36 observations are produced by multiplying $6 by 6 when two fair dice are rolled.
What is meant by probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability. The likelihood that something will happen is known as probability. The number of possible outcomes is divided by the total number of possible outcomes to determine probability.When two fair dice are rolled, $6 multiplied by 6 results in 36 observations.
[tex]& P(X=2)=P(1,1)=\frac{1}{36} \\[/tex]
[tex]& P(X=3)=P(1,2)+P(2,1)=\frac{2}{36}=\frac{1}{18} \\[/tex]
[tex]& P(X=4)=P(1,3)+P(2,2)+P(3,1)=\frac{3}{36}=\frac{1}{12} \\[/tex]
[tex]& P(X=5)=P(1,4)+P(2,3)+P(3,2)+P(4,1)=\frac{4}{36}=\frac{1}{9} \\[/tex]
[tex]& P(X=6)=P(1,5)+P(2,4)+P(3,3)+P(4,2)+P(5,1)=\frac{5}{36} \\[/tex]
[tex]& P(X=7)=P(1,6)+P(2,5)+P(3,4)+P(4,3)+P(5,2)+P(6,1)=\frac{6}{36}=\frac{1}{6} \\[/tex]
[tex]& P(X=9)=P(3,6)+P(4,5)+P(5,4)+P(6,3)=\frac{4}{36}=\frac{1}{9}[/tex]
[tex]& P(X=10)=P(4,6)+P(5,5)+P(6,4)=\frac{3}{36}=\frac{1}{12} \\[/tex]
[tex]& P(X=11)=P(5,6)+P(6,5)=\frac{2}{36}=\frac{1}{18} \\[/tex]
[tex]& P(X=12)=P(6,6)=\frac{1}{36}[/tex]
Therefore, the required probability distribution is as follows.
Then, E(X) = [tex]\sum \mathrm{X}_{\mathrm{i}} \cdot[/tex] [tex]\mathrm{P}\left(\mathrm{X}_{\mathrm{i}}\right)$[/tex]
[tex]& =2 \times \frac{1}{36}+3 \times \frac{1}{18}+4 \times \frac{1}{12}+5 \times \frac{1}{9}+6 \times \frac{5}{36}+7 \times \frac{1}{6}+8 \times \frac{5}{36}+9 \times \frac{1}{9}+10 \times \frac{1}{12}+ \\[/tex]
[tex]& 11 \times \frac{1}{18}+12 \times \frac{1}{36} \\[/tex]
[tex]& =\frac{1}{18}+\frac{1}{6}+\frac{1}{3}+\frac{5}{9}+\frac{5}{6}+\frac{7}{6}+\frac{10}{9}+1+\frac{5}{6}+\frac{11}{18}+\frac{1}{3} \\[/tex]
=7
[tex]& \mathrm{E}\left(\mathrm{X}^2\right)=\sum \mathrm{X}_{\mathrm{i}}^2 \cdot \mathrm{P}\left(\mathrm{X}_{\mathrm{i}}\right) \\[/tex]
[tex]& =4 \times \frac{1}{36}+9 \times \frac{1}{18}+16 \times \frac{1}{12}+25 \times \frac{1}{9}+36 \times \frac{5}{36}+49 \times \frac{1}{6}+64 \times \frac{5}{36}+81 \times \frac{1}{9}+ \\[/tex]
[tex]& 100 \times \frac{1}{12}+121 \times \frac{1}{18}+144 \times \frac{1}{36} \\[/tex]
[tex]& =\frac{1}{9}+\frac{1}{2}+\frac{4}{3}+\frac{25}{9}+5+\frac{49}{6}+\frac{80}{9}+9+\frac{25}{3}+\frac{121}{18}+4 \\[/tex]
[tex]& =\frac{987}{18}=\frac{329}{6}=54.833 \\[/tex]
[tex]& \text { Then, } \mathrm{V} \text { ar }[/tex][tex](\mathrm{X})=\mathrm{E}\left(\mathrm{X}^2\right)-[\mathrm{E}(\mathrm{X})]^2 \\[/tex]
[tex]& =54.833-(7)^2 \\[/tex]
= 54.833 - 49
=5.833
[tex]& \therefore \text { Standard deviation }=\sqrt{\mathrm{V} \text { ar }(\mathrm{X})} \\[/tex]
[tex]& =\sqrt{5.833} \\[/tex]
= 2.415
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use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the function.
