The complement of the angle is 38 degrees and the supplement of the angle is 128 degrees.
Find the complement of the angle shown.The given angle is
Angle = 52 degrees
To find the complement of an angle, we need to subtract its measure from 90 degrees.
Therefore, the complement of an angle with a measure of 52 degrees is:
90 degrees - 52 degrees = 38 degrees
So, the complement of the angle shown is 38 degrees.
Find the supplement of the angle shown.To find the supplement of an angle, we need to subtract its measure from 180 degrees.
Therefore, the supplement of an angle with a measure of 52 degrees is:
180 degrees - 52 degrees = 128 degrees
So, the supplement of the angle shown is 128 degrees.
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If the midpoint of 2 sides of a triangle are connected with a segment then
The Midpoint is the middle- point of the line member. The midpoint connecting two sides of a triangle is resemblant to the third side and half as long.
The midpoint is the middle of the line member. It's equidistant from both endpoints and is the centroid of the member and endpoints. Cut a member in two.
The midpoint theorem states that a line member drawn from the midpoint of two sides of a triangle is resemblant to the third side and half the length of the third side of the triangle.
The mean theorem helps us find the missing values for the sides of triangles. Connects the sides of a triangle with a line member drawn from the midpoints of two sides of the triangle.
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5. Solve the following problems. Note: In those problems the geometric multiplicity is less than algebraic multiplicity. (a)d/ dx = ( 1 −44 −7) x2−30
Answer:
-130
Step-by-step explanation:
Keenan scored 80 points on an exam that had a mean score of 77 points and a standard deviation of 4. 2 points. Rachel scored 78 points on an exam that had a mean score of 75 points and a standard deviation of 3. 7 points. Find Keenan's z-score, to the nearest hundredth
Keenan's z-score is 0.71, rounded to the nearest hundredth.
The z-score measures how many standard deviations an individual's score is from the mean, and can be calculated using the formula:
z = (x - μ) / σ
where x is the individual's score, μ is the mean score, and σ is the standard deviation.
For Keenan's exam:
z = (80 - 77) / 4.2
z = 0.71
Therefore, Keenan's z-score is 0.71, rounded to the nearest hundredth.
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.
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for h(x) = 4x-1, find h(0) and h(2)
Answer:
- 1 and 7
Step-by-step explanation:
to find h(0) substitute x = 0 into h(x)
h(0) = 4(0) - 1 = 0 - 1 = - 1
to find h2) substitute x = 2 into h(x)
h(2) = 4(2) - 1 = 8 - 1 = 7
Michelle asked 30 people entering a movie theater how many movies they had seen over the past year. Here are the results of her poll. 0, 5, 3, 2, 6, 8, 10, 12, 11, 16, 0, 3, 4, 7, 2, 0, 1, 9, 6, 4, 4, 8, 14, 16, 17, 18, 5, 3, 6, 8 (a) Create a frequency table for the data with 5 classes. (b) Create a histogram from your frequency table. Label the axes and give the histogram a title. Answer: (c) Number of movies Frequency
Part (a) of this sentence displays the frequency chart, and part (c) displays the histogram (b) .
what is histogram ?A graph that displays the distribution of a collection of continuous data is called a histogram. It is composed of a number of bars, each of which represents a set of values, and whose height denotes the frequency or number of data points that lie within a given range. Histograms are used to depict a distribution's shape, centre, and spread graphically. They are frequently used to find patterns and trends in data in areas like statistics, data analysis, and scientific study.
given
(A) We must first identify the data's range before dividing it into 5 intervals of equal width in order to construct a frequency table with 5 classes. The values are in the range of 0 to 18.
(b) We plot the class intervals on the x-axis and the frequency on the y-axis to generate a histogram from the frequency chart. The counts are used to illustrate how frequently each class interval occurs.
Part (a) of this sentence displays the frequency chart, and part (c) displays the histogram (b).
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I cant figure it out
4x - 4/4x² + x is the value of linear equation.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
28x³ - 28x²/28x⁴ + 7x³
= 28x²( x - 1 )/7x³( 4x + 1)
= 4( x - 1)/x( 4x + 1)
= 4x - 4/4x² + x
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If P = 2y² + 4xy + 4
Q = − 3y² + 7 - 3xy
R=- 3xy + 8
Find P+Q=R.
Answer:
P = [tex]2y^{2}[/tex] + 4xy +4
Q = [tex]-3y^{2}[/tex] + 7 -3xy
R = -3xy +8
Step-by-step explanation:
In Bitcoin, the standard practice for a merchant is to wait for n confirmations of the paying transaction before providing the product. While the network is finding these confirming blocks, the attacker is building his own branch which contradicts it. When attempting a double-spend, the attacker finds himself in the following situation. The network currently knows a branch crediting the merchant, which has n blocks on top of the one in which the fork started. The attacker has a branch with only m additional blocks, and both are trying to extend their respective branches. Assume the honest network and the attacker has a proportion of p and q of tire total network hash power, respectively. 1. [10 pts] Let az denote the probability that the attacker will be able to catch up when he is currently z blocks behind. Find out the closed form for az with respect to p,q and z. Detailed analysis is needed. (Hint: az satisfies the recurrence relation az=paz+1+qaz−1) 2. [10 pts] Compared with the Bitcoin white paper, we model m more accurately as a negative binomial variable. m is the number of successes (blocks found by the attacker) before n failures (blocks found by the honest network), with a probability q of success. Show that the probability for a given value m is P(m)=(m+n−1m)pnqm.
In Bitcoin, when a merchant waits for n confirmation of a payment transaction before providing the product, there is a risk of a double-spend attack. In this situation, the network is aware of a branch crediting the merchant, which has n blocks on top of the one in which the fork started.
By simulating m as a negative binomial variable, P(m) = (m + n - 1m)pnqm can be used to more precisely compute this probability for a given value of m.
The attacker, on the other hand, has a branch with only m additional blocks. If we assume the honest network and the attacker have a proportion of p and q of the total network hash power, respectively, the probability of the attacker catching up when he is currently z blocks behind is given by az = paz+1 + qaz−1, where a is a constant.
To calculate the probability more accurately, we can model m as a negative binomial variable.
This is the number of successes (blocks found by the attacker) before n failures (blocks found by the honest network), with a probability q of success.
The probability for a given value m is then given by P(m) = (m + n - 1m)pnqm.
Thus, when dealing with a double-spend attack in Bitcoin, the probability that the attacker will be able to catch up is given by az = paz+1 + qaz−1, where a is a constant.
This probability can be more accurately calculated by modeling m as a negative binomial variable, with the probability for a given value m given by P(m) = (m + n - 1m)pnqm.
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How to do matrix multiplication in MIPS?
To perform matrix multiplication in MIPS, we can use nested loops to iterate over the rows and columns of the matrices.
The outer loop iterates over the rows of the first matrix, while the inner loop iterates over the columns of the second matrix. We then perform the dot product of the corresponding row and column, which involves multiplying the elements and summing the products.
To perform multiplication efficiently, we can use MIPS registers to store intermediate values and avoid accessing memory unnecessarily. We can also use assembly instructions like "lw" and "sw" to load and store values from memory, and "add" and "mul" to perform arithmetic operations.
In summary, matrix multiplication in MIPS involves nested loops, efficient use of registers and assembly instructions, and arithmetic operations.
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If the GM between √2 and 2√2 is a find the value of a.
Answer:
If the GM between √2 and 2√2 is a find the value of a.
Step-by-step explanation:
To find the geometric mean between two numbers, we simply take the square root of their product.
In this case, we want to find the geometric mean between √2 and 2√2.
Their product is:
√2 * 2√2 = 2√4 = 2*2 = 4
So, the geometric mean between √2 and 2√2 is the square root of 4, which is:
√4 = 2
Therefore, the value of a is 2.
Which of the following represents vector vector t equals vector PQ in trigonometric form, where P (–13, 11) and Q (–18, 2)?
t = 10.296 sin 60.945°i + 10.296 cos 60.945°j
t = 10.296 sin 240.945°i + 10.296 cos 240.945°j
t = 10.296 cos 60.945°i + 10.296 sin 60.945°j
t = 10.296 cos 240.945°i + 10.296 sin 240.945°j
The correct answer is option (C).
What are the fundamental forms of trigonometry?Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent are the six functions (cot).
The equation t = Q - P, where Q and P are the specified locations, can be used to determine the components of the vector t. Therefore:
t = (–18, 2) – (–13, 11) = (–18 + 13, 2 – 11) = (–5, –9) (–5, –9)
The vector's magnitude is given by:
|t| = √(–5)^2 + (–9)^2 = √106 ≈ 10.296
The formula = tan1 (y/x), where x and y are the vector's components, can be used to determine the direction of the vector t. The direction must be expressed in terms of sine and cosine functions because we are required to represent the vector in trigonometric form.
θ = tan⁻¹ (–9/–5) ≈ 60.945°
In trigonometric form, the vector t is thus represented as follows:
t = [t|cos|i] + [t|sin|j]
We get the following by altering the values of |t| and:
t = 10.296 cos I + 10.296 sin j of angle 60.945
As a result, the following is the proper trigonometric representation of the vector t:
t = 10.296 cos I + 10.296 sin j of angle 60.945
Thus, alternative is the right response (C).
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This is a modification of A7 - Quadratic Approximation. Create a Matlab function called myta which takes four arguments in the form myta(f,n,a,b). Heref is a function handle, n is a nonnegative integer, and a and b are real numbers. The Matlab function should find the nth Taylor Polynomial to f(x) at x = a and plug in x = b, then it should return the absolute value of the difference between this value and f(b). The the nth Taylor Polynomial to f (x) is the function g(x) = f(a) + f'(a)(x – a) += f'(a)(x – a)? + 1 1 f''(a)(x – a)3 + + f(n)(a)(x – a)". 1 3! n! 3 Here are some samples of input and output for you to test your code. When you submit your code the inputs will be different. Here vpa is being used to show lots of digits
As we have defined the Matlab function called myta which takes four arguments in the form myta(f,n,a,b).
The purpose of the function is to find the nth Taylor polynomial of the function f(x) at x = a and evaluate it at x = b. Then, it should return the absolute value of the difference between this value and f(b).
Now that we have the nth Taylor polynomial of f(x) at x = a, we can evaluate it at x = b and calculate the absolute difference between this value and f(b).
function result = myta(f,n,a,b)
syms x; % define x as symbolic variable
g = f(a); % initialize g as f(a)
for i=1:n % iterate from 1 to n
deriv = diff(f,x,i-1); % calculate the ith derivative of f
term = deriv*(x-a)^(i-1)/factorial(i-1); % calculate the ith term of the Taylor series
g = g + term; % add the ith term to g
end
result = abs(g - f(b)); % calculate the absolute difference between g(b) and f(b)
end
This code calculates the absolute difference between g(b) and f(b) using the "abs" function and assigns it to the output variable "result".
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a bin can hold 28 pounds. each toy car weighs 7 ounces. how many toy cars can the bin hold? (2 points) 64 toy cars 72 toy cars 88 toy cars 92 toy cars
A bin can hold 28 pounds. each toy car weighs 7 ounces., so the bin can hold 64 toy cars.
How to determine the number of toy carsTo determine the number of toy cars the bin can hold, we must first convert the weight limit of the bin and the weight of the toy cars to a uniform unit of measure.
We'll then divide the weight limit of the bin by the weight of one toy car. After that, we'll multiply the resulting value by the number of ounces in one pound (16).
Here's how to solve the problem:
1 pound = 16 ounces
Therefore, a bin that can hold 28 pounds can hold:28 × 16 = 448 Ounces
The weight of one toy car is 7 ounces.
Divide the weight limit of the bin (448 ounces) by the weight of one toy car (7 ounces):
448 ÷ 7 = 64
Therefore, the bin can hold 64 toy cars.
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(4) 2. Determine the exact answer for each of the calculations in question 2.1 above, by working out the errors caused by rounding, and compensating for them. 2.2.1. 723 + 586 2.2.2. 2850-1155
3. When x = 6, which number is closest to the value of y on the line of best fit in the graph below?
09
01
07
10
0987
65
432
2
1
➤X
0 1 2 3 4 5 6 7 8 9 10
Answer:
9
Step-by-step explanation:
please help i have been trying to get an answer for 5+ hours
How is the quotient of 556 and 16 determined using an area model?
Enter your answers in the boxes to complete the equations. Your final answer should be a mixed number in simplest form.
Answer:
To use an area model to determine the quotient of 556 and 16, we can divide a rectangle of area 556 into 16 equal parts. Each part will have an area of 556/16.
We can start by dividing 556 into 16 groups of 10 (160), and then into 16 groups of 3 (48). That leaves us with a remainder of 4.
So we have:
556 = 16 x 34 + 48 + 4
This shows that 556 can be written as 16 times some whole number (34) plus a remainder of 48 + 4/16.
Simplifying the remainder, we have:
48 + 4/16 = 48 + 1/4 = 48.25
Therefore, the quotient of 556 and 16 is:
556/16 = 34 1/4
The quotient of 556 and 16 using an area model can be determined by producing a rectangle with the total area of 556 and one side of 16. The length of the other side will be the quotient. In this case, the quotient is 34 3/4.
Explanation:When asked to determine the quotient of 556 and 16 using the area model, one way to think of this is making a rectangle. The total area is 556 and one side is 16. The length of the other side will be the quotient.
Start by first estimating how many times 16 could fit into 556. Let's take 30 as an estimate, because 30*16 = 480, which is relatively close to 556. Draw a rectangle with the width of 16 and the length of 30.
Find the difference between the rectangle's area and 556. So, 556 - 480 = 76. Now, 76 is our remaining area to fill. 16 goes into 76 four more times, adding up to 64.
There is still a leftover area, which is 76-64 = 12. This is smaller than our width of 16. So, your final answer is 34 12/16 or 34 3/4 in simplest form.
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I need help I need to show my work please help
Answer: 19
Step-by-step explanation:
This is an isosceles trapezoid. Note that because this is an isosceles trapezoid, QN and MP are equal. Use the lengths given and solve:
3x + 1 + 6 = 6x - 5
3x = 12
x = 4
Plug x = 4 in 3x + 1 + 6, and we get 3(4) + 1 + 6 = 12 + 7 = 19
Hope this helps!
Q4.
The diagram shows a regular hexagon OABCDE.
a
E
OA = a
AB = b
M is the midpoint of OE.
N is the midpoint of AB.
(a) Find MN in terms of a and/or b.
b
B
D
Diagram NOT
accurately drawn
By answering the presented question, we may conclude that So, the Pythagorean theorem length of MN is expressed in terms of a and b.
What is Pythagorean theorem?Its Pythagorean theorem is just a fundamental mathematical principle that explains the connection between the sides of a triangle that is right. It asserts that the sum of the squares of both the widths of the other two sides is a square of both the width of the hypotenuse (the side facing the perfect angle) the side opposite the right angle). The mathematical mathematics is as follows: c2 = a2 + b2 At which "c" indicates the length of the right triangle and "a" and "b" reflect the extents of the additional two sides, started referring to as the legs.
Because M is the midpoint of OE and N is the midpoint of AB, we can draw a line segment connecting M and N that is parallel to OB and AE and perpendicular to AB.
the Pythagorean theorem
[tex]OE² = OX² + XE²OE²[/tex]
[tex](a + b/2)² + (2a - b/√3)²OE² = 7a²/4 + 3ab/2 + b²/4AN²[/tex]
[tex]AE² + EN²AN² = (2a√3)² + (b/2)²AN²[/tex]
[tex]12a² + b²/4MN² = AN² + AM²MN² \\\\ 12a² + b²/4 + (7a²/4 + 3ab/2 + b²/4)MN²\\\\19a²/2 + 3ab/2 + b²/2MN = √(19a²/2 + 3ab/2 + b²/2)[/tex]
So, the length of MN is expressed in terms of a and b.
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listed are 29 ages for academy award winning best actors in order from smallest to largest. 18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77 a. (5pts) find the score at the 20th percentile
The score at the 20th percentile is 27.
To find the score at the 20th percentile of the 29 ages for Academy Award winning best actors, follow the steps below:
Arrange the given ages from smallest to largest.
18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77
Determine the total number of data points
n = 29
Find the rank of the percentile
20th percentile = (20/100) * 29 = 5.8 = 6 (rounded to the nearest whole number).The rank of the percentile is 6.
Use the rank to determine the corresponding data value. The corresponding data value is the value at the 6th position when the data is arranged in ascending order. The score at the 20th percentile is 27.
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calculator may be used to determine the final numeric value, but show all steps in solving without a calculator up to the final calculation. the surface area a and volume v of a spherical balloon are related by the equationA³ - 36πV² where A is in square inches and Vis in cubic inches. If a balloon is being inflated with gas at the rate of 18 cubic inches per second, find the rate at which the surface area of the balloon is increasing at the instant the area is 153.24 square inches and the volume is 178.37 cubic inches.
Answer:
10.309 in²/s
Step-by-step explanation:
Given A³ = 36πV² and V' = 18 in³/s, you want to know A' when A=153.24 in² and V=178.37 in³.
DifferentiationUsing implicit differentiation, we have ...
3A²·A' = 36π·2V·V'
A' = (36π·2)/3·V/A²·V' = 24πV/A²·V'
A' = 24π·(178.37 in²/(153.24 in²)²·18 in³/s
A' ≈ 10.309 in²/s
The surface area is increasing at about 10.309 square inches per second.
__
Additional comment
There are at least a couple of ways a calculator can be used to find the rate of change. The first attachment shows evaluation of the expression we derived above. The second attachment shows the rate of change when the area is expressed as a function of the volume.
The result rounded to 5 significant figures is the same for both approaches.
1. The line segment AB has endpoints A(-5, 3) and B(-1,-5). Find the point that partitions the line segment in
a ratio of 1:3
Answer:
To find the point that partitions the line segment AB in a ratio of 1:3, we can use the following formula:
P = (3B + 1A) / 4
where P is the point that partitions the line segment in a ratio of 1:3, A and B are the endpoints of the line segment, and the coefficients 3 and 1 represent the ratio of the segment we are dividing.
Substituting the values, we get:
P = (3*(-1, -5) + 1*(-5, 3)) / 4
P = (-3, -7)
Therefore, the point that partitions the line segment AB in a ratio of 1:3 is (-3, -7).
Step-by-step explanation:
A barista mixes 12lb of his secret-formula coffee beans with 15lb of another bean that sells for $18 per lb. The resulting mix costs $20 per lb. How much do the barista's secret-formula beans cost per pound?
Answer: $22.50
Step-by-step explanation:
Let x be the cost per pound of the secret-formula coffee beans.
The total cost of the secret-formula beans is 12x dollars.
The total cost of the other beans is 15 × 18 = 270 dollars.
The total cost of the mix is (12 + 15) × 20 = 540 dollars.
Since the barista mixed 12 pounds of the secret-formula beans with 15 pounds of the other beans, the total weight of the mix is 12 + 15 = 27 pounds.
We can set up an equation based on the total cost of the mix:
12x + 270 = 540
Subtracting 270 from both sides:
12x = 270
Dividing both sides by 12:
x = 22.5
Therefore, the barista's secret-formula coffee beans cost $22.50 per pound.
We revisit a probabilistic model for a fault diagnosis problem from an earlier homework. The class variable C represents the health of a disk drive: C = 0 means it is operating normally; and C = 1 means it is in failed state. When the drive is running it continuously monitors itself using temperature and shock sensor, and records two binary features, X and Y. X =lif the drive has been subject to shock (e.g;, dropped) , and X = 0 otherwise Y =1if the drive temperature has ever been above 70*C, and Y = 0 otherwise. The following table defines the joint probability mass function of these three random variables: pxyc(r,y, c) 0.1 0.2 0.2 0 0 0 0 0 0 0.05 0.25
The probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.
The given table represents the joint probability mass function of the random variables, pxyc (r, y, c). r, y, and c denote the temperature, shock sensor, and health status of the disk drive. The values of r, y, and c are binary.The joint probability mass function of three random variables r, y, and c can be represented as follows:pxyc (r, y, c)= P(r, y, c)Here,P(r=0, y=0, c=0)= 0.1, P(r=0, y=1, c=0)= 0.2, P(r=1, y=0, c=0)= 0.2,P(r=0, y=0, c=1)= 0, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0,P(r=0, y=0, c=0)= 0, P(r=0, y=1, c=0)= 0, P(r=1, y=1, c=0)= 0.05,P(r=0, y=0, c=1)= 0.25, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0.From the given table, the probability of the disk drive being in a normal state, C=0, is P(C=0)=P(r=0, y=0, c=0)+P(r=0, y=1, c=0)+P(r=1, y=0, c=0)=0.1+0.2+0.2=0.5Hence, the probability of the disk drive being in a failed state, C=1, is:P(C=1)=P(r=0, y=0, c=1)+P(r=0, y=1, c=1)+P(r=1, y=0, c=1)+P(r=1, y=1, c=0)=0.25+0+0+0.05=0.3Therefore, the probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.
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For triangles ABC and DEF, ∠A ≅ ∠D and B ≅ ∠E. Based on this information, which statement is a reasonable conclusion?
a. ∠C ≅ ∠D because they are corresponding angles of congruent triangles.
b. CA ≅ FD because they are corresponding parts of congruent triangles.
c. ∠C ≅ ∠F because they are corresponding angles of similar triangles.
d. AB ≅ DE because they are corresponding parts of similar triangles.
the triangles are similar, corresponding parts of the triangles are equal in measure. Thus, it is reasonable to conclude that [tex]AB ≅ DE.[/tex]
It is reasonable to conclude that [tex]AB ≅ DE[/tex]because triangles ABC and DEF are similar.
This means that corresponding parts of the two triangles are equal in measure. Specifically, ∠A and ∠D are equal in measure, as are ∠B and ∠E.
Therefore, the corresponding sides AB and DE are equal in measure.
A way to show that the two triangles are similar is by using the AA Similarity Postulate.
This postulate states that if two angles of one triangle are equal in measure to two angles of a second triangle, then the two triangles are similar. In this case, [tex]∠A ≅ ∠D and B ≅ ∠E[/tex], which means the two triangles are similar.
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Remove brackets of 3(2a+5b)
ABCD is a quadrilateral A) Calculate the value of x. B) When ABCD is drawn to scale, would the lines AD and BC be parallel or not? You must justify your answer without using a scale drawing
A) The value of x = 45 degrees
B) Lines AD and BC are not parallel when ABCD is drawn to scale.
To solve this problem, we can use the fact that the sum of the angles in a quadrilateral is 360 degrees.
A) angle A + angle B + angle C + angle D = 360
2x + 90 + x + 3x = 360
6x + 90 = 360
6x = 270
x = 45
Therefore, x = 45 degrees.
B) To determine if lines AD and BC are parallel, we can look at the opposite angles of the quadrilateral. If they are supplementary (add up to 180 degrees), then the lines are parallel.
angle A + angle C = 2x + x = 3x = 135 degrees
angle B + angle D = 90 + 3x = 90 + 135 = 225 degrees
Since angle A + angle C and angle B + angle D do not add up to 180 degrees, the opposite angles are not supplementary, and therefore, lines AD and BC are not parallel.
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The given question is incomplete, the complete question is:
ABCD is a quadrilateral A) Calculate the value of x. B) When ABCD is drawn to scale, would the lines AD and BC be parallel or not?
Gary's backpack weighs 1.2 pounds. His math textbook weighs 3.75 pounds, and his science textbook weighs 2.85 pounds. How much will his backpack weigh with the math and science textbooks in it?
Answer:
To find out how much Gary's backpack will weigh with the math and science textbooks in it, we need to add the weight of the textbooks to the weight of the backpack:
Total weight = backpack weight + math textbook weight + science textbook weight
Total weight = 1.2 + 3.75 + 2.85
Total weight = 7.8 pounds
Therefore, Gary's backpack will weigh 7.8 pounds with the math and science textbooks in it.
Answer: His backpack will weigh 7.8 pounds
Step-by-step explanation:
Gary's backpack already weights 1.2 pounds without the science and math textbook, now we add the weights of both the math and science textbook.
1.2 + 3.75 = 4.95
4.95 is the weight with only his math textbook in his bag
now we add the science textbooks weight to 4.95
4.95 + 2.85 = 7.8
7.8 is the weight of his backpack with both his science and math textbook in his bag
In an introductory psychology class with n = 50 students, there are 9 freshman males, 15 freshman females, 8 sophomore males, 12 sophomore females, and 6 junior females. A random sample of n = 2 students is selected from the class. If the first student in the sample is a male, what is the probability that the second student will also be a male?
a. 8/14
b. 12/20
c. 20/44
d. 20/50
Answer: Total number of males= C
Step-by-step explanation:
1 point) Consider the linear system -3-21→ a. Find the eigenvalues and eigenvectors for the coefficient matrix. 0 and 42 b. Find the real-valued solution to the initial value problem yj 5y1 +3y2, y2(0) = 15. = Use t as the independent variable in your answers. y (t) = y(t) =
(a) The eigenvalues of the coefficient matrix is [-1,3] and for λ=42, we get the eigenvector [1,5].
Itcan be found by solving the characteristic equation |A-λI|=0, where A is the coefficient matrix and λ is the eigenvalue. Solving for λ, we get λ=0 and λ=42.
o find the eigenvectors, we substitute each eigenvalue into the equation (A-λI)x=0 and solve for x. For λ=0, we get the eigenvector [-1,3]. For λ=42, we get the eigenvector [1,5].
(b) The solution is y(t) = c1e^(0t)[-1,3] + c2e^(42t)[1,5].
To find the real-valued solution to the initial value problem, we can use the eigenvectors and eigenvalues to diagonalize the coefficient matrix. We have A = PDP^-1, where P is the matrix whose columns are the eigenvectors and D is the diagonal matrix with the eigenvalues on the diagonal.
Using the initial condition y2(0) = 15, we can solve for the constants c1 and c2.
The solution is y(t) = c1e^(0t)[-1,3] + c2e^(42t)[1,5]. Solving for c1 and c2 using the initial condition, we get
y(t) = [-15e^(42t) + 3e^(0t), 15e^(42t) + 5e^(0t)].
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consider using a z test to test h0: p 5 .6. determine the p-value in each of the following situations. a. ha:p..6,z51.47 b. ha:p,.6,z522.70 c. ha:p?.6,z522.70 d. ha:p,.6,z5.25
a) P-value = P(z<1.47) = 0.9292.
b) P-value = P(z>2.70) = 0.0036.
c) P-value = 2 × P(z>2.70) = 0.0072.
d) P-value = P(z>2.5) = 0.0062.
Z-test is a statistical test for the null hypothesis, which refers to the population mean, where the population standard deviation is known. P-value represents the probability value for any hypothesis, where a small p-value indicates that the null hypothesis is less accurate.
P-value, for the given values of z-test is calculated as follows: a) For ha: p < .6, z=1.47The p-value for this hypothesis test is calculated as follows: P-value = P(z<1.47) = 0.9292. Therefore, the P-value is 0.9292. b) For ha: p > .6, z=2.70The p-value for this hypothesis test is calculated as follows.
P-value = P(z>2.70) = 0.0036. Therefore, the P-value is 0.0036.c) For ha: p ≠ .6, z=2.70The p-value for this hypothesis test is calculated as follows: P-value = 2 × P(z>2.70) = 0.0072.
Therefore, the P-value is 0.0072.d) For ha: p > .6, z=2.5The p-value for this hypothesis test is calculated as follows: P-value = P(z>2.5) = 0.0062. Therefore, the P-value is 0.0062.
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