HELP ME BRAINLY AND 20 POINTS IF U ANSWER THIS QUESTION PLEASE

a) Yes, A ⊆ B. For any x in A, x^2 < 9, and since x^2 is always less than 9 for x < 3, A is a subset of B.

b) No, B ⊈ A. There exist elements in B (e.g., x = 2) that do not satisfy x^2 < 9, thus B is not a subset of A.

a) To determine if A ⊆ B, we need to verify if every element in set A is also an element of set B.

Set A is defined as A = {x ∈ ℝ | x^2 < 9}, which means A consists of all real numbers whose square is less than 9.

Set B is defined as B = {x ∈ ℝ | x < 3}, which means B consists of all real numbers that are less than 3.

To show that A ⊆ B, we need to prove that for any x in A, x must also be in B.

Let's consider an example. If we choose x = 2, it satisfies the condition x^2 < 9 (since 2^2 = 4 < 9), and it also satisfies the condition x < 3 (since 2 is less than 3).

Since x = 2 belongs to both sets A and B, we can conclude that A is a subset of B: A ⊆ B.

b) To determine if B ⊆ A, we need to verify if every element in set B is also an element of set A.

Using the definitions of sets A and B from the previous part:

Set A is defined as A = {x ∈ ℝ | x^2 < 9}, and set B is defined as B = {x ∈ ℝ | x < 3}.

To show that B ⊆ A, we need to prove that for any x in B, x must also be in A.

Let's consider an example. If we choose x = 2, it satisfies the condition x < 3 (since 2 is less than 3), but it does not satisfy the condition x^2 < 9 (since 2^2 = 4 is not less than 9).

Since x = 2 belongs to set B but not to set A, we have found a counterexample. Therefore, B is not a subset of A: B ⊈ A.

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Answer:

9 and -4

Step-by-step explanation:

Finding these 2 numbers can be found by guessing and checking. By doing this, it will get you the numbers 9 and -4.

First, test if they multiply to -36:

9(-4)

= -36

Then, check if they add up to 5:

9 + (-4)

= 5

So, 9 and -4 are the 2 numbers that multiply to -36 and add to 5

A simultaneous equation refers to two or more equations that are solved at the same time.

A simultaneous equation refers to two or more equations that are solved at the same time. Now we shall solve each of the equations;

a. 2x + y = 3 ------(1)

   x - y = 4 ------ (2)

x = 4 + y  ----- (3)

Substituting (3) into (1)

2(4 + y) + y = 3

8 + 2y + y = 3

8 + 3y = 3

3y = 3 - 8

3y = -5

y = -5/3

Hence;

 x - y = 4

x - (-5/3) = 4

x = 4 + 5/3

x = 17/3

b. 2x + 6y =9 -----(1)

x + 3y = 2 ------ (2)

x = 2 - 3y ------ (3)

Substitute (3) into (1)

2( 2 - 3y)  + 6y =9

4 - 6y + 6y = 9 (From this stage we can see that it is not possible to solve the quadratic)

c. 6x - 3y = 12 -----(1)

4x + 2y = 10 ---- (2)

12x - 6y = 24 ---- (3)

12x + 6y = 30 --- (4)

Add (3) to (4)

24x = 54

x= 54/24 = 9/4

Hence;

4(9/4) + 2y = 10

9 + 2y = 10

2y = 10 - 9

y = 1/2

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Therefore, in a 2x2 table, the pattern of cell frequencies that would indicate independence is d. All cell frequencies are exactly the same.

In a 2x2 contingency table, the expected cell frequencies under the null hypothesis of independence are equal for all cells. If the observed cell frequencies in the table are approximately equal to the expected cell frequencies, then we can conclude that there is no significant association between the two variables being studied. In other words, the pattern of observed cell frequencies is consistent with the null hypothesis of independence. Therefore, if all cell frequencies are exactly the same, it suggests that the variables are independent, as each cell has an equal chance of being filled by any observation regardless of the value of the other variable.

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Answer:

here you go! :))

n= 2

m=3

a= 10

q= 50

The correct way to write a confidence interval is an option [LU]

A confidence interval is typically written as [lower bound, upper bound], where the square brackets indicate that the bounds are included in the interval.

For example, a 95% confidence interval for a population mean might be written as [15.2, 20.8]. This means that we are 95% confident that the true population mean lies between 15.2 and 20.8.

In the answer choices, option (O [LU]) is the correct way to write a confidence interval because it follows this convention of using square brackets to indicate the inclusion of the bounds.

Option (O [LU)) uses a parenthesis for the upper bound, which could be confusing since parentheses typically indicate exclusion.