Analytical techniques or a graphing tool can be used to locate the function's vertical asymptotes.
On a function graph, a vertical asymptote is a line that the graph approaches but never crosses. It can be discovered by examining the function's equation and how it behaves as it gets closer to infinity. By resolving the equation and determining the values of x that cause the denominator to equal 0, one can use analytical techniques to determine the vertical asymptotes of the function. For instance, the function will have a vertical asymptote at x = 5 if the equation is f(x) = (x-3)/(x-5), as the denominator of the equation equals 0 at this point. Vertical asymptotes can also be found using graphing tools. One can observe the behavior of the equation by charting its graph.
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Select the correct answer.
Which hyperbola's asymptote rectangle has the greatest perimeter?
Correct option is D, The greatest perimeter of hyperbola is in (D) ⇒ the perimeter = 60 units
When using hyperbola,
- A hyperbola's standard form of the equation with
transverse axis parallel to the x-axis and the center (h, k) are
[tex]\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2}[/tex]equals one.
The transverse axis' length is 2a.
The conjugate axis' length is 2b.
The asymptote rectangle's circumference is 2(2a + 2b).
* Let's review the results to determine the largest perimeter.
A)[tex]\frac{ (x - 4)^2}{11^2} - \frac{(y + 2)^2}{3^2} = 1[/tex]
* Compare it to the equation in standard form.
∵ a = 11 ⇒ 2a = 22
∵ b = 3 ⇒ 2b = 6
The circumference is 2(22 + 6) = 56.
B) [tex]\frac{(x - 2)^2}{4^2} - \frac{(y + 1)^2}{10^2} = 1[/tex]
* Compare it to the equation in standard form.
∵ a = 4 ⇒ 2a = 8
∵ b = 10 ⇒ 2b = 20
The circumference is 2(8 + 20) = 56.
C) [tex]\frac{(x + 5)^2}{5^2} - \frac{(y - 3)^2}{9^2} = 1[/tex]
* Compare it to the equation in standard form.
∵ a = 5 ⇒ 2a = 10
∵ b = 9 ⇒ 2b = 18
The circumference is 2(10 + 18) = 56.
D) [tex]\frac{(x - 7)^2}{8^2} - \frac{(y - 2)^2}{7^2} = 1[/tex]
* Compare it to the equation in standard form.
∵ a = 8 ⇒ 2a = 16
∵ b = 7 ⇒ 2b = 14
The circumference is 2(16 + 14) = 60.
* The largest boundary is in (D)
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given the standard deviation of 3.7 for a data set, what is the approximate value of the variance?
In this case, the standard deviation is 3.7, so the variance is 3.7², or 13.69. This means that the data points in the data set are, on average, 13.69 units away from the mean.
The variance of a data set is a measure of how the data points are distributed around the mean. It is calculated by squaring the standard deviation, which is the average distance of the data points from the mean.
Variance is a useful measure for quantifying the spread and variability of the data points in a data set. By knowing the variance, it is possible to make predictions about how likely it is that a given data point will fall within a certain range from the mean.
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Kristen does 215 jumping jacks in 4 minutes. About how many jumping jacks does she do in 1 minute?
Answer:
average approximately 54
Step-by-step explanation:
215/4 = 53.75
assuming she's a robot & doesn't get tired LOL
Which operation is NOT used in the phrase "three times a number, decreased by 2, divided by 6" ?
Answer:
Addition (+)
Step-by-step explanation:
If we were to take the problem and form an expression, it would look like this:
3 times a number (3 ×?) decreased by 2 (- 2) divided by 6 (÷ 6)
Putting it all together it forms:
3 ×? - 2 ÷ 6The four operations are addition, subtraction, multiplication and division.
We can see the multiplication, subtraction, and division, but not addition.
Therefore, the operation that is missing is Addition.
Simplify 6.5k + 1.6m - 3.2k.
Answer:
[tex]3.3k+1.6m[/tex]
Step-by-step explanation:
Subtract [tex]3.2k[/tex] from [tex]6.5k[/tex].
on any given day, a child is either healthy or sick. of children who are healthy today 95% will be healthy tomorrow. of the children who are ill today, 55% will still be ill tomorrow. if 20% of children are ill, what fraction of the children are likely to be ill in two days?
3% of children are likely to be ill in two days.
Let's call the fraction of children who are ill today x.
The fraction of children who are healthy today is (1 - x).
The fraction of children who were healthy today and will be healthy tomorrow is (1 - x) * 0.95.
The fraction of children who were ill today and will still be ill tomorrow is x * 0.55.
The fraction of children who will be ill in two days is x * 0.55 + (1 - x) * 0.05 = 0.55x + 0.05 - 0.95x = -0.4x + 0.05.
So, if 20% of children are ill today, then x = 0.2, and the fraction of children who are likely to be ill in two days is -0.4 * 0.2 + 0.05 = 0.03.
Therefore, 3% of children are likely to be ill in two days.
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3% of children are likely to be ill in two days.
Let's call the fraction of children who are ill today x.
The fraction of children who are healthy today is (1 - x).
The fraction of children who were healthy today and will be healthy tomorrow is (1 - x) * 0.95.
The fraction of children who were ill today and will still be ill tomorrow is x * 0.55.
The fraction of children who will be ill in two days is x * 0.55 + (1 - x) * 0.05 = 0.55x + 0.05 - 0.95x = -0.4x + 0.05.
So, if 20% of children are ill today, then x = 0.2, and the fraction of children who are likely to be ill in two days is -0.4 * 0.2 + 0.05 = 0.03.
Therefore, 3% of children are likely to be ill in two days.
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The radiu of a circle i 6 centimeter. What i the circle' area?
Ue 3. 14 for . Quare centimeter
The Area of the circle is = 3.14 x (6 cm)^2
Area = 113.04 cm^2
What is the area of circle?The theory used in this question is the formula for the area of a circle, which states that the area of a circle is equal to π multiplied by the square of the radius.
given below
Step 1: Use the formula A = πr^2 to calculate the area of the circle.
Step 2: Identify the radius, r, which is equal to 6 cm.
Step 3: Substitute the values into the formula, A = πr^2.
Step 4: Calculate the area by multiplying 3.14 (π) by the square of 6 cm (6 cm x 6 cm).
Step 5: The area of the circle is 113.04 cm^2.
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If A and B are 8 × 9 matrices, and C is a 3 × 8 matrix, which of the following are defined? A. B+ A B. AC
C. C-B
D. BT E. ABT
F. CB
Due to the difference in the number of columns in A and B, the operation B+A is not defined. ACC - This operation cannot be defined because A's number of columns and C's number of rows are not equal.
What do you mean by matrix?A matrix is a row-and-column-organized rectangular array containing numbers, symbols, or expressions. In mathematics, science, and engineering, matrices are frequently used to represent and manipulate data as well as to resolve linear equation systems.
The following are defined given that A, B, and C are all 8 by 9 matrices:
A. B+A - This operation is not described because A and B have different numbers of columns.
B. ACC - This operation is undefinable since A's number of columns and C's number of rows are not equal.
C. C-B - This operation is not described because C has more rows than B does because B has more columns.
D. Assuming B is a matrix with a diagonal of 9, this operation is defined and produces a matrix with a diagonal of 3.
E. AB - This operation is known as AB if A's number of columns and B's number of rows are equal. The outcome is an 8 by 9 matrix.
F. CB - If the number of columns is 1, then this operation is defined.
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Due to the difference in the number of columns in A and B, the operation B+A is not defined. ACC - This operation cannot be defined because A's number of columns and C's number of rows are not equal. C-B - This operation is not described because C has more rows than B does because B has more columns.
What do you mean by matrix?A matrix is a row-and-column-organized rectangular array containing numbers, symbols, or expressions. In mathematics, science, and engineering, matrices are frequently used to represent and manipulate data as well as to resolve linear equation systems.
