Answers
Answer:
fourth option
Step-by-step explanation:
Common difference is given by difference of two consecutive term
d = nth term - (n-1)th term
______________________________________
for all the series lets take second term as nth term
and first term as (n-1)th term
_________________________________________
for first series
n th term = -3 1/2 = -3.5
(n-1)th term = -5
therefore
d= -3.5 -(-5) = -3.5 +5 = 1.5
______________________________________
for second series
n th term = 4 1/2 = 4.5
(n-1)th term = 2 1/2 = 2.5
therefore
d= 4.5 -(2.5) =2
_________________________
for third series
n th term = 3
(n-1)th term =1.5
therefore
d= 3 - 1.5 = 1.5
__________________________________
for fourth series
n th term = -1.5
(n-1)th term = -4
therefore
d= -1.5 -(-4) = -1.5 + 4 = 2.5 = 2 1/2
___________________________________
Thus, based on above solution option four has common difference of 2 1/2
Related Questions
solve for x: 7^2x+3 =2401 . show substitution of your solution to verify the equation. show steps. show work.
Answers
Answer:
X= 1/2
Step-by-step explanation:
7^2x+3 =2401
7^(2x+3 )=2401
7^(2x+3 )= 7^4
Taking away the base because its equal to 7
Then solving the power as an equation
2x+3= 4
2x= 4-3
2x= 1
X=1/2
Now substituting x into the equation to know if we are correct
7^(2x+3 )=2401
Where x= 1/2
7^(2*(1/2) +3)= 7^4
7^(1+3)= 7^4
7^4= 7^4
7^4= 2401
Find the measure of a.
A. 60
B. 57
C. 40
D. 80
Answers
Answer:
Option (C)
Step-by-step explanation:
Since angle 'a' is the inscribed angle of the given triangle
Therefore, angle measure of the intercepted arc will be equal to the double of the inscribed angle.
x = 2a ⇒ a = [tex]\frac{x}{2}[/tex]
By the tangent-chord theorem,
"Angle between a chord and tangent measure the half of the angle measure of intercepted minor arc"
[tex]\frac{x}{2}[/tex] = 40°
Therefore, a = [tex]\frac{x}{2}[/tex] = 40°
Option (C) will be the answer.
Find secα, if sinα=−2/3 and 3π/2 <α<2π . Also the α=alpha symbol
Answers
Answer:
Step-by-step explanation:
Given sinα=−2/3, before we can get secα, we need to get the value of α first from sinα=−2/3.
[tex]sin \alpha = -2/3[/tex]
Taking the arcsin of both sides
[tex]sin^{-1}(sin\alpha) = sin^{-1} -2/3\\ \\\alpha = sin^{-1} -2/3\\ \\\alpha = -41.8^0[/tex]
Since sin is negative in the 3rd and 4th quadrant. In the 3rd quadrant;
α = 180°+41.8°
α = 221.8° which is between the range 270°<α<360°
secα = sec 221.8°
secα = 1/cos 221.8
secα = 1.34
As a bowling instructor, you calculate your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. What was that bowler's average?
Answers
Answer:
154.2
Step-by-step explanation:
To find the average of the bowlers scores, you have to find the mean by adding the values and dividing by the number of values.
To find the bowlers average add the scores and divide by the number of games.
143+156+172+133+167/5=154.2 is the average score for the bowler.
