h(n) = 41 - 5n
Complete the recursive formula of h(n).
h(1) =
h(n) = h(n-1)

Answer:

4*6=24

Step-by-step explanation:

It's simple multiplication. she has 4 rows of tomatoes and each row has 6 tomatoes so 4 times 6 equal 24 which means that the full garden has 24 tomatoes in total

hop that helped:))

Answer:

10^4

Step-by-step explanation:

10×10×10×10=10,000, which is given number.

The method of moments is used to estimate the parameters ẞ and o² in a linear model with exogenous regressors, while the generalized method of moments (GMM) is used when the regressors are endogenous. GMM incorporates instrumental variables to address endogeneity and provides a more efficient estimator than ordinary least squares (OLS).

(a) In the case of exogenous regressors, the method of moments is used to estimate the parameters ẞ and o². This method involves equating the population moments (expectations) of the model to their sample counterparts. By solving these moment equations, we can estimate the parameters of interest. The method of moments is suitable when the regressors are not affected by the error term, ensuring consistent and efficient estimation.

(b) When the regressors are endogenous, we can use the generalized method of moments (GMM) to address endogeneity. GMM extends the method of moments by incorporating instrumental variables. Instrumental variables are variables that are correlated with the endogenous regressors but uncorrelated with the error term. The GMM estimator, denoted as BGMM, minimizes the distance between the sample moments and their population counterparts using an optimal weighting matrix. This estimator provides consistent and efficient estimates of the parameters, including ẞ.

The GMM estimator is closely related to the instrumental variable (IV) estimator. In fact, the IV estimator is a special case of the GMM estimator when the weighting matrix is chosen appropriately. Both estimators address endogeneity by using instrumental variables, but the GMM estimator allows for more flexibility in selecting the weighting matrix and can handle more complex models.

(c) The generalized method of moments (GMM) offers several advantages over ordinary least squares (OLS). Firstly, GMM can handle endogeneity issues that OLS cannot address. By incorporating instrumental variables, GMM provides consistent and efficient estimates even in the presence of endogenous regressors. This is particularly important when there are omitted variables or measurement errors, which can lead to biased OLS estimates.

Secondly, GMM allows for efficiency gains by exploiting additional information in the moment conditions. By selecting an appropriate weighting matrix, GMM can take advantage of the information contained in the instruments and construct more efficient estimates compared to OLS.

Furthermore, GMM is a more flexible estimation method than OLS. It can handle models with heteroscedasticity or serial correlation by specifying suitable moment conditions. GMM also accommodates weak instrument problems, where instrumental variables are only weakly correlated with the endogenous regressors.

Overall, GMM provides a powerful framework for estimating parameters in econometric models, addressing endogeneity, improving efficiency, and accommodating various model specifications. Its advantages make it a valuable tool in empirical research, particularly in the presence of endogenous regressors and instrumental variables.

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17 i think! :]

byeee

A paired t-test can be used to test the hypothesis that the vitamin supplement gives recipients a longer attention span based on the given data of twin pairs and their respective attention span measurements. Additionally, a 95% confidence interval can be constructed to estimate the difference in the population means of attention spans between twins given the placebo and the vitamin supplement.

(a) To test the hypothesis that the vitamin supplement gives recipients a longer attention span, we can use a paired t-test since the data consists of pairs of observations (Twin A and Twin B) who received different treatments. The null hypothesis, denoted as H0, is that there is no difference in the mean attention spans between the two treatments, while the alternative hypothesis, denoted as H1, is that the vitamin supplement results in a longer attention span. By calculating the mean difference (TwinA - TwinB) and the standard deviation of the differences, we can calculate the t-test statistic. Using the critical value or p-value at the 0.05 significance level, we can determine whether to reject or fail to reject the null hypothesis.
(b) To construct a 95% confidence interval for the difference in the population means of attention spans between twins given the placebo and the vitamin supplement, we can use the formula: mean difference ± (t * standard error of the difference). The t-value corresponds to the critical value from the t-distribution for a 95% confidence level with the degrees of freedom equal to the number of twin pairs minus 1. The standard error of the difference is the standard deviation of the differences divided by the square root of the sample size. The resulting confidence interval provides an estimate of the range within which the true difference in population means is likely to fall.
In conclusion, a paired t-test can be conducted to test the hypothesis that the vitamin supplement improves attention spans. Additionally, a 95% confidence interval can be constructed to estimate the difference in population means between twins given the placebo and the vitamin supplement. Specific calculations and results can be obtained by performing the necessary calculations using the provided data.


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The sales of the laser saber can be determined by calculating the difference between the number of invisible shields and x-ray vision glasses, and then multiplying that result by 1.5.

Let's assume that the number of invisible shields is represented by the variable "IS" and the number of x-ray vision glasses is represented by the variable "XVG".
The formula for calculating the sales of the laser saber would then be:

Sales of laser saber = 1.5 * (IS - XVG)
In terms of the given terms, the sales of the laser saber can be expressed as being equal to 1.5 times the difference between the number of invisible shields and x-ray vision glasses.

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The correct response is 110.

Consider two numbers that are inside 1000.

324 and 434 are these two numbers.

As a result, for any number abc, the terms a, b, and c each have a place value of 100, 10, and 1.

We will therefore add the corresponding digits and multiply them by their place value when adding the two numbers abc and def.

In order to add 324 and 434, we will

(3+4)×100 + (2+3)×10 + (4+4)×1

The solution is 700+50+8=758.

This is equivalent to (324 + 434 = 758)

Similar steps apply for subtraction; simply choose the larger number and continue the same procedures, changing the + sign in the inner bracket to a -.

(4-3)×100 + (3-2) (3-2)×10 + (4-4)×1

Therefore, the correct response is 110.

This equals (434-324) = 110.

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Answer:

-616

Step-by-step explanation:

First subtract 35 with 21 since 35 is a negative. then subtract 45 with 1

for the first parenthesis would be -14. the second parenthesis would be 44.

then multiply both of the answers together to get -616

Answer:-220

Step-by-step explanation:

Answer: a. (-4, 3)

b. (4, 2)

c. (8, 0)

d. (-3, -5)

e. (0, -7)

f. (5, -5)

g. (9, -6)

Step-by-step explanation:

a. 4 units left and 3 units up

b. 4 units right and 2 units up

c. 8 units right

d. 3 units left and 5 units down

e. 7 units down

f. 5 units right and 5 units down

g. 9 units right and 6 units down

When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

The measure of angles are

The length of the hypotenuse of the right triangle = 11 inches

The length of the one leg = 10 inches

Then the length of the other leg is the square root of the sum of the hypotenuse square and one leg square

Then the equation will be

The length of the other leg = \(\sqrt{11^2-10^2}\)

= \(\sqrt{121-100}\)

= 4.58 inches

Therefore AC = 11 inches

AB = 10 inches

BC = 4.58 inches

The angle B = 90 degrees

Consider the angle A

cos θ = Adjacent side / hypotenuse

cos θ = 10 /11

θ = 24.61 degrees

Consider the angle C

cos θ = Adjacent side / Hypotenuse

cos θ = 4.58 / 11

θ = 65.39 degrees

Hence, the measure of angles are

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Answer:

The digits arranged in order from least to largest is 3.011, 3.09, 3.9, 9.3

Step-by-step explanation:

The arrangement of decimals in order from smallest to largest can be done by  taking note of the  digit in the unit portion, the tenths, hundredths and thousandths.

The numbers are;

9.3

3.09

3.9

3.011

The largest number is the 9.3

Of the three numbers with 3 as unit, the lowest hundredths is 0.011, therefore, we have;

Therefore, the least (lowest) number = 3.011

The next is the 3.09 as 0.09 is larger than 0.011

Then the second number is 3.9

The digits arranged in order from least to largest is then 3.011, 3.09, 3.9, 9.3.

Explanation is in the image!

Based on his speed and the distance driven within that time, Kwan will have driven 144 miles in 2 hours

First find out Kwan's speed per hour:

Speed = Distance / Time

Convert the time to decimals:

= 1 + 1/4 hours

= 1 + 0.25

= 1.25 hours

Speed:

= 90 / 1.25

= 72 miles per hour

In 2 hours therefore, Kwan would have gone:

= 72 x 2 hours

= 144 miles

In conclusion, Kwan would have driven 144 miles.

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The distance kwan drive in 2 hours at this rate is known as 144 miles

Given that kwan is driving at a constant speed after 1/1/4 hours he has driven a total distance of 90 miles, this can be expressed as:

90 miles = 1 1/4 hours

To determine the total distance covered in 2 hours, this can be expressed as;

x = 2hours

Divide both expressed as:

90/x = (1 1/4)/2

90/x = (5/4)/2

90/x = 5/8

5x = 8 * 90

5x = 720

x = 720/5

x = 144

This shows that the distance kwan drive in 2 hours at this rate is known as 144 miles

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An expression for the number of bracelets of n beads, where rotations.

Whats an expression for the bracelets?

In mathematics, the term "bracelets" can refer to a type of combinatorial object, specifically, a set of beads arranged in a circular pattern. An expression for the number of bracelets of n beads, where rotations and reflections are considered identical, can be given as follows:

B(n) = (1/n) * (2raise to the power (n-1) + Σ(d|n, d<n) μ((n/d)) * 2 raise to the power ((n/d)-1))

Here, B(n) represents the number of distinct bracelets of n beads, Σ denotes the summation, d|n denotes "d divides n", and μ is the Möbius function.

The first term in the expression, (1/n) * (2 raise to the power (n-1)), represents the number of bracelets that are invariant under rotation. The second term takes into account the bracelets that are not invariant under rotation, but are invariant under reflection, and involves the Möbius function.

This expression can be used to calculate the number of bracelets for any value of n, by plugging in the value of n and evaluating the expression.

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Answer:

2/3 i guess

Step-by-step explanation:

Answer:

second option

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y )

then

A (5, - 2 ) → (- 5, - 2 )

B (0, 3 ) → (0, 3 )

C (- 4, 1 ) → (4, 1 )

Helena experience similar temperatures during January due to their subarctic climate regime, but the moderating effect of the oceanic currents on Anchorage's climate makes its winters milder than those of Helena.

what is temperatures ?

"Temperatures" refers to the degree of hotness or coldness of a substance, usually measured in degrees Fahrenheit (°F) or Celsius (°C). In the context of the original question, "temperatures" refers to the measure of how hot or cold it is in a particular location, specifically in Anchorage and Helena.

In the given question,

Anchorage and Helena are both located in high latitude regions where the climate is dominated by polar or subarctic air masses. The prevailing westerly winds carry these cold air masses from the Arctic towards the continental interiors, affecting the climate of both Anchorage and Helena. Although Anchorage is located further north than Helena, it is situated along the coast of the Gulf of Alaska, which is influenced by the relatively warm oceanic currents such as the North Pacific Current and the Alaska Current. These currents help to moderate the cold air masses coming from the north, resulting in a maritime subarctic climate in Anchorage.

In contrast, Helena is situated in the interior region of Montana, which is far away from any major water bodies, leading to a continental subarctic climate with relatively colder and drier conditions compared to Anchorage. Therefore, despite their different latitudes, both Anchorage and Helena experience similar temperatures during January due to their subarctic climate regime, but the moderating effect of the oceanic currents on Anchorage's climate makes its winters milder than those of Helena.

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Answer:

Let's simplify step-by-step.

−x+5−7x−8

=−x+5+−7x+−8

Combine Like Terms:

=−x+5+−7x+−8

=(−x+−7x)+(5+−8)

=−8x+−3

not sure if I'm correct but this is just to simplify

Answer:

90x+ 50 y ≤  $40,000------  A

30x+ 80y ≤ $ 30,000-------  B

x + y ≤ 500 --- C

Step-by-step explanation:

Let x and y be the numbers of acres of potatoes and corn, respectively.

Then according to the given conditions

90x+ 50 y ≤  $40,000------  A

30x+ 80y ≤ $ 30,000-------  B

x + y ≤ 500 --- C

where both x and y equal to or greater than zero and cannot take a value less than zero.

x + y ≤ 500 --- C

gives us an idea that the total arable land is less or equal to  500 acres.

90x+ 50 y ≤  $40,000------  A

tells us that the total cost of planting potatoes and corn is less or equal to $ 40,000

30x+ 80y ≤ $ 30,000-------  B

tells us that the total cost of fertilizers for  potatoes and corn is less or equal to $ 30,000

In each of these x and y cannot have negative values or less than zero.

Answer:

I am currently taking a unit test and I just got this question. I believe it is the answer but I haven't submitted yet.

Step-by-step explanation:

The answer I chose seems to be the only logical answer.

The number of adults that bought the tickets is 176 and the number of students that bought the tickets is 108 if total tickets were sold out for two days for a theater that has a capacity of 142 people and the total sales were $1,948,

Let the number of adults that bought the tickets = x

the number of children that bought the tickets = y

If the capacity of the theater is 142, for sold out on both Friday and Saturday, and 284 tickets are sold

Thus, x + y = 284 -----(i)

Cost of one adult ticket = $8

Cost of x adults ticket = $8x

Cost of one student ticket = $5

Cost of y students ticket = 5y

Total sales = $1948

8x + 5y = 1948 ------(ii)

Multiply the equation (i) by 5

5x + 5y = 1420 ---- (iii)

Subtract the equation (ii) and (iii)

8x + 5y - 5x - 5y = 1948 - 1420

3x = 528

x = 176

Put the x in equation (i)

176 + y = 284

y = 284 - 176

y = 108

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We'll observe that the evaluated expression equals 244 in the next step.

To evaluate an expression, we only need to swap out the variables with the desired values.

When x = 5 x = 5 x=5, you can be asked to "Evaluate 3 x 3x 3x." In the formula 3 x 3x 3x, take note of the proximity of the number 3 to the variable x. This denotes "x times three."

Here, we must assess:

2(s+t)³-6

By substituting them in the formula for t = 2 and s = 3, we obtain:

2(3+2)³- 6

= 2*(5) (5)³ - 6

= 2*125 - 6

= 244

Consequently, the evaluated expression equals 244.

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Using Taylor's Theorem, e^x cannot be uniformly approximated by polynomials on R.

To prove that e^x cannot be uniformly approximated by polynomials on R, we will use Taylor's theorem and show that there exists a specific choice of x and ε for which |e^x - p(x)| ≥ ε holds for any polynomial p(x) with coefficients in R.

Taylor's theorem states that for a function f(x) that is infinitely differentiable on an interval I containing a point c, the Taylor series expansion of f(x) around c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

In the case of the function f(x) = e^x, the Taylor series expansion around c = 0 (also known as the Maclaurin series) is:

e^x = 1 + x + x^2/2! + x^3/3! + ...

Now, let's assume that there exists a polynomial p(x) with coefficients in R that uniformly approximates e^x on R, meaning |e^x - p(x)| < ε for all x in R and for some ε > 0.

Consider the term in the Taylor series expansion of e^x with the highest degree, which is x^n/n!. For large values of n, this term dominates the other terms. Let's denote this term as T(x) = x^n/n!.

Since p(x) is a polynomial, it is also of the form p(x) = a_0 + a_1x + a_2x^2 + ... + a_k*x^k, where a_i are the coefficients of the polynomial.

Now, let's choose a value of x such that |T(x) - p(x)| is maximized. This can be achieved by setting x = M, where M is a sufficiently large positive number.

For this choice of x = M, we have:

|T(M) - p(M)| = |M^n/n! - (a_0 + a_1M + a_2M^2 + ... + a_k*M^k)|

Since M is sufficiently large, the term M^n/n! dominates the polynomial term on the right-hand side, and we can rewrite the inequality as:

|T(M) - p(M)| ≥ |M^n/n!|

Now, we can see that for any ε > 0, we can choose a sufficiently large value of M such that |M^n/n!| > ε.

This implies that there exists a value of x = M for which |e^x - p(x)| ≥ ε, contradicting the assumption that e^x can be uniformly approximated by polynomials on R.

Therefore, we have shown that e^x cannot be uniformly approximated by polynomials on R.

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The closure property refers to the mathematical law that states that if we perform a certain operation (addition, multiplication) on any two numbers in a set, the result is still within that set.In the expression (2x3 x2 - 4x) - (9x3 - 3x2), we are simply subtracting one polynomial from the other.

To simplify it, we'll start by combining like terms. So, we'll add all the coefficients of x3, x2, and x, separately.The given expression becomes: (2x3 x2 - 4x) - (9x3 - 3x2) = 2x3 x2 - 4x - 9x3 + 3x2We will then combine like terms as follows:2x3 x2 - 4x - 9x3 + 3x2 = 2x3 x2 - 9x3 + 3x2 - 4x= -7x3 + 5x2 - 4x

Therefore, the correct simplification of the expression is -7x3 + 5x2 - 4x. The demonstration of the closure property is shown as follows:The subtraction of two polynomials (2x3 x2 - 4x) and (9x3 - 3x2) results in a polynomial -7x3 + 5x2 - 4x. This polynomial is still a polynomial of degree 3 and thus, still belongs to the set of polynomials. Thus, the closure property holds for the subtraction of the given polynomials.

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