Mathematics College

A poll commissioned by Friends of the Earth and conducted by the Mellman Group found that 72% of American voters are in favor a carbon tax. Suppose that six voters in the United States are randomly sampled and asked whether they favor a carbon tax. Determine the probability that the number answering in the affirmative is a. Exactly four. b. At least two

Answers

Answer 1

Answer:

$P(X = 4) = 0.31599$

$P(X \ge 2) = 0.9921 $

Step-by-step explanation:

From the question we are told that

The proportion in favor of carbon tax is $p = 0.72$

The sample size is n = 6

Generally the distribution of poll follows a binomial distribution

i.e

$X \~ \ \ \ B(n , p)$

and the probability distribution function for binomial distribution is

$P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}$

Here C stands for combination hence we are going to be making use of the combination function in our calculators

Generally the probability that the number answering in the affirmative is 4 is mathematically represented as

$P(X = 4) = ^{6}C_4 * (0.72)^4 * (1- 0.72)^{6-4}$

=> $P(X = 4) = 0.31599$

Generally the probability that the number answering in the affirmative is At least two is mathematically represented as

$P(X \ge 2) = 1 - P( X < 2 ) $

$P(X \ge 2) = 1- [ P(X = 0 ) + P( X = 1)] $

=> $P(X \ge 2) = 1- [ [ 1 * 1 * 0.00048 ]+ [ 6 * 0.72 * 0.00172] $

=> $P(X \ge 2) = 1- [ 0.00791 ] $

=> $P(X \ge 2) = 0.9921 $

Related Questions

Use the approximate half-life formula for the case described below. Discuss whether the formula is valid for the case described. Poaching is causing a population of elephants to decline by 4 % per year. What is the half-life for the population? If there are 10,000 elephants today, how many will remain in 50 years? Question content area bottom Part 1 Use the approximate half-life formula. What is the half-life for the population? enter your response here years (Type an integer or decimal rounded to the nearest hundredth as needed.)

Answers

The approximate half-life formula is:

t(1/2) ≈ 0.693 / r

where r is the annual rate of decline as a decimal. In this case, r = 0.04, since the population is declining by 4% per year. Therefore:

t(1/2) ≈ 0.693 / 0.04 ≈ 17.325 years

So the half-life for the population of elephants is approximately 17.325 years.

The approximate half-life formula is valid for this case since the rate of decline is relatively small (4% per year) and the formula is designed for exponential decay with small rates of change. However, it is important to note that the formula is only an approximation and may not be accurate for large rates of change or over long periods of time.

To find the number of elephants that will remain in 50 years, we can use the formula:

N(t) = N0 * (1 - r)^t

where N0 is the initial population (10,000), r is the annual rate of decline as a decimal (0.04), and t is the time in years (50). Therefore:

N(50) = 10,000 * (1 - 0.04)^50 ≈ 4,877

So there will be approximately 4,877 elephants remaining in 50 years. Answer: 4,877.

Which statement is true ?
- 4 is the domain of f(g)
- 4 isn’t in the domain of f(g)

Answers

The statement -4 is not in the domain of f(g) is true.

What is domain?

The domain is defined by the set of values of independent variables. The set of inputs that a function will accept is known as the domain of the function in mathematics. The collection of all potential inputs for a function is known as its domain.

what is range?

In a function for each domain, we get a possible output from dependent variable which is termed as range.

From the diagram shown -4 cannot be used as domain because the output might be an imaginary number.

So, -4 is not in the domain of f(g) is true

hence, -4 cannot be a domain of given function f(g)

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The statement -4 is not in the domain of f(g) is true.

What is domain?

The domain is defined by the set of values of independent variables. The set of inputs that a function will accept is known as the domain of the function in mathematics. The collection of all potential inputs for a function is known as its domain.

What is range?

In a function for each domain, we get a possible output from dependent variable which is termed as range.

From the diagram shown -4 cannot be used as domain because the output might be an imaginary number.
So, -4 is not in the domain of f(g) is true
hence, -4 cannot be a domain of given function f(g)

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More than two-thirds of undergraduate students who graduated with a bachelor's degree had student loan debt. The average student loan debt among these graduating seniors was $28,654. The average interest rate on student loans was 6.1%. How much interest did a student with $28,654 in student loan debt pay in the first year? Round to the nearest cent.

Answers

The interest paid for the loan is $1748

Given that there is a 6.1% interest rate for a loan of $28,654 in student loan debt pay in the first year,

We need to find the interest paid for the same.

So,

Simple Interest = principal × time × rate / 100

= 28654 × 1 × 6.1 / 100

= 28654 × 0.061

= 1747.894

= 1748

Hence the interest paid for the loan is $1748

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4. Monica wants to join a gym. Gym A: $20 joining fee and $30 monthly charge. Gym B: No
joining fee and $40 monthly charge. Enter the number of months it will take for the total cost
for both gyms to be equal.

Answers

Answer:

it would take 2 months

Step-by-step explanation:

gym a= 20 +30+30 =80

Gym b = 40 + 40 = 80

pls help i’ll give brainlist

Answers

Answer:

The answer must be 95. (The red one.)

Step-by-step explanation:

The two smallest sides of a triangle when added together MUST be more than the longest side. 95+25 is 120! I hope this helps!

Econo motel charges $260 for 4 nights. At that rate, how much would 7 nights cost

Answers

Divide the cost for 4 nights by 4 to get cost per night.

260/4 = 65 per night.

Multiply cost per night by 7:

65 x 7 = 455

It would cost $455 for 7 nights.

The period of the sinusoidal graph shown is:
3 п
2
A П
В
2п
C
-2п -п
-3
-3
-6
у
TT
2п х

The period of the sinusoidal graph shown is:3 2A 2C-2 --3-3-6TT2

Answers

The period of a sinusoidal graph is the distance between two consecutive peaks or troughs of the graph. From the given graph, we can see that the graph completes one full cycle from x = 0 to x = 2π. Therefore, the period of the graph is 2π.

How can we determine the period of a sinusoidal graph?

The period of a sinusoidal graph is the distance between two consecutive peaks or troughs of the graph. It can be determined by calculating the length of one complete cycle of the graph.

What does the period of a sinusoidal graph tell us about the function?

The period of a sinusoidal graph tells us how often the function repeats itself. It is an important characteristic of the function that can help us analyze its behavior and make predictions about its future values.

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Which expression is equivalent to 12x12x12x12x12x12x12x12x12x12x12

Answers

Answer:

$12 {}^{11} $

Amanda is going to build some large wooden storage boxes. The boxes are shaped like rectangular prisms, as shown below. She wants to cover all the sides of each box with special wallpaper. If she has a total of of wallpaper, how many boxes can she cover?

Answers

The number of boxes that Amanda can cover with W square inches of wallpaper will be equal to W/2(lw + lh + wh).

Let's assume that Amanda wants to build n wooden storage boxes. All of these boxes are shaped like rectangular prisms, as shown in the image below.

She wants to cover all the sides of each box with special wallpaper. If she has a total of W square inches of wallpaper, we need to find out how many boxes she can cover. Let's solve this problem mathematically.

Mathematical Solution:

Each rectangular prism has six sides (faces). If we want to cover all the six sides of a rectangular prism with special wallpaper, we need to find the total surface area of that rectangular prism. Therefore, the surface area of each rectangular prism can be calculated by the formula:

Surface Area = 2lw + 2lh + 2wh,

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

We know that Amanda has W square inches of wallpaper to cover all the boxes. Therefore, the total surface area of n boxes will be:

n × Surface Area = W.

Substituting the value of the Surface Area, we have:

n × (2lw + 2lh + 2wh) = W

2n(lw + lh + wh) = W

n(lw + lh + wh) = W/2

n = W/2(lw + lh + wh).

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0.5x + 6 > 3
I don’t know how to solve

Answers

Answer:

x > -6

Step-by-step explanation:

Move 6 to the other side:

0.5x > -3

x > -6

The length of a rectangle is 5 cm more than its width. If the perimeter is 58cm, calculate:

(a) Write an equation to show the perimeter of the rectangle ?

(b) calculate:
I.width

II.length

III. the area of the rectangle

Answers

The equation to show the perimeter of the rectangle is P = 2(2w + 5)

Writing an equation to show the perimeter of the rectangle

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

Length = 5 more than the width

Also, we have

Perimeter = 58

This means that

P = 2(w + 5 + w)

P = 2(2w + 5)

Calculating the dimensions and the area

In (a), we have

P = 2(2w + 5)

This gives

2(2w + 5) = 58

So, we have

2w + 5 = 29

2w = 24

w = 12

Next, we have

l = 12 + 5

l = 17

Lastly, we have

Area = 17 * 12

Area = 204

Answers

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

Answer:

Step-by-step explanation:

Hi tag brainliest ❣️

Thanks

Since the shaded area equal 4

our answer is A

that is the number of shaded area ÷ the total number of points

Need help with short problem 1

Answers

As stated in the problem description, matrix A transforms the input vector (x, y, and z) into the output vector (y+z, 2x-z, 0).

The matrix A is: | 0 1 1 |, | 2 0 -1 |, | 0 0 0 |

What is a matrix?

A matrix, sometimes known as matrices, is a rectangular array or table of letters, numbers, or other symbols organized in rows and columns that are used to represent a mathematical object or a characteristic of one.

In linear algebra, matrices describe linear mappings and enable explicit computations. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices. The composition of linear maps, for instance, is represented by matrix multiplication.

Not every matrix has a connection to linear algebra. This is especially true for incidence matrices and adjacency matrices in graph theory.

The matrix A is:

| 0 1 1 |

| 2 0 -1 |

| 0 0 0 |

Applying the matrix multiplication A x y z to any random vector (x, y, z) will demonstrate why:

| 0 1 1 | | x | | y + z |

| 2 0 -1 | x | y | = | 2x - z |

| 0 0 0 | | z | | 0 |

Hence, as stated in the problem statement, matrix A transforms the input vector (x, y, and z) into the output vector (y+z, 2x-z, 0).

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What is 4(-6)/12*2?

Answers

Step-by-step explanation:

$ \frac{4 \times - 6}{12 \times 2} $

$ = \frac{ - 24}{24} $

$ = - 1$

What is / mean in math equation

Answers

Step-by-step explanation:

If there's a number that has for example 6/5 the / means dividing

The slash stands for division.

The children at Colin Powell Middle School donated 400 can goods to help
feed the homeless. 100 of the cans were corn. When the children sort the
cans in boxes, what is the probability (in percent) of the first can pulled
being a can of corn?

Answers

Answer:

25%

Step-by-step explanation:

400 divided by 100 = .25 which is 25%

Find m and c for this line

Y+3x=1

Answers

Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

What is the domain of the function y = 2 StartRoot x minus 5 EndRoot?
x greater-than-or-equal-to negative 5
x greater-than-or-equal-to 2
x greater-than-or-equal-to 5
x greater-than-or-equal-to 10

Answers

Answer:

The domain of the function should be:

'x greater than or equal to negative -5'.

Hence, option A is true.

Step-by-step explanation:

Given the expression

$2\sqrt{x-5}$

The domain of a function is the set of input or arguments for which the function is real and defined

We know that the value, inside the radicand, is the number found inside a radical symbol which must be greater than 0, otherwise, it would make the function undefined,

i.e.

x-5 ≥ 0

x ≥ 5

In other words, the domain of the function should be:

'x greater than or equal to negative -5'.

Therefore, the domain of the function:

x ≥ 5

$\mathrm{Domain\:of\:}\:2\sqrt{x-5}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:5\:\\ \:\mathrm{Interval\:Notation:}&\:[5,\:\infty \:)\end{bmatrix}$

Hence, option A is true.

The domain of the function y = 2√(x - 5) will be x greater-than-or-equal-to 5. Then the correct option is C.

What are domain and range?

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

y = 2√(x - 5)

Then the domain of the function will be

We know that the value inside the square root should be greater than or equal to zero. Then the domain will be

x - 5 ≥ 0

Simplify the inequality, then the domain of the function will be

x - 5 ≥ 0

x ≥ 5

The domain of the function y = 2√(x - 5) will be x greater-than-or-equal-to 5.

Then the correct option is C.

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You bought the following items at 20% off. How much did you pay total?
Tent $70, jacket $60, gloves $25, snowboard $350, goggles $30

Answers

Answer:

$524.30

Step-by-step explanation:

70+60+25+350+30= 535

535*.02(20%)

10.7

535-10.7=

524.3

Answer:

$107

Step-by-step explanation:

First you have to add up the costs and you get a total of $535

Then you need to make 535 equivalent to 100 then divide by 20 to get 107

Hope that helps and have a great day!

Hove
Find the average rate of change indicated below.
y = 4x+1
[-1, 1)

A.15
B.3.75
C.1.875
D.7.5

Answers

The average rate of change of the function over the interval is 4

Finding the average rate of change

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

y = 4x + 1

The interval is given as

[-1, 1)

The function is a linear function

This means that it has a constant average rate of change

From y = 4x + 1, we have

Rate = 4

Hence, the rate is 4

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y=2x2+18 find coordinates of the vertex

Answers

Answer:

Step-by-step explanation:

x- coordinate of the vertex is

x= -b/2a = -0/2*2 = 0

y-coordinate is

y= 2*0 +18 = 18

so vertex is at (0, 18)

In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, what would the same 30 second commercial have cost during the first Super Bowl in 1967, when the CPI was 33.4? Round your answer to the nearest hundred dollars.

Answers

In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.

To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).

The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.

Given data:

Cost of a 30-second commercial in 2021 = $5.6 million

CPI in 2021 = 271.4

CPI in 1967 = 33.4

To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:

Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)

Cost in 1967 = ($5.6 million) * (33.4 / 271.4)

Cost in 1967 ≈ $0.689 million

To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:

Cost in 1967 ≈ $68,900

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what is the least whole number that rounds to 230000 when rounded to the nearest ten thousand?

Answers

The least whole number that can be rounded to 230,000 is 225,000.

What is the least whole number?

The ten thousand number (10,000) is usually the fifth digit in a number when counting from the right to the left. For example, in 132,456, 3 is the ten thousand number.

To round off to the nearest ten thousand, if the thousand digit is equal to or greater than 5 (i.e. 5,6, 7, 8, 9), 1 is added to the ten thousand digit and other numbers less than the ten thousand digit becomes 0. For example, when 234,612 is rounded to the nearest ten thousand, the number becomes 235,000.

If the thousand digit is less than 5 (i.e. 0, 1, 2, 3, 4), there is no change in the ten thousand digit other numbers less than the ten thousand digit becomes 0. For example, when 234,412 is rounded to the nearest ten thousand, the number becomes 234,000.

The numbers that can be rounded off to 230,000 are: 225,000, 226,000, 227,000, 228,000, 229,000, 230,000, 231,000, 232,000, 233,000, 234,000

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What is the meaning of "if $\varphi (x)$ has no parameters $p_{i}$ then the class C is definable"?

$What is the meaning of "if [tex]\varphi (x)[/tex] has no parameters [tex]p_{i}[/tex] then the class C$

Answers

The meaning of the statement, "if the function has no parameters, then the class C is definable" is that if there are no parameters given then the class c can be defined with an empty set but if there are no parameters, then the class cannot be defined.

What is the meaning of the statement?

The meaning of the above statement is that if no parameters are provided for this function, then the given class represented as c can be defined with an empty set that is enclosed in parameters.

Also, if the parameters are given then the class c is not defined.

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What is the product of -2/7 and -3/7 ?

Answers

Answer:

6/49

Step-by-step explanation:

-2/7 * -3/7 = (-2 * -3) / (7*7) = 6/49

can i get a OHHHHHH YEAHHHH

Answers

Answer:

AW YEAHHHHHHHHHHHHHHHHHHHHHHHHHHH

Step-by-step explanation:

Answer:

OH YEAHHHH

Step-by-step explanation:

lol

parallel lines are two lines that never meet. find an example that contradicts this definition. How would you change the definition to make it more accurate?

Answers

A more modern explanation would be, "Parallel lines are two lines within a given plane that never intersect."

Two lines on a sphere are an illustration that defies the notion of parallel lines. Meridians are the name given to longitude lines on spheres like the Earth.

Meridians are lines that run parallel to one another from the North Pole to the South Pole. However, if we take into account two meridian lines, they will cross at the North and South Poles. Two lines that are originally parallel will, therefore, eventually intersect at the poles on a sphere, defying the notion of parallel lines.

We can change the original definition of parallel lines to read, "Parallel lines are two lines that do not intersect within a given plane."

This adjustment accounts for the fact that lines can exist in many geometrical contexts, such as on a sphere or in three-dimensional space, where the idea of parallelism may be different. By including the phrase "within a given plane," we restrict the concept to the typical geometry seen in Euclidean geometry, where parallel lines do not meet.

A newer definition may therefore read, "Parallel lines are two lines within a given plane that never intersect." This updated definition makes clear that parallel lines must be taken into account inside a certain plane in order to maintain their validity, while also acknowledging the limitations of the idea.

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Simplest form 816/10

Answers

It’s 408/5 in the simplest form. To find the answer just divide the numbers.

The simplest form of 816/10 is 408/5

Please mark my answers as brainlist....

which can be represented using the product (50)*(-5) ?

Answers

The expression that can be represented by product (50)*(-5) is 250

Which expression represented using the product (50)*(-5) ?

Any number that can be expressed as the product of 50 and -5 can be represented using the expression (50)*(-5).

For example, if we multiply 50 and -5, we get -250. Therefore, -250 can be represented using the expression (50)*(-5).

Similarly, if we multiply 50 and -5 by any other number, we can represent the product using the expression (50)*(-5).

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