Your kite is stuck in a tree that is 45 feet tall. The angle your string makes with the ground is 68°. Rather than worrying about the kite, you decide to calculate how much string you have let out. Assuming the string is held tight and makes a straight line to the ground, how much string have you let out?
Answers
Answer:
48.53 = 49 feet
Step-by-step explanation:
sin 0 = opposite/hypotenuse
sin 68 = AB/AC = 45/x
x = 45/sin 68 = 45/0.9272 = 48.53
48.53 rounded = 49 feet
Answer:
You have let out 48.5 feet of string
Step-by-step explanation:
Attached is a sketch of the problem.
We can use SOH CAH TOA to find our answer.
In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.
We can calculate the length of the string by using the SIN function.
So we can say the sine of angle x is the opposite side divided by the hypotenuse.
[tex]sin(x)=\frac{O}{H}[/tex]
Lets solve for [tex]H[/tex].
Multiply each term by [tex]H[/tex].
[tex]H*sin(x)=\frac{O}{H} *H[/tex]
Simplify the right side by cancelling the common factor of [tex]H[/tex].
[tex]H*sin(x)=O[/tex]
Divide both sides of the equation by [tex]sin(x)[/tex].
[tex]\frac{H*sin(x)}{sin(x)} =\frac{O}{sin(x)}[/tex]
Simplify the right side by cancelling the common factor of [tex]sin(x)[/tex].
[tex]H=\frac{O}{sin(x)}[/tex]
Now lets evaluate the length of the string.
In this example we are given
[tex]x=68\\O=45[/tex]
[tex]H=\frac{45}{sin(68)}[/tex]
[tex]H=48.5341[/tex]
Related Questions
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
Answers
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.
How to find the distribution of sample mean?
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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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.)
Answers
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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Find the equation for the plane through Po(-4,-3,8) perpendicular to the following line.
x= -4+t, y=-3-3t, z= -4t, -∞
Answers
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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PLEASE HELP!!!!! Complete the two-column proof.
Answers
The equation will be 5x + 7x = 180. Then the value of the variable 'x' will be 15.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
∠TSR = 5x and ∠UVW = 7x
Angle ∠TSR and angle ∠UVW are the supplementary angles. Then the equation is given as,
5x + 7x = 180
12x = 180
x = 180 / 12
x = 15
The equation will be 5x + 7x = 180. Then the value of the variable 'x' will be 15.
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dillon places a ladder against the wall the base of the ladder is 5 feet from the wall the ladder is 12 feet long how will shorting the distance between the base of the ladder and the wall affect the dimentions of the triangle they form explain in terms of the pyhagoren therom
Answers
The base distance will be 10.9 feet .
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
The Pythagorean theorem states that, in a right triangle, the length of the hypotenuse squared equals the sum of the squares of the other two sides or legs of the triangle. Algebraically, a2+b2=c2. In your example, the length of the ladder would be the hypotenuse and the distance from the wall would be one of the legs. So substitute these values into the equation to get: 25+b2=144 or 25+b2=144 and then subtract 25 from both sides to get b2=119. Therefore b=√119≈10.908. If your problem requires an exact answer in its most simplified form, please note that √119=10.9
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What is the length of the apothem of a regular hexagon with side length of 8 ft?
Answers
The length of the apothem of a regular hexagon is 4√3
How to determine the length of the apothemThe apothem of a regular hexagon is the distance from the center of the hexagon to the midpoint of one of its sides.
To find the length of the apothem, we can use the formula:
apothem = (side length) / (2 * tan(180/n))
where n is the number of sides of the polygon.
In this case, n = 6 (since the hexagon is regular).
So, to find the apothem of a regular hexagon with a side length of 8 ft, we can plug these values into the formula:
apothem = (8 ft) / (2 * tan(180/6))
This gives
apothem = 8 ft / (2 * tan(30))
Evaluate
apothem = 4√3 ft
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AB + BC = AC by what property?
O Distributive Property
O Segment Addition Postulate
O Definition of ≅ Segments
O Transitive Property
Answers
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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a student has only a few hours to prepare for two different exams tomorrow morning. the above table shows alternative possible exam outcomes with three alternative uses of the student's time. the opportunity cost of scoring an 84 on the history exam rather than 76 is:
Answers
The opportunity cost of scoring a 84 on the economics exam rather than a 76 is 15 points on the History exam.
How to determine the opportunity cost?Opportunity Cost is what a person sacrifices when they choose one option over another. It is calculating by subtracting the return of the best forgone option with the return of the chosen option. The outcome could be beneficial or prejudicial, depending on the case.
In the example (refer to the attached table), if the student chooses to score 94 in the economics exam then the student will get 76 in the History test. Thus, The opportunity cost of getting 94 instead of 77 in the Economics test, implies getting 76 instead of 91 in the History exam. It implies:
Opportunity cost of the History exam = 91-76
Opportunity cost of the History exam = 15
Therefore the opportunity cost of scoring 94 on the Economics exam rather than a 77 is 15 points on the History test.
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ABC is a dilation of J HG centered at the origin.
Find the scale factor of the dilation.
Answers
Answer:
2 is the scale of dilation
consider the following argument, premise 1: if the sum of the digits in (student id) is divisible by 3 then (student id) is divisible by 3. premise 2: the sum of the digits in (student id) is divisible by 3. conclusion: (student id) is divisible by 3. substitute your eight-digit numeric student id for (student id) in the above argument and determine whether the argument, filled-in with your student id, is sound or unsound. justify your answer and include your student id in your explanation.
Answers
The argument, filled-in with the student ID 12345678, is sound because the two premises are true and the conclusion follows logically from them. The sum of the digits in 12345678 is 36, which is divisible by 3, so the first premise is true.
My student ID is 12345678.
The argument, filled-in with my student ID, is sound. This is because the two premises are true and the conclusion follows logically from them. The sum of the digits in 12345678 is 36, which is divisible by 3, so the first premise is true. The second premise is also true since it states that the sum of the digits in 12345678 is divisible by 3, which is the case. Therefore, the conclusion that 12345678 is divisible by 3 is logically valid from the two premises.
Student ID: 12345678
The argument, filled-in with the student ID 12345678, is sound because the two premises are true and the conclusion follows logically from them.
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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.
Answers
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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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
Answers
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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how to simplify 32/5
Answers
Answer: 6 2/5
Step-by-step explanation:
32 divided by 5 equals 6 with a remainder of 2.
I don't understand how to calculate IQR here. Is 2 the median?
Answers
A statement which is false about the distribution of Kobe’s streak lengths from the 2009 NBA finals include the following: E. The shortest streak is of length 1.
How to determine the false statement?In this scenario, the distribution of Kobe’s streak lengths from the 2009 NBA finals is plotted on a histogram with the length represented by the x-coordinate (x-axis) while the count is represented by the y-coordinate (y-axis).
By critically observing the histogram, we can reasonably infer and logically deduce the following true statements:
The distribution of Kobe’s streak lengths is right skewed and unimodal because it has only one clear peak (most frequent value).Since the median of the distribution of Kobe’s streak lengths is at 0, the typical length of a streak is equal to 0.The interquartile range (IQR) of the distribution is 1 i.e IQR = Q₃ - Q₁.In conclusion, the shortest streak lengths is 0 while the longest streak of baskets is of length 4.
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Complete Question:
Which of the following is false about the distribution of Kobe’s streak lengths from the 2009 NBA finals.
A. The distribution of Kobe’s streaks is unimodal and right skewed.
B. The typical length of a streak is 0 since the median of the distribution is at 0.
C. The IQR of the distribution is 1.
D. The longest streak of baskets is of length 4.
E. The shortest streak is of length 1
Penny created a circle graph to show what percentage of students in her class walk to school, ride the bus, or ride in a car.
What percent of students in Penny’s class ride the bus to school?
HELPPPP ASAPPPPP
Answers
Answer:
45
Step-by-step explanation:
100-25-30=45
create the following matrices with the help of the matrix generation functions eye , ones, diag and triu. see the on-line help on these functions if required (i.e. help eye). do not enter the matrices explicitly. each matrix should be generated with a single command. m
Answers
The required solution is above with the help of matrix generation.
Now, According to the question:
A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.
With the help of the matrix generation functions eye , ones, diagonal and trigonal .
Command to generate matrix such as M,N,P,Q
M=6*eye(3)
N= triu (5*ones(3))
P=7*ones (3,2)
Q=diag ([2 3 4])
Therefore, the required solution is above with the help of matrix generation.
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The given question is incomplete, complete question is:
Create matrices with eye, ones, diag and triu Create the following matrices with the help of the matrix generation functions eye , ones, diag and triu. See the on-line help on these functions if required (i.e. help eye)M =[6 0 00 6 00 0 6]N =[5 5 50 5 50 0 5 ]P =[7 77 77 7]Q =[2 0 00 3 00 0 4]
The following inequalities form a system. y is greater than or equal to two-thirds times x plus 1 y is less than negative one-fourth times x plus 2 Which ordered pair is included in the solution to this system? (−6, 3.5) (−6, −3) (−4, 3) (−4, 4)
Answers
Answer: The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality.
What exactly is inequality?
A variation between two values indicates whether one is smaller, larger, or otherwise unrelated to the other.
In other words, inequality is the inverse of equality. For example, if 2 = 2, it is equal; however, if I say 3 = 6, it is incorrect; the correct expression is 3 6.
Step-by-step explanation:As per the given phrase,
y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ (2/3)x + 1
y is less than negative one-fourth times x plus 2 ⇒ y < (-1/4)x + 2
Substitute, point (−6, −3)
-3 ≥ (2/3)(-6) + 1
-3 ≥ -3
Substitute in second inequality,
-3 < (-1/4)(-6) + 2
-3 < 7/2
Solve
X/2 -3 = 5
A- x=4
B- x=16
C- x=13
Answers
Answer:
x=16
Step-by-step explanation:
x/2=5+3
x/2=8
x=8×2
x=16
x + (-2)3/2 = 5
x - 2.3/2 = 5
x=16
what is the answer???
Answers
Answer: Semi-Conservative, and old.
Step-by-step explanation:
In the supermarket, 7/12 of Marco’s bill is for fruit and vegetables. If 1/8 is for fruit, what fraction is for vegetables?
Answers
In other words, 3/4 fraction of the bill are for vegetables, while 1 part is for fruit.
How is this determined?Using the data provided in the issue, we can determine what percentage of Marco's bill is made up of veggies. We are aware that fruit and vegetables account for 7/12 of the total bill and make up 1/8 of the total. By deducting the portion of the bill that is for fruit from the portion that is for fruit and vegetables, we can determine the portion of the cost that is for vegetables.
We must identify a common denominator for the two fractions in order to accomplish this. Since 12 and 8 have a denominator of 24, we convert both fractions to have a denominator of 24.
1/8 turns becomes 3/24
7/12 changes to 21/24.
We deduct 3/24 from 21/24 in order to derive the percentage of fruit from the percentage of fruit and vegetables.
21/24 - 3/24 = 18/24
Vegetables make up 18/24, or 3/4, of Marco's bill.
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a student sets up the following equation to convert a measurement. (the ? stands for a number the student is going to calculate.) fill in the missing part of this equation. (39 . N/cm) . ____ = ? N/mm
Answers
The resulting answer is 39000 N/mm, this equation can be used to convert a given measurement from N/cm to N/mm.
39000/1 = ? N/mm
Multiply 39 by 1000 to convert centimeters to millimeters.
39000/1 = ? N/mm
Divide the measurement 39000 N/cm by 1 to convert it to N/mm.
The answer is 39000 N/mm.
To convert a measurement from N/cm to N/mm, the equation that needs to be set up is 39000/1 = ? N/mm. This equation can be broken down into two steps. First, the measurement needs to be multiplied by 1000 to convert centimeters to millimeters. Then, 39000/1 needs to be divided to convert the measurement from N/cm to N/mm. The resulting answer is 39000 N/mm. Therefore, this equation can be used to convert a given measurement from N/cm to N/mm.
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evaluate x^3 - 2x^2 +3x - 7
______________
x - 1
Answers
The expression on being divide by x-1 gives -5 as remainder and quotient (x²-x+2)
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x²-5x+11
Given here: The expression as x³-2x²+3x-7 which is to be divide by x-1
Thus dividing using the long divsion method we get
x-1)x³-2x²+3x-7(x²-x+2
x³-x²
-________
0-x²+3x
x²+x
-________
2x-7
2x-2
-__________
-5
Thus The expression can be written as x³-2x²+3x-7 =(x-1)×(x²-x+2)-5
Hence, On dividing the given expression by x-1 by long divison method we get the remainder as 2.
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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
Answers
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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480,000 in scientific notation.
Answers
Answer:4.8×105 g
Step-by-step explanation:
what is the area of a triangular prism with dimensions of 13ft, 5 ft,12 ft, 6 ft
Answers
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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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?
Answers
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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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).
Answers
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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What is the total area, in square inches, of the shaded sections of the trapezoid below? 5 in 6.3 in 8 in 5.4 in
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The total area of the shaded sections of the trapezoid in square inches is 32.76 square inches.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely fill the entire surface of an enclosed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
The shaded sections in the trapezoid are triangles.
The area of the triangle is given by the following formula:
A = 1/2 (b)(h)
For the first triangle, b = 5 and h = 6.3. Substituting the value in the formula we have:
A1 = 1/2 (5)(6.3)
A1 = 15.75
For the second triangle, b = 5.4 and h = 6.3. Substituting the value in the formula we have:
A2 = 1/2 (5.4)(6.3)
A2 = 17.01
The total area of the shaded region of the trapezoid is calculated by adding the area of the individual shaded portion:
A = A1 + A2
A = 15.75 + 17.01
A = 32.76
Hence, the total area of the shaded sections of the trapezoid in square inches is 32.76 square inches.
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B = 1 4 1 2
0 1 3 -4
0 2 6 7
2 9 5 -1
Can every vector in R^4 be written as a linear combination of the columns of the matrix B above? Do the columns of B span R^3
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Yes, every vector in R^4 can be written as a linear combination of the columns of the matrix B.
This can be proven using the definition of linear combinations, which is as follows: a vector v in R^n can be written as a linear combination of vectors v1, v2, ..., vk if and only if there exist scalars c1, c2, ..., ck such that v = c1*v1 + c2*v2 + ... + ck*vk. With this definition, we can prove that the columns of B span R^4 by showing that for any vector v in R^4, there exist scalars c1, c2, c3, c4 such that v = c1*B1 + c2*B2 + c3*B3 + c4*B4, where B1, B2, B3, B4 are the columns of the matrix B above. To prove this, we can simply solve the system of equations given by c1*B1 + c2*B2 + c3*B3 + c4*B4 = v for c1, c2, c3, c4. This can be done by using Gaussian elimination, which will yield a set of scalars c1, c2, c3, c4 that can be used to express any vector in R^4 as a linear combination of the columns of the matrix B, thus proving that the columns of B span R^4.
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which of the following is an example of within-subject variable?
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Answer:
A within-subject variable is a type of variable in which the same subjects are used to measure multiple levels or conditions of the variable. One example of a within-subject variable would be measuring a person's reaction time to a stimulus both before and after a training intervention.
For example: measuring a person's reaction time to a visual stimulus before and after a training program in which the participant learns to react faster to the stimulus, here reaction time is the within-subject variable.