Suppose a jar contains 19 purple M&Ms and 24 yellow M&Ms. If you reach in the jar and pull out two M&Ms at random at the same time:
Answer the following using a fraction or a decimal rounded to three places where necessary.
a) Are the events dependent or independent? Select an answer Dependent Independent
b) Why? Select an answer The M&Ms are chosen at the same time The total number of M&Ms is known The M&Ms are drawn from a jar with a large number of M&Ms Each M&M is replaced before the next M&M is drawn
c) Find the probability that both are purple.

Answer:

(5π/12)(11) = about 14.4 inches

Answer:Joanie watched 4/15 of the movie  at night

Step-by-step explanation:

Let total amount of movie to watch = 1 whole since we are dealing with fractions

Amount of movie watched in the morning = 1/3

Amount watched at night = x

Amount remaining= 2/5

so that  Total amount of movie to watch - Amount watched in morning and night = Amount remaining to watch

1 - ( 1/3 + x ) = 2/5

1- 2/5 = 1/3 + x

3/5 =1/3 + x

3/5 - 1/3 = x

9- 5/15 = x

x= Amount watched at night = 4/15

Equations for common surfaces:

1. Plane: Ax + By + Cz + D = 0

2. Sphere: (x - h)² + (y - k)² + (z - l)² = r²

3. (Elliptic) Paraboloid: z = ax² + by² + c

4. Hyperbolic Paraboloid: z = ax² - by² + c

5. (Circular) Cylinder: (x - h)² + (y - k)² = r²

6. Half Cone: z = √(x² + y²)

For each surface:

1. Plane: The easiest coordinate system to express the equation is the Cartesian coordinate system (x, y, z) since the equation involves linear terms in all three variables.

2. Sphere: The Cartesian coordinate system (x, y, z) is most suitable for expressing the equation of a sphere because it directly relates to the distance between the center of the sphere and any point on its surface.

3. (Elliptic) Paraboloid: The Cartesian coordinate system (x, y, z) is most convenient for expressing the equation of a (elliptic) paraboloid because it allows a direct representation of the quadratic terms in x and y.

4. Hyperbolic Paraboloid: Similar to the (elliptic) paraboloid, the Cartesian coordinate system (x, y, z) is best suited for expressing the equation of a hyperbolic paraboloid due to its direct representation of the quadratic terms.

5. (Circular) Cylinder: The cylindrical coordinate system (ρ, φ, z) is easiest to express the equation of a (circular) cylinder because it naturally separates the radial distance from the axis (ρ) and the angle in the xy-plane (φ).

6. Half Cone: The Cartesian coordinate system (x, y, z) is most suitable for expressing the equation of a half cone since it provides a direct representation of the relationship between the coordinates and the square root of the sum of their squares.

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The inverse function is used to find the temperature in Celsius,

the temperature in celsius is  -12.22°C and 32.22°C.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator).

Given expression for temperature calculation

Original function: F =  9/5​C + 32

Inverse function: C = (F − 32)5/9

where C is temp. in Celsius and F is temp. in Fahrenheit,

so when the temperature is given in Fahrenheit we have to use the inverse function formula to calculate the temperature in degree celsius,

because it will be easy to calculate.

temperature = 10°F

C = (F − 32)5/9

C = (10 - 32)5/9

C = -22 x 5/9

C =  -12.22°C

when temperature = 90°F

C = (90 - 32)5/9

C = 32.22°C

Hence the temperature is  -12.22°C and 32.22°C.

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96% confidence interval for the population mean life of light bulbs produced by the electrical firm to be between 747.63 and 812.37 hours. This can be answered by the concept of standard deviation.

To calculate the confidence interval, we first need to determine the standard error of the mean, which can be calculated using the formula:

Standard Error of Mean = (Standard Deviation of Population) / sqrt(Sample Size)

In this case, the standard deviation of the population is given as 40 hours, and the sample size is 30. Thus, the standard error of the mean can be calculated as:

Standard Error of Mean = 40 / sqrt(30) = 7.32

Next, we need to find the critical value of t for a 96% confidence level with 29 degrees of freedom (n-1). Using a t-distribution table or calculator, we find this to be 2.048.

Using these values, we can calculate the confidence interval using the formula:

Confidence Interval = Sample Mean +/- (Critical Value * Standard Error of Mean)

Substituting the given values, we get:

Confidence Interval = 780 +/- (2.048 * 7.32) = 780 +/- 15.02

Therefore, the 96% confidence interval for the population mean life of light bulbs produced by the electrical firm is between 747.63 and 812.37 hours. This means we can be 96% confident that the true mean life of all light bulbs produced by the firm falls within this interval.

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The length of the second lawn that Sid mows is 60 feet. We simply calculated the area of lawn here.

The area of the first lawn is given by:

A1 = 60 x 50 = 3000 square feet

Let L2 be the length of the second lawn. Since the width of the second lawn is the same as the first lawn, the area of the second lawn can be expressed as:

A2 = L2 x 150

Since the area of the second lawn is 3 times as big as the first lawn, we have:

A2 = 3A1

Substituting A1 and simplifying, we get:

L2 x 150 = 3 x 3000

L2 x 150 = 9000

L2 = 60 feet

Therefore, the length of the second lawn is 60 feet.

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The sign of displacement is negative.

Displacement: It is defined as the change in the position of an object. It is a vector quantity, means it has both direction and magnitude. It is the shortest distance between two position of an object.

It is the difference between final and the initial position of an object.

Initial position, \(x_i\) = 5m

Final position, \(x_f\) = 3m

Displacement, \(d = x_f - x_i\)  = (3 - 5)m

= -2m

negative sign shows that the direction of the an object is towards negative x-axis.

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A right trapezoid is a quadrilateral that has exactly one pair of perpendicular lines, one pair of parallel sides, and no sides with equal lengths.

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are trapezium, square, rectangle and so on.

A right trapezoid is a quadrilateral that has exactly one pair of perpendicular lines, one pair of parallel sides, and no sides with equal lengths.

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The relationship between variable F and x is 2x + 12000000/x

Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence.

Let F represent the length of fencing in feet.

Area of fencing = 6000000 ft²

Area of fencing = x * (y + y) = x * 2y

Area of fencing = 2xy

6000000=2xy

xy = 3000000

y = 3000000/x

The perimeter is:

F = x + y + y + x + y + y

F = 2x + 4y

F = 2x + 4(3000000/x)

F = 2x + 12000000/x

Therefore the relationship between variable F and x is 2x + 12000000/x

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Value for multiplication of 6.75 x 10⁶ and 1.2 × 10⁶ : 8.1 x 10¹²

What is Multiplication?

The process of finding the sum of two or more numbers is known as multiplication. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of the same size, we employ multiplication.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

We have the given values to multiply:

6.75 x 10⁶ and 1.2 × 10⁶

Now,

= 6.75 x 10⁶ x 1.2 × 10⁶

= (6.75 x 1.2) x (10⁶ x 10⁶)

= (8.1) x 10⁽⁶⁺⁶⁾

= 8.1 x 10¹²

Hence, the value of multiplication of 6.75 x 10⁶ and 1.2 × 10⁶ is 8.1 x 10¹²

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Answer:

29

Step-by-step explanation:

The volume of the cone is 441π cubic meters.

The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base of the cone, h is the height of the cone, and π is the mathematical constant pi.

Substituting the given values, we get:

V = (1/3)π(7²)(27)

Simplifying, we get:

V = (1/3)π(49)(27)

V = (1/3)π(1323)

V = 441π

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To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

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Answer:

4 hours

Step-by-step explanation:

16.5+x2

7.5+x4

16.5+2=17.5+2=19.5+2=21.5+2=23.5

7.5+4=11.5+4=15.5+4=19.5+4=23.5

Answer:

Hello! Just did the assignment! Your answer would be d. x-axis! Hope you stay safe! :)

Answer:

p=49 n=76 (b)

Step-by-step explanation:

p+n=125

p+3.52n=316.52

Therefore:

p=125-n

Now if we plug in for p

125-n+3.52n=316.52

Now solve

-125 both sides and simplify=

191.52 = 2.52n

Now divide

n=76.

Now plug in 76 for the top one

p+76=125

Simplify=

p=49

Hope this Helped <3

Answer:

A

Step-by-step explanation:

Let's subract both these equations.

P+N = 125

and

P+3.52N = 316.52

2.52 = 191.52

191.52/2.52 = 76

P = 76

76 + N = 125

N = 49

Check:

49 + 76 = 125

Answer is A

Answer:

4y-4 Hope this helps! :)

Step-by-step explanation:

The expected value of the discrete distribution is of 20.97, hence option C gives the correct answer.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Hence, according to the table, the expected value is given by:

E(X) = 12 x 0.08 + 18 x 0.15 + 20 x 0.31 + 22 x 0.08 + 24 x 0.15 + 25 x 0.23 = 20.97.

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Answer:

the right answer is the third one

Answer:

its the second one

Step-by-step explanation:

took the test

Liberal arts colleges have a higher median SAT score and a lower acceptance rate compared to research universities, while research universities have a higher expenditure per student and a higher percentage of top 10% high school graduates.

Descriptive statistics were calculated for liberal arts colleges and research universities based on the data given in the Excel file. The summary of descriptive statistics for each variable by school type is as  shown in the table.

Based on the results, it appears that liberal arts colleges have higher median SAT scores, lower acceptance rates, and lower expenditures per student than research universities. On the other hand, research universities have higher mean expenditures per student and higher median percentages of top 10% high school graduates than liberal arts colleges. Overall, there are differences in the characteristics of these two types of colleges.

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--The complete question is, Compute descriptive statistics for liberal arts colleges and research universities in the Excel file Colleges and Universities. Compare the two types of colleges. What can you conclude?

Colleges and Universities

School Type Med SAT Accept Rate Exp./Student Top 10% HS Grad %

Amherst Lib Arts 1315 22% $26,636 85 93

Barnard Lib Arts 1220 53% $17,653 69 80

Bates Lib Arts 1240 36% $17,554 58 88

Berkeley Univ 1176 37% $23,665 95 68

Bowdoin Lib Arts 1300 24% $25,703 78 90

Brown Univ 1281 24% $24,201 80 90

Bryn MawrLib Arts1255 56% $18,847 70 84

Cal Tech Univ 1400 31% $102,262 98 75

Carleton Lib Arts 1300 40% $15,904 75 80

Carnegie University1225 64% $33,607 52 77

Claremont Lib Arts1260 36% $20,377 68 74

Colby Lib Arts 1200 46% $18,872 52 84

Colgate Lib Arts 1258 38% $17,520 61 85

ColumbiaUniversity1268 29% $45,879 78 90

Cornell University1280 30% $37,137 85 83

DavisdsonLib Arts 1230 36% $17,721 77 89

Duke University 1310 25% $39,504 91 91

GeorgetownUniv 1278 24% $23,115 79 89

Grinnell Lib Arts 1244 67% $22,301 65 73

HamiltonLib Arts 1215 38% $20,722 51 85

Harvard Univ 1370 18% $46,918 90 90

HaverfordLib Arts 1285 35% $19,418 71 87

Johns Hop. Univ 1290 48% $45,460 69 86

MiddleburyLib Arts 1255 25% $24,718 65 92

MIT University 1357 30% $56,766 95 86

Mount Lib Arts 1200 61% $23,358 47 83

NWrn University 1230 47% $28,851 77 82

Oberlin Lib Arts 1247 54% $23,591 64 77

Occidental Lib Arts 1170 49% $20,192 54 72

Pomona Lib Arts 1320 33% $26,668 79 80

Princeton University 1340 17% $48,123 89 93

Rice University 1327 24% $26,730 85 88

Smith Lib Arts 1195 57% $25,271 65 87

Stanford University 1370 18% $61,921 92 88

Swarthnore Lib Arts 1310 24% $27,487 78 88

U of MI University 1195 60% $21,853 71 77

U of Chi University 1300 45% $38,937 74 73

U of Roc University 1155 56% $38,597 52 73

U PA University 1280 41% $30,882 87 86

U Va University 1218 37% $19,365 77 88

UCLA University 1142 43% $26,859 96 61

UNC University 1109 32% $19,684 82 73

Vassar Lib Arts 1287 43% $20,179 53 84

Wash U University 1225 54% $39,883 71 76

Wash & Lee Lib Arts 1234 29% $17,998 61 78

Wellesley Lib Arts 1250 49% $27,879 76 86

Wesleyan Lib Arts 1290 35% $19,948 73 91

Williams Lib Arts 1336 28% $23,772 86 93

Yale University 1350 19% $52,468 90 93--

Answer:

3 each

Step-by-step explanation:

36 / 12 = 3

.................................................

The curvature of r(t) = 3t, t2, t3 at the point (3, 1, 1) is 0.178

In this question we need to find the curvature of r(t) = <3t, t^2, t^3> at the point (3, 1, 1).

The derivative of r(t) with respect to t is:

r'(t) = <3, 2t, 3t^2>

The point (3, 1, 1) corresponds to t = 1,

and r′(1) = <3, 2(1), 3(1)^2>

r'(1) = <3, 2, 3>

|r'(1)| = √(3^2 + 2^2 + 3^2)

|r'(1)| = √(9 + 4 + 9)

|r'(1)| = √(22)

|r'(1)| = 4.69

Now, r''(t) = <0, 2, 6t>

and r′'(1) = <0, 2, 6(1)>

r''(1) = <0, 2, 6>

r′(1) × r′′(1) = <0, 4, 18>

|r′(1) × r′′(1) |

= √(0^2 + 4^2 + 18^2)

= √(16 + 324)

= √340

= 18.44

So, the curvature of r(t) would be,

κ(1) = |r′(1) × r′′(1)| ÷ |r′(1)|^3

k(1) = 18.44 / 4.69³

k(1) = 0.178

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Answer:

20

Step-by-step explanation:

The slope formula is y= mx+b

m= slope

x= x (the variable)

b= y-intercept

in this case, 20 would be m in the formula.

remember slope is rise/run. (Rise up, then go left or right)

hope this helps :)

ANSWER

Area of the shaded figure is 77.7 square unit (rounded to 1 decimal place).

EXPLANATION

Given:

Rectangle with length = 12 and breadth = 7.

Semi-Circle with diameter = 4

Desired Outcome:

The area of the shaded region.

Looking at the figure carefully, you will notice that it was only half of the circle that was fixed with the rectangle.

Determine the Area of a semi-circle

Area of a semi-circle is half of the area of a circle

Area of the Rectangle

Determine the area of the shaded figure

Hence, the Area of the shaded figure is 77.7 square unit (rounded to 1 decimal place).

Answer:

14,000

Step-by-step explanation:

if wrong i'm sorry

Quantitative data from census and survey data play a crucial role in providing information about changes in population composition and size in urban areas.

These data sources collect numerical information on various demographic characteristics of the population, such as age, gender, ethnicity, education level, income, occupation, and household size. By analyzing this quantitative data, researchers and policymakers can gain insights into the following aspects:

Population Size: Census and survey data provide accurate and comprehensive counts of the population in urban areas. They help determine the total number of individuals residing in specific geographic regions, allowing for the identification of population growth or decline over time.

Population Density: Quantitative data can reveal the concentration of population in urban areas by assessing the number of individuals per unit area. This information is crucial for urban planning, resource allocation, and infrastructure development.

Age Structure: Census and survey data provide information on the age distribution of the urban population. By examining age cohorts and changes over time, it is possible to identify trends such as population aging, shifts in generational composition, and potential implications for healthcare and social services.

Ethnic and Racial Composition: Quantitative data allow for the identification of ethnic and racial groups within urban areas. This information helps monitor changes in diversity and assess the impact of migration patterns, assimilation, and integration processes.

Socioeconomic Characteristics: Census and survey data capture information on income levels, educational attainment, employment status, and occupation. Analyzing these variables provides insights into the socioeconomic composition of urban populations, disparities, and potential social and economic challenges.

Housing and Household Characteristics: Quantitative data provide information on housing types, tenure, overcrowding, and household size in urban areas. This data is valuable for urban planning, housing policies, and understanding the dynamics of residential patterns.

By utilizing quantitative data from censuses and surveys, researchers and policymakers can monitor changes in population composition and size, identify social and economic trends, inform policy decisions, and address the specific needs and challenges of urban areas.

The complete question is:

Explain how quantitative data from census and survey data provide information about changes in Population composition and size in urban areas.

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Total cost in dollars of the meal, tax and tips is $18.75

Tips are bonus or extra payment that a customer wants to pay to the counter of restaurant or to certain workers to express the gratitude toward their hospitality. How much money will be paid is determined by the customer himself.

given, cost of meal = $15 before tax and tip

After that $7% tax and $18% tip are included upon the cost of meal

Now, cost for tax = $ (7/100 × 15) = $1.05

cost for tip = $ (18/100 × 15) =$2.7

Total cost for meal, tax and tips = cost for meal + cost for tax + cost for tip

 Total cost = $18.75

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Answer: n=5

Step-by-step explanation:

7n + 2 = 4n + 17, so first we subtract 2 from both sides.

      -2           -2

Now the equation should look like this:

7n= 4n + 15

Now since 4n is smaller than 7n we are going to subtract 4n from both sides.

7n = 4n  +15

-4n  -4n  

Now the equation should look like this:

3n = 15

All that is left to do is divide by 3 on both sides.

3n/3 = 15/3

n = 5

The equivalent value of the expression is n = 5

Given data ,

Let the equation be represented as A

Now , the value of A is

7n + 2 = 4n + 17

On simplifying the equation , we get

7n + 2 = 4n + 17

So , the left hand side of the equation is equated to the right hand side by the value of ( 4n + 17 )

Subtracting 4n on both sides , we get

3n + 2 = 17

Subtracting 2 on both sides , we get

3n = 15

Divide by 3 on both sides , we get

n = 15/3

On simplifying , we get

n = 5

Therefore , the value of n = 5

Hence , the expression is n = 5

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