Use probability notation to describe the chance of each event. Let S, C, W, and R represent sunny, cloudy, windy, and rainy weather, respectively.


rainy weather if it is windy

Answer:

<

Step-by-step explanation:

8x-2 - -4x2< 4+10

-16+8<4+10

-8<14

9514 1404 393

Answer:

  8×(−2)−(−4)^2 < 36÷9+2×5

Step-by-step explanation:

The left side expression evaluates as ...

  8×(−2)−(−4)^2

  = 8×(−2) − 16

  = -16 -16

  = -32

__

The right side expression evaluates as ...

  36÷9+2×5

  = 4 + 10

  = 14

__

It should be no mystery that any negative number is less than any positive number:

  -32 < 14

  8×(−2)−(−4)^2 < 36÷9+2×5 . . . . . . . . "less than" symbol is required

Answer:

m needs 3 pounds of vegetables for a vegetable soup recipe. He already has 2/3 pound of carrots and 1/4 pound of celery.

Step-by-step explanation:

Answer:

I think the answer is D. Not possible.

Step-by-step explanation:

it leads to 0 in the end.

The base of the rectangle , b = 28 cm

The area of the rectangle , A = 588 cm^2

Therefore , the height of the rectangle , h = A/b

=588/28 cm = 21 cm .

Answer:

m=33.7g

Step-by-step explanation:

See attachment

Answer:The cost of a ticket is $12 per student

Step-by-step explanation:

36/3=$12 per students

$72/6=$12 per student

Answer:

5040

Step-by-step explanation:

an illustration of permutations

The given parameter is:

number of days

dinners for 7 days

Substitute known values

Answer:

11

Step-by-step explanation:

The distance formula is:

\(d = \sqrt {\left( {x_2 - x_1 } \right)^2 + \left( {y_2 - y_1} \right)^2 }\)

Plug the given coordinates into the equation:

\(d = \sqrt {\left( {4- 4} \right)^2 + \left( {4 - (-7) } \right)^2 }\)

\(d = \sqrt {\left( {0} \right)^2 + \left( {4+7} \right)^2 }\)

\(d = \sqrt {0 + \left( {11 } \right)^2 }\)

\(d=\sqrt{121}\)

\(d=11\)

Answer:-3/2

Step-by-step explanation: Just did the test.

Answer:

Radius:  √ 61

Step-by-step explanation:

Complete the square for  x^ 2 + 12 x = ( x + 6 ) ^2 − 36

Substitute   ( x + 6 ) 2 − 36  for  x 2 + 12 x  in the equation  x 2 + y 2 + 12 x − 10 y = 0

= ( x + 6 ) 2 − 36 + y 2 − 10 y = 0

Move  − 36  to the right side of the equation by adding  36  to both sides

= ( x + 6 ) 2 + y 2 − 10 y = 0 + 36

Then you know the rest: radius will be √ 61

The center coordinate of the circle is (6,5) with a radius = 7.34

The equation of the circle is: \((x-a)^{2} + (y-b)^{2} = r^{2} x^{2}\)

Substituting the values in the equation:

\((x-a)^{2} + (y-b)^{2} = r^{2} x^{2} - 2ax + a^{2} + y^{2} - 2by +b^{2} - r^{2} = 0\)

⇒  -2ax =  -12x

⇒  a = 6.

-2by = -10y

b= 5.

⇒ a² + b² - r² =  -7

⇒  6² + 5² + r² = -7

⇒ 36 + 25 + r² =  -7

⇒ r² = 54

⇒ r = 7.34

Center coordinate (6,5) with r = 7.34

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The value is used for the term p^2 in the equation p^2+ 2pq + q^2 = 1 is 0.16.

According to the statement

we have given that the allele frequency of the dominant allele is 0.4, and we have to find that the value of p^2 in the equation p^2+ 2pq + q^2 = 1.

So, For this purpose, we know that the

The allele frequency represents the incidence of a gene variant in a population. Alleles are variant forms of a gene that are located at the same position, or genetic locus, on a chromosome.

And here

allele frequency is the 0.4 and represent the value of P.

So, The value of p is 0.4 and the

Then p^2 = (0.4)^2

so, the value becomes

p^2 = (0.4)^2

p^2 = 0.16.

So, The value is used for the term p^2 in the equation p^2+ 2pq + q^2 = 1 is 0.16.

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Sampling is the use of a subset of the population to represent the whole population or to inform about processes that are meaningful beyond the particular cases, individuals or sites studied.

In non-probability sampling, the sample is selected based on non-random criteria, and not every member of the population has a chance of being included. Common non-probability sampling methods include convenience sampling, voluntary response sampling, purposive sampling, snowball sampling, and quota sampling.

Answer:

6*10^-3  >  5*10^-3

Step-by-step explanation:

\(6*10^{-3}\\6*\frac{1}{10^{3} }\\6*\frac{1}{1000}\\\frac{6}{1000}=\frac{3}{500}=0.006\)

\(5*10^{-3}\\5*\frac{1}{10^{3} }\\5*\frac{1}{1000}\\\frac{5}{1000}=\frac{1}{200}=0.005\)

0.006>0.005, therefore, 6*10^-3>5*10^-3

Answer: 19.42

Step-by-step explanation:

To find the distance, we need to use the distance formula.

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

With the given points, we can plug them in and solve.

\(d=\sqrt{(7-3)^2+(-11-8)^2}\)          [parenthesis]

\(d=\sqrt{(4)^2+(-19)^2}\)                       [exponent]

\(d=\sqrt{16+361}\)                               [add]

\(d=\sqrt{377}\)                                       [square root]

\(d=19.42\)

Now, we know the distance is 19.42.

Answer:

Area of sector of circle = 7.6302 inches (Approx.)

Step-by-step explanation:

Given:

Angle of section = 35°

Radius of circle = 5 inch

Find:

Area of shaded section

Computation:

Area of shaded section  = Area of sector of circle

Area of sector of circle = [θ/360][πr²]

Area of sector of circle = [35/360][(22/7)(5)²]

Area of sector of circle = [0.0972][(3.14)(25)]

Area of sector of circle = [0.0972][78.5]

Area of sector of circle = 7.6302 inches (Approx.)

Answer:

g(x) = 1/2x² is the correction option.

Hence, option B is true.

Step-by-step explanation:

Please check the attached graph.

It means when we multiply the parent function by a number 'b' which is less than 1, then the parent function f(x) = x² is vertically compressed by b.

Here, the graph is vertically compressed by 1/2, therefore we conclude that g(x) = 1/2x² is the result of vertical compression of the parent function by 1/2.

Therefore, g(x) = 1/2x² is the correction option.

Hence, option B is true.

Answer: 6

Step-by-step explanation:

got it right

The area of the rectangular parking lot is 929.03 square meters.

Use the formula for the area of a rectangle to calculate the area of the rectangular parking lot, which is given as:

Area = length × width

We know that the parking lot is 67.5 ft wide and 148 ft long, the area can be calculated as follows:

Area = 67.5 ft × 148 f

t= 9990 sq. ft

However, the question asks for the area in square meters, so we need to convert square feet to square meters. 1 square foot is equal to 0.092903 square meters, so we can use this conversion factor to convert square feet to square meters.

Area in square meters = Area in square feet × 0.092903

= 9990 sq. ft × 0.092903

= 929.03 sq meters

Therefore, the area is 929.03 square meters.

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Answer:m<1 = 111 degrees, m<2 = 69 degrees

Step-by-step explanation:The measure of angles 1 and 2 are supplementary, (two angles adding up to 180 degrees). Using this, set up the equation:

x + 88 + 3x = 180  

4x = 108

x=23 degrees

Next, substitute 23 into the given angles:

m<1 = (23 + 88) = 111 degrees

m<2 = 23 * 3 = 69 degrees

Thus, m<1 = 111 degrees, m<2 = 69 degrees.

The equations of the lines are y = 3x - 5 and y = (1/2)x - 7

An equation is an expression that shows how numbers and variables are related to each other.

A linear function is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Two lines are parallel if they have the same slope

1) y = 3x + 6; (4, 7)

The parallel line would have a slope of 3 and pass through (4, 7), hence:

y - 7 = 3(x - 4)

y = 3x - 5

2) y = (1/2)x + 5; (4, -5)

The parallel line would have a slope of 1/2 and pass through (4, -5), hence:

y - (-5) = (1/2)(x - 4)

y = (1/2)x - 7

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(a) The probability that you will go to class tomorrow can be calculated by finding the complement of the event that you cut class.

The probability of cutting class can be calculated by considering the probabilities of each weather condition and the corresponding probabilities of cutting class given each condition:

P(Cut class) = P(Rain) * P(Cut class|Rain) + P(Snow) * P(Cut class|Snow) + P(Clear) * P(Cut class|Clear)

           = 0.5 * 0.6 + 0.1 * 0.9 + 0.4 * 0.8

           = 0.3 + 0.09 + 0.32

           = 0.71

Since the question asks for the probability of going to class, we need to find the complement of cutting class:

P(Go to class) = 1 - P(Cut class)

              = 1 - 0.71

              = 0.29

Therefore, the probability that you will go to class tomorrow is 0.29.

(b) The probability that it rained given that you cut class can be calculated using Bayes' theorem:

P(Rain|Cut class) = (P(Cut class|Rain) * P(Rain)) / P(Cut class)

                = (0.6 * 0.5) / 0.71

                = 0.3 / 0.71

                ≈ 0.423

Therefore, if you cut class tomorrow, the probability that it rained is approximately 0.423.

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The number of shelves that fit in the alcove is given by the height of each shelve and the height of the bookshelf above the ground

The number of bookshelves that fit into alcove, is 8 bookshelves

Reason:

Height of the alcove = 2.5 m

Height of the books = 210 mm = 0.21 m

The gap above each book = 30 mm = 0.03 m

The thickness of the shelves = 20 mm = 0.02 m

Width of the alcove = 1.2 m

Height of the bottom shelf above the ground = 300 mm = 0.3 m

Required:

The number of shelves that can be fitted into the alcove

Solution;

Let x, represent the number of shelves that can be fitted into the alcove

We have;

An initial height of the bookshelves above the ground = 0.3 m

Height of a shelve, H = Height of books + Gap above books + Thickness of shelves

Height above ground, including the bottom shelve = 0.3 m

Therefore, the maximum number of whole bookshelves that can be fitted into alcove, x ≈ 8 bookshelves

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The distance traveled in the first 8 minutes is 1.75 d2

Speed is the rate of change of distance with time. it is a scalar quantity and it is measured in meter per second.

speed = distance /time

time = distance /speed

total time = 16

represent u by the first 8minutes and v by the second 8 minutes

u = 1.75v

8 = d1/1.75v

8 = d2/v

d1/1.75v = d2/v

d1 ×v = 1.75v × d2

d1 = 1.75d2

therefore ;

d1 = 1.75d2

where d1 and d2 are the distances for the first 8 minutes and second 8minutes respectively.

therefore the distance in the first 8minutes is 1.75 times greater than the second 8 minutes

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Answer:

n = - 1 , n = 3

Step-by-step explanation:

n² - 2n - 3 = 0 ( add 3 to both sides )

n² - 2n = 3

to complete the square

add ( half the coefficient of the x- term)² to bpth sides

n² + 2(- 1)n + 1 = 3 + 1

(n - 1)² = 4 ( take square root of both sides )

n - 1 = ± \(\sqrt{4}\) = ± 2 ( add 1 to both sides )

n = 1 ± 2

Then

n = 1 - 2 = - 1

n = 1 + 2 = 3

Answer:

57 degrees

Step-by-step explanation:

because it is the same as the other side

Answer:

3.4 kilometers on both days

Step-by-step explanation:

\(1.45+0.5=1.95\)

\(1.45+1.95=3.4\)

The two equations x + 3y = 5 and 4x + 12y = 20 represent a system of linear equations.

To solve this system, we can use the method of substitution. Let's begin by solving the first equation for x in terms of y:

x + 3y = 5

Subtract 3y from both sides:

x = 5 - 3y

Now, substitute this expression for x into the second equation:

4x + 12y = 20

Replace x with 5 - 3y:

4(5 - 3y) + 12y = 20

Distribute the 4:

20 - 12y + 12y = 20

Combine like terms:

20 = 20

The equation 20 = 20 is true for any value of y. This means that the system of equations has infinitely many solutions. In other words, any pair of x and y values that satisfy the equation x + 3y = 5 will also satisfy the equation 4x + 12y = 20.

To summarize, the two equations x + 3y = 5 and 4x + 12y = 20 represent a system of linear equations that has infinitely many solutions.

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In the given video clip, Daniela analyzes Jose's characterization by asking, Later she goes on to confirm that "society." Daniela's question and her later statement help to connect the ideas expressed during the discussion because it helps the viewers to understand who or what "they" refers to.

By clarifying that "they" refers to society, Daniela connects the idea of Jose's character being influenced by society.In the video, Jose discusses his experiences of being an immigrant and how it influenced his identity and personality. Daniela's question and later confirmation help to emphasize the societal factors that played a role in Jose's experience as an immigrant and how it shaped his character. By asking "Who's this they we're hearing about?" Daniela directs the conversation towards the external factors that affected Jose. Her later statement confirming that "they" refers to society connects the idea that Jose's character was molded by societal norms and expectations. This highlights how societal factors play a key role in shaping our personality and identity, as seen in Jose's experience as an immigrant. Therefore, Daniela's question and later statement help to connect the ideas expressed during the discussion.

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The actual concentration of fine particulates at the school is 31.4 µg/m3 - 32.6 µg/m³.The correct answer is option B.

To estimate the actual concentration of fine particulates at the school with 99.7% confidence, we can use the concept of confidence intervals. The confidence interval represents a range within which we are confident the true population parameter lies.

In this case, since we have a sample average and the standard deviation of the sample measurements, we can construct the confidence interval using the formula:

Confidence Interval = Sample Average ± (Z * (Standard Deviation / √Sample Size))

The Z-value for a 99.7% confidence level is approximately 3. Therefore, plugging in the given values:

Confidence Interval = 32 ± (3 * (3 / √225))

Simplifying the equation:

Confidence Interval = 32 ± (3 * (3 / 15))

Confidence Interval = 32 ± 0.6

The resulting confidence interval is (31.4, 32.6) µg/m³.

Therefore, the correct answer is option B: 31.4 µg/m³ - 32.6 µg/m³. This means we can be 99.7% confident that the actual concentration of fine particulates at the school falls within this range based on the sample data collected.

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