The position of an object at time t is given by s(t) = -9 - 3t. Find the instantaneous velocity at t = 8 by finding the derivative. I think its either -3 or -36
Answers
Answer:
[tex] \boxed{\sf Instantaneous \ velocity \ (v) = -3} [/tex]
Given:
Relation between position of an object at time t is given by:
s(t) = -9 - 3t
To Find:
Instantaneous velocity (v) at t = 8
Step-by-step explanation:
To find instantaneous velocity we will differentiate relation between position of an object at time t by t:
[tex] \sf \implies v = \frac{d}{dt} (s(t))[/tex]
[tex] \sf \implies v = \frac{d}{dt} ( - 9 - 3t)[/tex]
Differentiate the sum term by term and factor out constants:
[tex] \sf \implies v = \frac{d}{dt} ( - 9) - 3 (\frac{d}{dt} (t))[/tex]
The derivative of -9 is zero:
[tex] \sf \implies v = - 3( \frac{d}{dt} (t)) + 0[/tex]
Simplify the expression:
[tex] \sf \implies v = - 3( \frac{d}{dt} (t))[/tex]
The derivative of t is 1:
[tex] \sf \implies v = - 3 \times 1[/tex]
Simplify the expression:
[tex] \sf \implies v = - 3 [/tex]
(As, there is no variable after differentiating the relation between position of an object at time t by t so at time t = 8 is of no use.)
So,
Instantaneous velocity (v) at t = 8 is -3
the definition of parallel lines requires the undefined terms line and plane by the definition of perpendicular lines requires the undefined terms of line and point. what charcteristics of these geometric figures create the different requirements?
Answers
Answer:
Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.
Step-by-step explanation:
A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? 3 a. 0.22 c. 0.44 b. 0.78 d. 0.23
Answers
Answer:
.22
Step-by-step explanation:
The number of times a 3 was rolled is 44 out of 200
The experimental probability is 44/200 = .22
The frequency of rolling a 3 was 44.
So... 44/200
After dividing we get 0.22
Therefore, the answer is A
Best of Luck!
Original price of a soda: $800 tax 7% selling price: $
Answers
Answer:
$856
Step-by-step explanation:
Find 7% of $800 and then add it to $800
Please answer this correctly without making mistakes
Answers
Answer:
355/12
Step-by-step explanation:
Answer:
355/12mi
Step-by-step explanation:
9 1/2 = 19/2
20 1/12 = 241/12
19/2 + 241/12 = 355/12mi
a=5,and 5+z=14,so a+z=14
Answers
Answer:
Z=9
Step-by-step explanation:
Insert A into A+Z=14
5+z=14
Subtract 5 on both sides, to find Z.
-5 -5
z=9
Algebraic Expressions
Evaluate
The weight of a bag of oranges is 1.3 pounds. There are 9 bags of oranges. What is the total weight?
Help please :)
Answers
Answer:
11.7 pounds
Step-by-step explanation:
Multiply the weight of one bag of oranges by 9 bags.
Please answer this correctly without making mistakes
Answers
Answer:
so first convert to fraction so
9 3/4 = 39/4
so it was spread among 3
so this is division so you do 39/4 divided by 3
so you keep switch flip
which is 39/4 *1/3
answer is 13/4
Answer:
3 1/4 bagsStep-by-step explanation:
[tex]9\frac{3}{4}= \frac{(4 \times 9)+3}{4}= \frac{39}{4} \\\\\frac{39}{4} = 3 \:vegetable \: beds\\x \:\:\:= 1 \: vegetable \:bed\\\\3x = \frac{39}{4} \\\\\frac{3x}{3} = \frac{\frac{39}{4} }{3} \\\\x = \frac{13}{4} \\\\x = 3\frac{1}{4}[/tex]
I need help with this math problem please (3x+2)(5x-7)
Answers
Answer:
Hey there!
Using the foil method: (3x+2)(5x-7)
15x^2+10x-21x-14
15x^2-11x-14
Let me know if this helps :)
Here’s your answer (3x+2)x(5x-7)
Determine the point estimate of the population proportion and the margin of error for the following confidence interval.Lower boundequals0.212,upper boundequals0.758,nequals1200The point estimate of the population proportion is . 485.(Round to the nearest thousandth as needed.)The margin of error is 0.273.(Round to the nearest thousandth as needed.)
Answers
Answer: The point estimate of the population proportion is . 485.
The margin of error is 0.273.
Step-by-step explanation:
Confidence interval for population proportion(p):
sample proportion ± Margin of error
Given: Lower bound of confidence interval = 0.212
Upper bound = 0.758
⇒sample proportion - Margin of error=0.212 (i)
sample proportion + Margin of error= 0.758 (ii)
Adding (i) and (ii) , we get
2(sample proportion) =0.970
⇒ sample proportion = 0.970÷2= 0.485
Since sample proportion is the point estimate of the population proportion.
So, the point estimate of the population proportion= 0.485
Now put sample proportion =0.485 in (ii), we get
0.485+ Margin of error= 0.758
⇒ Margin of error= 0.758 - 0.485 =0.273
i.e. The margin of error is 0.273.
Apply the distributive property to factor out the greatest common factor. 40f+30 =
Answers
Answer:
10(4f+3)
Step-by-step explanation:
boo
One number is 4 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 370, find the numbers.
The three numbers are
(Use a comma to separate answers as needed.)
Answers
Answer:
45, 180, 145
Step-by-step explanation:
Let n represent the first number. Then "one number" is 4n, and the third number is n+100. The sum of the three numbers is ...
n + 4n + (n+100) = 370
6n = 270
n = 45
4n = 180
n+100 = 145
The three numbers are 45, 180, 145.
wo independent samples have been selected, 100 observations from population 1 and 76 observations from population 2. The sample means have been calculated to be x⎯⎯⎯1=11.9 and x⎯⎯⎯2=12.9. From previous experience with these populations, it is known that the variances are σ21=27 and σ22=23. (a) Determine the rejection region for the test of
Answers
Answer:
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
Step-by-step explanation:
A test for the difference between two population means is to be performed.
As the population variances are known, the z-test will be used.
The hypothesis can be defined as follows:
H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ₂
Assume that the significance level of the test is, α = 0.05.
The critical region can be defined as follows:
The critical value of z for α = 0.05 is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025} =-1.96\\\\z_{1-\alpha/2}=z_{1-0.05/2}=z_{0.975} =1.96[/tex]
Use a z-table.
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
PLEASE HELP !! (4/5) -50 POINTS-
Answers
2 -7 6 | 7
Second: x + 3y - 4z = 5
1 3 -4 | 5
Third: x + 6y - 15z = -6
1 6 -15 | -6
Arranged augmented matrix:
2 -7 6 | 7
1 3 -4 | 5
1 6 -15 | -6
Answer:
2 -7 6 7
1 3 -4 5
1 6 -15 -6
Step-by-step explanation:
An augmented matrix is the coefficients of the variables and then the solution in rows
Rewriting the equations
2x -7y +6x = 7
x +3y -4z = 5
x +6y -15z = -6
The matrix is
2 -7 6 7
1 3 -4 5
1 6 -15 -6
Suppose babies born in a large hospital have a mean weight of 3316 grams, and a standard deviation of 324 grams. If 83 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams?
Answers
Answer: 0.129
Step-by-step explanation:
Let [tex]\overline{X}[/tex] denotes a random variable that represents the mean weight of babies born.
Population mean : [tex]\mu= \text{3316 grams,}[/tex]
Standard deviation: [tex]\text{324 grams}[/tex]
Sample size = 83
Now, the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams will be :
[tex]P(|\mu-\overline{X}|>54)=1-P(\dfrac{-54}{\dfrac{324}{\sqrt{83}}}<\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{-54}{\dfrac{324}{\sqrt{83}}})\\\\=1-[P(-1.518<Z<1.518)\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-[P(Z<1.518)-P(z<-1.518)]\\\\=1-[P(Z<1.518)-(1-P(z<1.518))]\\\\=1-[2P(Z<1.518)-1]=2-2P(Z<1.518)\\\\=2-2(0.9355)\ [\text{By z-table}]\\\\=0.129[/tex]
hence, the required probability = 0.129
X = y + 12
How to solve for variable
Answers
Answer:
x-y=12
Step-by-step explanation:
Eliminate the parameter for the following set of parametric equations: x= t^2 + 2 y= 4t^2
Answers
Answer:
Solution : y = 4x - 8
Step-by-step explanation:
The first thing we want to do is isolate t², rather than t. Why? As you can see when we substitute t² into the second equation, it will be easier than substituting t, as t is present in the form t². So, let's isolate t² in the first equation --- ( 1 )
x = t² + 2,
t² = x - 2
Now let's substitute this value of t² in the second equation --- ( 2 )
y = 4t²,
y = 4(x - 2),
y = 4x - 8 ~ And hence our solution is option c.
