Find the next three terms in each geometric sequence.

3. 400,200,100,50, .......

4. 4,-12,36,-108, ........

The function f(n) = 4n + 1 is one-to-one, but it is not onto

The function f(n) = 4n + 1 is one-to-one because for every input value there is a unique output value. To prove this, we can use the definition of one-to-one functions, which states that if f(a) = f(b), then a = b. Let's assume that f(a) = f(b):

4a + 1 = 4b + 1

4a = 4b

a = b

Therefore, the function f(n) is one-to-one.

Now let's consider if the function is onto. An onto function is one where every element in the codomain has a corresponding element in the domain. In other words, for every n in the codomain, there exists an m in the domain such that f(m) = n. Let's assume that f(m) = n:

4m + 1 = n

4m = n - 1

m = (n - 1)/4

Since m is an integer, this means that n must be an integer that is one more than a multiple of 4. However, not all integers in the codomain fit this description, so there are some values of n that do not have a corresponding value of m. Therefore, the function f(n) is not onto.

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To solve a differential equation with exponential equations, start by isolating the dependent variable and any coefficients that may exist on either side of the equation. Next, take the natural logarithm of both sides of the equation and use the properties of logarithms to simplify the equation. Solve for the dependent variable. Finally, take the exponential of both sides of the equation and simplify it to get the solution.

For example, consider the differential equation dy/dx = 2y.

Isolate the dependent variable to get y = dx/2.

Then, take the natural logarithm of both sides to get ln(y) = ln(dx/2).

Use the property ln(a/b) = ln(a) - ln(b) to get ln(y) = ln(dx) - ln(2).

Solve for ln(y) to get ln(y) = ln(dx) - ln(2).

Then, take the exponential of both sides to get \(y = e^{ln(dx) - ln(2)}\) and simplify to get the solution \(y = (dx/2) e^{ln(dx)}\).

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The sequence is arithmetic Progression whose Common difference is -5, 52nd term is -250 with explicit term of -20-5n

Arithmetic progression is a type of sequence whose consecutive  terms are derived by the addition or subtraction of a constant difference

The given sequence is -25,, -30, -35, -40, ...

Common difference = -30-(-25)

=-30+25=-5

d=-5

The nth term is give by

T\(_{n}\)=a+(n-1)d

52\(_{52}\)= -25+(52-1)-5

Solve the equation

=-25+(51*-5)

=-25+(-225)

=-250

The explicit term is =the last term

L=a+(n-1)d

l=-25+(n-1)-5

l=-25-5n+5

l=-20-5n

Therefore, the common difference is -5, the 52nd term is -250 and the explicit term is -20-5n.

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Answer:

xz=255

Step-by-step explanation:

17 is prime so yz has to be 1*17

if that's the case xy=15*1

so 15*17=255

Answer:

it c hope it helped

Step-by-step explanation:

so its c

Answer:

the answer is 112

Step-by-step explanation:

8×(14)

8×(10+4)

8×10+8×4

80+32

=112

Answer:

1/3

Step-by-step explanation:

3/3 = 1

2/4 = 1/2

1/8 = 1/8

What is missing? = 1/3

Answer:

The answer is 64.

16-12=4.

4×16×1=64.

Answer:

The answer is 64.

Step-by-step explanation:

16-12=4.

4×16×1=64.

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the coefficient of determination.

What is coefficient of determination?

The effectiveness of a statistical model in forecasting a result is shown by the coefficient of determination (R²). The dependent variable in the model is a representation of the result.

R² can have a value of 0 or 1, with 1 being the maximum achievable. Simply said, a model's R² will be closer to 1 the more accurate its predictions are.

R² is a more precise measure of goodness of fit. The amount of volatility in the dependent variable that the model can account for.

You can typically tell whether your linear regression data's R² is high or low by graphing it. The graphs below, for instance, display two sets of simulated data:

Dots represent the observations.

The line of best fit, or predictions of the model, is displayed as a black line.

Purple lines represent the deviations (the residuals) between the data and their expected values.

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Answer:

(-12+6+7+12-6+1)÷ 6

=8÷6

=1.3333

Answer:

x = 60

Step-by-step explanation:

Answer:2>x>−3

Step-by-step explanation: Hope this helps

The width of the interval based on 100 men would be about three times the width of the interval based on 900 men.

What is the width of the interval?

The width of a confidence interval for a proportion is proportional to the standard error of the sample proportion, which is proportional to the square root of the sample size.

The standard error is defined as the standard deviation of the sampling distribution of the sample proportion, which is estimated by the standard deviation of the Bernoulli distribution (square root of the sample proportion times (1 - sample proportion) divided by the sample size).

So, if the sample size is reduced by a factor of 9 (from 900 to 100), the standard error (and hence the width of the confidence interval) would increase by a factor of 3 (square root of 9).

Therefore, The width of the interval based on 100 men would be about three times the width of the interval based on 900 men.

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Answer:

see pic

Step-by-step explanation:

see pic

Answer:

y > 5

Step-by-step explanation:

22-3y > 7

-22       -22

-3y > -15

/-3      /-3

y > 5

Answer: d or a i think

Step-by-step explanation:

Answer:

free points

Step-by-step explanation:

hahahahahaha

The exponential growth formula for bacteria growth is P(t) = 8600 \((2)^(t/5)\).

What is exponential growth?

     Exponential growth is a pattern of data that exhibits a greater increase over time, resulting in an exponential curve. Exponential is also a mathematical term meaning "with exponents". For example, if you raise a number to the 10th power, the number increases exponentially. Exponential growth is growth that increases at a constant rate.

Here given take Initial number of bacteria = 8600. rate of growth = 2.

It doubles every year. Then doubling time = 5 hours.

Now population growth after t years,

P(t) = Po \((2)^(t/5)\)

=> P(t) = 8600 \((2)^(t/5)\)

Therefore exponential growth formula is P(t) = 8600 \((2)^(t/5)\).

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the general formula of a parabola is

we can replace the the points to find a,b and c

First (0,4)

Then (-5,1.5) and c=4

Answer:

251.32741

Step-by-step explanation: Later Surface Area Formula: 2(pi)rh

The length of segment AB is 25 units.

The length of segment AB is calculated by applying chord theorem of a circle.

The chord theorem, also known as the intersecting chords theorem or power of a point theorem, states that if two chords intersect inside a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

AB = BC

9x - 2 = 7x + 4

9x - 7x = 4 + 2

2x = 6

x = 6/2

x = 3

The length of segment AB is calculated as;

AB = 9x - 2

AB = 9(3) - 2

AB = 25

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Answer:

Square root of 16 is rational beacuse Square root of 16=4 Whlie the others are Irational.

Step-by-step explanation:

Answer:

Step-by-step explanation: squarefoot of 16 is rational cause 16=4

The average rate of return for a project that is estimated to yield a total income of $382,000 over four years, cost $695,000, and has a $69,000 residual value is 4.5% .

Here's how to solve for the average rate of return:

Total income = $382,000

Residual value = $69,000

Total cost = $695,000

Total profit = Total income + Residual value - Total cost

Total profit = $382,000 + $69,000 - $695,000

Total profit = -$244,000

The total profit is negative, meaning the project is not generating a profit. We will use the negative number to find the average rate of return.

Average rate of return = Total profit / Total investment x 100

Average rate of return = -$244,000 / $695,000 x 100

Average rate of return = -0.3518 x 100

Average rate of return = -35.18%

Rounded to one decimal place, the average rate of return is 35.2%. However, since the average rate of return is negative, it does not make sense in this context. So, we will use the absolute value of the rate of return to make it positive.

Average rate of return = Absolute value of (-35.18%)

Average rate of return = 35.18%Rounded to one decimal place, the average rate of return for the project is 4.5%.

