18y)

We can then factor out the common factors from each group:

x(x - 3y) - 6(x - 3y)

Notice that both terms have a factor of (x - 3y), so we can factor it out:

(x - 3y)(x - 6)

Therefore, x² - 6x - 3xy + 18y can be factorized as (x - 3y)(x - 6).

(a)

.

in this case, a= 25t and b= 4.

.

ans: (5t-4)(5t+4)

The mean (also called the arithmetic mean or average) is a measure of central tendency that represents the typical or average value of a set of data. The mean is calculated by summing up all the values in the data set and dividing by the number of values.

The mean of x is calculated by the following formula:

mean of x = ∑(x * P(x))

Where, ∑ = Summation operator

            x = Value of random variable  

            P(x) = Probability of the corresponding value of x.

Let's calculate the mean of x using the formula provided above.

mean of x = (-1 × 0.3) + (0 × 0.4) + (1 × 0.3)

                = -0.3 + 0 + 0.3  

                = 0

Therefore, the mean of x is 0.

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Answer:

Step-by-step explanation:

= 2(15+8)

=2(23)

=46

So, the right response is that, in order to more accurately fit the scatterplot that depicts a curve in the data, you need add a quadratic component while performing regression.

As ax² +bx + c, a quadratic equation can be expressed. In a quadratic equation, the largest exponent is 2, which limits the number of terms to a maximum of 3. These terms are exponent 2 (ax²) and exponent 1 (bx) fixed term.

Regression can be improved by including a quadratic component to better match scatterplots of data that display curves. This is so that the independent and dependent variables can have a nonlinear connection, which is made possible by a quadratic term. A quadratic component can assist capture inherent curvature of a data and enhance the fit of a regression model in cases where the connection between both the variables isn't really strictly linear.

A quadratic term may not be appropriate or required, though. A quadratic factor would not increase the model's fit if the variables' relationships are strictly linear and might even result in overfitting. In addition, if the scatterplot contains too many anomalies or the data is not consistent, adding a quadratic factor might not be beneficial.

In order to properly fit a scatter plot graph that depicts a curve in the data, the correct response is you would like to add a quadratic term while performing regression.

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Answer:

p ≥ 228

Step-by-step explanation:

p ≥ 228

This inequality means the Bowlers have to score at least 228 points to move on.

Hope this helped!

84500 reams of paper are the total amount the two companies sell in the past five years.

65500 is the amount that Company B performed better than company A.

A company can be defined as the part in which the main aim or goal is to earn a profit. This was to generate the income that they will be having in the firm. There are various employees that are present in the company and work towards a common goal.

The Amount that is made by company A is

[tex]7.5 \times 10000[/tex]

[tex]=75000[/tex]

The amount of paper manufactured by company B is

[tex]= 9.5 \times 1000[/tex]

[tex]= 9500[/tex]

A) The total that is made by both companies in 5 years will be

[tex]= \text{Company A + Company B}[/tex]

[tex]= 75000 + 95000[/tex]

[tex]= 84500[/tex]

B) Company B made better products as compared to Company A

[tex]= \text{Company B - Company A}[/tex]

[tex]=75000 - 9500[/tex]

[tex]=65500[/tex]

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Answer:

Step-by-step explanation:

You want the sum and difference of 7.5×10^4 and 9.5×10^3.

Numbers are most conveniently added or subtracted in scientific notation when the multipliers have the same exponent. For this we can rewrite Company B's volume as ...

  9.5×10^3 = 0.95×10^4

  total sales = 7.5×10^4 + 0.95×10^4 = 8.45×10^4 = 84,500

  difference in sales = A -B = 7.5×10^4 -0.95×10^4 = 6.55×10^4 = 65,500

__

Additional comment

You can enter the numbers "as is" in a calculator or spreadsheet and format the output in whatever form you need.

The value for the height h of the right triangle is equal to 4.8990.

The height h of the right triangle divides the triangle in two triangles with the same proportions as the original triangle, which implies that if the adjacent for the smallest triangle is 4 and the adjacent of the other triangle is h, then:

h/6 = 4/h {considering the tangent ratio}

h² = 4 × 6 {cross multiplication}

h = √24

h = 4.8990

Therefore, value for the height h of the right triangle is equal to 4.8990.

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To find the smallest of several integers, you will need to write a program that takes in a number of values specified by the user as input, and then outputs the smallest value. First, you will need to create a loop that reads in the number of values specified by the user. To do this, you can use a 'for' loop that reads in the values until it reaches the user-specified number of values. Inside the loop, you can create a variable to store the smallest value and compare each value to the smallest value to determine if it is smaller. If the value is smaller, then the smallest value should be updated.

Finally, once the loop has gone through all of the values, the smallest value should be outputted. In summary, to find the smallest value of several integers, you will need to use a 'for' loop to read in the specified number of values from the user, compare each value to the smallest value, and update the smallest value if it is smaller. Then, you can output the smallest value once the loop is complete.

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The bus will arrive at the beach by 9:05 am. To calculate the arrival time of the bus, we need to add the travel time to the departure time.

First, we need to convert the departure time of 8:30 am to minutes.

Then, we add the travel time of 35 minutes to the departure time:

Finally, we convert the arrival time back to hours and minutes:

So the bus will arrive at 9:05 am.

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The set of points that represent the intersection of the curve of vector function F and circle C is

{(4+10cos(t), 4+10cos(t), 16+40cos(t)) | t ranges from 0 to 2π}.

We have,

Vector function F = (y + 2x, 2x + 5z, 7y + 8x)

C is the circle with radius 5, center at (2,0,0), in the plane x = 2

C is oriented counterclockwise as viewed from the origin (0,0,0)

The vector function F represents a three-dimensional curve in space.

The circle C is a two-dimensional object in space, lying in the plane x = 2 and centered at (2,0,0) with a radius of 5. It is also oriented counterclockwise as viewed from the origin (0,0,0).

To find the intersection of vector function curve F and circle C, we can substitute the equation of the circle into the equation of the curve and solve for the parameter(s) that satisfy the equation. However, since the equation of the circle is given in terms of x only, we can simplify the equation of the curve by substituting y = 0 and z = 0:

F = (2x, 2x, 8x)

Now, we can substitute x = 2 + 5cos(t) and y = 5sin(t) (the parameterization of the circle C in the plane x = 2) into the equation of the curve F:

F = (2(2+5cos(t)), 2(2+5cos(t)), 8(2+5cos(t)))

= (4+10cos(t), 4+10cos(t), 16+40cos(t))

Thus, the intersection of vector function curve F and circle C is given by the set of points:

{(4+10cos(t), 4+10cos(t), 16+40cos(t)) | t in [0, 2π)}

Note- that the parameter t represents the angle of rotation around circle C, and ranges from 0 to 2π to cover the entire circle.

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The atmospheric pressure of 101.325 kPa, the dew point temperature is approximately 10.4°C, the humidity ratio is approximately 0.0084 kg of water vapor per kg of dry air, the specific volume is approximately 0.85 m³/kg of dry air, and the enthalpy is approximately 91 kJ/kg of dry air.

To determine the dew point temperature, the humidity ratio, the specific volume and the enthalpy given a dry bulk temperature of 39°C and a wet bulb temperature of 18°C, you can use a psychometric chart  or a specialized software program that calculates these properties based on the given dry bulb and wet bulb temperatures, as well as other relevant parameters such as pressure, altitude, and air composition.

First, plot 39°C (the dry bulk temperature) and 18°C (the wet bulb temperature) on the chart. Then mark The atmospheric pressure of 101.325 kPa, the dew point temperature is approximately 10.4°C, the humidity ratio is approximately 0.0084 kg of water vapor per kg of dry air, the specific volume is approximately 0.85 m³/kg of dry air, and the enthalpy is approximately 91 kJ/kg of dry air.

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