Answer:
aₙ = -3n + 8Step-by-step explanation:
The nth term of an arithmetic sequence: aₙ = a₁ + d(n - 1)
{d = common difference}
a₁ = 5
a₄ = 5 + d(4 - 1)
-4 = 5 + 3d
-4 - 5 = 3d
3d = -9
d = -3
Therefore;
aₙ = 5 + (-3)(n - 1)
aₙ = -3n + 8
Check: a₁₀ = 5 + (-3)(10 - 1) = 5 - 27 = - 22
The nth term of the sequence is Tn = 8 - 3n
How to determine the function of the nth term?The given parameters are:
a = 5, first term
T4 = -4 --- the 4th term
T10 = -22 --- the 10th term
The nth term of an arithmetic sequence is:
Tn = a + (n - 1) * d
So, we have:
T4 = a + (4 - 1) * d
Substitute known values
-4 = 5 +(4 -1) * d
This gives
-4 = 5 + 3d
Subtract 5 from both sides
3d = -9
Divide by 3
d = -3
Recall that:
Tn = a + (n - 1) * d
So, we have:
Tn = 5 + (n - 1) * -3
Expand
Tn = 5 + 3 - 3n
Solve
Tn = 8 - 3n
Hence, the nth term of the sequence is Tn = 8 - 3n
Read more about arithmetic sequence at:
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Abir walks four twelfths of a mile to school. Nadia walks two twelfths of a mile to school. How much farther does Abir walk than Nadia?
Answer:
SHe has walked 2 more miles more than the other person
Step-by-step explanation:
Is rolling a 5 on a traditional number cube
1. Impossible
2. Unlikely
3. Likely
4. Certain
Answer:
3. Likely
Step-by-step explanation:
6) The cost of a computer system increases with increased processor speeds. The cost C
of a system as a function of processor speed is estimated as C = 1234 - 35 + 1900,
where S is the processor speed in MHz. Find the processor speed for which cost is at a
minimum. [4 marks]
Answer:
The speed is: 0.0142MHz
Step-by-step explanation:
Given
[tex]C(s) = 1234s^2 - 35s + 1900[/tex]
Required
The processor speed when the cost is at minimum
First, differentiate C(s) with respect to s
[tex]C(s) = 1234s^2 - 35s + 1900[/tex]
[tex]C'(s) = 2468s - 35[/tex]
The cost is at minimum when [tex]C'(s) = 0[/tex]
So, we have:
[tex]C' = 2468s - 35 = 0[/tex]
[tex]2468s - 35 = 0[/tex]
Solve for s
[tex]2468s = 35[/tex]
[tex]s=\frac{35}{2468}[/tex]
[tex]s\approx0.0142[/tex]
Find the slope of the line:
Solve: x - (-6) = -2
Answer: = -8
Step-by-step explanation: Your welcome!
Can you give me the answer to this
Answer:
C. a translation of 1 unit right and 2 units up, followed by a dilation by a factor of 3
Step-by-step explanation:
I need the answer quickly!
Please and Thank you!
Answer:
Option A
Step-by-step explanation:
Given expression = [tex] \frac{ - 1}{2} [/tex]
Lets multiply both numerator and denominator by -1.
[tex] = > \frac{ - 1 \times - 1}{2 \times - 1} [/tex]
[tex] = > \frac{1}{ - 2} [/tex]
Hence , Option A is the correct answer.
How do you find the value of x while working with adjacent and vertical angles? The angle is adjacent btw if that helps... I am in 7th grade and need help with this topic
Answer:
The angles are adjacent because they have a common side and vertex. Basically, they are both right next to each other.
x = 28
Step-by-step explanation:
When (x + 6)° and 56° are added together, they need to equal 90° since they are both parts of a right angle.
(x + 6) + 56 = 90
x + 62 = 90
x = 28
i need the prosces plis is for tomorrow
Answer:
p) = 17/30 or 0.56
q) = 191/60 or 3 11/60
Write a function for the graph.
Answer:
(x-4)^2 -4 = y
Step-by-step explanation:
The graph is translated 4 to the right and 4 downwards.
Michael is opening a savings account for college. The expression 2,300(1.002)12t represents the dollar amount in the account after t years.
Part A
What does the value 2,300 represent in the expression?
Answer:
2300 represents the amount Michael initally depoisitedin his savings account.
Step-by-step explanation:
An expression is defined as a set of numbers, variables, and mathematical operations. The value 2,300 represented in the expression is representing the initial amount that was in the account.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given that the expression [tex]2,300(1.002)^{12t}[/tex] represents the dollar amount in the account after t years. Therefore, the value 2,300 represented in the expression is representing the initial amount that was in the account.
Learn more about Expression:
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Please help me I will mark...BRAINLIEST
I need volume and surface area
Answer:
1. V=60m³ SA=94m²
2. V=32m³ SA=88m²
3. V=2000mm³ SA=1000mm²
4. SA=376.8cm² V=552.64cm³
5. SA=1130.4cm² V=1356.48mm³
Step-by-step explanation:
1. Volume=5*4*3=60m³
Surface Area=2*(3*4)+2*(5*3)+2*(4*5)=24+30+40=94m²
2. Volume=8*4*1=32cm³
Surface Area=2*(8*1)+2*(8*4)+2*(4*1)=16+64+8=88cm²
3. Volume=10*10*20=2000mm³
Surface Area=2*(10*10)+2*(20*10)+2*(20*10)=200+400+400=1000mm²
4. SA of the cylinder=(2πr*h)+(2*πr²)=(2*(3.14)*4*11)+(2*3.14*16)
=(276.32)+(100.48)=376.8cm²
Volume=hπr²=11*(3.14)*16=552.64cm³
5. SA of cylinder=(2πr*h)+(2*πr²)=(2*(3.14)*12*3)+(2*3.14*144)
=(904.32)+(226.08)=1130.4mm²
Volume=hπr²=3*(3.14)*144=1356.48mm³
What is the vertex of the graph of the function f(x) = x2 + 8x - 2?
O (4.18)
O (0,-2)
O (-8,-2)
0 (4-18)
Answer:
Vertex is (-4, -18)
Step-by-step explanation:
f(x) = [tex]ax^{2} +bx +c[/tex]
Let (h, k) be the vertex
An easy way to find h is to use the formula h = -b/2a
In your case where f(x) = [tex]x^{2} +8x - 2[/tex] a = 2 and b = 8
So, h = -8/2(1) = -8/2 = -4
Substitue -4 in for x to find k
k = ([tex]-4^{2}[/tex]) + 8(-4) - 2
= (16) - 32 - 2
= 16 - 32 - 2
= -18
Vertex is (-4, -18)
Note: Another way to find the vertex is to complete the square, but this can really be difficult in some cases
Answer:
Option D, (-4,-18)
Step-by-step explanation:
got it right on edge
The following chart shows a store?s records of sales of stuffed toys for two months. 2 circle graphs. A circle graph titled September. Teddy bears is 346, rabbits is 297, cats is 199, horses is 245, other is 225. A circle graph titled October. Teddy bears is 308, rabbits is 260, cats is 285, horses is 186, 275 is other. Which of the following are accurate assessments of trends displayed in this graph? I. Sales of teddy bears decreased by about 2.9% between September and October. II. The change in sales of rabbits is roughly equal to the change in sales of all toys. III. Roughly 24.1% fewer horses were sold in October than in September. a. I and II b. II only c. I and III d. III only
Answer:
d
Step-by-step explanation:
..........
Answer:
d
Step-by-step explanation:
e d g e
Use the box method to distribute and simplify (2 + 1)(2x - 3). Drag and drop the
terms to the correct locations of the table.
Answer:
2x^2-x-3
(2x)(-3)
(x)
(1)
Step-by-step explanation:
Distribute
(2x^2) (-3x)
(2x) (-3)
GIVING BRAINLIEST PLEASE DUE TODAY
A. For babysitting, Nicole charges a flat fee of $3, plus $5 per hour.
Write an equation for the cost, C, after h hours of babysitting.
B. How much money will she make if she babysits for 5 hours?
C. If Nicole earned $48.00, how many hours did she babysit?
Question: The mean birth weight of male babies born to 121 mothers taking a vitamin supplement is 3.67 kilograms (based on New York department of health data). The national average birth weight of male babies 3.39 kilograms.
Discuss the significance of the sample observation given that the probability of observing such a .sample estimated to be 0.0015
Answer:
The significance of the sample is that at it is statistically significant at 0.01 level ( i.e. of observing the sample < 0.01 )
Step-by-step explanation:
The sample observation which is 121 mothers that take vitamin supplements have male babies with mean weight of : 3.67 kg
while the National average birth weight = 3.39 kg
probability of observing such a sample = 0.0015
Hence the significance of the sample is that at it is statistically significant at 0.01 level ( i.e. of observing the sample < 0.01 )
How do you expand (4x+2)2
Answer:
=8x+4
Step-by-step explanation:
=2(4x+2)
a=2,b=4x,c=2
=2 x 4x + 2 x 2
Simplify- 2 x 4x + 2 x 2: 8x + 4
I NEED HELP ASAP!!!!!!
Answer:
I give bases example the triangle pyramid
According to the latest real estate report from a suburban town, the mean number of home purchases during last quarter was 175 homes with a population standard deviation of 6 homes. A real estate agent believes that the recent increase of mortgage interest rates is causing a decline in home purchases. To test this, the real estate agent randomly selects 60 recent home purchases. What is the probability that the mean of this sample of home purchases is between 173 and 174 homes
Answer:
The probability that the mean of this sample of home purchases is between 173 and 174 homes
P(173≤X≤174) = 0.0936
Step-by-step explanation:
Step(i):-
Given that the mean of the Population = 175
Given that the standard deviation of the Population = 6
Let 'x⁻' be the mean of the random sample
Given that x₁⁻ = 173
[tex]Z_{1} = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{173-175}{\frac{6}{\sqrt{60} } } =-2.58[/tex]
Given that x₂⁻ = 174
[tex]Z_{2} = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{174-175}{\frac{6}{\sqrt{60} } } = -1.29[/tex]
Step(ii):-
The probability that the mean of this sample of home purchases is between 173 and 174 homes
P(X₁≤X≤X₂) = P(Z₁≤Z≤Z₂)
= P(Z≤Z₂) - P(Z≤Z₂) ( both values 'Z' values are negative)
= 0.5 -A(Z₁) - (0.5 -A(Z₂))
= |A(Z₂) -A(Z₁)|
P(173≤X≤174) = | A(2.58)-A(1.29)|
= 0.4951 - 0.4015 (∵ from normal table)
= 0.0936
Final answer:-
The probability that the mean of this sample of home purchases is between 173 and 174 homes
P(173≤X≤174) = 0.0936
I need help with this please lol
Answer:
360 degrees
Step-by-step explanation:
Round to the nearest tenth
8.94427191
Answer:
8.9
Step-by-step explanation:
8.94427191
Answer:
8.9
Step-by-step explanation:
8.94427191 the number 1 spot to the right of the decimal point is tenths. the number is 9 the number to the right of that is 4. unless that number 2 digits to the right of the decimal point is 5 or over the 9 stays the same
Can somebody plz help answer these questions correctly (only if u know how to do them) thx sm! :3
WILL MARK BRAINLIEST WHOEVER ANASWERS FIRST :DDDD
Answer:
s= 100
r= 130
x= 38
y= 30
Step-by-step explanation:
HELP
4(x-2+y)=???????
Answer:
4+4−8
Step-by-step explanation:
*WILL GIVE BRAINLIEST FOR THE BEST ANSWER PLEASE HELP AND IF YOU DONT KNOW THE ANSWER DONT ANSWER!*How many people participated in the survey given the data in the histogram below?
Question 1 options:
7 people
12-15 people
20 people
0 people
Answer:
20 people participated in the survey.
The center and a point on a circle are given. Find the circumference to the nearest tenth.
center:(5, −5);
point on the circle: (25, 10)
The circumference is about ?
Answer: 50pi or about 157
Step-by-step explanation: Find the distance between the two points using the Pythagorean theorem, and since that is the radius double it to get the diameter, then multiply that by pi to get the answer. Hope this helps!
Answer:
Circumference ~ 157
Step-by-step explanation:
Use the distance formula to find the radius. The radius is 25. Plug 25 into the formula 2(pi)r to get 50pi or about 157.
Solve each equation mentally
I'm stuck. plz help I dont know how
Answer:
1) regular price ⇒ $X
Sale price:75,24
Regular price: 100, X
2) The Ratio of the numbers in the first column equals the to ratio
of numbers in the second one
so.. [tex]\frac{75}{124}=\frac{100}{x} \\[/tex]
X=100 ×24/75
X=$32
Regular price-sale price=32-24=$8
hope it helps...
Can anyone pls help
Answer:
50
Step-by-step explanation:
if im thinking right
im SOO sorrYYy if its wrong
A sphere has a radius of 9 feet. A second sphere has a radius of 6 feet. What is the difference of the volumes of the spheres? The volume of the larger sphere is π cubic feet greater than the volume of the smaller sphere.
Answer:
684 π
Step-by-step explanation:
volume of a sphere = (4/3) x (n) x (r^3)
n = 22/7
r = radius
volume of larger sphere
4/3 x n x 9³ = 972 n
4/3 x n x 6³ =288n
972n - 288n = 684n