The smallest number in our sample of 11 numbers that is greater than or equal to 40% of the numbers.
what is percentage ?In arithmetic, a percentage is a ratio or ratio that is presented as a part of 100. Usually, the acronyms "pct.," "pct," and "pc" are also utilized. Yet it is broadly classified into the following by the percent sign, "%." The % sum has no dimensions. Rates are essentially fractions when the sum is 100. Use the percent sign (%) to indicate that a number seems to be a percentage by placing it next to it. For illustrate, you score a 75% if you properly answer 75 out of 100 respondents on a test (75/100). Divide the money by total and multiply it by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.
given
The 40th percentile's ordinal rank is equal to (40/100) X 10 (or 4).
50 is the 40th percentile and the following rank is 5 with 50 as the data value.
We observe that 50 is greater than 10, 20, 30, or 40% of the data,
4/10 = 0.4.
The smallest number in our sample of 11 numbers that is greater than or equal to 40% of the numbers.
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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 1) and (0, 1). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
Group of answer choices
y > 2x + 2
y ≥ One-halfx + 1
y > 2x + 1
y ≥ One-halfx + 2
The correct linear inequality would be y > 2x + 1.
Option (A) is correct.
What is linear inequality?
A linear inequality is an inequality that can be written in the form of a linear equation with an inequality symbol, such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
We can see that the line passes through the points (-1, -1) and (0, 1), and has a positive slope. The equation of the line can be found using the point-slope form:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points on the line.
Using the point (-1, -1) and the slope 2, we get:
y - (-1) = 2(x - (-1))
y + 1 = 2x + 2
y = 2x + 1
Since the line is dashed, the inequality is not inclusive of the points on the line. Therefore, we use the inequality symbol > rather than ≥.
so the linear inequality would be y > 2x + 1.
Therefore, the correct linear inequality would be y > 2x + 1.
Option (A) is correct.
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A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 8-lb batches. Let suppose that X has the following pmf = the number of batches ordered by a randomly chosen customer, and p(x) 0.3 0.5 0.1 01 Compute E(X) and VIX) E(X)2 их-0.8 batches batches Compute the expected number of pounds left after the next customer's order is shipped and the variance of the number of pounds left. [Hint: The number of pounds left is a linear function of X.,] expected weight left variance of weight left lb lb
The expected weight left after the next customer's order shipped is 92 pounds, and the variance of the weight left is 51.2 lb²
What is the probability mass function?
A probability mass function (PMF) is a mathematical function that describes the probability of each possible value of a discrete random variable. In simpler terms, the PMF gives the likelihood of a specific outcome occurring when you randomly select an item from a finite set of possible outcomes.
The PMF assigns a probability to each outcome, such that the sum of all probabilities equals 1. The PMF is often presented in a table or a graph to show the probabilities associated with each possible value of the random variable.
The given probability mass function (pmf) for the number of batches ordered by a randomly chosen customer, X, is:
X P(X)
0 0.3
1 0.5
2 0.1
3 0.1
To calculate the expected value of X, we use the formula:
E(X) = Σ [x * P(X=x)]
E(X) = (0 * 0.3) + (1 * 0.5) + (2 * 0.1) + (3 * 0.1)
E(X) = 0 + 0.5 + 0.2 + 0.3
E(X) = 1
To calculate the variance of X, we first need to calculate the squared values of X:
X²
0² = 0
1² = 1
2² = 4
3² = 9
Then, we use the formula:
Var(X) = E(X²) - [E(X)]²
E(X²) = Σ [x² * P(X=x)]
E(X²) = (0² * 0.3) + (1² * 0.5) + (2² * 0.1) + (3² * 0.1)
E(X²) = 0 + 0.5 + 0.4 + 0.9
E(X²) = 1.8
Var(X) = E(X²) - [E(X)]²
Var(X) = 1.8 - 1²
Var(X) = 0.8 batches²
The expected number of pounds left after the next customer's order is shipped can be calculated as:
E(Weight left) = 100 - 8X
where X is the number of batches ordered by the next customer.
Using the formula for the expected value of X that we found earlier, we can write:
E(Weight left) = 100 - 8E(X)
E(Weight left) = 100 - 8(1)
E(Weight left) = 92 lb
To calculate the variance of the number of pounds left, we first need to find the variance of X, which we already calculated as 0.8 batches² Then, we use the formula for the variance of a linear function of a random variable:
Var(aX + b) = a² * Var(X)
where a = -8 (the negative sign indicates that the weight left decreases as X increases) and b = 100.
Var(Weight left) = (-8)² * Var(X)
Var(Weight left) = 64 * 0.8
Var(Weight left) = 51.2 lb^2
Therefore, the expected weight left after the next customer's order is shipped is 92 pounds, and the variance of the weight left is 51.2 pounds squared.
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if sin = - square root 3/2 and pi <0<3pi/2 what are the values of cos and tan
tanθ = √3 are the values of cos and tan in Trigonometric Ratios .
How are trigonometric ratios defined?
As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.
Sinθ = -√3/2
cosθ = √1 - sin²θ
= √1 - (-√3/2)²
= √ 1 - 3/4
= √4-3/4
= √1/4
cosθ = 1/2
since π<θ<3π/2 in third quadrant.
We know, cosθ in third quadrant is negative.
cosθ = -1/2
tanθ = sinθ/cosθ
tanθ = -√3/2/-1/2
tanθ = √3
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