The coordinate matrix LFE of L relative to the ordered bases E and F is
[tex]\left(\begin{array}{ccc}3&1&10\\3&3&2\\0&3&3\\0&0&3\end{array}\right)[/tex].
Since here L is a linear transformation from a vector space of dimension 3 to a vector space of dimension 4, the coordinate matrix of L relative to the given ordered bases must be a (4×3) matrix,
Linear transformation is given by,
L(P(t)) = 5p"(t) + 1p' (t) + 3p(t) + 3tp(t)
The given basis is IP² is E = (C1, C2, C3) where, e1(t) = 1, e2(t) = t, e3(t) = t².
Also the given basis of IP³ is (f1, f2, f3, f4) where, f1(t) = 1, f2(t) = t, f3(t) = t², f4(t) = t³.
Now to find the coordinate matrix,
Now,
L(e1(t)) = 5.0 + 1.0 + 3.1 + 3t.1
= 3 + 3t
= 3f1(t) + 3f2(t) + 0.f3(t) + 0.f4(t)
L(e2(t)) = 5.0 + 1.1 + 3.t + 3t.t
= 1 + 3t + 3t²
L(e3(t)) = 5.2 + 1.2t + 3.t² + 3t.t²
= 10 + 2t + 3t² + 3t³
Now writing the coefficients as a column vector we get,
[tex]\left(\begin{array}{ccc}3&1&10\\3&3&2\\0&3&3\\0&0&3\end{array}\right)[/tex]
The coordinate matrix LFE of L relative to the ordered bases E and F is
[tex]\left(\begin{array}{ccc}3&1&10\\3&3&2\\0&3&3\\0&0&3\end{array}\right)[/tex].
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A hypothesis test is performed to determine if the proportion of all six packs of seltzers sold in a particular grocery store near a college campus that are alcoholic exceeds 50%. A random sample of 152 customers that purchased seltzer is acquired (assume no customer purchases more than one six pack at time, alcoholic or not); the sample proportion of these purchases that are alcoholic is obtained. From this sample a test statistic of 2.60 is calculated, which has a corresponding P-value of 0.0047.Which of the following is true?Select one:a. The probability the null hypothesis is true is 1-0.0047 = 0.9953.b. The probability that 50% of customers purchasing seltzers will be purchasing alcoholic seltzer on any given day is 0.0047.c. The probability that, in a random sample of 152 customers purchasing seltzers, more than 50% of those customers will have purchased alcoholic seltzer is 0.0047.d. None of these statements is true.e. The probability the null hypothesis is true is 0.0047.
If the hypothesis test is performed to determine if the proportion of all six packs of seltzers sold in a particular grocery store near a college campus that are alcoholic exceeds 50% Then complement of the P-value gives the probability that the null hypothesis is true, which is 1 minus 0.0047, or 0.9953.
The probability the null hypothesis is true is 1-0.0047 = 0.9953 because ,
The given P-value is 0.0047,
which is the probability of observing a test statistic as extreme as 2.60 or more extreme if the null hypothesis is true. Since this P-value is less than the significance level of 0.05 (assuming a typical significance level), we reject the null hypothesis and conclude that the proportion of all six packs of seltzers sold in the grocery store that are alcoholic exceeds 50%.
Therefore, statement (a) is true and all the other statements are incorrect. The complement of the P-value gives the probability that the null hypothesis is true, which is 1 minus 0.0047, or 0.9953.
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What is the next term on 45__31,24,17
Consider the function f(x) graphed below.
Solve the inequality f(x) ≥0
State your answer using interval notation.
Assume arrows if no symbols are shown at the ends of the graph
Answer:
(-∝, 0)
Step-by-step explanation
f(x) will extend from negative infinity and approach but never reach the point where x = 0.
So the solution is x > -infinity and < 0.
Graph the line with slope 3 passing through the point (1,-5),
Can somebody help me
Answer:
Step-by-step explanation:
To graph the line with slope 3 passing through the point (1,-5), we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is a point on the line.
Substituting the given values, we get:
y - (-5) = 3(x - 1)
Simplifying the equation, we get:
y + 5 = 3x - 3
Subtracting 5 from both sides, we get:
y = 3x - 8
Now we have the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Comparing this equation to the one we just found, we can see that the slope is 3 and the y-intercept is -8.
To graph the line, we can plot the y-intercept at (0,-8) and then use the slope to find other points on the line. Since the slope is 3, we can go up 3 units and to the right 1 unit to find another point on the line. We can repeat this process to find more points on the line, and then connect them to graph the line.
The equation y=ax describes the graph of a line. If the value is negative, The Line: A. Is vertical.
B.is horizontal.
C.goes up and to the right.
D.goes down and to the right.
What are the exact lengths of BC and CF?
The length, in feet, of BC is the square root of.
The length, in feet, of CF is the square root of
The length, in feet, of BC is the square root of √242 and, The length, in feet, of CF is the square root of √363
Cube:
In geometry, a cube is a three-dimensional solid object bounded by six faces, facets, or square sides, with three points of intersection at each vertex. Seen from a certain angle, it is a hexagon and its canvas is often represented by a cross.
Cube is the only regular hexahedron and one of the five Platonic solids. It has 6 faces, 12 edges and 8 vertices. Cube is also a cube, an equilateral cuboid, a rhombus and a 3-sonohedron.
Three orientations are square prisms and four orientations are triangular trapezoids. A cube is twice as large as an octahedron. It has cubic or octahedral symmetry. Cube is the only convex polyhedron whose faces are square.
Then the length CB is given by the Pythagorean theorem as:
CB = √(AC² +AB²)
= √{(2 cm)² + (√2 cm)²}
= √(4 +2) cm
CB = √6 cm
Now,
The length, in feet, of BC is the square root of
√242
And,
The length, in feet, of CF is the square root of
√363
Complete Question:
A cube. The top face has points C, A, B, D and the bottom face has points G, E, F, H. Diagonals are drawn from B to C and from C to F. Side B F is 11 feet.
What are the exact lengths of BC and CF?
The length, in feet, of BC is the square root of
The length, in feet, of CF is the square root of
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Answer:
The length, in feet, of BC is the square root of
✔ 242
The length, in feet, of CF is the square root of
✔ 363
Step-by-step explanation:
For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are [1 - 20x + 150x^2 + cx^3 ]. find c?
Using binomial theorem we can expand the equation but We are not given the value of a or n, so we cannot determine c exactly.
What is the difference between real and integer?Integers are real numbers that only comprise positive and negative whole integers as well as natural numbers. Because of rational and irrational numbers, real numbers may include fractions, whereas integers cannot.
What's a real number?A real number is a quantity in mathematics that may be expressed as an infinite decimal expansion. Real numbers, as opposed to natural numbers such as 1, 2, 3,..., which are generated from counting, are used in measures of continually changing quantities such as size and time.
by applying the binomial theorem:
[tex](1 + ax)^n = C(n, 0) + C(n, 1)(ax) + C(n, 2)(ax)^2 + C(n, 3)(ax)^3 + ...[/tex]
where C(n, k) is the binomial coefficient, which equals[tex]n!/(k!(n-k)!).[/tex]
The first few terms of this expansion are:
[tex](1 + ax)^n = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]
Comparing with the given expression [1 - 20x + 150x^2 + cx^3], we have:
[tex]1 - 20x + 150x^2 + cx^3 = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]
Equating coefficients of [tex]x^3[/tex] on both sides, we get:
[tex]c = n(n-1)(n-2)(a^3/6)[/tex]
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suppose that 27.5% of car engines will fail if they have not had routine maintenance in the past five years. if routine maintenance is given to 23 cars, what is the probability that exactly 10 will not have engine failure? round your answer to six decimal places.
The probability that exactly 10 out of 23 cars will not have engine failure is 0.007638.
Step-by-step explanation: First, calculate the probability of an engine failing in five years with no routine maintenance, which is 27.5%. This can be written as a decimal, 0.275.Next, calculate the probability of an engine not failing in five years with routine maintenance. This probability is 100%-27.5% = 72.5%, written as a decimal 0.725.
Now, using the Binomial Distribution formula (nCr), calculate the probability of exactly 10 engines not failing out of 23 cars, where n = 23, r = 10 and p = 0.725. The equation would be [tex](23C10)*(0.725^{10})*(0.275^{13}) = 0.0076379904[/tex]
Finally, round the result to 6 decimal places, giving an answer of 0.007638.
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can someone complete Q2 with an explanation? (15 points)
Answer:
To find the average distance away from the mean, we need to first find the mean distance from the mean. To do this, we need to find the mean of the distances from the mean:
|32 - 33| = 1
|45 - 33| = 12
|23 - 33| = 10
|35 - 33| = 2
|30 - 33| = 3
Mean distance from the mean = (1 + 12 + 10 + 2 + 3) / 5 = 6. However, the question asks for the average distance away from the mean, so we need to take the absolute value of this result:
Average distance away from the mean = |6| = 6
Therefore, the answer is C) 5.6 feet.
To find the mean absolute deviation, we first need to find the deviations from the mean:
12.7 - 15.2 = -2.5
22 - 15.2 = 6.8
23.5 - 15.2 = 8.3
24 - 15.2 = 8.8
11 - 15.2 = -4.2
22 - 15.2 = 6.8
Next, we need to take the absolute value of each deviation:
|-2.5| = 2.5
|6.8| = 6.8
|8.3| = 8.3
|8.8| = 8.8
|-4.2| = 4.2
|6.8| = 6.8
The sum of these absolute deviations is:
2.5 + 6.8 + 8.3 + 8.8 + 4.2 + 6.8 = 37.4
To find the mean absolute deviation, we divide this sum by the number of data points:
Mean absolute deviation = 37.4 / 6 = 6.23
Therefore, the answer is not listed among the choices given.
Answer:
B. 33
Step-by-step explanation:
1) Find the mean
32+45+23+35+30/5
165/5
=33
Determine the length of the missing side of the given triangle. Round to the nearest tenth.
The hypotenuse is 7.7
The leg is 3.4
Answer:
6.9 or 7.0 .
Step-by-step explanation:
*Note that ^2 means raised to the power of two or squared
a^2 + b^2 = c^2
The hypotenuse is always the C, and the leg can be either a or b.
Fill in the blanks with the numbers that we have:
Hypotenuse: 7.7 | Leg: 3.4
3.4^2 + b^2 = 7.7^2
Square the numbers given
3.4 x 3.4 = 11.56
7.7 x 7.7 = 59.29, which leads us to:
11.56 + b^2 = 59.29
To find what b equals, we need to subtract 11.56 from 59.29
59.29 - 11.56 = 47.73
b^2 = 47.73
We need to take the square root of 47.73 to find b. b and b^2 are two different things.
The square root of 47.73 is about 6.90869017977. It asks for the answer to be rounded to the nearest tenth, giving us 6.9 or 7.0.
What is the median of the following data set? 5, 9, 6, 6, 7, 5, 8, 7, 6 A 6 B 9 C 7 D 5
Answer: The median is 6
Step-by-step explanation: The median is the data value separating the upper half of a data set from the lower half.
Arrange data values from lowest to highest value
The median is the data value in the middle of the set
If there are 2 data values in the middle the median is the mean of those 2 values.
The function
�
=
�
(
�
)
y=f(x) is graphed below. What is the average rate of change of the function
�
(
�
)
f(x) on the interval
−
6
≤
�
≤
5
−6≤x≤5?
Answer:
-10/11
Step-by-step explanation:
You want the average rate of change of f(x) on the interval [-6, 5].
Average rate of changeThe average rate of change of function f(x) on the interval [a, b] is ...
AROC = (f(b) -f(a))/(b -a)
= (f(5) -f(-6))/(5 -(-6))
= (-20 -(-10))/5 +6 = (-20 +10)/(5 +6)
AROC = -10/11
The average rate of change on the interval is -10/11.
urn contains 6 white, 5 red and 3 blue chips. A person selects 4 chips without replacement. Determine the following probabilities: (Show work. Final answer must be in decimal form.) a) P(Exactly 3 chips are white) Answer Answer b) P(The third chip is blue The first 2 were white) c) P(The fourth chip is blue Answer The first 2 were white) 6. Suppose we have a random variable X such that E[X]= 7 and E[X²]=58. Answer a) Determine the variance of X. b) Determine E[2X2 - 20X +5]
the variance of X is 9. b) Determine E [2X² - 20X +5]:
Using linearity of expectation, we can find E [2X² - 20X +5] as:
E [2X² - 20X +5] = 2E[X²] - 20E[X] + 5
by the question.
The number of ways to select the first 2 white chips is given by:
Number of ways = (6C2) (5C0) (3C0) = 15
The number of ways to select the third chip as blue given that the first 2 chips were white is given by:
Number of ways = (3C1) = 3
Therefore, the probability of selecting the third chip as blue given that the first 2 chips were white is:
P(The third chip is blue the first 2 were white) = Number of ways / Total number of ways = 3 / 350 = 0.0086 (rounded to 4 decimal places)
c) P(The fourth chip is blue the first 2 were white):
The number of ways to select the first 2 white chips is given by:
Number of ways = (6C2) (5C0) (3C0) = 15
The number of ways to select the third chip as non-white given that the first 2 chips were white is given by:
Number of ways = (8C1) = 8
The number of ways to select the fourth chip as blue given that the first 2 chips were white, and the third chip was non-white is given by:
Number of ways = (3C1) = 3
Therefore, the probability of selecting the fourth chip as blue given that the first 2 chips were white is:
P(The fourth chip is blue the first 2 were white) = Number of ways / Total number of ways = 8*3 / 350 = 0.0686 (rounded to 4 decimal places)
Suppose we have a random variable X such that E[X]= 7 and E[X²] =58.
a) Determine the variance of X:
The variance of X is given by:
Var[X] = E[X²] - (E[X]) ²
Substituting the given values, we get:
Var[X] = 58 - (7) ² = 9
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Select the correct answer.
Solve:
|x − 3| − 10 = -5
A.
x = -2 or x = 8
B.
x = -8 or x = 2
C.
x = 2 or x = 8
D.
x = 8 or x = 18
Answer:
A. x = -2 or x = 8
Good luck!!
Step-by-step explanation:
(x - 3) - 10 = -5
x - 3 = - 5 + 10
x - 3 = 5
x = 5 + 3
x = 8
Cara's new car holds 13.5 gallons of gas. If gas costs $2.98 per gallon, how much would it cost her to fill the gas tank from empty?
Thus, the total cost of gas for fill the tank of car tank is $40.23.
Explain about unitary method?Finding the sum of the values of one unit and then multiplying its amount by the sum of the values of one unit to get the value of even more or fewer units is the unitary method's formula. In this illustration, the "unit" represents the quantity of books, and the "value" is their purchase price.
When we visit the market to purchase any item, we inquire about the item's pricing from the shopkeeper. The term for this is unit price.
For the stated question:
Capacity of car = 13.5 gallons of gas.
Gas cost = $2.98 per gallon
So, cost to fill the tank:
Total cost = gas costs per gallon * Capacity of car
Total cost = $2.98 * 13.5
Total cost = $40.23
Thus, the total cost of gas for fill the tank of car tank is $40.23.
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Solve equation for x
216=6^4x+5
Answer: x=211/1296
Step-by-step explanation:
HELP! I WILL MAKE U BRAINLIST! DUE BY 12:00 AM!
I have inserted what you need to do and just search Buzzfeed "Can TV Make Us Not Hate Ourselves?" and read it!
I often see myself represented in the media as a strong, independent woman who lives fearlessly and passionately. I'm a black woman, and I'm proud to be a part of the diverse range of people in our society.
What is passionately ?Passionately is an adjective that describes a person who is filled with intense emotion and enthusiasm. This can be expressed through action or behavior. When someone is passionate about something, they often feel an overwhelming urge to pursue it with great intensity. Being passionate about something is often associated with seeking to make a difference or make an impact on the world.
My representation in the media is not always positive, however. I've been depicted as being too opinionated, too outspoken, or too headstrong. I'm often seen as a stereotype, or as someone who doesn't fit into the roles that society has determined for me.
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I see myself represented in the media by characters who are strong, independent, and confident.
What is media?Media is the broad term used to describe any form of communication that can be used to disseminate information to a large group of people. Media includes traditional media such as newspapers, magazines, radio, and television, as well as more modern forms such as digital media, including websites, social media, and online streaming.
They may have had a difficult start, but they don't let it define them. They are determined to make something of themselves, regardless of the odds. They are resilient and are not afraid to stand up for what they believe in. Through these characters, I can relate to and identify with the struggles and successes of the journey.
My own writer's voice is often reflective and contemplative. I strive to be thoughtful and honest in my writing, and often use metaphors and imagery to make a point. For example, I might write, "Her journey was like a rollercoaster, with highs and lows along the way, but she kept her eyes on the horizon, never losing sight of her goals." Here, I am using an analogy to convey the idea of how a person's path might not always be easy, but they can remain focused on the end result.
The author of the essay used rhetorical questions to emphasize their points and express their opinion. I have also adopted this technique in my writing. For example, I might write, "Do we ever really know how our stories will unfold? Or what it takes to get there?" The use of rhetorical questions captures the reader's attention and sparks their imagination.
Overall, I feel that my writer's voice is distinct and I am confident in my use of literary devices. By incorporating the use of rhetorical questions and analogies, I am able to effectively convey my opinion and perspective in a unique way.
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Use Pythagoras' theorem to work out the length of AD in this triangular prism. Give your answer in centimetres (cm) to 1 d. P
The length of AD in the triangular prism is 9.8 cm.
The length of AD in the triangular prism can be found using Pythagoras' theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The base of the prism is a right triangle, so:
AD² = AE² + ED²
AD² = 4² + 9²
AD² = √97
AD = √97
AD = 9.8 cm (rounded to 1 decimal)
Therefore, the length of AD in the triangular prism is 9.8 cm.
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Complete Question:
Use Pythagoras' theorem to work out the length of AD in this triangular prism. Give your answer in centimeters (cm) to 1 decimal point.
Could anyone help out with this?
The volume of the frustum is 970 cm².
What is frustum?
In geometry, a frustum is a three-dimensional solid that is created by cutting a larger solid, such as a cone or pyramid, with a plane parallel to its base, and then removing the smaller solid that lies above the plane. The resulting solid has two parallel bases of different sizes, and its sides are trapezoidal in shape.
We know that, volume of frustum is given by
V = (1/3) * h * (A + B + sqrt(A * B))
where V is the volume of the frustum, h is the height of the frustum, A is the area of the rectangular base, and B is the area of the rectangular top.
So, A = base × height = 8 × 16
= 128 cm²
Similarly, B = base × height = 3 × 6
= 18 cm²
and, given height of frustum = 15 cm
Now, putting all values into the formula:
So, V = (1/3)× h × (A + B + sqrt(A×B))
= 1/3 × 15 × ( 128+18 + √(128×18))
= 5 × ( 146 + 48 )
= 970 cm²
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the number 0.1271 represents the area under the standard normal curve below a particular z-score. what is the z-score? enter your answer,as a decimal to the nearest hundredth, in the box.
Thus, a 0.1271 area under the standard normal curve corresponds to a z-score of roughly -1.14.
what is standard deviation ?The degree of variance or dispersion in a set of data values is measured by standard deviation. It computes the deviation of each data point from the mean (average) of the data. While a high standard deviation suggests that the data points are dispersed throughout a broader range of values, a low standard deviation suggests that the data points tend to be close to the mean. In statistics, the standard deviation is frequently used to evaluate the level of variability or dispersion within a data collection.
given
Using a normal distribution function on a calculator or a standard normal distribution table, we can determine the z-score that corresponds to an area of 0.1271 under the standard normal curve.
We can enter the following data into a calculator equipped with a normal distribution function:
Area = 0.1271
Mean = 0 (because we are using the usual normal distribution) (since we are using the standard normal distribution)
Standard deviation equals one (since we are using the standard normal distribution)
Calculating this, we obtain:
Z is equal to invNorm(0.1271, 0, 1) = -1.14.
Thus, a 0.1271 area under the standard normal curve corresponds to a z-score of roughly -1.14.
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Answer:
it is -1.14
Step-by-step explanation:
I took the k12 quiz
I need helppp, I’ll give brainliest
The set of all possible y-values for the function h constitutes its range. The range is therefore [-3, 0].
what is range ?The collection of all feasible output values (dependent variable) of a function is known as the range in mathematics. It is the totality of all possible numbers that the function can accept as input (an independent variable) and output. On the number line, the range is frequently represented by an interval or group of intervals. For instance, the range can be written as [-3, 3] if the domain of a function f(x) is [-2, 2] and its output numbers fall within [-3, 3].
given
The collection of all x-values for which h(x) is specified is the domain of the function h.
The graph's [-2, 4] domain can be determined by looking at the graph, which shows that it begins at x=-2 and concludes at x=4.
The set of all possible y-values for the function h constitutes its range. Looking at the graph, we can see that it takes all values between y=-3 and y=0, and that it begins at y=-3.
The range is therefore [-3, 0].
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The complete question is :- The entire graph of the function h is shown in the figure below. Write the domain and range of h as intervals or unions of intervals.
-2
-3-
4-
domain =
range =
a college student takes the same number of credits each semester. before beginning college, the student had some credits earned while in high school. after 2 semesters, the student had 45 credits, and after 5 semesters, the student had 90 credits. if c(t) is the number of credits after t semesters, write the equation that correctly represents this situation.
The equation that correctly represents this situation is c(t) = 45 + 45(t-2). This equation states that the total number of credits the student will have after t semesters is equal to 45 (the number of credits they had before beginning college) plus 45 times the number of semesters after two (t-2).
To explain this equation in more detail, we need to break it down. First, the student had some credits earned while in high school, so the equation starts off with c(t) = 45, which is the number of credits the student had before beginning college.
Next, 45(t-2) represents the number of credits earned in the additional semesters since college began. The t-2 part of the equation means that the total number of credits earned in the additional semesters starts at zero for t = 2. Then, for each additional semester, 45 credits are added. So, for example, when t = 5, 45 credits are added to the initial 45 credits the student had before beginning college, resulting in 90 credits.Therefore, the equation c(t) = 45 + 45(t-2) correctly represents this situation.
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How do you solve ratio??
Answer:
How to solve a ratio problem:
Add together the parts of the ratio to find the total number of shares.
Divide the total amount by the total number of shares.
Multiply by the number of shares required.
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AOC is a right-angle AOB: BOC - 2:3 what is the size of angle BOC
Angles AOB and BOC are complimentary angles if AOC is a right angle. Let's use x to represent the angle BOC's size. Next, we have: Angle AOB plus Angle BOC equals 90° (definition of complementary angles).
BOC/AOB angle equals 2/3 (given) Angle AOB may be expressed in terms of angle BOC using the second equation: (3/2) × angle BOC, where angle AOB (multiplying both sides by angle AOB) Angle BOC plus angle (3/2) equals 90 degrees. When we simplify this equation, we obtain: BOC angle (5/2) times equals 90 degrees. By multiplying both sides by 5, we obtain: BOC angle = (2/5) x 90 degrees BOC angle is 36 degrees. Hence, the angle's size Substituting this expression into the first equation, we get: (3/2) x angle BOC + angle BOC = 90 degrees Simplifying this equation, we get: (5/2) x angle BOC = 90 degrees.
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Given that a=14 and b=25, work out the height of the triangle
The height of the triangle is 1.12 units (rounded to two decimal places).
The height of a triangle is the perpendicular distance from the base of the triangle to the opposite vertex. In other words, it is the length of the line segment that is perpendicular to the base and passes through the opposite vertex.
We can use the formula for the area of a triangle:
Area = (1/2) * base * height
And since we know the values of the base (b) and the area (a), we can rearrange the formula to solve for the height (h):
h = (2a) / b
Plugging in the values of a and b:
h = (2 * 14) / 25
h = 28 / 25
Therefore, the height of the triangle is 1.12 units (rounded to two decimal places).
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21. The measures of the segments formed by the altitude to the hypotenuse of a right triangle are in the ratio 1: 4. The length of the altitude is 14.
a. Find the measure of each segment.
b. Express, in simplest radical form, the length of each leg.
Answer:
Step-by-step explanation:
1. add 14 to 24
2. ur done!
Naive Nelson uses RSA to receive a single ciphertext c, corresponding to the message m. His public modulus is n and his public encryption exponent is e. Since lie feels guilty that his system was used only once, he agrees to decrypt any ciphertext that someone sends him, as long as it is not c, and return the answer to that person. Evil Eve sends him the ciphertext 2°c (mod n). Show how this allows Eve to find m.
We have that, based on the system of the module, by sending Nelson 2ec (mod n), Eve can use her system to find m without ever sending him c.
How can we find the value?Naive Nelson's RSA system works using the equation c = me (mod n), where c is the recorded text, m is the message, e is the recorded exponent, and n is the public modulus. Therefore, to find m, Eve needs to solve the equation 2ec = me2 (mod n). Since 2e and m2 are known values, Eve can calculate more:
m = 2ec / m2 (module n)
So by sending Nelson 2ec (mod n), Eve can use her system to find m without ever sending him c.
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12. In the accompanying diagram, DE || BC, DB = 6,
and AE = 8. If EC is three times AD, find AD.
B
6
D
A
8
E
C
Answer:
AD=4
Step-by-step explanation:
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As a town gets smaller, the population of its high school decreases by 7% each year. The senior class has 320 students now. In how many years will it have about 100 students? Write
an equation. Then solve the equation without graphing.
Write an equation to represent this situation. Let n be the number of years before the class will have 100 students.
(Type an equation using n as the vanable. Use integers or decimals for any numbers in the equation)
Help again please
Therefore, in about 15 years and 2 months, the senior class will have about 100 students.
What is equation?An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.
Given by the question.
Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).
Then, we can write the following equation to represent the situation:
P[tex](1-r)^{n}[/tex] = 100
We know that the current population of the senior class is 320, so we can substitute these values into the equation:
320[tex](1-0.07)^{n}[/tex] = 100
Simplifying the equation, we get:
[tex]0.93^{n}[/tex] = 0.3125
Taking the natural logarithm of both sides, we get:
n ln (0.93) = ln (0.3125)
Dividing both sides by ln (0.93), we get:
n = ln (0.3125) / ln (0.93)
Using a calculator, we find that n is approximately equal to 15.21 years.
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Solve each absolute value inequality and show its solution set. l) −2x−5 ≤5
To solve this inequality, we must first isolate the absolute value on one side of the equation.
Step 1: Add 5 to both sides of the equation.
−2x−5 + 5 ≤ 5 + 5
Step 2: Simplify the left side.
−2x ≤ 10
Step 3: Divide both sides by -2.
x ≥ -5
Step 4: Graph the solution on a number line.
The solution set is {x | x ≥ -5}