the function f is defined by f(x)={2x−1for x<3for x≥3. what is the value of ∫51f(x)dx?

Answer: A) 2 buses B) 7 vans C) 21 cars

Step-by-step explanation:

You divide 84 by the number of people the vehicle can take.

For a. 84/42=2, so you need 2 buses.

For b. 84/12=7, so you need 7 vans

For c. 84/4=21, so you need 21 cars

The null and alternative hypotheses are:

H₀ : µ ≥ 280

Hₐ : µ < 280

It would be claiming µ < 280  when the new method does not lower costs. This mistake could result in implementing the method when it would not lower costs.

It would be claiming µ ≥ 260 when the method really would lower costs. This mistake could result in not implementing a method that would lower costs.

We know that the type 1 occurs when we reject the null hypothesis when it is true and the type 11 error occurs when we do not reject the null hypothesis when it is not true. For the given scenario, the type 1 error is to reject the null and conclude that new method not lower costs, when actually it lowers.

Hence we get the required answer.

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Answer:    c=a2+b2=372+152≈39.92493

Step-by-step explanation:

Step-by-step explanation:

0.91666666...

is the sum of

0.91 and 0.006666666...

0.66666666... = 2/3

0.0066666666... = 2/300

0.91 = 91/100

so,

0.91666666... = 91/100 + 2/300 =

= 91×3/300 + 2/300 =

= 273/300 + 2/300 = 275/300 =

= 11/12

if you fail to find a fraction at the beginning (like the 2/3 we did), remember the following basics

0.1111111111... = 1/9

0.2222222... = 2/9

0.33333333... = 3/9 = 1/3

0.44444444... = 4/9

0.55555555... = 5/9

0.66666666... = 6/9 = 2/3

0.777777777... = 7/9

0.88888888... = 8/9

0.99999999... = 9/9 = 1

if you want to repeat a pattern like

0.125 to

0.125125125125125...

remember this simple trick

0.125 = 125/1000

0.125125125125125... = 125/999

you must use as many 9s as you have digits in the basic pattern.

227/999 = 0.227227227227227...

6382/9999 = 0.63826382638263826382...

and so on.

Answer:

11/12

Step-by-step explanation:

1. Let x = 0.916 (6 repeating)

2. Identify the FIRST repeating digit's place value:

   6 is in the 1000ths place

3. Multiply BOTH sides of x = ... by the value you got in step 2

   x = 0.916 (6 repeating)

   1000x = 916.6 (6 repeating)

4. Subtract the x = ... from the 1000x = ...:

   1000x = 916.666...

           x =     0.916...

    999x = 915.75

5. Divide both sides by 999:   [tex]x=\frac{915.75}{999}[/tex]

6. Rewrite as a corrected fraction: [tex]x=\frac{91575}{99900}[/tex]

7. Simplify as far as possible: [tex]x=\frac{91575}{99900}/\frac{8325}{8325}=\frac{11}{12}[/tex]

The statements that are true in the right triangle are

A right angled triangle is a triangle in which one of its angles is 90°.

Since the area model at the right shows a right triangle with side lengths a, b, and c such that a² + b² = c².

If the side lengths a increases by a small amount, but the lengths a increases by a small amount, but the lengths b and c do not change, we  need to show which of the following statements will be true.

Now, if the side a increases by a small amount Δa, we have that

a + Δa > a

Squarring both sides, we have that

(a + Δa)² > a²

Adding b² to both sides, we have that

(a + Δa)² + b² > a² + b²

(a + Δa)² + b² > c²  since  a² + b² = c²

So, a² + b² > c² where a is the new value of a = a + Δa

Also, since a is perpendicular to b, we have that angle m∠ACB = 90°. Increasing a by a small amount  Δa does not change a from being perpendicular to b, so we still have that m∠ACB = 90°.

So, the statements that are true in the right triangle are

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Answer:

Write in standard form.

2x+7y=−49

Step-by-step explanation:

A random variable is a quantitative outcome of a chance experiment.

A probability distribution includes the likelihood of each possible outcome.

A random variable is a variable whose value is determined by chance or randomness. It is often used to represent a numerical outcome of a chance experiment, such as the result of a coin toss, the roll of a die, or the outcome of a survey. Random variables can take on any numerical value, but it is often useful to assign probabilities to each possible value. This probability, known as a probability distribution or probability density function, describes the likelihood that a given value of the random variable will occur.

A normal distribution is a type of probability distribution that is symmetrical and bell-shaped, with the mean, median, and mode all equal. The values of the distribution are spread out around the mean, with the majority of the values within one standard deviation of the mean. A normal distribution is also known as a Gaussian distribution, as it was discovered by Carl Friedrich Gauss in the early 19th century.

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Answer:

V = 5πX^2 + 50πX + 75π

Step-by-step explanation:

The volume of a cylinder with radius r and height h is given by the formula:

V = πr^2h

Substituting the values for the radius and height of the cylinder in this formula, we get:

V = π(5X + 5)^2(5X + 3)

This can be written in standard form as:

V = 5πX^2 + 50πX + 75π

So, the polynomial in standard form that best describes the total volume of the cylinder is:

V = 5πX^2 + 50πX + 75π

The total number of adults who attended the play are 210.

Here, we are given that tickets for a play cost $ 7 for students and $ 10 for adults.

Total number of seats = 380

Box office revenue on opening night =  $ 3290

Let the number of adults be x

Then, the number of students will be = (380 - x)

thus, we can form the following equation-

10x + 7(380 - x) = 3290

10x + 2,660 - 7x = 3290

3x + 2,660 = 3290

3x = 3290 - 2660

3x = 630

x = 630/3

x = 210

Thus, the total number of adults who attended the play are 210.

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Median and IQR are better statistics than mean and standard deviation for describing skewed probability distributions because it's based on values that come from the middle half of the distribution, it's unlikely to be influenced by outliers.

Because it is unaffected by outliers, the IQR is frequently regarded as a more accurate measure of spread than the range. The variance and standard deviation are indicators of how widely the data are dispersed from the mean. Each observed data value's proximity to the mean is summarized.

The best indicator of variability in data sets with outliers or skewed distributions is the interquartile range. It's unlikely to be impacted by outliers because it's based on values that come from the middle half of the distribution.

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Answer:

Below

Step-by-step explanation:

12 C 2  = 12! / ( 10! 2!) = 66 ways

Answer:

‎

Step-by-step explanation:

‎

(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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Total number of students is 70.

What do you mean by ratio?

A ratio is a comparison of two quantities. The ratio of a to b can also be expressed as:  a:b

A ratio is the equality of two ratios. Write ratios to help you find equivalent ratios and solve for unknown quantities.

Two common types of relationships are part-to-part and part-to-whole.

In a library, the ratio of students with younger siblings to those without younger siblings was 4:3

There were 42 students without younger siblings.

As the given ratio is 4:3

So, let the number of students with younger siblings  = 4x

let the number of students without younger siblings = 3x

There were 42 students without younger siblings.

3x = 42

x = 42/3

x = 14

Let y be the number of students with younger siblings

y = 4x = 4(14) = 56

Total students = students with younger siblings + students without younger siblings

= 14 + 56

= 70

Therefore, total number of students is 70.

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Answer:

Sandwich = 2

Cookie = 1

Step-by-step explanation:

Let

This would mean :

3x + 2y = 8  and 7x + 2y = 16

Because we have two similar terms in the equations, (2y) we can subtract the two equations from each other cancelling out the terms resulting in us having one term that we can solve for. This is known as the elimination method

  7x + 2y = 16

-  3x + 2y  = 8

-----------------------

4x   +   0y   = 8

==> 4x = 8

==> x = 2

We can now plug in the value of x into one of the equations and solve for y

==> 7x + 2y = 16

==> 7(2) + 2y = 16

==> 14 + 2y = 16

==> 2y = 2

==> y = 1

We can conclude that the cost of a sandwich is 2 and the cost of a cookie is 1

Answer:

Below

Step-by-step explanation:

Any 5 points you want

pick out 5 values of x      say     -4    -1     0      3   7  

  and calculate the value of the corresponding 'y' using the equation....then plot those points

Answer: 8x

Step-by-step explanation: We will start by writing out our equation which is 10x2y-2x2y. Next we will subtract using only like terms

10x - 2x = 8x

2y-2y=0

8x plus 0 = 8x.

