Answer:
the answer is 8
Step-by-step explanation:
n a division problem, the divisor is twenty times the quotient and five times the remainder. If remainder is 16, the number will be:
Option 1 : 3360 Option 2 : 336 Option 3 : 1616 Option 4 : 20516
The half-life of a radioactive substance is the time required for half of a sample to undergo radioactive decay, or for the quantity to fall to half its original amount. Carbon 14 has a half-life of 5,730 years. Suppose given samples of carbon 14 weigh (fraction 5/8) of a pound and (fraction 7/8) of a pound. What was the total weight of the samples 11460 years ago
(show work please)
Answer:
Amount of C-14 taken were 2.5 pounds and 3.5 pounds respectively.
Step-by-step explanation:
Radioactive decay is an exponential process represented by
[tex]A_{t}=A_{0}e^{-kt}[/tex]
where [tex]A_{t}[/tex] = Amount of the radioactive element after t years
[tex]A_{0}[/tex] = Initial amount
k = Decay constant
t = time in years
Half life period of Carbon-14 is 5730 years.
[tex]\frac{A_{0} }{2}=A_{0}e^{-5730k}[/tex]
[tex]\frac{1}{2}=e^{-5730k}[/tex]
Now we take ln (Natural log) on both the sides
[tex]ln(\frac{1}{2})=ln[e^{-5730k}][/tex]
-ln(2) = -5730kln(e)
0.69315 = 5730k
[tex]k=\frac{0.69315}{5730}[/tex]
[tex]k=1.21\times 10^{-4}[/tex]
Now we have to calculate the weight of samples of C-14 taken for the remaining quantities [tex]\frac{5}{8}[/tex] and [tex]\frac{7}{8}[/tex] of a pound.
[tex]\frac{5}{8}=A_{0}e^{(-1.21\times 10^{-4}\times 11460)}[/tex]
[tex]\frac{5}{8}=A_{0}e^{(-1.21\times 10^{-4}\times 11460)}[/tex]
[tex]\frac{5}{8}=A_{0}e^{(-1.3863)}[/tex]
[tex]A_{0}=\frac{5}{8}\times e^{1.3863}[/tex]
[tex]A_{0}=\frac{5}{8}\times 4[/tex]
[tex]A_{0}=\frac{5}{2}[/tex]
[tex]A_{0}=2.5[/tex] pounds
Similarly for [tex]\frac{7}{8}[/tex] pounds
[tex]\frac{7}{8}=A_{0}e^{(-1.21\times 10^{-4}\times 11460)}[/tex]
[tex]\frac{7}{8}=A_{0}e^{(-1.21\times 10^{-4}\times 11460)}[/tex]
[tex]\frac{7}{8}=A_{0}e^{(-1.3863)}[/tex]
[tex]A_{0}=\frac{7}{8}\times e^{(1.3863)}[/tex]
[tex]A_{0}=\frac{7}{8}\times 4[/tex]
[tex]A_{0}=\frac{7}{2}[/tex]
[tex]A_{0}=3.5[/tex] pounds
Express each fraction as a percent .round to the nearest whole number 178 over 450
1. Julia deposited $250 in a savings account that earns 2.7% simple interest. How much interest has Julia earned by the end of the first year?
$6.75
$92.59
$256.75
$675.00
2. Armand deposited $389.42 in a savings account that earns 3.2% simple interest. What is Armand’s account balance after seven years?
$87.23
$401.88
$476.65
$872.30
3. Andy deposited $1,567.12 in a savings account that earns 1.9% simple interest. What will Andy’s account balance be in nine months?
$1,567.12
$1,589.45
$1,596.90
$1,835.10
Answer:
Step-by-step explanation:
Simple interest formula is : [tex]p\times r\times t[/tex]
t is always in years here.
1.
p = 250
r = 2.7% or 0.027
t = 1
Simple interest earned = [tex]250\times0.027\times1[/tex] = $6.75
2.
p = 389.42
r = 3.2% or 0.032
t = 7
Simple interest earned = [tex]389.42\times0.032\times7[/tex] = $87.23
Amount after 7 years will be = [tex]389.42+87.23[/tex] = $476.65
3.
p = 1567.12
r = 1.9% or 0.019
t = [tex]9/12=0.75[/tex]
Simple interest earned = [tex]1567.12\times0.019\times0.75[/tex] = $22.33
Account balance after 9 months = [tex]1567.12+22.33[/tex] = $1589.45
Understanding this proof for the proposition "For all integers a, gcd(9a+4, 2a+1) = 1.
Proof: gcd(9a+4, 2a+1) = gcd(2a+1, a) = gcd(a, 1). Since gcd(a, 1)=1, gcd(9a+4, 2a+1) =1.
First line because 4(2a+1)=8a+4 and 9a+4-(8a+4)= a
Second line because a times 2 =2a and 2a+1-2a=1
Although the second equality is more or less obvious since 2a+1 leaves a remainder of 1 when divided by a.
Which type of triangle is RST?
a. equilateral
b. isosceles
c. scalene
d. right
9. Write an equation of the line that contains the median of traingle RST from S to RT .
a. x + 2 y = -10
b. x + 2 y = 6
c. x + 2 y = 8
d. x + 2 y = 10
10. Write the equation of the line that contains the altitude of triangle RST from T to RS .
a. 2x - 3y = -13
b. 3 x -2 y = -2
c. 2 x + 3 y = 29
d. 3 x + 2 y = 26
Multiplying a trinomial by a trinomial follows the same steps as multiplying a binomial by a trinomial. Determine the degree and maximum possible number of terms for the product of these trinomials: (x2 + x + 2)(x2 – 2x + 3). Explain how you arrived at your answer.
The product of the given trinomials will have a degree of 4, and since there are 9 terms, the maximum possible number of terms for the product is 9.egree of 4 and a maximum possible number of terms of 9.
When multiplying two polynomials, the degree of the resulting polynomial is the sum of the degrees of the two polynomials being multiplied.
In this case, both trinomials have a degree of 2.
The maximum possible number of terms in the product of two polynomials is the product of the number of terms in each polynomial.
For the first trinomial, there are 3 terms, and for the second trinomial, there are also 3 terms.
Multiplying these together gives a maximum possible number of terms of 9.
To arrive at this conclusion, you can use the distributive property, where each term in the first trinomial is multiplied by each term in the second trinomial, resulting in a total of 9 possible term combinations.
Therefore, the product of the two trinomials will have a dTo multiply two trinomials, like [tex]\( (x^2 + x + 2)(x^2 - 2x + 3) \)[/tex], you apply the distributive property repeatedly, multiplying each term in the first trinomial by each term in the second trinomial and then summing up the products.
Each term in the first trinomial needs to be multiplied by each term in the second trinomial, resulting in a total of [tex]\( 3 \times 3 = 9 \)[/tex] products.
Now, regarding the degree, when you multiply two polynomials, you add the degrees of the polynomials.
Here, both polynomials are of degree 2, so the resulting polynomial will be of degree 2 + 2 = 4.
Thus, the product of the given trinomials will have a degree of 4, and since there are 9 terms, the maximum possible number of terms for the product is 9.egree of 4 and a maximum possible number of terms of 9.
Choose the equation of the vertical line passing through the point (-4, 2). i picked x = -4.. ...?
Which of the sets of ordered pairs represents a function?
A = {(−4, 5), (1, −1), (2, −2), (2, 3)}
B = {(2, 2), (3, −2), (9, 3), (9, −3)}
1. Only A
2. Only B
3. Both A and B
4. Neither A nor B
The graph shows the processing speeds of computers as a function of time since 1980.
Which statements are true about the function?
Select each correct answer.
A. The range is y≥16 , so the processing speeds are always positive.
B. The point (0,16) represents an initial processing speed of 16 MHz.
C. The point (10,256) represents the maximum processing speed.
D. The domain is x>0 , so the processing speed increases over time.
E. The graph is ascending, indicating that the processing speed increases over time.
Answer:
A, B and E are correct.
Step-by-step explanation:
We are given a function representing the processing speed of computers with respect to time.
Let, x-axis = axis corresponding generation and y-axis = axis corresponding the processing speed.
We can see that the the starting point of the function is (0,16). This gives us that the range of the function is y≥16 and (0,16) represents the initial speed of the computer.
So, option A and B are correct.
As, we can see that the function is going upwards after passing the point (10,256). This gives us that, this point does not the represent the maximum processing speed.
So, option C is not correct.
Also, only the domain being x>0 does not imply that the processing speed increases.
So, option D is not correct
Further, as the graph is ascending, so we see that as time increases, the processing speed increases.
So, option E is correct.
Answer:
The correct statements are in bold.
A. The range is y≥16 , so the processing speeds are always positive. (As the initial point is 16 and the graph is going upwards from there hence,the range y≥16 shows positive speed growth. Below this range, the speed will fall.)
B. The point (0,16) represents an initial processing speed of 16 MHz. (This is clearly visible in the graph.)
C. is not right as the graph is going up from 10256.
D. This is also not right. The given domain is not specific of speed.
E. The graph is ascending, indicating that the processing speed increases over time. (We can see as the time increases, the processing speed increases.)
What is to find an approximate value for a number is called? any words starting with the letter 'r'?
factored form of 25x^2+40x+16
1.5x-2<10 how do you solve this
Four out of fifteen people surveyed say they plan to vote yes on Measure 2. Based on this sample, how many people out of 210 would you expect to vote yes?
Answer:
56
Step-by-step explanation:
The answer is 56 just clarifying the top answer :))
What other information is needed to prove that the two triangles congruent by SAS?
Picture description: there are two triangles showing line LT = line MQ and L=M
A.
B.
C. Line GT = line NQ <<
D. Line LG = line MN
What other information is needed to prove the two triangles congruent by SAS? Pick 2.
A. S = U<<
B. T = V
C. S = V
D. T = U
E. Line RS = line WU<<<
F. line RT = line VU
Answer:
D. LG = MN
Step-by-step explanation:
Final answer:
To prove two triangles congruent by SAS, we require equality of two sides and the included angle. Given line LT = line MQ and angle L = angle M, we also need line GT = line NQ and line LG = line MN. For the second part, line RS = line WU and line RT = line VU are necessary to fulfill SAS criteria.(Options C and D for first and Option E and F for second)
Explanation:
When proving two triangles are congruent using the Side-Angle-Side (SAS) postulate, you need to know that two sides and the included angle (the angle between the two sides) of one triangle are exactly equal to two sides and the included angle of another triangle.
In the given problem, we're told that line LT is congruent to line MQ and angle L is congruent to angle M. The additional information needed to prove triangle congruence by SAS would be to show that the second pair of sides around the included angle are also congruent (as in option C Line GT = line NQ) and to ensure congruence on the corresponding parts of the other triangle (as in option D Line LG = line MN).
Answering the second part, to prove congruence by SAS, we would need two corresponding sides and the included angle. Therefore, the correct choices are option E Line RS = line WU which provides the second side, and option F line RT = line VU ensures the sides are corresponding in the two triangles, enclosing the angle which is already given as equal.
Find all points of extrema on the interval [0,2pi] if y=x-cosx ...?
The function y=x-cosx has an extremum on the interval [0,2pi] at x=3pi/2, determined by setting the first derivative equal to zero. The second derivative test is inconclusive at this point, but the point (3pi/2, 3pi/2) is a minimum due to the nature of the function.
To find all points of extrema on the interval [0,2pi] for the function y=x-cosx, we first need to find the derivative of the function and determine where it is equal to zero. The first derivative of y=x-cosx is y' = 1 + sinx. The critical points occur where y' = 0, which translates to 1 + sinx = 0 or sinx = -1. The only point in the interval [0,2pi] where sinx = -1 is at x = 3pi/2. To determine if this critical point is a maximum or minimum, we apply the second derivative test.
The second derivative of the function is y'' = cosx. At x = 3pi/2, the second derivative y'' = cos(3pi/2) = 0; since the second derivative is zero, the second derivative test is inconclusive. However, we can analyze the function around the critical point to conclude or use other methods like analyzing the first derivative's sign change.
For y=x-cosx, since the original function is a combination of a linear increasing function and cosine function, the critical point at x = 3pi/2 will be a minimum as the function increases both before and after this point.
Therefore, the point of extrema on the interval [0,2pi] for the function y=x-cosx are at (3pi/2, 3pi/2 - cos(3pi/2)), which simplifies to (3pi/2, 3pi/2).
Find all real values of x, such that f(x)=0.
f(x)=15-3x ...?
Hydra are small freshwater animals. They can double in number every two days. Suppose there is an initial population of 60 hydra, when will there be more than 5000 hydra?
Factor and simplify: 4a^2c^2(a^2-b^2+c^2)^2
In a family with eight children, what is the probability that exactly six are boys? a. 7168 b. 28 c. 0.109375 d. 0.015625
The probability that exactly six children in the family are boys is 0.015625.
What is Combination?An arrangement of objects where the order in which the objects are selected does not matter.
The probability of having exactly six boys in a family with eight children can be calculated using the binomial distribution formula:
[tex]P(X = k) =^nC_{k} p^k(1-p)^(^n^-^k^)[/tex]
P(X = k) is the probability of having exactly k boys, n is the total number of children, k is the number of boys we want to find , p is the probability of having a boy and (1-p) is the probability of having a girl (also 1/2 in this case)
Substituting the values into the formula, we get:
P(X = 6) = ⁸C₆ (1/2)⁶ (1/2)⁸⁻⁶
= (8! / (6! ×2!)) (1/2)⁸
= (87/21) × (1/2)^8
= 0.015625
Therefore, the probability that exactly six children in the family are boys is 0.015625.
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Factor completely 50a2b5 – 35a4b3 + 5a3b4
Answer
10b2 – 7a2 + ab
a2b3(50b2 – 35a2 + 5ab)
5(10a2b5 – 7a4b3 + a3b4)
5a2b3(10b2 – 7a2 + ab)
...?
Answer:
The factored form of the given expression is [tex]5a^2b^3(10b^2-7a^2+ab)[/tex]
Step-by-step explanation:
We have been given the expression [tex]50a^2b^5-35a^4b^3+5a^3b^4[/tex]
In order to factor it completely we can check for the GCF (greatest common factor) among all the three terms
The GCF is [tex]5a^2b^3[/tex]
On factor out the GCF, we are left with
[tex]5a^2b^3(10b^2-7a^2+ab)[/tex]
Therefore, the factored form of the given expression is [tex]5a^2b^3(10b^2-7a^2+ab)[/tex]
Answer:
given expression is [tex]5a^{2} b^{3} (10b^{2}-7a^{2} +ab)[/tex]
Step-by-step explanation:
The distance from the school to Brandi's house is 1,240 meters. Leaving the school, she rides her bicycle for 60 seconds at a speed of 5 meters per second. If Brandi continues cycling at this speed, how many more seconds will it take her to arrive at her house?
Brandi rides her bike at a speed of 5 m/s from school to her house. She will take an additional 188 seconds to cover the remaining distance of 940 meters to arrive at her house.
Explanation:Brandi's situation:
Distance to house: 1,240 metersSpeed leaving school: 5 m/sTime taken initially: 60 secondsTo find: Additional time needed to reach house.
Calculations:
Time taken initially: 60 secondsRemaining distance: 1,240 - (60*5) = 940 metersTime to cover the remaining distance: 940 / 5 = 188 secondsTotal time: 60 + 188 = 248 secondsFactor each polynomial (1)64-40ab
use the concept of slope to find t such that three points are collinear
(-3,3) (t,-1) (8,6)
If n is a positive integer, then lim (n-->infinity) (1/n) [1/(1+(1/n)) + 1/(1+(2/n))+...+1/(1+(n/n)] is?
the above can be expressed as
a.) integral from 0 to 1 of (1/x) dx
b.) integral from 1 to 2 of (1/(x+1))dx
c.) integral from 1 to 2 of (x)dx
d.) integral from 1 to 2 of (2/(x+1))
e.) integral from 1 to 2 of (1/x)
The given sequence is in the form of a Riemann sum for the integral of the function 1/(1+x) from 1 to 2. So, the correct answer is b) 'integral from 1 to 2 of (1/(x+1)) dx'.
Explanation:The sequence in the question seems to be in the form of a Riemann sum for an integral. The term inside the summation loop can be expressed as 1/(1+i/n) where i varies from 1 to n. The limit of the sequence as n tends to infinity can be thus represented as the integral from 0 to 1 of the function 1/(1+x) dx. The function 1/(1+x) is a continuous function over the interval [0,1], so the integral exists and the limit of the sequence is legitimately defined.
Therefore, looking in the options provided, the answer to your question will be 'b.) integral from 1 to 2 of (1/(x+1)) dx'. This integral is the limit of the given series as n approaches infinity.
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The limit as 'n' approaches infinity of this summation is equal to the integral from 1 to 2 of (1/(x+1))dx. Essentially, this question is turning the sum into an integral as 'n' approaches infinity.
Explanation:This question is asking for the limit of a sum as n approaches infinity, which is essentially the definition of an integral. Every term in the sum could be expressed as 1/(1+i/n), where 'i' is the sum index. Each term, when 'n' becomes infinitely large, becomes a term of the form i/n, or Δx, which is a small piece of the variable we’re integrating. Similarly, each 1/(1+i/n) term turns into 1/x for that small piece.
Given these transformations and the fact that the index i ranges from 1 to n, it's clear that as n approaches infinity, we are integrating the function 1/x from 1 to 2.
Thus, the correct answer would be: b.) integral from 1 to 2 of (1/(x+1))dx
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There are 4 quarters in 1 dollar. The total number of dollars is a function of the number of quarters. Does this situation represent a linear or nonlinear function? Explain why.
The situation represents the linear function.
Given that,
There are 4 quarters in one dollar. The total no of dollars represents the function of the no of the quarter.Based on the above information, we can say that
When dollar presents y value and the quarter presents x value
So, the slope should be [tex]\frac{1}{4}[/tex]
The linear function should be [tex]y = \frac{1}{4}x[/tex]
Therefore we can conclude that the situation represents the linear function.
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how many numbers are between 100 and 200?
What is the result when -2.5 is divided by 1.8?
5.1(x 2)=1.02 how do i solve it
Rita's company reimburses her expenses on food, lodging, and conveyance during business trips. The company pays $55 a day for food and lodging and $0.45 for each mile traveled. Rita drove 300 miles and was reimbursed $2,335. Part A: Create an equation that will determine the number of days x on the trip. (3 points) Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points) Part C: How many days did Rita spend on this trip? (1 point)
Part A)
m = miles traveled
x = days on trip
y = reimbursement
55x + .45m = y
Part B)
55x + .45(300)= 2335
55x+ 135 = 2335
subtract 135 on both sides
55x= 2200
divide by 55 on both sides
x= 40
Part C) Rita Spent 40 Days on This Trip