Answer: split it into smaller solids and calculate their separate volumes.
Step-by-step explanation:
Solve the following trigonometric equation on the interval
[0,2π).Express your answers in exact form if possible. Otherwise,
round to two decimal places.2 cos2θ+ 5 cosθ+ 2 = 0
The solutions to the given trigonometric equation on the interval [0,2π) are θ = 2π/3 and θ = 4π/3. These values can also be expressed in decimal form as θ = 2.09 and θ = 4.19, rounded to two decimal places
To solve the given trigonometric equation on the interval [0,2π), we need to use the quadratic formula.
First, let us rewrite the equation in terms of x:
2x^2 + 5x + 2 = 0
Next, we can apply the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
Plugging in the values from the equation:
x = (-(5) ± √((5)^2 - 4(2)(2)))/(2(2))
Simplifying:
x = (-5 ± √(25 - 16))/4
x = (-5 ± √9)/4
x = (-5 ± 3)/4
This gives us two possible values for x:
x = (-5 + 3)/4 = -2/4 = -0.5
x = (-5 - 3)/4 = -8/4 = -2
Now we need to convert these values back to θ by using the inverse cosine function:
θ = cos^-1(-0.5)
θ = cos^-1(-2)
The first value, θ = cos^-1(-0.5), gives us two solutions on the interval [0,2π):
θ = 2π/3 and θ = 4π/3
The second value, θ = cos^-1(-2), does not give us any solutions on the interval [0,2π) because the cosine function only takes on values between -1 and 1.
Therefore, the solutions to the given trigonometric equation on the interval [0,2π) are θ = 2π/3 and θ = 4π/3. These values can also be expressed in decimal form as θ = 2.09 and θ = 4.19, rounded to two decimal places.
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Card Name (APR %) Existing Balance Credit Limit Mark2 (6.5%) $475.00 $3,000.00 Bee4 (10.1%) $1,311.48 $2,500.00 You have $450.00 each month to pay off these two credit cards. You decide to pay only the interest on the lower interest card and the remaining amount to the higher interest card. Complete the following two tables to help you. Lower Interst Card (Payoff Option) Month 1 2 3 4 5 6 7 8 9 10 Principal Interest Accrued Payment End-of-month balance Higher Interest Card Month 1 2 3 4 5 6 7 8 9 10 Principal Interest Accrued Payment End-of-month balance 1) How long does it take to pay off the higher interest card? 2) What is the amount of the last payment on the higher interest card? Why? 3) At the end of the month that you pay off the higher interest card, after you have started to pay down your debt on the lower interest card, what is the balance of the lower interest card? Why? 4) Rework the problem so that you pay off the lower interest card first. 5) How much money do you save by paying off the higher interest card first?
-
I really need help on this one
1. 9 months 2) $163.06, because it is the remaining balance after paying off the principal and interest accrued for that month. 3) $348.16, because it is the balance remaining on the lower interest card after paying off the higher interest card and making the monthly payment for that month. 4) 9 months 5) $168.79, because it is the difference between the total amount paid to each card when paying off the higher interest card first versus paying off the lower interest card first.
What is interest ?Interest is the fee paid for the use of borrowed money, usually expressed as a percentage of the borrowed amount.
According to given information :Based on the payment plan described, it will take 12 months to pay off the higher interest card.The amount of the last payment on the higher interest card will be $173.01. This is because the remaining balance after 11 months of payments will be $173.01, which is the amount needed to fully pay off the card.At the end of the month that you pay off the higher interest card, the balance of the lower interest card will be $404.17. This is because during the first 11 months, only the interest was being paid on the lower interest card, so the balance remained the same. However, in the month that the higher interest card is paid off, the full $450 payment will be applied to the lower interest card, reducing the balance by $45.83 to $404.17.If the lower interest card is paid off first, the payment plan and balances would be as follows: Lower Interst Card (Payoff Option) Month 1 2 3 4 5 6 7 8 9 10 Principal Interest Accrued Payment End-of-month balance $475.00 $6.46 $6.46 $6.46 $6.46 $6.46 $6.46 $6.46 $6.46 $6.46 $0.00 Higher Interest Card Month 1 2 3 4 5 6 7 8 9 10 Principal Interest Accrued Payment End-of-month balance $1,311.48 $10.69 $10.69 $10.69 $10.69 $10.69 $10.69 $10.69 $10.69 $10.69 $0.00. Under this payment plan, the lower interest card is paid off in 10 months, and then the remaining payments are applied to the higher interest card, which is paid off in an additional 2 months.By paying off the higher interest card first, you save a total of $141.27 in interest charges over the course of the payment plan.Therefore, 1. 9 months 2) $163.06, because it is the remaining balance after paying off the principal and interest accrued for that month. 3) $348.16, because it is the balance remaining on the lower interest card after paying off the higher interest card and making the monthly payment for that month. 4) 9 months 5) $168.79, because it is the difference between the total amount paid to each card when paying off the higher interest card first versus paying off the lower interest card first.
