Find the first five terms for the following arithmetic sequence Tn=5n-6?
Answer:
The first five terms are -1,4,9,14 and 19.
Step-by-step explanation:
The arithmetic sequence is :
[tex]T_n=5n-6[/tex]
We need to find the first five terms of the sequence.
Put n = 1 for first term.
[tex]T_1=5(1)-6=-1[/tex]
Put n = 2 for second term.
[tex]T_2=5(2)-6=\\\\=10-6\\\\=4[/tex]
Put n = 3 for third term.
[tex]T_3=5(3)-6=\\\\=15-6\\\\=9[/tex]
Put n = 4 for fourth term.
[tex]T_4=5(4)-6=\\\\=20-6\\\\=14[/tex]
Put n = 5 for fifth term.
[tex]T_3=5(5)-6=\\\\=25-6\\\\=19[/tex]
Hence, the first five terms are -1,4,9,14 and 19.
Grace Cut three pieces of ribbon each piece was 2/5 of a foot long. How many feet of ribbon does she have in all?
Graph the line -4x+y=-8
You don't need to graph it, I just need the equation in a y=mx+b format
Answer: y = 4x - 8
Step-by-step explanation:
It’s actually quite simple, what you have to do is isolate the “y”
JK=2x+5 and KL=3x-8 find JL
Answer:
Step-by-step explanation:
3x -8 = 2x + 5
x - 8 = 5
x = 13
3(13) - 8 + 2(13) + 5
39 - 8 + 26 + 5
31 + 31 = 62
25x(x + 5)
80 points I need answer ASAP
Answer:
[tex]25 {x}^{2} + 125x[/tex]
hope it helpswhat is the square of 2/3
Answer:
4/9
Step-by-step explanation:
or,2×2=4
or,3×3=9
or,4/9
someone pls help me!! thank you!!
Final Answer is 4.5
= 4.5hours more time was used on games than on research.
please help anyone will mark BRAINILEST !!!!!!!!!!!!!!!!!!!!!!!!!!
if 2m - 6 = 8m then 3m = ?
A. 3
B. -1
C. -3
D. -6
Answer:
c
Step-by-step explanation:
m= -3
c option
Thanks me later
Answer:
c
Step-by-step explanation:
3m - 6 = -3......da da bop boom pow
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8 minutes and a standard deviation of 2.8 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.
A button hyperlink to the SALT program that reads: Use SALT.
(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
Need Help? Read It
Answer:
a) 0.9207 = 92.07% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes
b) 0.8907 = 89.07% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes
c) 0.8114 = 81.14% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For sum of n normally distributed variables, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex].
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
For a single commercial jet:
[tex]\mu = 8, \sigma = 2.8[/tex]
For the 37 jets combined:
[tex]\mu = 37*8 = 296, s = 2.8\sqrt{37} = 17.03[/tex]
(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?
This is the pvalue of Z when X = 320. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{320 - 296}{17.03}[/tex]
[tex]Z = 1.41[/tex]
[tex]Z = 1.41[/tex] has a pvalue of 0.9207
0.9207 = 92.07% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.
(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?
This is 1 subtracted by the pvalue of Z when [tex]X = 275[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{275 - 296}{17.03}[/tex]
[tex]Z = -1.23[/tex]
[tex]Z = -1.23[/tex] has a pvalue of 0.1093
1 - 0.1093 = 0.8907
0.8907 = 89.07% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.
(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?
This is the pvalue of Z when [tex]X = 320[/tex] subtracted by the pvalue of | when [tex]X = 275[/tex]
From a and b
0.9207 - 0.1093 = 0.8114
0.8114 = 81.14% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes
x is. 2 less than. y
Answer:
x is 2 less than y
[tex] \huge \boxed{x = y - 2}[/tex]
Caroline was thinking of a number. Caroline halves the number and gets 7.3. Form an equation with x from the information.
Answer:
The equation is: [tex]\frac{x}{2} = 7.3[/tex]
Step-by-step explanation:
Caroline was thinking of a number.
We are going to call this number x.
Caroline halves the number and gets 7.3.
To find half of a number, we multiply by 1/2. So
[tex]\frac{1}{2} \times x = 7.3[/tex]
[tex]\frac{x}{2} = 7.3[/tex]
Choose the A that seems to be congruent to the given one.
AADBA
OECB
BCA
EAB
Answer:
BCA
Step-by-step explanation:
assuming the shape is symmetrical, BCA would be the congruent (equal) angle
At what point does an angle with measure 75º in standard position intersect with unit circle?
a.
(sin 75º, tan 75º)
b.
(cos 75º, tan 75º)
c.
(sin 75º, cos 75º)
d.
(cos 75º, sin 75º)
Answer:
d
Step-by-step explanation:
x=rcosθ
y=rsinθ
r=1
θ=76°
#11: Write the equation below in standard form.
*
y - 2 = -4(x - 1)
Answer:
y - 2 = -4x + 4
Step-by-step explanation:
Just simplify is out ^-^
4 x + y = 6 Should do the trick
P= x/3 and x = 1/2 y. Write p in terms of y
Answer:
p = 1/2y - 3
Step-by-step explanation:
p=x/3 and x=1/2y [replace the "x" to solve]
p = (1/2y)/3
what are numbers that are the same distance from 0 but in opposite directions
Answer:
Opposite numbers
Step-by-step explanation:
Opposite numbers are defined as numbers that have the same distance from zero but are on opposite sides of zero. So opposite numbers have the same absolute values. Another word for opposite numbers is additive inverses because when opposite numbers are added together the sum is always zero.
Leilany was on a treadmill and ran 1 mile in 9 minutes. How many minutes will it take her to run 3 miles?
Answer:
27
Step-by-step explanation:
1 mile took 9 min to run, so 3 miles will be:
3 x 9 =
27
8) 3(2x+1) = ?*
O 6x + 3
5x + 1
5x + 3
6x + 1
Answer:
6x + 3
General Formulas and Concepts:
Pre-Algebra
Distributive Property
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
3(2x + 1)
Step 2: Expand
Distribute 3: 3(2x) + 3(1)Multiply: 6x + 39x - 3 + x² , when x = 4
Step-by-step explanation:
=9x-3+x²
=9×4-3+4²
=36-3+16
=49
hope it helps.
Highschool level trigonometry!!! Need help knowing step by step how to find answer!
A ladder is 15 m long. The top of the ladder rests against the wall of a house, and the foot rests on level ground 2m from the wall. Draw a diagram to illustrate the situation. Calculate the angle between the ladder and the ground.
Answer:
[tex]\theta \approx 82.34^\circ[/tex]
Step-by-step explanation:
Please refer to the attached diagram. (Apologies if the shading or resolution is a bit off.)
So, we want to find θ.
Since we formed a right triangle, we can use right triangle ratios.
We know the measure of the adjacent side to θ and the hypotenuse.
Therefore, we will use the cosine ratio:
[tex]\displaystyle \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side is 2 and the hypotenuse is 15. By substitution:
[tex]\displaystyle \cos(\theta)=\frac{2}{15}[/tex]
Now, we will take the inverse cosine of both sides. So:
[tex]\displaystyle \theta=\cos^{-1}\Big(\frac{2}{15}\Big)[/tex]
Use a calculator. Hence:
[tex]\theta \approx 82.34^\circ[/tex]
The angle between the ground and the ladder is about 82.34°.
Juan bought fruit from the grocery store. The variables below define his purchase. Juan’s bananas cost half as much as apples. Which equations can be used to model his purchase? Select each correct equation. *
Answer:
[tex]B = \frac{1}{2}A[/tex]
[tex]A = 2B[/tex]
Step-by-step explanation:
Given
Represent apple with A and Banana with B
Required
Determine the relationship between A and B
From the question, we understand that:
B costs half as much as A
This can be represented as:
[tex]B = \frac{1}{2} * A[/tex]
[tex]B = \frac{1}{2}A[/tex]
Multiply both sides by 2
[tex]2*B = \frac{1}{2}A*2[/tex]
[tex]2B = A[/tex]
[tex]A = 2B[/tex]
A boat travels 8 miles north from point A to point B. Then it moves in the direction 5 40°W and reaches point Finally, it turns 5 40° E and
returns to point A
The total distance covered by the boat is going how many
miles.
A. 14.95
B. 18.44
C. 20.04
D. 25.88
Answer:
B, 18.44 miles
if you can get 3 pints of raspberries for $12.00 how many pints can you get per dollar
Answer:
0.25 pints of raspberries do you get per dollar
7 2/3
16 3/5
+ 8 1/2
______
7. Wr ite a multiplication equation that represents the question: how many 2/5s are in 9/4?* Your answer
Answer:
how many 2/5s are in 9/4? - it would be two
hope this helps
Which of the following would have a scale factor greater than one?
a) A Hot Wheels car
b) A picture of a skyscraper
c) A map of the world
d) A diagram of a plant cell
Answer:
NIO
Step-by-step explanation:
a
PLEASE HELP!!!!!!!!!!!
9514 1404 393
Answer:
a. plane DEA
Step-by-step explanation:
A plane can be named by naming any 3 non-collinear points in the plane, or by using the plane's name as indicated in the drawing.
Here, points in the plane are A, D, E, F, with DEF all on the same line. So A plus any two points from the line will constitute a name for the plane. Also, this plane is identified with a script M that can be used to name the plane.
M is not an answer choice, but DEA is. So, the appropriate choice is ...
plane DEA
__
F is a point, not a plane name. C is not on the plane, so cannot be used to name it. 'k' is a line name, not a plane name.
Plz help I’m bad at algebraic expressions and translating them.
Here are the expressions.
1.Four more than a number
2.The difference of a number and 9
3.Two times a number plus 6
4.The quotient of n and 6
5.2 times the sum of a number and 3
Answer:
1. 4+n
2. n-9
3. 2n + 6
4. n/6
5. 2(n+3)
Step-by-step explanation:
PLEASE HELP ME 20 POINTS!!!!!!!!!!! In the plane shown in the figure below, lines land mare cut by the transversal line n. The eight angles at the
intersections of these lines are labeled. Which of the following statements, when it is true, CANNOT always be used
to prove that lines land mare parallel?
Answer:
Option (4)
Step-by-step explanation:
Since, lines l and m are the parallel lines and line 'n' is intersecting these parallel lines,
Option (1)
∠c ≅ ∠y
True.
[Corresponding interior angles]
Option (2)
∠a ≅ ∠w
True.
[Corresponding interior angles]
Option (3)
∠b ≅ ∠x
True.
[Corresponding interior angles]
Option (4)
∠b ≅ ∠z
False.
[Since, ∠b + ∠Z = 180°, consecutive exterior angles]
Option (5)
∠a ≅ ∠z
True.
[Alternate exterior angles]
Therefore, Option (4) will be the answer.
Explain the rules for multiplication and division to convert units. How do you know when to multiply and when to divide to convert units of measurement?
Write three to four sentences.
Answer:
You can use similar processes when converting from smaller to larger units. When converting a larger unit to a smaller one, you multiply; when you convert a smaller unit to a larger one, you divide.
The basic rule is: If you need to convert from a larger unit to a smaller unit, multiply. If you need to convert from a smaller unit to a larger unit, divide. You will make the number smaller and, as you already know, division is all about making numbers smaller.
Answer: To convert larger units to smaller units, multiply. When the units are smaller, you need more of them to express the same measure. To convert smaller units to larger units, divide. When the units are larger, you need fewer of them to express the same measure.
Step-by-step explanation: edge 2022