The following are defined given that A, B, and C are all 8 by 9 matrices:
A. B+A - This operation is not described because A and B have different numbers of columns.
B. ACC - This operation is undefinable since A's number of columns and C's number of rows are not equal.
C. C-B - This operation is not described because C has more rows than B does because B has more columns.
D. Assuming B is a matrix with a diagonal of 9, this operation is defined and produces a matrix with a diagonal of 3.
E. AB - This operation is known as AB if A's number of columns and B's number of rows are equal. The outcome is an 8 by 9 matrix.
F. CB - If the number of columns is 1, then this operation is defined.
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a research study randomly assigned participants into two groups. one group was given vitamin e to take daily. the other group received only a placebo pill. the research study followed the participants for eight years. after the eight years, the proportion of each group that developed a particular type of cancer was compared. what is the primary reason that the study used random assignment?
The primary reason for the use of random assignment in the research study was to ensure that participants in each group were similar to each other in terms of relevant factors, such as age, gender, or health status.
By randomly assigning participants into two groups, the researchers could ensure that any difference observed between the two groups was due to the intervention and not due to any other factor.
Random assignment eliminates the possibility of bias being introduced into the study, as the two groups are as similar as possible.
This means that any observed difference between the two groups can be attributed directly to the intervention, in this case, the vitamin E supplement.
By randomly assigning participants, the researchers could be sure that the results of the study were valid and could be relied upon.
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I need to know how long my shadow would be
Your height and the length of your shadow are related by the formula 1/Tangent (height of the sun). Your shadow would be 5.67 times longer than you if the sun were to be at its lowest point in the sky (10 degrees). At 5 degrees, the proportion is 11.43. (A person of average height (5.8 feet) would therefore cast a shadow that is 66 feet long.)
How would one describe a shadow's length?The length of the shadow is influenced by the Sun's position in the sky. The shadows are long when the Sun is low in the horizon. The shadows are substantially shorter when the Sun is high in the sky.
How far does your morning shadow extend?Because the sun's rays are slanted in the morning and evening but are directly overhead at noon, the shadows are longer in the morning and evening and shorter in the noon. The distance of the object from the light source affects how big the shadow is.
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a car travels at na average speed of 64 miles per hour how many miles does it travel. in 5 hours and 45 minutes
Answer:
Step-by-step explanation:
(64)5.45= 348.8
what is 2log5 (5x^3) + 1/3 log5 (x^2 + 6) written as a single logarithm?
[tex]\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]2\log_5(5x^3)+\cfrac{1}{3}\log_5(x^2+6)\implies \log_5( ~~ (5x^3)^2 ~~ )+\log_5\left( ~~ (x^2+6)^{\frac{1}{3}} ~~ \right) \\\\\\ \log_5( ~~ 25x^6 ~~ )+\log_5\left( ~~ (x^2+6)^{\frac{1}{3}} ~~ \right)\implies \log_5\left( ~~ (25x^6)\sqrt[3]{(x^2+6)} ~~ \right)[/tex]
For finding median in continuous series, which amongst the following are of importance?Select one:a. all of theseb. Particular frequency of the median classc. Lower limit of the median classd. cumulative frequency preceeding the median class
For finding median in continuous series, all of the four factors are important.
The median is a central value in a data set that separates the upper and lower halves of the data.
In a continuous series, it is important to find the median because it gives us a good indication of the typical value in the series.
To find the median in a continuous series, four factors are important:
a. Particular frequency of the median class: This refers to the number of observations that fall into the median class.
b. Lower limit of the median class: The lower limit of the median class defines the start of the interval in which the median falls.
c. Upper limit of the median class: The upper limit of the median class defines the end of the interval in which the median falls.
d. Cumulative frequency preceding the median class: This refers to the total number of observations that fall into classes before the median class.
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how to solve x3 -x = 80
The solution of the equation is [tex]x = x^{1/3} + 80^{1/3}[/tex]
An equation is a mathematical statement that says that two things are equal. Solving an equation means finding the value of the variable that makes the equation true.
In this case, we want to solve for x in the equation x³ - x = 80.
To solve this equation, we can start by isolating the x terms on one side of the equation and the constant 80 on the other side.
To do this, we will add x to both sides of the equation to cancel out the subtraction of x on the left-hand side. The equation becomes
=> x³ = x + 80.
Next, we will take the cube root of both sides to isolate x on one side of the equation. The cube root of x³ is just x, so we get
[tex]x = x^{1/3} + 80^{1/3}[/tex]
Now, we have a simple equation in x and can use basic algebraic techniques to solve for x.
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Which sets do the square root of 7 belong to
A.) integers and irrational numbers
B.) irrational and real numbers
C.) real and rational numbers
D.) rational and whole numbers
The square root of 7 belongs to the set of irrational numbers and the set of real numbers. Option B is correct.
What is a rational number?In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.
The square root of 7 is an irrational number because it cannot be expressed as a finite decimal or a fraction. Irrational numbers are a subset of real numbers, which is a set that includes all the real numbers, including both rational and irrational numbers.
Option B) "irrational and real numbers" is the correct answer.
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The population of Exeter is about 15 thousand people. The population of the United States is about 300 million people. What percent of the US population lives in exeter ?
The percent of the US population lives in Exeter is 0.005%
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given that, the population of Exeter is about 15 thousand people and the population of the United States is about 300 million people, we need to find what percent of the US population lives in Exeter
15,000 = 0.015 millions
The percentage of people who live in Exeter = 0.015 / 300 × 100
= 0.005%
Hence, the percent of the US population lives in Exeter is 0.005%
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The percent of the US population lives in Exeter is 0.005%, when the population of Exeter is about 15 thousand people. The population of the United States is about 300 million people.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
Given that, the population of Exeter is about 15 thousand people and the population of the United States is about 300 million people, we need to find what percent of the US population lives in Exeter
we know,
15,000 = 0.015 millions
now,
The percentage of people who live in Exeter = 0.015 / 300 × 100
= 0.005%
Hence, the percent of the US population lives in Exeter is 0.005%
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A storage area is shaped like a rectangular prism. It has a width of 6 feet, a height of 5 feet, and a volume of 570 cubic feet.
What is the length of the storage area?
Answer:
19 feet
The length of the storage area is 19 feet.
Step-by-step explanation:
Volume of a rectangular prism (a box shape) is given by:
Volume = length * width * height
We are given three out of four of these numbers. Fill them in and solve for the missing number.
570 = x * 6 * 5
570 = 30x
divide by 30
19 = x
The length is 19 feet. The storage area is 19 feet long.
Answer:
19 feet
Step-by-step explanation:
because I took this question already
Find the diagonal of a square whose sides are of the given measure.
Given = 7√3
Step-by-step explanation:
Use the Pythagorean theorem: a^2 + b^2 = c^2. In this case, sides a and b are each 7sqrt(3), and c is the diagonal of the square.
a^2 + b^2 = c^2
(7sqrt3)^2 + (7sqrt3)^2 = c^2
294 = c^2
c = sqrt(294) = 7sqrt(6)
Substitute b = 2 into the equation and
evaluate. Then, determine if b = 2 makes
the equation true?
15 = 5b
15 = 5(?)
15 =?
b = 2
make this equation true
b = 2 does not make the equation true
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
15 = 5b
when b=2,
15=5(2)
15 = 10
This is not true
So, b = 2 does not make the equation true
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Find the sum of the measures of the interior angles of the figure.
Answer:
720
Step-by-step explanation:
Sum of the interior angles of any polygon is (n−2)×180.
So 6-2=4
4*180 = 720
Please please please help
An open cylindrical water tank has base radius x metres and height h metres. Each square metre of the
base costs a dollars to manufacture and each square metre of the curved surface costs b dollars. The
combined cost of the base and curved surface is c dollars.
a Find c in terms of a, b, x and h.
X
b
Show that the volume of the tank is given by V = -(c – παχ2).
2b
c As x varies, prove that V is at its maximum when the cost of the base is dollars.