Options (O (UL)) and (O (UL)) switch the order of the bounds, which would be incorrect since the lower bound should come first.

The other options either use parentheses instead of brackets or reverse the order of the bounds, which are both incorrect.

Therefore,

The correct way to write a confidence interval is an option [LU]

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Answer:

1/6x = 9

x = 54

Step-by-step explanation:

Let x = number

1/6x = 9

Multiply each side by 6

1/6x * 6 = 9*6

x = 54

Answer:

1/6n = 9 ---> the equation

x = 54 ----> equation's answer

Step-by-step explanation:

The variable used can be either x or n, doesn't really matter.

It says 1/6th of a number is 9 --> write 1/6, n for the number, and then = 9

so, 1/6n = 9

Now, you are going to multiply each side by 6

1/6x * 6 = 9 * 6 --------> 54

x = 54

The velocity function v(t) is equal to -82t + 91. The derivative of each term in the position function was calculated using the sum or difference rule and the constant rule.

To find the velocity function v(t) from the given position function s(t) = -41t² + 91t - 51 + 4, we used the following rules:

1. Sum or difference rule: This rule allows us to differentiate each term separately and then add or subtract the derivatives. We applied this rule to differentiate each term in the position function:

  - The derivative of -41t² is -82t.

  - The derivative of 91t is 91.

  - The derivative of -51 is 0 (since it's a constant).

2. Constant rule: This rule states that the derivative of a constant is zero. We used this rule for the constant term 4.

By applying these rules, we obtained the derivative of s(t):

v(t) = -82t + 91.

Therefore, the velocity function v(t) is given by v(t) = -82t + 91.

To summarize, we found the velocity function by differentiating each term in the position function using the sum or difference rule and the constant rule. The final velocity function is v(t) = -82t + 91.

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Answer:

T = 1     I = 5     R = 40

Step-by-step explanation:

Use cross multiply method or use scientific calculator to find it by shift solve method

Answer:

T= 1

I= 5

R= 40

Step-by-step explanation:

T: 28/7 = 4 so you should divide 7 by 7 to get t

I: 12/4 is 3 so you should divide 20 by 4 to get I

R: 36/9 is 4 so multiply 10 times 4 to get R

Simplified expression of \(\rm (8/12)^{(x/y)} \times (x/y)\) is (\(\rm 2^{y}\))/(\(\rm 3^{x/y^2}\)).

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

Assuming you meant to write the expression as:

\((8/12)^{(x/y)}\)* (x/y)

We can simplify it as follows:

First, we can simplify the fraction 8/12 to 2/3:

\((2/3)^{(x/y)}\) * (x/y)

Next, we can apply the properties of exponents to simplify \((2/3)^{(x/y)}\) as follows:

\((2/3)^{x/y}\) = \((2^{x/y}/3^{x/y})^x\)

= \(2^{x/y}\)/\(3^{x/y}\)

Substituting this back into the original expression, we get:

(\(2^{x/y}\)/\(3^{x/y}\)) * (x/y)

= (\(2^{x/y*x}\))/(\(3^{x/y*y}\))

= (\(\rm 2^{y}\))/(\(\rm 3^{x/y^2}\)).

So the final simplified expression is (\(\rm 2^{y}\))/(\(\rm 3^{x/y^2}\)).

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Complete question:

Factorize the given term to simplest form:

\(\rm (8/12)^{(x/y)} \times (x/y)\)

We can find the value of the integral ∫ 0 8 4 x sin(x^2) dx by using the substitution u = x^2 and evaluating the resulting integral ∫ 0 64 sin(u) du/2. The final answer is 4 - 4cos(64).

To solve this problem, we need to use a substitution. Let u = x^2, then du = 2x dx. We can rewrite the integral as:

∫ 0 8 4 x sin(x^2) dx = ∫ 0 64 sin(u) du/2

Using the limits of integration, we can evaluate the integral as follows:

∫ 0 64 sin(u) du/2 = [-cos(u)/2] from 0 to 64
= (-cos(64)/2) - (-cos(0)/2)
= (cos(0)/2) - (cos(64)/2)
= (1/2) - (cos(64)/2)

Therefore, the answer to the integral is:

∫ 0 8 4 x sin(x^2) dx = 8 · 1/2 - 8 · cos(64)/2
= 4 - 4cos(64)

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Given

3.8y+5.6y-2=2.7

Find

Solve

Explanation

3.8y+5.6y-2=2.7

Final Answer

Hence , the value of y is 0.5

Answer:

y = 1/2

Step-by-step explanation:

3.8y+5.6y-2=2.7

Solve for y

Combine like terms

9.4y-2=2.7

Add 2 to each side

9.4y-2+2=2.7+2

9.4y = 4.7

Divide each side by 9.4

9.4y / 9.4 = 4.7/9.4

y = 1/2

Answer:

C / four-fifths

Step-by-step explanation:

Answer: C

Step-by-step explanation: I got a 100% , you can trust me :)

The apothem (x) is 11.62 units, the radius of the circle is 12 units, and the area of each segment is 48π − 23.25√3 square units.

