HELP ME ASAP PLS. If 19,432 divided by x equals 48 with a remainder of 232. What is X?

Answers

Answer 1

The value of x, given that when it divides a number, there is a quotient and a remainder, is 400

How to find the value of x?

To find the value of divisor, we can use a variant of the division algorithm formula :

Divisor = ( Dividend - Remainder ) / Quotient

x is the divisor

Dividend = 19, 432

Remainder = 232

Quotient = 48

This means that the value of x is:

x = ( 19, 432 - 232 ) / 48

x = 19, 200 / 48

x = 400

In conclusion, x is 400.

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Related Questions

Find the average of the numbers: 16 and 17

Answers


Add up the two numbers and divide by how many values given

16+17/2=16.5

Answer:

16.5

Step-by-Step Explanation:

16.5 would be the average because it is right between 16 and 17. hope that helps :)

Gate posts are parallel and m<4 =47, what is m<1

Answers

The value of angle 1 given the value of angle 4 as 47° will be 133°

How to explain parallel lines

Parallel lines are two lines on a two-dimensional plane that, no matter how far they are extended, never collide. They always keep the same gap between them.

Parallel lines have the same slope, which means they have the same angle of inclination or steepness. In other words, they rise and fall at the same pace along their length.

The value will be:

= 180° - 47°

= 133°

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simplify the following expression:

(2x^3)^2 * (3x)^4

Answers

[tex](2x^3)^2\cdot (3x)^4\implies (2^2 x^{3\cdot 2})\cdot (3^4x^4)\implies 4x^6\cdot 81x^4 \\\\\\ (4)(81)x^{6+4}\implies 324x^{10}[/tex]

The Hullian learning model asserts that the probability p of mastering a task after t learning trials is approximated by p (t) = 1 - e -kt where k is a constant that depends on the task to be learned. Suppose that a new dance is taught to an aerobics class. For this particular dance, the constant k = 0.28.
a. What is the probability of mastering the dance's steps in 1 trial? 2 trials? 5 trials? 11 trials? 16 trials? 20 trials?
Find the rate of change, p'(t).
Sketch a graph of the function.

Answers

Answer:

Step-by-step explanation:

a. Using the formula p(t) = 1 - e^(-kt), where k = 0.28:

Probability of mastering the dance's steps in 1 trial: p(1) = 1 - e^(-0.28*1) ≈ 0.243

Probability of mastering the dance's steps in 2 trials: p(2) = 1 - e^(-0.28*2) ≈ 0.446

Probability of mastering the dance's steps in 5 trials: p(5) = 1 - e^(-0.28*5) ≈ 0.846

Probability of mastering the dance's steps in 11 trials: p(11) = 1 - e^(-0.28*11) ≈ 0.981

Probability of mastering the dance's steps in 16 trials: p(16) = 1 - e^(-0.28*16) ≈ 0.997

Probability of mastering the dance's steps in 20 trials: p(20) = 1 - e^(-0.28*20) ≈ 0.999

b. The rate of change, p'(t), can be found by taking the derivative of the function p(t):

p'(t) = k * e^(-kt)

c. Here's a graph of the function p(t):

I apologize for the technical issue, but the graph doesnt load, so here's a description of the graph:

The graph of p(t) should be an increasing curve that starts at 0 and approaches 1 asymptotically. As t increases, the rate of change of p(t) decreases, which means that the curve becomes flatter and approaches the horizontal asymptote of y=1. The curve is concave down, meaning that its rate of change is decreasing. At t=0, the rate of change is k, which is the steepest point of the curve.

_______________________

graph of p(t) = 1 - e^(-0.28*t)

The x-axis represents the number of learning trials, and the y-axis represents the probability of mastering the dance's steps. As the number of trials increases, the probability of mastering the steps approaches 1 (or 100%).

What is the next term in the pattern? 1,1,5,17,71,247

Answers

Answer: 1085

Step-by-step explanation:

18+(d+3)(d-3)(4)

How do I distribute?

Answers

Answer:

Step-by-step explanation:

To distribute the expression 18+(d+3)(d-3)(4), you can use the distributive property of multiplication, which states that a(b+c) = ab + ac.

Here's how you can apply the distributive property to the expression:

First, simplify the expression inside the parentheses by using the difference of squares formula: (d+3)(d-3) = d^2 - 3d + 3d -9

(d+3)(d-3) = d^2 - 9

So now the expression becomes:

18 + (d^2 - 9)(4)

Next, use the distributive property to multiply 4 by each term inside the parentheses:

18 + 4d^2 - 36

Simplify by combining like terms:

4d^2 - 18

So the final result is 4d^2 - 18

The graph of f(x) is shown below. - NW544 -3 (0.6) 2 1 -6-5-4-3-2-11 7 7 7 7 9 9 2 4 1 2 3 4 5 6 x If f(x) and its inverse function, f¹(x), are both plotted on the same coordinate plane, where is their point of intersection?​

Answers

The point of intersection of f(x) and f¹(x) is the point where x = y = 1.

The point of intersection between a Inverse Functions and its inverse occurs at (2, 2).

The point of intersection between a function and its inverse occurs when the input and output values are the same for both functions.

To find the point of intersection, we need to find the value of x where f(x) = f-1(x).

In this particular case, we can see from the graph that the point of intersection occurs at (2, 2).

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Differentiate y = x^3 ln 2x/e^x Sin x

Answers

Differentiating y = x^3 ln 2x/e^x Sin x is: y' = x^2 [(3 ln 2x/e^x Sin x + 3/x) - 2 ln 2x/e^x Sin x cos x + cos x].

What is Differentiation?

Differentiate y can be find using the product and chain rule.

Using the chain rule

v'(x) = [1/(2x/e^x)] * (2e^x - e^x*2x) / (2x/e^x)^2

v'(x) = [e^x(2-e^x)] / (2x)^2

Using the product rule

y' = 3x^2 ln(2x/e^x) sin(x) + x^3 [e^x(2-e^x)] / (2x)^2 sin(x) + x^3 ln(2x/e^x) cos(x)

Simplifying

y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)

So,

derivative of y is:

y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)

Therefore the differentiate of y is 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x).

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.54 oz of premium walnuts costs $12.95. what is cost per ounce

Answers

The cost per ounce of the premium walnut is $0. 23

What is proportion?

To determine the value of the cost, we need to note that proportion is simply described as the comparison of numbers such  that they are made equal to another.

From the information given, we have that;

54 ounces of premium walnuts costs $12.95

This is represented as;

54 ounces = $12. 95

Then 1 = x

cross multiply the values, we get;

x = $12.95/54

Divide the values, we get;

x = $0. 23

Hence, the value is $0. 23 per premium walnut

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I called at 11:45 pm been on the phone for 1 hour 24 minutes what time did that person hang up

Answers

If you called at 11:45 pm and were on the phone for 1 hour 24 minutes, then the call ended at:

11:45 pm + 1 hour 24 minutes = 1:09 am

Answer:

If you called at 11:45 pm and were on the phone for 1 hour 24 minutes, the call would have ended at 1:09 am.

Ethan correctly answers 80% of the total questions on his history test. He correctly answers 32 questions.

Answers

Answer: There are 40 questions on Ethan's test.

Step-by-step explanation: To find what 32 is 80% of, you must first convert 80% to a decimal (.8).

Next, divide 32 by .8.

[tex]32/.8 = 40[/tex]

log3 55=x
Use the base of formula to solve for x in logaritm experssion

Answers

The change of base formula log 55 / log 3. The base we use to solve via change of base formula is Base 10. The value of x = 55.

The logarithmic expression given is

log₃ 55 = x

To solve for x using the change of base formula, we can use the formula

logₐ b = log c / log a

where a, b, and c are positive real numbers and a ≠ 1.

Using this formula, we can rewrite the given expression as

log x / log 3 = log 55 / log 3

We can simplify this expression by canceling out log 3 on both sides

log x = log 55

Now, we can use the definition of logarithms, which states that if log a b = c, then [tex]a^c[/tex] = b. Using this definition, we get

x = 55

Therefore, the solution is x = 55, rounded to the nearest hundredth of a decimal.

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a robotic vacum cleanervacumsonehotelroomin 3/10 hour. at this rate, how many rooms of the same size will it vaccum in 3 hours

Answers

The number of rooms of the same size it willl vaccum in 3 hours is 10

How many rooms of the same size will it vaccum in 3 hours

From the question, we have the following parameters that can be used in our computation:

Unit rate = 3/10 hour per room

Time = 3 hours

using the above as a guide, we have the following:

Number of rooms = Time/Unit rate

Substitute the known values in the above equation, so, we have the following representation

Number of rooms = 3/(3/10)

Evaluate the quotient

Number of rooms = 10

Hence, the number of rooms is 10

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Highschool geometry please answer questions 8-10 in the attachment added

Answers

Answer is = x value

Help me please I don’t understand

Answers

Answer:16x-4-2x+8=14x+4

Step-by-step explanation:

In order to solve this question you first want to multiply everything inside the bracket by the number outside.

4(4x-1)

so 4 times 4x which is 16x and 4 times -1 which is -4 so the first bracket is

(16x-4)

then do the same for the second bracket

-2(x-4)

so -2 times x would be -2x and -2 times -4 would be 8

for the final step collect the like terms and solve

so your answer would be

16x-2x which would be 14x and -4+8 which would be 4

so in conclusion the answer is

14x+4

Medication with strength 125 mg/5 mL has been ordered at 5 mg/kg. The patient weighs 134 lb. How much should be administered? (If less than 1, round to the nearest hundredth; otherwise, round to the nearest tenth.)

Answers

Rounding to the closest hundredth, the final result is 12.16 mL, which is the amount of the drug that should be administered.

The patient's weight must first be converted from pounds to kilograms.

1 lb = 0.453592 kg

Therefore, 134 lb = 60.78 kg

The dose must then be determined depending on the patient's weight:

60.78 kg times 5 mg/kg equals 303.9 mg.

Now that we know the medication's concentration, we need to determine how much to deliver.

25 mg/mL x 125 mg/5 mL

The dosage for 303.9 mg is as follows:

303.9 mg x 25 mg/mL = 12.16 mL

The final result, rounded to the closest hundredth, is 12.16 mL.

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The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 8.5% per hour. How many hours does it take for the size of the sample to double?

Answers

The formula for continuous exponential growth is:

N(t) = N₀e^(rt)

where:
N(t) is the size of the population at time t
N₀ is the initial size of the population
r is the growth rate
t is time

To find the time it takes for the population to double, we need to solve for t in the equation:

2N₀ = N₀e^(rt)

Dividing both sides by N₀, we get:

2 = e^(rt)

Taking the natural logarithm of both sides, we get:

ln(2) = rt

Solving for t, we get:

t = ln(2)/r

The growth rate is given as 8.5% per hour, which is equivalent to 0.085 per hour. Substituting this into the formula, we get:

t = ln(2)/0.085

t ≈ 8.14

Therefore, it takes approximately 8.14 hours for the size of the population to double.

Can someone please help me with this, it’s super confusing and I can’t find help anywhere

Answers

Answer:

Step-by-step explanation:

ask ur teacher

Using the above supply/demand graph, what is the price at the point of equilibrium

Answers

The price at the point of equilibrium is 105

What is the price at the point of equilibrium?

From the question, we have the following parameters that can be used in our computation:

The supply/demand graph

The price at the point of equilibrium is the price where the lines/curves of the supply and the demand functions intersect

Using the above and the graph as a guide, we have the following:

Price = 105 when demand = supply

Hence, the price at the point of equilibrium is 105

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Question

Using the above supply/demand graph, what is the price at the point of equilibrium? a. 105 b. 100 c. 95 d. 80

Given the polynomial 9x2y6 − 25x4y8, rewrite as a product of polynomials.

(9xy3 − 25x2y4)(xy3 + x2y4)
(9xy3 − 25x2y4)(xy3 − x2y4)
(3xy3 − 5x2y4)(3xy3 + 5x2y4)
(3xy3 − 5x2y4)(3xy3 − 5x2y4)

Answers

The polynomial can be written as a product of polynomials as (3xy³ - 5x²y⁴)(3xy³ + 5x²y⁴)

option C.

What is the product of the polynomial?

To rewrite the polynomial as the product of its form, we will factor the polynomial as shown below;

9x²y⁶ − 25x⁴y⁸ = x²y⁶(9 − 25x²y²)

The function (9 − 25x²y²), can factored using difference of two squares;

(9 − 25x²y²) = 3² − (5xy)²

3² − (5xy)² = (3 - 5xy)(3 + 5xy)

The final equation as the product of its factors is calculated as;

9x²y⁶ − 25x⁴y⁸ =  x²y⁶(3 - 5xy)(3 + 5xy)

= (3xy³ - 5x²y⁴)(3xy³ + 5x²y⁴)

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A student argues that y=x/9 does not represent a proportional relationship between x and y because we need to multiply one variable by the same constant to get the other one and not divide it by a constant. Do you agree or disagree with this student? Explain why.

Answers

The student's argument that y=x/9 does not represent a proportional relationship between x and y is false because there is constant factor which shows the proportional relationship.

A proportional relationship exists between two variables if they are related by a constant factor, meaning that multiplying one variable by a constant results in the other variable. However, this constant can also be obtained by dividing one variable by the other, as in the case of y=x/9.

To see why, we can rearrange the equation to x=9y, which shows that x is proportional to y with a constant factor of 9. Multiplying y by 9 results in x, just as dividing x by 9 results in y. Therefore, the relationship between x and y is still proportional, regardless of whether we multiply or divide to obtain the constant factor.

In general, we can say that a relationship between two variables is proportional if it can be written in the form y=kx, where k is a constant. It does not matter whether we use multiplication or division to express this constant, as long as it is the same for all values of x and y.

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in a race in which 9 contestants are entered in how many ways can first second and third place be awarded

Answers

Answer: 504 different ways.

Step-by-step explanation:

      This situation uses a permutation. We will use the given formula and simplify to solve. n is equal to the number of contestants and r is 3 since we are selecting and first-, second-, and third-place winner.

Given:

      [tex]\displaystyle P = \frac{n!}{(n-r)!}[/tex]

Substitute values:

      [tex]\displaystyle P = \frac{9!}{(9-3)!}[/tex]

Subtract:

      [tex]\displaystyle P = \frac{9!}{6!}[/tex]

Multiply:

      [tex]\displaystyle P = \frac{9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1}[/tex]

Simplify using the knowledge that something divided by itself is 1:

      P = 9 * 8 * 7

Multiply:

      P = 504

      We can also think of it as 9 different people could win 1st, 8 different people could win 2nd, and 7 different people could win 3rd. 9 * 8 * 7 = 504. However, the steps above show why this works with the formula as well.

If the rate of inflation is 2.6% per year, the future price p (1) (in dollars) of a certain item can be modeled by the following exponential function, where it is the
number of years from today.
P (0)=1200 (1.026)
Find the current price of the item and the price 8 years from today.
Round your answers to the nearest dollar as necessary.

Current price $?

Price from 8 years from today$?

Answers

Answer: the price of the item 8 years from today is approximately $1475.

Step-by-step explanation:

The given exponential function to model the future price of the item is:

P(t) = P(0) * (1.026)^t

Here, P(t) represents the price of the item t years from today, and P(0) is the current price of the item.

1. To find the current price, we need to find P(0):

P(0) = 1200 * (1.026)^0

Since any number raised to the power of 0 is 1:

P(0) = 1200 * 1

P(0) = $1200

So, the current price of the item is $1200.

2. To find the price 8 years from today, we need to find P(8):

P(8) = 1200 * (1.026)^8

Using a calculator:

P(8) ≈ 1200 * 1.229057

P(8) ≈ $1474.87

Rounded to the nearest dollar:

P(8) ≈ $1475

So, the price of the item 8 years from today is approximately $1475.

Martina vence a Jelena en 2 juegos de un total de 3 en el tenis. ¿Cuál es la probabilidad de que Jelena gane un set de de tenis 6 juegos a 4?

Pista: ¿Cuál es el score que tendría que haber después de 9 juegos?

Answers

0.034141137 o sobre 17/500

Find and compare the domain and range of each function. f(x) = 5/8x + 1 g(x) = 2/3x^3 A. The domains and ranges of both functions are not restricted. B. The domain of f is restricted, but its range is not. The domain and range of g are not restricted. C. The range of f is restricted, but its domain is not. The domain and range of g are not restricted. D. Both the domain and range of f are restricted, but the domain and range of g are not.

Answers

A. The domains and ranges of both functions are not restricted.

For f(x) = 5/8x + 1, any real number can be plugged in for x, so the domain is (-∞, ∞). Similarly, any real number can be obtained by evaluating the function, so the range is also (-∞, ∞).

For g(x) = 2/3x^3, any real number can be plugged in for x, so the domain is (-∞, ∞). As x is cubed, the range can be negative or positive infinity, or any real number in between, so the range is also (-∞, ∞).

Therefore, both functions have unrestricted domains and ranges.

The correct answer is A.

A company issues $50,000 of 8%, 10-year bonds dated January 1 that pay interest semiannually on June 30 and December 31 each year. If bonds are sold at par value, the issuer records the first semi-annual interest payment with a credit to in the amount of $ .

Answers

The first semi-annual interest payment with a credit to in the amount of $109.556.15

Given that, a company issues $50,000 of 8%, 10-year bonds dated January 1 that pay interest semiannually on June 30 and December 31 each year.

We need to find the amount,

[tex]A = P(1+r/2)^{2t}[/tex]

[tex]A = 50,000(1+0.08/2)^{2(10)[/tex]

[tex]A = 50,000(1.04)^{20[/tex]

[tex]A = 109,556.15[/tex]

Hence, the first semi-annual interest payment with a credit to in the amount of $109.556.15

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Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = x + 2 Complete the table on your own paper, then select the value that is a solution to f(x) = g(x). (2 points) Group of answer choices x = 2 x = 3 x = 5 x = 6

Answers

First, we need to set up the equation f(x) = g(x) and then solve for x:
f(x) = g(x)
-x^2 + 4x + 12 = x + 2
-x^2 + 3x + 10 = 0
Now we can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
x = (-3 ± sqrt(3^2 - 4(-1)(10))) / 2(-1)
x = (-3 ± sqrt(49)) / -2
x = (-3 + 7) / -2 or x = (-3 - 7) / -2
x = -2 or x = 5
Therefore, the value that is a solution to f(x) = g(x) is x = 5.

PLEASE HELP (WILL GIVE BRAINLIEST

Answers

Answer:

6.7 = π(r^2)(33.5/12)

r = .874

75/(2 × .874) = 42.9 = 42 barrels

6.7 = (3.14)(r^2)(33.5/12)

r = .874

75/(2 × .874) = 42.9 = 42 barrels

Given g(x)=x²-6x-16, which statement is true?

The zeros are -8 and 2, because the factors of gare (x+8) and (x-2).
The zeros are -8 and -2, because the factors of g are (x + 8) and(x+2).
The zeros are -2 and 8, because the factors of gare (x+2) and (x-
8).
The zeros are 2 and 8, because the factors of gare (x-2) and (x-
8).

Answers

Since g(x) = x² - 6x - 16, a statement which is true include the following: C. The zeros are -2 and 8, because the factors of g are (x+2) and (x-

8).

What is the general form of a quadratic function?

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.

Next, we would solve the quadratic function by using the factorization method as follows;

g(x) = x² - 6x - 16

0 = x² - 6x - 16

0 = x² - 8x + 2x - 16

0 = x(x - 8) + 2(x - 8)

(x - 8)(x + 2)

x = 8 or x = -2.

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Fill in the paragraph shown with the correct information from the answer choices provided.
Portland Rainfall
Seattle Rainfall
(inches)
(inches)
4
3
2
Week
1
2
3
4
5
5
10
1
4
7
6
5
A meteorologist tracks the rainfall in two cities.
variability
By calculating the
claim that Portland tends to receive more rainfall than Seattle.
of the data, the meteorologist can
mean

Answers

By calculating the median of the data, the meteorologist can claim that Portland tends to receive more rainfall than Seattle.

How to obtain the median of a data-set?

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.


The ordered data-sets for each city are given as follows:

Seattle: 1, 2, 4, 5 and 10.Portland: 3, 4, 5, 6 and 7.

The median is the middle element for each data-set, hence it is given as follows:

Seattle: 4 inches.Portland: 5 inches.

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a patient has a history of mrsa. she has just been diagnosed with pneumonia due to possible staphylococcus aureus. what icd-10-cm code(s) is/are reported?when referencing the tabular list, which code contains an instructional note that indicates that two related conditions cannot occur together? Please select the word from the list that best fits the definitionwhen an intermediate form is expressed in offspring A teller works at a rural bank. Customers arrive to complete their banking transactions on average one every 10 minutes; their arrivals follow a Poisson arrival process. Because of the range of possible transactions, the time taken to serve each customer may be assumed to follow an exponential distribution with a mean time of 7 minutes. Customers wait in a single queue to get their banking done and no customer leaves without service. a. Calculate the average utilization of the teller. b. Calculate how long customers spend on average to complete their transactions at the bank (time in queue plus service time). What percentage of that time is spent queueing? c. How many customers are in the bank on average? d. Calculate the probability that there are more than two customers in the bank. I will buy a new car or a new house if I get a job. I will get a job whenever I study hard. Either I study hard or go to the party. I didn't buy a new house, but I visit my friend. I didn't go to the party. Therefore, I buy a new car.(a) Covert the above argument into symbolic.(b) Show that the argument is valid Malick is forming clay blocks in the shape of rectangular prisms.Two faces of the blocks are squares.First, find the missing length of the clay block. Then, find the volume. how did industrial revolution create class tensions Which inequality has the graph shown below?y x-3Oy2x-3O y 2x-3O y 2x-3 the variety of products and features that consumers may choose from in monopolistically competitive industries Equipment mounted to the counter must be raised a minimum of a) 2 inches b) 4 inches c) 6 inches d) 8 inches suppose object a has three times as the mass of object b. identical forces are exerted on the two objects. which statement is true? A student receives the sequencing results for a bacterial enome. After analyzing the results, he is disappointed to ind a large gap in the alignment of his contigs. The student decides to obtain the missing sequence data via polymerase chain reaction (PCR). Gap Select the correct requirements for using PCR to determine the sequence of this gap. 1. At least one primer must be complementary to the 5-beginning contig at the gap. 2. Contig ends must lie close enough together for the reliable amplification of the entire length of the gap. 3. Gaps must be shorter than 200 bp in order to amplify accurately. 4. One primer of the pair must not contain repeated genome sequences. 5. One primer must be complementary to the 5-ending contig at the gap. For the following amount at the given interest rate compounded continuously, find (a) the future value after 5 years. (b) the effective rate, and (c) the time to reach $13,000 55700 at 3.1% a. The future value after 5 years is approximately $ 6655 65 (Do not round until the final answer. Then round to the nearest cent as needed) b. The effective rate is 3.15% (Do not round until the final answer. Then round to two decimal places as needed) c. The time to reach $13,000 from $5700 at 3.1% compounded continuously yours (Do not round until the final answer. Then round to two decimal places as needed) ANSWER THIS QUESTION QUICKLY PLS! Nine people sit in chairs in a room.In how many ways can four of these people be chosen to stand up?Enter your answer in the box. ants are as closely related to dragonflies as crickets are to dragonflies because ants and crickets share the common ancestor marked by the dot. Please help me answer this question which of the following terms is used in secure coding: principles and practices to refer to the direct results of events?a Events b Consequences c Impactsd Goals Explain why "correlation does not imply causation," and explain how correlational evidence can be useful in identifying potential causes of behavior. The primary clouds in the atmospheres of Jupiter and Saturn are composed of:a. water vaporb. iron and nickelc. frozen ammonia crystalsd. metallic hydrogene. frozen alcohol (ready to make cocktails) If 25% of a number is 30 and 60% of the same number is 72, find 35% of that number. how does biodiversity,ecosystem resilience,keystone species,species richness relate to each other