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Answer:

431,880

Step-by-step explanation:

(I Use PEMDAS to answer this question)

90 x 40 = 3,600

3,600 x 120 = 432,000

432,000 - 120 = 431,880

\(\\ \sf\longmapsto \dfrac{2}{4}\)

\(\\ \sf\longmapsto \dfrac{1}{2}\)

\(\\ \sf\longmapsto \dfrac{1(5)}{2(5)}\)

\(\\ \sf\longmapsto \dfrac{5}{10}\)

\(\\ \sf\longmapsto 0.5\)

#2

\(\\ \sf\longmapsto \dfrac{3}{4}\)

\(\\ \sf\longmapsto \dfrac{3(25)}{4(25)}\)

\(\\ \sf\longmapsto \dfrac{75}{100}\)

\(\\ \sf\longmapsto 0.75\)

#3

\(\\ \sf\longmapsto \dfrac{7}{8}\)

\(\\ \sf\longmapsto \dfrac{7(125)}{8(125)}\)

\(\\ \sf\longmapsto \dfrac{875}{1000}\)

\(\\ \sf\longmapsto 0.875\)

#3

\(\\ \sf\longmapsto \dfrac{3}{8}\)

\(\\ \sf\longmapsto \dfrac{3(125)}{8(125)}\)

\(\\ \sf\longmapsto \dfrac{375}{1000}\)

\(\\ \sf\longmapsto 0.375\)

Answer: the figure and it’s image are similar and the image has been translated 3 units up.

Step-by-step explanation:

The correct answer is A) -12t.

To evaluate this expression, we need to use the order of operations. The order of operations is a set of rules that specifies the sequence in which operations should be performed in a math expression to get the correct result. The order of operations is typically abbreviated as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Following the order of operations, we first need to evaluate the expression inside the parentheses, which is 2+(-4t). This gives us 2-4t. Next, we need to perform the multiplication, which gives us 3(2-4t) = 6-12t. Finally, we need to perform the addition, which gives us -6+6-12t = -12t. Therefore, the expression -6+3(2+(-4t)) is equivalent to -12t.

Option B) 12t-12 is incorrect because the multiplication and addition operations are not performed in the correct order.

Option C) none of the above is incorrect because the correct answer is A) -12t.

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This expression gives:

(f+g)(3) = 21

To find (f+g)(x), we first substitute the expressions for f(x) and g(x) into the equation:

(f+g)(x) = f(x) + g(x) = (x - 9) + 3x^2

Next, we simplify the expression by combining like terms:

(f+g)(x) = 3x^2 + x - 9

This is the simplified expression for (f+g)(x).

Now, to find (f+g)(3), we substitute x=3 into the expression:

(f+g)(3) = 3(3)^2 + 3 - 9

We simplify the expression further using the order of operations (exponentiation before multiplication and addition/subtraction):

(f+g)(3) = 3(9) + 3 - 9

(f+g)(3) = 27 + 3 - 9

(f+g)(3) = 30 - 9

(f+g)(3) = 21

Therefore, when x=3, (f+g)(3) equals 21.

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if the visitor runs at a rate of 6 mph and swims at a rate of 2.5 mph., then the visitor  would run 14 .45 miles  before swimming to minimize the time it takes to reach the island .

we are given that an island is 1 mi due north of its closest point along a straight shoreline., where the visitor is staying at a cabin on the shore that is 15 mi west of that point, in some point the visitor runs at a rate of 6 mph and swims at a rate of 2.5 mph. Considering x be the distance the visitor runs. so the total time will be :

Time (T)= x/6 + √((15-x)²+1²)/2.5

Differntiating both sides respect to  x , we get

dT/dx = 1/6 -(15-x)/√(15-x)²+1)/2.5

=>1/6 = (15-x)/√(15-x)²+1)/2.5

=>6(15-x) = 2.5√(15-x)²+1)

Now considering   15 - x = y, we get  

=>6y = 2.5√(y²+1)

=>36y² = 6.25y² + 6.25

=>29.75y² = 6.25

y = √(25/119),  therefore ,x = 15 - √(25/119) = 14 .45

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