a) From the given information, [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]
be a random sample of size 5 from a normal population with mean 0 and variance 1. Hence,
[tex]W=(\sum_{i=1}^5 Y_{i}^2)\sim X_{5}^2[/tex]
b) From the given information, the random variable is [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]
and [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]
representing the standard normal variables. Hence,
.[tex]U=(\sum_{i=1}^5 (Y_{i} - \bar{Y})^2) \sim X_{5}^2[/tex]
c) From the given information,[tex]Y_{1}, Y_{2},...........Y_{5}[/tex]
representing the standard normal variables and moreover, [tex]Y_{6}[/tex]
is independent standard normal variable. Hence, [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2\sim X_{5}^2[/tex]
and
.[tex]Y_{6}^2\sim X_{1}^2[/tex]
What is Chi-square distribution?
Chi-square distribution with k degrees of freedom is defined as the sum of the k standard normal variables. This is also defined as the square of the deviations taken from the mean. Chi-square distribution is used for testing goodness of fit and independence in contingency tables.
• If [tex]z_{1}, z_{2},...........z_{k}[/tex]
are independent standard normal variables, then
[tex]\sum_{i=1}^k z_{i}^2\sim X_{k}^2[/tex]
• If [tex]X\sim X_{m}^2[/tex]
and [tex]Y\sim X_{n}^2[/tex]
, then
[tex](X+Y)\sim X_{m+n}^2[/tex]
Step: 1
(a)
The distribution of [tex]\sum_{i=1}^5 Y_{i}^2[/tex]
is obtained below:
From the given information, [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]
be a random sample of size 5 from a normal population with mean 0 and variance 1. Hence,
[tex]W=(\sum_{i=1}^5 Y_{i}^2)\sim X_{5}^2[/tex]
The random variable, [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]
representing the sum of squares of standard normal variables and hence, the distribution of [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]
is identified as chi-square distribution.
Hint:
Use chi-square distribution to find the distribution of
.[tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]
Step: 2
(b)
From the given information, the random variable is [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]
and [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]
representing the standard normal variables. Hence,
.[tex]U=(\sum_{i=1}^5 (Y_{i} - \bar{Y})^2) \sim X_{5}^2[/tex]
The random variable [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]
representing the sum of squares of deviations taken from the mean for 5 standard normal variables and hence, the distribution of
[tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]
is chi-square distribution with 5 degrees of freedom.
Hint:
Use [tex](X+Y)\sim X_{m+n}^2[/tex]
to find the distribution of
[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2[/tex]
Step: 3
(c)
From the given information,[tex]Y_{1}, Y_{2},...........Y_{5}[/tex]
representing the standard normal variables and moreover, [tex]Y_{6}[/tex]
is independent standard normal variable. Hence, [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2\sim X_{5}^2[/tex]
and
.[tex]Y_{6}^2\sim X_{1}^2[/tex]
Therefore,
[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2\sim X_{5+1}^2[/tex]
[tex]\sim X_{6}^2[/tex]
The distribution of [tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2[/tex]
is identified as chi-square distribution with degrees of freedom is obtained by adding the degrees of freedom of[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]
and the degrees of freedom of [tex]Y_{6}^2[/tex].
The distribution of [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]
is chi-square distribution with 5 degrees of freedom.
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pls help
Given right triangle ABCABC with altitude \overline{BD}
BD
drawn to hypotenuse \overline{AC}
AC
. If AD=7AD=7 and DC=5,DC=5, what is the length of \overline{BD}
BD
in simplest radical form?
The given assertion states that the length of BD in its simplest radical version is 7/√2.
In arithmetic, what is a triangle?A triangle is indeed a 3-sided shape that is occasionally (though not frequently) referred to as the trigon. There are three edges and three angles in every triangle, some of which could be the same.
Since BD is an altitude of the right triangle ABC, we can use the Pythagorean Theorem to find the length of BD. First, let's determine the size of AC:
AC² = AD * DC = 7 * 5 = 35
When we square the two edges, we obtain:
AC = √35
Now, we can use the fact that BD is an altitude to write:
BD = (AC * AD) / hypotenuse
where hypotenuse is the length of BC.
Using the Pythagorean Theorem, we can find the length of BC:
BC² = AC² + AB²
Since triangle ABC is a right triangle, we have AB = BC, so we can write:
BC² = AC² + BC²
Simplifying, we get:
BC² / AC² = 2
When we square the two edges, we obtain:
BC / AC = √2
Multiplying both sides by AC, we get:
BC = AC * √2 = √35 * √2 = √70
Now, we can substitute the values of AC, AD, and BC into the formula for BD:
BD = (AC * AD) / BC = (√35 * 7) / √70 = 7 / √2
Therefore, the length of BD in simplest radical form is 7 / √2.
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Let g'(x) be constant. Find the fifth derivative of fog(x) for an arbitrary five-times-differentiable function f.
The derivative of a composite function is given by the chain rule: the fifth derivative of fog(x) depends only on the second and fourth derivatives of f.
d(fog(x))/dx = df/d(g(x)) * d(g(x))/dx
The fifth derivative of fog(x) can be calculated by taking the derivative five times:
d^5(fog(x))/dx^5 = d^5f/d(g(x))^5 * (dg(x)/dx)^5 + 5 * d^4f/d(g(x))^4 * d^2g(x)/dx^2 * (dg(x)/dx)^3 + 10 * d^3f/d(g(x))^3 * (dg(x)/dx)^2 * (d^2g(x)/dx^2)^2 + 10 * d^2f/d(g(x))^2 * (dg(x)/dx) * (d^3g(x)/dx^3) + 5 * df/d(g(x)) * (d^4g(x)/dx^4)
Since g'(x) is constant, dg(x)/dx is also constant, and its derivative is 0. Therefore, all the terms with derivatives of g(x) higher than 1 are 0, leaving us with:
d^5(fog(x))/dx^5 = 5 * d^2f/d(g(x))^2 * (dg(x)/dx)^2 * d^2g(x)/dx^2 + 5 * df/d(g(x)) * d^4g(x)/dx^4
Since g'(x) is constant, dg(x)/dx and d^2g(x)/dx^2 are also constant, and can be replaced by their values. Therefore, the fifth derivative of fog(x) depends only on the second and fourth derivatives of f.
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Write a problem about a real-life situation involving temperature or money. The situation should include a number and its opposite that results in an answer of zero
Therefore , The negative linear equation result indicates that the coffee shop made $56 less from hot coffee drinks than from iced coffee drinks yesterday.
A linear equation is precisely what?A straightforward regression graph is created using the equation y=mx+b. The y-intercept is m, and the slope is B. Despite the fact that the line before it contains independent parts, it is repeatedly alluded to as a "mathematical formula combining many factors." Only two factors are present in bivariate linear equations. There are no known solutions to application issues concerning linear equations. Y=mx+b.
Here,
Let H be the number of hot coffee drinks sold yesterday, and I be the number of iced coffee drinks sold yesterday. We know that:
H + I = 100 (since a total of 100 cups were sold)
We also know that the average price of a hot coffee drink was $3.50 and the average price of an iced coffee drink was $2.00. Therefore, the total revenue from hot coffee drinks is:
3.50H
And the total revenue from iced coffee drinks is:
2.00I
To find the difference in revenue between the hot and iced coffee drinks sold yesterday, we need to subtract the revenue from iced coffee drinks from the revenue from hot coffee drinks:
3.50H - 2.00I
We want this expression to equal zero, so we can set it equal to zero and solve for H:
3.50H - 2.00I = 0
3.50H = 2.00I
H = (2/3.50)I
H ≈ 0.57I
Since H + I = 100, we can substitute 0.57I for H in the equation:
0.57I + I = 100
1.57I = 100
I ≈ 63.7
Rounding to the nearest whole number, we get:
I = 64
Therefore, H = 100 - I = 36
So the difference in revenue between the hot and iced coffee drinks sold yesterday is:
3.50H - 2.00I = 3.50(36) - 2.00(64) = $72 - $128 = -$56
The negative result indicates that the coffee shop made $56 less from hot coffee drinks than from iced coffee drinks yesterday.
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The complete question is "Write a problem about a real-life situation involving temperature or money. The situation should include a number and its opposite that results in an answer of zero
A local coffee shop sells iced and hot coffee drinks. Yesterday, the shop sold a total of 100 cups of coffee. The average price of a hot coffee drink was $3.50 and the average price of an iced coffee drink was $2.00.
What is the difference in revenue between the hot and iced coffee drinks sold yesterday?"
Como se hace este problema? X+4x=235
Respuesta:
x = 47
Explicación paso a paso:
Necesitamos resolver x en este problema.
[tex]x+4x=235[/tex]
Combinar los términos x juntos
[tex]5x=235[/tex]
Divide 5 en ambos lados
[tex]x=47[/tex]
Nuestra respuesta es 47
a bad contains pennies nickels dimes and quarters they're 50 coins and all of the coins 12% of pennies and 44 dimes there are eight more nickels than pennies how much money does a bag contain
The total amount of money in the bag is M = $ 2.98
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as M
Now , the value of M is
Let the total amount of money in the bag be M
The number of coins in the bag = 50 coins
The number of pennies = 12 % of coins
So , the number of pennies = ( 12/100 ) x 50 = 6 pennies
The number of dimes in the bag = 44 % of the coins
The number of dimes in the bag = ( 44/100 ) x 50 = 22 dimes
The number of nickels = 8 + number of pennies = 8 + 6
The number of nickels = 14 nickels
The remaining number of coins are quarters
On simplifying the equation , we get
So , the number of quarters = 50 - 6 - 22 - 14 = 8 quarters
And , the value of 6 pennies = $ 0.06
The value of 22 dimes = $ 0.22
The value of 14 nickels = $ 0.70
The value of 8 quarters = $ 2.00
Therefore , the total amount in the bag = $ 2.00 + $ 0.70 + $ 0.22 + $ 0.06
The total amount of money in the bag = $ 2.98
Hence , the total money in the bag is $ 2.98
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Hide Assignment Information
Instructions
In this module we learned about statistical inference. The idea in this type of analysis is to use samples that are selected randomly to extract knowledge related to a larger population group that is the focus of the study question.
A normally distributed blood test results has a mean of 79 and a standard deviation of 8.2. According to the central limit theorem, if a large number of samples are taken from a population with a variance, the mean of the samples will eventually be equal to the population mean.
Discuss the below points in the assignment:
This is a normally distributed dataset for blood test results, Explain the range [mean - one standard deviation , mean + one standard deviation]? After identifying the limits (start/end) of the range discuss the percentage of the blood test results that will be included in this range. (Sixty eight percent of the dataset area is within one standard deviation of the mean in a normal distribution, ninety five percent of the data values will be within 2 standard deviation o the mean, and ninety nine point seven percent of the data values will be within 3 standard deviation of the mean).
Find the percentage of scores that are between 75 and 85.
The Inferential statistics is given below.
What is statistics?Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.
Given is to discuss the statistical inference.
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger populationTherefore, the Inferential statistics is given above.
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QUICK!! 50 POINTS PLUS BRAINLIEST AND THANKS
Which programs were parts of FDR's New Deal?
Choose all answers that are correct.
Responses
Works Progress Administration
Civil Rights Act
Federal Deposit Insurance Corporation
Fair Labor Standards Act
Federal Deposit Insurance Corporation, programs were parts of FDR's New Deal.
What is Social Security?Social security is the protection that a society provides to individuals and households to ensure access to health care and to guarantee income security, particularly in cases of old age, unemployment, sickness, invalidity, work injury, maternity or loss of a breadwinner.
here, we have,
One of Franklin D. Roosevelt's most well-known and widespread programmers, Social Security was first introduced in 1935. One of the New Deal initiatives that helped the nation emerge from the Great Depression and recover its assets and wealth as well as give the economy new life was Social Security.
In order to help the aged and disabled better support themselves while they were unable to work, Social Security established safety net protections.
The Social Security programmed and Fannie Mae, or The Federal National Mortgage Association, both still exist today, despite the fact that the majority of the New Deal policies were abandoned when the United States entered World War II. After World War II, Fannie Mae contributed to funding and fueling the housing boom for soldiers coming home.
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The scores on a standardized test are normally distributed with a mean of 105 and standard deviation of 15. What test score is 1.2 standard deviations above the mean?
87 is the test score is 1.2 standard deviations above the mean.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that scores on a standardized test are normally distributed with a mean of 105 and standard deviation of 15.
We need to find the test score is 1.2 standard deviations above the mean
1.2 standard deviations is 1.2×15 =18
So 105-18=87
87 is the score that is 1.2 standard deviations from the mean.
Hence, 87 is the test score is 1.2 standard deviations above the mean.
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2 wholes 4 by 5 minus 4 wholes 1 by 3
Pablo's is a popular Mexican restaurant, known especially for its homemade salsa. During dinner last night at Pablo's, 7 tables of people ordered chips and salsa for every 2 tables that did not. Pick the diagram that models the ratio in the story. A total of 108 tables of people dined at Pablo's last night. How many of the tables ordered chips and salsa?
Answer: Let X be the number of tables that ordered chips and salsa. Then, 7X tables did not order chips and salsa. So, X + 7X = 108, which simplifies to 8X = 108. Dividing both sides by 8, we have X = 13.5.
Since X must be a whole number, we round down to get X = 13 tables ordered chips and salsa.
Step-by-step explanation:
The slope line below is:
Answer: 4/3
Step-by-step explanation:
Look at the points (0,-4) (3,0)
Formula: y2-y1/x2-x1
Substitute: 0-(-4)/3-0 = 4/3
Please make me brainliest, I would also add you as friend if you make me brainliest!
Let's consider what the question asks for:
--> slope of line
The slope of the line is calculated by:
[tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
--> where:
[tex](x_1,y_1)-- > \text{any one point on the line}\\\\(x_2,y_2)-- > \text{another point on the line}[/tex]
Let's find our points
[tex](x_1,y_1)-- > (3,0)\\\\(x_2,y_2)-- > (0,-4)[/tex]
Let's plug these points into our equation:
[tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{-4-0}{0-3}=\dfrac{-4}{-3} =\dfrac{4}{3}[/tex]
Answer: 4/3
Ann is 24 years older than Denny. In 10 years, Ann will be 3 times as old as Denny. How old is Ann now?
Answer I think Ann is 36 and Denny is 12 Im not for sure but thats what i got
Step-by-step explanation:
What is the area, in square feet, of the
isosceles trapezoid below?
8 ft
6.2 ft
15.4 ft
Answer:
86.4 ft^2
Step-by-step explanation:
I need to find the slope of the graph at x= -1
And the answer for A, B, C, D (I really need help)
Answer:
See below
Step-by-step explanation:
The derivative function f' is the slope of the function at any given 'x'
A) f ' = 8 x^3 - 24 x^2
B ) put in x = -1 and compute 8 ( -1)^3 -24(-1)^2 = -8 - 24 = - 32 slope
C) we know the slope (-32) and the x coordinate (-1) put this value of x into the original equation to find y = 2(1^4) - 8(-1)^3 + 6 = 16
so point slope form of the line is
y - 16 = -32 (x - -1) re-arrange:
y = -32x -16
D) where slope (f ') = 0 the slope is 0 and thus the tangent line is horizontal 8x^3 - 24x^2 = 0
8x^3 = 24x^2
8x = 24
x = 3
Maria kept a log of the number of miles she jogged each time she went for a run as she trained for an upcoming marathon. She displayed the logged runs in the histogram below.
A histogram titled Maria's Monthly Jogging has miles run on the x-axis and number of runs on the y-axis. 1 to 1.99 miles is 2 runs; 2 to 2.99 miles is 5 runs; 3 to 3.99 miles is 5 runs; 4 to 4.99 miles is 3 runs; 5 to 5.99 miles is 4 runs; 6 to 6.99 miles is 7 runs; 7 to 7.99 miles is 4 runs.
What is the range of the number of miles Maria jogged?
0 to 7
0 to 7.99
1 to 7.99
1 to 8
Answer:
1 to 7.99 miles
Step-by-step explanation:
According to the given histogram, Maria logged runs for 1 to 7.99 miles, and the number of runs for each mile range is also given. Therefore, the range of the number of miles Maria jogged is 1 to 7.99 miles.
Note that the histogram shows that there were no recorded runs for exactly 8 miles, so the range does not include 8.
Carly has 2.85 pounds of cat food she uses 0.19 pound of cat food to feed one cats. How many cats can Carly feed
Answer:
To find the number of cats Carly can feed, divide the total weight of cat food by the weight of cat food used per cat.
2.85 lbs ÷ 0.19 lbs/cat = 15 cats
Therefore, Carly can feed 15 cats.
PLEASE HELP I DONT UNDERSTAND!
Write the following polynomial in descending powers of the variable and with no missing powers
3x^3 -70
3x^3 -70=?
with no missing powers, meaning including any "stepping down" values, anyhow, let's do so
[tex]3x^3-70\implies \boxed{\begin{array}{llll} 3x^3+0x^2+0x^1 + 0x^0 - 7 \\\\\\ 3x^3+0x^2+0x^1 - 7 \end{array}}[/tex]
now, notice, the others were there all along, however their coefficient is 0, thus anything times 0 goes poof, however they were there all along.
some folks like to use the 1st form there, I usually use the 2nd form, but both are acceptable.
13. ABCD is
a. Congruent
b. Similar
c. Neither
to A'B'C'D'.
Sorry I cant do this for much points, But i need help asap pleaseeee!
The perimeter of the figure is given by the sum of the perimeter of rectangle and a semicircle P = 20.28
What is the Perimeter of a Rectangle?The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P of rectangle = 2 ( Length + Width )
Given data ,
Let the perimeter of the figure be represented as P
Let the width of the rectangle W = 4
So , the radius of the circle = 4 / 2 = 2
Now , the length of the rectangle = 5
And , the perimeter of the figure = 5 + 5 + 4 + ( perimeter of semicircle )
where the perimeter of semicircle = πr
On simplifying , we get
The perimeter of the figure P = 14 + 2π
The perimeter of the figure P = 14 + 6.28
The perimeter of the figure P = 20.28
Hence , the perimeter of the figure is 20.28
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would someone be able to help me out with this problem? thank you so much if u can! been stuck on it for 20 minutes now
Answer:
Form W-2 is completed by an employer and contains important information that you need to complete your tax return. It reports your total wages for the year and the amount of federal, state, and other taxes withheld from your paycheck.
Form 1040 is used by U.S. taxpayers to file an annual income tax return.
Head of household offers wider tax brackets, a bigger standard deduction and faster eligibility for other write-offs.
Step-by-step explanation:
We bow down before Your divine presence and bring You our deepest worship as we experience Your tender love, Father!
What is the equation of Shrödinger?
Answer:
see attached
Step-by-step explanation:
The Schrödinger equation, sometimes called the Schrödinger wave equation, is a partial differential equation. It uses the concept of energy conservation (Kinetic Energy + Potential Energy = Total Energy) to obtain information about the behavior of an electron bound to a nucleus.
see attached
Answer:
[tex]\hat{H} \Psi=E \Psi[/tex]
Step-by-step explanation:
[tex]\hat{H}[/tex]= the total energy of a system in all aspects. this includes both potential and kinetic energy.
[tex]\Psi[/tex]= wave function. if I remember right the wave function is exactly that, the function in which the wave is behaving, reflected on a graph.
[tex]E[/tex]= energy
Find and identify the traces of the quadric surface
x2 + y2 − z2 = 4
given the plane.
x = k
Find the trace.
Identify the trace.
circle ellipse hyperbola parabola
y = k
Find the trace.
Identify the trace.
circle ellipse hyperbola parabola
z = k
Find the trace.
Identify the trace.
circle ellipse hyperbola parabola
Describe the surface from one of the graphs in the table.
ellipsoid elliptic paraboloid hyperbolic paraboloid cone hyperboloid of one sheet hyperboloid of two sheets
(b) If we change the equation in part (a) to
x2 − y2 + z2 = 4,
how is the graph affected?
The graph is rotated so that its axis is the x-axis.
The graph is rotated so that its axis is the y-axis.
The graph is rotated so that its axis is the z-axis
The graph is shifted one unit in the negative y-direction.
The graph is shifted one unit in the positive y-direction.
(c) What if we change the equation in part (a) to
x2 + y2 + 2y − z2 = 3?
The graph is rotated so that its axis is the x-axis.
The graph is rotated so that its axis is the y-axis.
The graph is rotated so that its axis is the z-axis
The graph is shifted one unit in the negative y-direction.
The graph is shifted one unit in the positive y-direction.
The answer of the questions:
a) The surface is an ellipsoid,
(b) If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, and
(c) If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore,
What is an ellipsoid?
An Ellipsoid is a closed surface on which all plane cross sections are either ellipses or circles. An ellipsoid is symmetrical about three mutually perpendicular axes that intersect at the center.
(a)
x = k:
Trace: Circle in the x-z plane
Identification: Circle
y = k:
Trace: Circle in the y-z plane
Identification: Circle
z = k:
Trace: Circle in the x-y plane
Identification: Circle
The surface is an ellipsoid, which is a 3-dimensional surface that is the result of stretching or compressing a sphere along different axes.
(b)
If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, but it is rotated so that its axis is the x-axis.
(c)
If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore, and its shape cannot be determined from the equation alone.
This is because the equation contains a linear term (2y) that makes it non-quadratic.
To find the shape of the surface, a more in-depth analysis would be required.
Hence, the answer of the questions:
a) The surface is an ellipsoid,
(b) If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, and
(c) If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore,
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Write each rate as a unit rate. $ 46 for 5 toys.
Answer:
$9.20 per toy or $9.20/1
Step-by-step explanation:
$46/5 hours=9.2
The length of a rectangle is 4 in longer than its width.
If the perimeter of the rectangle is 40 in, find its area.
Answer:
Step-by-step explanation:
Let, width = x
length = x+4
perimeter, 2(x+4+x) = 40
4x+8 = 40
4x = 32
x = 8
so, (x+4) = 8+4 = 12
so, the area would be,
= 12 * 8 = 96 in²
Please help due tonight!!!!!!
Answer: -4,9 I AM PRETTY SURE FROM ALL OF MY RESEARCH SIORRY IF I AM WRONG I WISH YOU GOODLUCK
Step-by-step explanation:
translate then solve:five times the difference of twice and number and three decreased by the sum of the number and 8 equals 13
Answer: x = 4
Step-by-step explanation:
Translating the problem into mathematical terms:
Let's call the number x. Then the problem can be written as:
5 * (2x - 3) - (x + 8) = 13
Expanding the left side of the equation:
5 * 2x - 5 * 3 - x - 8 = 13
Simplifying the left side of the equation:
10x - 23 - x - 8 = 13
Combining like terms:
9x - 31 = 13
Adding 31 to both sides of the equation:
9x = 44
Dividing both sides of the equation by 9:
x = 4.88888...
Since x has to be a whole number, we round down to the nearest whole number:
x = 4
Therefore, the number that satisfies the equation is 4.
Which objective function models the total profit from neck-
laces and wristbands?
Let x = the number of necklaces Mack makes.
Let y = the number of wristbands Mack makes.
A P(x, y) = 25x+40y
B P(x, y)=40x + 25y
c P(x, y) = 3x + 2y
D P(x, y) = 2x + 3y
In 2009, a laptop computer was purchased for $800. Each year since, the resale value has decreased by 27%.
Let t be the number of years since 2009. Let y be the value of the laptop computer, in dollars.
Write an exponential function showing the relationship between y and t.
On solving the provided question we can say that by percentage y = $1900(77/100)t
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
In 2005, a laptop computer was purchased for 81900. Each year since, the resale value has decreased by 23%. Let t be the number of years since Let Y be the value of the laptop computer, in dollars. Write an exponential function showing the relationship between Y and
t. value of laptop in 2005 81900 decrease in resale \/aIUe each year
23 77% resale value of laptop after each year = 100
resale value after one x $1,900
Now, Hence relation between value of the laptop computer and time is
y = $1900(77/100)t
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The Wilson family's back yard is a rectangular plot that has a length of 100 feet and a width of 80 feet. The family planted a garden with a length and width of 60 feet. The family planted a lawn in the remaining area of the back yard, as shown.What is the area, in square feet, of the lawn in the Wilson family's back yard?
The area of the lawn in the Wilson family's back yard is 4400 square feet.
The Wilson family's back yard is a rectangular plot that has a length of 100 feet and a width of 80 feet.
Let us assume that A₁ be the area of the reactangular plot.
Using the formula for the area of rectangle,
A₁ = 100 × 80
A₁ = 8000 sq. ft.
The family planted a garden with a length and width of 60 feet.
This means, the shape of the garden must be square.
Using the formula for the area of square,
A₂ = 60 × 60
A₂ = 3600 sq. ft.
The family planted a lawn in the remaining area of the back yard, as shown.
Let us assume that A represents the area of the lawn in the Wilson family's back yard.
A = A₁ - A₂
A = 8000 - 3600
A = 4400 sq. ft.
Therefore, the required area is: 4400 sq.ft.
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Been stuck on this question please help me.
Answer:
Step-by-step explanation:
Using the Pythagorean Theorem, we know the hypotenuse is 2[tex]\sqrt{26}[/tex]
sin = Opp/hyp ----> [tex]\frac{5}{2\sqrt26}[/tex]
csc = hyp/opp -----> [tex]\frac{2\sqrt{26} }{5}[/tex]
cot = adj/opp -------> [tex]\frac{7}{5}[/tex]