Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. f(x) = 4x (3) = f(5) = f(-2) = f(0.4) =

Answer:

22

Step-by-step explanation:

if mai scores 5 points and noah scores 3 times that then noah scored 15 points, and if tyler scores four less than noah than he scored 11 points, which you multiply by 2 to get elena's score which is 22

a.The closed-form expression for the given recurrence is: an = 8 * [tex]2^{(n-1)} + 6.[/tex]

b.In the proof by induction, we showed that the closed-form expression for the recurrence, an = 8 * [tex]2^{(n-1)}[/tex] + 6, holds true for both the base case and the inductive step. Thus, confirming its equivalence to the given recurrence.

The closed-form expression for the given recurrence, an = [tex]2^n[/tex] * 8 - [tex]2^1[/tex] + 6, represents a direct formula to calculate the value of each term in the sequence. It involves exponentiation and arithmetic operations to determine the value based on the position (n) in the sequence.

In the proof by induction, we will first establish the base case, which is n = 1. From the recurrence, we have a1 = 8 * [tex]2^{(1-1)}[/tex] + 6 = 8. Substituting n = 1 into the closed-form expression, we also get a1 = 8 * [tex]2^{(1-1)}[/tex] + 6 = 8. The base case holds.

Next, we assume that the closed-form expression is true for an arbitrary positive integer k, i.e., ak = 8 * [tex]2^{(k-1)}[/tex] + 6.

Now, we will prove that it holds for k + 1, i.e., ak+1 = 8 * [tex]2^k[/tex] + 6.

Using the recurrence, we have ak+1 = 2 * ak-1 + 8 = 2 * (8 * [tex]2^{(k-1)}[/tex] + 6) + 8 = 16 * [tex]2^{(k-1)}[/tex] + 12 + 8 = 8 * [tex]2^k[/tex] + 6.

By comparing this with the closed-form expression, we see that ak+1 = 8 * [tex]2^k[/tex] + 6.

Therefore, the closed-form expression holds for k + 1.

By the principle of mathematical induction, we have proven that the closed-form expression, an = 8 * [tex]2^{(n-1)}[/tex] + 6, is equivalent to the given recurrence.

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The solution to the recurrence relation T(n) = T(n-1) + 2, with T(1) = 0, is T(n) = 2k.

To solve the given recurrence relation T(n) = T(n-1) + 2, for n > 0, with the initial condition T(1) = 0, we can use backward substitution.

1. Start with the base case T(1) = 0.

2. Substitute T(n-1) with T(n-2) + 2 in the original recurrence relation:  
T(n) = T(n-1) + 2  
    = (T(n-2) + 2) + 2  
    = T(n-2) + 4

3. Repeat the substitution process until we reach the base case:
T(n) = T(n-1) + 2  
    = (T(n-2) + 2) + 2  
    = ((T(n-3) + 2) + 2) + 2  
    = T(n-3) + 6

4. Continue this process until n - k = 1, where k is a positive integer.

5. Finally, substitute n - k with 1:
T(n) = T(n-1) + 2  
    = (T(n-2) + 2) + 2  
    = ((T(n-3) + 2) + 2) + 2  
    = ...  
    = T(1) + 2k

6. Since T(1) = 0, we have:  
T(n) = 0 + 2k  
    = 2k

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The point labeled D is to the right of the intersection of the two linear functions. This means that its x-coordinate is greater than the x-coordinate of the point of intersection.

We can find the point of intersection by setting the two functions equal to each other:

3x + 4 = (-1/2)x - 5

Solving for x, we get:

(7/2)x = -9

x = -18/7

So the point of intersection is (-18/7, -29/7).

Since the x-coordinate of point D is greater than -18/7, we can eliminate options A and C.

Now we need to check whether option B or option D includes point D as a solution. To do this, we can simply plug in the coordinates of D into the two inequalities and see which one holds true.

Option B:

f(x) ≥ 3x + 4

2 ≥ 3(D) + 4

2 ≥ 3D + 4

-2 ≥ 3D

D ≤ -2/3

g(x) ≤ (-1/2)x - 5

2 ≤ (-1/2)(D) - 5

7 ≤ -D

D ≥ -7

Since -2/3 is less than -7, option B does not include point D as a solution.