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The rapid evolution of computer hardware and software has made it easier to conduct computer-based and Web-based (i.e. electronic) surveys. A Professor would like to compare the response rates of electronic surveys and traditional print surveys. The two surveys were developed for customers who had purchased products on the Internet. Of the 631 customers who mailed the printed questionnaire, 261 returned usable responses. Of the 414 customers who sent Web-based (i.e. electronic) questionnaire, 155 returned
usable responses. Estimate a 90% confidence interval for the difference between the usable response rates of the two surveys. Interpret the result.
The 90% confidence interval for the difference between the usable response rates of the two surveys is (-0.0124, 0.0912).
The difference between the usable response rates of the two surveys can be estimated using the formula for the difference between two proportions:
d = p1 - p2
Where p1 is the usable response rate for the printed survey, and p2 is the usable response rate for the electronic survey. To calculate these response rates, we can use the formula:
p = x/n
Where x is the number of usable responses, and n is the total number of customers who were sent the survey. For the printed survey, we have:
p1 = 261/631 = 0.4138
And for the electronic survey, we have:
p2 = 155/414 = 0.3744
So the difference between the two response rates is:
d = 0.4138 - 0.3744 = 0.0394
To estimate a 90% confidence interval for this difference, we can use the formula:
CI = d ± z*√[(p1(1-p1)/n1) + (p2(1-p2)/n2)]
Where z is the critical value for a 90% confidence level, which is 1.645. Plugging in the values we have:
CI = 0.0394 ± 1.645*√[(0.4138(1-0.4138)/631) + (0.3744(1-0.3744)/414)]
CI = 0.0394 ± 1.645*√[0.000407 + 0.000581]
CI = 0.0394 ± 1.645*0.0315
CI = 0.0394 ± 0.0518
CI = (-0.0124, 0.0912)
So the 90% confidence interval for the difference between the usable response rates of the two surveys is (-0.0124, 0.0912). This means that we can be 90% confident that the true difference between the two response rates is between -0.0124 and 0.0912.
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Please help solve and explain!
The exponential function is y = 5*(∛2)^x and the value after 10 days is 50.4
How to write the function?Here we can see an exponential function of the form y = a*b^x
First, notice that it passes through (0, 5), then:
5 = a*b^0 = a
5 = a
So we got the initial value, so we can write the equaton like:
y = 5*b^x
And now we need to find the value of b.
We also can see that it passes through (3, 10), then:
10 = 5*b^3
10/5 = b^3
2 = b^3
∛2 = b
So the function is:
y = 5*(∛2)^x
b) The value after 10 days is what wet when we evaluate the function above in x = 10, then we will get:
y = 5*(∛2)^10 = 50.4
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A 5-year Treasury bond has a 3.65% yield. A 10-year Treasury
bond yields 6.3%, and a 10-year corporate bond yields 9.75%. The
market expects that inflation will average 3% over the next 10
years (IP10
The real yeild is 0.65%.
The Estimated 10-year Treasury bond yield is 3.65%.
The 10-year Treasury bond yield can be estimated using the 5-year Treasury bond yield and the expected inflation rate of 3%.
This is done by calculating the real yield, which is the difference between the nominal yield and the expected inflation rate.
The 10-year Treasury bond yield can be estimated by adding the real yield of the 5-year Treasury bond to the expected inflation rate of 3%.
Real yield = Nominal yield - Expected inflation rate
Real yield (5-year Treasury bond) = 3.65% - 3% = 0.65%
Estimated 10-year Treasury bond yield = 0.65% + 3% = 3.65%
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All the real zeros of the given polynomial are integers. Find the zeros. P(x) = x^(3) - 9x^(2) + 20x - 12
The real zeros of the given polynomial P(x) = x³ - 9x² + 20x - 12 are 3 and 2. The real zeros of the given polynomial P(x) = x³ - 9x² + 20x - 12 can be found by factoring the polynomial and setting each factor equal to zero.
Step 1: Factor the polynomial
P(x) = x³ - 9x² + 20x - 12
= (x - 3)(x - 2)(x - 2)
Step 2: Set each factor equal to zero and solve for x
x - 3 = 0 => x = 3
x - 2 = 0 => x = 2
x - 2 = 0 => x = 2
Step 3: The real zeros of the polynomial are the values of x that make each factor equal to zero.
So, the real zeros of the polynomial are x = 3 and x = 2.
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1. determine the derivative of a function by applying the appropriate derivative rules for both equations.
2. apply the derivative to determine other information about a function for both equations.
Differentiate 2 of the following Please
f(x) = (3 – 2x^3)^3 / f(t) = 100(6-t)/t+3
solve for t to get t = 4
1. To find the derivative of f(x) = (3 – 2x^3)^3 we can apply the power rule, the chain rule, and the product rule. The power rule states that the derivative of f(x) = x^n is f'(x) = nx^n-1. The chain rule states that the derivative of f(x) = g(h(x)) is f'(x) = g'(h(x))*h'(x). The product rule states that the derivative of f(x) = uv is f'(x) = u'v + uv'. In this case, we can rewrite f(x) as f(x) = (h(x))^3 where h(x) = 3 - 2x^3. We then apply the chain rule to get f'(x) = 3(3 - 2x^3)^2(-6x^2). Similarly, we can find the derivative of f(t) = 100(6-t)/t+3. We can rewrite f(t) as f(t) = u(t)v(t) where u(t) = 100 and v(t) = (6-t)/t+3. Applying the product rule, we get f'(t) = 100(-1/(t+3)^2) + (6-t)(-1/(t+3)^2).
2. To find other information about a function, we can use the derivative we just found. For example, if we want to find the maximum or minimum values of a function, we can set the derivative equal to 0 and solve for the x or t values. In the case of f(x), we can set 3(3 - 2x^3)^2(-6x^2) = 0 and solve for x to get x = (sqrt(3/2))^(1/3). Similarly, for f(t) we can set 100(-1/(t+3)^2) + (6-t)(-1/(t+3)^2) = 0 and solve for t to get t = 4. We can also use derivatives to find the equation of a tangent line to a function at any given point. In this case, we would use the derivative we found in order to calculate the slope of the tangent line at any given point and then use point-slope form to find the equation of the line.
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Alex has 1400 ft of irrigation pipping. He wants to use it to irrigate his back lawn. He wants to lay the pipping in such a manner as to cut off 3 equal size rectangle regions in the yard. What are the dimensions that would produce the maximum enclosed area.
The dimensions that would produce the maximum enclosed area are 350ft x 350ft, which will cut off 3 equal size rectangle regions in the yard.
To understand why this is the case, let's consider the problem step-by-step. If Alex wants to cut off three equal size rectangle regions in the yard, he will need to divide the lawn into four equal size rectangles. Let's call the dimensions of two of these rectangles "x" and "y".
To maximize the enclosed area, we want to maximize the area of the lawn that is left over after the three rectangles are cut out. This area can be represented by the equation A = (350-x)(350-y). We know that the total length of the piping is 1400 ft, so the perimeter of the enclosed area (the sum of all four sides) is 1400 ft. This means that 2x + 2y + 1400 = 1400, or 2x + 2y = 0.
Solving for y, we get y = -x + 700. Substituting this equation into the area equation, we get A = (350-x)(350-(-x+700)), which simplifies to A = x(350-x). To find the maximum area, we can take the derivative of this equation with respect to x, set it equal to 0, and solve for x. Doing this, we find that x = 175, which means that y = 525 - x = 350. Therefore, the dimensions that would produce the maximum enclosed area are 350ft x 350ft.
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What is the interquartile range for the data set?
341, 330, 301, 345, 309, 311, 342, 301, 304, 328, 343
Answer:
38
Step-by-step explanation:
Interquartile Range
IQR = Q3 - Q1
Quartiles are the values that divide a list of numbers into quarters:
Put the list of numbers in order. Then cut the list into four equal parts.301, 301, 304, 309, 311, 328, 330, 341, 342, 343, 345
Hence,
Quartiles:
Q1 --> 304
Q2 --> 328
Q3 --> 342
And since, IQR = Q3 - Q1
Then,
342 - 304 = 38
As a result, the interquartile range for the data set is 38.
RevyBreeze
Show that the set is linearly dependet by finding a nontrival linear combination of vectors in the set whose sum is the zero vector. (use s1, s2, s3 resepectively for the vectors in the set)
S={(5,4),(−1,1),(2,0)}
(0,0)= Express the vector s1 in the set as a linear combination of the vectors s2 and s3. s1=
The vector s₁ in the set can be expressed as a linear combination of the vectors s₂ and s₃:
s₁ = (-4/3)s₂ + (1/3)s₃
How to express that the vector S₁ is a linear combination of the vectors S₂ and S₃?The set S = {(5,4),(−1,1),(2,0)} is linearly dependent if there exists a nontrivial linear combination of the vectors in the set whose sum is the zero vector. In other words, if there exists scalars a, b, and c such that:
a(5,4) + b(−1,1) + c(2,0) = (0,0)
Expanding the above equation gives us:
(5a - b + 2c, 4a + b) = (0,0)
This implies that:
5a - b + 2c = 0
4a + b = 0
Solving the above system of equations gives us:
a = 1/3, b = -4/3, c = 1/3
Therefore, the nontrivial linear combination of the vectors in the set whose sum is the zero vector is:
(1/3)(5,4) + (-4/3)(−1,1) + (1/3)(2,0) = (0,0)
To express the vector s₁ in the set as a linear combination of the vectors s₂ and s₃, we can use the above solution and write:
s₁ = (-4/3)s₂ + (1/3)s₃
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If p(z)=8z^(4)-17z^(3)-20z^(2)-4z+15, use synthetic division to find p(3) Submit
The value of p(3) is p(3)=12.
Here, we have,
Synthetic division :
It is a shorthand method of dividing polynomials for the special case of dividing by a linear factor whose leading coefficient is 1.
The given function is,
p(z)=8z⁴-17z³-20z²-4z+15
We have to find p(3)
Substitute z= 3 in above function.
p(3)=8×3⁴-17×3³-20×3²-4×3+15
=12
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two runners are racing against each other. jeri graphs a linear equation for each runner that shows the runners distance from the starting line over time. the two equations form a system that has infinitely many solutions. describe the intersection points of the lines an situations explain what solution means in this
Answer:If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. the intersection points (-3,3) Since the system is infinite it means there is 1 line on the graph-
Step-by-step explanation:
In Booneville, the use of landlines has been declining at a rate of 20% every year. If there are
25,300 landlines this year, how many will there be in 5 years?
If necessary, round your answer to the nearest whole number.
Answer:
8290
Step-by-step explanation:
Explanation is on the pic
The table below gives approximate probabilities for scoring 0, 1, 2, 3, or 4 runs in one inning of Major League Baseball. (Although it is possible to score more than 4 runs in one inning, the probability is very small, so it is ignored in this question.) 3 P(x) | 0 0.74 10.12 20.07 30.04 4 0.03 Round solutions to three decimal places, if necessary. Compute the sum of these probabilities: EP(z) = Compute the mean number of runs per inning, using this probability distribution: Compute the standard deviation of this probability distribution:
The sum of these probabilities is 1, the mean number of runs per inning is 0.46, and the standard deviation of this probability distribution is 0.839.
The sum of these probabilities is simply the sum of the values in the table:
EP(x) = 0.74 + 0.12 + 0.07 + 0.04 + 0.03 = 1
The mean number of runs per inning can be calculated using the formula for the expected value of a discrete random variable:
E(x) = ∑xP(x) = (0)(0.74) + (1)(0.12) + (2)(0.07) + (3)(0.04) + (4)(0.03) = 0.46
The standard deviation of this probability distribution can be calculated using the formula for the standard deviation of a discrete random variable:
σ = √[∑(x - E(x))^2P(x)]
=> √[(0 - 0.46)^2(0.74) + (1 - 0.46)^2(0.12) + (2 - 0.46)^2(0.07) + (3 - 0.46)^2(0.04) + (4 - 0.46)^2(0.03)]
=> 0.839
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For what values of a will the quadratic y=ax^(2)-6x+3 have no real zeroes? (1) a=1 (3) a=-5 (2) a=-2 (4) a=7
For a=7 the quadratic equation have no real roots. (4)
For a quadratic equation y=ax^(2)-6x+3 to have no real zeroes, the discriminant of the equation must be less than zero. The discriminant of a quadratic equation is given by the formula b^(2)-4ac, where a, b, and c are the coefficients of the equation. In this case, a=a, b=-6, and c=3.
Plugging these values into the formula for the discriminant, we get:
(-6)^(2)-4(a)(3)<0
36-12a<0
12a>36
a>3
Therefore, the values of a that will make the quadratic equation have no real zeroes are those that are greater than 3. This means that the correct answer is (4) a=7, since this is the only value of a that is greater than 3.
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Olaf lives in a dorm in a tiny room that he shares with three others. He wants to live off campus next year with his friends, but he needs more money from his parents to finance the move. He decides to build a scale model of his dorm room so that when he goes home for break, he can show his parents the cramped conditions he lives in. He decides to let 1 inch represent 30 inches of the actual lengths in the room. His desk is a right rectangular prism 40 inches high, 36 inches long, and 20 inches wide. He decides that his scaled desk should be 1 1/3 inches high, but a roommate says it should be 10 inches high. Who is right and why? What are the other dimensions of the scaled desk?
The roommate is wrong. The scaled desk should be 1 1/3 inches high, as per Olaf's initial scaling of 1 inch representing 30 inches of actual length in the room. The other dimensions of the scaled desk would be 12 inches long and 6 2/3 inches wide.
When Olaf decided to let 1 inch represent 30 inches of actual length in the room, he created a scale factor of 1:30. This means that for every inch in the scale model, there are 30 inches in the actual room. Using this scale factor, the scaled desk height should be 40/30 = 4/3 inches. Therefore, the roommate's suggestion of 10 inches high is incorrect.
To find the other dimensions of the scaled desk, we need to apply the same scale factor of 1:30. The scaled length would be 36/30 = 12 inches, and the scaled width would be 20/30 = 2/3 inches. However, it's easier to work with whole numbers, so we can multiply both dimensions by 10 to get 120 inches long and 6 2/3 inches wide, which is equivalent to 12 inches long and 2/3 inches wide in the scaled model.
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The rectangular floor of a classroom is 20 feet in length and 30 feet in width. A scale drawing of the floor has a length of 4 inches. What is the area, in square inches, of the floor in the scale drawing?
Answer:
24inches ²
Step-by-step explanation:
Scale of length is 20ft : 4inches = 5ft : 1inch
Scale of width will be 5ft: 1inch = 30ft: 6inches
Area of scale =length x width
Area = 4inches x 6inces
A varies directly as B and inversely as C . A is 12 when B is 6 and C is 2 . What is the value of A when B is 12 and C is 3 .
O 4 O 8 O 12
O 16
If A varies directly as B and inversely as C then The value of A when B is 12 and C is 3 is 16.
To find the value of A, we can use the formula for direct and inverse variation of the given :
A = k*B/C
We are given that A is 12 when B is 6 and C is 2. We can plug these values into the formula to find the value of k:
12 = k*6/2
12 = 3k
k = 4
Now that we know the value of k, we can plug in the new values for B and C to find the value of A:
A = 4*12/3
A = 48/3
A = 16
Therefore, the value of A when B is 12 and C is 3 is 16. The correct answer is O 16.
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Desminos Pizza's online menu offers small, medium, and large pizzas. Using the digits 0-9, without repeating, fill in each blank such that each equation is true. MENU SIZE PRICE MEDIUM $15+$2 PER TOPP
15 + 2x = Price
The price of a medium-sized pizza at Desminos Pizza's online menu is $15 plus $2 per topping. The equation for this is 15 + 2x = Price, where x represents the number of toppings.
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In the cinema below a) what is the angle of elevation from Row A to the bottom of the screen b) what is the angle of depression from Row P to the bottom of the screen Give your answers to 1 d.p. Screen 2.5 m 5.8 m 11° Row A 21.3 m Row P Not drawn accurately
Seven Subjects S1, S2, S3, ...,S7 Are To Be Scheduled In An Examination. The Following Pairs Of Subjects Have Common Students: 2 1 a. {S1, S2}, {S1, S3},{S1, S4},{Sı, S7} b. {S2, S3}, {S2, Sa}, {S2, S5}, {S2, S7}, c. {S3, S4}, {S3, S6},{S3, S7},{S4, S5}, {S4, Sc}, d. {S5,S6},{S5, St}, And {S6, S7} How Can The Examination Be Scheduled So That No Student Has Two examination at same day?
To schedule the examination so that no student has two examinations on the same day, we can use graph coloring. Graph coloring is the process of assigning colors to the vertices of a graph in such a way that no two adjacent vertices have the same color.
1. First, we can create a graph with the seven subjects as vertices and the pairs of subjects with common students as edges.
2. Next, we can assign a color to each vertex, starting with S1 and moving clockwise around the graph. We can use the smallest available color for each vertex, making sure that no two adjacent vertices have the same color.
3. Once we have assigned a color to each vertex, we can use the colors to schedule the examinations. Each color represents a different day, and all of the subjects with the same color can be scheduled on the same day.
The resulting schedule would look something like this:
Day 1: S1, S5
Day 2: S2, S4
Day 3: S3, S6
Day 4: S7
This schedule ensures that no student has two examinations on the same day, since no two adjacent vertices in the graph have the same color.
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Which of these rules are functions on an appropriate domain? Select all that apply.
$\vspace{.05in}$
$A$ inputs a real number, subtracts $100$, then outputs the square root of the result if it is real.
${}B$ inputs a date, then outputs the name of a person born on that date.
$C$ inputs a real number $x$, then outputs a real number $y$ that is less than $\frac{1}{1000}$ larger than $x$. $\smallskip$
$D$ inputs a real number $x$, then outputs the result of the calculation $\dfrac{x^2-1}{(x-1)(x+1)}$.
$E$ inputs a real number $x$, then a coin is flipped. If the coin flips heads, the output is $x+2$. If the coin flips tails, the output is $x+3$.
$F$ inputs a person, then outputs their birth date.
D and F are functions on an appropriate domain. A, C, and D are functions that take in a real number and output a real number, so they are valid functions on the domain of real numbers.
What is domain?A domain is a set of names or IP addresses that are associated with a particular website or web server. It is what allows users to access a website's content using a web browser. Domains are typically purchased from a domain registrar and can be used to host websites, email accounts, and other services.
B and F are invalid functions because they take in a real number and output something that is not a real number.
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Find the 12th term of the geometric sequence 9, - 18, 36, .
The 12th term of the geometric sequence 9, - 18, 36, is 18,432.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.Next, we would determine the common ratio as follows;
Common ratio, r = a₂/a₁
Common ratio, r = -18/9
Common ratio, r = -2
For the 12th term, we have:
a₁₂ = 9(2)¹²⁻¹
a₁₂ = 18,432.
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Did I get these Zeros right while factoring?
Answer:
You forgot the +- part when taking the square roots
Step-by-step explanation:
5 x^2 = -2
x^2 = -2/5
x = +- sqrt ( -2/5) <==== note sqrt(-2/5) NOT sqrt (-2) / 5
x = ± i sqrt(2/5)
x^2 = 8
x = ±sqrt 8
x = ±2 sqrt (2)
Part A
Which equation can be used to determine the total cost, y, for a tickets ordered in a transaction?
O y = 2.25x + 15.50
O y = 15.50x +2.25
x = 2.25y + 15.50
O = 15.50y +2.25
Part B
If the total cost of a transaction is $157.25, how many movie tickets were ordered?
Enter the correct answer in the box
tickets:
a) The equation that can be used to determine the total cost, y, for a tickets ordered in a transaction is y = 15.50x + 2.25
b) The number of movie tickets sold is x = 10 tickets
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the total cost of the movie be represented as y
Let the number of tickets sold be x
Now , the cost of one movie ticket = $ 15.50
And , the cost of x tickets = $ 15.50x
The cost of the transaction = $ 2.25
So , the total cost y = cost of x tickets + cost of the transaction
On simplifying the equation , we get
y = 15.50x + 2.25 be equation (1)
b)
Let the number of tickets be x
Now , the total cost of the transaction is y = $ 157.25
So , y = 15.50x + 2.25
On simplifying , we get
157.25 = 15.50x + 2.25
Subtracting 2.25 on both sides , we get
15.50x = 155
Divide by 15.5 on both sides , we get
x = 10 tickets
Hence , the number of tickets sold is 10 tickets
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The complete question is attached below :
Part A
Which equation can be used to determine the total cost, y, for a tickets ordered in a transaction?
O y = 2.25x + 15.50
O y = 15.50x +2.25
x = 2.25y + 15.50
O = 15.50y +2.25
Part B
If the total cost of a transaction is $157.25, how many movie tickets were ordered?
1. Which creature is least numerous? Estimate how many times more ants there are. 2. Which creature is the least massive? Estimate how many times more massive a human is. 3. Which is more massive, the total mass of all the humans or the total mass of all the ants? About how many times more massive is it? 4. Which is more massive, the total mass of all the krill or the total mass of all the blue whales? About how many times more massive is it?
By answering the above question, we may state that As a result, the equation mass of all krill is about 11,485 times more than the mass of all blue whales.
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A formal statement that proves the equality of two calculations is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two phrases that are inscribed on opposite sides of a letter. Frequently, the logo and indeed the particular software are identical. like in 2x - 4 = 2, for example.
Given that there are several species with a wide range in population numbers, it is challenging to identify which animal is the least numerous. The vaquita porpoise, Javan rhinoceros, and Amur leopards are some of the rarest animals, albeit they all exist in the wild. The number of ants on Earth is believed to be 10 quadrillion, which is around 10,000,000,000,000,000 times greater than the population of any of the rarest species.
The estimated mass of all krill on Earth is around 379 million tonnes, whereas the estimated mass of all blue whales is approximately 33,000 tonnes. As a result, the mass of all krill is about 11,485 times more than the mass of all blue whales.
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Which of the numbers below is less than -3.5? Select all that apply A)-4.2 B)-3.8 C)-9/2 D) -5/3 E)-1.5
Answer: A) -4.2, B) -3.8 C) -9/2 (-4.5)
Step-by-step explanation: Think of a number line, you have 0-10, and -10-0, as you keep going down the number like, the numbers become less and less, just like how -4.2 is less than -3.5, because it is further to the left of the number line, meaning it is less than. Hope this helps!
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proof attached in image !!
The proof that ∠B ≅ ∠C is:
D is the midpoint of of BC - Given...................(1)
Thus
BD = DC ................................................................(2)
∠EDC ≅ ∠FDB - Given......................................(3)
DE ⊥ AB - Given...................................................(4)
DF ⊥ AC - Given ..................................................(5)
∠AED = ∠DEB = 90° - perpendicular bisector theorem ....(6)
∠AFD = ∠DFC = 90° - perpendicular bisector theorem ....(7)
∠EAF = ∠EDF = 90° - Properties of the angles of a Quadrilateral
Since ∠EDC ≅ ∠FDB, as in (3) above, and
Both comprise of ∠EDF,
thus,
(∠EDC - ∠EDF) ≅ (∠FDB - ∠EDF)
Since
∠EDB = (∠FDB - ∠EDF); and
∠FDC = (∠EDC - ∠EDF)
Thus,
∠EDB ≅ ∠FDC
thus,
∠EDB = ∠FDC = 45° (Sum of Angles on a Straight line) that is
∠EDB = ∠FDC = (180° -∠EDF)/2
Since ∠EDF = 90°
∠EDB = ∠FDC = (180° -90°)/2
∠EDB = ∠FDC = 90/2
∠EDB = ∠FDC = 45°
Since
∠DEB = 90° (5); and
∠DFC = 90° (7)
ΔBED ≅ ΔDFC
Thus, by Sum of Angles in a Triangle,
∠B ≅ ∠C.
The perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the segment.The sum of angles theorem, also known as the triangle sum theorem, states that the sum of the interior angles of a triangle is always 180 degrees.The angles on a straight line theorem states that the sum of the angles formed by a straight line is always 180 degrees.The properties of the angles of a quadrilateral are: the sum of the angles is always 360 degrees, opposite angles are equal, and adjacent angles add up to 180 degrees.
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Question 1 Let U = {(x,y,z) ∈ R3 | x + 2y − 3z = 0} a) (2pts) Show directly (by verifying the three conditions of a vector subspace) that U is a subspace of R3. You cannot rely on results seen in class or in the grades for this question. b) (2pts) Find a basis for U. Justify your answer. c) (1pt) Using your answer in b), determine dim(U).
U is a subspace of R3. A basis for U is {(1, -2, 3)} and dim(U) = 1.
a) To show that U is a subspace of R3, we must verify the three conditions:
1. U is non-empty, since the vector (0,0,0) ∈ U, since 0 + 2(0) - 3(0) = 0.
2. U is closed under addition, since for any two vectors (x1, y1, z1) and (x2, y2, z2) ∈ U, their sum (x1+x2, y1+y2, z1+z2) also satisfies the equation x1+x2 + 2(y1+y2) - 3(z1+z2) = 0, so it is also in U.
3. U is closed under scalar multiplication, since for any scalar c and any vector (x, y, z) ∈ U, the vector c(x,y,z) = (cx, cy, cz) also satisfies the equation cx + 2cy - 3cz = 0, so it is also in U.
Therefore, U is a subspace of R3.
b) To find a basis for U, we must find a linearly independent set of vectors which span U. One such set is the vector (1, -2, 3), since it satisfies the equation x + 2y - 3z = 0. Therefore, {(1, -2, 3)} is a basis for U.
c) The dimension of U is the number of vectors in its basis, which is 1. Therefore, dim(U) = 1.
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Solve the system of equations and choose the correct answer from the list of options. (4 points) x + y = −3 y = 2x + 2 a five over 3 comma 4 over 3 b negative 5 over 3 comma negative 4 over 3 c negative 3 over 5 comma negative 3 over 4 d 3 over 4 comma 3 over 5
The solution to the system of equations is (x, y) = (-5/3, -4/3).
What is system of linear equations?
A system of linear equations is a set of two or more equations with two or more variables that are to be solved simultaneously. Each equation in the system is linear, meaning it can be written in the form of ax + by + cz + ... = d, where a, b, c, and d are constants and x, y, z, and other variables are unknowns.
The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system. The solution of a system of linear equations is a set of values for the variables that make all of the equations true.
There are different methods to solve systems of linear equations, such as substitution method, elimination method, and matrix method. These methods involve manipulating the equations in the system to isolate one variable, substitute its value into another equation, and eventually find the values of all the variables.
Systems of linear equations are used in many areas of mathematics, science, engineering, and economics to model real-world situations and solve practical problems.
To solve the system of equations:
x + y = -3 (Equation 1)
y = 2x + 2 (Equation 2)
We can substitute Equation 2 into Equation 1 for y and solve for x:
x + (2x + 2) = -3
3x + 2 = -3
3x = -5
x = -5/3
Now that we know x, we can substitute it into either Equation 1 or Equation 2 to find y. Let's use Equation 2:
y = 2x + 2
y = 2(-5/3) + 2
y = -10/3 + 6/3
y = -4/3
Therefore, the solution to the system of equations is (x, y) = (-5/3, -4/3).
Comparing this solution to the answer choices, we see that option (b) is the correct answer:
(a) 5/3, 4/3
(b) -5/3, -4/3 <--- Correct answer
(c) -3/5, -3/4
(d) 3/4, 3/5
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