How is the pattern changing to get from one term to the next ? -48, -44, -40, -36, -32, . . .
The given pattern is
\(-48,-44,-40,-36,-32\)We will find the difference between the consecutive terms
\(\begin{gathered} -44-(-48)=-44+48=4 \\ -40-(-44)=-40+44=4 \\ -36-(-40)=-36+40=4 \\ -32-(-36)=-32+36=4 \end{gathered}\)Then the pattern is increasing by 4 units
The pattern is changing by adding 4
Evaluate ∫ c
fds, where f(x,y,z)=z and c(t)=(tcost,tsint,t) for 0≤t≤t 0
.
The value of the integral ∫c f ds is (√3/2) t₀²
The given integral is ∫c f ds
where f (x,y,z) = z and c (t) = (t cos t, t sin t, t) for 0 ≤ t ≤ t₀.
To find the integration, we first need to find the derivative of the position vector
r(t) = (t cos t)i + (t sin t)j + tk.
Now,
r'(t) = cos t i + sin t j + k
Integrating r'(t) between the limits of 0 and t₀, we get
r(t₀) - r(0) = cos t₀ i + sin t₀ j + k - (i + 0 j + 0 k)
= (cos t₀ - 1)i + sin t₀ j + k
= c(t₀) - c(0)
Now, ||r'(t)|| = √(1² + 1² + 1²) = √3
The given integral is∫c f ds = ∫₀^t₀ z √(dx/dt)² + (dy/dt)² + (dz/dt)² dts = ∫₀^t₀ t √3 dt = (√3 t²/2)|₀^t₀ = (√3/2) t₀²
Thus, the value of ∫c f ds is (√3/2) t₀².
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A line is drawn on a scatter plot, as shown below:
A graph shows values till 10 on both x- and y axis with increments of 1.Dots are shown at 0.5, 7.5 and 1.8, 6.5 and 3, 6 and 4.4, 5 and 4.8, 4 and 5.9, 3.2 and 6.6, 2 and 7.5, 2.5 and 8, 1 and 8.8, 0. A straight line joins the ordered pairs 0, 7.9 and 10, 0.
Which statement best describes the line?
Answer:
It can be the line of best fit because it closely fits the data points.
Step-by-step explanation:
The line is near the data points and goes down from left to right just like the data points. It is just above or just below the data points.
Answer:
guy above is right
Step-by-step explanation:
PLEASE HELP FAST EMERGENCY
Answer:
C because you add 1 to both sides
Solve the equation for x:
2(x+3)−12=18
Answer: X=12
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Which graph best represents the solution set of -4x ≤ 6y − 54?
Answer:
a
Step-by-step explanation:
if its the same one i saw, the answer is a :)
If the mean of a given dataset is 131 and the standard deviation is 8, where will a majority of the data lie?
A. 123 to 139
B. 131 to 139
C. 123 to 131
Answer:
A
Step-by-step explanation:
The reason it has to be A is because you don't have to even thing about the standard deviation right here because the only answer that has a mean of 131 is answer A.
Hope it helps have a great afternoon:)
Jarvis is buying a boat that costs $6,000. He has $500 for a down payment. He is deciding between a 2-year loan and a 3-year loan. Use the rates in the table to determine how much money he will save if he chooses the 2-year loan instead of the 3-year loan. Round to the nearest cent.
Answer:
247.5
Step-by-step explanation:
i know this because i did this last week and got it correct
Answer:247.5
Step-by-step explanation:
At a charity fund-raiser, adult tickets were sold for $7 each and children's tickets were sold for $2 each. Write an algebraic expression for the total amount of
money raised from the sale of tickets. How much money was raised if the fundraiser fsold 246 adult tickets and 380 children's tickets?
Let a = the number of adult tickets and let c = the number of child tickets. Then, an algebraic expression for the total money raised from the sale of tickets is
Answer:
x is amount of money
c + a = 646
2c + 7a = x
2(380) + 7(246) = 2486
x = $2486
Graph the line
y=-4x+2
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Answer:It would be -4 across and go two up
Step-by-step explanation:
Answer:
It would be -4 across and go two up
Step-by-step explanation:
Just B please. It’s not 4:3 tho please can someone helo
Answer:
The workout ratio of the online sales to shop sales is 1:3
Step-by-step explanation:
Given:
A jewelry shop sells 240 necklaces in a month. 180 of the necklaces were sold via the shops website. The rest were sold in a High Street shop.