Option D:

f(x) ≥ 3x + 4

2 ≥ 3(D) + 42 ≥ 3D + 4

-2 ≥ 3D

D ≤ -2/3

g(x) ≥ (-1/2)x - 5

2 ≥ (-1/2)(D) - 5

7 ≥ -D

D ≤ -7

Since -2/3 is less than -7, option D does not include point D as a solution either.

Therefore, neither option B nor option D includes point D as a solution. The correct answer is that neither system of inequalities has point D as a solution.

Answer:

Following are the responses to these question:

Step-by-step explanation:

Because every player has 5 cards handed

The card ratio is 5:1 per player.

So, if there are three teams

5 times 3=15 Cards 

Four players=four times five=20 cards

Five players=5 times five=25 cards

6 cards=6 times 5=30 cards

The card ratio is 5:1 per player.

The share of money Alan receives is $850. Therefore, option C is correct answer.

Given that, the total amount is $1190 and the ratio Alan: Beth = 5:2.

We need to find the how much money Alan gets.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other.

Now, 5+2=7

Money Alan receives=5/7×1190

=$850

The share of money Alan receives is $850. Therefore, option C is correct answer.

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Answer:

C is the answer also can I have brian list

Step-by-step explanation:

Answer: Should be 7

Step-by-step explanation:

14/2 is 7

Answer:

{-3, 5}.

Step-by-step explanation:

y = x + 8

x + y = 2

Substitute y = x + 8 in the second equation:

x + x + 8 = 2

2x + 8 = 2

2x = -6

x = -3

Now plug this into the first equation

y = -3 + 8 = 5.

Answer:

x=-6, y=-7

Step-by-step explanation:

Answer:

x = -6, y = -7

Step-by-step explanation:

One way to solve for x and y is using the substitution method

(1) 3x + 4y = -46

(2) 6x + y = -43

Solve for y in equation (2)

6x + y =-43, so y = -43 - 6x

Substitute y = -43 -6x into equation (1)

3x + 4(-43 -6x) = -46

3x -172 -24x = -46

-21x -172 = -46

-21x = 126

x = -6

Find y by substituting x = -6 into equation (2)

6(-6) + y = -43

-36 + y = -43

y = -7

Answer:

The first one

Step-by-step explanation:

Because

Answer: 1/4

Step-by-step explanation:

3/12 simplified so divide the numerator and denominator by 3, you get 1/4

Answer:

The answer is D

hope this helps

Answer:

hypotenuse = 102.69

Step-by-step explanation:

7(13) + 4 = 95

3(13) = 39

hypotenuse² = 95² + 39² = 9025 + 1521 = 10546

hypotenuse = √10546 = 102.69

Answer:

Step-by-step explanation:

Let (h) is the hypotenuse so

[tex]h^{2} = {(7x + 4)}^{2} + {(3x)}^{2} \\ x = 13 \\ h^{2} = (95)^{2} + {(39)}^{2} \\ h = \sqrt{10546} \\ h = 102.7[/tex]

I hope that is useful for you :)

Based on the sample data, we can construct a 99% confidence interval estimate for the percentage of girls born as approximately 85.1% to 94.9%.

To construct a confidence interval estimate for the percentage of girls born, we can use the formula for estimating a proportion.

First, we calculate the sample proportion, which is the number of successes (girls) divided by the total number of trials (babies born):

Sample proportion (p-hat) = Number of girls / Total number of babies born

= 288 / 320

= 0.9

Next, we can construct the confidence interval using the sample proportion. Since we want a 99% confidence interval, we need to find the critical value corresponding to that level of confidence. For a two-tailed test, the critical value is obtained from the standard normal distribution (Z-distribution).

Using a Z-table or calculator, the critical value for a 99% confidence level is approximately 2.576.

The margin of error (E) can be calculated as:

Margin of error (E) = Critical value * Standard error

The standard error (SE) for estimating a proportion is given by:

Standard error (SE) = [tex]\sqrt {(p-hat * (1 - p-hat)) / n}[/tex]

where p-hat is the sample proportion and n is the sample size.

Using these values, we can calculate the margin of error:

Standard error (SE) = [tex]\sqrt {(0.9 * (1 - 0.9)) / 320}[/tex]

≈ 0.019

Margin of error (E) = 2.576 * 0.019

≈ 0.049

Finally, we can construct the confidence interval:

Confidence interval = Sample proportion ± Margin of error

= 0.9 ± 0.049

≈ (0.851, 0.949)

Therefore, based on the sample data, we can construct a 99% confidence interval estimate for the percentage of girls born as approximately 85.1% to 94.9%.

Since the interval includes the value of 0.5 (50%), which represents an equal chance of having a girl or a boy, it suggests that the method used in the clinical trial does not significantly increase the probability of conceiving a girl.

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Answer:

4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{48}[/tex]

= [tex]\sqrt{16(3)}[/tex]

= [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex]

= 4[tex]\sqrt{3}[/tex]

Answer:

B I think

Step-by-step explanation:

I think it's B because in b it says so on which means his raise keeps going up each year

After considering the given data we conclude that the z-score for each situation is
The area concerning left of z is .2119: z = -0.81
The area amongst -z and z is .9030: z = 1.44
The area amongst -z and z is .2052: z = 0.84
The area concerning left of z is .9948: z = 2.59
The area concerning right of z is .6915: z = 0.48

To evaluate the z-score for each situation, we can apply the z-table . Here are the steps to find the z-score for every situation:
The area concerning left of z is .2119:
Applying the z-table, we can evaluate that the z-score is -0.81.
The area amongst -z and z is .9030:
Applying the z-table, we can evaluate that the z-score is 1.44.
The area amongst -z and z is .2052:
Utilising the z-table, we can express that the z-score is 0.84.
The area concerning left of z is .9948:
Applying the z-table, we can calculate that the z-score is 2.59.
The area concerning right of z is .6915:
We need to evaluate the area concerning left of z first, which is

1 - 0.6915 = 0.3085.
Applying the z-table, we can compound that the z-score is 0.48.
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Answer: B)

Step-by-step explanation:

By checking which graph is satisfied, we choose points that the function has pass through.

First, we know that y = mx + b, where m is the slope, how the line change; and b is the y-intercept. In this equation, the slope is 24 which the line is increased. So we can eliminate the choice D, the line in D decreased.

Then we find where the first point and second point this graph will be.

When x = 0, y = 24x = 24(0) = 0, (0,24)

When x = 1, y = 24x = 24(1) = 24, (1,24)

1 package can have 24 cookies, only B have 24 cookies in 1 package.

Answer:

150

Step-by-step explanation:

'x' = number of students out of 500 who selected math

18/60 = x/500

cross-multiply:

60x = 9000

x = 150

Answer:

It's 8

Step-by-step explanation:

The solution to the differential equation 5y'' - 2y' = 2x + 5 - e^(-2x) using the method of undetermined coefficients is given by y = C1 + C2e^(2x) - (5/2)x + B, where C1, C2, and B are constants determined by the initial or boundary conditions.

To solve the differential equation 5y'' - 2y' = 2x + 5 - e^(-2x) using the method of undetermined coefficients, we assume a particular solution of the form:

y_p = Ax + B + Ce^(-2x)

where A, B, and C are undetermined coefficients to be determined.

Taking the derivatives:

y_p' = A - 2Ce^(-2x)

y_p'' = 4Ce^(-2x)

Substituting these derivatives into the original differential equation, we have:

5(4Ce^(-2x)) - 2(A - 2Ce^(-2x)) = 2x + 5 - e^(-2x)

Simplifying the equation:

20Ce^(-2x) - 2A + 4Ce^(-2x) = 2x + 5 - e^(-2x)

(24C)e^(-2x) - 2A = 2x + 5 - e^(-2x)

For the equation to hold for all x, the coefficients on both sides of the equation must be equal.

Matching the coefficients:

24C = 0 -> C = 0

-2A = 5 -> A = -5/2

Therefore, the particular solution is:

y_p = (-5/2)x + B

To find the value of B, we substitute the particular solution back into the original differential equation:

5(-5/2) - 2(0) = 2x + 5 - e^(-2x)

-25/2 = 2x + 5 - e^(-2x)

Solving for x and e^(-2x) in terms of B:

2x = -25/2 - 5 + e^(-2x)

2x = -35/2 + e^(-2x)

As the left side is a linear function of x and the right side is a constant plus an exponential function, there is no value of x that satisfies this equation for all x. Hence, the equation is inconsistent, and there is no particular solution in the form y_p = Ax + B.

Therefore, the solution to the given differential equation using the method of undetermined coefficients is the complementary function (homogeneous solution) plus the particular solution, which is:

y = y_c + y_p = C1 + C2e^(2x) + (-5/2)x + B

where C1 and C2 are constants determined by the initial or boundary conditions, and B is an arbitrary constant.

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Answer:

12

Step-by-step explanation:

Write down multiples of each number:

3, 6, 9, 12 . . .

4, 8, 12 . . .

6, 12 . . .

The first one they all have is the LCM.

Answer:

12

Step-by-step explanation:

Think of it this way. Simplifying 3, 4 and 6 into their simplest factors:

[tex]3=3[/tex]

[tex]4=2*2[/tex]

[tex]6=3*2[/tex]

6 is a multiple of both 3 and 2, which are both represented by the factors of 3 and 4. Thus, as it is doubled in these, it is not necessary to find the lowest common multiple of the numbers.

Now the LCM can be multiplied with the factors of the remaining numbers:

LCM[tex]=3*2*2[/tex]

Notice the first two numbers equal 6, the second and third equal 4, and the first only equals 3. This means the three numbers are represented in the LCM.

[tex]3*2*2=24[/tex]

And that is the LCM, so we are done. QED

The cash flow stream consisting of $14,000 today followed by $6,000 each year for the next 11 years, discounted at a rate of 7.1%, is worth approximately $52,743 to you today.

To determine the present value of the cash flow stream, we need to discount each cash flow back to the present using the appropriate discount rate.

The present value (PV) of each cashflow can be calculated using the formula:

[tex]PV = CF / (1 + r)^n[/tex]

where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of periods.

Calculating the present value of each cash flow and summing them up, we get:

[tex]PV = \$14,000 + \$6,000 / (1 + 7.1\% / 100)^1 + \$6,000 / (1 + 7.1\% / 100)^2 + ... + \$6,000 / (1 + 7.1\% / 100)^11[/tex]

Evaluating the expression, we find that the present value of the cash flow stream is approximately $52,743 when rounded to the nearest dollar.

This means that if you discount the future cash flows at a rate of 7.1%, the combined value of all the cashflows today would be approximately $52,743.

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Answer:

109.9 cm

Step-by-step explanation:

Circumference = (pi)(diameter)

They tell you diameter = 35

c = (3.14)(35)

c = 109.9 cm

Please lmk if you have questions.

Answer:

circumference : 109.96 cm

Step-by-step explanation:

The radius of a circle is half its diameter. The radius of a circle with a diameter of 35cm is 17.5cm.

The circumference of a circle is found by 2πr . So that would be 2π 17.5

which would be equal to 109.96cm (2 sig. fig.).

The area of a circle is found by πr2 . So that's π⋅17.5 which is equal to 962.11cm (2 sig.fig.).

The variance of the sampling distribution for the difference of the two means is 0.0147142857.

The correct option is D. 0.051.

The variance of the sampling distribution for the difference of two means of sample populations can be calculated using the formula given below:

[tex]\Large\frac{{{\sigma }_{1}}^{2}}{n_{1}}+\frac{{{\sigma }_{2}}^{2}}{n_{2}}[/tex]

Where,[tex]{{\sigma }_{1}}$ and ${{\sigma }_{2}}[/tex] are the standard deviations of the two populations respectively, and [tex]{{n}_{1}} and ${{n}_{2}}[/tex] are the sample sizes of the first and second populations respectively.

Substituting the given values, we get

[tex]\Large\frac{0.9^2}{25}+\frac{0.8^2}{35}=0.009+0.0057142857[/tex]

=0.0147142857

Therefore, the variance of the sampling distribution for the difference of the two means is 0.0147142857.

Sampling distribution approaches normal distribution:

True. Regardless of the shape of the population, the sampling distribution of the mean approaches a normal distribution as the sample size increases.

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Answer:

Your answer would be D. I know this is kind of late, but maybe other people that come up here could get some help

Step-by-step explanation: