Each cube in this figure is a -millimeter cube. What is the total volume of the prism?



2 mm 3
6 mm 3
4 mm 3
9 mm 3

Answer:

the probability that the two committees have at least one member in common is approximately 0.3622.

Step-by-step explanation:

To find the probability that two committees have at least one member in common, we can use the complement rule, which states that the probability of an event happening is 1 minus the probability of the event not happening.

Let A be the event that the two committees have no members in common. To calculate the probability of A, we can first find the number of ways to choose three people out of 20 without any overlap, and then use this to find the total number of ways to choose two committees of three people each without any overlap:

Number of ways to choose 3 people out of 20 without overlap:

C(20,3) = (201918)/(321) = 1140

Number of ways to choose 3 people out of 20 with overlap:

C(20,3) - C(2,1)C(17,2) = 1140 - 2(2*136) = 680

The first term is the total number of ways to choose 3 people out of 20, and the second term is the number of ways to choose 3 people out of 20 such that one particular person is included. We multiply by 2 because there are two committees.

The total number of ways to choose two committees of three people each without any overlap is:

C(20,3) * C(17,3) = (1140*680) = 775200

Therefore, the probability that the two committees have no members in common is:

P(A) = 775200 / (C(20,3)*C(17,3)) = 0.6378

So the probability that the two committees have at least one member in common is:

P(at least one member in common) = 1 - P(A) = 1 - 0.6378 = 0.3622

Therefore, the probability that the two committees have at least one member in common is approximately 0.3622.

Answer:

please dont blame me if i get this wrong this is what i put.

Step-by-step explanation:

Using the following 3 equations, answer the questions:

11x + y =4, x+y = -2, x - 2y = 18

How can you determine which equations can be graphed more easily using x- and y-intercepts, rewriting in slope-intercept form, or using a table of values?

you can determin which is eiser to graph by wether or not they have numbers infront of the x and y intercepts.  i find it mutch eiser if they allready have the numbers there. its also eiser to graph 11x + y =4 and x - 2y =18 on a slope intercept rather than table of values because you allready can find the points for those two eiser than the last one which would be used on the table of values.  for the problem x+y=-2 you would use x and y intercepts. for 11x+y=4, rewriting in slope form is the corect method to use. and finaly use the table of values method for x-2y=18.

Which method works best for you personally? When does it not work as well?

the one that i find works best for me personally is probably gonna be the slope intercept method as apposed to many other methods. it doesnt work all the time because nothing can but normaly when i have a problem with this method i can just go to the table of values method and get the answer. (sorry if this is wrong this is what im putting for my answer. dont copy and paste this though if u do desiede to use it, read it and turn it into your own words so its not obvious you found the answer on the internet. and tbh i didnt read the lesson i just am ok at comming up with answers useing the question and getting away with it. )

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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A formula without free variables is a formula that does not contain any variables that are not quantified.

Sentences are commonly referred to as formulas devoid of any unrestricted variables. These statements hold a truth value independent of the variable values, hence the reason.

Open formulas are frequently referred to as formulas with free variables. These are not actually declarations; instead, they are arrangements that can transform into declarations by allotting definite values to the independent variables.

Formulas without free variables are often easier to work with than formulas with free variables.

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Answer:

y = -3

Step-by-step explanation:

y = | x | - 4

y = | -1 | - 4

y = 1 - 4

y = -3

Comment any questions!

Answer:

A ∩ B = {7, 8}

Step-by-step explanation:

A = {1, 2, 5, 7, 8}

B = {6, 7, 8, 9}

A ∩ B = set of elements in both A and B

A ∩ B = {7, 8}

Answer:

B. Positive linear

Step-by-step explanation:

First, this graph is a linear graph because a linear graph is a straight line. The graph in the diagram is also a straight line, so it is linear.
Also, notice how as x increases, y increases. This means that the graph is positive

The equivalent ratios are 8: 6 and 12:9.    

Two ratios are equivalent if they represent the same proportion or relative size. To find an equivalent ratio, we can multiply both terms of the ratio by the same non-zero number. This doesn't change the condition between the two terms.  

Here we have 4:3

To find equivalent ratios, we can multiply both terms by the same number.

Multiplying by 2

=> 4 × 2 : 3 × 2

=> 8 : 6

Multiplying by 3

=> 4 × 3 : 3 × 3

=> 12: 9

Therefore,

The equivalent ratios are 8: 6 and 12:9.    

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Complete Question

What is the equivalent ratio for 4: 3

The equivalent fraction for 1, using the number line and dividing it into four equal parts, is 1/4.

To find an equivalent fraction using a number line, we need to determine a fraction that represents the same value as the given fraction.

Let's assume the given fraction is 1. On a number line, the fraction 1 can be represented as the distance between 0 and 1. Now, we want to find an equivalent fraction, so let's choose a different representation on the number line.

To find an equivalent fraction that represents the same value, we can divide the number line segment between 0 and 1 into equal parts. Let's say we divide it into 4 equal parts.

Now, we need to determine which of the four equal parts represents the fraction 1. Since we divided the segment into four equal parts, each part represents 1/4 (one-fourth) of the whole segment.

Therefore, the equivalent fraction for 1, using the number line and dividing it into four equal parts, is 1/4.

So, the equivalent fraction for 1 is 1/4.

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i) It has been proven that CD/GH​ =  AC/FG by Corresponding Sides of Similar Triangles

ii)  △DCB ∼△HGE by the AA criterion of similarity

iii) △DCA ∼△HGF by the AA criterion of similarity

In △ABC and △FEG, we are told that they are similar and as such we can denote as:

△ABC ∼ △FEG

Thus, we can say that:

∠ACB = ∠EGF (Corresponding angles of similar triangles)

We are told that, CD and GH are bisectors of ∠ACB and ∠EGH respectively and as such we can say that:

∠ACB = 2∠ACD = 2∠BCD

∠EGF = 2∠FGH = 2∠HGE

Thus, by substitution, we can say that:

∠ACD = ∠FGH and ∠DCB = ∠HGE ...................(1)

Similarly:

∠A = ∠F and ∠B = ∠E ...............(2)

With respect to equations 1 and 2 we can establish that:

△ACD ∼ △FGH by the AA criterion of similarity

Similarly, △DCA ∼△HGF

Thus:

CD/GH​ =  AC/FG (Corresponding Sides of Similar Triangles)

Similarly, In △DCB and △HGE, we can also establish that

△DCB ∼△HGE by the AA criterion of similarity

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Answer:

Therefore, the constant of proportionality for the given proportional relationship is 5.

Step-by-step explanation:

To determine the constant of proportionality in the given proportional relationship, we can use the formula:

Constant of Proportionality = Tickets / Games

Let's plug in the values from the table:

For the first set of values (4 games and 20 tickets):

Constant of Proportionality = 20 / 4 = 5

For the second set of values (7 games and 35 tickets):

Constant of Proportionality = 35 / 7 = 5

For the third set of values (10 games and 50 tickets):

Constant of Proportionality = 50 / 10 = 5

In all three cases, the constant of proportionality is equal to 5.

Therefore, the constant of proportionality for the given proportional relationship is 5.

Answer:

Question 1) Is option C: 2. (Question 2) The correct answer is 1.09 for the K12 program. Question 3) Option A: The value of a motorcycle decreases by 12% each year. (Option C) Every year, the number of online subscribers to a service is 4 times what it was the previous year.

The ratio of outputs for any two inputs that are one value apart is 4 thus option (A) is correct. The ratio of outputs for any two inputs that are two values apart is 1/8. The situation in option (3) represents the exponential function.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given table,

The ratio of outputs for any two inputs that are one value apart = (-1/2)/(-1/8) = 4

The ratio of outputs for any two inputs that are two values apart = (-1/8)/(-1) = 1/8

Every year, the number of online subscribers to a service is 4 times what it was the previous year's exponential function with a 4^x exponent.

Hence "The ratio of outputs for any two inputs that are one value apart is 4. The ratio of outputs for any two inputs that are two values apart is 1/8 and the third statement shows exponential function".

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The given limit is 0.

To solve the given limit, we can recognize the sum as a Riemann sum and convert it into an integral.

The given sum can be rewritten as:

\(\lim_{n \to \infty} \sum_{i=1}^{n} \frac{3}{n} \sqrt{1+\frac{3i}{n}}\)

Let's rewrite it in terms of integration:

\(\lim_{n \to \infty} \frac{3}{n} \sum_{i=1}^{n} \sqrt{1+\frac{3i}{n}}\)

Since we are taking the limit as n approaches infinity, we can approximate the sum as an integral.

The integral that corresponds to the given sum is:

\(\lim_{n \to \infty} \frac{3}{n} \sum_{i=1}^{n} \sqrt{1+\frac{3i}{n}} \approx \lim_{n \to \infty} \frac{3}{n} \int_{0}^{1} \sqrt{1+3x} ,dx\)

To solve this integral, we can use a change of variables.

Let u = 1 + 3x, then du = 3dx.

The integral becomes:

\(\lim_{n \to \infty} \frac{3}{n} \int_{0}^{1} \sqrt{1+3x} ,dx = \lim_{n \to \infty} \frac{1}{n} \int_{1}^{4} \sqrt{u} ,du\)

Integrating \(\sqrt{u}\), we get,

\(\lim_{n \to \infty} \frac{1}{n} \int_{1}^{4} \sqrt{u} ,du = \lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} u^{3/2}\right]_{1}^{4}\)

Substituting the limits, we have:

\(\lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} (4)^{3/2} - \frac{2}{3} (1)^{3/2}\right]\)

Simplifying further:

\(\lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} (8 - 2)\right] = \lim_{n \to \infty} \frac{1}{n} \left[\frac{12}{3}\right] = \lim_{n \to \infty} \frac{4}{n} = 0\)

Therefore, the given limit is 0.

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It should be noted that Polygon 3 and polygon 4 are similar to polygon 1.

In geometry, it should be noted that a polygon is a plane figure which is described by a finite number of straight line segments that are connected in order to form a closed polygonal chain.

In this case, the bounded plane region, the bounding circuit, may be called a polygon. Also, a similarity transformation is the conformal mapping whose transformation matrix are identical.

In this case, it should be noted that Polygon 3 and polygon 4 are similar to polygon 1.

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Answer:

157.62

Step-by-step explanation:

Answer:

1cy

Step-by-step explanation:

c(8)+4y=12

8c+4y=12

12cy /12cy=12 /12cy

1cy

Answer:A unique line is defined by any two distinct (not identical) points. You have two distinct, which means you have a line. To find the equation for the line, we start with the slope-intercept equation for a line. This is only a template for a generic line, so we will have to find the specific values of m (slope) and b (y-intercept) that define your line.

The template: y = mx + b

b is the y-intercept, which, if you look at (0,–2), you will see is –2; it is where the line crosses the y-axis. Fill that value of b into our template to get:

y = mx – 2

Now, we only need the value of m, which is the slope. If you have two points on a line, you can calculate the slope of that line. The slope is the change (difference) of y over the change in x (difference) of x for two given points on the line. It's a fraction or ratio though sometimes it can be reduced to an integer.

So, taking your two points, you calculate the slope, m, in the following way:

(x1,y1) = (0,–2)

(x2,y2) = (5,1)

        y2 – y1                   1 – (–2)                1 + 2               3

m = ________   =     ________    =     ________  =    ____

       x2 – x1                      5 — 0            

Step-by-step explanation:

Multivariable methods include a number of specific procedures to simultaneously assess the relationships between several exposure or risk factor variables and a single.

The above statement is True.

Multivariate statistical methods are used to analyze the joint behavior of multiple random variables. A wide range of multivariate methods are available. These techniques can be performed using Stat graphics multivariate statistical analysis.

Multivariate statistics is a subdivision of statistics that involves the simultaneous observation and analysis of multiple outcome variables. Multivariate statistics is about understanding the different goals and backgrounds of different forms of multivariate analysis and how they relate to each other. The practical application of multivariate statistics to a particular problem requires the use of various types of univariate and multivariate analyzes to understand the relationships between variables and their relevance to the problem under study. .

Multivariate statistics are also related to multivariate probability distributions in terms of how they can be used to describe the distribution of observed data.

Certain types of problems with multivariate data, such as simple linear regression and multiple regression, are generally not considered special cases of multivariate statistics. This is because the analysis takes into account the (univariate) conditional distribution of a single outcome variable given the other variables.

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Answer:

The original cost of the digital camera is Rs. 18,500.

Step-by-step explanation:

Let c be the original cost of the digital camera

Since VAT of 13% was added then we can say that the amount that was paid was 13% more than the original price. So the payment made was 113% of the original amount or 1.13 in decimal

Payment = original cost + 13% VAT

20, 905 = c + 0.13c

20, 905 = 1.13c

Divide both sides of the equation by 1.13

20905/1.13 = 1.13c/1.13

18,500 = c

c = Rs. 18,500

The amount Luca needs to charge per client to reach his profit goal is $670.76.

The correct answer is Option D.

Given data:

Let x be the amount Luca needs to charge per client.

Total monthly revenue = Number of clients * Amount charged per client

Total monthly revenue = 37 * x

Total monthly expenses = Fixed monthly expenses + (Variable expenses per client * Number of clients)

Total monthly expenses = $3,345 + ($267 * 37)

Monthly profit = Total monthly revenue - Total monthly expenses

$11,594 = (37 * x) - ($3,345 + ($267 * 37))

On solving for x:

$11,594 = 37x - $13,224

37x = $11,594 + $13,224

37x = $24,818

On simplifying the equation:

x = $24,818 / 37

x ≈ $670.756

Hence, Luca needs to charge $670.76 per client to reach his profit goal.

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Answer:

x=10 and x=-4

Step-by-step explanation:

When the absolute value is all by itself on one side of the equation, the next step is to remove the absolute value bars. This will create TWO separate equations.

| x - 3 | = 7

x-3 = 7 This is one of the equations. Just straight up copied the equation but without the bars.

Here is the second equation:

x - 3 = -7

It is the left side copied, without the bars, but the right side has the opposite sign.

Solve these both separately to find the answers.

x-3=7 and x-3=-7

x=10 and x=-4

Answer:

As = 256\(\pi\) or 804.25cm

Step-by-step explanation:

By formula As = \(4\pi r^{2}\)

As = 256\(\pi\) or 804.25cm

Answer:

Explanation:

A.

The standard form of a quadratic equation is given as;

Given the below quadratic equation;

If we compare the given quadratic equation with the standard form of a quadratic equation, we can see that;

B.

We can tell if the graph of the given equation will open up or down by considering the coefficients of x^2.

If the coefficient of x^2 is greater than zero, then the parabola will open upwards but if the coefficient of x^2 is less than zero, then the parabola will open downwards.

Since the coefficient of x^2 in the given equation is greater than zero, then the parabola will open upwards.

C.

To find t

The value of x in the equation given as 1/6(x - 3) = 1/3(x + 2) is 7

The equation is given as

1/6(x - 3) = 1/3(x + 2)

From the question, we can see that the equation is a linear equation with one variable

As a general rule: linear equations are equations that have constant average rates of change.

We start by multiplying both sides of the equation by 6

So, we have the following equation

6 * 1/6(x - 3) = 1/3(x + 2) * 6

Next, we evaluate the products

So, we have the following equation

x - 3 = 2x + 4

Next, we collect the like terms

So, we have the following equation

2x - x = 3 + 4

Evaluate the like terms in the above equation

x = 7

This means that the solution of the equation is 7

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Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Answer:

 x ≠ -5

Step-by-step explanation:

The easiest way is to factor the numerator.

x2 + 9x + 20 = (x + 4)(x + 5)

Then

(x2 + 9x + 20)/(x + 5) = (x + 4)(x + 5) / (x + 5) = x + 4,

with the restriction that x ≠ -5

There is evidence to suggest that the market share for the Honda Civic in the city is different from its national market share of 20% by using Hypothesis test. 95% confident that the proportion of compact cars sold in the city that are either a Honda Civic, Toyota Corolla, or Nissan Sentra is between 0.512 and 0.613.

Conduct a hypothesis test at the 5% level of significance to determine if the market share for the Honda Civic in the city is different from its national market share of 20%. First, we need to calculate the expected frequencies for each category based on the national market shares:

Honda Civic: 0.20 x 400 = 80

Toyota Corolla: 0.17 x 400 = 68

Nissan Sentra: 0.12 x 400 = 48

Hyundai Elantra: 0.10 x 400 = 40

Chevrolet Cruze: 0.10 x 400 = 40

Ford Focus: 0.08 x 400 = 32

Others: 0.23 x 400 = 92

Then, we can use the chi-squared goodness-of-fit test to determine if the observed frequencies in the sample are significantly different from the expected frequencies.

The test statistic is calculated as follows:

chi-squared = sum((observed - expected)^2 / expected)

Using the observed and expected frequencies from the sample, we get:

chi-squared = ((99-80)^2/80) + ((73-68)^2/68) + ((53-48)^2/48) + ((45-40)^2/40) + ((41-40)^2/40) + ((26-32)^2/32) + ((63-92)^2/92) = 14.68

The degrees of freedom for this test are df = k - 1 = 7 - 1 = 6, where k is the number of categories. Using a chi-squared distribution table with 6 degrees of freedom and a significance level of 0.05, the critical value is 12.59.

Since our calculated chi-squared value of 14.68 is greater than the critical value of 12.59, we reject the null hypothesis and conclude that there is evidence to suggest that the market share for the Honda Civic in the city is different from its national market share of 20%.

b) Construct a 95% confidence interval for the proportion of compact cars sold in the city that are either a Honda Civic, Toyota Corolla, or Nissan Sentra.

We can use the formula for a confidence interval for a proportion:

CI = p ± zsqrt(p(1-p)/n)

where p is the proportion of interest, z is the critical value from the standard normal distribution (1.96 for a 95% confidence interval), and n is the sample size.

We want to find the proportion of compact cars sold in the city that are either a Honda Civic, Toyota Corolla, or Nissan Sentra. From the sample, the total number of sales for these three models is 99 + 73 + 53 = 225. The total sample size is 400.

So, the proportion we are interested in is:

p = 225/400 = 0.5625

Plugging in the values, we get:

CI = 0.5625 ± 1.96sqrt(0.5625(1-0.5625)/400) = 0.512 to 0.613

Therefore, we can be 95% confident that the proportion of compact cars sold in the city that are either a Honda Civic, Toyota Corolla, or Nissan Sentra is between 0.512 and 0.613.

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_____The given question is incommplete, the complete question is given below:

Based on 2017 sales, the six top-selling compact cars are the Honda Civic Toyota Corolla_ Nissan Sentra Hyundal Elantra_ Chevrolet Cruze; and Ford Focus (New York Daily News) . The 2017 market shares are Honda Civic 20 %, Toyota Corolla 17%, Nissan Sentra 12 %, Hyundar Elantra 10 %, Chevrolet Cruze 10%_ and Ford Focus 8% with other small car models comprising the remaining 23%. sample of 400 compact car sales in Chicago showed the following number of vehicles sold_ Excel File: datal2-27xlsx Honda Civic Toyota Corolla Nissan Sentra Hyundai Elantra Chevrolet Cruze Ford Focus Others Use goodness of fit test to determine whether the sample data indicate that the market shares for cars in Chicago are different than the market shares suggested by nationwide 2017 sales_ Using 0.05 level of significance what is the P-value? Use Table of Appendix The p-value Select your answer What is your conclusion? Conclude that the markets shares for the seven compact cars in Chicago Select your GMAAT the market shares reported_ What market share differences, if any; exist in Chicago? Round your answers to three decimal places Enter negative values as negative numbers_ Sample Hypothesized Market Share Compact Car Market Share Honda Civic Difference Toyota Corolla Nissan Sentra Hyundai Elantra Chevrolet Cruze 0.10 0.10 Ford Focus Others 0.23