Answer:
$5
Step-by-step explanation:
Let the cost of a children's ticket be x.
The cost of an adults ticket would be x + 3. (adult ticket costs $3 more than a children's ticket.)
200 adult tickets would cost 200(x+3), and 100 children's ticket would cost 100x.
The combined costs of children's ticket and adult would be 200(x+3) + 100x.
Using these information, the equation: 200(x+3) + 100x = 2100 can be formed.
200(x+3) + 100x = 2100
200x + 600 + 100x = 2100
300x = 1500
x = 5
The children's ticket cost $5.
Double check.
200*8 + 100*5 = 2100.
7 raised to the power 2 divided by 7 raised to the power 3
The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Given expression,
7 raised to the power 2 divided by 7 raised to the power 3
7 ^ 2 / 7 ^ 3
The value of a ^ m / a ^ n = a ^ m-n
= 7 ^ (2-3)
= 7 ^ ( -1)
= 1 / 7 .
Therefore, The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7
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The chart to the right shows a country'sannual egg production. Model the data in the chart with a linear function,using the points (1995,52.7)and (1999,61.3).Let x represent the year,where x=0 represents 1995,x=1 represents 1996,and so on,and let y represent the egg production (inbillions). Predict egg production in 2001.
The predicted egg production in 2001 is given as follows:
65.6 billion.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the yearly change.The intercept b represents the production in 1995.The production in 1995 was of 52.7, hence the intercept b is given as follows:
b = 52.7.
In 4 years, the production increased to 61.3, hence the slope m is given as follows:
m = (61.3 - 52.7)/4
m = 2.15.
Hence the function is of:
y = 2.15x + 52.7.
2001 is 6 years,hence the estimate is given as follows:
y = 2.15(6) + 52.7
y = 65.6 billion.
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Prove that the union of two subspaces of V is a subspace of V if and only if one of the subspaces of v is contained in the other. [duplicate]
The union of two subspaces of V is a subspace of V if and only if one of the subspaces of v is contained in the other
Let [tex]$V_1, V_2$[/tex] be the two subspaces of V. Suppose [tex]$V_1 \cup V_2$[/tex] is a subspace of V.
Then if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then we must have [tex]$x_1 \in V_1 \cup V_2$[/tex] and[tex]$x_2 \in V_1 \cup V_2$[/tex] so that we must have [tex]$x_1+x_2 \in V_1 \cup V_2$[/tex].
If and only if one of the subspaces is contained in the other, the union of the two subspaces is a subspace.
But this by definition means [tex]$x_1+x_2 \in V_1$[/tex] or [tex]$x_1+x_2 \in V_2$[/tex]. Either way, by the existence of additive inverses and the closure properties for the subspaces we have:
[tex]\left(x_1+x_2\right)+\left(-x_1\right) \in V_1[/tex]
Or
[tex]\left(x_1+x_2\right)+\left(-x_2\right) \in V_2[/tex]
By the associative/commutative properties, we have:
[tex]x_2 \in V_1 \text {, or, } x_2 \in V_1[/tex]
Thus we have shown if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then [tex]$x_1 \in V_2$[/tex] or [tex]$x_2 \in V_1$[/tex]. If [tex]$x_1 \in V_2$[/tex] for all [tex]$x_1 \in V_1$[/tex] then we have [tex]$V_1 \subseteq V_2$[/tex]. If [tex]$x_2 \in V_1$[/tex] for all [tex]$x_2 \in V_2$[/tex] then [tex]$V_2 \subseteq V_1$[/tex]. In either case, we see one subspace is a subset of the other.
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A rectangular garden has a length of 57 m and a width of 42 m. How many m2 will decrease the area of a garden, if the ornamental fence with a width of 60 cm will be planted inside its perimeter?
The area of the rectangular garden can be calculated as follows: 57 m * 42 m = 2406 m^2.
