How many terms of the series 2 + 5 + 8 + … must be taken if their sum is 155
9514 1404 393
Answer:
10
Step-by-step explanation:
The sum of terms of an arithmetic series is ...
Sn = (2a +d(n -1))·n/2 = (2an +dn^2 -dn)/2
For the series with first term 2 and common difference 3, the sum is 155 for n terms, where ...
155 = (3n^2 +n(2·2 -3))/2
Multiplying by 2, we have ...
3n^2 +n -310 = 0 . . . . . arranged in standard form
Using the quadratic formula, the positive solution is ...
n = (-1 +√(1 -4(3)(-310)))/(2(3)) = (-1 +√3721)/6 = (61 -1)/6 = 10
10 terms of the series will have a sum of 155.
Step-by-step explanation:
[tex]\displaystyle \ \Large \boldsymbol{} S_n=\frac{2a_1+d(n-1)}{2} \cdot n =155 \\\\ \frac{4+3(n-1)}{2} \cdot n =155 \\\\\\ 4n+3n^2-3n=310 \\\\ 3n^2+n-310=0 \\\\D=1+3720=3721=61^2\\\\n_1=\frac{61-1}{6} =\boxed{10} \\\\\\n_2=\frac{-61-1}{3} \ \ \o[/tex]
What is the surface area of this figure in square centimeters?
A.96
B.75
C.84
D.60
9514 1404 393
Answer:
A. 96
Step-by-step explanation:
The surface area is the sum of the areas of the two triangular bases and the areas of the three rectangular lateral faces.
A = 2(1/2)bh + PH
where b is the base of the triangle, h is its height, P is the perimeter of the triangle, and H is the height of the prism.
A = (3 cm)(4 cm) +(3 +4 +5 cm)(7 cm) = 12 cm² +84 cm²
A = 96 cm²
The surface area of the triangular prism is 96 square cm.
A hypothesis test is to be performed in order to test the proportion of people in a population that have some characteristic of interest. Select all of the pieces of information that are needed in order to calculate the test statistic for the hypothesis test:
No piece of information is supplied to choose from ; However, the requirements for the test statistic of the hypothesis in question is given below.
Answer:
Kindly check explanation
Step-by-step explanation:
The hypothesis in the question above which is to be tested is a one sample proportion test ;
The test statistic formula for a one sample proportion test is given as :
Test statistic = (Phat - P) / √[P(1 - P) / n] ;
Where;
Phat = sample proportion
P = population proportion
n = sample size
Sample proportion = x / n ;
Therefore, once the parameters (Sample proportion, population proportion and sample size are given) then obtaining the test statistic is possible.
Task: Population of a Species
The population of a species in the wild in Asia has been decreasing exponentially since 1980. This function represents the wild population of the species t years after 1980: W(t)=20000(0.95)t.
The Wildlife Refuge Foundation noticed this trend before 1980
and decided to try to help reduce the population decline by
breeding the species in captivity. The graph shows the number
of these animals that have been born in captivity since 1980.
(Note: The function W(t) and the graph are not the same function!)
[15 points] Use the graph to create a function to represent the number of the species that have been born in captivity, C(t).
Answer:
C(t) = 20t
Step-by-step explanation:
The graph of C(t) appears to be linear
The y intercept is 0
The slope is 200/10 = 20
y = mx+b where m is the slope and b is the y intercept
y = 20x+0
y = 20x
C(t) = 20t
Answer:
the answer is c (t) = 20 t
Step-by-step explanation:
[tex]\sf{}[/tex]
:,-)
♛┈⛧┈┈•༶♛┈⛧┈┈•༶
ASAP ITS TIMED
What is the following sum? Assume x20 and 20.
W x ² + 2 / x 374 + xy ſy
0 x ²7² ſy- 2xy?
0 2xy ſy + 2xy ² x
0 4xy dx
o 2xyxy
وی در مورد
Answer:
The right answer is the 2nd one
hope it will help :)
The given sum is option B. 2xy√y + 2xy²√x.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expression of sum is,
√(x²y³) + 2√(x³y⁴) + xy √y
We have to find the sum.
√(x²y³) = √x² √y³ = x√y³ = x√(y²)√y = xy√y
Now,
2√(x³y⁴) = 2[√x² √x √(y²)²] = 2x√x y² = 2xy²√x
Substituting these,
√(x²y³) + 2√(x³y⁴) + xy √y = xy√y + 2xy²√x + xy √y
= 2xy√y + 2xy²√x
Hence the equivalent sum is 2xy√y + 2xy²√x.
Learn more about Expressions sum here :
https://brainly.com/question/15284271
#SPJ7
in a 5 liter milk jar water and milk are in the ratio 2:3. If 1 liter of milk and 1 liter of water is added. what will be the new ratio.
Give me answer with steps . and the answer is 3:4. but how I want to know
Answer:
ratio of water and milk=2:3
i.e. water=2
milk=3
now adding 1 liter of water in 2
2+1=3
and 1 liter of milk in 3
3+1=4
hence,
the new ratio is 3:4
Step-by-step explanation:
i hope this will help
plz mark as brainliest
The following are on a parabola defining the edge of a ski
(-4, 1), (-2, 0.94), (0.1)
The general form for the equation of a parabola is:
Ax^2+ Bx +C= y
Required:
a. Use the x- and y-values of 1 of the points to build a linear equation with 3 variables: A, B, and C.
b. Repeat this process with 1 of the other to build a 2nd linear equation.
c. Record your equation here. Repeat this process with the other point to build a 3rd equation.
9514 1404 393
Answer:
a) 16A -4B +C = 1
b) 4A -2B +C = 0.94
c) C = 1
Step-by-step explanation:
Substitute the x- and y-values into the general form equation.
a. A(-4)² +B(-4) +C = 1
16A -4B +C = 1
__
b. A(-2)² +B(-2) +C = 0.94
4A -2B +C = 0.94
__
c. A(0)² +B(0) +C = 1
C = 1
_____
Additional comment
Solving these equations gives A=0.015, B=0.06, C=1. The quadratic is ...
0.015x² +0.06x +1 = y
[tex]log(x) * log(2)[/tex]
Why can't this problem be solved?
Answer:
Because it is not an equation.
Step-by-step explanation:
[tex] log(x) \times log(2) \\ = log(x + 2) [/tex]
Which equation is represented by the graph?
Answer:
I don't knowledge bro sorry
Find the unit rate.
1/3 kilometer in 1/3hour
Answer:
1 kilometer in 1 hour
Step-by-step explanation:
unit rate is km(kilometer) per hour(hr)
1/3 km = 1/3 hr
multiply both sides by 3
1 km in 1 hour
Question 20 plz show ALL STEPS and hurry PLEASE
Answer:
(a) You will get ten
Step-by-step explanation:
single cell = 3 min
30 min = ?
30 divided by 10 = 3
Have a good day!
Which of the following equations have no solutions?
Choose all answers that apply:
-60.2 + 32 = 32x + 60
-60.X + 32 = 322 - 60
-60.2 + 32 = -60.2 + 60
-60x + 32 = -60.2 - 32
Option 3 is not possible
-60.2 + 32 = -60.2 + 60
And these are not equal
Rest all options have x and are solvable
Must click thanks and mark brainliest
find each measurement indicated round your answers to the nearest tenth. Part 1d. NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Answer:
see explanation
Step-by-step explanation:
Using the Sine rule in all 3 questions
(1)
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values , firstly calculating ∠ B
[ ∠ B = 180° - (78 + 49)° = 180° - 127° = 53° ]
[tex]\frac{a}{sin78}[/tex] = [tex]\frac{18}{sin53}[/tex] ( cross- multiply )
a sin53° = 18 sin78° ( divide both sides by sin53° )
a = [tex]\frac{18sin78}{sin53}[/tex] ≈ 22.0 ( to the nearest tenth )
(3)
[tex]\frac{c}{sinC}[/tex] = [tex]\frac{a}{sinA}[/tex] , substitute values
[tex]\frac{35}{sinC}[/tex] = [tex]\frac{45}{sin134}[/tex] ( cross- multiply )
45 sinC = 35 sin134° ( divide both sides by 35 )
sinC = [tex]\frac{35sin134}{45}[/tex] , then
∠ C = [tex]sin^{-1}[/tex] ( [tex]\frac{35sin134}{45}[/tex] ) ≈ 34.0° ( to the nearest tenth )
(5)
Calculate the measure of ∠ B
∠ B = 180° - (38 + 92)° = 180° - 130° = 50°
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values
[tex]\frac{BC}{sin38}[/tex] = [tex]\frac{10}{sin50}[/tex] ( cross- multiply )
BC sin50° = 10 sin38° ( divide both sides by sin50° )
BC = [tex]\frac{10sin38}{sin50}[/tex] ≈ 8.0 ( to the nearest tenth )
Louise has a hard time keeping her workspace clean at her job. She tries, but it just ends up getting messy again. Which of the following is a likely outcome of her consistent messiness? O a) She will have fewer safety issues. b) She will feel more productive. c) Customers will think she is very busy. O d) She will have a hard time focusing.
Option C
Customers will think she is very busy
A messy desk indicates that the person is very busy.
Must click thanks and mark brainliest
ZA and ZB are complementary angles. If m A = (8x + 27)° and m
ZB = (6x – 21)°, then find the measure of ZB.
Answer:
15
Step-by-step explanation:
Complementary angles add to 90 degrees
8x+27 + 6x-21 = 90
Combine like terms
14x+6 = 90
Subtract 6 from each side
14x+6-6 = 90-6
14x = 84
Divide by 14
14x/14 = 84/14
x=6
We want angle B
B = 6x-21 = 6*6-21 =36-21 = 15
95% confident that the true mean difference in mean crying time after being given a vitamin K shot between infants using conventional methods and infants held by their mothers is between ____________and ___________________. In other words, the mean crying time of infants given vitamin K shot using conventional methods is anywhere from ______________ less than to _______________more than the mean crying time of infants given vitamin K shot using new methods.
Solution :
Two sample T-test and CI : Conventional methods, New methods
Two sample T for conventional method Vs new method
N Mean StDev Se Mean
Conventional mean 30 35.3 20.8 3.8
New methods 30 35.1 22.3 4.1
Difference = μ (conventional method) - μ (new method)
Estimate for difference : 0.17
95% CI for difference : (-10.976, 11.309)
T-Test of difference = 0(vs <): T-value = 0.03 P-value =0.5119 DF = 57
95% confident that the true mean difference in mean crying time after being given a vitamin K shot between infants using conventional methods and infants held by their mothers is between -10.976 and 11.309. In other words, the mean crying time of infants given vitamin K shot using conventional methods is anywhere from -10.976 less than to 11.309 more than the mean crying time of infants given vitamin K shot using new methods.
Rs 600 will gave Rs 90 simple interest at 5 % per annum.
Step-by-step explanation:
interest=90
principal=600
rate=5%
time = I × 100/p×r
= 90×100/600×5
= 3 years.
Four people share a taxi to the airport the fare was $36 and they gave the driver a tip equal to 25% of the fair. If they equally share the cost of the fair tip, how How much did each person pay?
Answer:
$11.25
Step-by-step explanation:
Total money given to the taxi driver=36+25% of 36=45
Each person will pay (45/4)=11.25
Factor the polynomial expression 3x4 + 24x.
Answer:
3x ( x+2)(x^2−2x+4)
Step-by-step explanation:
3x^4 + 24x.
Factor out the greatest common factor
3x*x^3 + 3x*8
3x(x^3+8)
Then factor the cubic term
The sum of cubes is a^3+b^3=(a+b)(a^2−ab+b^2)
3x ( x+2)(x^2−2x+4)
From -13°C to 15°C.
a. -28°C
b. -2°C
C. 28°C
d. 2°C
ccccccccccccccccccccccc
Answer:
Option B
-13°c-2°c= 15°c
hope it helps
product of a positive and a negative integer is ___________
Answer:
negative
Step-by-step explanation:
because when positive and negative integers are multiplied it results to a negative answer
A cell phone carrier charges a fixed monthly fee plus a constant rate for each minute used. Part 1. In January, the total cost for 150 minutes was $ 62 while in February, the total cost for 175 minutes was $ 64 . The constant charge for each minute used is:
a. 0.09
b. 0.1
c. 0.08
Part 2. The fixed montly fee charged by the carrier is;
fee = $__________________
9514 1404 393
Answer:
c. $0.08
fee = $50
Step-by-step explanation:
We are given two ordered pairs:
(minutes, charges) = (150, 62) and (175, 64)
The slope of the graph of charges is ...
m = (y2 -y1)/(x2 -x1) = (64 -62)/(175 -150) = 2/25 = 0.08
The charge for each minute is $0.08.
__
The y-intercept of the graph can be found from ...
b = y -mx
b = 62 -150(0.08) = 62 -12 = 50
The fixed monthly fee is $50.
Find the measure of TU
A. 8
B. 12
C. 14
D. 11
Answer:
D. 11
Step-by-step explanation:
First apply the secant-secant theorem to find the value of x.
Thus,
VU(TU + VU) = VW(BW + VW) (secant-secant theorem)
Substitute
(7)(x + 4 + 7) = (9)(-2 + x + 9)
7(x + 11) = 9(7 + x)
7x + 77 = 63 + 9x
Collect like terms
7x - 9x = 63 - 77
-2x = -14
Divide both sides by -2
x = 7
✔️Find TU
TU = x + 4
Substitute get value of x
TU = 7 + 4 = 11
Answer:
11
Step-by-step explanation:
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
9514 1404 393
Answer:
10·2^-8 grams
Step-by-step explanation:
The each day, the initial amount for that day is multiplied by 1/2. After 8 days, the initial amount has been multiplied by (1/2)^8, where the exponent of 8 signifies that (1/2) is a factor 8 times in the product.
After n days, the quantity remaining is ...
q(n) = 10·(1/2)^n = 10·2^(-n)
after 8 days the remaining amount is ...
q(8) = 10·2^-8 . . . grams
There are 3 red marbles and 8 blue marbles in a bag. (a) What is the ratio of all marbles in the bag to blue marbles? (b) What is the ratio of red marbles to all marbles in the bag?
Answer:
a.) 11:8
b.) 3:11
Step-by-step explanation:
a)
Add all marbles
8 + 3 = 11
Blue marbles = 8
So, the ratio will be 11:8
b)
Red marbles = 3
All marbles = 11
So, the ratio will be 3:11
Hope this helps.
Answer:
Step-by-step explanation:
SI unit of areaWhat is the SI unit of area
square meter is the SI unit of area.
Find the line integral with respect to arc length ∫C(9x+5y)ds, where C is the line segment in the xy-plane with endpoints P=(2,0) and Q=(0,7).
(a) Find a vector parametric equation r⃗ (t) for the line segment C so that points P and Q correspond to t=0 and t=1, respectively
(b) Rewrite integral using parametrization found in part a
(c) Evaluate the line integral with respect to arc length in part b
(a) You can parameterize C by the vector function
r(t) = (x(t), y(t) ) = P (1 - t ) + Q t = (2 - 2t, 7t )
where 0 ≤ t ≤ 1.
(b) From the above parameterization, we have
r'(t) = (-2, 7) ==> ||r'(t)|| = √((-2)² + 7²) = √53
Then
ds = √53 dt
and the line integral is
[tex]\displaystyle\int_C(9x(t)+5y(t))\,\mathrm ds = \boxed{\sqrt{53}\int_0^1(17t+18)\,\mathrm dt}[/tex]
(c) The remaining integral is pretty simple,
[tex]\displaystyle\sqrt{53}\int_0^1(17t+18)\,\mathrm dt = \sqrt{53}\left(\frac{17}2t^2+18t\right)\bigg|_{t=0}^{t=1} = \boxed{\frac{53^{3/2}}2}[/tex]
A farmer weighs a dozen chicken eggs. The heaviest egg is 56 g.
Step-by-step explanation:
hi
what is your question?
Step-by-step explanation:
please tell full questions
trig..experts...help! Will give brainly!
Answer:
Step-by-step explanation:
189² = 215² + 123² - 2(215)(123)cos x°
35,721 = 46,225 + 15,129 - 52,890 cos x°
35,721 = 61,354 - 52,890 cos x°
52,890 (cos x° ) = 25,633
cos x° = 25,633 ÷ 52,890 ≈ 0.4846
x° ≈ 61.01°
2/5 = 6/ = 10/30 = 14/
Please tell asap
Answer:
6/15.
14/42.
Step-by-step explanation:
2/5 = 6/x
Cross multiply:
2x = 5*6
x = 15
Similarly:
10/30 = 14/x
10x = 30*14
x = 420/10
x = 42.
