PLZZZ HELLPPP SOON REWARD BRRIANIESTTT

A. we can observe that 1(x) is continuous at x = kπ- for any integer k, and hence, it is continuous only at x = kπ, where k is an integer.

B. We have proved that limx → 2 (x2 - 1) = 3 using the definition of a limit.

A. To prove that 1(x) = {(sin(x) × EQ (x) XER-Q, X = zkπ, K 6 z is continuous only at x = kπ, where k is an integer without using L'Hospital's Rule, we can use the concept of limits.Let's consider the left limit of the function at x = kπ+ (where ε > 0 is a small value).

Here, we can observe that:

lim x → kπ+ 1(x) = lim x → kπ+ sin(x)/x > 0 since sin(x) > 0 when x is in (kπ, kπ + ε/2) and x is in (kπ - ε/2, kπ)

So, 1(x) = {(sin(x) × EQ (x) XER-Q, X = zkπ, K 6 z is continuous at x = kπ+ for any integer k.

Similarly, we can observe that 1(x) is continuous at x = kπ- for any integer k, and hence, it is continuous only at x = kπ, where k is an integer.

B. To prove that limx → 2 f(x) = 3, we can use the following definition of a limit:

For any ε > 0, there exists a δ > 0 such that |f(x) - 3| < ε for all 0 < |x - 2| < δ.

Here, f(x) = x2 - 1, and we need to prove that limx → 2 (x2 - 1) = 3.

Using algebraic manipulation, we can write x2 - 1 - 3 = (x + 2)(x - 2).Now, |(x + 2)(x - 2)| = |x + 2||x - 2|.

Therefore, we need to find δ such that |(x + 2)(x - 2)| < ε whenever 0 < |x - 2| < δ.

In order to ensure this, we can put an upper bound on |x + 2| and |x - 2|:|x + 2| < 4 (since x is close to 2)|x - 2| < δ

From the above inequalities, we can say that |(x + 2)(x - 2)| < 4δ.

Then, we can say that |(x2 - 1) - 3| = |(x + 2)(x - 2)| < 4δ < ε.

So, we can choose δ = ε/4.

Hence, we have proved that limx → 2 (x2 - 1) = 3 using the definition of a limit.

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Answer:

The equation is 3/10 × s = 162

Alexandra's salary before taxes for the pay period was $540

Step-by-step explanation:

Let

Alexander's salary before taxes

=s

3/10 if Alexander's take home pay is $162 after taxes

3/10 of s = $162

The equation is

3/10 × s = 162

Divide both sides by 3/10

s = 162 ÷ 3/10

= 162 × 10/3

= 1620 / 3

= $540

Alexandra's salary before taxes for the pay period was $540

For spinning the spinner one time A could be {1, 2, 3} or, A = {1, 2, 3, 4} is possible.

The set is mathematical model for a collectionof different things;a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables or even other sets.

The given spinner is divided into 8 equal sized sections, so the possible set can be written as-

S = {1, 2, 3, 4, 5, 6, 7, 8}

Now the possible subsets can be-

Even numbers = {1,3,5,7}

Odd numbers = {2,4,6,8}

Any number or group from 1 to 8, inclusive

Hence for spinner the spinner for one time, suppose A be the possible set. Then,

    A could be {1, 2, 3}.

or, A = {1, 2, 3, 4}.

where A is the subset of S.

Hence, For spinning the spinner one time A could be {1, 2, 3} or, A = {1, 2, 3, 4} is possible.

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Answer:

0.20x(1000/55)

Step-by-step explanation:

Answer:

x-intercept(s): ( 8 , 0 )

Step-by-step explanation:

Answer:

x-intercept(s):

( 8,0)

Step-by-step explanation:

To find the x-intercept, substitute in

0

for

y

and solve for

x

. To find the y-intercept, substitute in

0

for

x

and solve for

y

.

.

Which function represents this situation when x represents the actual mpg the car gets and f(x) represents the difference between the actual mpg and listed mpg is f(x)= |x| - 20. Option C

We have the function as;

f(x)= |x| - 20

In this function, x represents the actual mpg the car gets, and by subtracting 20 from x, we obtain the difference between the actual mpg and the listed mpg of 20 miles per gallon.

This function allows us to calculate the deviation from the listed fuel efficiency and provides a measure of how many miles per gallon the car is either above or below the listed value.

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Hi again! The equation to the function would be..

y = 1/2x + 1 (assuming that the initial value is one)

Answer:

We found the factors and prime factorization of 32 and 48. The biggest common factor number is the GCF number. So the greatest common factor 32 and 48 is 16.

Step-by-step explanation:

What is the GCF of 32and 48?

16

Greatest common factor (GCF) of 32 and 48 is 16.

Answer:

C) x ≥ 0 and y ≥ 0

0.5x + y ≤ 500

x + 1.5y ≤ 800

Step-by-step explanation:

A children clothing manufacturer has 500 yards of material to make shirts and skirts. A shirt requires 0.5 yards of fabric, and a skirt requires 1 yard of fabric. It takes 1 hour to make a shirt and 1.5 hours to make a skirt. The manufacture has 800 hours available to make shirts and skirts.

Which system of inequalities represent the constraints for this situation? Let x = number of shirts, and let y = number of skirts.

A) x ≤ 0 and y ≤ 0

0.5x + y ≤ 800

x + 1.5y ≤ 500

B) x ≤ 0 and y ≤ 0

0.5x + y ≥ 800

x + 1.5y ≥ 500

C) x ≥ 0 and y ≥ 0

0.5x + y ≤ 500

x + 1.5y ≤ 800

D) x ≥ 0 and y ≥ 0

0.5x + y ≥ 500

x + 1.5y ≥ 800

number of shirts,x and number of skirts,y must be greater than 0 since it can not be a negative value

x ≥ 0 ; y ≥ 0

Inequality for number of yards

x = 0.5 yards ; y = 1 yard

Total yards = 500

The inequality is

0.5x + y ≤ 500

Inequality for hours of production

x = 1 hour ; y = 1.5 hours

Total available hours for production = 800

The inequality is

x + 1.5y ≤ 800

Therefore, the system of inequalities which represent the constraints for this situation is

x ≥ 0 ; y ≥ 0

0.5x + y ≤ 500

x + 1.5y ≤ 800

x ≥ 0 and y ≥ 0

0.5x + y ≤ 500

x + 1.5y ≤ 800

When graphed the system shows that the manufacturer should make 200 shirts and 400 skirts for a maximum profit.

The next number in the given sequence is 126. it does not follow a simple arithmetic or geometric progression.

To determine the pattern and find the missing number in the sequence, let's analyze the given numbers and identify any recurring patterns or relationships between them.

Looking at the sequence, we can observe that it does not follow a simple arithmetic or geometric progression. However, there are some patterns we can identify to find the missing number.

First, let's consider the alternate numbers: 2, 3, 5, 28, 7, 82, and so on. These numbers do not follow a clear pattern, but they seem to be increasing in a somewhat irregular manner.

Next, let's consider the numbers in between the alternate numbers: 4, 10, 5, 11, 8, 29, and so on. These numbers also do not follow a straightforward pattern, but they seem to be related to the corresponding alternate numbers.

Now, if we observe carefully, we can notice that the numbers in between the alternate numbers are the squares of the corresponding alternate numbers. For example, 4 is the square of 2, 10 is the square of 3, 5 is the square of 5, and so on.

Based on this pattern, we can deduce that the missing number in the sequence should be the square of the next alternate number, which is 11.

Therefore, the missing number in the sequence is 11^2 = 121.

To verify our pattern, let's continue the sequence:

2, 4, 3, 10, 5, 5, 28, 11, 7, 8, 82, 29, 121

Now, let's observe the next alternate number: 7. The number in between the alternates should be the square of 7, which is 49. So, the next number in the sequence would be 49.

Continuing the sequence:

2, 4, 3, 10, 5, 5, 28, 11, 7, 8, 82, 29, 121, 49

Finally, let's consider the next alternate number, which is 8. The number in between the alternates should be the square of 8, which is 64. Thus, the next number in the sequence would be 64.

In conclusion, the missing number in the given sequence 2, 4, 3, 10, 5, 5, 28, 11, 7, 8, 82, 29, _ is 121. The next numbers in the sequence are 49 and 64, respectively.

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Answer:

it is C

Step-by-step explanation:

Its c because i had the exact same problem

Answer:

H (x= -3 , y=5)

I (x=8 , y=2)

J (x= -3 , y= -5)

D is the distance between the 2 points so just plug in the x and y cords of each of the corresponding points

so for (HI)

you plug in 2 on the red x

and 8 on the red y

then -3 in the blue x

and 5 in the blue y

If a segment XZ joining two endpoints X\((x_1,y_1)\) and Z\((x_2,y_2)\) is divided by a point Y(x, y) externally in the ratio of m : n,

Coordinates of the point will be,

x - coordinates → \(\frac{mx_2-nx_1}{m-n}\)

y - coordinates → \(\frac{my_2-ny_1}{m-n}\)

If the coordinates of the endpoints X and Z are (1, 9) and (5, -11) respectively and the ratio in which a point Y divides the segment is 1 : 5,

(Since, XY : XZ = 1 : 4 therefore, XY : YZ = 1 : 5)

Therefore, coordinates of Y will be,

x- coordinates → \(\frac{1(5)-5(1)}{1-4}=0\)

y-coordinates → \(\frac{1(-11)-5(9)}{1-5}=\frac{-56}{-4}=14\)

Therefore, coordinates of Y will be \((0,14)\).

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Answer:

47 - 2n

Step-by-step explanation:

An algebraic expression is an idea of representing numbers using letters or alphabet.

From the question above,

The variable = n

twice the number = 2× n = 2n

Translating:

47 - 2n

Answer:Let the magnitude of smaller force is P, the magnitude of larger force is Q and the resultant force is R.

As the resultant force makes 90

∘

 with the smaller force P then Q forms the hypotenuse of the triangle.

Thus, it can be written as,

Q

2

−P

2

=R

2

Q

2

−P

2

=(12)

2

Q

2

−P

2

=144                                (1)

The sum of magnitudes of two forces is given as,

P+Q=18

Q=18−P                                     (2)

Substituting the value from equation (2) in equation (1), we get

(18−P)

2

−P

2

=144

P=5N

Substituting the value of P in equation (1), we get

Q=18−5

=13N

Thus, the magnitude of the forces are 5N and 13N.

Step-by-step explanation:

Answer: \(4\frac{4}{5}\)

Step-by-step explanation:

To see how many \(\frac{1}{6}\) pound servings are in \(\frac{4}{5}\) of a pound of chicken we must divide \(\frac{4}{5}\) by \(\frac{1}{6}\)

\(\frac{4}{5}\)÷\(\frac{1}{6}\)

When dividing by a fraction you can take the reciprocal (flip the numerator and denominator) and you can multiply instead of dividing

\(\frac{4}{5}\)×\(\frac{6}{1}\)=\(\frac{24}{5}\)=\(4 \frac{4}{5}\)

Answer:

24/5, or 4.8, servings

Step-by-step explanation:

Let s represent the number of servings. We have:

\( \frac{1}{6} s = \frac{4}{5} \)

\(s = \frac{24}{5} = 4.8\)

The formula ensures that all three conditions must be met for the customer to be served, aligning with the given rule.

The given rule implies that wearing shoes and a shirt alone does not guarantee service. It suggests that there might be an additional condition, such as wearing pants, that could affect whether the customer gets served.

To represent this in a propositional formula, we can introduce a new variable, "pants," to account for this condition. Then, we can construct the formula as follows:

(shoes ∧ shirt ∧ pants) → service

This formula states that if the customer is wearing shoes, a shirt, and pants, then they will receive service. It acknowledges the possibility that wearing shoes and a shirt alone is not sufficient for service and introduces the requirement of wearing pants as an additional condition. The formula ensures that all three conditions must be met for the customer to be served, aligning with the given rule.

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2: V = 330 m^2

3: V = 144 m^2

Step-by-step explanation:

All the figures shown are rectangular prisms.

You can find the volume of a rectangular prism through this formula:

\(V = wlh\), where w is the width, l is the length, and h is the height.

To find the volume of a composite figure, find the volume of each smaller figure, then add them together.

Question 2: 330 m^2

V = 3 * 5 * 6 (smaller prism)

V = 8 * 5 * 6 (larger prism)

smaller prism = 90 m^2

larger prism = 240 m^2

240 + 90 = 330 m^2

Question 3: 144 m^2

V = 3 * 4 * 2 (small prism 1)

V = 3 * 4 * 2 (small prism 2)

V = 12 * 4 * 2 (large prism)

small prisms: 24 m^2

large prism: 96 m^2

24 + 24 + 96 = 144 m^2

Answer:

I think it is 7.86.

Step-by-step explanation:

You should change 8 1/3% to a decimal that equals 8.33333333333. I then had took 64/8.33333333333 which equaled 7.86.

If this helped please feel free to click the thanks button below. Thank you! :-D

To answer these questions, we need to use the formula for the uniform distribution, which is:
f(x) = 1/(b-a)
where a is the lower bound of the distribution and b is the upper bound.

a. To find the probability that a randomly selected videotape will be returned between 3 and 4 days late, we need to calculate the area under the curve between 3 and 4 on the x-axis. Since the uniform distribution is a rectangle, the area of the rectangle is equal to the height times the width. In this case, the height is f(x) = 1/(4-0) = 0.25 and the width is 4-3 = 1. Therefore, the probability is:
P(3 ≤ x ≤ 4) = height × width = 0.25 × 1 = 0.25
So the answer is 0.25.

b. To find the probability that a randomly selected videotape will be returned more than 1 day late, we need to calculate the area under the curve to the right of 1 on the x-axis. Since the distribution is uniform, the area to the right of 1 is equal to the width of the rectangle from 1 to 4, which is 4-1 = 3. Therefore, the probability is:
P(x > 1) = 3/(4-0) = 0.75

So the answer is 0.75.
In summary, the probability that a randomly selected videotape will be returned between 3 and 4 days late is 0.25, and the probability that a randomly selected videotape will be returned more than 1 day late is 0.75.

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The alternative theorem states that if "p" is a prime number and "a" is a positive integer, then \(a^{(p)}\) is congruent to "a" modulo p. This theorem can be derived from Fermat's Little Theorem.

Fermat's Little Theorem states that if "p" is a prime number and "a" is an integer not divisible by p, then \(a^{p-1}\) is congruent to 1 modulo p. To derive the alternative theorem, we can start by applying Fermat's Little Theorem to the case where "a" is not divisible by p, resulting in \(a^{p-1}\) ≡ 1 (mod p).

Now, consider the case where "a" is divisible by p. In this scenario, "a" can be written as a = kp, where k is a positive integer. Substituting this into the alternative theorem, we have \((kp)^p\) ≡ kp (mod p). Expanding the left side using the binomial theorem, we get \(k^p * p^{p-1}\) ≡ kp (mod p).

Since "p" is a prime number, p^p-1 is congruent to 1 modulo p by Fermat's Little Theorem. Therefore, the equation simplifies to \(k^p\)k^p ≡ kp (mod p). We can cancel the common factor of p on both sides, giving \(k^p\) ≡ k (mod p). Finally, recognizing that k is a positive integer, we conclude that this congruence is valid for any positive integer k.

Hence, we have derived the alternative theorem, which states that if "p" is a prime number and "a" is a positive integer, then \(a^{(p)}\) is congruent to "a" modulo p, regardless of whether "a" is divisible by p or not.

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As a result, for the same data set, a 99% confidence interval would have a greater margin of error than a 90% confidence interval.

Answer: If a 90% confidence interval is constructed based on a sample of data, and it is 74% + 3%, a 99% confidence interval based on this same sample of data would have a larger margin of error and probably a different center.

What is a confidence interval? A confidence interval is a statistical technique used to establish the range within which an unknown parameter, such as a population mean or proportion, is likely to be located. The interval between the upper and lower limits is called the confidence interval. It is referred to as a confidence level or a margin of error.

The confidence level is used to describe the likelihood or probability that the true value of the population parameter falls within the given interval. The interval's width is determined by the level of confidence chosen and the sample size's variability. The confidence interval can be calculated using the standard error of the mean (SEM) formula

.A 90% confidence interval indicates that there is a 90% chance that the interval includes the population parameter, while a 99% confidence interval indicates that there is a 99% chance that the interval includes the population parameter.

When the level of confidence rises, the margin of error widens. The center, which is the sample mean or proportion, will remain constant unless there is a change in the data set. Therefore, alternative A is the correct answer.

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Answer:

the rate of change from 4 to 8 is 4

Step-by-step explanation:

you can find this by subtracting the first number from the secone number and if the two numbers were in a diffrent order being 8 and 4 the answer would still be 4 because when you subtract 8 from 4 you ger-4 but with rate of change you always use the absolute value

hope this helped

The correct transformations:

1) 3 x Equation [A2] + Equation [A1] → Equation [B1]

2). 1/11 x Equation [B1} → Equation [C1]

The correct options are D and A respectively.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

We have three systems of linear equations.

To transform system A into system B:

Multiply 3 to the equation A2 and then add to equation A1,

we get,

-7x +18x -6y + 6y = 10- 54

11x = -44

equation B1.

To transform system B into system C:

Multiply 1/11 to equation B1,

we get,

x = -4

equation C1.

Therefore, the transformations are given above.

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The parametric equations for the line of intersection are:
x = 61 - 5t
y = 2t - 30
z = t

To find the parametric equations for the line of intersection of the given planes, we first need to solve the system of equations:

1. x + 2y + z = 1
2. 2x + 5y + 32 = 4

Step 1: Solve for x from equation 1:
x = 1 - 2y - z

Step 2: Substitute x in equation 2 with the expression found in step 1:
2(1 - 2y - z) + 5y + 32 = 4

Now we can use elimination to solve for one variable. Let's eliminate y by multiplying the first equation by 5 and subtracting it from the second equation:

Step 3: Simplify and solve for y:
2 - 4y - 2z + 5y + 32 = 4
y - 2z = -30

Step 4: Designate z as the parameter t:
z = t

Step 5: Substitute z with t in the expression for y:
y = 2t - 30

Step 6: Substitute z with t in the expression for x:
x = 1 - 2(2t - 30) - t
x = 1 - 4t + 60 - t
x = 61 - 5t

Now we have the parametric equations for the line of intersection:
x = 61 - 5t
y = 2t - 30
z = t

Note that we can choose any value of z for the parameter t, since z is unconstrained.

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Answer:

------------------

Let the angle be x.

Its complement is 90 - x and its supplement is 180 - x.

Set up an equation to reflect that its complement is 1/4 its supplement​:

The true mean of the data-set is given as follows:

46.35.

The mean of a data-set is calculated as the sum of all observations divided by the number of observations.

In this problem, the sum is given by the multiplication of the mid-values by the number of students with each value, as follows:

S = 37.5 x 30 + 42.5 x 20 + 47.5 x 15 + 52.5 x 13 + 57.5 x 22 = 4635.

The total number of students is given as follows:

30 + 20 + 15 + 13 + 22 = 100.

Hence the mean is calculated as follows:

Mean = 4635/100 = 46.35.

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