If the average temperature on Saturday was 62.6 F what was the actual temperature

The probability of P(3 < X ≤ 6) is approximately 0.6575.

The study of probabilities, which are determined by the ratio of favourable occurrences to probable cases, is known as probability.

To find P(3 < X ≤ 6), where X represents the number of times heads is tossed when a fair coin is tossed 10 times, we need to calculate the probability of obtaining more than 3 but less than or equal to 6 heads.

Since the coin is fair, the probability of getting heads on any single toss is 0.5, and the probability of getting tails is also 0.5.

We can use the binomial probability formula to calculate the probability for a specific number of heads in a given number of coin tosses:

P(X = k) = (n choose k) * \(p^k\) *\((1-p)^{(n-k)\),

where n is the number of trials, k is the number of successful outcomes, p is the probability of success on each trial, and (n choose k) is the binomial coefficient.

In this case, n = 10 (10 coin tosses), p = 0.5 (probability of heads), and we want to calculate the probability for 4, 5, and 6 heads.

P(3 < X ≤ 6) = P(X = 4) + P(X = 5) + P(X = 6)

Using the binomial probability formula, we can calculate these probabilities:

P(X = 4) = (10 choose 4) * \((0.5^4) * (0.5^6)\) = 210 * 0.0625 * 0.015625 = 0.2063

P(X = 5) = (10 choose 5) * \((0.5^5) * (0.5^5)\) = 252 * 0.03125 * 0.03125 = 0.2461

P(X = 6) = (10 choose 6) * \((0.5^6) * (0.5^4)\) = 210 * 0.015625 * 0.0625 = 0.2051

Finally, we can calculate the desired probability:

P(3 < X ≤ 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.2063 + 0.2461 + 0.2051 = 0.6575

Therefore, P(3 < X ≤ 6) is approximately 0.6575.

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The required final answer is option a) Incentre

The point of concurrency of the angle bisectors of a triangle is known as the "Incentre".

It is the center of the circle inscribed within the triangle, which is equidistant from all three sides of the triangle.

The incentre is the point where the angle bisectors of a triangle intersect, forming the incircle, which is the largest circle that can be inscribed inside the triangle.

The incentre is always within the triangle and is equidistant from all three sides of the triangle, making

it a useful tool in construction and design applications. In summary, the incentre is the center of the incircle of a triangle, and it is the point where the angle bisectors of the triangle intersect.

Thus, required answer is "Incentre".

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Answer:

17.628 = 17.6

Step-by-step explanation:

The forecast for the first week in April is Option B, 217.33.

By using a three-week moving average to forecast the rate of new driver's license applications for the first week of April, means that we will average the rate of new driver's license applications over the last three weeks to forecast the rate for the next week.

Let's calculate the moving average for the first week of April.

Given weeks 2, 3, and 4 of March are 199, 215, and 212, respectively.

To find the three-week moving average, we add these three rates and divide by three:

(199 + 215 + 212) / 3 = 208.67

Therefore, the forecast for the rate of new driver's license applications for the first week of April using the three-week moving average is 208.67, rounded to two decimal places, the closest option to 208.67 is option B, which is 217.33.

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Answer:

y<-1

Step-by-step explanation:

This exponential function will never approach y=-1, but it goes "under" the line of -1, so it is y<-1

Answer:

between 6 and 7

hope it helps you budy

Answer:

6 and 7

Step-by-step explanation:

Given that the square root of 40 is 6.32..., the decimal is between 6 and 7.

For the given statement, we have to correctly rejecting the null hypothesis.

According to the statement

we have to find the outcome when hypothesis test evaluating a treatment that has a very large and robust effect.

For this purpose, we know that the

A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

And according to the given statement it is clear that the by this we have to rejected this hypothesis.

because this treatment and the large effects are not possible for the independent values of the hypothesis.

In other words, we can say that the we have to correctly rejecting the null hypothesis.

So, For the given statement, we have to correctly rejecting the null hypothesis.

