A quantity with an initial value of 970 grows exponentially at a rate of 3.5% every 3 weeks. What is the value of the quantity after 49 days, to the nearest hundredth?

Answer:

x = 17

Step-by-step explanation:

let x be the number she is thinking about

5x + 8 = 93

Rearrange

5x = 85

x = 17

Answer:

wouldnt it be 2.05

Step-by-step explanation:

Answer:

c) 3x - 45 = 10

Step-by-step explanation:

\(\frac{1}{5}x-3=\frac{2}{3}\\\\\frac{1}{5}x-\frac{3*5}{1*5}=\frac{2}{3}\\\\\frac{x-15}{5}=\frac{2}{3}\\\)

Cross multiply,

3*(x - 15) = 2*5

3*x - 3*15 = 10

3x - 45 = 10

Answer:

\(a. (4x + 2) + (-7x + 4) \\ c. -3(x - 2) \\ d. 1/2(-6x + 12) \\ \: are \: the \: once \: that \\ apply\)

\( \fbox{(2,5)}\)

Hello, substitute all the given coordinates & see if RHS match with LHS

given equation,

y = 4x-3

First coordinate,

(x,y) = (2,5)

5= 4×2-3

5=5

Hence, first solution satisfies the given equation,

let's solve for rest other cordinates,

second coordinate,

(x,y) = (5,5)

5= 4×5-3

5 ≠ 17

does not satisfy,

third coordinate,

(x,y) = (4,5)

5= 4×4-3

5 ≠ 13

does not satisfy,

fourth coordinate,

(x,y) = (4,5)

5 = 4×3-3

5 ≠ 9

does not satisfy.

Hence the correct answer is (2,5)

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The internal energy of the system is given by U = -2ε/kT exp(-ε/kT) + (1/kT) exp(-2ε/kT), where ε is the energy difference between the first and second energy levels, T is the temperature, and k is Boltzmann's constant.

The internal energy U of the system can be calculated using the canonical ensemble partition function:

Z = Σi \(g_i\) exp(-\(E_i\)/kT)

where \(g_i\) is the degeneracy of the \(i_{th}\) energy level and Ei is the energy of the \(i_{th}\) level. The internal energy is then given by:

U = - (∂lnZ/∂β)|V,N

where β = 1/(kT) is the inverse temperature.

Substituting the energy levels and degeneracies, we have:

Z = 1 + 2 exp(-ε/kT) + exp(-2ε/kT)

Taking the natural logarithm of both sides, we get:

lnZ = ln[1 + 2 exp(-ε/kT) + exp(-2ε/kT)]

Using the Taylor series expansion of ln(1+x), we can approximate lnZ as:

lnZ ≈ 2 exp(-ε/kT) - (1/2) exp(-2ε/kT)

Differentiating lnZ with respect to β, we obtain:

(∂lnZ/∂β)|V,N = -kT^(-2) (∂lnZ/∂T)|V,N

= kT^(-2) [2ε/kT^2 exp(-ε/kT) - ε/kT^2 exp(-2ε/kT)]

Substituting this expression into the formula for the internal energy, we get:

U = -kT^(-2) [2ε/kT^2 exp(-ε/kT) - ε/kT^2 exp(-2ε/kT)]

Simplifying, we get:

U = -2ε/kT exp(-ε/kT) + (1/kT) exp(-2ε/kT)

Therefore, the internal energy of the system is given by U = -2ε/kT exp(-ε/kT) + (1/kT) exp(-2ε/kT), where ε is the energy difference between the first and second energy levels, T is the temperature, and k is Boltzmann's constant.

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A customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day.

Charge for first 5 charged = $ 4.50

Charge for additional time = $ 0.50 per minute

Starting time = 9:35 p.m.

End time = 11:15 p.m.

Total minutes = 100 minutes

Total charge = 4.50 + (95 x 0.50)

                  = 4.50 + 47.50

                  = 52.00

Hence, a customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day i.e. for 100 minutes.

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The resulting equation if Becca isolated x² in the first equation and then substituted it into the second equation is (9-y²) / 25 - y²/36 = 1

x² + y² = 9

x²/25 - y²/36 = 1

From (1)

x² = 9 - y²

substitute x² = 9 - y² into (2)

x²/25 - y²/36 = 1

(9-y²) / 25 - y²/36 = 1

Therefore, the resulting equation is option C; (9-y²) / 25 - y²/36 = 1

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Answer:

(9-y²) / 25 - y²/36 = 1

Step-by-step explanation:

Answer:

would it be negative 4

Step-by-step explanation:

Answer:

  42, 38, 34, 30

Step-by-step explanation:

You want the first 4 terms of the sequence described by ...

  an = 42 -4(n -1), n ∈ ℕ

You can write the first 4 terms of the sequence by evaluating the 'an' expression for n = 1, 2, 3, 4.