3
V is at its maximum when [tex]a = b\ \pi x[/tex], [tex]V = \pi x2h[/tex], and [tex]c = a x2 + b\ \pi xh[/tex].
Determine the cost of the tank.This question uses the principles of geometry, specifically the formulas for the area of a circle and the area of a curved surface. In addition, the concept of cost maximization is used to determine the cost of the tank when the volume is at its maximum.
Given,
[tex]c = a x2 + b\ \pi xh[/tex]
This equation states that the cost of the tank is equal to the cost of the base plus the cost of the curved surface.
The cost of the base is equal to the area of the base multiplied by the cost per square metre, which is a.
The area of the base is equal to [tex]\pi x2[/tex], where x is the radius of the base. The cost of the curved surface is equal to the area of the curved surface multiplied by the cost per square metre, which is b.
The area of the curved surface is equal to πxh, where h is the height of the tank.
Combining these two equations gives the equation for c.
[tex]V = \pi x2h[/tex]
This equation states that the volume of the tank is equal to the area of the base multiplied by the height.
The area of the base is equal to [tex]\pi x2[/tex], where x is the radius of the base. The height of the tank is h. Combining these two equations gives the equation for V.
V is at its maximum when [tex]a = b\pi x[/tex]
This equation states that the volume of the tank is maximized when the cost of the base is equal to the cost of the curved surface.
The cost of the base is equal to the area of the base multiplied by the cost per square metre, which is a.
The area of the base is equal to [tex]\pi x2[/tex], where x is the radius of the base. The cost of the curved surface is equal to the area of the curved surface multiplied by the cost per square metre, which is b.
The area of the curved surface is equal to πxh, where h is the height of the tank.
Setting a equal to bπx gives the equation for the maximum volume.
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How are position vs time graph useful ?
An object's distance from its beginning point during the course of its motion is displayed as a position-time graph. A line's slope increases with its steepness, and an object's motion changes more quickly as a result.
How would you explain a time graph?We can see how the speed of a moving object varies over time by looking at a speed-time graph. The acceleration is larger the steeper the graph is. The object is moving steadily if there is a horizontal line. An object is said to be slowing down when a line dips downward.The vertical axis (y-axis) of a distance-time graph will display the distance (in meters, kilometers, miles, etc.) and the horizontal axis will display the time (in seconds, minutes, hours, etc). ( x-axis). On this page, we will examine some distance-time graphs, all of which will be drawn using straight lines. The velocity of the object is shown on a time graph. Therefore, the slope's value at a particular instant indicates the object's velocity at that instant.To learn more about time graph, refer to:
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How much is 100 grams to cups?
100 grams to convert the cups is 1/2 cup.
How do you weigh 100 g?Utilizing a scale is the only accurate technique to measure in grammes. Kitchen spoons and cups, for example, offer an approximate approximation. Additionally, always have a conversion calculator or chart on hand so you can measure grammes without a scale.There are 240 grammes in a cup when measuring using a typical U.S. measuring cup.Using a calculator, you may convert between cups and grammes. You have a choice of 20 well-liked kitchen ingredients or may just write in the product density.You may calculate grammes using this method without a scale. Three teaspoons are equal to one soup spoon.To learn more about grams refer to:
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Try it
According to medical research, teenagers need to sleep Which value of g is least likely to occur if the
9 hours per night.
An article in the school newspaper claims that 50% of the newspaper's claim is correct?
1,200 students at their high school are not getting enough o 0. 50
A sample of 50 students are selected from this population O 0. 60
and asked if they get the recommended number of hours
O 0. 70
of sleep per night. Let P = the proportion of students in
O 0. 80
the sample who do not get enough sleep.
sleep.
According to medical research, teenagers' need to sleep, (0.60, 0.70, and 0.80) is higher than 0.50, so they are less likely to occur.
The value of g that is least likely to occur is 0.50.
The article in the school newspaper claims that 50% of the 1,200 students at the high school are not getting enough sleep,
which would mean that P = 0.50.
However, the sample of 50 students is likely to differ from the population of 1,200 students,
So it's possible that the proportion of students in the sample who do not get enough sleep is different from 0.50.
The other values of g (0.60, 0.70, and 0.80) are higher than 0.50, so they are less likely to occur.
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When The Exponential Distribution Probability Is Given As P(X ≤ 9 ) = 1 − E−9/18 The Average Value For X Is A. 18 B. 1/2 C. 9/18 D. 9
The average value for X is 9/18. Hence, the answer is D. 9.
The exponential distribution probability is given as P(X ≤ 9 ) = 1 − E−9/18. The average value for X is calculated as follows.
The expected value (mean) of an exponential distribution of a random variable X with rate parameter λ is given by E[X] = 1/λ.
In the given problem, λ = 18. Thus, the expectation of the random variable X is 1/18.
The calculation for the expected value of X can be represented as:
E[X] = 1/λ = 1/18
Thus, the average value for X can be represented as:
Average Value of X = E[X] = 1/18 = 9/18
Therefore, the average value for X is 9/18. Hence, the answer is D. 9.
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suppose that the point (x, y) is in the indicated quadrant. decide whether the given ratio is positive or negative. recall that in quadrant i, is positive or negative?
The ratio of x/y is then 2/3, which is a positive number.
In quadrant I, both the x and y coordinates are positive. Therefore, a ratio of x/y will be positive. To illustrate this, let's say that the point (x, y) is located at (2, 3). This means that x=2 and y=3. The ratio of x/y is then 2/3, which is a positive number.
To calculate the ratio, we divide the x coordinate by the y coordinate: x/y = 2/3. This will give us the ratio of the point (x, y) in the indicated quadrant. If the result is a positive number, then the ratio is positive. If the result is a negative number, then the ratio is negative. In this example, the result is a positive number, so the ratio is positive.
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The congruent angles of an isosceles right triangle measure:
a. 90° each
b. 45° each
c. 60° each
d. 180° each
The congruent angles of an isosceles right triangle measure is 45° each.
How big should the angles be in an isosceles right triangle?Properties of an Isosceles Right TriangleOne of its angles is 90 degrees. The base and height of this triangle are the perpendicular legs, which are also referred to as the base and height. In an isosceles right triangle, the other two angles are sharp, congruent, and measure 45 degrees each.Due to the equality of the two sides, the corresponding angle is congruent. As a result, two sides of an isosceles right triangle are congruent, and the associated angles are each 45 degrees, adding up to 90 degrees. The triangle's three angles will thus add up to 180 degrees.To learn more about congruent angles refer to:
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What is the sum of the rational expressions below? 3x + 2 / x-1 + 2x - 5 / x-1 ASAP please
To add the two rational expressions, we need to find a common denominator:
3x + 2 / x - 1 + 2x - 5 / x - 1 = (3x + 2)(x - 1) / (x - 1)(x - 1) + (2x - 5)(x - 1) / (x - 1)(x - 1)
Now that we have a common denominator, we can add the numerators and simplify:
= (3x^2 - x + 2x - 5) / (x - 1)(x - 1)
= (3x^2 + x - 5) / (x - 1)(x - 1)
This is the simplified sum of the two rational expressions.
Priya writes the equation y=-1/2x-7. Write an equation that has: a. Exactly one solution in common with Priya's equation
There are other equations that have the same number of solutions as Priya's equation, y = -1/2x - 7. For instance:
y = -1/2x - 7 + k (where k would be any constant value)
or
y equals mx plus b, where m is -1/2 and b is -7.
Single Solution Equation Y=-1/2x-7The slope and y-intercept of the equations are the same as Priya's equation. This means that the equations will meet Priya's equation at exactly one point, giving them the same solution. However, it is important to note that the constant value (k) or the y-intercept (b) can be changed to make the equation different from Priya's equation, but as long as the slope (m) remains the same, the two lines will intersect at exactly one point.
I determined that because both equations have the same slope (-1/2) and the same y-intercept (-7). This means that they will intersect at exactly one point on the coordinate plane, resulting in one solution in common.
The slope of a line is represented by the coefficient of x in the equation, and the y-intercept is represented by the constant term. In both equations, the slope is -1/2 and the y-intercept is -7, so they are the same line, and therefore will have exactly one solution in common.
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