Hello,
[tex]if\ n=1\ then\ 1^2=1\ and\ \dfrac{1}{6}*1*2*3=1:\ true\ for\ n=1\\[/tex]
We suppose the property true for n:
1²+2²+...+n²=n(n+1)(2n+1) / 6
and we are going to demonstrate that the property is true for n+1:
1²+2²+..+(n+1)²=(n+1)*(n+2)*(2n+3)/6
[tex]1^2+2^2+...+n^2+(n+1)^2\\\\=n*(n+1)*(2n+1)/6+(n+1)^2\\\\=(n+1)/6*[n(2n+1)+6n+6]\\\\=(n+1)/6*(2n^2+7n+6)\\\\=(n+1)(n+2)(2n+3)/6\\[/tex]
what is the sum of a 7 term geometric series if the first term is 6 the last term is -24576 and the common ratio is -4
Answer:
Sum = 19,662
Step-by-step explanation:
Given that this is a finite geometric series (meaning it stops at a specific term or in this case -24,576), we can use this formula:
[tex]\frac{a(1-r^n)}{1-r}[/tex], where a is the first term, r is the common ratio, and n is the number of terms.
Substituting for everything and simplifying gives us:
[tex]\frac{6(1-(-4)^7)}{1-(-4)} \\\\\frac{6(16385}{5}\\ \\\frac{98310}{5}\\ \\19662[/tex]
Point Q is the centroid of △ABC. QF = _____ centroid
Answer:
Q is the centroid the after you can do it your self by looking forward
Answer:
QF = 5
Step-by-step explanation:
On a median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint, that is
QF = [tex]\frac{1}{2}[/tex] BQ = [tex]\frac{1}{2}[/tex] × 10 = 5
Solve the formula for t
Answer:
Step-by-step explanation:
S - 4πc^2 = 6πct
t = (S - 4πc^2)/6πc
t = S/(6πc) - 2/3 c
assuming c ≠ 0
A student has test scores of 75 and 82respectively. What is the student’s average score for a third test
Answer:
78.5 (I think 90% sure)
Step-by-step explanation:
sum of both scores
75+82 = 157
average for a third test
157÷2=78.5
If f(x) = 4x and gx) = 2x- 1, what is g(f(-2))?
-17
-13
-8
-5
Answer:
-17
Step-by-step explanation:
We are given these following functions:
[tex]f(x) = 4x[/tex]
[tex]g(x) = 2x - 1[/tex]
g(f(-2))
First we find f when x = -2, then we find g for this value(f when x = -2). So
[tex]f(-2) = 4(-2) = -8[/tex]
[tex]g(f(-2)) = g(-8) = 2(-8) - 1 = -16 - 1 = -17[/tex]
Thus -17 is the answer.
solve the system of equations using substitution or graphing.
Step-by-step explanation:
I think substitution would be the easiest since you already have one of the variables solved for.
[tex]y=-x^2+4x+5\\y=x+1\\x+1=-x^2+4x+5\\x^2-3x-4=0\\(x-4)(x+1)=0\\x-4=0\\x=4\\x+1=0\\x=-1[/tex]
(You can just set the equations equal to each other since they both equal y).
Now, to get the points, plug in x = 4 and x = -1 into one of the equations (I'm going to plug them into y = x+1 because that one is much simpler)
[tex]y(4)=4+1\\y(4)=5\\y(-1)=-1+1\\y(-1)=0[/tex]
So, your final points are:
(4,5) and (-1,0)
Answer: A
Step-by-step explanation:
We can use substitution to solve this problem. Since we are given y=-x²+4x+5 and y=x+1, we can set them equal to each other.
-x²+4x+5=x+1 [subtract both sides by x]
-x²+3x+5=1 [subtract both sides by 1]
-x²+3x+4=0
Now that we have the equation above, we can factor it to find the roots.
-x²+3x+4=0 [factor out -1]
-1(x²-3x-4)=0 [factor x²-3x-4]
-1(x+1)(x-4)=0
This tells us that x=-1 and x=4.
We can narrow down our answer to A, but let's plug in those values to be sure it is correct.
-(-1)²+4(-1)+5=(-1)+1 [exponent]
-1+4(-1)+5=-1+1 [multiply]
-1-4+5=-1+1 [add and subtract from left to right]
0=0
-------------------------------------------------------------------------------------------
-(4)²+4(4)+5=(4)+1 [exponent]
-16+4(4)+5=4+1 [multiply]
-16+16+5=4+1 [add and subtract from left to right]
5=5
Therefore, we can conclude that A is the correct answer.
Answer correctly and 40 points. Thx. Will report if wrong. ASAP plz! Thx!
Answer:
-7
Step-by-step explanation:
if you multiply by 7 positive it wont work because u cant cancel 7x out and a fraction wont work because theres no fraction involved in this so ur answer is A
So for this problem I got the scientific notation however I can not seem to figure out the standard notation. I thought it is the same answer but it is not. Can someone please help me out here please?
Answer:
567000000
Step-by-step explanation:
Standard is the actual number. Multiply 5.67 and 10^8.
Use the appropriate reciprocal identity to find the exact value of sin for the given value of csc . Rationalize denominators when applicable. csc 27/5 sin
Answer:
[tex]\sin(\theta) = \frac{5}{27}[/tex]
Step-by-step explanation:
Given
[tex]\csc(\theta) = \frac{27}{5}[/tex]
Required
Determine [tex]\sin(\theta)[/tex]
In trigonometry identity;
[tex]\sin(\theta) = \frac{1}{\csc(\theta)}[/tex]
So, we have:
[tex]\sin(\theta) = \frac{1}{\frac{27}{5}}[/tex]
Take inverse of the fraction
[tex]\sin(\theta) = \frac{5}{27}[/tex]
Jen recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was 8 miles per hour faster than on her way home. If jen
spent a total of 2 hours bicycling find the two rates.
the answer is in the picture above
Express the following composite numbers as products of prime factors 64
Answer:
64 is a composite number, and it is 8 squared. 64 = 1 x 64, 2 x 32, 4 x 16, or 8 x 8. Factors of 64: 1, 2, 4, 8, 16, 32, 64. Prime factorization: 64 = 2 x 2 x 2 x 2 x 2 x 2, which can also be written 64 = 2⁶.
HELP ME PLSSSSSSSS I tryed to solvessss
Answer:
x≥-4
Step-by-step explanation:
Xavier is testing different types of planting soil to determine which type is most effective in growing blueberry bushes. He purchases two different brands of planting soil from a local store. Xavier applies Brand A to an area of the yard that receives full sunlight and Brand B to another area of the yard that is in partial sunlight. He waters the area with Brand B daily; he waters the area with Brand A every other day. At the end of the study, Xavier concludes Brand A is more effective in growing blueberry bushes. Why is his conclusion not valid?
Answer:
He did not control for lurking variables and their impacts on the results of his experiment. Amount of sunlight and water received are two outside variables(or confounding variables) that may impact the growth of his plants and influence the results. He needs to apply the same amount of sunlight and water to each plant within a different planting soil in order to rule out the influence of those two variables and test the sole effect of the soil brand on the plant growth. Otherwise, it would be hard to determine whether his plant growth was because of the soil brand or the different amounts of sunlight and water received
Answer:
Invalid
Step-by-step explanation:
Xavier did not control variables or the impacts of the results. Confounding variable being sunlight and water received are two outside variables that can impact growth influence results. Within a different planting soil, Xavier will apply the same amount of sunlight & water to each plant to rule out the influence of those two variables. The test for sole effect on the plant with growth otherwise be determine. Is the plant growth because of the soil brand or the different amounts of sunlight and water received? This could and will impaired the results of this experiment, therefore, making it invalid.
Solve. SHOW ALL YOUR WORK
2.51 * .2
77/ 1.2
Answer:
0.502
64.1666
Step-by-step explanation:
Detained explanation of the product operation and division operation is attached below.
2.51 * 0.2 = 0.502
(after multiplying) the number of decimal places of the town values is added and counted from the right in the product to place the data Comal point appropriately.
77/1.2 ; values were multiplied by 10 in other to obtain inter values for the denominator.
O EXPONENTAL AND LOGARITHMIC FUNCTIONS
Finding the initial or final amount in a word problem on...
An initial amount of money is placed in an account at an interest rate of 2% per year, compounded continuously. After two years, there is $1269.79 in the
account. Find the initial amount placed in the account. Round your answer to the nearest cent.
Answer:
$ 1220.00
Step-by-step explanation:
1269.79 = A [tex]e^{.02 * 2}[/tex]
1269.79 /A = [tex]e^{.04}[/tex]
ln(1269.79 /A) = .04 ln(e)
ln(1269.79 /A) = .04
1269.79 /A = [tex]e^{.04}[/tex]
1269.79 /A = 1.0408
A = 1269.79 / 1.0408
$ 1220.00
¿Pueden ayudarme por favor?
I need help please and thank you.
Answer:
option a.
[tex] + - \frac{13}{5} [/tex]
Step-by-step explanation:
[tex]25x^2\: - \:169 = 0 [/tex]
[tex]25x^2 = 169[/tex]
[tex] {x}^{2} = \frac{169}{25} [/tex]
[tex]x = + - \sqrt{ \frac{169}{25} } [/tex]
[tex]x = + - \frac{13}{5} [/tex]
jenny has 3 cherry candies and 3 orange candies. She takes out 2 candies without looking.What is the probability in fractions that both are cherry?
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW?
1. Suppose y varies inversely with x, and y = 25 when x = 1/5. What is the value of y when x = 5?
a. 15
b. 5
c. 25
d. 1
2. Suppose y varies inversely with x, and y = a when x = a^2. What inverse variation equation related x and y?
a. y = a^2/x
b. y = a^3/x
c. y= a^3x
d. y = ax
3. Suppose y varies inversely with x, and y = 3 when x = 1/3. What is the inverse variation equation that relates x and y?
a. y = 1/x
b. y =x
c. y = 3x
d. y = 3/x
Answer:
1. D. 1
2. B. y=a³/x
3. A. y=1/x
Step-by-step explanation:
too long to give te explanations but they're there in the attachments
Problem is in the picture below
Answer:
90 maybe is a correct answer
Answer:
Y=40°
Step-by-step explanation:
VUW~YXZ
VWU~YZX
YXZ+XYZ+YZX=180°
70°+XYX+70°=180°
140°+XYZ=180°
XYZ=180°-140°
XYZ=40°
expand and simplify (x-2)(x+5)(2x-1)
Answer:
simplified: 2x^3+5x^2-23x+10
Step-by-step explanation:
Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):
Demand for Service
Service Strong Weak
Full price $960 -$490
Discount $670 $320
1. What is the decision to be made, what is the chance event, and what is the consequence for this problem?
2. How many decision alternatives are there?
Number of decision alternatives =
3. How many outcomes are there for the chance event?
Number of outcomes =
4. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?
a. Optimistic approach
b. Conservative approach
c. Minimax regret approach
here i attached the answer
The decision to be made is the type of service to be provided. The chance event is the level of demand for the air service.
What is Air Service?The services performed by an airline, as flights between various destinations to transport passengers, freight, and mail.
The decision to be made is the type of service to be provided. The chance event is the level of demand for the air service. The consequence can be considered as the amount of quarterly profit. Full price and discount price services are two decision alternatives. The number of outcomes for chance event is two, which are strong demand and weak demand.
Learn more about Airline Service from:
https://brainly.com/question/14725385
#SPJ2
Which are the roots of the quadratic function f(q) = 92 – 125?
Answer:
There are no solution/no roots for f(q) = 92 - 125
The average THC content of marijuana sold on the street is 9.6%. Suppose the THC content is normally distributed with standard deviation of 1%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible,
a. What is the distribution of X? X ~ N(
9.6
Correct,
1
Correct)
b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 9.8.
c. Find the 67th percentile for this distribution.
%
Answer:
Im sorry but why is this a question? Like what school gives this out
NEED HELP ASAP GIVING BRAINLIEST!!!!!!!!!!!!!!!!!!
Answer:
option D
Step-by-step explanation:
[tex]sin^2 ( \frac{3\pi}{2}) + cos^2(\frac{3\pi}{2}) = 1\\\\( -1)^2 + 0^2 = 1[/tex]
Explanation:
[tex]sin x = cos( \frac{\pi}{2} - x)\\\\sin(\frac{3\pi}{2}) = cos ( \frac{\pi}{2} - \frac{3\pi}{2})\\[/tex]
[tex]=cos(\frac{\pi - 3\pi}{2})\\\\ =cos(\frac{2\pi}{2})\\\\=cos \ \pi\\\\= - 1[/tex]
Therefore ,
[tex]sin^2( \frac{3\pi}{2}) = ( - 1)^2[/tex]
HELPP
-1-3(5m+8) ≥-85
i need help :D
Answer:
- 1 - 3(5m + 8) ≥ -85
-1 - 15m - 24 ≥ -85
-15m ≥ -85 + 1 + 24
-15m ≥ 25 - 85
-15m ≥ -60
(-1)(-15)m ≤ -60(-1)
15m ≤ 60
m ≤ 4
OMG THIS IS SO HARD
Answer:
Answer to the first question is D. Answer to the second question is also D.
Step-by-step explanation:
First question:
All the sides of the square are equal meaning you just have to multiply 1 side by 4 to get the perimeter(all the sides added together.) If one side is (s+3) then you either add that to itself 4 times or multiply it by 4. It's the same thing so it's 4(s+3) and (s+3)+(s+3)+(s+3)+(s+3).
Second question:
Adding a negative number is equivalent to subtracting a positive number. In this case, 59.2-84.7 = 59.2+(-84.7)
The original price of a set lunch was 30 dollars. It is now sold at a 20%
discount. There is an extra discount of 10% for students. How much
should a student pay to order a set lunch?
Please help with problem
9514 1404 393
Answer:
∠CAE ≈ 16.7°DF ≈ 5.3Step-by-step explanation:
a) Angle CAE can be found using the tangent relation.
tan(∠CAE) = CE/AE
tan(∠CAE) = 6/20
∠CAE = arctan(6/20) ≈ 16.7°
__
b. The length of DF can be found using the law of cosines.
DF² = FA² +DA² -2·FA·DA·cos(A)
DF² = 14² +10² -2·14·10·cos(16.7°) ≈ 27.8086
DF ≈ √27.8086
DF = 5.3
Police Chase: A speeder traveling 40 miles per hour (in a 25 mph zone) passes a stopped police car which immediately takes off after the speeder. If the police car speeds up steadily to 55 miles/hour in 10 seconds and then travels at a steady 55 miles/hour, how long and how far before the police car catches the speeder who continued traveling at 40 miles/hour
Answer:
a. 18.34 s b. 327.92 m
Step-by-step explanation:
a. How long before the police car catches the speeder who continued traveling at 40 miles/hour
The acceleration of the car a in 10 s from 0 to 55 mi/h is a = (v - u)/t where u = initial velocity = 0 m/s, v = final velocity = 55 mi/h = 55 × 1609 m/3600 s = 24.58 m/s and t = time = 10 s.
So, a = (v - u)/t = (24.58 m/s - 0 m/s)/10 s = 24.58 m/s ÷ 10 s = 2.458 m/s².
The distance moved by the police car in 10 s is gotten from
s = ut + 1/2at² where u = initial velocity of police car = 0 m/s, a = acceleration = 2.458 m/s² and t = time = 10 s.
s = 0 m/s × 10 s + 1/2 × 2.458 m/s² (10)²
s = 0 m + 1/2 × 2.458 m/s² × 100 s²
s = 122.9 m
The distance moved when the police car is driving at 55 mi/h is s' = 24.58 t where t = driving time after attaining 55 mi/h
The total distance moved by the police car is thus S = s + s' = 122.9 + 24.58t
The total distance moved by the speeder is S' = 40t' mi = (40 × 1609 m/3600 s)t' = 17.88t' m where t' = time taken for police to catch up with speeder.
Since both distances are the same,
S' = S
17.88t' = 122.9 + 24.58t
Also, the time taken for the police car to catch up with the speeder, t' = time taken for car to accelerate to 55 mi/h + rest of time taken for police car to catch up with speed, t
t' = 10 + t
So, substituting t' into the equation, we have
17.88t' = 122.9 + 24.58t
17.88(10 + t) = 122.9 + 24.58t
178.8 + 17.88t = 122.9 + 24.58t
17.88t - 24.58t = 122.9 - 178.8
-6.7t = -55.9
t = -55.9/-6.7
t = 8.34 s
So, t' = 10 + t
t' = 10 + 8.34
t' = 18.34 s
So, it will take 18.34 s before the police car catches the speeder who continued traveling at 40 miles/hour
b. how far before the police car catches the speeder who continued traveling at 40 miles/hour
Since the distance moved by the police car also equals the distance moved by the speeder, how far the police car will move before he catches the speeder is given by S' = 17.88t' = 17.88 × 18.34 s = 327.92 m