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The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = (5/2)^x - 5, we need to find the minimum and maximum values of y that can be obtained by plugging in all possible x values.

To find the maximum value of f(x), we can take the limit as x approaches infinity:

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Answer:

The height (h) of the ball is termed as the dependent variable and the time (t) is called the independent variable.

Step-by-step explanation:

We know that the function

y = f(x)

where y is a function of x.

Here:

Given the function of the height of the ball as a function of time is modeled by the equation

h(t) = -16t² + 90t + 5

As the height of the ball depends upon the time as the height of the ball is a function of time.

Thus, the height (h) of the ball is termed as the dependent variable and the time (t) is called the independent variable.

Answer:

0.267

Step-by-step explanation:

Answer:

To solve this problem, we can use a proportion.

Let x be the change of water in 12 weeks.

We know that in 7 weeks, the water decreased by 9 5/8 pints.

So, we can set up the proportion:

9 5/8 pints / 7 weeks = x / 12 weeks

To solve for x, we can cross-multiply and simplify:

9 5/8 pints * 12 weeks = 7 weeks * x

115 1/2 pints = 7 weeks * x

x = 115 1/2 pints / 7 weeks

x = 16 1/2 pints per 12 weeks

Therefore, the change of water in 12 weeks is 16 1/2 pints.

Step-by-step explanation:

Answer:

5     3

6     4

4     2

Step-by-step explanation:

Using even and odd functions, the coordinates of the points are given as follows:

a) (3/2, 4).

b) (3/2, -4).

Even and odd functions are classified as follows:

Hence, the coordinates are found as follows:

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Answer: To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and y-intercept (b) of the line.

We can use the two given points (-8, -4) and (-6, -1) to find the slope:

m = (y2 - y1) / (x2 - x1)

m = (-1 - (-4)) / (-6 - (-8))

m = 3 / 2

Now that we have the slope, we can use either of the two given points to find the y-intercept:

y = mx + b

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

-1 = -9 + b

b = 8

Therefore, the equation of the line in slope-intercept form is:

y = (3/2)x + 8

Step-by-step explanation:

Answer: pi/3

Step-by-step explanation:

To find standard posiition add or subtract 2\(\pi\) (a full revolution) until the sign changes

In order to make the sign change, in you problem, you need to add 2\(\pi\) because your problem is -

since the denominator is 2 \(2\pi = \frac{6\pi }{3}\)

\(\frac{-11\pi }{3} + \frac{6\pi }{3}\)

\(=\frac{-5\pi }{3} + \frac{6\pi }{3}\)      Add another 2pi because still -

\(=\frac{\pi }{3}\)            Now there is a sign change, this is your answer

As we can see from the graph, the values that the variable x or all the possible acceptable values it can take have no restrictions here. That is, the variable, x, can take any possible value. Therefore, we can say that the domain for this function is:

Therefore, the correct option is option A.

Answer:

use the equation your teacher gave you

Answer:

Step-by-step explanation:

16×2/3

32/3

104

A system of vectors v1, v2, . . . , vn in a vector space v of dimension n is linearly independent if and only if it spans v.

Let's first assume that the system of vectors v1, v2, . . . , vn in v is linearly independent. This means that none of the vectors can be written as a linear combination of the others. Since there are n vectors and v has dimension n, it follows that the system is a basis for v. Therefore, every vector in v can be written as a unique linear combination of the vectors in the system, which means that the system spans v.

Conversely, let's assume that the system of vectors v1, v2, . . . , vn in v spans v. This means that every vector in v can be written as a linear combination of the vectors in the system. Suppose that the system is linearly dependent. This means that there exists at least one vector in the system that can be written as a linear combination of the others. Without loss of generality, let's assume that vn can be written as a linear combination of v1, v2, . . . , vn-1. Since v1, v2, . . . , vn-1 span v, it follows that vn can also be written as a linear combination of these vectors. This contradicts the assumption that vn cannot be written as a linear combination of the others. Therefore, the system must be linearly independent.