The ornamental fence with a width of 60 cm has a width of 0.6 m. If the fence is planted inside the perimeter of the garden, the length of the garden will decrease by 2 * 0.6 m = 1.2 m and the width of the garden will decrease by 2 * 0.6 m = 1.2 m.
So, the new length and width of the garden will be 57 m - 1.2 m = 55.8 m and 42 m - 1.2 m = 40.8 m, respectively.
The new area of the garden can be calculated as follows: 55.8 m * 40.8 m = 2270.784 m^2.
Finally, the decrease in area can be calculated as follows: 2406 m^2 - 2270.784 m^2 = 35.216 m^2.
Therefore, the area of the garden will decrease by 35.216 m^2.
Answer:
The width of the ornamental fence is 60 cm, which is equal to 60/100 = 0.6 meters.
The total length of the ornamental fence that will be planted inside the perimeter of the rectangular garden is 2 * (57 m + 42 m) = 2 * 99 m = 198 m.
The decrease in the area of the garden due to the ornamental fence is 0.6 m * 198 m = 118.8 m^2.
Evaluate the expression. 8+12x7
Answer:
92
Step-by-step explanation:
We first do 12x7 which equals to 84
Then we add 8 which equals to 92
Find the number of ordered pairs $(x,y)$ of positive integers that satisfy $x \le 2y \le 60$ and $y \le 2x \le 60$.
The number of ordered pairs $(x,y)$ of positive integers that satisfy the equation would be 480.
We only count one ordered pair by substituting 2 for 60 in this case. We count four ordered pairs by doing with 4.
We got 7 pairings from 6 people. I add 8 to get 12, thus. the difference between neighboring phrases by moving on and doing so (1,3,3,5,5,...).
We believe that if 2n were substituted for 60, we would find 1+3+3+5+5+7+7.... where n words will be present.
So, 1+3+3+5+5... 29+29+31 = 16*30 = 480 is our response.
The number of ordered pairs $(x,y)$ of positive integers that satisfy the equation would be 480.
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The full question:
Find the number of ordered pairs $(x,y)$ of positive integers that satisfy the following equation
A tourist asked a zookeeper how many birds and lions are in the zoo. The zookeeper replied there are 31 heads and 96 feet. Find the number of each.
By concept of linear equations, The number of birds is 14 and number of lions is 17.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Let no. of birds=x and no. of lions=y
Given heads=31
and feet=96
Therefore, the equations will be
x+y=31 and 2x+4y=96
from given equations x=14 and y=17.
Hence,
The number of birds is 14 and number of lions is 17.
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Find the equation of the line passing through the points (8, -16) and (1, 5).
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-16})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{(-16)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{8}}} \implies \cfrac{5 +16}{-7} \implies \cfrac{ 21 }{ -7 } \implies - 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-16)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{8}) \implies y +16 = - 3 ( x -8) \\\\\\ y+16=-3x+24\implies {\Large \begin{array}{llll} y=-3x+8 \end{array}}[/tex]
Given a set of seven distinct positive integers, prove that there is a pair whose sum or whose difference is a multiple of 10. you may use the fact that if the one digit is a 0 it is divisible by 10. hint: create six categories of integers based on their ones digit. I cant figure out the six categories.
Six categories of integers based on their ones digit are:
Integers ending in 0 or 5.Integers ending in 1 or 9.Integers ending in 2 or 8.Integers ending in 3 or 7.Integers ending in 4 or 6.Prove Pair Sum/Diff Multiple of 10The cases when sum or difference of the pair is divisible by 10:
If the integers have the same units digit (e.g. both end in 5 or both end in 0), then their sum is a multiple of 10.If one integer ends in 0 or 5 and the other integer ends in 1 or 9, then their difference is a multiple of 10.If one integer ends in 0 or 5 and the other integer ends in 2 or 8, then their sum is a multiple of 10.If one integer ends in 0 or 5 and the other integer ends in 3 or 7, then their difference is a multiple of 10.If one integer ends in 0 or 5 and the other integer ends in 4 or 6, then their sum is a multiple of 10.Therefore, no matter which seven integers we choose, there is always a pair that meets the condition.
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Solve for the length of the unknown side in the following right triangle. (Side AC is the hypotenuse.) Round your answer to two places, where applicable. Side AB Side BC Side AC ? 12 19
The length of the unknown side or, the length of AC = 22.62.
To calculate the length of the unknown side in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides or, in familiar algebraic notation, a2 + b2 = c2.
In this Question, side AC is the hypotenuse, so we can use the Pythagorean theorem to find the length of side AC:
AC^2 = AB^2 + BC^2
We know that AB = 12 and BC = 19, so we can substitute these values into the equation:
AC^2 = 12^2 + 19^2
AC^2 = 144 + 361
AC^2 = 505
To find the length of AC, we can take the square root of 505:
AC = √505
Rounded to two decimal places, the length of AC = 22.62.
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find the function of the form y= A sin(kx)+C or y= A cos (kx) +C
Answer:
[tex]y \: = 2cos \: ( \frac{\pi}{5} x) - 3[/tex]
A population has a mean of 50 and a standard deviation of 12. For a sample size of 4, what is the expected value of the mean?
50
4
36
need more information to determine the answer
Expected value of the mean = 50 (the population mean)
How is expected value of the mean determined?The expected value of the mean for a sample size of 4 from a population with a mean of 50 and a standard deviation of 12 can be calculated using the central limit theorem.
According to the central limit theorem, the expected value of the mean of a sample from a population approaches the population mean as the sample size increases. In other words, as the sample size becomes larger, the sample mean becomes a more accurate estimate of the population mean.
In this case, the expected value of the mean of a sample of 4 from a population with a mean of 50 and a standard deviation of 12 can be calculated as follows:
Expected value of the mean = 50 (the population mean)
It is important to note that the expected value of the mean is equal to the population mean, regardless of the sample size. The central limit theorem states that the sample mean approaches the population mean as the sample size increases, but for a sample size of 4, the expected value of the mean is still equal to the population mean.
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Two numbers are in a ratio 3:5. What is the ratio between their squares?
Answer:
let the two numbers be x and y.
Given ,
[tex] \underline{\underline{\frac{x}{y} = \frac{3}{5}}} \\ [/tex]
To find - ratio of squares of the two numbers.
[tex]\longrightarrow \: \frac{ {x}^{2} }{ {y}^{2} } = ( \frac{ {3}^{2} }{ {5}^{2} } ) \\ \\ \longrightarrow \: \boxed{\frac{ {x}^{2} }{ {y}^{2} } = \frac{9}{25} }[/tex]
Therefore ,
[tex] \underline{\underline{ratio \: of \: the \: squares \: of \: two \: numbers \: = \: 9 \: : \: 25}} [/tex]
hope helpful! :)
Two parabolas have the same x-intercepts (one positive
x-intercept, and one negative x-intercept. The maximum or minimum value of
the first is 2 times the maximum or minimum value of the other. Sketch these
parabolas on the same coordinate grid (with at least 3 points)
Pls include all steps and picture of the graph
The equation of the parabolas are
y = (x - 2)(x + 2)
y = (x - 2)(x + 2) -4
The graph is attached below.
What is a coordinate grid?
Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis. The origin is the location where the x- and y-axes intersect.
Assume the x-intercepts are 2 and -2.
The equation of a parabola whose x-intercepts a and b is y = (x-a)(x-b)
The equation of a parabola is
y = (x-2)(x-(-2))
y = x² - 4 .....(i)
The vertex of the parabola is (0,4).
The parabola's maximum or minimum value is the vertex's y-coordinate.