To find:
Work out the ratio of online sales to shop sales.
Solution:
Total no necklaces = 240
Necklace sold on website = 180
Remaining necklace sold via street = 240 - 180 = 60
Ratio = 60 : 180 = 1 : 3
Find the radius when d=18
Answer:
9
Step-by-step explanation:
radius is half of the diameter
A shot-putter throws a shot and its height is noted every 20 feet, the data is in the table below:
Feet Traveled Feet Above Ground
20 25
40 40
60 55
80 65
100 71
120 77
140 77
160 75
180 71
200 64
Please find the quadratic function of best fit for these data and, to the hundredths place, say what height, in feet, the shot started its flight.
The quadratic function of best fit for the data is given as follows:
h(t) = -0.004t² +1.032t + 5.667.
Using this function, the initial height of the shot is of 5.67 feet.
Why a quadratic function of best fit is used, and how to find it?The input and the output of the data are given as follows:
Input: feet traveled.Output: feet above the ground.As the input increases, the output increases and then it decreases. Since this behavior of increase/decrease is not uniform over the entire domain of the relation, a quadratic function best models this data.
To find the quadratic function of best fit, we insert the points (input,output) into a calculator, from point (20, 25) to point (200,64).
Inserting the points into the calculator, the function is defined as follows:
h(t) = -0.004t² +1.032t + 5.667
The height in which the shot started its flight is given by the height when t = 0, hence:
h(0) = -0.004(0)² + 1.032(0) + 5.667 = 5.667 feet = 5.67 feet (rounded to the hundredths place).
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What is the solution to -(2x + 4) + x = 3x − 4x − 4?
Answer:
all real numbers
Step-by-step explanation:
-(2x + 4) + x = 3x − 4x − 4
Distribute the negative sign on the left side. It is the same as having a -1 to the left of the parentheses.
-1(2x + 4) + x = 3x − 4x − 4
-2x - 4 + x = 3x - 4x - 4
Combine like terms on the left side. Combine like terms on the right side.
-x - 4 = -x - 4
Add 4 to both sides.
-x = -x
Add x to both sides.
0 = 0
You end up with a true equation. Therefore, there is an infinite number of solutions. Every real number is a solution.
Answer: all real numbers
Q2) C: The probability that a randomly selected elementary or secondary school teacher from a city is a female is 0.68, holds a second job is 0.38, and is a female and holds a second job is 0.29. Find the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job. a. 0.77 b. 0.99 c. 0.66 d. 0.88
The probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job is 0.77, the correct answer is a.
To find the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job, we can use the inclusion-exclusion principle.
Let's denote:
P(F) = Probability of being a female
P(S) = Probability of holding a second job
From the given information:
P(F) = 0.68
P(S) = 0.38
P(F ∩ S) = 0.29 (Probability of being a female and holding a second job)
Using the inclusion-exclusion principle, the probability of the union (female or holding a second job) is given by:
P(F ∪ S) = P(F) + P(S) - P(F ∩ S)
Substituting the values:
P(F ∪ S) = 0.68 + 0.38 - 0.29
P(F ∪ S) = 0.77
Therefore, the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job is 0.77. Hence, the correct answer is a. 0.77.
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if the area of the triangle is 261 square meters, find the value of x.
The value of x which is the length of the base of the triangle in the question is; 29 meters
What is a triangle?A triangle is a three sided polygon, with three interior angles.
Please find attached the possible diagram in the figure, (created with MS Word), which is a question from a mathematics textbook posted on the internet
The diagram indicates that the altitude or height of the triangle = 8 meters
The specified area of the triangle is; A = 261 square meters
The base length of the triangle = x
The formula for the area of a triangle, A, is; A = (1/2) ×Base length × Height
Therefore;
A = 261 m² = (1/2) × x × 18 m
x = 261 m² ÷ ((1/2) × 18 m) = 29 m
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Consumers in a certain state can choose between three long-distance telephone services: GTT, NCJ, and Dash. Aggressive marketing by all three companies results in a continual shift of customers among the three services. Each year, GTT loses 20% of its customers to NCJ and 15% to Dash, NCJ loses 5% of its customers to GTT and 5% to Dash, and Dash loses 25% of its customers to GTT and 15% to NCJ. Assuming that these percentages remain valid over a long period of time, what is each company's expected market share in the long run?
GTT's expected market share:
NCJ's expected market share:
Dash's expected market share:
GTT's expected market share is 45.45%, NCJ's expected market share is 31.82%, and Dash's expected market share is 22.73%. these percentages add up to 100%, as expected.
To find the long-run expected market share for each company, we need to use the concept of steady-state or equilibrium. In the long run, the market share of each company will remain constant if the number of customers gained is equal to the number of customers lost. This means that the rate of change of each company's market share will be zero.
Let's define the market share of each company at any point in time as follows:
GTT's market share = SGTT
NCJ's market share = SNCJ
Dash's market share = SDash
We can write the equations for the rate of change of each company's market share as follows:
dSGTT/dt = -0.2 SGTT + 0.05 SNCJ + 0.25 SDash
dSNCJ/dt = -0.05 SNCJ + 0.05 SGTT + 0.15 SDash
dSDash/dt = -0.15 SDash + 0.25 SGTT + 0.15 SNCJ
Note that the negative coefficients represent the percentage of customers lost by the company, and the positive coefficients represent the percentage of customers gained by the company.
To find the steady-state values of SGTT, SNCJ, and SDash, we need to set the rate of change of each company's market share to zero:
-0.2 SGTT + 0.05 SNCJ + 0.25 SDash = 0
-0.05 SNCJ + 0.05 SGTT + 0.15 SDash = 0
-0.15 SDash + 0.25 SGTT + 0.15 SNCJ = 0
We can solve these equations to get the steady-state values of SGTT, SNCJ, and SDash:
SGTT = 0.4545
SNCJ = 0.3182
SDash = 0.2273
Therefore, the expected long-run market share for each company is as follows:
GTT's expected market share: 45.45%
NCJ's expected market share: 31.82%
Dash's expected market share: 22.73%
Therefore, these percentages add up to 100%, as expected.
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help this is my last try!!!!!!!!!!!!!!!!!!!!!!!!11
Answer:
2^8=256
Step-by-step explanation:
Multiply the exponents and simplify
Suppose that the function f(x) = 5.32 + 0.80x represents the cost of mailing an object that weighs x pounds. What is f(36)?
The value of function at x = 36 is 34.12.
To find the cost of mailing an object that weighs 36 pounds, we can substitute the value of x into the function f(x) = 5.32 + 0.80x.
The function f(x) = 5.32 + 0.80x represents a linear relationship between the weight of the object (x) and the cost (f(x)) with a base cost of $5.32 and an additional cost of $0.80 per pound. By plugging in the value of 36 into the function, we can calculate the specific cost for that weight.
Plugging in x = 36, we have:
f(36) = 5.32 + 0.80 * 36
Simplifying the expression:
f(36) = 5.32 + 28.8
f(36) = 34.12
Therefore, f(36) is equal to 34.12. This means that it would cost $34.12 to mail an object weighing 36 pounds according to the given function.
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For a school project two students shona and miguel record the number of text messgaes each of them sent each day for 60- day period. the box plots summarize the record data
The range of the data for Shona and Miguel will be 35 and 30, while the median of the data will be 40 and 42.5.
What is a boxplot?A boxplot is a visual representation of a data set's dispersion and centers.
The interquartile range and the mean of the data set are two examples of spread measures. The mean, average, and median are examples of center measures.
The data set of the Miguel is;
25,30,35,40,45,50,55
The median of the data is;
\(\rm Median =( \frac{n+1}{2}) ^{th} term \\\\ Median =( \frac{7+1}{2} )^{th} term \\\\ Median = 4 ^{th} term \\\\ Median = 40\)
Shona's data is;
25,30,35,40,45,50,55,60
The median of Miguel's data is;
\(\rm Median_{shona} = \rm \frac{40+45}{2} \\\\ Median_{shona} =42.5\)
The range of Miguel's data is;
⇒ 55-25
⇒ 30
The range of Shona's data is;
⇒60-25
⇒35
Hence, the median of the data for Shona and Miguel will be 40 and 42.5 and the range of the data for Shona and Miguel will be 35 and 30.
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The midpoint of AB is M(3, -2). If the coordinates of A are (8,4), what are the
coordinates of B?
Answer:
B(-2, -8)Step-by-step explanation:
M being midpoint of AB means:
\(x_B-x_M=x_M-x_A\qquad\quad\ \wedge\qquad y_B-y_M=y_M-y_A\\\\x_B-3=3-8\qquad\quad\wedge\qquad\quad y_B-(-2)=-2-4\\\\x_B-3=-5\qquad\quad\ \wedge\qquad\quad y_B+2=-6\\\\x_B=-5+3\qquad\quad\ \wedge\qquad\quad y_B=-6-2\\\\x_B=-2\qquad\qquad\ \wedge\qquad\qquad y_B=-8\)
simplify.
\( {y }^{ - 3} \)
Options:
3/y
-1/y^3
-3y
1/y^3
Answer:
Rewrite the expression using the negative exponent rule [text]{b}^{-n } = 1/bn
Step-by-step explanation:
1/y^3
PLEASE HELP. I WILL GIVE YOU 50 POINTS
What are the real and imaginary parts of the complex number?
−6+2i
Answer:
The real number is - 6 and the imaginary number is 2.
Answer:
Step-by-step explanation:
the real numbers are -6 and 2
the imaginery is i
Order the numbers from least to greatest: 0.82, 0.8, 0.83 repeating.
Answer: 0.83,0.82,0.8
just points for whomever help me
Answer:
with what do you need help with your life
Step-by-step explanation:
One side of a rectangle is 2 yd longer than two times another side. The area of the rectangle is 84 yd2. Find the length of the shorter side.
Answer:
6 yds
Step-by-step explanation:
If we label the shorter side as x, the longer side can be represented as 2x + 2. Now, we can write an equation to model the situation. The area of a rectangle is the sides multiplied by each other:
84 = x(2x + 2)
84 = 2x^2 + 2x
Since all terms are divisible by two, we can divide both sides by it:
42 = x^2 + x
We can write the quadratic equation in standard form:
x^2 + x - 42 = 0
Now, we can factor. We are looking for numbers that multiply to -42 and add to 1. These numbers are 7 and -6. Factored the equation would be written as followed:
(x + 7)(x - 6) = 0
Using the zero-product property, we can obtain two equations and solve them:
x + 7 = 0
x = -7
x - 6 = 0
x = 6
Since the side of a rectangle can't be negative, the answer must be 6 yds.
There are 1,044 apartments in Baldwin County this year, which is approximately an 8.1% increase from last
year. How many apartments were there in Baldwin County last year?
Given :
Total apartments 1044 .
Increase in apartments , 8.1 % .
To Find :
How many apartments were there in Baldwin County last year.
Solution :
Let , amount of apartments last year is x .
So ,
\(\dfrac{1044-x}{x}\times 100=8.1\\\\(1044-x)\times 100=8.1x\\\\104400-100x=8.1x\\\\108.1x=104400\\\\x=\dfrac{104400}{108.1}\\\\x=965\)
Hence , this is the required solution .
Please help on number 3 I’m so confused and it’s urgent. It’s due soon please help
By using function notation, you should write an equation or expression for each statement as follows;
The temperature at 12 p.m ⇒ f(12).
The temperature was the same at 9 a.m. and at 4 p.m ⇒ f(9) = f(16).
It was warmer at 9 a.m. than at 6 a.m ⇒ f(9) > f(6).
Some time after midnight, the temperature was 24 degrees Celsius. ⇒ f(t) = 24.
What is a function?In Mathematics, a function simply refers to a mathematical expression which can be used for defining and showing the relationship that exist between two or more variables in a data set.
This ultimately implies that, a function typically shows the relationship between input values (x-values or domain) and output values (y-values or range) of a data set, as well as showing how the elements in a table are uniquely paired (mapped).
For the statement, "The temperature was the same at 9 a.m. and at 4 p.m." we have:
4 p.m = 12 + 4 = 16
In function notation, we have:
f(9) = f(16) or f(16) = f(9)
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Find the slope of a line perpendicular to y = 5/2x +1
A.-2/5
B.2/5
C.-5/2
D. 5/2
Answer:
a-2/5 that the correct anwers
One side of a square is (x+3) units. The
perimeter of the square is 32 units. What
is X?
Answer:
x = 5
Step-by-step explanation:
So the perimeter of a square is 4 times the side length.
4 (x+3) = 32 is the equation we can make out with the given information.
Solve for x:
Distribute the 4 to the terms inside the parenthesis; 4x + 12 = 32
Subtract 12 from both sides; 4x = 20
Divide both sides by 4; x = 5
By isolating x, we get 5 as the value of x.