If X1, X2, X3, and X4 are (pairwise) uncorrelated random variables, each having mean 0 and variance 1, compute the correlations of (a) X1 + 2X2 and X2 + 3X3; (b) Xi + 1,000, 000X2 and X3 + 1, 000, 000X4_ Note: This problem will be graded without partial credit each part receiving 0 or 1.5 points
If X1, X2, X3, and X4 are (pairwise) uncorrelated random variables, each having mean 0 and variance 1, the correlations of X1 + 2X2 and X2 + 3X3, the value will be 0.5.
Define variance.Variance is the anticipated squared variation of a random variable from its population mean or sample mean in probability theory and statistics. Variance is a measure of dispersion, or how far apart from the mean a group of data are from one another.
Given,
X1, X2, X3, and X4 are (pairwise) uncorrelated random variables, each having mean 0 and variance 1,
Cov(X1+X2 , X2+X3)
= Cov(X1,X2) + Cov(X1,X3)+Cov(X2,X2)+Cov(X2,X3)
= 0+0+V(X2)+0
= 1
V(X1+X2)
=V(X1)+V(X2)+2Cov(X1,X2)
= 1+1-2*0
=2
Similarly V( X2+ X3) =2
So, correlation between ( X1+X2 and X2+x3) is
Corr( X1+X2, X2+x3)
= Cov(X1+X2 , X2+X3) / \sqrt{}(V(X1+X2)*V( X2+ X3))
=1/\sqrt{}(22)
= 0.5
To learn more about variance, visit:
https://brainly.com/question/29505178
#SPJ4
what is 5.37 divided by 3 equals put 5.37 at the top and 3 at the bottom PLEASE EXPLAIN YOUR ANSWER I HAVE 19 MINS TO TURN THIS IN
The answer is 1.79.
What is division?Division is breaking a number up into an equal number of parts.
Given that, 5.37 divided by 3
5.37÷3 = 1.79
Hence, 5.37 divided by 3 equals to 1.79.
For more references on division, click;
brainly.com/question/21416852
#SPJ1
an independent random sample is selected from an approximately normal population with unknown standard deviation. find the degrees of freedom and the critical t-value (t*) for the given sample size and confidence level.
a) The critical value 90% is 1.833
b) The critical value for 98% is 2.528
c) The critical value of 90% is 1.645
d) 3.169 is the critical value of 99%.
What is meant by critical value?The critical probability (p*) = 1 - (α / 2), where α equals 1 - (confidence level / 100).
Given that an independent random sample is drawn from a population with an essentially normal standard deviation.
To calculate the degrees of freedom and crucial t-value for a given sample size and confidence level.
n-1 degrees of freedom
Critical t can be obtained from the internet's t table.
a) degree of liberty = 5
The critical 90% is 1.833
b) degree of freedom is 20.
The critical value for 98% is 2.528
c) degree of freedom =28
The critical value of 90% is 1.645
d) degree of freedom =10.
3.169 is the critical value of 99%.
To know more about critical value, visit:
https://brainly.com/question/14508634
#SPJ4
Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (3, 0, 0) (x, y, z) (b) (10, pi/3, pi/4)
the rectangular coordinates of the point whose spherical coordinates are given. (3, 0, 0) are (0.0.3)
What is spherical coordinates?
The coordinate system that is most frequently employed in three-dimensional systems is called spherical coordinates of the system, represented as (r,Ф,∅ ). The surface area in three dimensions is calculated using the spherical coordinate system. Radial distance, polar angles, and azimuthal angle are the three numbers that these coordinates indicate. Additionally known as spherical polar coordinates.
Given (r,Ф,∅ ) = (3,0,0)
x = rsin∅ cosФ = 3 * sin0 *cos0 = 0
y = rsin∅ sinФ = 3*0*0 = 0
z = rcos∅ = 3*1 = 3'
SO (x,y,y) = (0,0,3)
Hence the rectangular coordinates of the point whose spherical coordinates are given. (3, 0, 0) are (0.0.3)
Learn more about spherical coordinates, by the following link
https://brainly.com/question/4465072
#SPJ4
9. a plane flies from base camp to lake a, 280 km away, in a direction of 200 north of east. after dropping off supplies it flies to lake b, which is 190 km at 30 0 west of north from lake a. graphically and check using trig, determine the distance and direction from lake b to camp.
The distance from lake b to camp is 310 km and the direction of lake b to camp is 57° S of W.
Distance is a numerical value. The length between the two points is measured by distance. The face or position of an object or person can be said by direction.
There are four cardinal directions which are the main four compass directions. The four directions are North, East, West and South. North-East, North-West, South-East and South-West also come under directions.
As per the question,
Distance from base camp to lake a = 280 kmThe direction of the plane = 20.0° north of east Distance to lake b = 190 kmThe direction of the plane = 30.0° west of northWith a scale of unit 1, the vector from the base camp to the lake to the vector connecting lakes a and b is graphically represented.
Therefore, 310 km is the distance from the lake b to base camp and 57.0° south of west is the direction of the plane.
To know more about distance and direction refer to:
https://brainly.com/question/26550516
#SPJ4
What are similarities in poems?.
Because both poems highlight the wonders of nature and the cyclical rhythm of the seasons, they are similar.
What is similarities?
The state of likeness can be referred to as a similarity. When two elements, things, ideas, or people resemble one another, they are said to be similar. Example: In terms of the number of sides, a square and a rectangle are comparable. The state of being different can be used to define a difference.
The moods and tones of two poems by the same author may be similar or dissimilar. You may, for instance, contrast and compare two poems written by the same author, such as Robert Frost's "A Prayer in Spring" and "A Late Walk." Because both poems highlight the wonders of nature and the cyclical rhythm of the seasons, they are similar. On the other hand, "A Prayer in Spring" has a joyful, lovely tone and a calm, appreciative atmosphere. On the other hand, "A Late Walk" has a gloomy, solemn tone and a downcast, pessimistic mood. Frost successfully contrasts the beauty of spring and the aridity of fall in each instance.
Look for similarities and variations in the two poems' language, style, and format. The length of each line or stanza, the meter, the rhythm, and the author's word choice should all be considered. For instance, some poets, like Dr. Seuss, favor monosyllabic words and short lines, while others, like William Wordsworth, favor polysyllabic words and lengthy lines or stanzas. Determine the level of technicality your teacher expects from your comparisons and contrasts, such as whether she wants you to talk about iambic pentameter, stressed syllables, and feet..
Learn more about similarities in poems click here:
https://brainly.com/question/17337304
#SPJ4
if f(x) is a polynomial of degree 7, and g(x) is a polynomial of degree 7, then what is the product of the minimum and the maximum possible degrees of f(x) g(x)? (assume that f(x) g(x) is nonzero.)
The maximum degree of f(x) g(x) will be 14 and the minimum degreee of f(x) g(x) will be 0.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Function f(x) is a polynomial of degree 7,
And, g(x) is a polynomial of degree 7.
Now,
Since, Function f(x) is a polynomial of degree 7,
And, g(x) is a polynomial of degree 7.
Hence, The maximum degree of f(x) g(x) = 7 + 7 = 14
And, The minimum degree of f(x) g(x) = 0
Thus, The maximum degree of f(x) g(x) will be 14 and the minimum degree of f(x) g(x) will be 0.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
How many statements below are true? 1. Given two square matrices, AB-I, then BA-I 2. Given two matrices, Al is an eigenvalue of AB, then A is an eigenvalue of BA 3. If AB BA for all square matrices B, then A must be a multiple of the identity matrix. Pick one of the choices 0 1 O 2 0 3 Clear selection
The correct option: 3. If AB BA for all square matrices B, then A must be a multiple of the identity matrix.
Define the term identity matrix?A square matrix called an identity matrix is one in which all of the primary diagonal members are one and all other components are zero.
As per the stated question-
In order to determine whether a b is equal to I we were first given two square matrices, a b & b a, both of which are equal to i. Therefore, a b is equal to i. A homogeneous system b x = 0 is subsequently taken into consideration. We could indeed transform b to row reduced echelon form using only elementary rule operations, but we then have that b is going to be invertible and an is the inverse of b, as such yes, we have that a b is equivalent to b a which is equal to i. This tells us that x is equal to 0 seems to be the only solution to the homogeneous system.Thus, if A is a multiple of the identity matrix if AB BA for all square matrices B.
To know more about the identity matrix, here
https://brainly.com/question/2361951
#SPJ4
Monique has three different types of pencils. She wants to investigate which type of pencil stays sharpened the longest. She writes the same thing on a
piece of paper with each pencil. In this scenario, what is the dependent variable?
O The type of pencil sharpener.
O Time the pencil takes to become dull.
The type of pencil.
O What she is writing with the pencil.
In this scenario, the dependent variable is the time the pencil takes to become dull and the type of pencil.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that, there are three different pencils that Monique possesses. She's interested in finding out what kind of pencil maintains its sharpness the longest. Each pencil she uses leaves an identical mark on a piece of paper.
There are often two different sorts of variables in analytics. We obtained that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.
Thus, in this scenario, the dependent variable is the time the pencil takes to become dull and the type of pencil.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
What is an equation of the line that passes through the points (-2, -5) (−4,−4
Answer:
y=ax+b
a=(y2-y1) /(x2-x1) =(-4+2)/(-4+5)=-2
The equation becomes:
y=-2x+b
Substitute (-2,-5) in the equation:
-5=-2(-2)+b
b=-9
y=-2x-9
trey plants a 6-inch tomato plant in his garden. the plant grows by about 16% per week for several months. which function defintion represents the height of the tomato plant (in inches) as a function of the number of weeks, t since the tomato plant was planted?
The function that represents the number of weeks with the height of the tomato plants is 4t - 25y = -150.
When the week has started, the height of the plant in inches is 6 inches.
So, one point can be (0,6).
Now, it is said that the plants grows at a rate of 16% per inches for several months.
So, it means that the slope of the equation is 0.16.
Now, we can use the point slope form of the line.
So, the required equation of the line is,
(y-6)/(t-0) = 0.16
y-6 = 0.16t
16t - 100y = -600
4t - 25y = -150
So, the above equation of line is the function that will relate number of weeks with the height of the plant.
To know more about Equation of line, visit,
https://brainly.com/question/18831322
#SPJ4
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The total amount the college student has in his saving account if 13000 dollars was invested and earned 3% compounded quarterly for 5 years is $15,095.39
How to find the total amount the student have in her/his saving?The total amount a college student has in a saving account if 13000 dollars was invested and earned 3% compounded quarterly for 5 years can be calculated as follows:
Therefore,
[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]
where
p = principalr = rate t = timen = number of time compoundedTherefore,
p = 13000 dollars
t = 5 years
n = 4
r = 3% = 0.03
Therefore,
[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]
[tex]A = 13000(1+ \frac{0.03}{4} )^{(4)(5)}[/tex]
A = 13,000.00(1 + 0.0075)²⁰
A = $15,095.39
learn more on loan here:https://brainly.com/question/13423008?referrer=searchResults
#SPJ1
(Ch 8.2) True or False? In any random sample drawn from a population, the sample mean is an unbiased estimator of the population mean.
11. (Ch 8.2) A consistent estimator for the population mean a. collapses on the true parameter μ as the variance increases. b. collapses on the true parameter μ as the sample size increases. c. consistently follows a normal distribution. d. is impossible to obtain using real sample data.
12. (Ch 8.3) The Central Limit Theorem (CLT) implies that a. the population will be approximately normal if the sample size n is at least 40. b. repeated samples must be taken to obtain normality. c. the distribution of the sample mean is approximately normal for a large n. d. the sample mean is not an unbiased estimator of the population mean.
13. (Ch 8.3) True or False? The Central Limit Theorem says that, if the sample size n exceeds 30, then it must be the case that the population will be normal.
14. (Ch 8.4) True or False? A higher confidence level leads to a narrower confidence interval.
T
B
C
F
F
True , In any random sample drawn from a population, the sample mean is an unbiased estimator of the population mean.
What is the central limit theorem formula?
The central limit theorem gives a formula for the sample mean and the sample standard deviation when the population mean and standard deviation are known. This is given as follows: Sample mean = Population mean = μ μ Sample standard deviation = (Population standard deviation) / √n = σ / √n.
learn more about of central limit theorem here
https://brainly.com/question/18403552
#SPJ4
a garden table and a bench cost $1023 combined. the garden table costs $73 more than the bench. what is the cost of the bench?
The required Cost of the bench will be $475
Let the cost of a garden table be $x
And the cost of a bench be $y
Now, according to the question
Combined cost of garden table and bench are $1023
Therefore, we can write
x + y = 1023……….(i)
Now, again the cost of garden table is $73 more than that the cost of the bench
Therefore, we can write
x - y = 73………..(ii)
Subtracting equation (i) and (ii) we get
2x = 1096
x = 1096/2 = 548
x = 548
Putting the value of x in equation in (i) we get
y = 1023 - 548 = 475
Cost of garden table is $x = $548
Cost of bench is $y = $475
To know more about word problem on two variables, visit here:
https://brainly.com/question/5282141
#SPJ4
What is a doubles plus one fact for 7 7?.
The doubles plus one fact for 7 7 is 7+7+1=15.
In layman's terms, Double Plus One Fact is a strategy for adding two consecutive numbers (numbers that are next to each other). To get the final result, simply add a smaller number to itself or double it and add 1.
Doubles fact are the numbers which are added with itself. such as 5+5=10, 3+3=6
so the doubles plus one fact are nothing but adding 1 to the result of doubles fact.
for given, doubles plus one fact for 7 7 is 7+7=14 and then adding 1 gives 14+1=15.
Hence, 7+7+1=15 is the doubles plus one fact for 7 7.
To learn more about doubles fact refer here
https://brainly.com/question/7871475
#SPJ4
Which system of equations can be used to find the roots of the equation 12 x cubed minus 5 x = 2 x squared + x + 6?.
We use the quadratic formula to find the roots of the quadratic equation.
The quadratic equation is given below:
f(x) = a[tex]x^{2}[/tex] + bx + c = 0 where a, b, c
The system of equations used to find roots of equation is y = 12[tex]x^{3}[/tex]-5x and y=2[tex]x^{2}[/tex]+x+6.The given equation will be,12[tex]x^{3}[/tex]-5x=2[tex]x^{2}[/tex] + x + 6.
Now we take the root of equation into two parts:
1. Left-hand side
2. Right-hand side
Equation no.1 : 12[tex]x^{3}[/tex]-5x=0
Equation no.2: 2[tex]x^{2}[/tex]+x+6=0
Now we contains system of equation 0 with y.
So, the equation will be:
12[tex]x^{3}[/tex]-5x=y
2[tex]x^{2}[/tex]+x+6=y
However,system of equations can be used to find the roots of the equation 12[tex]x^{3}[/tex]-5x=2[tex]x^{2}[/tex]+x+6 is:
y = 12[tex]x^{3}[/tex]-5x and y = 2[tex]x^{2}[/tex]+x+6
To learn more about roots of equation, click here
brainly.com/question/28034005
#SPJ4
What is the domain and range of y=|x| ?
Answer:
Below
Step-by-step explanation:
x values are the DOMAIN....for this equation 'x' can have any value :
(- inf, + inf)
the y values that the function can have define the RANGE of the function. Due to the absolute value bars.....'y' can only be positive values or zero:
[ 0 , + inf)
17. A 50 foot tall tree casts a 72 foot shadow. Find the measure of the angle of elevation of the sun
The measure of the angle of elevation of the sun to the nearest degree is 35 degrees.
Given:
A 50 foot tall tree casts a 72 foot shadow.
Here tree height is opposite to angle of elevation and shadow is adjacent to angle of elevation.
Let E be the angle of elevation.
tan(E) = opposite side / adjacent side
= 50/72
= 25/36
= 0.694
E = tan^-1(0.694)
= 34.99 degrees
≈ 35 degrees.
Therefore The measure of the angle of elevation of the sun to the nearest degree is 35 degrees.
Learn more about the angle of elevation here:https://brainly.com/question/16716174
#SPJ1
An open box is to be constructed so that the length of the base is 4 times larger than the width of the base. If the cost to construct the base is 2 dollars per square foot and the cost to construct the four sides is 1 dollars per square foot, determine the dimensions for a box to have volume = 70 cubic feet which would minimize the cost of construction. The values for the dimension of the base are: ?, ? The height of the box is: ?
The length and height of the box with a volume of 70 cubic feet to reduce construction costs is 8.572 and 3.81.
Given that,
The base of an open box must be built with the length of the base being four times more than the width of the base. If building the base costs two dollars per square foot and building the four sides costs one dollar per square foot.
We have to identify the dimensions of a box with a volume of 70 cubic feet to reduce construction costs.
We know that,
The volume =70 cubic feet
L=4w ------>equation(1)
Volume= l×w×h
70=4w×w×h
h=70/4w² ------>equation(2)
The construction cost is
C= 4(lw)+2(wh)+2(hl)
C=4(4w×w)+2(w×70/4w²)+2(4w×70/4w²)
C=4(4w²)+2(70/4w)+2(70/w)
C=16w²+70/2w+140/w
Now,
To determine the minimum cost,
dC/dw
16w-70/4w²-140/w²=0
16w³=1/w²(70/4+140)
16w³=1/w²(315/2)
16w³=315/2
w³=315/32
w=2.143
From equation(1)
L=4w=4×2.143=8.572
H=70/4w²=70/4(2.143)²=3.81
Therefore, The length and height of the box with a volume of 70 cubic feet to reduce construction costs is 8.572 and 3.81.
To learn more about height visit: https://brainly.com/question/10726356
#SPJ4
Directions - Use the compound interest formula to calculate the final balance.
*
Formula: P (1+7
Compound Interest Formula: P
$300 compounded quarterly at 5% for 8 years.
Final balance = $
(if necessary, round to two decimal places)
The final balance is $446.44
What is compound interest ?
Compound interest is when you add the interest you've already earned back into your principal balance, which increases your returns by compounding them. Consider that you have $1,000 in a savings account with a 5% annual interest rate. You would make $50 in the first year, giving you a new balance of $1,050.
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
r = 5/100
r = 0.05 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 300.00(1 + 0.05/4)^(4)(8)
A = 300.00(1 + 0.0125)^(32)
A = 446.44
To learn more about compound interest from the given link
https://brainly.com/question/24274034
#SPJ1
What are the end behavior of the graph of a polynomial function with a positive leading coefficient and has an even degree?.
If a polynomial's degree is even and its leading coefficient is positive, then f(x) → ∞ as x → ±∞
What is a polynomial?A polynomial is a mathematical statement that solely uses the operations of addition, subtraction, multiplication, and positive-integer powers of variables. It is made up of indeterminates (also known as variables) and coefficients. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. x3 + 2xyz2 yz + 1 is a three-indeterminate example.
Numerous branches of mathematics and science use polynomials. For instance, they are used to define polynomial functions, which show up in contexts ranging from basic chemistry and physics to economics and social science, and they are used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to encode a wide range of problems, from simple word problems to complex scientific problems. In higher mathematics, polynomials are used to build algebraic varieties and polynomial rings, two fundamental ideas in algebra and algebraic geometry.
How to check the end behaviour of polynomials?The endpoints of the graphed lines entered and exited the same side of the image in each of the four images above. Like every positive quadratic you've ever graphed, the ends of the graphs of functions with positive leading coefficients came in and left off the top of the image. Like every negative quadratic you've ever graphed, the ends of the graphs of functions with negative leading coefficients came in and left out the bottom of the image.
Every polynomial of even degree will exhibit these characteristics. You can recall the end behavior of every even-degree polynomial if you can remember the behavior for quadratics (or for parabolas).
Hence from the above explanation:-
If a polynomial's degree is even and its leading coefficient is positive, then f(x) → ∞ as x → ±∞
To learn more about polynomials click on
https://brainly.in/question/32727945
#SPJ4
What is an example of a linear function table?.
An example of a linear function table is y=3x
A linear function is used to relate an independent variable and a dependent variable by introducing a rate of change(function) of which the independent variable is equated to find the dependent variable. Linear functions are those whose graph is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
for example:
y=3x hence is the dependent variable as it depends on the change of x and 3 is the rate of change which is a constant and is determined by the division of the values of y/x hence to make a table of y over x of which y is determined by the rate of change the unrelated variable x, 3.
Read more about linear function tables at:
https://brainly.com/question/25173046
#SPJ4
bernard drew a scale drawing of a campsite. the scale of the drawing was 1 inch : 5 feet. in the drawing, the tent is 3 inches long. what is the length of the actual tent?
Length of the actual tent is 15 feet.
Actual length is any distance between points that is not foreshortened by the view type.
Given that the scale of drawing is
1 inch : 5 feet
and length is 3 inches.
We have to find actual length of the tent.
Let us denote actual length of the tent by 'x'
We have by given data
3 inches : x = 1 inch : 5 feet
multiplying LHS by 3 we get,
3 : x = 3 : 15
By comparing both the sides
x = 15
Therefore the actual length of the tent is 15 feet.
To know more about length here
https://brainly.com/question/28873869
#SPJ4
FILL IN THE BLANK. the ___ is the probability, assuming is true, of observing a value for the test statistic that is as extreme as or more extreme than the value actually observed
What makes a triangle congruent by HL?.
The HL postulate states that two triangles are congruent if the hypotenuse and leg of one right triangle are congruent with the hypotenuse and leg of another right triangle.
Hypotenuse Leg Theorem
hypotenuse theorem proof shows how a given set of right triangles is congruent when the corresponding hypotenuses and one leg are of equal length.
Statement:
Two triangles are congruent by the hypotenuse leg theorem if the hypotenuse and one leg of a right triangle are congruent with the hypotenuse and leg of another right triangle.
given: where ABC is an isosceles triangle, AB = AC, and AD is perpendicular to BC.
Proof : AD as altitude is perpendicular to BC and forms ADB and ADC as right triangles. AB and AC are the respective hypotenuses of these triangles and we know they are equal. Because AD = AD is common for both triangles.
That is, AB = AC and AD is common.
Therefore, the hypotenuse and pair of legs of the two right-angled triangles satisfy the definition of the HL theorem.
We know that angles B and C are equal (property of isosceles triangle).
We also know that the angles BAD and CAD are equal (AD bisects BC and BD equals CD).
Therefore, △ADB ≅ △ADC
To learn more about Hypotenuse Leg congruance, refer:
https://brainly.com/question/2292563
#SPJ4
When you add a positive number and a negative number how can you tell whether the sun will be positive or negative
Step-by-step explanation:
it depends on what the numbers are now if it's negative 10 and you're positive number is like over 10 then your number will be positive now if the negative number is more than the positive number then you know your answer is going to be negative so negative 10 - -5 is -5 so there would be your answer now if it was negative 10 - 20 that would be positive 10 does that make any sense
A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 31 ft/s. Its height in feet after t seconds is given by y = 31 t − 23 t 2 . A. Find the average velocity for the time period beginning when t=1 and lasting .01 s: .005 s: .002 s: .001 s: NOTE: For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator. Estimate the instanteneous velocity when t=1.
The average velocity for the time period is -15 feet per second
The velocity of the ball = 31 feet / seconds
The function of the height is
y = 31t - 23t^2
Time period beginning when t = 1 and lasting .01 s, .005 s, .002 s, .001 s
The average velocity = f(1.01) - f(1) / 1.01 - 1
f(t) = 31t - 23t^2
f(1.01) = 31(1.01) - 23(1.01)^2
= 31.31 - 23.46
= 7.85 feet per second
Similarly
f(1) = 31(1) - 23(1)^2
= 31 - 23
= 8 feet per second
The average velocity = 7.85 - 8 / 1.01 - 1
= -0.15 / 0.01
= -15 feet per second
Hence, the average velocity for the time period is -15 feet per second
Learn more about function here
brainly.com/question/20534410
#SPJ4
The perimeter of a triangle is 59 in. The shortest side is 10 in. less than the longest side. The middle side is 21 in. less than the combined lengths of the
shortest and longest sides. Find the lengths of the three sides.
The lengths of the three sides are 15 inches , 19 inches and 25 inches respectively.
Let a represent the length of the shortest side.
Let b represent the length of the mid-length side.
Let c represent the length of the longest side.
From the question, we have
The perimeter of a triangle is 59 in.
a + b + c = 59
The shortest side is 10 in. less than the longest side.
a = c-10
The middle side is 21 in. less than the combined lengths of the shortest and longest sides.
b=(a+c)-21
b=(59-b)-21
2b = 38
b = 19 inches
substituting the value we get
a+c = 40................(i)
a-c = -10................(ii)
Solving, we get
2a = 30
a = 15 inches
c=25 inches
The lengths of the three sides are 15 inches , 19 inches and 25 inches respectively.
Addition:
The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.
To learn more about addition visit: https://brainly.com/question/680614
#SPJ1
What is the value of x in the equation?
Answer:
x=11
Step-by-step explanation:
we need to change 3/2 to have a denominator of 6
3x3/2x3
9/6
Now we set x-2 equal to 9
x-2=9
+2 +2
x=11
Hopes this helps please mark brainliest
Answer:
[tex]\huge\boxed{\sf x = 11}[/tex]
Step-by-step explanation:
Given equation:[tex]\displaystyle \frac{x-2}{6} = \frac{3}{2} \\\\Cross \ Multiply\\\\2(x-2)=3 \times 6\\\\Distribute\\\\2x - 4 = 18\\\\Add \ 4 \ to \ both \ sides\\\\2x = 18+4\\\\2x = 22\\\\Divide \ 2 \ to \ both \ sides\\\\x = 11\\\\\rule[225]{225}{2}[/tex]
A researcher at a major clinic wishes to estimate the proportion of the adult population of the united states that has sleep deprivation. what size sample should be obtained in order to be ​% confident that the sample proportion will not differ from the true proportion by more than ​%? round up to the nearest whole number.
A population proportion is estimated to be around 541.
We can use the formula for the minimal sample size required for an interval estimate of a population proportion to address the problem.
n = pq ((Z/2) / E)^2
We use the conventional p and q, which are 0.5 and 0.5, because p is not defined.
The reason for this is that, if we choose values for p and q that range from 0.1 to 0.9, we will see that this is the point at which pq reaches its greatest value.
The value of (Z/2) will then be determined. We may determine that (Z/2) = 2.326 with a 98% confidence level by looking at the Z-table. We now begin changing the values in the formula above.
n = (0.5)×(0.5) × (2.326/0.05)^2
n = 541.027
n ≅ 541.
So, population proportion is estimated to be around 541
To learn more about Z-table click here:
brainly.com/question/6096474
#SPJ4
