The measures of the angles formed by the parallel lines and their common transversal are;
Part A; B. c is equal to b
Part B; c = 60°
Second part; Angle P is 80°
Third part; The missing reason in step 3 is the option D.
Fourth part; Angle B is 72°
What are parallel lines?Parallel lines are lines in the same plane that have the same slope. The perpendicular distance between parallel is constant, such that they do not meet.
D. Vertical angles are congruent
Fourth part; Angle B is
Part A; JK is parallel to LM
Angle ∠c and angle ∠b are corresponding angles, therefore;
∠c and ∠b are congruent
∠c = ∠b
Therefore;
B. c is equal to b
Part B
Angle ∠b and 2·∠b are linear pair angles
Linear pair angles are supplementary, therefore
∠b + 2·∠b = 180°
3·∠b = 180°
∠b = 180°/3 = 60°
∠b = 60°
∠c = ∠b = 60°
B. c = 60°
Second part;
Angle P and the vertical angle to the 100° angle are same side interior angles.
Vertical angles are congruent, therefore;
Angle P and 100° are same side interior angles
Same side interior angles are supplementary, therefore;
m∠P + 100° = 180°
m∠P = 180° - 100° = 80°
Third part;
Angle ∠2 and angle ∠3 are formed by the transversal t and w, therefore, they are vertical angles
Vertical angles theorem states that two sets of linear pair angles, that have congruent angles are formed from the intersection of two lines.
Therefore:
∠2 ≅ ∠3, reason: D. Vertical angles are congruent
Fourth part;
Line A is parallel to line B
The angles, 4·m -24, and 3·m are corresponding angles
Corresponding lines formed by the transversal and two parallel lines are congruent, therefore;
4·m - 24 = 3·m
4·m - 3·m = 24
m = 24 degrees
Taking angle ∠B as the angle formed at the intersection of line B and the transversal, 4·m - 24 we get;
∠B = 4·m - 24
∠B = 4 × 24 = 72°
Angle ∠B = 72°
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Trinagle ABC has vertices at A(0,5), B(-3,3), and C(0,-5) Classify the triangle according to the side lengths
The classification of the triangle according to its side lengths and vertices would be scalene triangle.
How to classify the triangle?To classify the triangle, you first need to find the lengths of the sides of the triangle. You can do this by finding the distance between the vertices given.
To find the vertices, the formula is:
= √ ( ( x₂ - x₁ ) ² + ( y ₂ - y ₁) ² )
The length of AB is therefore 3.61 units
The length of BC is 8.54 units
The length of AC is 10 units.
None of the side lengths of this triangle are the same so it is a scalene triangle.
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Which statements are true about box plots? Check all that apply.
They help describe sets of data.
They include the mean.
They show the data split into four parts.
They show outliers through really short “whiskers.”
Each section of a box plot represents 25% of the data.
Merry Christmas!
The true statements are they help describe sets of data, they show the data split into four parts and each section of a box plot represents 25% of the data.
What is the box-and-whisker plot?A box and whisker plot displays a "box" with its left edge at Q₁, right edge at Q₃, "center" at Q₂ (the median), and "whiskers" at the maximum and minimum.
The box plot is also called box-and-whisker plot.
The data is divided into sections by box plots, with each section containing around 25% of the total data.
Box plots are useful as:
They offer a visual overview of the data,
making it simple for researchers to spot skewness,
the dispersion of the data set.
The minimum value, first quartile, median, third quartile, and maximum value are the five values that make up a box plot.
And they don't include mean.
From the above discussion,
we have three statements that are true and those statements are;
they help describe sets of data, they show the data split into four parts and each section of a box plot represents 25% of the data.
Therefore, the correct statements are A, C and E.
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Amanda is spreading new grass seed on her yard. The area of her yard is 4,995 square feet. The instructions on the bags of grass seed say that one bag of seed should be used for every 100 square yards. How many bags of grass seed should Amanda use?
Group of answer choices
The number of bags of grass seed that Amanda should use to spread her yard is 16.65 bags, meaning she needs to buy not more than 17 bags, using mathematical operations.
What are mathematical operations?The basic mathematical operations we use are subtraction, addition, division, and multiplication.
In this situation, we use the division operation.
The division operation involves four parts:
The dividend (numerator or the number being divided).The divisor (denominator or the number dividing).The quotient (the result of the division operation).The equal symbol (that shows that two values are equal).The area of the yard = 4,995 ft²
1 yard = 3 feet
Area of the yard = 1,665 square yards(4,995/3)
The number of bags per 100 square yards = 1 bag
For 1,665 square, the number of bags = 16.65 bags (1,665 ÷ 100)
Thus, Amanda requires 16.65 bags of the grass seed for her yard.
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stirling's approximation is an incredibly accurate approximation of factorials using a continuous and differentiable function.
In mathematics, Stirling's approximation (or Stirling's formula) is a factorial approximation. A good approximation that gives accurate results even for small values of n. It is named after James Stirling and was first given by Abraham de Moivre, although relevant but less accurate.
Factorial is one of thein mathematics. It is also an important mathematical concept ubiquitous concepts used in data science. Factors are used to model probability distributions in Poisson processes. The probability mass function of the Poisson distribution has a factorial formula in the denominator. You can't find the probability of a Poisson random variable without a way to compute the factorial.
Factorials are also related to combinatorics. For example, hmm! is the number of permutations of n unique objects. From the point of view of statistical mechanics, entropy is defined as a combinatorial problem. Entropy also has its own definition in information theory. Comparing the two alternative definitions, they are identical.
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Please tell me ALL the partial products of 3.4 times 1.2
Answer:
34
× 12
---------
8
60
40
+ 300
----------
= 408
5 Barb has 8 white balls, Tom has 3 white balls and 9 blue balls, Clare has 2 green balls and 1 blue ball. How many blue balls do Barb, Tom
and Clare have?
1 blue ball
O9 blue balls
7 blue balls
10 blue balls
Skip
4/6 complete
a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5. in the last year for standard deviation seems to have changed she bases this on a random sample of 25 students whose final exam had a mean a 80 with a standard deviation of 4.2 test the professor's claim that the current mean is different from 82.4. use a equals 0.05 Assume that o is known to be 6.5
Express the claim in symbolic form. Express the claim in symbolic form. Group of answer choices A )σ > 6.5 B) σ = 6.5 C) σ < 6.5 D) σ ≠ 6.5 E) σ ≥ 6.5 F) σ ≤ 6.5 28) What is the alternative hypothesis, H1? Group of answer choices A) σ < 6.5 B) σ ≤ 6.5 C) σ ≠ 6.5 D) σ = 6.5 E) σ > 6.5 F) σ ≥ 6.5 29) Find the critical value(s). (Round to the nearest thousandth. If more than one value is found, enter the smallest critical value.) 30) Find the value of the test statistic. (Round to the nearest ten-thousandth.) 31) What is the statistical conclusion? Group of answer choices A)Fail to reject H0 B) Reject H0 32) State the conclusion in words. Group of answer choices A) There is not sufficient sample evidence to support the claim that the current standard deviation is different from 6.5 . B) The sample data support the claim that the current standard deviation is different from 6.5 . C) There is not sufficient evidence to warrant rejection of the claim that the current standard deviation is different from 6.5 . D) There is sufficient evidence to warrant rejection of the claim that the current standard deviation is different from 6.5 .
The value of the standard deviation does not change and remains the same.
Given, a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5.
The mean μ = 82.4
The standard deviation σ = √[ ((x - μ)2 + (y - μ)2 + (z - μ)2)/3 ]
we have to find the variance,
We now add a constant k to each data value and calculate the new mean μ'.
μ' = ((x + k) + (y + k) + (z + k)) / 3 = (x + y + z) / 3 + 3k/3 = μ + k
We now calculate the new mean standard deviation σ'.
σ' = √[ ((x + k - μ')2 +(y + k - μ')2+(z + k - μ')2)/3 ]
Note that x + k - μ' = x + k - μ - k = x - μ
also y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ
Therefore σ' = √[ ((x - μ)2 +(y - μ)2+(z - μ)2)/3 ] = σ
If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. The standard deviation does not change.
Hence, the standard deviation does not change.
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If a number is added to the numerator of 1/7 and twice the number is subtracted from the denominator, the result is 4. Find the number.
Answer:
2
Step-by-step explanation:
Determine if x and y are inversely proportional. If applicable, find the constant of variation.
The relationship between x and y is and the constant of variation is 24.
What is inversely proportional?
One kind of proportionality relationship is inverse proportion. If two quantities are inversely related, one will increase while the other will decrease. Building a wall would be an example of an inverse proportion in action.
Given that x and y are inversely proportion.
Assume that the relationship between x and y is
y = k/x where k is constant of variation.
Putting x = 3 and y = 8 in y = k/x :
8 = k/3
Multiply both sides by 3:
k = 8 × 3
k = 24
Putting x = 4 and y = 6 in y = k/x :
6 = k/4
Multiply both sides by 4:
k = 6 × 4
k = 24
The relationship is y = 24/x and the constant of variation is 24.
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Answer:
x and y are not inversely proportional.
Image:
a researcher wants to discover if age has any influence on how many hours a person spends doing/reading/answering emails in a week. they collect the following data, where there are 2 categories of age and the number of hours per week someone spends on email: 36 and under
over 36
28
0
4
2
2
0
25
1
15
5
3
2
15
4
20
8
10
5
1
10
What is the t statistic?
From given data we can conclude that there is no influence of age on how many hours a person spends doing/reading/answering emails in a week.
In this question, the given data has 2 categories of age and the number of hours per week someone spends on email.
Let H0(null hypothesis): age has any influence on how many hours a person spends doing/reading/answering emails in a week.
Ha = age has no influence on how many hours a person spends doing/reading/answering emails in a week.
36 and under over 36 x - y (x - y)²
28 0 28 784
4 2 2 4
2 0 2 4
25 1 24 576
15 5 10 200
3 2 1 1
15 4 11 121
20 8 12 144
10 5 5 25
1 10 -9 81
Total : 86 1940
Using the formula for t-score:
t = (∑D / N)/[√(∑D² - (∑D)²/N)/(N-1)N]
where
∑D = sum of differences
∑D² = sum of squared differences
(∑D)² = square of sum of differences
t = (86 / 10)/[√(1940 - 7396/10)/(10-1)10]
t = 8.6/√((1940 - 739.6)/90)
t = 8.6 /√(1200.4/90)
t = 8.6 /√13.34
t = 2.35
The p-value with degree of freedom = 9 and alpha-level = 0.05 is 0.021653
Since calculated value is greater than the p-value, we reject the null hypothesis.
Therefore, age has no influence on how many hours a person spends doing/reading/answering emails in a week.
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Let's say you keep 2 capybaras as pets. Every Monday, you adopt 1 capybara. Every Friday, you multiply the capybaras by the amount you had over 2. (If it's an odd number you own, divide it so it's as close as possible to one half).
Starting on Monday (Before you adopted), how many capybaras will you own after 14 days? (Including the 14th day)
The number of capybaras that you will get after 14 days is given as follows:
3 capybaras.
How to obtain the number after 14 days?Initially, the number of capybaras that you have is given as follows:
2 capybaras.
The pattern is then given as follows:
Every Monday: Adopt 1 capybara.Every Friday: Halve the amount of capybaras that you had.The time composed by 14 days is of 2 weeks, then the procedure will finish on the Monday 2 weeks from now.
The number of capybaras in that Monday than can be calculated step by step as follows:
First Monday: 2 + 1 = 3 capybaras.Friday: 3/2 = 1.5 = 2 capybaras, rounding up.7 days after: 2 + 1 = 3 capybaras.Friday: 3/2 = 1.5 = 2 capybaras, rounding up.Monday 14 days after: 2 + 1 = 3 capybaras.More can be learned about patterns at https://brainly.com/question/17386984
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a chain of sport shops catering to beginning skiers, headquartered in aspen, colorado, plans to conduct a study of how much a beginning skier spends on his or her initial purchase of equipment and supplies. based on these figures, it wants to explore the possibility of offering combinations, such as a pair of boots and a pair of skis, to induce customers to buy more. a sample of 44 cash register receipts revealed these initial purchases: $ 180 $ 186 $ 130 $ 263 $ 258 $ 159 $ 127 $ 84 $ 208 180 104 233 92 223 176 216 219 209 205 150 241 110 239 124 173 174 264 232 182 261 216 193 196 223 239 176 261 150 245 84 232 152 95 233 click here for the excel data file required: a. arrive at a suggested class interval. (round your answer up to the next multiple of 5.) b. organize the data into a frequency distribution using a lower limit of $70.
