Null hypothesis for the investigation Ha=0.38
The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.
This hypothesis is either rejected or not rejected based on the viability of the given population or sample.
In other words, the null hypothesis is a hypothesis in which the sample observations results from the chance.
It is said to be a statement in which the surveyors wants to examine the data. It is denoted by H0.
Here, the hypothesis test formulas are given below for reference.
The formula for the null hypothesis is:
H0: p = p0
The formula for the alternative hypothesis is:
Ha = p >p0, < p0≠ p0
The formula for the test static is:
[tex]z=\frac{p-p0}{\sqrt{\frac{p0(1-p0)}{n} } }[/tex]
Remember that, p0 is the null hypothesis and p – hat is the sample proportion.
38 percent of people living in region w have the blood type o positive.
w region
38% - o positive
x region
100 random sample
35 o positive
means 35/ 100*100
35% 0 positive
a hypothesis test to investigate whether the percent of people in region x with o positive blood is different from that of in region w
The formula for the null hypothesis is:
H0: p = p0 =0.38
Ha = p >p0, < p0≠ p0
Ha=0.38
Null hypothesis for the investigation Ha=0.38
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NO LINKS!! NOT MULTIPLE CHOICE!!!
57. The population of Asheville, NC can be modeled by P(t) = 90000 · e^(0.027t) as a function of years since the start of 2020.
a. State the growth rate. Round to three places
b. How many residents does the model predict will live in Asheville, NC in 2030.
Answer:
a) Growth rate of 2.737% (3 d.p.) per year
b) 117,897
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function with base $e$}\\\\$f(t)=ae^{rt}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $e$ is Euler's number. \\ \phantom{ww}$\bullet$ $r$ is the continuous growth/decay rate.\\ \phantom{ww}$\bullet$ $t$ is time.\\\end{minipage}}[/tex]
If a > 0 and r > 0, the function is an exponential growth function.
If a > 0 and r < 0, the function is an exponential decay function.
Given exponential function:
[tex]P(t) = 90000\cdot e^{0.027t}[/tex]
As r > 0 the function is an exponential growth function.
The annual growth rate is:
[tex]\begin{aligned}\textsf{Annual growth rate}& = e^{0.027}-1\\&=1.02736780...-1\\&=0.0273678027...\\&=2.73678027...\%\\&=2.737\%\; \sf (3\;d.p.)\end{aligned}[/tex]
To calculate how many residents the model predicts will live in Asheville, NC in 2030, substitute t = 10 into the given function:
[tex]\begin{aligned}\implies P(10) &= 90000\cdot e^{0.027 \cdot 10}\\&= 90000\cdot e^{0.27}\\ &= 90000\cdot 1.30996445...\\&=117896.800...\\&=117897\; \sf (nearest\;whole\;number)\\\end{aligned}[/tex]
Therefore, the model predicts that there will be a population of approximately 117,897 living in Asheville, NC in 2030.
identify the sampling method that was used. three representatives from each employee type (faculty, staff, administrators) are chosen for a salary committee.
The sampling method that was used. three representatives from each employee type (faculty, staff, administrators) are chosen for a salary committee. This uses stratified sampling.
ABOUT STRATIFIED SAMPLEIn a stratified sample, researchers divide a population into homogeneous subpopulations called strata (the plural of stratum) based on specific characteristics (e.g., race, gender identity, location, etc.). Every member of the population studied should be in exactly one stratum.
Each stratum is then sampled using another probability sampling method, such as cluster sampling or simple random sampling, allowing researchers to estimate statistical measures for each sub-population.
Researchers rely on stratified sampling when a population’s characteristics are diverse and they want to ensure that every characteristic is properly represented in the sample. This helps with the generalizability and validity of the study, as well as avoiding research biases like under coverage bias.
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what is the area of a triangular prism with dimensions of 13ft, 5 ft,12 ft, 6 ft
The area of a triangular prism with dimensions of 13ft, 5 ft, & 12 ft, and 6 ft will be 240 square feet.
What is the surface area of a triangular prism?Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and W be the width of the rectangle.
Then the surface area of the triangular prism will be
Surface area = 2 Area of triangle + 3 Area of rectangle
Surface area = (h x b) + (L₁ + L₂ + L₃) x W
The dimension of the triangle is 13 feet, 5 feet, and 12 feet. And the width of the rectangle is 6 feet.
The surface area of the triangular prism will be given as,
Surface area = 5 x 12 + (5 + 12 + 13) x 6
Surface area = 60 + 180
Surface area = 240 square feet
The area of a triangular prism with dimensions of 13ft, 5 ft, & 12 ft, and 6 ft will be 240 square feet.
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Find the equation for the plane through Po(-4,-3,8) perpendicular to the following line.
x= -4+t, y=-3-3t, z= -4t, -∞
Equation of a plane perpendicular to a given line with direction ratios <a, b, c> and passing through a point (x1, y1, z1) is given by: a(x - x1) + b(y - y1) + c(z - z1) = 0.
How do you find the equation of a plane given a point and a perpendicular line?The slope of the line we're looking for is 1/2 since perpendicular lines have opposite-reciprocal slopes. When we enter the supplied point into the equation y = 1/2x + b and solve for b, we obtain b = 6. The line's equation is therefore y = 12x + 6.
Rearranged, it is -x/2 + y = 6. a plane that is outlined by vectors that are perpendicular to a normal. As a result, when given a vector with the coordinates a, b, and c, we can infer that all planes perpendicular to this vector have the form ax+by+cz=d, and any surface with this form is a plane perpendicular to a, b, and c.
Get a direction vector to the two points first, then get the supplied normal from the plane's equation. The normal is then produced by adding the direction vector to the normal.
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This is hard to do I need help
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The following data represent glucose blood levels (mg/100 ml) after a 12-hour fast for a random sample of 70 women (Reference: American Journal of Clinical Nutrition, Vol. 19, pp. 345-351).
45 66 83 71 76 64 59 59 76 82
80 81 85 77 82 90 87 72 79 69
83 71 87 69 81 76 96 83 67 94
101 94 89 94 73 99 93 85 83 80
78 80 85 83 84 74 81 70 65 89
70 80 84 77 65 46 80 70 75 45
101 71 109 73 73 80 72 81 63 74
For this problem, use six classes.
(a). Find the class width
(b). Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Give relative frequencies to 4 decimal places.
(c). Draw a histogram.
(d). Draw a relative-frequency histogram.
(e). Categorize the basic distribution shape.
(f). Draw an ogive. (Graph each point and the closed line segments connecting the points to create your graph.)
The graph can be used to determine the median, quartiles, and other statistical measures.
(a). Class width = (maximum value - minimum value)/ number of classes = (109 - 45)/6 = 9
(b).
Class Limits Class Boundaries Midpoints Frequencies Relative Frequencies Cumulative Frequencies
45 - 54 44.5 - 54.5 49.5 2 0.0741 2
55 - 64 54.5 - 64.5 59.5 7 0.2593 9
65 - 74 64.5 - 74.5 69.5 17 0.6207 26
75 - 84 74.5 - 84.5 79.5 20 0.7407 46
85 - 94 84.5 - 94.5 89.5 14 0.5185 60
95 - 104 94.5 - 104.5 99.5 7 0.2593 67
(c). Histogram
(d). Relative-Frequency Histogram
(e). The basic distribution shape is right-skewed.
(f). Ogive
The ogive graph is a cumulative frequency plot that shows the number of data values that lie at or below each given value on the x-axis. It is constructed by plotting the cumulative frequencies of each data value on the y-axis against the corresponding data values on the x-axis. The points are then connected using closed line segments to form the ogive graph. The graph can be used to determine the median, quartiles, and other statistical measures.
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in a certain large population of adults, the distribution of iq scores is strongly left-skewed with a mean of 122 and a standard deviation of 5. suppose 200 adults are randomly selected from this population for a market research study. for srss of size 200, the distribution of sample mean iq score is
If in a certain large population of adults. the distribution of sample mean iq score is: approximately Normal with mean 122 and standard deviation 0.35.
Given data:
Mean = 122
Standard deviation = 5
Sample size = 200
Now let find the the standard deviation of the sampling distribution of the mean sample using this formula
Distribution of sample mean = Standard deviation/√Sample size
Let plug in the formula
Distribution of sample mean = 5 /√ 200
Distribution of sample mean = 5/14.14
Distribution of sample mean = 0.35
Therefore the distribution of sample mean iq score is: approximately Normal with mean 122 and standard deviation 0.35.
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An exit poll shows how certain parties voted on Proposition #1. Explain how the given graph is deceptive.
Complete the statements based on the pie chart.
Pie charts are used to compare
, not
. This misleads the viewer to think
half the people in all three parties voted Yes on Issue #1, when
half of Republicans and Independents actually voted Yes on Issue #1.
1) ✔ parts of a whole
2)✔ the difference between groups
3)✔ less than
4)✔ more than
Pie charts are used to compare parts of a whole, not the difference between groups. This misleads the viewer to think more than half the people in all three parties voted Yes on Issue #1, when less than half of Republicans and Independents actually voted Yes on Issue #1.
What is a pie chart?This is a type of graph that resembles a pie because it is a circle that shows the proportion of different groups.
How to interpret the pie chart?Pie charts are used to determine percentages out of 100%, however, you cannot use them to compare groups.Due to this, you should be careful when interpreting the information. For example, in this case, you might think more than half the people in all three parties voted Yes but this might not be true.Note: Here is the missing information
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if you are standing 45 feet away from a school and the angle of elevation is 66 degrees how tall is the building?
Answer:
50 m
Step-by-step explanation:
The angle of elevation of the top of the building from the foot of the tower is 30 and the angle of the top of the tower from the foot of the building is 60. the tower is 50 m high
Caitlin currently owes $13,000 to a friend who is charging him interest of 2.90% p.m. He is required to settle the loan with two equal payments, one today and the other in six months. Calculate the size of the payments using six months as the focal date.
The size of the payments that need to be made today and in six months are both $ 6, 961.69.
How to find the payment ?To find the payment that Caitlin needs to make today and in six months, assume this amount of x.
The payment in 6 months would be:
= (13, 000 - x) ( 1 + 2.4 / 100)⁶
The payment today would be x.
Equate them to find the payment:
x = (13, 000 - x) ( 1 + 2.4 / 100)⁶
x = 14, 988 - 1.1529x
x = 14, 987.979 / 2.1529
= $ 6, 961.69
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now view the partitioned circle as a protractor, and think of using it to measure angles that are drawn on a page. give examples and make (rough) math drawings to show how this protractor could measure the following kinds of angles. in each case, determine the size of the angle in degrees and explain your answer.
The instrument used here is a protractor.
ProtractorAn instrument used to measure angles in degrees is a protractor. When measuring angles using a protractor, it's crucial to check that the vertex of the angle is in the protractor's centre and that the angle's base is lined up with the protractor's baseline.
Acute Angle: - An angle that is less than 90 degrees is considered to be acute. For instance, if the angle is 30 degrees, we would line up the vertex of the angle with the protractor's centre and one of its sides with the baseline. The measurement would be read off the protractor scale, which in this instance would be 30 degrees.
Right Angle: - A right angle is a triangle with a 90 degree angle on each side. Using a protractor, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline to measure a right angle. The measurement would be read off the protractor scale, which in this instance would be 90 degrees.
Obtuse Angle: - An angle that is more acute than 90 degrees is referred to as an obtuse angle. When using a protractor to measure an obtuse angle, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline. The measurement would then be taken from the protractor scale and would be more than 90 degrees in this instance.
Straight Angle: - A straight angle is one that is 180 degrees in length. Using a protractor, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline to measure a straight angle. The measurement would then be taken from the protractor scale, which would be 180 degrees in this instance.
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ABC is a dilation of J HG centered at the origin.
Find the scale factor of the dilation.
Answer:
2 is the scale of dilation
A wage earner receives a gross pay of $983.15 for 52.5 hours of work. What is his hourly rate of pay if a regular workweek is 44 hours and overtime is paid at timeand-a-half the regular rate of pay?
Answer:
$17.32
Step-by-step explanation:
44 hours
52.5 - 44 = 8.5 hours over time for 1.5x regular pay
assume regular pay is x
so 44x + 8.5 * 1.5x =983.15
44x + 12.75x = 983.15
56.75x=983.15
x=17.324
check to see if it's correct
44*17.324 + 12.75*17.324 = 983.14
On January 1, 2017, the capital balances in Hollings worth Company are Lois Holly $26,000 and Jim Worth $24,000. In 2017 the partnership reports net income of $30,000. The income ratio provides for salary allowances of $12,000 for Holly and $10,000 to Worth and the remainder to be shared equally. Neither partner had any drawings in 2017, Instructions
(1) Prepare a schedule showing the distribution of net income in 2017.
Answer:
see below
Step-by-step explanation:
1-1-2017
H 26K
W 24K
Net income 30K
H salary 12K
W salary 10K
remain: 8K shared EQUALLY so each gets 4K extra
Distribution:
30K - H gets12+4 =16K, and W gets 10+4 = 14K
Quadrilateral PQRS is located at P (0, 1), Q (3, 2), R (4, −1), and S (1, −2). Russell and Jamie have both classified PQRS differently. Examine their proofs. Who is correct?
A. Russell
B. Jamie
C. Both
D. Neither
The correct person regarding the classification of quadrilaterals is given as follows:
B. Jamie.
How to classify the quadrilaterals?The slopes of each segment are given as follows:
-3 and 1/3.
The multiplication of these slopes is given as follows:
-3 x 1/3 = -1.
As the multiplication of the slopes is of -1, the adjacent sides meet at an angle of 90º, meaning that they are perpendicular, and hence the quadrilateral is classified as a square.
This means that Jamie is correct.
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The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s) to f(x)=g(x)? Explain your answer(s).
a. The solutions to the system of equations f(x) = g(x) are given as follows: x = 0 and x = 1.
b. The explanation is that they have the same numeric value at these values of x.
How to interpret the solution of a system of equations?A system of equations is composed by multiple equations.
The solution to the system of equations is the point of intersection of all these equations, which happen when all these equations have the same numeric value.
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How is the work energy theorem represented as an equation? (1 point)
a. ΔW = E
b.W = ΔΕ
c.W = E
d. ΔW = ΔΕ
The work energy theorem represented as an equation is ΔW = ΔΕ is appropriate option.
Option D is correct.
The work-energy theorem is what?A fundamental physics principle known as the work-energy theorem asserts that the amount of work done to an object is proportional to the change in its kinetic energy. To put it another way, the kinetic energy of an object is proportional to the net work done to it.
The work-energy theorem can be expressed as an equation because the change in an object's kinetic energy (W) is equal to the change in its work (W). It states that a change in an object's kinetic energy equals the net work done on it. The conservation of energy is a fundamental physics principle that states that energy cannot be created or destroyed; rather, it can only be transferred or converted from one form to another.
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what is the constant of proportionality for the relationship shown in this table?
The required constant of proportionality for the relationship is 1/2.
What is Constant of proportionality?As an illustration, we may write y = kx, where x is the amount of gas in gallons, y is the price in dollars, and k is the proportionality constant. In other words, the cost is directly related to the number of gallons pumped.
According to question:Let the relation between x and y is
y = kx
Where k is proportionality constant.
Using the given values of x ad y
1 = k(2)
k = 1/2
So, the constant of proportionality for the relationship is 1/2.
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Suppose H(x)=7 root x-3 . Find two functions f and g such that (fog)(x)=H(x) .
The two functions such that composition (fog) (x) = H(x) are f(x) = 7x and g(x) = [tex]\sqrt{x-3}[/tex].
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
We have a function H(x) = 7 [tex]\sqrt{x-3}[/tex]
We have to find two functions f and g such that (fog) (x) = H(x).
Let f(x) = 7x
g(x) = [tex]\sqrt{x-3}[/tex]
The composition of these functions is,
(fog)(x) = f (g(x))
= 7 . g(x)
= 7 [tex]\sqrt{x-3}[/tex]
= H(x)
Hence the functions are f(x) = 7x and g(x) = [tex]\sqrt{x-3}[/tex].
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AB + BC = AC by what property?
O Distributive Property
O Segment Addition Postulate
O Definition of ≅ Segments
O Transitive Property
It is very important to note that this property is only valid for addition and multiplication. If, AC = AB + BC, then AB + BC = AC by the commutative property.
What is called commutative property?
According to the commutative property, a mathematical principle, the product will not be affected by the order in which we multiply the integers. The commutative property of addition states that the sum is unaffected by the order of the addends.
Only addition and multiplication processes can use the commutative property. So, when adding or multiplying any two integers, we can swap the numbers around or modify their order. This is one of the fundamental characteristics of integers.
Adjective. involving, pertaining to, or involving commutation, exchange, substitution, or interchange. Mathematics. Commutative law for multiplication makes reference to the binary operation's property that one term working on another is equal to another term operating on the first, as in a + b = b a.
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Use the following frequency distribution of the weights in lb of 100 college students. Get the mean, the variance and the standard deviation. What is the range of weights from one standard deviation, below the mean to the mean?
Interval Frequency (f)
130 – 139
140 – 149
150 – 159
160 – 169
170 – 179
180 – 189
4
15
28
33
14
6
Total f=100
The required mean and standard deviation of the frequency distribution of weights is 160.10 and 11.94 respectively.
Statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
From the table,
Mean = ∑fx / ∑f
Mean = 16010 / 100
Mean = 160.10
Standard deviation,
σ = √∑fd²/∑f
σ = √14265/100
σ = 11.94
The required range of weights from one standard deviation, below the mean is given as
= 160.10 - 11.94 ≤ mean
Thus, the required mean and standard deviation of the frequency distribution of weights is 160.10 and 11.94 respectively.
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how to simplify 32/5
Answer: 6 2/5
Step-by-step explanation:
32 divided by 5 equals 6 with a remainder of 2.
A student looks out of a second story school window and sees the top of the school flagpole at an angle of evelation of 22 degrees. The student is currently 18 feet above the ground. The building is 50 ft from the base of the flagpole. a. Draw a diagram of the above scenario. b. Find the height of the flagpole
The flagpole is visible to the student from 18 feet away and at a 22-degree inclination to the ground. The flagpole is 40.3 feet tall and 50 feet away from the structure.
At an elevation of 22 degrees, the student is looking out of a second-story school window. The building is 50 feet from the flagpole's base, and the window is 18 feet above the ground. We may compute the angle of the triangle formed by the window, the ground, and the top of the flagpole using the tangent ratio to determine its height. The opposing side (the flagpole) divided by the neighboring side equals the tangent of 22 degrees (the window to the ground). Consequently, the flagpole is 40.3 feet tall (50 divided by 1.224). This indicates that the student is 18 feet above the ground and is looking down at the flagpole.
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Solve
X/2 -3 = 5
A- x=4
B- x=16
C- x=13
Answer:
x=16
Step-by-step explanation:
x/2=5+3
x/2=8
x=8×2
x=16
the output column, s, was created from the student id 21444368 using the algorithm: if id digit n (left-to-right) is an even integer, place a 0 in s, row n (top-down) if id digit n (left-to-right) is an odd integer, place a 1 in s, row n (top-down) create a similar table, but with s reflecting the result of the algorithm applied to your student id (do this on scratch paper). on the quiz essay: record your student id, id
My student ID is 21444367.
The algorithm states that if the digit in the student ID (from left to right) is an even number, then a 0 is placed in the s column in the corresponding row (from top to bottom). If the digit in the student ID (from left to right) is an odd number, then a 1 is placed in the s column in the corresponding row (from top to bottom). Thus, the result of the algorithm applied to my student ID is s = 01101000.
This can be calculated by multiplying the even digits of the student ID by 0 and the odd digits of the student ID by 1 and then adding them together.
For my student ID, 21444367, the calculation would be:
0 * 2 + 1 * 1 + 0 * 4 + 1 * 4 + 0 * 4 + 1 * 3 + 0 * 6 + 1 * 7 = 01101000.
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PLEASE HURRY
Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?
Start at the origin. Move 3 and one-half units right because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between 3 and 4. Move 2 units down because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units left because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.
Commence at the beginning. The x-coordinate is Negative 3 and 12 units, thus move 3 and 12 units to the right. The difference between 3 and 4 is negative three-half.
What is the coordinate point?A point's exact location on a two-dimensional plane is determined by a pair of numbers called its coordinates. The x and y axes, which are two axes that are at right angles to one another, are known as the coordinate plane's axes. How far along each axis a specific point is located is indicated by its coordinates.
Ordered pairs are a way of describing locations on the coordinate plane. A point's location is revealed by an ordered pair by linking the point's positions along the x-axis (the ordered pair's first value) and the y-axis (the second value of the ordered pair).
To locate points, one uses the numbers on a coordinate grid. Using an ordered pair of numbers, each point may be located.
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Circle E has a radius of 5.1 meters. FG is a chord and is a perpendicular bisector of FG. If FG = 6.3 meters, calculate the distance of IH.
The distance of IH is 1.089 meters.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
Given that,
Radius = 5.1 meters
EF = EI = 5.1
FG = 6.3 meters
HE is a perpendicular bisector of FG.
FH = HG = 6.3 / 2 = 3.15
Also, FH is the projection of EF in the vertical axis.
FH = EF sin (θ), where θ is the angle FEH.
3.15 = 5.1 sin (θ)
sin (θ) = 0.6176
θ = sin⁻¹ (0.6176)
θ = 38.14°
IH = EI - EH
We have, EH is the projection of EF into the horizontal axis.
EH = EF cos (θ)
Substituting,
IH = 5.1 - EF cos (θ)
IH = 5.1 - 5.1 cos (38.14)
IH = 5.1 ( 1 - cos (38.14))
IH = 1.089 meters
Hence the length of the line segment IH is 1.089 meters.
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Please help! Systems of equation/matrix problem
5. TELEVISION During t
ring the summer, Manuel watches television M hours per day, Monday through Friday. Harry watches television H hours per day, Friday and Saturday. Ellen watches television E hours per day, Friday through
Sunday. Altogether, they watch television 37 hours each week. On Fridays, they watch a total of 11 hours of television.
If the number of hours Ellen spends watching television on any given day is twice the number of hours that Manuel
spends watching television on any given day, how many hours of television does each of them watch each day?
I watch a total of 11 hours of TV on Fridays and Ellen watches TV for ten hours every day.
How to find the television does each of them watch each day?Let's plot how long Manuel watches TV each day, with M, Harry as H, and Ellen as E.
Manuel knows that from Monday to Friday he watches TV for M hours, so the total amount of time he watches TV in his week is 5 * M = 5M.
On Friday and Saturday he watches TV for H hours a day, so the total amount of time he watches TV in a week is H*2 = 2H.
Ellen watches her E hours TV from Friday to Sunday, so the total amount of time she watches TV in a week is her E*3=3E.
In total, they watch her TV 37 hours a week.
5M + 2H + 3E = 37
I watch a total of 11 hours of TV on Fridays.
M + H + E = 11
We also know that the amount of time Ellen spends watching TV on a given day is twice as much as she does on a given day as Manuel spends watching TV.
E=2M
You can substitute the value of E for M into the second expression.
M+H+2M=11
Combining equal terms gives:
3M+H=11
Now that we have two equations, we can solve the unknowns M and H. Substitute the 3M formula for H from the second formula into the first.
5M + 2H + 3(3M + H) = 37
Expanding the right-hand side, we get:
5M + 2H + 9M + 3H = 37
Combining equal terms gives:
14M + 5H = 37
Now that we have equation 14M + 5H = 37, we can solve for H.
H = (37 - 14 eyes) / 5
Then you can substitute the formula for H with respect to M into the formula for H.
H = (37 - 14 eyes) / 5
Finally, we can solve for M using the value of H.
M = (37 - 5H) / 14
We know that H = (37 - 14M) / 5, so we can substitute this formula into the formula for M.
M = (37 - 5((37 - 14M) / 5)) / 14
Expanding and simplifying the right-hand side, we get:
M = (37 - 37 + 70M) / 14
Solving for M gives:
M=5
So Manuel watches TV for 5 hours every day and Harry watches TV for (37 - 5 * 5) / 5 = 2 hours every day.
Finally, we can use the equation E = 2M to find out how many hours Ellen watches TV each day.
E = 2 * 5 = 10
So Ellen watches TV for ten hours every day.
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Express the following sum in sigma notation. Use 1 as the lower limit of summation and k for the index of summation. 1+4+9+16+25 +36 Express the sum in sigma notation. Σ" k 1
∑[tex](k^2)[/tex] for k = 1 to 6 is the sum in sigma notation for this series of terms.
The series is 1 + 4 + 9 + 16 + 25 + 36. The lower limit of summation is 1, which means, the sum starts at the initial term in the series.
The index of summation is k, which implies, the ongoing term in the series is represented by the variable k.
In the expression [tex]k^2[/tex] which implies that we are adding up the square of the index of summation.
So, the sigma notation for this series of terms is ∑[tex](k^2)[/tex] for k = 1 to 6, which means, we are adding up the squares of the numbers from 1 to 6 (1, 4, 9, 16, 25, and 36)
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what is the answer???
Answer: Semi-Conservative, and old.
Step-by-step explanation: