Review the table showing wind speed, y, in miles per hour, measured x hours after midnight.


Hours after Midnight


Wind Speed (mph)


1


4. 3


2


4. 2


4


5


7


6. 8


9


8


10


8. 1


13


7. 2


17


6


20


5. 1


Which trigonometric function best models this data?


y = 1. 87sin(0. 29x + 6. 13) + 4. 79

y = 1. 87sin(0. 29x + 4. 79) + 6. 13

y = 1. 87sin(–0. 29x + 6. 13) + 4. 79

y = 1. 87sin(–0. 29x + 4. 79) + 6. 13

The conversion of the equation from slope-form to standard form is -2x + y = -3.

In Mathematics, the slope-intercept form of a line can be represented or modeled by using this linear equation:

y = mx + c

Where:

Generally speaking, the standard form of a linear function is given by this mathematical expression:

Ax + By = C

Where:

A, B, and C represents a numerical value (number).

Rewriting the given linear function in standard form, we have the following:

-2x + y = -3.

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If we are interested in the number of customers in the two queues that will form for the counters, we would take all the ordered pairs in the form of (x,y) as sample space.

The suitable sample space for the number of customers in the two queues formed in the post office should be the set of all possible combinations of the number of customers in each queue formed. This can be represented in the form of a set of ordered pairs, in which the first element of the ordered pair would represent the number of customers in the first queue and the second element of the same ordered pair would represent the number of customers in the second queue.

For example, if we consider a maximum of 15 customers in the first queue and a maximum of 20 customers in the second queue, the sample space would consist of all the ordered pairs in the form of (x,y),

where x will represent the possible number of customers in the first queue ranging from 0 to 15

and y will represent the possible number of customers in the second queue ranging from 0 to 20.

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Sides [tex]\overline{JM}[/tex] and [tex]\overline{KL}[/tex] are not given to be parallel.

The value of K is 20

The LHS (Left Hand Side) reduces to 2 x 10^1005

2 x 10^1005  =k x 10^1004                    

k =[2 x10^1005] / [10^1004] = 2 x 10

k =20                                                    

A positive integer is defined as a whole number greater than zero. All counting numbers are included in the set of positive integers.

Positive numbers include: 1, 2, 88, 800, 9000, and so on. Positive numbers are whole numbers with the symbol (+) in front of the numerical value. Most of the time, the plus sign is simply represented without the symbol. Positive numbers outnumber negative numbers and zero. On the number line, positive numbers are represented to the right of zero

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If the triangle has sides with lengths of 49 cm, 68 cm, and 92 cm , then the triangle is not a Right Triangle .

If the Triangle is a right triangle , then the sides of the triangle should satisfy the Pythagoras Theorem which states that the sum of the square of two smaller sides is equal to square of longest side(hypotnuse) .

that means ⇒ (Hypotnuse)² = (Perpendicular)² + (Base)² ;

Substituting the longest value as 92 and other values as 49 and 68 ,

we get ;

⇒ 92² = 49² + 68² ;

⇒ 8464 = 2401 + 4624 ;

⇒ 8464 ≠ 7025 .

the sides 49 cm, 68 cm, and 92 cm do not satisfy Pythagoras theorem ,

Therefore , the side lengths do not form a Right Triangle .

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If a ship is 90 miles South and 20 miles east of Port , then for the captain to travel directly to port , the captain should take a bearing of N 12.53° W .

the distance of ship = 90 miles south and 20 miles east of port .

let the bearing that the captain should take to directly travel to the port is = θ ;

So , the bearing angle can be calculated by using the trigonometric ratio ;

⇒ Tanθ = 20/90 ;

⇒ Tanθ = 2/9 ;

⇒ θ = arctan(2/9) = N 12.53° W   ;

Therefore , The captain should take a bearing of N 12.53° W .

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The mathematical model of communication would classify this issue as channel capacity.

The greatest quantity of data that can be transferred error-free across a communication channel, such as a mobile phone network, is represented by the channel capacity. In this instance, the phone's battery power determines the channel capacity. As the battery depletes, the phone's ability to send and receive information declines, making it impossible to hear the person on the other end of the line.

Communication models are streamlined depictions of the communication process. Most models attempt to explain both verbal and nonverbal communication, and frequently regard it as a message-exchange. Their purpose is to provide a concise picture of the intricate communication process.

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The research hypothesis would be Ha : μ > 80,000.

The research hypothesis for a consumer group testing the claim that a large tire manufacturing company's top line tire will last more than 80,000 miles would be: "The large tire manufacturing company's top line tire will last more than 80,000 miles."

Ha : μ > 80,000

A research hypothesis for a consumer group testing the claim that a large tire manufacturing company's top line tire will average more than 80,000 miles would be Ha : μ > 80,000 miles. The "Ha" stands for the alternative hypothesis, which states that the population mean (μ) of the tire's mileage is greater than 80,000 miles. This hypothesis is chosen because it represents the claim made by the tire manufacturing company and it is what the consumer group is trying to test against the null hypothesis (H0) which is the opposite of the claim, in this case, H0 : μ <= 80,000 miles.

So, the research hypothesis would be Ha : μ > 80,000.

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The required part of a bag of popcorn will each student receive is 2/5.

Use "part" when a part of the whole lacks significance on its own; use "a part" when a part of the whole has meaning when combined with other meaningful parts of the same total. For instance, this object is a part of my collection even if my leg is a part of my body.

We have,

4 bags of popcorn for the party and There are 10 students in the class.

Part of popcorn bag each student receive.

Part of popcorn = 4/10 = 2/5

Thus, 2/5 part of bag each  student receive.

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So each student will receive 0.4 bags of popcorn or 4/10 which is 2/5 of a bag of popcorn.

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The answer to the question can be calculated by using the average formula.

The average of a set of numbers is calculated by adding all of the numbers together and dividing the sum by the number of numbers in the set. In this case, the five alepeople earned a total of $176,506, and when divided by 5, the average annual income comes to $35,516.

To calculate the fifth aleperson's income, we subtract the income of the first four alepeople from the total income earned, $176,506. Subtracting the income of the first four alepeople, $36,230 + $34,500 + $38,250 + $33,000, gives us a remaining total of $24,026. When we divide this remaining total by 1, the average annual income for the fifth aleperson comes to $24,026.

Therefore, the fifth aleperson earned an annual income of $24,026. This can be expressed using the formula (total income – (income of aleperson 1 + income of aleperson 2 + income of aleperson 3 + income of aleperson 4)) / number of alepeople = income of fifth aleperson. In this case, (176,506 – (36,230 + 34,500 + 38,250 + 33,000)) / 1 = 24,026.

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Answer:

Step-by-step explanation:

No, The Salk vaccine study found that it did not prevent polio but rather caused it in youngsters.

Data is information that has been converted into a format that can be moved or processed effectively in computers. Data is information that has been translated into binary digital form for the computers and transmission mediums of today. Both a singular subject and a plural subject can be used when referring to data.

A collection of information, whether numerical or not, can take any shape and is referred to as data in mathematics. Calculable information, such as student test scores, employee salaries, football team member heights, etc., is known as numerical data and is always gathered in numerical form. facts compiled in the form of words, statistics, measurements, and observations. discrete information.

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After class, Mrs. Sandoval picked up several pieces of paper containing students' work from the floor and  Mrs Sandoval probably picked up the pieces of paper because she wanted to properly dispose of them.

The second reason for her act is she may have also wanted to make sure that students' work was not lost or damaged.

A thing is an action when it is carried out, not just thought about or said. A person might do anything from blink to invade a nation. Agere, a Latin verb that means "to do," is where action originates.

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The area of figures 1 and 2 will be 438 square yards and 110 square inches, respectively

The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

1.  The area of figure 1 is given as,

A = Sum of area of (Trapezoid + Rectangle + Rectangle)

A = 1/2 x (6 + 8) x 10 + 8 x 36 + 10 x 8

A = 70 + 288 + 80

A = 438 square yd

2.  The area of figure 2 is given as,

A = Area of a triangle - Area of a rectangle

A = 1/2 x (8 + 7) x (10 + 14) - 7 x 10

A = 180 - 70

A = 110 square inches

The area of figures 1 and 2 will be 438 square yards and 110 square inches, respectively

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The Greatest Common Factor(GSF) of -6x12y and -3xy is 3xy.

To find the greatest common factor (GCF) between two numbers or expressions, we need to identify the highest power of each common factor that divides both numbers or expressions.

In this case, we are trying to find the GCF between -6x12y and -3xy.

The prime factorization of the first expression is -6x12y = -2 * 3 * x * 2 * 2 * 3 * y

And, the prime factorization of the second expression is -3xy = -3 * x * y. The common factors between these two expressions are 3, x, and y.

Since, we are finding the greatest common divisor, we neglect the minus sign to obtain the largest value possible.

We can see that both expressions share a factor of 3, x, and y.

Since the GCF is the highest power of each common factor that divides both expressions, in this case, the GCF of -6x12y and -3xy is 3xy.

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The volume can be calculated by simply multiplying the base's area by its height. The prism's two sides should be measured using the same units. To get cubic feet, it is ideal to measure in feet.

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The height of the rectangular prism is 8 ft.

The base's area and height alone can be used to determine the volume. The two sides of the prism should be measured in the same units. It's best to measure in feet to get cubic feet.

The rectangular prism's volume is equal to the base's area times the height. Length x Width x Height, in cubic units, equals the volume of a rectangular prism.

The base's area and height alone can be used to determine the volume. The two sides of the prism should be measured in the same units. It's best to measure in feet to get cubic feet.

Given the volume rectangular prism = 220 ft²

(x - 5.5)(x + 3)(x) = 220 ft²

(x - 5.5)(x + 3)(x) = 220 ft²

x³ −2.5x² −16.5x = 220

x = 8

Thus, the height of the rectangular prism is 8 ft.

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Answer:

Step-by-step explanation:

y= 12+c

Answer:

[tex]\rm{ \dfrac{1250}{7776}\; or\; 0.16075\\\\}[/tex]

Step-by-step explanation:

This probability can be determined using combinatorics. The number of ways a sample of size r can be obtained from a larger set of n items is given by the formula

[tex]C(n,r) = \dfrac{n!}{( r! (n - r)! )}[/tex]

We pronounce C(n, r) as n choose r

We are rolling the die five times. So n = 5

On each roll a 2 can appear or not

We need two 2's . This is our r

The number of ways two 2's can appear is given by 5 choose 2

[tex]C(5,2)\\\\= \dfrac{5!}{( 2! (5 - 2)! )}\\\\= \dfrac{5!}{2! \times 3! }\\\\[/tex]

5! is the factorial of 5, 2! is the factorial of 2 and 3! is the factorial of 3

5! = 5 x 3 x 3 x 2 x1

3! = 3 x 2 x 1

2! = 2 x1

[tex]C(5,2) = \dfrac{5\times 4 \times 3 \times 2 \times 1}{((2 \times 1) \times (3 \times 2 \times 1)}\\\\= 10\\[/tex]

You need not go through this laborious process to find 5 choose 2 there are calculators available

So two 2's can appear 10 times.

The probability of getting a 2 on one roll is 1/6 and the probability of not getting a 2 on a single roll is 1-1/6 = 5/6

This works out to a binomial probability which can be computed by the formula

P(x) = C(n, x) pˣqⁿ⁻ˣ

Where x is the number of times the desired outcome succeeds and n the total number of trials

Here x = 2, n = 5, C(5, 2) = 10

[tex]\rm{So\:P(two\:2s\:on\:5\:throws)\: = 10 \cdot \left(\dfrac{1}{6}\right)^2\cdot \left(\dfrac{5}{6}\right)^3\\\\[/tex]

[tex]{= \dfrac{10 \cdot 1\cdot 125}{{6^5}} = \dfrac{1250}{7776} = 0.16075\\\\[/tex]

0.3 is the value of Probability Distribution Table X P(X)

Now, According to the question:

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.

Here X is a random variable. P(X) is its probabilities corresponding to the different values of X.

So here to find the value of the probability of X corresponding to the value 16 we should use the following steps:

Sum of given probabilities = (0.3+ 0.2 + 0.2) = 0.7

Required probability = 1 - sum of given probabilities = 1 - 0.7 = 0.3

Hence the complete probability table is:

X        P(X)

19       0.3

17       0.2

16       0.3

55      0.2

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Answer:

The supervisor started with ___77____ pieces of construction paper.

Step-by-step explanation:

Each student received 3 pieces of construction paper.

There are 25 students.

25 × 3 = 75

The students received 75 pieces altogether.

She had 2 pieces left.

75 + 2 = 77

She started with 77 pieces.

The supervisor started with ___77____ pieces of construction paper.

Option B is correct :- n ÷ 3

The given verbal expression is " the quotient of a number and 3."

We have to convert this verbal expression to algebraic expression.

The quotient of a number and 3, represents the division between an unknown number and the number 3.so the possible answer is n ÷ 3.

Here "Quotient" means "Division"

Let "n" be a number and it is divided by 3.

So,

we can write "the quotient of n and 3" as n÷3.

Algebraic expression

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations . Expressions are made up of terms.

Expression

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

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Using the equation y = 50x/3 + 350, Beth will have $700 after 21 months.

We have to determine how much money Beth will have after 21 months.

The equation is:

y = 50x/3 + 350

The value of x = 21.

Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. A condition on a variables is an expression when it implies that equations in the variable share the same value.

Putting the value of x in equation y = 50x/3 + 350

y = (50×21)/3 + 350

y = 50 × 7 + 350

Simplify

y = 350 + 350

y = 700

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The number of muffins that the quick bread recipe will yield is given as follows:

24 muffins.

The number of muffins that the quick bread recipe will yield is obtained applying the proportions in the context of this problem.

We have that:

Hence the number of muffins that the quick bread recipe will yield is calculated as follows:

6/(1/4) = 6 x 4 = 24 muffins.

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1. The probability of drawing a red or yellow ball from a standard set of pool balls is 4/7.

2. The probability of first getting a 3 and then getting another odd number is 1/12.

1. Tom has a standard set of pool balls, which includes 7 different colored balls: red, yellow, blue, purple, orange, green, and black. There are 2 red balls and 2 yellow balls out of 7 total balls.

To find the probability of drawing a red or yellow ball, we will add the probabilities of drawing each color separately.

Probability of drawing a red ball = 2/7

Probability of drawing a yellow ball = 2/7

Probability of drawing a red or yellow ball = (2/7) + (2/7) = 4/7

Hence, the probability of drawing a red or yellow ball is 4/7.

2. If a single die twice, the total possible outcomes are =  6x6 = 36.

To find the probability of getting a 3 on the first throw and then getting another odd number on the second throw, we have to find the number of outcomes that meet these conditions and then divide it by the total number of outcomes.

First throw: 3 (1 outcome)

Second throw: odd number (3, 5) (3 outcomes)

So there are a total of 1x3 = 3 outcomes that meet the given conditions.

Thus, Probability = 3/36 = 1/12

So, the probability of first getting a 3 and then getting another odd number is 1/12.

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The probability that the first item is not the first to be delivered is 0.6667

Let's call the events that the first, second, and third items arrive on the first day of February A, B, and C, respectively.

Therefore, the probability that one of the other two items arrives first is

1/3 + 1/3 = 2/3.

The probability that the first item is not the first to be delivered is

1 - 2/3 = 1/3

Evaluate

1 - 2/3 = 0.6667

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\mathbb{R}50000\\ r=rate\to 0.5\%\to \frac{0.5}{100}\dotfill &0.005\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &20 \end{cases}[/tex]

[tex]A = 50000\left(1+\frac{0.005}{1}\right)^{1\cdot 20}\implies A=50000(1.005)^{20} \implies \boxed{A \approx 55244.78} \\\\\\ 55244.78~~ - ~~50000 ~~ \approx ~~ \stackrel{earned~interest}{\boxed{5244.78}}[/tex]

If Kylie invested $2800 for interest rate of 5(1/2)% compounded annually and Ariana invested $2800 at rate of  5(3/4)% compounded continuously , then  after 12 yrs Ariana would have $259.023 more than Kylie.

We have to find the difference in amount of money in the Kylie and Ariana's accounts after 12 years, we need to calculate the value of each investment after 12 years .

For Kylie's investment:

The formula for calculating the future value of a sum invested at a interest rate compounded annually is:

Value = Principle × (1 + r)ⁿ

Where:

Amount invested (P) = 2800 ;

r = interest rate = 5(1/2)% = 11/2% = 5.5% = 0.055  ;

n (time) = 12 years

⇒ Value = $2800 ×  (1 + 0.055)¹²

= $2800 ×(1.055)¹²

= $5323.38 .

For Ariana's Investment , the rate is compounded continuously ;

the future value can be calculated by using exponential function ;

Value = 2800 × e^(rt) ;

Where: initial investment = 2800 ;

r = interest rate = 5(3/4)% = 23/4% = 5.75% = 0.0575  and

n (time) = 12 ;

⇒ Value = $2800 × e^(0.0575×12)  

= $5582.403  .

Therefore , After 12 years Ariana would have $5582.403 and Kylie would have $5323.38, Ariana would have $259.023 more than Kylie.

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Answer:

50 to 7

Step-by-step explanation:

number of stars to number of red stripes

all acceptable ways to represent ratios:

50 to 7

50 : 7

50 over 7

Answer:

B 3pi/2

Step-by-step explanation:

So half of a circle is pi therefore a quarter is pi/2.

So 15 mins is pi/2.

3 * pi/2 =45 mins

3pi/2 = 45 mins

689,323,148 is 100,000 less than 689,423,148 in the given comparison.

Comparing the digit count is important. Indicating a larger number is the presence of additional digits. We should compare the highest place values, or the digit that is farthest to the left of the numbers, if the number of digits in both numbers is the same.

Compare the amount of digits. A higher number is indicated by more digits. The higher place values should be compared if the number of digits is the same. The next place value to the right should be compared if the digits at the highest place value are the same.          

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