Thus replace - 4 with -8 of equation (i)
y = x² - 8
Puttin x = 0 in equations (i) and (ii)
y(0) = -4
y(0) = -8
Puttin x = 1 in equations (i) and (ii)
y(1) = -3
y(1) = -7
Puttin x = -1 in equations (i) and (ii)
y(-1) = -3
y(-1) = -7
The points on y = x² - 4 are (0,-4), (1,-3), and (-1,-3).
The points on y = x² - 8 are (0,-8), (1,-7), and (-1,-7).
Plot the points and join them.
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use the LCM to find equivalent fractions for each fraction pair. then use the symbol greater then or less than to show the bigger fraction. the numbers are 5/8 and 2/3 , 1/6 and 2/9, and 7/12 and 5/8
The comparison of the fractions are
15/24 < 16/24, 3/18 < 4/18 and 14/24 <15/24
How to determine the equivalent pairsFraction 1
Here, we have
5/8 and 2/3
The LCM of 8 and 3 is 24
So, the pair is
15/24 and 16/24
When compared, we have
15/24 < 16/24
Fraction 2
Here, we have
1/6 and 2/9
The LCM of 6 and 9 is 18
So, the pair is
3/18 and 4/18
When compared, we have
3/18 < 4/18
Fraction 3
Here, we have
7/12 and 5/8
The LCM of 12 and 8 is 24
So, the pair is
14/24 and 15/24
When compared, we have
14/24 <15/24
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Of all the metals, Mercury has the lowest melting point at
-37.8 degrees Celsius. Write an inequality to show all of the possible melting points for any other metal.
Mercury, gallium, and caesium often have low melting points, except gold. The only liquid metal with a 38 °C melting temperature is mercury.
What are the possible melting points for any metal?They have high melting and boiling points because melting and boiling require a lot of energy to break through the strong metallic connections present in a metal's massive structure.
Brass: 930 °C (1710 °F) Aluminium Bronze*: 1027-1038 °C (1881-1900 °F) Chromium: 1860 °C (3380 °F) Copper: 1084 °C (1983 °F).
In general, aluminium is an easy metal to melt, and it is easy to get your hands on. To make aluminum metal shapes, many people melt discarded soda cans made of aluminum. The aluminum should be heated until it melts completely.
Therefore, the melting or boiling point will be higher the more energy is required. Varying metals have different melting and boiling points because the force of attraction between the metal ions differs between them.
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William & LeAnna are both 40 years old. They would like to retire when they are 58. They have decided to deposit $7,500 annually into an account that earns 3.2%
interest compound annually. What is the account balance when they retire?
The account balance when they retire is $13,221.96
How to determine the account balance?The formula for compound interest is:
A = P (1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment/loan amount
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
A is the account balance when they retire
P = $7,500, r = 3.2% = 0.032, n = 1, t = 58-40 = 18 years
A = P (1 + r/n)^(nt)
A = 7,500(1 + 0.032/1)^(1*18)
A = 7,500(1 .032)¹⁸
A = $13,221.96
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Use the ALEKS calculator to approximate √172.
Round your answer to the nearest hundredth.
172 ~ 0
a squ
X
Ś
Using the ALEKS calculator , 13.1 would roughly equal 172, rounded to the closest hundredth.
Can ALEKS be used with a calculator?When necessary, ALEKS offers a calculator so that users may determine the difference. Instead of using your own calculator, just utilize ALEKS'. For the calculator to produce most accurate assessment results, it must only be used in the manner specified by ALEKS.
Is ALEKS superior to Khan Academy?Reviewers believed that Khan Academy and ALEKS better satisfy their needs as a business. Reviewers believed that Open Courseware is the best choice when considering the level of continuing product support. Our evaluators liked the approach of Online Courses over ALEKS for feature releases and roadmaps.
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What is a quotient
4 \ 1/6
A rectangular ar box of tissues 15 22 7mm long, 122mm wide, and 67mm tall Find the volume of the box
Answer:
hxxu u uu u. yy h gghchcvhhvuvuvuvuvhcuchchcjvj jvjcjcjcchhchcjcjc
Step-by-step explanation:
g g g g g. gg g
Y=601(1.05)^18 rounded to the nearest hundredth
The value of y is 1446.38.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
y = 601 [tex](1.05)^{18}[/tex]
Now,
y = 601 x 2.4066192336911
y = 1446.3781
y = 1446.38
Thus,
y = 1446.38
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Rewrite r(r) = (0.88)^4t in the form y = a(1 + r)'or y = a (1 - r)' to determine whether it represents exponential growth or exponential decay. Round a and r to the nearest hundredth if necessary.
The exponential function r=(0.88)^4t can be written as r=(1-0.12)^4t.
What are exponential functions?
An exponential function is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Now,
given exponential function is r(r) = (0.88)^4t
we can rewrite its as r=(1-0.12)^4t. to find whether it is increasing or decaying. As the - sign shows decrement.
hence,
Given exponential function is decaying in nature..
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You are interested in determining if the pandemic has caused people to become depressed. You randomly sample 20 individuals and administer a 30 item true/false psychological test designed to measure depression. Scores that are greater than 20 indicate significant levels of depression. Use the following descriptive statistics to determine if individuals in your sample are depressed.
N Mean Std. Deviation
Score 8 22.25 2.49
What is the value of the mean difference in the depression experiment?
In the depression experiment, degrees of freedom equals?
In the depression experiment, the critical t value (tcritical) equals _________.
In the depression experiment, the observed t value (tobs) equals _________.
The degrees of freedom equals 7.
The test statistic will be 2.55
The critical value will be 1.89.
How to calculate the valueFrom the information, they randomly sample 20 individuals and administer a 30 item true or false psychological test designed to measure depression and the scores that are greater than 20 indicate significant levels of depression.
The degree of freedom will be:
= n - 1
= 8 - 1
= 7
The test statistic will be:
= 22.25 - 20 /2.49 ✓8
= 2.55
The critical value will be 1.89.
Based on the information, it should be noted that we will fail to reject the null hypothesis.
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Parallelogram ABCD is reflected over the x-axis. What rule shows the input and output of the reflection, and what is the new coordinate of A'? (1 point) Parallelogram ABCD is shown. A is at negative 5, 1. B is at negative 4, 3. C is at negative 1, 3. D is at negative 2, 1.
The rule shows the input and output of the reflection is, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.
And, The new coordinate of A' = (- 5, - 1)
What is Refection?Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.
We have to given that;
Parallelogram ABCD is shown. A is at (-5, 1), B is at (-4, 3). C is at (-1, 3) . D is at (-2, 1).
We know that;
When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.
And, The reflection of point (x, y) across the x-axis is (x, -y).
Hence, The new coordinate of A' is,
⇒ (- 5, 1) = (- 5, - 1)
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Let X represent the lifetime in months of a battery, and someone claims that X~N(50,25). We wish to investigate the claim, so 16 batteries are life-tested and the average of the survival times of the 16 batteries is computed. If the claim is true, the average life of 16 batteries should EXCEED what value for 99% of the time?
53 is the value of the 99% of the time.
What is a normal distribution?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center
Given, Let X represent the lifetime in months of a battery, and someone claims that X~N(50,25). We wish to investigate the claim, so 16 batteries are life-tested and the average survival times of the 16 batteries are Comput.
μ = 50
σ² = 25
n = 16
So, the Population standard deviation
σ² = 25
σ = 5
To find the value 99% of the time
The z-score will be
P(z <Z) = 0.999
P(z < 2.326) = 0.999
Z = 2.326
To find a z score corresponding to a known probability, select fx, Statistical, NORMSINV, and enter the total area to the left of the given value.
Now we determine the z-score using the z-score formula
x = μ + (Z *σ / √n)
x = 53
Therefore, the value of 99% of the time is 53.