Each side of a quilt square measures approximately 4.25 inches. If there are about 2.54 centimeters in 1 inch, how long is each side of the square in centimeters? Use complete sentences to explain your reasoning.
Answers
Answer: approximately 10.8 centimeters
Step-by-step explanation:
We have a square, where each side measures approx. 4.25 in
Now we know that 1in ≈ 2.54 cm
Then, in 4.25 in, we have 4.25 times 1 inch, so we have 4.25 times the length of 2.54 cm
So the approximate measure of the sides in centimeters is:
4.25*(2.54)cm = 10.8 cm
So we have that each side measures approximately 10.8 centimeters
Find the midpoint of the segment between the points (8,−10) and (−10,−8) A. (−1,−9) B. (0,−6) C. (0,0) D. (−1,2)
Answers
Answer:
Hey there!
We can use the midpoint formula to find that the midpoint is (-1, -9).
Let me know if this helps :)
The midpoint of the segment between the points (8,−10) and (−10,−8) will be (−1, −9). Then the correct option is A.
What is the midpoint of line segment AB?
Let C be the mid-point of the line segment AB.
A = (x₁, y₁)
B = (x₂, y₂)
C = (x, y)
Then the midpoint will be
x = (x₁ + x₂) / 2
y = (y₁ + y₂) / 2
The midpoint of the segment between the points (8,−10) and (−10,−8)
x = (8 – 10) / 2
x = –1
y = (– 10 – 8) / 2
y = –9
Then the correct option is A.
More about the midpoint of line segment AB link is given below.
https://brainly.com/question/17410964
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An Internet service provider is implementing a new program based on the number of connected devices in each household currently,customers are charged a flat rate of $175 per month.the new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network.find the number of devices,x,for which the cost of the new plan is less than the cost of the current plan.
Answers
Answer:
(x=6) is less than 18 which would give you the cost of the current plan
Step-by-step explanation:
If you take six, first you must multiply 4.50 by 6, ($27) then add it, to $94, giving you $121. Now we have to find which phone will give us the same cost, for this I choose 18. if you do 18 x 4.50, you get $81, and if you add this to 94, it gives you 175.
Find the slope of the line whose x-intercept is 4 and the y- intercept is -9
Answers
Answer:
y = (9/4)x - 9
Step-by-step explanation:
The x-intercept is (4, 0) and the y-intercept is (0, -9).
As we move from (0, -9) to (4, 0), x (the 'run' increases by 4 and y (the 'rise' increases by 9. Thus, the slope of the line connecting these two points is m = rise/run = 9/4, from which we can write the desired equation in the form y = mx + b:
y = (9/4)x - 9
At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
Answers
Answer:
a) What is the cost of a chicken shawarma wrap?
$10.99
b) What is the cost of one order of spiced potatoes?
$4.99
c) If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
Step-by-step explanation:
Let x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes,
Cost of a chicken sharwarma wrap = x
Cost of an order of spiced potatoes = y
Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.
3x + 2y = $42.95 .............Equation 1
Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.
5x + 4y = $74.91 ................Equation 2
Hence, the Equations needed to solve the question is:
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
We use Elimination method to solve for this.
Multiply Equation 1 by coefficient of x in Equation 2
Equation 2 by coefficient of x in Equation 1
3x + 2y = $42.95 .............Equation 1 × 5
5x + 4y = $74.91 ................Equation 2 × 3
15x + 10y = 214.75..............Equation 3
15x + 12y = 224.73..............Equation 4
Subtract Equation 3 from Equation 4
2y = 9.98
y = 9.98/2
y = 4.99
Therefore, y = Cost of an order of spiced potatoes = $4.99
Subtitute 4.99 for y in Equation 1
3x + 2y = $42.95 .............Equation 1
3x +2(4.99) = 42.95
3x + 9.98 = 42.95
3x = 42.95 - 9.98
3x = 32.97
x = 32.97/3
x = 10.99
x = Cost of a chicken sharwarma wrap = $10.99
Therefore,
The cost of a chicken sharwarma wrap = $10.99
The cost of an order of spiced potatoes = $4.99
What is an overdraft fee list two reasons why banks charge overdraft fees?
Answers
Answer:
An overdraft fee is a fee banks charge for withdrawing more money from an account than the current balance of that account. Banks charge overdraft fees to discourage overdrawing accounts and to make money from fees.
Step-by-step explanation:
Answer: Overdraft fee is when you withdraw more money from an account than the current balance of that account.
Step-by-step explanation:
Fees are charged to discourage overdrawing accounts and to make money from fees.
Find the value of x. A: 15 B: 12 C: 10 D: 8
Answers
Answer:
[tex]\boxed{\sf C. \ 10}[/tex]
Step-by-step explanation:
[tex]\sf The \ intersecting \ chord \ theorem \ states \ that \ the \ products[/tex]
[tex]\sf of \ the \ lengths \ of \ the \ line \ segments \ on \ each \ chord \ are \ equal.[/tex]
[tex]NH \times HT = MH \times HY[/tex]
[tex](x+20) \times 8=12 \times 20[/tex]
[tex]\sf Expand \ brackets \ and \ multiply.[/tex]
[tex]8x+160=240[/tex]
[tex]\sf Subtract \ 160 \ from \ both \ sides.[/tex]
[tex]8x+160-160=240-160[/tex]
[tex]8x=80[/tex]
[tex]\sf Divide \ both \ sides \ by \ 8.[/tex]
[tex]\displaystyle \frac{8x}{8} =\frac{80}{8}[/tex]
[tex]x=10[/tex]
The value of x is 10.
We have a circle and inside it two chords MY and NT intersect at point H.
We have to find the value of x in the figure.
What is intersecting chord theorem?According to the intersecting chord theorem, when two chords say AB and CD intersect at point O, then
AO x OB = CO x OD
Applying the chord intersecting theorem to the figure in the question, we get -
MH x HY = NH x HT
12 x 20 = (x+20) x 8
240 = 8x + 160
8x = 80
x = 10
Hence the value of x is 10.
To solve more questions on Circles and chords, visit the link below -
https://brainly.com/question/15568573
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Logan wants to mix an 18% acid solution with a 48% acid solution to get 15L of a 38% acid solution. How many liters of the 18% solution and how many liters of the 48% solution should be mixed?
Answers
Answer:
5 gallons of 18% solution
10 gallons of 48% solution
Step-by-step explanation:
x = gallons of 18% solution
y = gallons of 48% solution
Total volume is:
x + y = 15
Total amount of fertilizer is:
0.18 x + 0.48 y = 0.38 (15)
Solve by substitution.
0.18 x + 0.48 (15 − x) = 0.38 (15)
0.18 x + 7.2 − 0.48 x = 5.7
0.3 x = 1.5
x = 5
y = 10
Select the correct answer.
Answers
Answer:
B
Step-by-step explanation:
With limits, the first thing one should always try is direct substitution. Therefore, let's try that.
[tex]\lim_{x \to 1} (\frac{x^2+1}{x+1}+x^2+3) \\= (\frac{(1)^2+1}{(1)+1}+(1)^2+3) \\=\frac{2}{2}+1+3\\ =1+4=5[/tex]
Therefore:
[tex]\lim_{x \to 1} (\frac{x^2+1}{x+1}+x^2+3) =5[/tex]