It is a locus of a point drawn equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

An equilateral triangle with side lengths equal to 12√3 units is inscribed in a circle.

And half a side length of the equilateral triangle is 6√3 units.

The apothem (x) is units long and the radius of the circle will be

x² = (9√3)² - (6√3)²

x² = 243 - 108

x² = 135

 x = 11.62

And the radius of the circle will be

\(\begin{aligned} \cos 30 &= \dfrac{6\sqrt3}{r}\\\\\dfrac{\sqrt3}{2}&= \dfrac{6\sqrt3}{r}\\\\r &= 12 \end{aligned}\)

Each segment of the circle has an area that will be

Area = the difference between the areas of the sector and triangle

Area = the areas of the sector - the areas of the triangle

The area of the sector will be

\(\rm Sector's \ area= \dfrac{120}{360} \pi *12^2 \\\\Sector's \ area= 48\pi\)

The area of the triangle will be

\(\rm Triangle's \ area = \dfrac{1}{2*3} * 11.62 * 12\sqrt3\\\\Triangle's \ area = 23.25\sqrt3\)

Then the area of each segment will be

Segment area = 48π − 23.25√3

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Answer:

1. 6

2. 12

3. 48

4. 36

Step-by-step explanation:

The parabola's vertex is located at (-2, 8). The parabola's graph is then depicted below.

Let a be the leading coefficient and the parabola's vertex be the point (h, k). The parabola's equation will therefore be stated as,

y = a(x - h)² + k

The parabola's equation is stated as,

y = -(x + 2)² + 8

The downward-pointing parabola is represented by the negative sign.

The vertex of the parabola is at (-2, 8), according to the equation above. The parabola's graph is then depicted below.

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h ≈ 0.25 cm

Hi there !

d = m/V

V = l×w×h

replace

2.17 = 438/(40×20)×h

2.17 = 438/800×h

2.17×800×h = 438

1736h = 438

h = 438/1736

h ≈ 0,25 cm

Good luck !

For fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error decreases as the margin of error increases.

The square root of the variance for the given set of numbers is what the standard deviation examines. It is employed to compute a confidence interval for making judgments (such as accepting or rejecting a hypothesis).

Here, the population standard deviation, and level of significance are the same.

As the margin of error increased.

So, with the increase in the value of the margin of error, there will surely decrease in the value of the sample size

\($$\begin{aligned}&\mathrm{MOE}_\gamma=z_\gamma \times \sqrt{\frac{\sigma^2}{n}}\\&\begin{aligned}\mathrm{MOE} & =\text { margin of error } \\\gamma & =\text { confidence level } \\z_\gamma & =\text { quantile } \\\sigma & =\text { standard deviation } \\n & =\text { sample size }\end{aligned}\end{aligned}$$\)

As the margin of error is in the denominator position in the sample size formula

Hence with an increase in the margin of error sample size decreases.

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Answer:

10% probability that the number is greater than 2, then P

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

Event A: Number greater than 2.

Event B: Letter P.

These events are independent, so:

\(P(A \cap B) = P(A) \times P(B)\)

P(A)

There are 5 numbers.

3, 4 or 5, that is, 3 numbers greater than 2.

3/5 = 0.6. So P(A) = 0.6.

P(B)

6 letters, one of which is P. So

P(B) = 1/6 = 0.1667.

What is the probability the number is greater than 2, then P?

\(P(A \cap B) = P(A) \times P(B) = 0.6 \times 0.1667 = 0.1\)

10% probability that the number is greater than 2, then P

(a) The dot product of A and B is given by: A · B = (2î + 3ĵ + 4k) · (î - 2ĵ + 3k)= 2(1) + 3(-2) + 4(3)= 2 - 6 + 12 = 8

Therefore, A · B = 8.

(b) The angle between two vectors A and B is given by:

θ = cos^(-1)((A · B) / (|A| |B|))

In this case, |A| is the magnitude of vector A and |B| is the magnitude of vector B. The magnitude of a vector is given by the square root of the sum of the squares of its components.

|A| = √(2² + 3² + 4²) = √(4 + 9 + 16) = √29

|B| = √(1² + (-2)² + 3²) = √(1 + 4 + 9) = √14

Plugging in the values:

θ = cos^(-1)(8 / (√29 √14))

(c) The scalar component of vector A in the direction of vector B is given by:

A_B = (A · B) / |B|

Plugging in the values:

A_B = 8 / √14

(d) The cross product of vectors A and B is given by:

A x B = (2î + 3ĵ + 4k) x (î - 2ĵ + 3k)

= (3(3) - 4(-2))î + (4(1) - 2(3))ĵ + (2(-2) - 3(3))k

= 17î - 2ĵ - 13k

Therefore,AXB = 17î - 2ĵ - 13k.

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(a) The dot product of A and B is given by: A · B = (2î + 3ĵ + 4k) · (î - 2ĵ + 3k)= 2(1) + 3(-2) + 4(3)= 2 - 6 + 12 = 8

Therefore, A · B = 8.

(b) The angle between two vectors A and B is given by:

θ = cos^(-1)((A · B) / (|A| |B|))

In this case, |A| is the magnitude of vector A and |B| is the magnitude of vector B. The magnitude of a vector is given by the square root of the sum of the squares of its components.

|A| = √(2² + 3² + 4²) = √(4 + 9 + 16) = √29

|B| = √(1² + (-2)² + 3²) = √(1 + 4 + 9) = √14

Plugging in the values:

θ = cos^(-1)(8 / (√29 √14))

(c) The scalar component of vector A in the direction of vector B is given by:

A_B = (A · B) / |B|

Plugging in the values:

A_B = 8 / √14

(d) The cross product of vectors A and B is given by:

A x B = (2î + 3ĵ + 4k) x (î - 2ĵ + 3k)

= (3(3) - 4(-2))î + (4(1) - 2(3))ĵ + (2(-2) - 3(3))k

= 17î - 2ĵ - 13k

Therefore,AXB = 17î - 2ĵ - 13k.

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The congruency statement which are applicable are :

BE ≅ ZX

Arc BE ≅ Arc ZX

Given,

⊙A ≅ ⊙V (congruent) .

Now,

According to the figure the the two circles are congruent to each other .

As two circles are congruent their corresponding line segments and arcs will be similar to each other.

Thus the conclusions which are true from the following are:

Line segment BE is congruent to line segment ZX .

∴ BE ≅ ZX

Arc BE is congruent to Arc ZX .

Arc BE ≅ Arc ZX

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Image of the question is attached below .

Step-by-step explanation:

Our equation is: y=(x-3)²

x should be replaced by x-4

The graph is still a parabola but with a different vertex

The vertex here is :

y'= 2x-14

solve y'=0

2x-14=0

2x=14

x=7

You can easily find it without derivating by dividing -14 by -2

since: x²-14x-49

a=1 b= -14  c=-49

-b/2a = 14/2 = 7

the image of 7 is:

y=(7-7)² = 0

so the coordinates of the new vertex are (7,0) and it's a maximum

since y">0

y'= 2x-14

y"= 2 wich is positive

The graph is shifted four units to the right.

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

This question is solved using the shifting concept.

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

In this question:

The original function is:

\(f(x) = (x - 3)^2\)

Replacing x by x - 4 is equivalent to finding f(x - 4), and so:

\(f(x - 4) = (x - 4 - 3)^2 = (x - 7)^2\)

Plotting functions f(x) and f(x-4), as in the end of this answer, it can be seen that the blue graph of f(x-4) is shifted four units to the right of the red graph of f(x).

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Step-by-step explanation:

s = 3 and t = 2

= 2(8 + t)³ - 6

= 2(8 + 2)³ - 6

= 2(10)³ - 6

= 2(1.000) - 6

= 2.000 - 6

= 1.994

To estimate the mean amount earned by a college student per month, we can use a point estimate and a 95% confidence interval. A point estimate is a single value that represents the best estimate of the population parameter, in this case, the mean amount earned by a college student per month. This point estimate can be obtained by taking the sample mean. To determine the 95% confidence interval, we need to calculate the margin of error and add and subtract it from the sample mean. This gives us a range of values that we can be 95% confident contains the true population mean. The conclusion is that the point estimate and 95% confidence interval can provide us with a good estimate of the mean amount earned by a college student per month.

To estimate the mean amount earned by a college student per month, we need to take a sample of college students and calculate the sample mean. The sample mean will be our point estimate of the population mean. For example, if we take a sample of 100 college students and find that they earn an average of $1000 per month, then our point estimate for the population mean is $1000.

However, we also need to determine the precision of this estimate. This is where the confidence interval comes in. A 95% confidence interval means that we can be 95% confident that the true population mean falls within the range of values obtained from our sample. To calculate the confidence interval, we need to determine the margin of error. This is typically calculated as the critical value (obtained from a t-distribution table) multiplied by the standard error of the mean. Once we have the margin of error, we can add and subtract it from the sample mean to obtain the confidence interval.

In conclusion, a point estimate and a 95% confidence interval can provide us with a good estimate of the mean amount earned by a college student per month. The point estimate is obtained by taking the sample mean, while the confidence interval gives us a range of values that we can be 95% confident contains the true population mean. This is an important tool for researchers and decision-makers who need to make informed decisions based on population parameters.

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The probabilities are as follows: 1. P(-1.12 < z < 1.82) ≈ 0.845 , 2. P(z < 2.65) ≈ 0.995 , 3. P(z > 0.36) ≈ 0.6406 , 4. P(-2.89 < z < -0.32) ≈ 0.4954

In order to compute the probabilities given, we need to refer to the standard normal distribution table or use appropriate statistical software. The standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1.

1. P(-1.12 < z < 1.82): This is the probability of the standard normal random variable, z, falling between -1.12 and 1.82. By looking up the values in the standard normal distribution table or using software, we find this probability to be approximately 0.845.

2. P(z < 2.65): This represents the probability of z being less than 2.65. By consulting the standard normal distribution table or using software, we find this probability to be approximately 0.995.

3. P(z > 0.36): This is the probability of z being greater than 0.36. Again, referring to the standard normal distribution table or using software, we find this probability to be approximately 0.6406.

4. P(-2.89 < z < -0.32): This represents the probability of z falling between -2.89 and -0.32. After consulting the standard normal distribution table or using software, we find this probability to be approximately 0.4954.

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The number of kilowatt-hours used KWH is 471.6 KWH.

Since the power bill for the month says you pay 15 cents per kilowatt-hour, this is the rate of the bill. We convert this a a dollar rate.

So, 15 cents per kilowatt-hour = 15 cents × $ 1/100 cents per kilowatt-hour (since $ 1 = 100 cents)

= 15 cents/100 × $ 1/100 cents per kilowatt-hour

= 0.15 × $ 1/100 cents per kilowatt-hour

= $ 0.15 cents per kilowatt-hour.

Since the power bill came out to be $ 70.74, we need to find the number of kilowatt-hours used KWH.

The total amount on bill = rate of bill × number of kilowatt-hours used.

So, number of kilowatt-hours used = total amount on bill/rate of bill

Total amount on bill = $ 70.74 and rate of bill =  $ 0.15 cents per kilowatt-hour.

So, number of kilowatt-hours used = total amount on bill/rate of bill

number of kilowatt-hours used = $ 70.74 /$ 0.15 cents per kilowatt-hour.

number of kilowatt-hours used = 471.6 KWH

So, number of kilowatt-hours used KWH is 471.6 KWH.

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Answer:

1 : 400

Step-by-step explanation:

\(\frac{3.5 x 10^{3} }{3.5 x 10^{3} } : \frac{1.4 x 10^{6 } }{3.5 x 10^{3} }\)

1 : .4 x \(10^{3}\)

1 : 4 x \(10^{2}\)

1 : 400

Answer:

(x+8)²-2=0

(x+8+√2)(x+8-√2)=0

x= - 8- √2 =  -9.41 lesser x

x= -8 + √2 = -6.59  greater x

Answer:

\(\mathrm{Decimal}:\quad x=-6.58578\ ,\:x=-9.41421\)

Step-by-step explanation:

\(\left(x+8\right)^2-2=0\\\mathrm{Add\:}2\mathrm{\:to\:both\:sides}\\\left(x+8\right)^2-2+2=0+2\\Simplify\\\left(x+8\right)^2=2\\\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\mathrm{Solve\:}\:x+8=\sqrt{2}:\quad x=\sqrt{2}-8\\x+8=\sqrt{2}\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\x+8-8=\sqrt{2}-8\\\mathrm{Simplify}\\x=\sqrt{2}-8\)

\(\mathrm{Solve\:}\:x+8=-\sqrt{2}:\quad x=-\sqrt{2}-8\\x+8=-\sqrt{2}\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\x+8-8=-\sqrt{2}-8\\\mathrm{Simplify}\\x=-\sqrt{2}-8\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=\sqrt{2}-8,\:x=-\sqrt{2}-8\\\mathrm{Decimal}:\quad x=-6.58578 ,\:x=-9.41421\)

Answer:

b your answer is 0, no need to yell.

Check the picture below.