Or, you can recognize the expression describes a sequence with a first term of 42 and a common difference of -4. That is, each term is 4 less than the one before.

The terms you want are ...

  42, 38, 34, 30

__

Additional comment

The equation for the n-th term of an arithmetic sequence is ...

  an = a1 +d(n -1)

where a1 is the first term, and d is the common difference. Comparing this to the given equation, we see a1 = 42, d = -4.

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The stopping distance for a car traveling at 55 mph is 60,500 feet.

The equation to solve this problem would look like the following

s = v²/k

The stopping distance s will increase (varies directly) as the velocity increases.

Putting in the values we know

45 = 30²/k

⇒ k = 45/900

⇒ k = 0.05

Now,

at 55 mph we would have

    s = 55²/0.05

⇒ s = 3025/0.05

⇒ s = 60,500

s = 60,500 feet to stop

Complete Question:

The stopping distance s of a car varies directly as the square of its speed v. If a car traveling at 30 mph requires 45ft to stop, find the stopping distance for a car traveling at 55 mph.

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The circumference of the circle subtended by 210° will be 210 times (1/360)th times circumference.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circular objects for example our bike wheel.

The perimeter of the circle = 2πr where r is the radius of the circle.

The circumference bound by 210° angle will be as,

(210/360)2πr = 210 (1/360)2πr

⇒ 210 times (1/360)th of circumference.

Hence "The circumference of the circle subtended by 210° will be 210 times (1/360)th times circumference".

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We have the expression:

We can simplify it by dividing the numerator by the denominator (division of polynomials):

The answer is: x²+4x+12+29/(x-3)

Answer:

its 1.4

Step-by-step explanation:

Answer:

1.4

Step-by-step explanation:

If the probability that interest rates will go up and house sales will decrease is estimated to be 0.15, the probability of an increase in interest rates and not a decrease in house sales is 0.05.

To find the probability of an increase in interest rates and not a decrease in house sales, we can use the formula for conditional probability:

P(Interest rates increase and house sales don't decrease) = P(Interest rates increase) - P(Interest rates increase and house sales decrease)

We are given that the probability of interest rates on housing loans going up in the next 6 months is 0.20, and the probability of house sales decreasing is 0.6. We are also given that the probability of interest rates going up and house sales decreasing is 0.15.

To find the probability of interest rates going up and not house sales decreasing, we subtract the probability of interest rates going up and house sales decreasing from the probability of interest rates going up:

P(Interest rates increase and house sales don't decrease) = 0.20 - 0.15 = 0.05

In summary, we can use conditional probability to calculate the probability of an increase in interest rates and not a decrease in house sales.

Given the probabilities of interest rates going up and house sales decreasing, we can subtract the probability of interest rates going up and house sales decreasing from the probability of interest rates going up to find the probability of interest rates going up and not house sales decreasing.

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Answer:

There are no solutions

Step-by-step explanation:

If y is greater or equal to 3x+1 it can not be less than 3x-3 since 3x-3 is 4 less than 3x+1. Therefore, there can not be any solutions for the system of inequalities.

It will take 15 days for Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day.

To determine the number of days, we first represent the number of days to do a piece of work by each one of them in fractions as follows;

Fraction of work completed by Akash in 1 day = 1/20

Fraction of work completed by Sunil in 1 day = 1/30

Fraction of work completed by Rakesh in 1 day = 1/60

The total work done in 1 day can be given as;

Total work done by the three in one day = [(1/20) + (1/30) + (1/60)] = 1/10

Work done by Akash in two days = 2 × (1/20) = 2/20 = 1/10

The work done in three days (1 day of all three together + Work done by Akash in two days) = (1/10) + (1/10) = 1/5

Therefore; the total work done in 3 days = 1/5

At this rate, the total number of cycles required to finish the work =

(1) ÷ (1/5) = 5

Since each cycle has three days, the total number of days required to finish the work can be calculated as follows;

5 × 3 = 15 days

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Answer:

f(x) = x^2 + 11x + 18.

Step-by-step explanation:

As the zeroes are -2 and -9 the factored form  is

f(x) = a(x - (-2))(x -  (-9))   where a is some constant.

As we want any quadratic function with theses zeros we  can let a = 1 so:

f(x) = (x + 2)(x + 9)

f(x) = x^2 + 2x + 9x + 18

f(x) = x^2 + 11x + 18.

The required quadratic function is given as x²+11x+18 = 0,

Given that,
To write a quadratic function f whose zeros are -2 and -9

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
x = -2 and x = -9
x  2 = 0  and x + 9 = 0
The function is given as,
(x + 2)(x + 9) = 0
x²+11x+18 = 0,

Thus, the required quadratic function is given as x²+11x+18 = 0,

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Answer:

The initial value is $5.00

Step-by-step explanation:

The question required us to find the y-intercept or c in the equation of the straight line.

We are given 4 different points on the graph and we are also told the hourly fee. As we know that the graph has total hours on x axis and total cost on y axis, we can calculate the gradient or slope of the graph.

m = (23 - 18.5) / (4 - 3)

m = 4.5

Taking point (3,18.5) for calculating c or y intercept from the equation of straight line that is,

y = m (x) + c

18.5 = 4.5 (3) + c

18.5 = 13.5 + c

18.5 - 13.5 = c

c = 5

So the admission fee is $5.

Answer:

$5.00

Step-by-step explanation:

Answer:

1 = 3

2 = 6

3 = 9

Step-by-step explanation:

for every # it is multiplied by 3 (ex. 7 • 3 = 21, 8 • 3 = 24, ect.)

therefore if it is multiplied by 3 each time

then 1 • 3 = 3

2 • 3 = 6

and 3 • 3 = 9

hope this helps :)

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

The range and the vertex is   4 ≤ y < [infinity] and  (5, 4).

To find the vertex, we can take the derivative of the function and set it equal to 0:

y' = |x − 5|' = 0

=> x − 5 = 0

=>  x = 5

Then, we can plug x = 5 into the original equation to find the y-value at the vertex:  

y = |x − 5| = |5 − 5| = |0| = 0

So, the vertex of y = |x − 5| is (5, 4).

To find the range, we need to consider the range of the absolute value function. The range of the absolute value function is:

−[infinity] < y < [infinity]. So, the range of y = |x − 5| is also −[infinity] < y < [infinity] (or 4 ≤ y < [infinity]).

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The solution is x = -1.28568 (correct to 5 decimal places), which has a relative error of 0.92%.

To solve the equation cos(x) + x + 1 = 0 using Newton-Raphson iterations,

we need to perform the following steps:

Step 1: Rearrange the equation as f(x) = cos(x) + x + 1 = 0.

Step 2: Find the first derivative of the function, f'(x) = -sin(x) + 1.

Step 3: Start with an initial guess, x0 = -1.5, and use the Newton-Raphson formula to find the next approximation.

The formula is: xn+1 = xn - f(xn) / f'(xn)

Step 4: Repeat step 3 until the desired accuracy is achieved.

We are asked to approximate the solution with a relative error less than 1%.

This means that we need to keep iterating until |(xn+1 - xn) / xn+1| < 0.01 or 1%.

We are given the equation cos(x) + x + 1 = 0 and asked to use Newton-Raphson iterations to find a solution with a relative error less than 1%.

Starting with an initial guess of x0 = -1.5, we use the Newton-Raphson formula to find the next approximation.

We repeat this process until the desired accuracy is achieved.

The solution is x = -1.28568 (correct to 5 decimal places), which has a relative error of 0.92%.

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Answer: i think C correct me if i am wrong

Step-by-step explanation:

The probabilities of the given events involving red marbles, blue marbles, odd-numbered marbles, and even-numbered marbles.

(a) The probability that the marble is red is \(\frac{3}{8}\). To find this, you need to divide the number of red marbles (6) by the total number of marbles (16). So, \(\frac{6}{16}=\frac{3}{8}\).

(b) The probability that the marble is odd-numbered is \(\frac{1}{2}\). To find this, count the odd-numbered marbles: 3 red (1, 3, 5) and 5 blue (1, 3, 5, 7, 9). So, there are 8 odd-numbered marbles. Divide this by the total number of marbles (16), giving \(\frac{8}{16}=\frac{1}{2}\).

(c) The probability that the marble is red or odd-numbered is \(\frac{11}{16}\). First, find the number of marbles that are red or odd-numbered: all 6 red marbles plus the 5 odd-numbered blue marbles (subtract 1 as blue marble number 1 was counted twice). This results in 10 unique marbles. So, the probability is \(\frac{5}{8}\) .

(d) The probability that the marble is blue or even-numbered is \(\frac{1}{2}\). This is complementary to the probability found in (c). Since the marble can only be red or odd-numbered, or blue or even-numbered, the probabilities must sum to 1. So, \(1 - \frac{5}{8}  = \frac{1}{2}\).

Your corrected answers are: (a) \(\frac{3}{8}\), (b) \(\frac{1}{2}\), (c) \(\frac{5}{8}\), and (d) \(\frac{1}{2}\).

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Answer:

\((2,-1)\)

Step-by-step explanation:

The solution of the systems of equations in the graph is 'the point of intersection'

The point of intersection is the point at which two lines meet or intersect.

For this graph, the point of intersection is the point where the the red and blue graph meet. The x and y values (or coordinates) have to be read from the graph.

From the graph:

x = 2

y = \(-1\)

Together these x and y values form an ordered pair

∴Ordered pair is \((2,-1)\)