write a variable expression to describe the rule of each progression then calculate the term 20 or 20 term1.) 6,12,18,24,...2.)3,6,9,12,...3.)1,5,9,13...
Answers
1) 6, 12,18,24
The rule used here is: Arithmetic Progression or Linear sequence
From the data above:
a = 6, d = 6
\(\begin{gathered} T_{n\text{ }}=\text{ a + (n-1)d} \\ \text{where n = 20} \\ T_{20\text{ }}=\text{ a + (20-1)d} \\ T_{20\text{ }}\text{ = a + 19d} \\ T_{20\text{ }}\text{ = 6 + 19}\times6 \\ T_{20\text{ }}\text{ = 6 + 114} \\ T_{20\text{ }}\text{ = 120} \end{gathered}\)2) 3,6,9,12
The rule used here is: Arithmetic Progression or Linear sequence
From the data above:
a = 3, d = 3
\(\begin{gathered} T_{n\text{ }}=\text{ a + (n-1)d} \\ \text{where n = 20} \\ T_{20\text{ }}=\text{ a + (20-1)d} \\ T_{20\text{ }}\text{ = a + 19d} \\ T_{20\text{ }}\text{ = 3 + 19 }\times3 \\ T_{20\text{ }}\text{ = 3 + 57} \\ T_{20\text{ }}\text{ = 60} \end{gathered}\)3) 1,5,9,13
The rule used here is: Arithmetic Progression or Linear sequence
From the data above:
a = 1, d = 4
\(\begin{gathered} T_{n\text{ }}=\text{ a + (n-1)d} \\ \text{where n = 20} \\ T_{20\text{ }}=\text{ a + (20-1)d} \\ T_{20\text{ }}\text{ = a + 19d} \\ T_{20\text{ }}\text{ = 1 + 19 }\times4 \\ T_{20\text{ }}\text{ = }1\text{ + 76} \\ T_{20\text{ }}\text{ = }77 \end{gathered}\)
Related Questions
Can someone help me and tell me where it’s located at I will mark u brilliant
Answers
Answer: You can do this!
Step-by-step explanation: For D. The x= -1 and the y= 1 for E same thing the x= 7 and the y= 1 so look for the 7 on the x-axes and the one on the y-axes get it. I believe that you got this!
Hope this helped love<3
Please help solve 3m/2/3 = 7
Answers
Answer:
the solution to the equation is m = 28/3, or approximately 9.3333
Step-by-step explanation:
To solve this equation, you need to get the variable, in this case "m," by itself on one side of the equation. To do this, you can start by isolating the fraction on the left side of the equation. You can do this by multiplying both sides of the equation by 2/3, which will cancel out the 2/3 on the left side:
3m/2/3 = 7
(2/3) * (3m/2/3) = (2/3) * 7
3m/2 = 7 * (2/3)
3m/2 = 14/3
Next, you can multiply both sides of the equation by 2 to get rid of the fraction on the left side:
(2) * (3m/2) = (2) * (14/3)
3m = 28/3
Finally, you can simplify the right side of the equation by dividing both sides by 3 to get the final solution:
(3m) / 3 = (28/3) / 3
m = 28/3
Therefore, the solution to the equation is m = 28/3, or approximately 9.3333.
Answer:
Maybe m = 14/9
Maybe m = 14
Step-by-step explanation:
It is not clear what you mean by the fraction on the left side.
Do you mean
3m/(2/3) = 7 ?
If so:
3m = 7 × 2/3
3m = 14/3
m = 14/9
Do you mean
(3m/2)/3 = 7 ?
If so:
3m/2 = 21
m = 21 × 2/3
m = 14
Do you mean something else?
Estimate the following quantities without using a calculator. Then find a more precise result, using a calculator if necessary. Discuss whether the approximation technique worked.
Answers
The approximate value of 63000 x 200 will be 12600000.
What is multiplication?
In mathematics, multiplication is defined as the sum of the numbers to the other number given. Like if 2 is multiplied by 3 then the multiplication will be the sum of the two-three times.
Given expression is 63000 x 200 so here we need to calculate the sum of the 63000 to 200 times.
E = 63000 x 200
E = 12600000
Therefore the approximate value of 63000 x 200 will be 12600000.
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Mr. Li and Ms. Brown both sell used cars. Mr. Li sells a car for $9950 and earns $447.75 commission. Ms. Brown sells a car for $10,300 and earns $453.20 commission. Who eams a greater commission
rate?
Answers
Answer:
Mr. Li
Step-by-step explanation:
$447.75 is 4.5% of $9,950 - Mr. Li earns a 4.5% commission
$453.20 is 4.4% of $10300 - Ms. Brown earns a 4.4% commission
An island is located 48 miles N23°38'W of a city. A
freighter in distress radios its position as N11°26'E of the
island and N12° 16'W of the city. How far is the freighter
from the city?
Answers
The freighter is approximately 164.33 miles from the city.
How to determine how far is the freighter from the city?We can use the Law of Cosines to solve this problem. Let's label the distances as follows:
d: distance between the city and the freighter
x: distance between the city and the island
y: distance between the island and the freighter
First, we need to find x using the given coordinates:
N23°38'W is equivalent to S23°38'E, so we have:
cos(23°38') = x/48
x = 48cos(23°38') ≈ 42.67 miles
Next, we can use the coordinates of the freighter to find y:
N11°26'E is equivalent to E11°26'N, and N12°16'W is equivalent to S12°16'E. This means that the angle between the island and the freighter is:
23°38' + 11°26' + 12°16' = 47°20'
cos(47°20') = y/d
We can rearrange this equation to solve for y:
y = dcos(47°20')
Now we can use the Law of Cosines to solve for d:
d² = x² + y² - 2xy cos(90° - 47°20')
d² = 42.67² + (d cos(47°20'))² - 2(42.67)(d cos(47°20')) sin(47°20')
d² = 1822.44 + d² cos²(47°20') - 2(42.67)(d cos(47°20')) sin(47°20')
d² - d² cos²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')
d² (1 - cos²(47°20')) = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')
d² sin²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')
d² = (1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')) / sin²(47°20')
d ≈ 164.33 miles
Therefore, the freighter is approximately 164.33 miles from the city.
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What is the slope of the line?
Answers
Answer:
The slope is 2
Step-by-step explanation:
From the y-intercept which is 1, to get to the next point, you would go up 2 and 1 right which is 2/1, and 2/1 is technically just 2.
Hope this helps and pls do mark me brainliest if you can:)
Jackson's car was making a rumbling noise for 2 weeks. He decided to take it to the mechanic to get it checked out. To diagnose the problem, the mechanic tells Jackson that he charges a flat, one-time fee of $60 and then $35 for each hour he spends trying to identify the problem. What is the slope in this scenario?
Answers
Answer:
The slope is 35
Step-by-step explanation:
Given
\(One\ Time\ Fee = \$60\)
\(Hourly\ Rate = \$35\)
Required
Determine the slope
First, we need to determine the equation.
Let y represents the total charges and x represents the number of hours.
y is calculated using;
\(y = One\ Time\ Fee + Hourly\ Rate * x\)
This gives:
\(y = 60 + 35* x\)
\(y = 60 + 35x\)
Reorder
\(y =35x + 60\)
The general form of an equation is:
\(y =mx + b\)
Where m represents the slope
By comparison of \(y =mx + b\) and \(y =35x + 60\)
\(m = 35\)
Hence, the slope is 35
TIME REMAINING
58:53
The solution to the system of equation below is (−2, −1).
2x − 3y = −1
11x − 9y = −13
When the first equation is multiplied by −3, the sum of the two equations is equivalent to 5x = −10.
Answers
Answer:
XD is an emoticon commonly used to symbolize dying from laughter. It represents 2 closed eyes with the X and mouth with the D.
The solution of the equations is (-2, -1)
System of equation:2x - 3y = -1
11x - 9y = -13
Using elimination method let multiply the first equation by -3.
Therefore,
-6x + 9y = 3
11x - 9y = -13
5x = -10
x = -10 / 5
x = -2
let's find y as follows;
2(-2) - 3y = -1
-4 - 3y = -1
-3y = -1 + 4
-3y = 3
y = 3 / -3
y = -1
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Please help me solve the following Geometry problems. I am including a screenshot of the math problems. They state as follows:
5.) Solve for x.
6.) Given EB // DC. Prove: triangle AEB -- triangle ADC. Use a flow chart.
7. Given that the line graphed to the right has tan (0) = 9/5 and goes through the point (0,7).
a.) What is the equation of the line?
b.) What is the x-intercept?
Answers
Answer:
a.) The equation of the line is y = 9/5x + 7.
b.) The x-intercept is (0,7).
What is the solution to the system of equations?
7z+3y=-11
2z+ 5y = 1
Answers
Answer:
y=1 , z=-2
Step-by-step explanation:
I will use the method of elimination :
Multiply the top equation by 5 to make equation 3 :
35z + 15y = -55
Multiply bottom equation by 3 to make equation 4:
6z + 15y = 3
Subtract equation 3 from equation 4 to eliminate the y :
-29z = 58
Divide both sides by -29 to solve for z :
z = 58 ÷ -29
z = -2
Substitute this value into either equation 1 or 2 to solve for y :
I chose equation 2 :
2(-2) + 5y = 1
-4 + 5y = 1
Add 4 to both sides :
5y = 5
Divide both sides by 5 :
y = 1
Hope this helped and have a good day
Colin slices a cake into 8 equal-sized slices. He and his friends eat 5 slices of the cake.
What fractional part of the cake do Colin and his friends eat?
Answers
Answer:
5/8
Step-by-step explanation:
there are 8 slices.
if he and his friends eat 5 pieces, they ate 5 out of 8 pieces.
in maths, we write 5 out of 8 like 5/8
hope this helped, any questions - just ask
good luck,
-cheesetoasty
A tank in the shape of a hemisphere has a diameter of 24 feet. If the liquid that fills the tank has a density of 92.5 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
The total weight of the liquid in the tank is approximately 12,628 pounds.
To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.
In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.
Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.
In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.
By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.
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Solving Inequalities Using Addition or Sub
Solve x - 4 < 5. Graph the solution
The solution is
Answers
Given 1 || m ||
|| n, find the value of x.
(x-6)⁰
60⁰
1
m
n
Answers
The value of x in the lines is 126 degree
We are given that;
Three parallel line and one intersecting line
Angles= (x-6) and 60
Now,
By supplementary angles property
Angle 1 + Angle 2 = 180 degree
Substituting the values of angles
x-6 + 60 = 180
x + 54 = 180
x = 180-54
x = 126
Therefore by supplementary angles answer will be 126 degree.
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The variable x represents w value in the set {4, 6, 7, 8}. Which value of x makes 2 (x - 4) + 3 = 7 a true statement
Answers
(12x)
B
(2x + 5)
с
E
x= Answer
MAD -
Answer
BC
Answer
MDC
Answer
mDBC
Answer
D
(17x-14)
Answers
Answer:
x = 9
m(AD) = 108°
m(BC) = 23°
m(DC) = 139°
m(DBC) = 162°
Step-by-step explanation:
AD = 12x°
BC = (2x + 5)°
DC = (17x - 14)°
m<AEB = right angle = 90°
AB = m<AEB = 90° (central angle theorem)
90 + 12x + (2x + 5) + (17x - 14) = 360 (full circle)
✔️Solve for x
90 + 12x + 2x + 5 + 17x - 14 = 360
Add like terms
81 + 31x = 360
31x = 360 - 81
31x = 279
x = 279/31
x = 9
✔️Find m(AD)
m(AD) = 12x
Plug in the value of x
m(AD) = 12(9) = 108°
✔️Find m(BC):
m(BC) = (2x + 5) = 2(9) + 5
m(BC) = 23°
✔️Find m(DC) = (17x - 14)° = 17(9) - 14
m(DC) = 139°
✔️Find m(DBC) = m(DC) + m(BC) = 139° + 23° = 162°
Mack is selling beaded necklaces and beaded wristbands at the Craft Market.
A necklace requires 40 minutes to make.
A wristband requires 25 minutes to make.
Mack has 360 minutes to make the necklaces and wristbands.
.
●
.
Additionally,
Mack wants to make no more than 12 items.
When Mack sells the necklaces and wristbands at the Craft Market, he will make $3.00 profit per necklace and
$2.00 profit per wristband.
Let x = the number of necklaces Mack makes.
.
.
Let y= the number of wristbands Mack makes.
TEXT ANSWER
Question 14
1 Points
Evaluate each vertex ordered pair in the profit function. Which vertex yields the maxi-
mum profit?
Answers
Mack should make 9 necklaces and 3.6 (rounded to 4) wristbands to maximize his profit.
We have,
The profit function is given by:
P(x,y) = 3x + 2y
The constraints are:
40x + 25y ≤ 360 (time constraint)
x + y ≤ 12 (item constraint)
x, y ≥ 0 (non-negative constraint)
To find the vertices, we need to solve the system of equations for each pair of intersecting lines. The vertices are the points where the lines intersect.
40x + 25y = 360
x + y = 12
Solving this system of equations, we get:
x = 6, y = 6 (vertex 1)
x = 9, y = 3.6 (vertex 2)
x = 0, y = 12 (vertex 3)
Now, we evaluate each vertex in the profit function:
P(6,6) = 3(6) + 2(6) = 24
P(9,3.6) = 3(9) + 2(3.6) = 30.6
P(0,12) = 3(0) + 2(12) = 24
Now,
Vertex 2 yields a maximum profit of $30.60.
Therefore,
Mack should make 9 necklaces and 3.6 (rounded to 4) wristbands to maximize his profit.
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The school has 220 students, 75 are participating in the dance. Write the participant students in simplest fraction, decimals and in percentage.
Answers
Decimals: 0.34090909
Percentage: 34.09%
Answer:
75 is written as 3/4 as a fraction in its simplest form .
0.75 as a decimal ..
75% as a percentage ..
Step-by-step explanation:
I hope this is right .!!^^
#2! thanks baebaeeeeeeeeee
Answers
HELP MEEEEEEEEE PLEASEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!
HELP MEEEEEEEEE PLEASEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!
HELP MEEEEEEEEE PLEASEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!
Answers
Answer: 3 or 4
Step-by-step explanation:
f(x)=0.48In(x+2)+27=28 multiply both sides by 100
48In(x+2)+2700=2800 subtract 2700 from both sides
48In(x+2)=100
In(x+2)=\(\frac{25}{12}\) apply log rule
x+2 = e\(\frac{25}{12}\)
x = e\(\frac{25}{12}\) - 2
x = 3.66
Express the confidence interval 71.6% ± 8.2% in the form of a trilinear inequality.
Answers
The confidence interval, expressed as a trilinear inequality, is 71.6%
What does a confidence interval mean?
The range of values we see in our sample and expect to find the value that most accurately represents the population are referred to as a confidence interval.
The lower bound is 71.6% - 8.2% = 63.4% and the upper bound is 71.6% + 8.2% = 79.8%.
Thus the confidence interval, expressed as a trilinear inequality, is 63.4% < p < 79.8%, where p= 71.6%.
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NBA players have heights that are normally distributed with μ =79 in. and σ =3.5 in.If one player is selected, find the probability that he is:a.) shorter than 75 inb.) between 73 and 83 inC.) What height would cut off the tallest 7% of players?Now, 16 players are selected.d.) Find the probability that their average height is above 80 in.
Answers
Given
\(μ=79in.\text{ }and\text{ }σ=3.5in.\)Explanation
Part A: shorter than 75 in
First we will find the z-score
\(\begin{gathered} z_{75}=\frac{x-\mu}{\sigma}=\frac{75-79}{3.5}=-1.14286 \\ \end{gathered}\)We can then get the P-value from Z-Table:
Answer:
\(P\left(x<75\right)=0.12655\)Part B: Between 73 and 83 in
\(\begin{gathered} When\text{ x =73} \\ Zscore=\frac{x-μ}{\sigma}=\frac{73-79}{3.5}=-1.71429 \\ When\text{ x =83} \\ Zscore=\frac{x-μ}{\sigma}=\frac{83-79}{3.5}=1.14286 \\ \end{gathered}\)We can then get the P-value from Z-Table for the range 73 to 83
\(P\left(-1.71429Answer:
\(P(73Part CTo solve this, we will find the z score for p(x>z)=7% . Using the z-score calculator.
\(\begin{gathered} For\text{ }p(x>z)=0.07 \\ z=1.476 \end{gathered}\)Then we will find the value of x using the z score formula;
\(\begin{gathered} z=\frac{x-\mu}{\sigma} \\ 1.476=\frac{x-79}{3.5} \\ 1.476\times3.5=x-79 \\ switch\text{ sides} \\ x-79=5.166 \\ x=79+5.166 \\ x=84.166 \end{gathered}\)Answer: Approximately 84
Part D
Since a sample of 16 students is now selected, the formula to use will be changed to accommodate the sample.
\(z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\)Therefore, the z score becomes
\(z=\frac{80-79}{\frac{3.5}{\sqrt{16}}}=\frac{1}{\frac{3.5}{4}}=\frac{4}{3.5}=1.14285\)Using the z-score calculator
\(p(x>80)=p(x>1.14285)=0.12655\)Answer: 0.12655
Jacob needs 48 ounces of tomatoes for the spaghetti sauce. He is choosing between two brands of tomatoes. Find the unit rate for each brand. Round to the nearest cent (hundredth).
Brand A costs
per ounce.
Brand B costs
per ounce.
Answers
Answer:
Brand A Costs 37.38 per ounce and Brand B cost 31.19 per ounce hope this helped ^-^
What is the median of the data set 50,54,62,48,49,52
Answers
Answer:
51
Step-by-step explanation:
arrange in ascending order
48,49,50,52 54,62
number of terms=6
median=(3rd term+4th term)/2=(50+52)/2=102/2=51
Answer:
51
Step-by-step explanation:
Hope it helps
A cell phone plan has a monthly cost that is shown in the table below. What is the correct statement regarding the average rate of change
during the 40-minute time of talk? (1 point)
Answers
Answer:
Second from top...
The average rate of change is $0.07, meaning that for each minute of talk time, the monthly bill increases by $0.07.
Step-by-step explanation:
Pick any two points and calculate the slope which will represent the rate of change:
(Minutes, Cost)
(0, 9.95)
(10, 10.65)
Rate of change:
slope m = (y₂ - y₁) / (x₂ - x₁)
= (10.65 - 9.95) / (10 - 0)
= 0.7 / 10
= 0.07
y is cost
m is rate of change
x is minute(s) use
b is fixed monthly cost regardless if any minutes is used
y = mx + b
y = .07x + 9.95
Can you please find and solve the unknown variable.
Answers
The value of x is; x = 3.14
Here, we have,
from the given diagram, we get,
there is a right angle triangle.
we have to find the value of x.
we know that,
Let the angle be θ , such that
cos θ = base / hypotenuse
here, we get,
cos 17 = 3/x
so, we have,
0.956 = 3/x
so, x = 3.14
Hence, The value of x is;x = 3.14
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What is the slope of the following line?
Answers
Answer:c, the answer is c
Step-by-step explanation:
In the xy-plane, the slope of the line y = mx − 4 is
less than the slope of the line y = x − 4. Which of the
following must be true about m?
[Show Workings}
I will give brainlist to the person with the right
Answers
If the slope of the line y = mx − 4 is less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement
The slope of a line defines the steepness of such a line. It is the ratio of the rise to the run of a line.
The general formula for calculating an equation of a line is expressed as:
\(y = mx + b\) where:
m is the slope of the line
Given the equation of the line, \(y=x-4\) the slope of the line will be derived through comparison as shown:
\(mx=1x\\\)
Divide through by x
\(\dfrac{mx}{x} = \dfrac{1x}{x}\\ m=1\)
Hence the slope of the line y = x - 1 is 1.
According to the question, since we are told that the slope of the line
y = mx − 4 is less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement
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Answer:
Step-by-step explanation:
Please help I’m begging someone p,ease help I can’t do this anymore help
Answers
Answer:
-5.99
-3
-6
-5.9
-1
-5.999
-5
2
Step-by-step explanation:
All these numbers are greater (or equal to) -6 because they are closer to 0
please see attachment
Answers
Answer:
a) The value of absolute minimum value = - 0.3536
b) which is attained at \(x = \frac{1}{\sqrt{2} }\)
Step-by-step explanation:
Step(i):-
Given function
\(f(x) = \frac{-x}{2x^{2} +1}\) ...(i)
Differentiating equation (i) with respective to 'x'
\(f^{l} = \frac{2x^{2} +1(-1) - (-x) (4x)}{(2x^{2}+1)^{2} }\) ...(ii)
\(f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} }\)
Equating Zero
\(f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0\)
\(\frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0\)
\(2 x^{2}-1 = 0\)
\(2 x^{2} = 1\)
\(x^{2} = \frac{1}{2}\)
\(x = \frac{-1}{\sqrt{2} } , x = \frac{1}{\sqrt{2} }\)
Step(ii):-
Again Differentiating equation (ii) with respective to 'x'
\(f^{ll}(x) = \frac{(2x^{2} +1)^{2} (4x) - 2(2x^{2} +1) (4x)(2x^{2}-1) }{(2x^{2}+1)^{4} }\)
put
\(x = \frac{1}{\sqrt{2} }\)
\(f^{ll} (x) > 0\)
The absolute minimum value at \(x = \frac{1}{\sqrt{2} }\)
Step(iii):-
The value of absolute minimum value
\(f(x) = \frac{-x}{2x^{2} +1}\)
\(f(\frac{1}{\sqrt{2} } ) = \frac{-\frac{1}{\sqrt{2} } }{2(\frac{1}{\sqrt{2} } )^{2} +1}\)
on calculation we get
The value of absolute minimum value = - 0.3536
Final answer:-
a) The value of absolute minimum value = - 0.3536
b) which is attained at \(x = \frac{1}{\sqrt{2} }\)