(a) Class interval of a given data is 36.
(b) Frequency distribution is 44.
We have given that,
total frequency = 44
lower limit = $70
number of class = 5
(a) we have to find class interval,
Class interval = [tex]\frac{Max. number - min. number}{no. of classes}[/tex]
here maximum number is 264 and minimum number is 84
Class interval = [tex]\frac{264 - 84}{5}[/tex]
= [tex]\frac{180}{5}[/tex]
Class interval = 36
we have to round our value to the next multiple of 5
so the class interval will be 40.
(b) A frequency distribution is the pattern of frequencies of a variable. It is the number of times each possible value of a variable occurs in a dataset. There are three types of frequency distribution such as Cumulative frequency distribution, Relative frequency distribution, Relative cumulative frequency distribution.
The frequency distribution is as follows:
Class interval Frequency
70 - 110 6
111 - 151 5
152 - 192 10
193 - 233 14
234 - 274 9
Total 44
This is the organize data into a frequency distribution.
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Let a, b, and c be real numbers where a b c 0. Which of the following functions could represent the graph below?
Answer:
[tex]f(x)=x^2(x-a)^2(x-b)^4(x-c)[/tex]
Step-by-step explanation:
There is a double root at [tex]x=0[/tex], which corresponds to [tex]x[/tex] raised to an even power.
There are also 2 more double roots and one more single root. This corresponds to two factors raised to an even power and one factoe raised to an odd power.
The only option that satisfies this is Option 1.
The graphical representation of the polynomial function is given by the relation f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the polynomial equation be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )
The factors (x - a), (x - b), and (x - c) indicate that the function has roots at x = a, x = b, and x = c. These roots are of multiplicity 2, 4, and 1 respectively, which means that they are repeated in the factors (x - a)², (x - b)⁴, and (x - c), respectively.
The factor x² indicates that the graph of the function opens upward, since the leading coefficient is positive.
Overall, the graph of this function will have eight "humps" or "bumps" corresponding to its eight roots, and the heights and shapes of these bumps will depend on the values of a, b, and c.
Hence , the graph of the function is plotted
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Find the Slope:
A. 2
B. -2
C. 1/2
D. -1/2
I need help with this please help me
Find the area of the triangle. [?] units² Round to the nearest hundredth.
The area of the triangle is 48 square units.
To calculate the length of each side of the triangle ACB, the radii of the circles should be added respectively.
Length of side BC = 9+3 = 12 units
Length of side CA = 3+5 = 8 units
Length of side BA = 9+5 = 14 units
Area of triangle = (1/2 × Base × Height) square units
Area of triangle ACB = 1/2 × CA× BC sq units
Area = 1/2 × 8 × 12 = 48 sq units
Hence, the area of triangle ACB is 48 square units.
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Answer:
47.91 units²
Step-by-step explanation:
The radius of each circle is:
Circle A: radius = 5Circle B: radius = 9Circle C: radius = 3Therefore, the side lengths of the triangle are:
AB = 5 + 9 = 14BC = 9 + 3 = 12AC = 3 + 5 = 8Heron's Formula allows us to find the area of a triangle in terms of its side lengths.
[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]
The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, half the perimeter of the triangle is:
[tex]\implies s=\dfrac{14+12+8}{2}=17[/tex]
To calculate the area of the triangle, substitute the sides lengths and the value of s into Heron's formula and solve for A:
[tex]\implies A=\sqrt{17(17-14)(17-12)(17-8)}[/tex]
[tex]\implies A=\sqrt{17(3)(5)(9)}[/tex]
[tex]\implies A=\sqrt{2295}[/tex]
[tex]\implies A=47.906158268...[/tex]
[tex]\implies A=47.91\; \sf units^2\;\;(nearest\;hundredth)[/tex]
derive the transfer function for the integrator of (figure 1). express your answer in terms of frequency f and imaginary unit j . express the coefficients using three significant figures. a(f)
The transfer function for the given integrator circuit in terms of frequency,f and imaginary unit,j is expressed as [tex]T(f)=-j0.00628f[/tex]
The figure of the integrator is shown at bottom of the answer.
The transfer function of an integrator can be expressed in form of impedances of the circuit elements connected to the op-amp.
Assume the impedance at the input side be [tex]Z_1[/tex] and impedance of the feedback be [tex]Z_2[/tex]
We can observe that at input, in consists of capacitor with capacitance,C [tex]= 0.1\mu F=10^{-7}F[/tex]
and at the feedback loop, the circuit element is a resistor with resistance,R [tex]= 10k\Omega = 10^4 \Omega[/tex]
Now,
the transfer function for an integrator can be written as ,
[tex]T(f) = -\frac{Z_2}{Z_1}[/tex]
We know that,
impedance of capacitor is [tex]Z_1=\frac{1}{j\omega C}=\frac{1}{j2\pi f C}[/tex]
impedance of resistor is [tex]Z_2=R[/tex]
Now,
[tex]T(f)=-\frac{R}{\frac{1}{j2\pi fC}}\\\\T(f)=-R*j2\pi f C\\\\T(f)=-j10^4*2\pi f 10^{-7}\\\\T(f)=-j0.00628f[/tex]
Hence, the transfer function is [tex]T(f)=-j0.00628f[/tex]
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How much would Howard Steele need to invest today so that he may withdraw $12,000 each year for the next 20 years, assuming a rate of 8% compounded annually?
Multiple Choice
$117,817.77
$454,144.00
$112,817.20
$549,144
Howard Steele needs to invest $117,817.77 today so that he may withdraw $12,000 each year for the next 20 years
What are simple and compound interests?Simple interest is often a predetermined percentage of the principal amount borrowed or lent paid or received over a specific time period.
Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the equation, [tex]P = \frac{A\times(1-(1+r)^{-n}}{r}[/tex] the annuity, and the present value of money, P, can be connected.
P = 12000, r = 0.08 and n = 20.
∴ [tex]12000 = \frac{A\times(1-(1.08)^{-20}}{0.08}[/tex].
A = $117,817.77.
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One of the 55 students are selected at random.written as a fraction what is the probability
If one of the 55 students is selected at random, the probability of this occurring can be written as a fraction by dividing the number of selected students by the total number of students. In this case, the probability would be 1/55.
if x= -1 is a root of x3+3x2-x-3=0 use synthetic division to factor the polynomial completely
The factors of the polynomial x³+3x²-x-3 are (x+1)(x-1)(x+3).
What are factors?A factor is a number that divides another number, leaving no remainder.
Given is a polynomial, x³+3x²-x-3
x = -1 is the root of the polynomial, which it will completely divide the polynomial x³+3x²-x-3,
On dividing, we get,
(x³+3x²-x-3)÷(x+1) = (x²+2x-3)
Factorizing, (x²+2x-3), we get,
(x-1)(x+3)
Hence, The factors of the polynomial x³+3x²-x-3 are (x+1)(x-1)(x+3).
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30/4+5•3-9
help me please!! ;)
Answer:
30/4+5•3-9
= 7.5+15-9
= 22.5-9
= 13.5
Step-by-step explanation:
the point (-4,-6,10) lies on the surface of a sphere with centre (2,3,-1). hence find the volume of the sphere
The radius of the sphere with the given point and the center is √238.
Here we have to find the radius of the sphere.
Given data:
The point on the surface of a sphere is (-4, -6, 10) and the point on the center is (2, 3, -1).
The formula for the radius:
r² = (x2 - x1)² + (y2 - y1)² + (z2 - z1)²
where (x1, y1, z1) = point on the center
(x2, y2, z2) = point on the sphere
Now putting the values we have
r² = (-4-2)² + ( -6-3)² + ( 10 +1)²
=( -6)² +(- 9)² + (11)²
= 36 + 81 + 121
= 238
r = √238.
Therefore the radius is √ 238.
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Let A be set of all prime numbers, B be the set of all even prime numbers, C be the set of all odd prime numbers, then which of the following is true? a) A = BUC b) B is a singleton set. c) A = CU{2} d) All of the mentioned
After analyzing the given data we will get to know that all the options mentioned above are true.
A = BUC, B is a singleton set, and A = CU2 if A is the set of all prime numbers, B is the set of all even prime numbers, and C is the set of all odd prime numbers. Therefore, option D - All of the specified - is the answer to this question.
We've got
The entire set of prime numbers is A.
A = {2, 3, 5, 7, 11, 13}
B is a collection of even prime numbers.
B = {2}
C is a collection of all odd prime numbers.
C = {3, 5, 7, 11, 13,}
We are aware that the only even prime number is two. As a result, Set B is a singleton set because it only has one element.
Additionally, if we combine sets B and C, we will obtain set A, which contains all prime numbers.
Thus, we obtain A = B U C.
Since B = 2 is a singleton set, if we have A = B U C, we can also say A = C U 2.
Therefore, each of the aforementioned choices is appropriate.
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Write an equation of the line that passes through (-1, 8) and is parallel to the line y = 6.
The equation of the line parallel to y = 6 and passing through (-1, 8) is y = 8.
What is slope?The slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Given that, an equation of the line that passes through (-1, 8) and is parallel to the line y = 6.
Slope of the parallel lines are equal to each other, therefore, solving for c,
8 = -1x0 + c
c = 8
Hence, The equation of the line parallel to y = 6 and passing through (-1, 8) is y = 8.
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Allison had a birthday on Saturday she set up six tables and had 5 friends sitting at each table. How many people were at Allison’s birthday?
Answer:
there was 30 people at her birthday party
dy is perpendicular to ac, xf is perpendicular to bc, ze is perpendicular to ab. prove triangle abc is similar to triangle yzx
Triangle ABC and triangle XYZ are congruent thus ∆ABC and XYZ are similar
What are similar trianglesSimilar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects.
if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
line DY bisects AC and line ZE bisects line AB.
Therefore line AD is congruent to line AE and line CD is congruent to line EB.
therefore AB = CD and similar XY = YZ
therefore ∆ABC and ∆XYZ are similar
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what was the mistake that was made?
Answer: they didnt distribute the 7 to the 4.5
Step-by-step explanation:
when distributing something outside of a parenthesis, you have to distribute it to all terms within the parenthesis, not just the variable
when vector vector a is added to vector vector b, the resultant is a vector vector r such that vector r is equal to vector a plus vector b. this resultant vector has component rx
a. When vector is added to vector , the resultant is vector such that its magnitude and direction is proportional to the resultant magnitude and direction of the component vectors.
b. ∅ = (Rx/Ry)
Vectors are used to represent physical quantities in terms of magnitude and direction. Vectors can be added using the parallelogram method or the triangle addition method. The magnitude and direction of the resulting vector are generally proportional to the magnitude and direction of the component vectors.
I have every vector in 2D that has both vertical and horizontal components.
There are vectors say: A = xi + yj
and, B =zi + wj
For example, adding two vectors gives the result
R = (x +z)i + (y + w) j.
The - component has y +w as z and the y component as w. The sum has the horizontal component as x + z and the vertical component as y + w. So we get the y component of the resulting vector R = A+ y component of B
The direction of the angle is found as
tan∅ = Rx/Ry
∅ = (Rx/Ry)
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The diagonals of an isosceles trapezoid are congruent. TRUE or FALSE
Answer: True.
Because the trapezoid is isosceles, the base angles are congruent by default.
Given isosceles trapezoid ABCD
Sides AB and DC are congruent
By the SAS postulate, triangles ABC and DCB are congruent
Therefore, segment AC is congruent to segment DB
6 suppose a die is tossed 1000 times, and the following frequencies are obtained for the number of pips up when the die comes to a rest. x1 x2 x3 x4 x5 x6 163 178 142 150 183 184 using the chi-squared goodness of fit test, assess whether we have evidence that this is not a symmetrical die. record the standardized residuals
We have evidence that this is not a symmetrical die the standardized residuals is 9.5699.
Given that,
The following frequencies are found for the number of pips up when the die comes to rest, assuming a die is tossed 1000 times. Find out if there is proof that this die is not symmetrical using the chi-squared goodness of fit test. The standardized residuals should be noted.
x₁ x₂ x₃ x₄ x₅ x₆
163 178 142 150 183 184
We know that,
observed expected Op-Ep (Op-Ep)²/Ep
x₁ 163 166.7 -3.7 0.082
x₂ 178 166.7 11.3 0.7659
x₃ 142 166.7 -24.7 3.6598
x₄ 150 166.7 -16.7 1.673
x₅ 183 166.7 16.3 1.5938
x₆ 184 166.7 17.3 1.7954
-----------
9.5699
Expected = 1/nΣXa=1/6(1000)=166.7
Therefore, We have evidence that this is not a symmetrical die the standardized residuals is 9.5699.
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