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Complete question:
solve for y
5/4 y = 13
Answer:
[tex]y = 10.5[/tex]
Step-by-step explanation:
[tex]\frac{5}{4} y = 13\\[/tex]
We transpose
[tex]y =\frac{13X4}{5}[/tex]
[tex]y = \frac{52}{5}[/tex]
[tex]y = 10.5[/tex]
Based on the completed Form 1040 and 2018 Taxable Income Tiers, what is the total tax
that the employee is responsible for paying?
Answer in complete sentences.
By assuming that the taxpayer has $100,000 as his income on the completed Form 1040, the total tax that the employee is responsible for paying will be: $17,836.
What are tax bracket or income tiers?A tax bracket is a range of incomes that are taxed at a specific rate. Tax brackets are part of a progressive tax system, which means that tax rates increase progressively as an individual's income increases. Low-income taxpayers pay relatively low tax rates, while higher-income taxpayers pay higher rates.
In 2022, for example, a single filer with taxable income of $100,000 will pay $17,836 in taxes, representing an average tax rate of 18%. However, your marginal tax rate or tax bracket is 24%. As a result, the total tax that the employee is responsible for is $17,836.
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let have the following distribution: 1 2 3 4 0.2 0.3 0.1 0.4 find (write it up to first decimal place).
After solving the value of E(x^2 + 3) is 11.7.
The distribution of x is:
x f(x) x^2 x^2·f(x)
1 0.2 1 0.2
2 0.3 4 1.2
3 0.1 9 0.9
4 0.4 16 6.4
We have to determine the value of E(x^2 + 3).
We can write it as
E(x^2 + 3) = E(x^2) + 3...........(1)
As E(x^2) = Sum of x^2·f(x)
E(x^2) = 0.2 + 1.2 + 0.9 + 6.4
E(x^2) = 8.7
Now putting the value of E(x^2) in equation 1, we get
E(x^2 + 3) = 8.7 + 3
E(x^2 + 3) = 11.7
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The complete question is:
Let x have the following distribution:
x 1 2 3 4
f(x) 0.2 0.3 0.1 0.4
Find E(x^2 + 3) (write it up to first decimal place).
Calcualtor find the exact values of the six trigonometric functions of a point on the terminal side of an angle
The exact values of each trigonometric function are 4/5, 3/5, 4/3, 5/4, 5/3, and 3/4.
Given, the terminal side of contains the point p(9, 12).
Each trigonometric function must have an exact value, which we must determine.
A line segment drawn from the origin to the point should have a length of r.
r = √x2 + y2
Here, x = 9 and y = 12
r = √(9)2 + (12)2
= √81 + 144
= √225
r = 15
sin θ = y/r = 12/15 = 4/5
cos θ =x/r = 9/15 = 3/5
tan θ = y/x = 12/9 = 4/3
cosec θ = 1/sin θ = 5/4
sec θ = 1/cos θ = 5/3
cot θ = 1/tan θ = 3/4
Consequently, each trigonometric function's precise values are 4/5, 3/5, 4/3, 5/4, 5/3, and 3/4.
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The full question:
The point p(9, 12) is on the terminal side of θ. Find the exact values of each trigonometric function.
Describe the relationship between the two quantities
I assume volume increases over time as the balloon is blown up. Is that correct?
This suggests that a gas's pressure decreases as its volume increases. Similar to this, a gas's pressure rises as its volume decreases. The balloon's expansion for the given implies that its volume grows. Boyle's law predicts that its pressure will decrease as a result.
Why does a balloon's volume grow bigger as it rises?In other words, as the atmospheric gas exerts less pressure on the surface of the balloon, the interior gas expands until the internal and external pressures are equal. This is why weather balloons grow larger as they ascend through the atmosphere to lower pressure regions because the volume of the gas has increased.
What is the relationship between the volume of the balloon and the number of moles?You can observe Avogadro's Law whenever you blow up a balloon. By inflating the balloon, you can add moles of gas, which increases the balloon's volume.
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