Answer:
an = −1,171,875(1/5)^n-1
Step-by-step explanation:
The given sequence is geometric sequence since they have the same common ratio r. The nth term of a geometric sequence is expressed as;
an = ar^n-1
n is the number of terms
r is the common ratio
a is the first term
From the sequence;
a = −1,171,875
r = −234,375 /−1,171,875 = -46,875/−234,375 = 0.2
r = 1/5
Substitute the values in the formula;
an = −1,171,875(1/5)^n-1
Hence the required explicit formula is an = −1,171,875(1/5)^n-1
The explicit rule that describes the sequence is [tex]\rm a_n = -1,171,875 (\dfrac{1}{5})^{n - 1 }[/tex]. Then the correct option is C.
What is a sequence?A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
The sequence is {−1,171,875;−234,375;−46,875;−9375,…}
The given sequence is the geometric sequence since they have the same common ratio r. Then the nth term of the geometric sequence will be
[tex]\rm a_n = a\ r^{n-1}[/tex]
Where
Number of terms (n)
First-term (a) = -1,171,875
Common ratio (r) = 1/5
Then nth term will be
[tex]\rm a_n = -1,171,875 (\dfrac{1}{5})^{n - 1 }[/tex]
The explicit rule that describes the sequence is [tex]\rm a_n = -1,171,875 (\dfrac{1}{5})^{n - 1 }[/tex]. Then the correct option is C.
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Which expression is equivalent to 7(a+2) when a= 6?
O 7(6)
916)
0 7(6)+2
7(6)+ 14
Answer:
when a = 6, substitute 6 in the equation for a:
7(a + 2) = 7(6)+ 14
Step-by-step explanation:
Answer:
56
Step-by-step explanation:
When a = 6
7(a+2)
7(6+2)
7(8)
56
An unknown radioactive element decays into non-radioactive substances. In 560 days the radioactivity of a sample decreases by 36 percent.
(a) What is the half-life of the element?
half-life:
(b) How long will it take for a sample of 100 mg to decay to 55 mg?
time needed:
After taking the given data into consideration we conclude that
a) the half-life of the unknown radioactive element is approximately 1921.7 days.
b) approximately 1011.4 days, or about 2.77 years, for a sample of 100 mg to decay to 55 mg.
(a) The half-life of a radioactive element is the time needed for half of the material to decay. To find the half-life of the unknown radioactive element, we can use the fact that in 560 days, the radioactivity of a sample decreases by 36 percent. Let T be the half-life of the element. Then, we have:
[tex]0.5 = (1 - 0.36)^{(560/T)}[/tex]
Simplifying this equation, we get:
[tex]0.5 = 0.64^{(560/T)}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(0.5) = ln(0.64)^{(560/T)}[/tex]
[tex]ln(0.5) = (560/T) * ln(0.64)[/tex]
Solving for T, we get:
[tex]T = -560 / (ln(0.64) * ln(0.5))[/tex]
[tex]T \approx 1921.7 days[/tex]
(b) To find how long it will take for a sample of 100 mg to decay to 55 mg, we can use the half-life formula:
[tex]N = N_0 * (1/2)^{(t/T)}[/tex]
where:
N is the final amount, which is 55 mg in this case
[tex]N_0[/tex] is the initial amount, which is 100 mg in this case
t is the time it takes for the sample to decay from [tex]N_0[/tex] to N
T is the half-life of the element, which we found to be approximately 1921.7 days
Substituting the values, we get:
[tex]55 = 100 * (1/2)^{(t/1921.7)}[/tex]
Simplifying this equation, we get:
[tex]0.55 = (1/2)^{(t/1921.7)}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(0.55) = (t/1921.7) * ln(1/2)[/tex]
Solving for t, we get:
[tex]t = -1921.7 * ln(0.55) / ln(1/2)[/tex]
[tex]t \approx 1011.4 days[/tex]
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Can someone please tell me if I’m correct, quick
Answer: I believe your answer is correct .
Answer:
yes i belive u got it right
Step-by-step explanation:
Find the slope And y-intercept
Answer:
Answer is (a)
Step-by-step explanation:
Well I didn’t really do any work but you can tell right away theres a ton of slope options so you can’t eliminate from there, BUT when you look at the y-intercept, 3 is the only y-intercept option here and the only choice with the y-intercept of 3 is (a).
what is the greatest common factor of 20 and 50
Answer:
the answer is 10
Step-by-step explanation:
Answer: 10
Why? Because 10x5=50 and then 10x2=20 ten can be used for both of them! Hope this helps^^ please give me brainlist if you could but you don’t have too!^^
A 2-g antibiotic vial stales "Reconstitute with 8.6 mL of sterile water for a final volume of 10 ml.* What is the concentration of the vial after reconstitution?
A. 2 g/8.6 mL
B. 232.6 mg/mL
C. 0.234 mg/mL
D. 200 mg/mL
The correct answer is option B. 232.6 mg/mL which is the concentration of the vial after reconstitution.
To determine that 232.6 mg/mL is the concentration of the antibiotic vial after reconstitution, we need to calculate the amount of antibiotic in grams divided by the final volume in milliliters.
The vial states that it needs to be reconstituted with 8.6 mL of sterile water for a final volume of 10 mL. This means that the antibiotic will be dissolved in 8.6 mL of sterile water.
Since the vial contains 2 grams of antibiotic, the concentration can be calculated as follows:
Concentration = Amount of antibiotic (g) / Final volume (mL)
Concentration = 2 g / 8.6 mL
Simplifying the expression, we get:
Concentration ≈ 0.2326 g/mL
Therefore, the correct option is B) 232.6 mg/mL, the concentration of the vial after reconstitution.
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Find an expression of a(t) if 8t (b) (2 points) If A(4) = 30, find A(2). 1+ t2
The expression for a(t) is 8(1-t)/(1+t)² and A(2) = -8/9.
What is the expression of a(t)?An expression is a combination of numbers, variables, and operations. Expressions can be used to represent quantities, relationships, and functions. While there are different types of expression such as arithmetic expression, algebraic expression and function, this as an algebraic expression.
To determine the expression that represents a(t); we have to factor the expression 8t/(1+t²).
8t/(1+t²) = 8t/(1+t)(1-t)
Dividing by 1 - t
a(t) = 8t/(1+t)
Simplifying further;
a(t) = 8(1-t)/(1+t)²
To solve for A(2), we need to plug t = 2 into the expression;
A(2) = 8(1-2)/(1+2)²
A(2) = -8/9
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Please help with these questions... I've been trying to figure them out for like twenty minutes and at this point I just don't have the energy anymore... I will pick brainliest! Always do...
Answer:
1. y=2x^2-8X-1
2. y=-6x^2+36x-63
3. y=-3x^2+18x-34
4. y=9x^2+54x+76
5. y=-x^2+8x-22
6. y=6x^2-48x+90
7. y=8x^2+16x+5
8. y=2x^2-8x+1
Have a great day :)
What is the slope of the line passing through the points (-9,-3) and (7,-7)
Answer:
The slope is [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]\frac{Y_{2} -Y_{1} }{X_{2}-X_{1} }[/tex]
-7-(-3)= -7+3= 4
4/?
7-(-9)= 7+9 = 16
4/16=1/4
I hope this helps :-)
[tex] \sqrt[3]{625} [/tex]
how would I simplify this without decimals & show work?
Answer:
[tex]5\sqrt[3]{5}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{625}[/tex] factor [tex]625^{1/3}[/tex]=[tex]5(5^{1/3} )[/tex]=5\sqrt[3]{5}
Hope that helps :)
I’m not an expert at simplifying, so I need help
Answer: it's 1 1/2
please give me brainlest
SQL A. Is portable among different implementations B. Is object oriented C. Is better than NoSQL D. Is based on relational algebra
SQL (Structured Query Language) is a widely used language for managing relational databases. It is portable among different implementations and based on relational algebra.
SQL is a language designed for managing and manipulating structured data in relational databases. It provides a standardized way to interact with databases and perform various operations such as querying, inserting, updating, and deleting data. One of the advantages of SQL is its portability, meaning that SQL code can be written to work with different database management systems (DBMS) as long as they support the SQL standard. This portability allows for easy migration of databases between different systems.
SQL is based on relational algebra, which is a mathematical framework for working with relational databases. It defines operations and rules for manipulating relations (tables) and performing relational queries. The foundations of SQL are rooted in the principles of relational algebra, providing a solid basis for database management.
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3.
Mrs Rita buys 6 cartons of soya bean milk. Each carton contains 1.251
of soya bean milk. Does Mrs Rita have enough soya bean milk to fill up
20 mugs with a capacity of 320 ml each? Explain.
Yes, it is possible to fill all twenty mugs.
Please help me to finish the table! D:
Answer: 32, 27, 20
Step-by-step explanation: This is a quadratic table.
let {bn} be a sequence of positive numbers that converges to 1/2 . determine whether the given series is absolutely convergent, conditionally convergent, or divergent.
[infinity]Σ bn^n cos nπ / n n=1
a. absololutely convergent
b. conditionally convergent
c. divergent
The given series Σ (bnₙⁿ cos nπ)/n is conditionally convergent.
To determine the convergence of the series, we need to examine the behavior of the terms and apply the convergence tests. Given that {bₙ} is a sequence of positive numbers that converges to 1/2, we can conclude that bnₙⁿ approaches 1/2 as n approaches infinity.
Considering the term (bnₙⁿ cos nπ)/n, we have the alternating factor cos nπ which oscillates between -1 and 1 as n varies. The absolute values of the terms bnₙⁿ/n decrease monotonically to zero.
By the Alternating Series Test, if a series has alternating signs and the absolute values of its terms decrease monotonically to zero, then the series is conditionally convergent. Therefore, the given series Σ (bnₙⁿ cos nπ)/n is conditionally convergent.
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Complete question - Let {bₙ} be a sequence of positive numbers that converges to 1/2 . determine whether the given series is absolutely convergent, conditionally convergent, or divergent.
[n =1 to infinity]Σ (bnₙⁿ cos nπ)/n =1
a. absolutely convergent
b. conditionally convergent
c. divergent
Choose the correct definition. Group of answer choices Sensitivity refers to the probability that a test correctly classifies as positive individuals who have preclinical disease. Sensitivity refers to the probability that a test correctly classifies individuals without preclinical disease as negative Specificity refers to the probability that a test correctly classifies individuals with preclinical disease as positive Specificity refers to the probability that a test correctly classifies as positive individuals who have preclinical disease.
Answer:
the probability that a test correctly classifies as positive individuals who have preclinical disease
Step-by-step explanation:
Sensitivity represents the true positive percentage
Lets take an example if there is 90% sensitivity that means there are 90% people who have the target disease considered the test positive
So according to the given options, it is the probability in which if the test is done in a correct manner so this means that the positive individuals have the preclinical disease
Therefore the first option is correct
The desired accumulated is $150,000 after 6 years invested in an
account with 2% interest compounded quarterly.
The amount to be invested now, or the present value needed, is
$__. Round to the nearest
The present value needed to accumulate $150,000 after 6 years with a 2% interest rate compounded quarterly is $131,488
To calculate the present value needed to accumulate $150,000 after 6 years with a 2% interest rate compounded quarterly, we can use the formula for compound interest:
Present Value = Future Value / (1 + r/n)^(n*t)
Where:
Future Value = $150,000
Interest Rate (r) = 2% = 0.02 (converted to decimal)
Number of Compounding Periods per Year (n) = 4 (quarterly compounding)
Number of Years (t) = 6
Substituting these values into the formula, we have:
Present Value = $150,000 / (1 + 0.02/4)^(4*6)
Calculating inside the parentheses first:
Present Value = $150,000 / (1 + 0.005)^(24)
Next, calculate the exponent:
Present Value = $150,000 / (1.005)^(24)
Using a calculator or spreadsheet, we can evaluate the expression inside the parentheses and then divide $150,000 by that result to find the present value. Rounding to the nearest dollar, the present value needed is $131,488.
Therefore, the amount to be invested now or the present value needed is $131,488.
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The Mavericks football team was losing when they got
control of the ball at midfield in the last minute of a game.
They lost 17 yards on the first play they ran. Then they
gained 3 yards on the second play. On the third play, the
Mavericks lost 21 yards, and on the fourth play, they lost
8 yards. What was the position of the ball relative to its
starting point after those four plays?
A 33 yd
B -50 yd
C 9 yd
D- 43 yd
Pls help I’m doing a renaissance test
Answer:
-43 yards is the answer...
What is the width of the terrace?
Answer:
12 feet or 4 feet.......
please help !! A golf ball is hit into the air from a platform located 6 meters above the ground. The graph represents the height above the ground of the golf ball as a function of time.
Part A: What is the maximum height, in meters, the golf ball reaches before hitting the ground? (blank) meters
Part B:Which of the following statements describe the golf ball? Select TWO that apply.
A.)At 0 seconds, the golf ball is on the ground.
B.)The golf ball is in the air for a total of 4 seconds.
C.)The golf ball is at a height of 6 feet 2 seconds after it was hit.
D.)Between 1 and 3 seconds, the ball is falling towards the ground.
Answer:
Part A: 8 meters
Part B: B, D
Step-by-step explanation:
Help Me Please Quick Will Mark Brainliest if correct : - )
Answer:
y=2x+3
Step-by-step explanation:
Lets verify
[tex]\\ \sf\longmapsto -1=2(-2)+3=-4+3=-1[/tex]
[tex]\\ \sf\longmapsto 1=2(-1)+3=-2+4=1[/tex]
Hence verified
Answer:
C): y = 2x + 3
Step-by-step explanation:
• when x is -2:
[tex]{ \tt{y = 2(- 2) + 3}} \\ { \tt{y = - 1}}[/tex]
• when x is -1:
[tex]{ \tt{y = 2( - 1) + 3}} \\ { \tt{y = 1}}[/tex]
• since y holds for -2 and -1, it'll hold for other positive integers.
Recall the following definition of an Geometric Sequence. A sequence do, 21, 22, ... is called an geometric sequence if, and only if there is a constant r such that ak = r.24-1 where k> 1. Also recall that we "claimed" the explicit formula for the nth term of the geometric sequence is given by an = no pot where n > 0. Use mathematical induction to prove that our claim is true.
To prove that the explicit formula for the nth term of a geometric sequence is given by an = a₀.rⁿ, we will use mathematical induction. Mathematical induction is a proof technique used to establish a statement or property for all natural numbers or integers greater than or equal to a starting value.
Step 1: Base Case
For n = 0, the formula gives a₀.r⁰ = a₀, which is the first term of the sequence. So, the formula holds true for the initial value.
Step 2: Inductive Hypothesis
Assume that the formula holds for some arbitrary value k, i.e., ak = a₀.rᵏ.
Step 3: Inductive Step
We need to prove that the formula also holds for k+1, i.e., a(k+1) = a₀.r^(k+1).
Using the definition of a geometric sequence, we have:
a(k+1) = r.aₖ
Now substitute the inductive hypothesis into the above equation:
a(k+1) = r.(a₀.rᵏ) = (r.a₀).rᵏ = a₀.r^(k+1)
Therefore, we have shown that if the formula holds for k, then it also holds for k+1.
Step 4: Conclusion
By the principle of mathematical induction, the explicit formula for the nth term of a geometric sequence, given by an = a₀.rⁿ, is true for all non-negative integers n.
Thus, we have proved the claim using mathematical induction.
The question should be:
Recall the following definition of an Geometric Sequence.
A sequence a₀, a₁, a₂, ... is called an geometric sequence if, and only if there is a constant r such that
ak = r.a_k_-1 where k≥ 1.
Also recall that we "claimed" the explicit formula for the nth term of the geometric sequence is given by
an = a₀.rⁿ where n≥ 0. Use mathematical induction to prove that our claim is true.
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Please help me with this questions please please ASAP ASAP please ASAP help please please ASAP please I'm begging you please please ASAP
Answer:
Question 3: 8000
Question 4: 300
Answer:
3. 8,000
4. 300
Step-by-step explanation:
3.
2/5 * 20,000 = 2 * 20,000/5 = 2 * 4,000 = 8,000
Answer: 8,000
4.
Use a proportion.
10/2 = x/60
5/1 = x/60
x = 5 * 60
x = 300
Answer: 300
A binomial experiment consists of 12 trials. The probability of success on trial 5 is 0.16. What is the probability of success on trial 9?
A. 0.1
B. 0.18
C. 0.33
D. 0.25
E. 0.16
F. 0.68
A binomial experiment consists of 12 trials. The probability of success on trial 5 is 0.16. The probability of success on trial 9 is 0.16.
In a binomial experiment, there are two outcomes that are possible in each trial: a success and a failure.
A binomial experiment consists of a fixed number of trials.
The term "probability" refers to the measure of how likely an event is to happen.
The probability of success on trial 5 is 0.16.
We are required to calculate the probability of success on trial 9.
Since the experiment consists of a fixed number of trials, we can say that probability of success in each trial is the same.
Let us assume the probability of success is p.
Therefore, the probability of failure in each trial is (1-p).
The probability of success on trial 5 is 0.16.
Therefore, p = 0.16.
The probability of failure on trial 5 is
1-p = 1-0.16
1-p = 0.84
The probability of success on trial 9 is given by:
P(success on trial 9) = p
P(success on trial 9) = 0.16.
Therefore, the probability of success on trial 9 is 0.16, which is option E.
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Solve for X, assume that all segmented that appear to be tangent are tangent.
Answer:
Step-by-step explanation:
x = 9
A bathtub in the shape of A rectangular prism is 20 meters long 10 meters wide and 2 meters deep how much water can the bathtub hold
Answer:
Topic : CIRCLE
1. Capture/ cut outs pictures that represents a Circle then paste it in a long band paper.
2. Make a reflection in CERA form
C-Content (min. 5sentence)
E- experience(min. 5 sen.)
R-reflection (min.5 sent.)
A- Application (min.5
can someone help me complete this???
Answer:
Part A
750, 2250, 6750, 20250, 60750
Part B
1640250
Which value of r indicates a stronger correlation:r = 0.818 or r= -0.926? Explain your reasoning. Choose the correct answer below. O A. r= -0.926 represents a stronger correlation because 0.818 > -0.926. O B. r=0.818 represents a stronger correlation because | -0.926) > 10.818). OC. r= -0.926 represents a stronger correlation because | -0.926) > 10.818|- OD. r=0.818 represents a stronger correlation because 0.818 > -0.926.
Hence, option D is the correct answer to the given question.
The correct answer to the given question is the option D. i.e r=0.818 represents a stronger correlation because 0.818 > -0.926. Explanation: The strength of the correlation can be determined by the magnitude of the correlation coefficient. The correlation coefficient values vary between -1 to 1. If the value of correlation coefficient is close to -1 or 1, it indicates strong correlation. On the other hand, if the value of correlation coefficient is close to 0, it indicates a weak correlation.A correlation coefficient value of -0.926 indicates a strong negative correlation. A correlation coefficient value of 0.818 indicates a strong positive correlation. Hence, option D is the correct answer to the given question.
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If 5.90 × 1.8 = 10.62, what does 106.2 ÷ 59 equal?
Answer:
1.8
Step-by-step explanation:
- hope this helps!!
Can someone plz help me
73.12 m2
Step-by-step explanation:
determine triangle area.
8x12=96 96/2=48
determine area of half circle
diameter=8
radius=4
4π²/2=25.1327412287
add two areas together.
48+25.1327412287=73.1327412287
round the nearest hundredth
73.1327412287=73.12 m2