Representing data sets using frequency distributions and using graphs of frequency distributions can have several benefits. Here are some of the benefits of representing data sets using frequency distributions:

a) Organizing the data into afrequency  distribution can make patterns within the data more evident. By organizing the data into classes or bins and counting the number of observations within each class, you can see how the data is distributed and identify patterns or trends that may not be immediately apparent when looking at the raw data.

b) Organizing the data into a frequency distribution makes it possible to graph quantitative data. Many types of graphs, such as bar graphs and histograms, are based on frequency distributions and can be used to visualize the distribution of data.

c) It is easier to determine the minimum and maximum values of a data set when it has been arranged into a frequency distribution. By organizing the data into classes, you can easily see the range of values within each class and determine the overall range of the data set.

Here are some of the benefits of using graphs of frequency distributions:

a) It can be easier to determine the class boundaries by looking at a graph of the frequency distribution. When you create a graph of a frequency distribution, the class boundaries are often marked along the x-axis, which makes it easy to see where one class ends and the next begins.

b) Graphing a frequency distribution makes it possible to determine the relative frequencies of each of the classes. By looking at the heights of the bars on a bar graph or the heights of the columns on a histogram, you can see how each class compares to the others and determine the overall shape of the distribution.

c) It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution. Graphs are a visual representation of data, and they can help you see patterns or trends that may not be immediately apparent when looking at the data in tabular form.

d) Graphing frequency distributions makes it possible to find the total number of observations. By adding up the frequencies of all the classes, you can determine the total number of observations in the data set.

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Answer:

x = 40°

y = 35°

Step-by-step explanation:

Let us take two triangles ∆ABC and ∆ADE

We know that, in a triangle the sum of all angles is equal to 180°

So,

For the traingle ABC

Now,

m∠A + m∠B + m∠C = 180°

80° + 60° + x° = 180°

140° + x° = 180°

x° + 140° - 140° = 180° - 140°

x = 40°

For the triangle ADE

Now,

m∠A + m∠D + m∠E = 180°

80° + 65° + y° = 180°

145° + y° = 180°

y° + 145° - 145° = 180° - 145°

y = 35°

Thus, The value of x and y is 40° and 35° respectively

The sample mean is 75.

Margin of error is 6.

Sample standard deviation is 17.53 .

What is the relationship between margin of error and confidence level?

Confidence level and marginal of error As the confidence level increases, the critical value increases and hence the margin of error increases. This is intuitive; the price paid for higher confidence level is that the margin of errors increases.

Part A:

The sample mean is at the midpoint of the lower and the upper values of the confidence interval.

Thus, the sample mean is given by:

=(69 + 81) / 2

= 150/2 = 75

Therefore, the sample mean is 75.

Part 2:

The margin of error is the distance between the upper and the lower confidence interval values from the sample mean.

Thus, margin of error is given by 81 - 75 = 75 - 69 = 6 .

Therefore, margin of error is 6.

Part 3:

The margin of error is given by

ME = t₍ᵃ/₂₎ ([tex]\frac{s}{\sqrt{n} }[/tex] )

where t₍ᵃ/₂₎  is the value of the t-distribution given the degree of freedom; s is the sample standard deviation and n is the sample size.

Since the sample size is 25, the degree of freedom is 25 - 1 = 24.

[tex]\frac{a}{2}[/tex] = [tex]\frac{1-0.9}{2}[/tex] = [tex]\frac{0.1}{2}[/tex] = 0.05

From the t-distrbution table, we have:

t₍ᵃ/₂₎ = 1.710882

Thus, margin of error is given by:

6=1.710882 [tex](\frac{s}{\sqrt{25} })[/tex]

⇒[tex]\frac{s}{\sqrt{25} }[/tex]   = [tex]\frac{6}{1.710882}[/tex]

⇒s= 17.53

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Answer: Accounting profit=$90,000 and Economic profit loss= $28,500

Step-by-step explanation:

Accounting profit = Total revenue - Explicit costs Accounting profit = ($65 × 4,000) - ($50,000 + $120,000) Accounting profit = $260,000 - $170,000 Accounting profit = $90,000

Economic profit = Total revenue - (Explicit costs + Implicit costs) Economic profit = ($65 × 4,000) - ($50,000 + $120,000 + Forgone interest on savings + Forgone wages) Economic profit = ($65 × 4,000) - [$50,000 + $120,000 + (0.06 x $25,000) + $60,000] Economic profit (loss) = $28,500

The value of (1 + i)^5 is -2 * 2^1.5 * (1 + i). De Moivre's describes how the power of a complex number can be calculated using the properties of its modulus and argument.

De Moivre's theorem states that for any complex number z and any integer n, we have (z^n) = (r^n)(cos(nθ) + i * sin(nθ)), where r is the magnitude of z and θ is the angle that z makes with the positive real axis in the complex plane. Using this theorem, we can easily find the fifth power of 1+i as follows:

First, we need to express 1+i in polar form, which is given by z = r * cis(θ), where r is the magnitude of z and cis(θ) is the complex number with magnitude 1 and angle θ in the complex plane. In this case, we have z = 1+i = sqrt(2) * cis(π/4), where sqrt(2) is the magnitude of 1+i and cis(π/4) is the complex number with magnitude 1 and angle π/4 in the complex plane.

Next, we substitute this expression for z into the formula for (z^n) given by De Moivre's theorem, which gives us

(1 + i)^5 = √2^5 * (cos(5 * 45) + i * sin(5 * 45))

        = 2^2.5 * (cos(225) + i * sin(225))

(1 + i)^5 = 2^2.5 * (-cos(45) + i * -sin(45))

        = 2^2.5 * (-1 + i * -1)

        = -2 * 2^1.5 * (1 + i)

Therefore, the value of (1 + i)^5 is -2 * 2^1.5 * (1 + i).

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To solve for the distance covered in the first two hours, we need to calculate the velocity at time t = 0 and t = 2.The car will have covered 44 miles during the first 2 hours of driving.

The velocity of the car t hours after leaving Austin is given by the equation V = 12 + 5t - 32. To solve for the distance covered in the first two hours, we need to calculate the velocity at t = 0 and t = 2.

At t = 0, V = 12 - 32 = -20. This means that the car was travelling at -20 miles per hour when it left Austin. Since velocity and distance are inversely proportional, the car had covered 0 miles when it left Austin.

At t = 2, V = 12 + 10 - 32 = -10. This means that the car was travelling at -10 miles per hour after 2 hours. Since velocity and distance are inversely proportional, the car had covered 44 miles after 2 hours by time.

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The first step is to draw a line longer than the given AB line.

An area or portion of a line with two endpoints is referred to as a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.

A line can be extended on both ends forever while a line segment has endpoints.

Step 1: You are instructed to copy line segment AB.

Step 2: A line segment that is longer than line segment AB is drawn in step two. Identify C as one of its endpoints.

Step 3: Position the anchor on one endpoint of line segment AB and the pencil point on the other endpoint of the segment by opening your compass.

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Answer: 994 mm^2

Step-by-step explanation:

Let's calculate the surface area of both the triangular surfaces. To find the area of a triangle, we multiply the base by the height and divide by 2. The height is 12 and the base is 33. (12*33)/2 = 198. Since there are two triangular surfaces, we have 198 * 2 = 396 mm^2.

Now we can calculate the base surface, which is 7 * 33 = 231 mm^2 (width times length is the formula for calculating area of a rectangle).

The rectangular surface to the left of the diagram is 16 * 12 = 192 mm^2.

The rectangular surface to the right of the diagram is 25 * 7 = 175 mm^2.

Now we add up all our values: 396 + 231 + 192 + 175 = 994 mm^2.

Answer:

(2,4)

Step-by-step explanation:

The simplified form of the given expression, (2c7)(9c), is 18c⁸

From the question, we are to simplify the given expression
The given expression is

(2c7)(9c)

First, we will write the expression properly

The given expression written properly is

(2c⁷)(9c)

Now, we will simplify the expression

Simplifying the expression

(2c⁷)(9c)

Multiply

2c⁷ × 9c

Collect like terms

2×9 × c⁷ × c

18 × c⁷⁺¹

18 × c⁸

18c⁸

Hence, the expression is 18c⁸

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In linear equation, Joshua should buy is 255 + 6s ≥ 333.

What is linear equation in math?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let the sets of spoons be represented by s

The restaurant needs at least 333 spoons.

Each set on sale contains 8 spoons

There are currently 333 spoons.

At least as an inequality is ≥

Hence:

255 + 6 × s ≥ 333

255 + 6s ≥ 333

Therefore, inequality tha can be used to determine s the minimum number of sets of spoons Joshua should buy is

255 + 6s ≥ 333

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