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The expression for how many animal toes there are in total is 20x-10.

Since cows have x+3 legs, with 3 toes on each leg. Chickens have 2x-4 legs, with 7 toes on each leg.

If your farm has only two cows and one chicken, the expression for total number of toes will be:

total = 2*3*(x+3) + 1*7*(2x-4 )

total = 6(x+3) + 7(2x-4)

total = 6x+18 + 14x-28

total = 20x-10

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Complete Question

In a different dimension, cows have x+3 legs, with 3 toes on each leg. Chickens have 2x-4 legs, with 7 toes on each leg. If your farm has only two cows and one chicken, what is the expression for how many animal toes are there in total (not including yours)?

Answer:

− ( q p 4 − 12 q p 2 + 36 q − p 2 + 6 )

Step-by-step explanation:

The slope of a beer's law plot represents that one can quantitatively determine the molar absorptivity of a substance, which is essential for accurately determining concentrations of unknown samples using spectrophotometric methods.

In Beer's law, the relationship between the concentration of a substance and its absorbance is described by the equation A = εbc, where A is the absorbance, ε is the molar absorptivity (also known as the molar absorptivity coefficient), b is the path length of the sample, and c is the concentration of the substance.

When plotting a graph of absorbance versus concentration, the slope of the line represents the molar absorptivity (ε). The molar absorptivity is a constant that reflects the substance's ability to absorb light at a specific wavelength. A higher molar absorptivity indicates that the substance has a greater tendency to absorb light and is more sensitive to changes in concentration.

Conversely, a lower molar absorptivity indicates weaker absorption characteristics.

In summary, by measuring the slope of the Beer's law plot, one can quantitatively determine the molar absorptivity of a substance.

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\( \leadsto f( \rm x) = - (x - 3)(x - 5)\)

\( \\ \\ \)

\( \leadsto f( \rm x) = - ( {x}^{2} - 5x - 3x + 15) \\ \)

\( \\ \\ \)

\( \leadsto f( \rm x) = - ( {x}^{2} - 8x + 15) \\ \)

\( \\ \\ \)

\( \leadsto f( \rm x) = - {x}^{2} + 8x - 15 \\ \)

Answer:

3rd option is correct

Step-by-step explanation:

hope this helps you :)

The area of the figure is 13 cm².

We have,

From the figure,

We can make two rectangles.

Now,

Length = 5 cm

Width =  1 cm

Area of one rectangle.

= 5 x 1

= 5 cm²

Length = 4 cm

Width = 2 cm

Area of another rectangle.

= 4 x 2

= 8 cm²

Now,

Area of the figure,

= 5 + 8

=  13 cm²

Thus,

The area of the figure is 13 cm².

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Answer:

107.25 metres.

Step-by-step explanation:

diameter of circle = 150m,

so,

radius = 75 m

perimeter of semi circle

= pi × r

= 3.14 × 75

= 235.5 m

perimeter of rectangle

= 2 × (l+b)

= 2 × (150 + 75)

= 450 m

perimeter of shaded region

= perimeter of rectangle - perimeter of semi circle/2

= 450 - 235.5/2

=107.25 metres

To determine whether the mean weight of two distinct turtle species is equal. It would take too much time and money to weigh each turtle because there are thousands of them in each group.

A two-sample t-test is used to determine whether or not genuine population means are equal.

The accompanying null hypothesis is usually used in a two-sample t-test:

\(H_0\): The two population averages are equivalent when 1 = 2.

The alternative hypothesis might have two tails, a left or right tail, or none at all:

Two-tailed \(H_1\): μ1 ≠ μ2 Neither of the two population means is equal.

(Left-tailed) \(H_1\): Population 1 mean is lower than population 2 mean by a factor of 1.

\(H_1\) (right-tailed): Populations 1 and 2 have mean values that are higher than each other.

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Answer:

2.33

Step-by-step explanation: