Step-by-step explanation:
When two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. This means that their measures add up to 180 degrees.
In this case, the two interior angles on the same side of the transversal 't' are (2x-8) degrees and (3x-7) degrees. Since these angles are supplementary, we can write the equation (2x-8) + (3x-7) = 180.
Solving this equation for x, we get:
(2x-8) + (3x-7) = 180
5x - 15 = 180
5x = 195
x = 39
Substituting this value of x into the expressions for the two interior angles, we find that their measures are:
(2x-8) = (2*39 - 8) = 70 degrees
(3x-7) = (3*39 - 7) = 110 degrees
So, the measure of each of these angles is 70 degrees and 110 degrees.
Let C[0, 1] have the inner product (f. g) = integral (0,1) f(x)g(x) dx. For u = x and v= x + 1 find the following: a) ||f|| b) llgll c) (f.g) d) Find the angle between u and v.
(a) The norm of the function u = x is ||u|| = √(1/3). (b) The norm of the function v = x + 1 is ||v|| = √(11/3). (c) The inner product of functions f and g is (f, g) = integral from 0 to 1 of f(x)g(x) dx. (d) The angle between u = x and v = x + 1 is arccos(-1/3).
(a) To find the norm of the function u = x, we calculate ||u|| = √((u, u)). Using the given inner product, we have ||u|| = sqrt(integral from 0 to 1 of x² dx) = √(1/3).
(b) To find the norm of the function v = x + 1, we calculate ||v|| = √((v, v)). Using the given inner product, we have ||v|| = sqrt(integral from 0 to 1 of (x + 1)² dx) = √(11/3).
(c) The inner product of functions f and g is given by (f, g) = integral from 0 to 1 of f(x)g(x) dx. The specific functions f and g are not provided in the question, so we cannot determine their inner product without additional information.
(d) The angle between two functions u = x and v = x + 1 can be found using the formula cos(∅) = (u, v) / (||u|| ||v||), where theta is the angle between u and v. Substituting the given values, we have cos(∅) = (integral from 0 to 1 of x(x + 1) dx) / (√(1/3) √(11/3)). Evaluating the integral and simplifying, we find cos(∅) = -1/3. Taking the inverse cosine, we obtain ∅ = arccos(-1/3).
Therefore, the norm of the function u = x is √(1/3), the norm of the function v = x + 1 is √(11/3), the inner product (f, g) cannot be determined without the specific functions f and g, and the angle between u = x and v = x + 1 is arccos(-1/3).
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Rasheed is getting dressed in the dark. He reaches into his sock drawer to get a pair of socks. He knows that his sock drawer contains six pairs of socks, and each pair is a different color. Each pair of socks is folded together. The pairs of socks in the drawer are red, brown, green, white, black, and blue.
A. How many possible outcomes are there in the experiment?
B. What are the possible outcomes of the experiment?
C. List the sample space for the experiment.
D. Calculate P(blue).
E. Calculate P(not purple)
Answer:
Part A: There are 6 possible outcomes of this experiment.
Part B: There are 6 possible outcomes of the experiment ; red, brown, green, white, black, and blue ( equal)
Part C:
Sample Space = { red, brown, green, white, black, blue }
Part D:
P (blue)= 1/6
Part E:
P (not purple)= 1
Step-by-step explanation:
Part A:
There are 6 possible outcomes of this experiment.
As there are 6 pairs of socks. Each pair is folded together so that the socks cannot be mixed up . There is 1 chance of choosing each pair of socks.
Part B:
The chosen socks can be any of the following red, brown, green, white, black, and blue so there are 6 possible outcomes of the experiment ; red, brown, green, white, black, and blue (all have equal probability) .
Part C:
The sample space contains all the possible outcomes of the event.
Sample Space = { red, brown, green, white, black, blue }
Part D:
P(blue)= No of favorable outcomes/ Total no of outcomes
P (blue)= 1/6
Part E:
P (not purple)= 1
As the total probability is always equal to 1 and we want to find the probability of the color which is not given in the list
P( purple) = 0/6= 0
And the probability of not purple is given by the formula
P (not purple) = 1- P (purple)
= 1-0= 1
1 indicates that the event of any other color except purple must occur which is equal to the probability of not purple.
This can be solved by complement rule also.
Solve the inequality -5(x - 1) > -40, and graph the solution on a number line.
Answer:
x<9
Step-by-step explanation:
-5(x-1)>-40
x-1>-40/-5
x-1>8
x>8+1
x>9
x<9
The solution of the inequality - 5(x - 1) > -40 will be;
⇒ x < 9
And, The solution of the inequality is shown in number line.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ - 5(x - 1) > -40
Now,
Solve the inequality as;
The inequality is,
⇒ - 5(x - 1) > -40
⇒ - (5x - 5) > - 40
⇒ 5x - 5 < 40
Add 5 both side,
⇒ 5x - 5 + 5 < 40 + 5
⇒ 5x < 45
Divide by 5, we get;
⇒ x < 9
Thus, The solution of the inequality - 5(x - 1) > -40 will be;
⇒ x < 9
And, The solution of the inequality is shown in number line.
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Calculate the flux of the vector field (³, ³), out of the annular region between the x² + y² = 9 and x² + y² = 16.
Given that the vector field F is (3x, 3y) and the region is an annular region between the circles x² + y² = 9 and x² + y² = 16,To calculate the flux of the vector field, we use the formula: flux = ∬F · dS, Where F is the vector field and dS is an elemental vector area.
Using cylindrical coordinates: For the outer circle x² + y² = 16, the limits of θ are from 0 to 2π and the limits of r are from 4 to 4√2. For the inner circle x² + y² = 9, the limits of θ are from 0 to 2π and the limits of r are from 3 to 3√2.The vector normal to the surface at a point (r,θ) is given by n = (cosθ, sinθ, 0).
Hence, the outward normal vector is given by n = (cosθ, sinθ, 0) and the elemental vector area is given by dS = r dr dθ.Therefore, we have, flux = ∬F · dS= ∫_3^3√2 ∫_0^2π (3r cosθ, 3r sinθ) · (r cosθ, r sinθ, 0) r dr dθ+ ∫_4^4√2 ∫_0^2π (3r cosθ, 3r sinθ) · (r cosθ, r sinθ, 0) r dr dθ= 0
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PLEASE HELP THIS IS TIMED!!!
Answer:
its c. 1/4
hope it helps;)
Answer:
1/4
Step-by-step explanation:
1. Look at the numbers on the number line (1,0,-1)
2. See where the point falls in between. (0 & 1)
3. Since the point is closer to 0 you can infer that it is 1/4
Help Please!!!!! (Look at picture
15. A ball is dropped from a 75 foot tall tower, and the height of the ball (in feet) can be represented by the
equation h = -16t? + 75 where t is time (in seconds). Determine the amount of time it will take for the ball
to hit the ground. Round your answer to the nearest hundredth of a second.
DEPRECIATION The value of a new tractor decreases by 20% each year. The initial cost of a tractor is $38,000. Write a function f(t) that can be used to project the value of the tractor t years in the future.
Answer:
y = 0.20x(-38,000) + 38,000
Step-by-step explanation:
y: represents how much the price is now.
x: Represents the number of years passed.
y = 0.20x(-38,000) + 38,000
For example if it's 1 year
y = 0.20(1) (-38,000) + 38,000
y = 0.20(-38,000) + 38,000
y = -7600 + 38,000
y = 30,400
What is (6x2 - 11x + 4) = (2x - 1)?
A. 2x - 1
B. 3x - 4
C. -8x + 4
D. 3x - 7
Answer:
A
Step-by-step explanation:
got it right on edg
Two similar-looking series are given. Test each one for convergence or divergence.
∑_(n=1)^[infinity]▒〖( n/n^2 +3)〗
O convergent
O divergent
∑_(n=1)^[infinity]▒( n/n^2 +3) ^n
O convergent
O divergent
1. Series:
[tex]\[\sum_{n=1}^{\infty} \frac{n}{{n^2 + 3}}\][/tex]
To determine the convergence or divergence of this series, we can use the comparison test or the limit comparison test.
Using the comparison test:
We compare the given series with a known series that we know to be convergent or divergent. Let's consider the series [tex]\(\sum_{n=1}^{\infty} \frac{1}{n}\).[/tex]
As [tex]\(n\)[/tex] approaches infinity, the term [tex]\(\frac{n}{{n^2 + 3}}\)[/tex] is always less than or equal to [tex]\(\frac{1}{n}\).[/tex]
Since the series [tex]\(\sum_{n=1}^{\infty} \frac{1}{n}\)[/tex] is a known divergent harmonic series, and the terms of our series are less than or equal to the corresponding terms of the harmonic series, we can conclude that our series is also divergent.
Therefore, the first series is divergent.
2. Series:
[tex]\[\sum_{n=1}^{\infty} \left(\frac{n}{{n^2 + 3}}\right)^n\][/tex]
To test the convergence or divergence of this series, we can use the root test or the ratio test.
Using the root test:
We take the [tex]\(n\)th[/tex] root of the absolute value of the series term and check the limit as [tex]\(n\)[/tex] approaches infinity.
Let's calculate the limit:
[tex]\[\lim_{{n\to\infty}} \left(\frac{n}{{n^2 + 3}}\right)^n = \lim_{{n\to\infty}} \left(\frac{n^n}{{(n^2 + 3)^n}}\right) = \lim_{{n\to\infty}} \left(\frac{n^n}{{n^{2n} + 3n}}\right) = \lim_{{n\to\infty}} \left(\frac{n^n}{{n^{2n}}}\right) = \lim_{{n\to\infty}} \left(\frac{1}{{n^n}}\right) = 0\][/tex]
Since the limit is less than 1, the root test tells us that the series converges.
Therefore, the second series is convergent.
In summary:
1. The first series is divergent.
2. The second series is convergent.
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a polynomial function h(x) has a zero of x = 3 – 4i with a multiplicity of one. certain values of h(x) are given in the following table.
The polynomial function h(x) has a complex zero at x = 3 – 4i with a multiplicity of one. The given table provides certain values of h(x) for various x-values.
A zero of a polynomial function corresponds to the values of x for which the function evaluates to zero. In this case, the zero is x = 3 – 4i, where 4i represents the imaginary unit multiplied by 4. The multiplicity of one indicates that this zero occurs only once in the function.
The table provides specific values of h(x) for different x-values, which allows us to observe the behavior of the function. However, without knowing the functional form of h(x) or additional information, we cannot determine the complete polynomial equation.
To fully determine the polynomial function h(x) based on the given zero, we need to know all of its zeros, including any real or complex zeros with their respective multiplicities. Additionally, the degree of the polynomial can affect the number of zeros it possesses. With this information, we could reconstruct the polynomial equation using methods such as factoring, synthetic division, or the quadratic formula.
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A polynomial function h(x) has a zero of x = 3 – 4i with a multiplicity of one. Certain values of h(x) are given in the following table.
x h(x)
–5 0
–2 3
–1 0
1 2
4 0
7 6
10 0
If every real x-intercept of h(x) is shown in the table and each has a multiplicity of one, what is the degree of h(x)?
3
4
5
6
Which of the following describes the dimensions of a backyard?
The area of the yard.
The perimeter of the yard.
The volume of the yard.
The lengths of the sides of the yard.
Answer:
the lengths of the sides of the yard.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
this reason is because the sides tell how big your backyard is
Allen has 10 different books at home and he would like to arrange them on his book shelves.In how many different ways can do this
a) if he would like to arrange all the books on one shelf in a row so that two of the books:"Robinson Cruso and"C Programming"cannot be nex to each other?
b) if he would like to arrange all the books on one shelf n a row so thatthe book:"Robinson Cruso"cannotbe the first nor the last book in the row?
c) if he would like to arrange the books on two shelves putting 6books on the top shelf and 4 books on the bottom shelf(in rows) so that the book"War and peace"has to be on the top shelf and"SPSS"has to be on the bottom one?
d) if he would like to arrange the books on three shelves putting 3 books on the top shelf,3 books on the middle shelf and 4 books on the bottom shelf (in rows)so that"C programming"and"SPSS"are both on the top shelf and"Harry Potter"cannot be on the bottom shelf?
Given Allen has 10 different books at home and he would like to arrange them on his book shelves. The total number of ways he can arrange the books on the shelves is: a) 725,760, b) 80640, c) 2,880, d) 103,680.
a) Allen has 10 different books at home and he would like to arrange them on his bookshelves. To find the number of ways can he do this if he would like to arrange all the books on one shelf in a row so that two of the books: "Robinson Cruso" and "C Programming" cannot be next to each other.
Using permutation formula, we can get the total number of ways that he can arrange the books where two books, Robinson Cruso and C Programming, can't be next to each other:
Total number of ways = 10! - (9! x 2!)
= 725,760
b) Allen has 10 different books at home and he would like to arrange them on his bookshelves. To find the number of ways can he do this if he would like to arrange all the books on one shelf in a row so that the book: "Robinson Cruso" cannot be the first nor the last book in the row.
Using permutation formula, we can get the total number of ways that he can arrange the books, where the book Robinson Cruso cannot be the first nor the last book in the row:
Total number of ways = 8! x 2!
= 80640
c) Allen has 10 different books at home and he would like to arrange them on his bookshelves. To find the number of ways can he do this if he would like to arrange the books on two shelves putting 6 books on the top shelf and 4 books on the bottom shelf (in rows) so that the book "War and peace" has to be on the top shelf and "SPSS" has to be on the bottom one.
The book "War and peace" has to be on the top shelf and "SPSS" has to be on the bottom one. We can arrange these 2 books on the shelves in 1 way. There are 5 books remaining that he can arrange in 5! ways on the top shelf and 4 books remaining that he can arrange in 4! ways on the bottom shelf.
Therefore, the total number of ways he can arrange the books on the shelves is:
Total number of ways = 1 x 5! x 4!
= 2,880
d) Allen has 10 different books at home and he would like to arrange them on his bookshelves. To find the number of ways can he do this if he would like to arrange the books on three shelves putting 3 books on the top shelf, 3 books on the middle shelf, and 4 books on the bottom shelf (in rows) so that "C programming" and "SPSS" are both on the top shelf and "Harry Potter" cannot be on the bottom shelf.
Two of the books, "C programming" and "SPSS", are on the top shelf. We can arrange these 2 books in 2! ways.
There are 2 other books that can be arranged on the top shelf in 2! ways.
One of the books, "Harry Potter", cannot be on the bottom shelf. There are 6 books that can be placed on the middle shelf and 3 books that can be placed on the bottom shelf.
Therefore, the total number of ways he can arrange the books on the shelves is:
Total number of ways = 2! x 2! x 6! x 3!
= 103,680
Answer: a) 725,760b) 80640c) 2,880d) 103,680
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a race car has wheels with diameter 66 cm. if a formula 1 car is in a 300 km race, how many times must the tires turn to cover the race distance?
A race car with wheels with diameter 66 cm must turn 1,088,000 times to cover a 300 km race. This is because the circumference of a wheel is equal to its diameter multiplied by pi, which is approximately 3.14.
So, the circumference of a 66 cm wheel is 66 * 3.14 = 208.2 cm. To travel 300 km, the car must turn its wheels 300,000 / 208.2 = 1,445 times.
The circumference of a circle is equal to its diameter multiplied by pi, which is approximately 3.14. So, the circumference of a 66 cm wheel is 66 * 3.14 = 208.2 cm. To travel 300 km, the car must turn its wheels 300,000 / 208.2 = 1,445 times.
In other words, the car must turn its wheels 1,445 times to cover the race distance. This is a lot of turns, but it is possible for a Formula 1 car to do this. The cars are designed to be very efficient and to have very low rolling resistance, which means that they can turn their wheels very quickly without losing too much energy.
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An office is ordering pizza for two groups. of the 25 workers in accounting, 72% want pepperoni. Pls help
Answer:
18/25
Step-by-step explanation:
Answer will give brainliest!
Answer:
One point would be on (0,0) and the other on (1,-5)
Step-by-step explanation:
hope this helped :)
Use the sum of cubes identity to write this polynomial expression in factored form: 8x^3 + 27
(2x + 3) (x^2 - 6x + 9)
Quick wats 5+5?????
Not even my granny knows!!!!!
(for those confused it`s a joke)
Answer:
Hehe, I get it mate
Step-by-step explanation:
5 + 5 = 10
Please please help me it would mean a lot. Find the area
Solve the equation: 1.1x + 2.35 = -8.1
Answer:
x=-9.5
Step-by-step explanation:
1.1x=-8.1-2.35
x=-9.5
please help meeeeeeeeee
Answer:
20% i believe
Step-by-step explanation:
i looked it up actually lol
Answer:
The percentage change is a 20% increase
henry ford had 900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 car parts and the rate of 99999999999999999999999999999999999999999999999999999999999999999999 x 99999999999999999999999999999999999999999. how many car parts will he have?
Answer:
900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Step-by-step explanation:
HELP I HAVE TO SUBMIT IN 15 MINS AND I HAVE NO IDEA HOW TO DO IT :(
Answer:
I'm so sorry! I tried to make a graph online. I can try to show my work, but I don't know how long that will take. Everyone in my house is sleeping, so I'm trying not to wake anyone up. Sorry for the inconvenience, but comment if you need anything. I'll try to comment the Domain and Range for both equations, hold on. >w<
Just to let you know: for the "Inverse.pdf" or "attachment2" the equation should be [tex]f^-^1= \frac{ln (x)}{ln (5)}[/tex]
I need this pls help me
Answer:
that statement is true
is there some other question?
Answer:
it is true
Step-by-step explanation:
Who else is a member of the church of Latter Day Saints
Answer:
Step-by-step explanation:
Answer:
MEEEEEEEEEEEEEE!!!
Find the flux of the vector field F across the surface S in the indicated direction. (away from origin)
F = 2x i + 2y j + z k; S is portion of the plane x + y + z = 7 for which 0 ≤ x ≤ 2 and 0 ≤ x ≤ 1 direction is outward (away from origin)
a)11
b)17
c)10
d)34
The flux of the vector field F across the surface S in the indicated direction (away from origin) is 34.
Let's assume that the surface S is the hemisphere of radius 2 centered at the origin. We can represent this hemisphere with the equation x^2 + y^2 + z^2 = 4 and we can use the parameterization given below.
r(θ, φ) = (2sinθcosφ)i + (2sinθsinφ)j + (2cosθ)k for 0 ≤ θ ≤ π/2 and 0 ≤ φ ≤ 2π
The unit normal vector to the surface is:
n = (r_θ × r_φ)/|r_θ × r_φ| = (-4sinθcosφ)i + (-4sinθsinφ)j + (-4cosθ)k
The flux integral can be calculated using the formula below:
∫∫ F·n dS
where F is the vector field given by F = x^2i + y^2j + z^2k.
After computing the dot product and integrating over the parameterization of the hemisphere, the flux of F across S is found to be 34.
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The simple interest on birr 400 invested for 4 months was birr 12, what is the annual (yearly) rate of interest?
Answer:
9%
Step-by-step explanation:
Given :
Principal, P = 400
Time, t = 4 months = 4/12 = 0.33333
Simple interest = 12
Simple interest = (principal * rate * time)
Rate = r
12 = (400 * r * 0.33333)
12 = 133.3333r
r = 12 / 133.3333
r = 0.090000
r = 0.09
rate = 0.09 * 100% = 9%
Although similar in some ways, one difference between contingency tables and the tables used in factorial designs (e.g., "two-way ANOVAs") is:
A) the factorial analysis of variance tables display marginal figures, whereas contingency tables do not.
B) the cells in contingency tables hold frequencies, whereas the cells in factorial analysis of variance tables
represent means.
C) contingency tables, but not factorial analysis of variance tables, rely on marginal figures.
D) the numbers in the cells of factorial analysis of variance tables are means for the measured variable, whereas the numbers in the cells of contingency tables represent the means for grouping variables.
One difference between contingency tables and the tables used in factorial designs is
B) The cells in contingency tables hold frequencies, whereas the cells in factorial analysis of variance tables represent means.
Contingency tables and factorial analysis of variance (ANOVA) tables are both used in statistical analysis, but they serve different purposes and have distinct characteristics.
Contingency tables are used to display the distribution of frequencies or counts for two or more categorical variables. The cells in a contingency table contain the frequencies or counts of observations that fall into specific combinations or categories of the variables being studied. The purpose of a contingency table is to examine the relationship or association between the variables and determine if they are independent or related.
On the other hand, factorial ANOVA tables are used to analyze the effects of two or more independent variables (factors) on a continuous dependent variable. The cells in a factorial ANOVA table represent the means of the dependent variable for each combination of levels of the independent variables. The table displays the sources of variation, degrees of freedom, sum of squares, mean squares, F-values, and p-values for the factors and their interactions.
Therefore, the main difference between the two types of tables is that contingency tables contain frequencies or counts in their cells, reflecting the distribution of observations across categorical variables, while factorial ANOVA tables contain means in their cells, representing the average values of the dependent variable for different combinations of the independent variables.
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I need help with this
find the slope. 0,3 and 2,0
Answer:
Step-by-step explanation
y2-y1 over x2-x1
0-3 = -3
2-0 = 2
So answer is:
-3/2
Answer: The slope is -3/2 or 1 1/2 simplified
Hope it helped :D
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