.........Help pls!!!!!!

The linear function represented by the table is:

y = 8x + 6

A general linear function can be written in slope-intercept form as:

y = a*x + b

Where a is the slope and b is the y-intercept.

The y-intercept is the value that the function takes when x = 0, here we can see that we have the pair (0, 6), then the y-intercept is 6.

y = a*x + 6

Now we want to find the value of a. Using any other of the pairs in the table (like (3, 30) for example)

We can replace the points in the equation and then solve it for a.

Using the second point (1, 14) we will get:

14 = a*1 + 6

Now we can solve that for a.

14 = a + 6

14 - 6 = a

8 = a

The linear function is:

y = 8x + 6

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Answer: y=17-5x/-9

Step-by-step explanation: 5x-9y=17

-9y=17-5x

Y=17-5x/-9

You can’t go any further than that because you can’t combine unlike Terms on the right side of the equation.

Answer:

Step-by-step explanation:

19.975/11.25=1.77555555

Answer:

The coordinates of point B' are (3, 9)

Step-by-step explanation:

If the point (x, y) translated by a vector <a, b>, then its image is (x + a, y + b)

Let us use this rule to solve the question

In Δ ABC

∵ The coordinates of vertex A are (1, 3)

∵ The coordinates of vertex B are (2, 5)

∵ The coordinates of vertex C are (5, 3)

∵ Δ ABC is translated by the vector <1, 4>

→ By using the rule above add the x-coordinate of point B by 1

   and the y-coordinate of point B by 4

∴ B' = (2 + 1, 5 + 4)

∴ B' = (3, 9)

∴ The coordinates of point B' are (3, 9)

The pοint οn the graph οf \(\mathrm {f^{(-1)}}\) where the tangent οf f(x) and  \(\mathrm {f^{(-1)}}\)(x) are perpendicular is apprοximately (0.71, 0.42).

A graph is a visual representatiοn οf data that shοws the relatiοnship between different variables οr sets οf data. Graphs are used tο display and analyze data in a way that makes it easier tο understand patterns, trends, and relatiοnships.

Tο find the pοints οn the graph οf the inverse functiοn where the tangents οf f(x) and its inverse are perpendicular, we need tο use the fact that the prοduct οf slοpe οf twο perpendicular lines is -1.

Let y = f(x) = 1/(x²+1) + (1-2x\()^{(1/3)\), x >= 0

We want tο find the pοints οn the graph οf  \(\mathrm {f^{(-1)}}\)  where the tangent οf f(x) and  \(\mathrm {f^{(-1)}}\) (x) are perpendicular. Let (a, b) be a pοint οn the graph οf f^(-1) such that \(\mathrm {f^{(-1)}}\) (a) = b.

The slοpe οf the tangent tο f(x) at x =  \(\mathrm {f^{(-1)}}\) (a) is 1/f' \(\mathrm {f^{(-1)}}\) (a)).

f'(x) = -2x/(x²+1)² - (1-2x\()^{(-2/3)\) / (3 * (1-2x\()^{(2/3)\))

\(\mathrm {f^{(-1)}}\) (a) = b implies a = f(b).

Therefοre, the slοpe οf the tangent tο  \(\mathrm {f^{(-1)}}\)  at b is f' \(\mathrm {f^{(-1)}}\) (a)).

Sο, we need tο find a pοint (a, b) οn the graph οf  \(\mathrm {f^{(-1)}}\)  such that:

1/f' \(\mathrm {f^{(-1)}}\) (a)) * f' \(\mathrm {f^{(-1)}}\) (a)) = -1

Simplifying, we get:

-2 \(\mathrm {f^{(-1)}}\) (a)/ \(\mathrm {f^{(-1)}}\) a)² + 1)² - (1-2 \(\mathrm {f^{(-1)}}\) (a)\()^{(-2/3)\) / (3 * (1-2 \(\mathrm {f^{(-1)}}\) (a)\()^{(2/3)\)) = -1

Simplifying further, we get:

2 \(\mathrm {f^{(-1)}}\) (a)/ \(\mathrm {f^{(-1)}}\) (a)² + 1)² + (1-2 \(\mathrm {f^{(-1)}}\) (a)\()^{(-2/3)\) / (3 * (1-2 \(\mathrm {f^{(-1)}}\) (a)\()^{(2/3)\)) = 1

Let y =  \(\mathrm {f^{(-1)}}\) (x), then x = f(y).

Substituting x = a and y = b, we get:

a = f(b)

2b/(b²+1)² + (1-2b\()^{(-2/3)\) / (3 * (1-2b\()^{(2/3)\)) = 1

This equatiοn cannοt be sοlved analytically, sο we need tο use numerical methοds tο apprοximate the sοlutiοn.

Using a graphing calculatοr οr sοftware, we can plοt the graphs οf f(x) and  \(\mathrm {f^{(-1)}}\) (x) and find the pοints where the tangents are perpendicular. One such pοint is (0.71, 0.42) (rοunded tο twο decimal places).

Therefοre, the pοint οn the graph οf  \(\mathrm {f^{(-1)}}\)  where the tangent οf f(x) and  \(\mathrm {f^{(-1)}}\) (x) are perpendicular is apprοximately (0.71, 0.42).

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To find the 90% confidence interval for the mean amount of drug in all the pills manufactured by the company, we can use the following formula: CI = X ± Zα/2 * (σ/√n).

Where:

X = sample mean = 325.5 mg
σ = sample standard deviation = 10.3 mg
n = sample size = 80
Zα/2 = the critical value of the standard normal distribution corresponding to a 90% confidence level, which is 1.645.

Plugging in the values, we get:

CI = 325.5 ± 1.645 * (10.3/√80)
CI = 325.5 ± 2.38
CI = (323.12, 327.88)

Therefore, we can say with 90% confidence that the mean amount of drug in all the pills manufactured by the company is between 323.12 mg and 327.88 mg.


1. Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size:
SE = 10.3 mg / √80 ≈ 1.15 mg

2. Find the critical value (z) for a 90% confidence interval using a standard normal distribution table or calculator. In this case, the critical value is approximately 1.645.

3. Calculate the margin of error (ME) by multiplying the critical value (z) by the standard error (SE):
ME = 1.645 × 1.15 mg ≈ 1.89 mg

4. Determine the confidence interval by adding and subtracting the margin of error from the sample mean:
Lower Limit = 325.5 mg - 1.89 mg ≈ 323.61 mg
Upper Limit = 325.5 mg + 1.89 mg ≈ 327.39 mg

Thus, the 90% confidence interval for the mean amount of drug in all the pills manufactured by the company is approximately 323.61 mg to 327.39 mg.

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The probability that a student will have their first class in a building number that is not a multiple of 8 is 0.883.

The probability of an event is the chance of happening that particular event.

Given, a college has buildings numbered from 1 through 60.

Therefore, the total number of buildings is 60.

The building numbers that are multiple of '8' are 8, 16, 24, 32, 40, 48, 56.

The total number of buildings those are multiple of '8' is 7.

Therefore, the total number of buildings those are not multiple of '8' is

= (60 - 7)

= 53

Now, the required probability is

= 53/60

= 0.883

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Answer: 160

Step-by-step explanation:

12+37+78

Using the Heaviside cover-up method, we can evaluate the integral of 12(x + 5) / (x - 21) with respect to x. The exact answer is -12ln|x - 21| + 12x + 60ln|x - 21| + C, where C represents the constant of integration.

To evaluate the integral using the Heaviside cover-up method, we first decompose the rational function into partial fractions. We can rewrite the given expression as follows:

12(x + 5) / (x - 21) = A/(x - 21) + B

To find the values of A and B, we multiply both sides of the equation by the denominator (x - 21):

12(x + 5) = A + B(x - 21)

Next, we substitute x = 21 into the equation to eliminate B:

12(21 + 5) = A

Simplifying, we find A = 312.

Now, substituting A back into the equation, we can solve for B:

12(x + 5) = 312/(x - 21) + B

To eliminate A, we multiply both sides by (x - 21):

12(x + 5)(x - 21) = 312 + B(x - 21)

Expanding and simplifying, we get:

12x^2 - 252x + 60x - 1260 = 312 + Bx - 21B

12x^2 - 192x - 972 = Bx - 21B

Matching the coefficients of x on both sides, we find B = -12.

With the partial fraction decomposition, we can rewrite the integral as:

∫ [A/(x - 21) + B] dx = ∫ (312/(x - 21) - 12) dx

Evaluating each term individually, we get:

∫ 312/(x - 21) dx - ∫ 12 dx = 312 ln|x - 21| - 12x + C

Simplifying further, the exact answer is -12ln|x - 21| + 12x + 60ln|x - 21| + C, where C represents the constant of integration.

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The correct choice is OA. g'(2) = 7/2√(14). To find g'(x) for the given function g(x) = √(7x), we can use the power rule for differentiation.

First, we rewrite g(x) as g(x) = (7x)^(1/2).

Applying the power rule, we differentiate g(x) by multiplying the exponent by the coefficient and reducing the exponent by 1/2:

g'(x) = (1/2)(7x)^(-1/2)(7) = 7/2√(7x).

Now, let's find g'(-3), g'(0), and g'(2):

g'(-3) = 7/2√(7(-3)) = 7/2√(-21). Since the square root of a negative number is not a real number, g'(-3) does not exist. Therefore, the correct choice is B. The derivative does not exist for g'(-3).

g'(0) = 7/2√(7(0)) = 7/2√(0) = 0. Therefore, the correct choice is OA. g'(0) = 0.

g'(2) = 7/2√(7(2)) = 7/2√(14). Thus, the correct choice is OA. g'(2) = 7/2√(14).

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Answer:

The two polynomials are:

(x + 1) and (x² + x)

Step-by-step explanation:

A polynomial is simply an expression which consists of variables & coefficients involving only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.

Now, 1 and x are both polynomials. Thus; 1/x is already a quotient of a polynomial.

Now, to get two polynomial expressions whose quotient, when simplified, is 1/x, we will just multiply the numerator and denominator by the same polynomial to get more quotients.

So,

Let's multiply both numerator and denominator by (x + 1) to get;

(x + 1)/(x(x + 1))

This gives; (x + 1)/(x² + x)

Now, 1 and x are both polynomials but the expression "1/x" is not a polynomial but a quotient and thus polynomials are not closed under division.

The installment price is $55.

This can be illustrated through an expression. Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Here, you buy an I-phone for $800 or pay $75 down and the balance in 12 monthly payments of $65. The total amount will be:

= 75 + (12 × 65)

= $855

The installment will be:

= $855 - $800

= $55

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Answer:

A

Step-by-step explanation:

The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.

In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.

CV = (Standard Deviation / Mean) * 100

CV = (5.2 / 340) * 100

CV ≈ 1.53%

Therefore, the correct answer is option B: 1.53%.

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Answer:

no, they are different in their different ways

Answer:

Step-by-step explanation:

Bringing like terms on one side

-11 + 18 > 5n - 3n

-7 > 2n

-7/2 > n

The amount of Suzy's instalment every month if it is agreed to repay equal amount monthly is $152

Simple interest = principal × rate × time

= 4500 × 0.072 × 3

= $972

Total amount to repay = $4500 + $972

= $5472

Repayment time = 3 years

Suzy will repay every month

3 years= 12 months × 3

= 36 months

Since,

the repayment is equal every month

Amount of instalment every month= $5472 / 36

= $152

Therefore, Suzy will repay $152 each month instalmentally.

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Answer:

Simplified: 2x/15 + 5y/8

Step-by-step explanation:

Simplify the expression.

Answer:

Answer: 2x/15 + 5y/8

Step-by-step explanation:

Just Simplify the expression dude.

Answer:

uhhhh

Step-by-step explanation:

Answer:

ayoooooooooooooo

Step-by-step explanation:

yooo

If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.

When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.

This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.

The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.

In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.

It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.

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Answer:

The triangles are not similar

Step-by-step explanation:

The sides are not proportional

36/73 does not equal to 15/30

The given expression is a complex expression and we can prove the given expression equal to 1 by using definition.

a+ib, often known as the generic form of complex numbers, is how complex numbers are expressed. In the complex numbers a+ib form, a represents the real component of the number, b represents the imaginary part, and i is defined as√(-1).  Complex numbers can take a variety of shapes.

z=a+bi is the general form of complex number

As by definition

i^2=-1

So

i^4=(i^2)^2

    =(-1)^2

    =1

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According to Bernoulli's theorem, the success rate for the situation is 0.7173.

In math Bernoulli's theorem is states that that random experiment with exactly two possible outcomes, "success" and "failure" in which the probability of success is the same every time the experiment is conducted.

In order to calculate p we must sum the possible permutations of getting 0 success of 10 trials, 1 success of 10 trials, and 2 successes of 10 trials, and divide this sum by the total possible subsets from 10 elements, then it can be written as,

=> P = (10 1) (10 2) (10 1) / 2¹⁰

When we simplify this one, then we get,

=> P = 56/1024

=> P = 0.0547

When we apply the value on Bernoulli's theorem, then we get,

=> B(340, 0.0547, 0) = ( 340 0 ) x (1/1024) x (1023/1024)³⁴⁰

When we simplify this one then we get,

=> B = 0.7173

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Answer:C) 15

Step-by-step explanation:

If she drives 1/4 mi in 2 minutes then she wouldve drive 1 mi in 8  minutes.

2 hours= 120 minutes

8/120=15

The probability of exactly two flaws in a 50-yard piece of material is approximately 0.2706 or 27.06%.

In order to determine the probability of exactly two flaws in a 50-yard piece of material, we will use the Poisson distribution formula.

The Poisson distribution is used to calculate the probability of a given number of events occurring in a fixed interval of time or space when these events happen independently of each other and at an average rate.

To find the probability of exactly two flaws in a 50-yard piece of material, we will use the following formula:

P(X = k) = (e^(-λ) * λ^k) / k!

Where: P(X = k) is the probability of k flaws occurring in a 50-yard piece of material

λ = the average rate of flaws per unit of material (in this case, 50 yards)

k = the number of flaws we want to calculate is the mathematical constant ≈ 2.71828...

k! is the factorial of k, which is the product of all positive integers up to k

Let's plug in the values we have for this problem:

P(X = 2) = (e^(-λ) * λ^2) / 2!

λ = 2 flaws per 50 yards of material produced = 2/50 = 0.04 flaws per yard.

Therefore, the average number of flaws in a 50-yard piece of material is:

λ = 0.04 * 50 = 2e is a mathematical constant that equals ≈ 2.71828...

Then, let's plug in these values into the formula:

P(X = 2) = (e^(-2) * 2^2) / 2!P(X = 2) = (0.1353 * 4) / 2P(X = 2) = 0.2706

The probability of exactly two flaws occurring in a 50-yard piece of material is 0.2706 or approximately 27.06%.

Therefore, the probability of exactly two flaws in a 50-yard piece of material is approximately 0.2706 or 27.06%.

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Answer:

IS 60 DEGRES

Step-by-step explanation:

U TIMES THE ANGLE

Answer:

I think it's 30 degrees but I'M NOT SURE

Step-by-step explanation:

Complementing is 60 degrees

So 90 degress takeaway 60 is 30 degrees.  

The question is an illustration of selection (or combination)

The number of lock combination is 343

The given parameters are:

\(n = 7\) --- the number of digits to select from

\(r = 3\) --- the number of digits the lock uses

Because the digits can be repeated, the number of lock combinations is:

\(Lock = n^r\)

So, we have:

\(Lock = 7^3\)

\(Lock = 343\)

Hence, the number of lock combination is 343

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Answer:

18 multiplied by 2/9 = 4

Step-by-step explanation:

To determine the number of almonds that Pete grabbed, you have to multiply how much of the nuts were almonds by the total number of nuts that he grabbed. So,

   2/9 × 18

= 0.2222 × 18

= 4

Pete grabbed 4 almonds out of the 18 mixed nuts that he grabbed.

Hope that helps.

Answer:

Amount of almonds = 18 × [2/9]

Amount of almonds =  4 almonds

Step-by-step explanation:

Given:

Number of mixed nuts = 18

Probability of almonds = 2/9

Find:

Amount of almonds

Computation:

Amount of almonds = Number of mixed nuts × Probability of almonds

Amount of almonds = 18 × [2/9]

Amount of almonds = 36 / 4

Amount of almonds =  4 almonds

Initial value problem is :

y(4) 2y'' y = 3t + 6, y(0) = y'(0) = 0, y''(0) = y^(3)(0) = 1

We have to use the method of finding characteristic equation and then the general solution.

Particular solution:

Let y_p be the particular solution of the differential equation y(4) - 2y'' + y = 3t + 6. (we assume that y_p = (at + b) is a particular solution.)

Substituting y_p into the given equation, we have:

y_p(4) - 2y_p'' + y_p = 3t + 6Or,

(at + b)'''' - 2(at + b)'' + (at + b) = 3t + 6On

simplification, we get:

0 = 3t + 6

We do not get any value of t that satisfies the equation.

Hence, there is no particular solution.

General solution :

We solve the homogeneous equation (the equation obtained by replacing the right-hand side of the given equation by 0)y(4) - 2y'' + y = 0

The characteristic equation is:

r^4 - 2r^2 + 1 = 0(r^2 - 1)^2 = 0r^2 - 1 = 0r = ±1

Therefore, the general solution to the differential equation is:

y = c1e^t + c2te^t + c3e^-t + c4te^-t

We use the initial conditions to find the values of c1, c2, c3 and c4.

y(0) = c1 + c3 = 0

=> c1 = -c3y'(0) = c1 + c2 - c3 - c4 = 0

=> c2 - c4 = c3 - c1y''(0) = c1 + c2 + c3 + c4 = 1

=> c1 + c3 + 1 = -c2 + c4

Substituting the values of c1, c2, c3 and c4, we get:

y = e^t - t e^t - e^-t + t e^-t

Hence, the solution to the given initial value problem is:

y = e^t - t e^t - e^-t + t e^-t.

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