let the n'th term be called x, and the value of the term y,
then there is a function y=a*x + b
that will give us all term we want.
this formula is also used for straight lines.
we just need a and b. we already got two data points. we can just plug the known x/y pairs into the formula
10.5 = a*12 + b
13.5 = a*18 + b
now lets manipulate these lines.
multiply the first line by 3 and the second line by 2
31.5 = a*36 + 3b
27 = a*36 + 2b
subtract the second line from the first line
4.5 = b
yey, we now know b, let's plus b into either line from above, I'll go with the first one, looks easier.
10.5 = a*12 + 4.5
6 = a*12
0.5 = a
now y=a*x + b can be filled with a and b
y = 0.5 * x + 4.5
for x=1 (the first term) it's f(1)=5
each step is 0.5, hence the common difference.
2and way:(13.5-10.5)/(18-12)
= 3 / 6
= 0.5
we got the comment difference by looking at the full difference over 6 steps and divined by these 6 steps.
from step 12 to step one it's 11 steps down
10.5 - 0.5*11
= 10.5 - 5.5
= 5
okay I admit... 2and way to do it might be faster and more intuitive... :Dwhat is 7/8 divided by 1/8
Answer:
7
Step-by-step explanation:
Concepts:
Division: a system of distributing a collection of things into equal partsFractions: #s that represent a part of a wholeDividing Fractions: dividing a fraction by another fraction = multiplying the fraction by the inverse (reciprocal) of the other oneInverse Operations: operations that are opposite of each other (e.g. inverse of addition is subtraction)Solving:
1. First, let's set up the equation:
7/8 ÷ 1/8
2. We can get the reciprocal of 1/8 by doing the opposite of division; multiplication. 1/8 becomes 1 · 8, and that's equal to 8.
3. Now, since we know dividing a fraction by another one is exactly the same as multiplying the fraction by the reciprocal of the other, let's multiply 7/8 by the inverse of 1/8, which is 8.
7/8 · 8 = 56/8 = 7
Therefore, 7/8 divided by 1/8 is equal to 7.
What is the length of the radius of a cylinder if the diagonal is 15 mm and the height is 12 mm?
Answer:
Step-by-step explanation:
Let d and r be the diameter and radius, respectively.
d² + 12² = 15²
d² = 15² - 12² = 81
d = √81 = 9
r = d÷2 = 4.5 mm
Three times one number added to another number is 39. Twice the first number minus the other is 6. What are the numbers?5
Answer:
Step-by-step explanation:
Could someone help me out?
Answers:
DE = 1.1DF = 1.6BC = 4.8===========================================================
Explanation:
I recommend drawing the two triangles as shown below. The diagram isn't to scale, but all that matters is that we get the general idea down.
Your teacher gave you this info:
angle A = angle E (red angles)angle C = angle F (blue angles)These two pieces of info are enough to prove that triangle ABC is similar to triangle EDF. Use the angle angle (AA) similarity theorem to do this proof. The order of the lettering matters because it helps us see how the letters pair up.
A and E go firstB and D in the middleC and F go lastSince the triangles are similar, the scale factor to go from ABC to EDF is EF/AC = 2/6 = 1/3
In other words, the side lengths of triangle EDF are exactly 1/3 that of the corresponding lengths of ABC. Or we can reverse things to say the sides of ABC are 3 times longer than the sides of EDF.
----------------------
Use this scale factor to help determine the missing length ED.
(ED)/(AB) = scale factor
(ED)/(AB) = 1/3
(ED)/(3.3) = 1/3
ED = (1/3)*(3.3)
ED = 1.1
Note how ED/AB = (1.1)/(3.3) = 11/33 = 1/3
----------------------
While we don't know how long sides BC or DF are, we are told that DF is 3.2 units shorter compared to BC.
This means
DF = BC - 3.2
DF = x - 3.2
Then we can say,
(DF)/(BC) = scale factor
(x-3.2)/(x) = 1/3
3(x - 3.2) = x*1
3x - 9.6 = x
3x - x = 9.6
2x = 9.6
x = (9.6)/2
x = 4.8
So BC is x = 4.8 units long and DF is x-3.2 = 4.8-3.2 = 1.6 units long
Suppose that d varies jointly with r and t, and d = 110 when r = 55 and t = 2. Find r when d = 40 and t = 3.
Answer:
r = 13.33
Step-by-step explanation:
d = k*r*t
Where,
k = constant of proportionality
d = 110 when r = 55 and t = 2
d = k*r*t
110 = k * 55 * 2
110 = 110k
k = 110/110
k = 1
Find r when d = 40 and t = 3
d = k*r*t
40 = 1 * r * 3
40 = 3r
r = 40/3
= 13.333333333333
Approximately,
r = 13.33
A shopkeeper sold a piece of kurta salwar for rs. 1080 at a loss of 10%.At what price should he sell to gain 10% on it
Answer:
1320 Rs.
Step-by-step explanation:
let cost price=x
loss=10 %
S.P.=x×90/100=9x/10
9x/10=1080
x=1080×10/9=1200 Rs
so C.P.=1200 Rs
gain=10%
S.P.=110/100×1200=1320 Rs
answer please it's urgent
Answer:
HOPE IT HELP YOU . Plz tell me if it is write or wrong .
what is the equation of the line that is parallel to the given line and passes through the point (-3,2)? no links.
Answer:
D) 4x +3y = -6
Step-by-step explanation:
paralell lines so m1 and m2 are equal
m = (3 +1 )/ (0 - 3 )
m = -4/ 3
y -2 = -4/3 (x +3)
y =-4x/3 -2
3y = -4x -6
4x +3y = -6
hlp mehhhhhhhhh plsssssssss
Answer:
graph - A
Step-by-step explanation:
find the missing side of the triangle
Answer:
x = 40
Step-by-step explanation:
3-4-5 triangle scale factor by 10
Missing side is 4
4*10 = 40 | Multiply by 10 bc of scale factor
x = 40
show that's ABE = EBC
Answer:
abe = ebc
Step-by-step explanation:
bcos both the seperate angels have the same degree
A box contains a yellow ball, an orange ball, a green ball, and a blue ball. Billy randomly selects 4 balls from the box (with replacement). What is the expected value for the number of distinct colored balls Billy will select?
Answer:
[tex]Expected = 0.09375[/tex]
Step-by-step explanation:
Given
[tex]Balls = 4[/tex]
[tex]n = 4[/tex] --- selection
Required
The expected distinct colored balls
The probability of selecting one of the 4 balls is:
[tex]P = \frac{1}{4}[/tex]
The probability of selecting different balls in each selection is:
[tex]Pr = (\frac{1}{4})^n[/tex]
Substitute 4 for n
[tex]Pr = (\frac{1}{4})^4[/tex]
[tex]Pr = \frac{1}{256}[/tex]
The number of arrangement of the 4 balls is:
[tex]Arrangement = 4![/tex]
So, we have:
[tex]Arrangement = 4*3*2*1[/tex]
[tex]Arrangement = 24[/tex]
The expected number of distinct color is:
[tex]Expected = Arrangement * Pr[/tex]
[tex]Expected = 24 * \frac{1}{256}[/tex]
[tex]Expected = \frac{3}{32}[/tex]
[tex]Expected = 0.09375[/tex]
what is 5cd when c = 3 and d = 4
[tex] \sf \: c = 3 \\ \sf \: d = 4 \\ \\ \sf \: 5cd \: = \: ?\\ \\ \sf \:5 cd \hookrightarrow \\ \sf = 5 \times (3) \times (4) \\ \sf = 5 \times 12 \\ = \underline{ \bf \: 60}[/tex]
-> Just substitute the values given for variables c & d in the equation 5cd & you'll get the answer.
WILL GIVE BRAINLIEST TO THE CORRECT ANSWER!!
Suppose you obtain a five-year lease for a Porsche and negotiate a selling price of $146,000. The annual interest rate is 8.4%, the residual value is $75,000, and you make a down payment of $3000. Find each of the following.
A.) The net capitalized cost.
B.) The money factor. (Rounded to four decimal places)
C.) The average monthly finance charge. (Rounded to the nearest cent).
D.) The average monthly depreciation. (Rounded to the nearest cent.)
E.) The monthly lease payment. (Rounded to the nearest cent.)
Answer:
Look down below
Step-by-step explanation:
A.)Net capitalized cost=146,000-3000= $143,000
Net capitalized cost = 143,000
B.)Money factor=8.4/100 over 24=0.084/24=0.0035
Money Factor= 0.0035
C.)Average monthly finance charge= (143,000+75,000)x 0.0035= 218,000 x 0.0035=$763
Average Monthly Finance Charge= $763
D.)Average monthly depreciation= 143,000-75000/5 x 12=68000/60=$1133.33
Average monthly deprecation= $1133.33
E.)monthly lease payment=1133.33/5= $226.66
Monthly lease payment= $226.66
3. Grace has twice as much money as tad
Together they have $36. How much Money
des Tad have?
Answer:
Tad has 12 dollars and Grace has 24
Step-by-step explanation:
Grace has twice as much, 24 is double 12. So Tad has 12 dollars.
Ed takes five 100-point tests in his algebra class. He scores 87, 85 and 87 points on the first three tests. If the scores of his last two tests differ by three points and he has a 90% average on his five tests, what was his highest test score?
PLS ANSWER QUICK WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
When we take an average of something, we have to add up all the data on the somethings and then divide by the number of somethings we have. Ed takes 5 tests, and we have scores for them; we also have his current average. What we don't know for sure are 2 of the 5 test scores, but we have enough to determine what they are.
If one test has a score of x, and the other test is 3 points less than that, the score on that last test is x - 3. Putting all of that together into an average problem:
[tex]\frac{87+85+87+x+(x-3)}{5}=90[/tex] and simplfiying a bit:
[tex]\frac{256+2x}{5}=90[/tex]. Multiply both sides by 5 to get
256 + 2x = 450; subtract 256 from both sides to get
2x = 194 and divide by 2:
x = 97
The one test score was a 97 and the other one, which was 3 less than that, was a 94.
Solve for 2. Round to the nearest tenth, if necessary.
51
66
H
Answer: 2
Submit Answer
attempt 1 out of 2
PLS HELP
Answer:
x = 53.4
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 51 = 66/x
x tan 51 = 66
x = 66/ tan 51
x=53.44574
Rounding to the nearest tenth
x = 53.4
find the measure of the indicated angle to the nearest degree
Answer:
71°
Step-by-step explanation:
12/36 = 1/3
inverse cos(1/3) = 70.53 = 71
Find the GCF for:
uv, ut
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
Answer:
-6/-2<-2x/-2
divide both sides by-2 to remain with the x variable on one side
I hope this helps
I need help asap!!Explain how to do the problem
Answer:
Step-by-step explanation:
the scale factor is 2. one length is 10, and the other is 5. pythagorean therom approved.
Marking brainliest
If a job interview says “tell me about yourself” what do u say
Answer:
I start to say from my name,age,family,qualifications and etc.
Answer:
In your response, do the following:
1. Mention past experiences and proven successes as they relate to the position.Begin by rereading the job description. Take note of the required skills that you have, and identify recent stories that demonstrate them . Ideally, you should draw primarily from recent professional experience; however, volunteer work can also support your narrative while demonstrating a commitment to your community.
2. Consider how your current job relates to the job you’re applying for.Is it a more senior role? If so, explain how you are taking on more responsibilities in your current position. If you are making a lateral transition to a role with different skills, describe how your current skills translate into the new position.
3. Focus on strengths and abilities that you can support with examples.When you start building the script of each example, focus on details and outcomes that you can quantify if possible. For example, stating that you “improved customer service” is less impactful than “increased customer service response rates each quarter by 10–15%.” If you don’t have the exact information, estimate a realistic value.
4. Highlight your personality to break the ice.Since the “Tell me about yourself” interview question is about getting to know you, it’s a good idea to share your personality with your interviewer—but not personal details. You may want to briefly mention hobbies that demonstrate intellectual development and/or community engagement (e.g., reading, music, sports league, volunteering) or those that showcase personal discipline and achievement (e.g., learning a new skill, training for a half marathon). Discussing personal interests is a good way to wrap up your response while maintaining a professional tone.
5. Format your response.For your response to be clear and concise, you’ll want to make sure you organize your answer following a format or formula. There are two common formulas you may consider:
Present, Past, FuturePast, Present, FutureBoth of these formulas work for your response, but you may choose one over the other based on the roles from your experience that are most relevant to the position you're interviewing for. For example, if your most recent role highlights many of the skills and qualifications that are required for the role you’re interviewing with, you may want to lead with the present. However, if you're making a career transition and your past experience is more closely related to the role than your current position, you may want to lead with your past.
On the midnight shift, the number of patients with head trauma in an emergency room has the probability distribution shown below. x 0 1 2 3 4 5 Total P(x) .07 .36 .27 .17 .10 .03 1.00
Answer:
1.96 ;
1.216
Step-by-step explanation:
Given the data :
x : __0 _ 1 _ 2 _ 3 _4 _5 Total
P(x) .07 .36 .27 .17 .10 .03 1.00
. The mean, also called the expected value is defined as ;
E(X) = Σx*p(x)
E(X) = (0*0.07) + (1*0.36) + (2*0.27) + (3*0.17) + (4*0.10) + (5*0.03) = 1.96
The standard deviation, ; √var(x)
Var(X) = Σx²*p(x) - E(X)²
Var(X) = [(0² * 0.07) + (1² * 0.36) + (2² * 0.27) + (3² * 0.17) + (4² * 0.10) + (5² * 0.03)] - 1.96²
Var(X) = 5.32 - 3.8416
Var(X) =14784
SD(X) = √1. 4784 = 1.216
find the missing side of the triangle
Answer:
7 sqrt(2) = c
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
7^2 + 7^2 = x^2
49+49 = c^2
98 = c^2
Taking the square root of each side
sqrt(98) = sqrt(c^2)
sqrt(49*2) = c
7 sqrt(2) = c
HELP I NEED HELP PLS IM FAILING ITS PYTHAGOREAN THEOREM
2^2 + 2^2 = h^2
8 = h^2
√8 = h
h = 2.82mm
Answered by Gauthmath must click thanks and mark brainliest
Find the area of a regular
polygon with 5 sides that has a
side length of 6 inches and an
apothem of 9 inches.
Answer:
Step-by-step explanation:
Height of the triangle = apothem = 9 inches
Base = 6 inches
[tex]Area \ of \ triangle = \frac{1}{2}bh\\\\=\frac{1}{2}*6*9\\\\= 3*9\\\\= 27 \ in^{2}[/tex]
Area of regular polygon = Area of 5 triangle.
= 5 * 27
= 135 square inches
URGENT PLS HELP . pls put explanation as well. thank you:)
Answer:
The promoters profit would be $46,350 if they sell 850 tickets
Step-by-step explanation:
The value 61 is likely the cost of each ticket, and the value 5,500 is likely the amount the promoter spent in order to promote at the concert since it was being subtracted from his profits
Hope this helps :)
A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean of thousand miles and a standard deviation of thousand miles. Complete parts (a) through (d) below.
Complete question is;
A trucking company determined that the distance traveled per truck per year in its entire fleet was normally distributed with a mean of 55 thousand miles and a standard deviation of 11 thousand miles.
a)A truck in the fleet traveled 42 thousand miles in the last vear. Calculate the z-score for this truck.
b) Interpret the z-score
c) The trucking company has a policy that any truck with mileage more than 2.5 standard deviations above the mean should be removed from the road and inspected. What is the probability that a randomly selected truck from the fleet will have to be inspected?
d) A randomly selected truck in the fleet traveled 85 thousand miles in the last year. Should this truck be removed from the road and inspected? Explain why or why not.
Answer:
A) z = - 1.18
B) Interpretation of the z-score in A above shows that the distance traveled per truck per year in its entire fleet is 1.18 standard deviations lesser than the distance traveled per truck on average
C) P(z > 2.5) = 0.0062
D) it's value of z is greater than 2.5 minimum and so the truck will be removed from the road and inspected
Step-by-step explanation:
A) We are given;
Population mean; μ = 55000
Sample mean; x¯ = 42000
Standard deviation; σ = 11000
Z-score formula is;
z = (x¯ - μ)/σ
z = (42000 - 55000)/11000
z = - 1.18
B) Interpretation of the z-score in A above shows that the distance traveled per truck per year in its entire fleet is 1.18 standard deviations lesser than the distance traveled per truck on average.
C) since it has a policy that any truck with mileage more than 2.5 standard deviations above the mean should be removed from the road and inspected, then it means that probability that it will be inspected is;
P(z > 2.5) = 1 - P(z < 2.5)
From p-values from z-score table, we have;
P(z > 2.5) = 1 - 0.9938
P(z > 2.5) = 0.0062
D) A randomly selected truck in the fleet traveled 85 thousand miles in the last year. Thus; x¯ = 85000.
Thus;
z = (85000 - 55000)/11000
z = 2.73
This value of z is greater than 2.5 minimum and so the truck will be removed from the road and inspected
Rationalise the denominator
Answer:
sqrt(3) /3
Step-by-step explanation:
1 / sqrt(3)
Multiply the top and bottom by sqrt(3)
1/ sqrt(3) * sqrt(3)/ sqrt(3)
sqrt(3) / sqrt(3)*sqrt(3)
sqrt(3) /3
Answer:
[tex] = { \sf{ \frac{1}{ \sqrt{3} } }} \\ \\ { \sf{ = \frac{1}{ \sqrt{3} } . \frac{ \sqrt{3} }{ \sqrt{3} } }} \\ \\ = { \sf{ \frac{ \sqrt{3} }{ {( \sqrt{3}) }^{2} } = \frac{ \sqrt{3} }{3} }} [/tex]
Find the range of the function f(x)=-4x-8 for the domain {0,1,2}
Answer:
Since this function is definable for all real values of x,
Domain(f(x)) = R = (-∞,∞)
Step-by-step explanation:
Now,
Let 4x-8=y
4x = y+8
x = (y+8)/4
Since x is definable for all real values of y,
Range(f(x)) = R = (-∞,∞)
