how is your day?
also for the sake of asking, whats 5×1
Love yallllll! ​

Answer:

{x | x R, x > 3}

Step-by-step explanation:

x - 5 > -2

Add 5 to each side

x - 5+5 > -2+5

x> 3

The MMPI-2 test is used for the assessment of psychopathology and personality of patients.

It includes 567 true-false questions, resulting in 10 clinical scales, among which one is the anxiety subscale.

A score of 30 or less is usually considered very low.

The questions are answered by the patient, usually in a clinical or research setting.

A one-sample t-test is conducted in the problem, whereby a sample of 18 participants in a yoga group is tested for anxiety scores.

The following are the parameters of the one-sample t-test:Groups:

18 participants

Null hypothesis: The anxiety scores of Felipe's yoga group are statistically equal to 30." value: 30

Type of test: One-tailed test

Alternative hypothesis: The anxiety scores of Felipe's yoga group are greater than 30.

Degrees of freedom: n - 1 = 17T-observed value: (35.2 - 30) / (10.4 / sqrt(18)) = 2.41T-critical value: 1.734

Reject or retain null hypothesis: Since the t-observed value (2.41) is greater than the t-critical value (1.734), Felipe should reject the null hypothesis, which implies that his yoga group's scores are greater than 30.P-value: 0.014Cohen’s d value: (35.2 - 30) / 10.4 = 0.5

If the " value were reduced to 0.01, Felipe would still reject the null hypothesis, since the p-value (0.014) is lower than the alpha level (0.01).

For the sample mean: 35.2CI for 42%: 35.2 ± 0.58CI for 79%: 35.2 ± 1.16CI for 95%: 35.2 ± 2.13

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Answer:

5,004,300

Step-by-step explanation:

The ordered pair that is the solution of the given system of inequalities is (2, -2)

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,

The inequalities are,

y < -x....(i)

2x+y > 2

y < 2-2x...(ii)

To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =

-x = 2 - 2x

x = 2

y = -2

Therefore, the ordered pair, is (2, -2) {look at the graph attached}

Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)

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The value of the given integral is: v = [(4√(3) - 5)π/3]

To evaluate the given integral, let's calculate it step by step:

First, let's integrate with respect to z from 1 to √(4 - x² - y²):

∫[1, √(4 - x² - y²)] dz = √(4 - x² - y²) - 1

Next, let's integrate the above expression with respect to y from -√(3 - x²) to √(3 - x²):

∫[-√(3 - x²), √(3 - x²)] (√(4 - x² - y²) - 1) dy

To simplify the integration, let's convert to polar coordinates:

x = r cosθ

y = r sinθ

The bounds of integration in polar coordinates will be:

r: 0 to √(3)

θ: 0 to 2π

Now, we can rewrite the integral in terms of polar coordinates:

∫[0, 2π] ∫[0, √(3)] (√(4 - r²) - 1) r dr dθ

Evaluating the inner integral with respect to r:

∫[0, 2π] [(-1/3) (4 - r²)\(^{3/2}\) - (1/2) r²] | [0, √(3)] dθ

∫[0, 2π] [(2√(3)/3) - (1/3)(4 - 3)\(^{3/2}\) - (1/2)(√(3))²] dθ

Simplifying further:

∫[0, 2π] [(2√(3)/3) - (1/3) - (3/2)] dθ

∫[0, 2π] [(2√(3)/3) - (5/6)] dθ

Now, integrating with respect to θ:

[(2√(3)/3)θ - (5/6)θ] | [0, 2π]

[(2√(3)/3)(2π) - (5/6)(2π)] - [(2√(3)/3)(0) - (5/6)(0)]

[(4√(3)/3)π - (5/3)π] = [(4√(3) - 5)π/3]

Therefore, the value of the given integral is: v = [(4√(3) - 5)π/3]

Complete Question:

Evaluate the integral:

v = ∫∫∫ [−√3, √3] [−√(3−x²), √(3−x²)] [1, √(4−x²−y²)] dz dy dx

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we find that you would need to deposit approximately $15,000 to have a retirement fund of $93,447 after 41 years, assuming no additional deposits are made to the account.

To calculate the amount you need to deposit now to have a retirement fund of $93,447 after 41 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment (retirement fund)
P = the principal amount (the initial deposit)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years

In this case, the future value (A) is $93,447, the annual interest rate (r) is 3% (0.03 in decimal form), the number of times interest is compounded per year (n) is 365 (since it is compounded daily), and the number of years (t) is 41.

Plugging in these values into the formula, we get:

93,447 = P(1 + 0.03/365)^(365*41)

To find the principal amount (P), we can isolate it on one side of the equation. Dividing both sides by (1 + 0.03/365)^(365*41), we have:

P = 93,447 / (1 + 0.03/365)^(365*41)

Calculating this expression, we find that you would need to deposit approximately $15,000 to have a retirement fund of $93,447 after 41 years, assuming no additional deposits are made to the account.

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1. The solution to the first differential equation is given by e^2yx - ysin(xy) + y^2 + C = 0, where C is an arbitrary constant.

2. The general solution to the second differential equation is x(3x - y^2) = C, where C is a positive constant.

To solve the first-order differential equations, let's solve them one by one:

1. (e^2y - ycos(xy))dx + (2xe^2y - xcos(xy) + 2y)dy = 0

We notice that the given equation is not in standard form, so let's rearrange it:

(e^2y - ycos(xy))dx + (2xe^2y - xcos(xy))dy + 2ydy = 0

Comparing this with the standard form: P(x, y)dx + Q(x, y)dy = 0, we have:

P(x, y) = e^2y - ycos(xy)

Q(x, y) = 2xe^2y - xcos(xy) + 2y

To check if this equation is exact, we can compute the partial derivatives:

∂P/∂y = 2e^2y - xcos(xy) - sin(xy)

∂Q/∂x = 2e^2y - xcos(xy) - sin(xy)

Since ∂P/∂y = ∂Q/∂x, the equation is exact.

Now, we need to find a function f(x, y) such that ∂f/∂x = P(x, y) and ∂f/∂y = Q(x, y).

Integrating P(x, y) with respect to x, treating y as a constant:

f(x, y) = ∫(e^2y - ycos(xy))dx = e^2yx - y∫cos(xy)dx = e^2yx - ysin(xy) + g(y)

Here, g(y) is an arbitrary function of y since we treated it as a constant while integrating with respect to x.

Now, differentiate f(x, y) with respect to y to find Q(x, y):

∂f/∂y = e^2x - xcos(xy) + g'(y) = Q(x, y)

Comparing the coefficients of Q(x, y), we have:

g'(y) = 2y

Integrating g'(y) with respect to y, we get:

g(y) = y^2 + C

Therefore, f(x, y) = e^2yx - ysin(xy) + y^2 + C.

The general solution to the given differential equation is:

e^2yx - ysin(xy) + y^2 + C = 0, where C is an arbitrary constant.

2. x(yy' - 3) + y^2 = 0

Let's rearrange the equation:

xyy' + y^2 - 3x = 0

To solve this equation, we'll use the substitution u = y^2, which gives du/dx = 2yy'.

Substituting these values in the equation, we have:

x(du/dx) + u - 3x = 0

Now, let's rearrange the equation:

x du/dx = 3x - u

Dividing both sides by x(3x - u), we get:

du/(3x - u) = dx/x

To integrate both sides, we use the substitution v = 3x - u, which gives dv/dx = -du/dx.

Substituting these values, we have:

-dv/v = dx/x

Integrating both sides:

-ln|v| = ln|x| + c₁

Simplifying:

ln|v| = -ln|x| + c₁

ln|x| + ln|v| = c₁

ln

|xv| = c₁

Now, substitute back v = 3x - u:

ln|x(3x - u)| = c₁

Since v = 3x - u and u = y^2, we have:

ln|x(3x - y^2)| = c₁

Taking the exponential of both sides:

x(3x - y^2) = e^(c₁)

x(3x - y^2) = C, where C = e^(c₁) is a positive constant.

This is the general solution to the given differential equation.

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Answer:

more info so i can help

Step-by-step explanation:

please

Answer:

x = (√10  -3)/2  and (-√10  -3)/2

Step-by-step explanation:

(2x+3)^2 = 10

To solve the equation, take the square root of each side

sqrt((2x+3)^2) = ±√10

2x+3 = ±√10

Subtract 3 from each side

2x+3-3 = ±√10  -3

2x = ±√10  -3

Divide each side by 2

2x/2 = (±√10  -3)/2

x = (±√10  -3)/2

There are two solutions

x = (√10  -3)/2

and (-√10  -3)/2

Answer:

\(\large {\textsf{A and D}}\ \implies \sf \sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}\)

Step-by-step explanation:

Given: (2x + 3)² = 10

In order to find the solutions to the given equation, we can take the (square) roots of the equation to find the zeros, which are also known as the x-intercepts. This is where the zeros intersect the x-axis.

Note: when taking the square roots of a quadratic equation, remember to use both the positive and negative roots.

Step 1: Square both sides of the equation.

\(\sf \sqrt{(2x + 3)^2} = \sqrt{10}\\\\\Rightarrow 2x+3=\pm\sqrt{10}\)

Step 2: Separate into possible cases.

\(\sf x_1 \implies 2x+3=-\sqrt{10}\\\\x_2 \implies 2x+3=\sqrt{10}\)

Step 3: Solve for x in both cases.

\(\sf \bold{x_1} \implies 2x+3=-\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=-\sqrt{10}-3\\\\\Rightarrow 2x=-\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{-\sqrt{10}-3}{2}\\\\\Rightarrow x_1=\dfrac{-\sqrt{10}-3}{2}\\\\\)

\(\sf \bold{x_2}\implies 2x+3=\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=\sqrt{10}-3\\\\\Rightarrow 2x=\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{\sqrt{10}-3}{2}\\\\\Rightarrow x_2=\dfrac{\sqrt{10}-3}{2}\)

Therefore, the solutions to this quadratic equation are: \(\sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}\)

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Answer:

1.4 estimate: 1

Step-by-step explanation:

the probability that exactly 2 of them do not require a vision correction is 0.6544.

Let p = Probability that an adult does not require vision correction q = Probability that an adult requires vision correction p = 16% = 0.16q = 1 - p = 1 - 0.16 = 0.84.

We know that,To find the probability of x successes in n trials is given by the formula,P(x) = nCx * px * q^(n-x)where nCx = n! / x! (n - x)!Here, n = 12, p = 0.16, q = 0.84 and x = 2.

So, the probability that exactly 2 of them do not require a vision correction,P(2) = 12C2 * (0.16)^2 * (0.84)^(12-2)P(2) = 66 * 0.0256 * 0.317P(2) = 0.6544.Hence, the required probability is 0.6544. Therefore, the probability that exactly 2 of them do not require a vision correction is 0.6544.

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Answer:

(6x² - 7x + 9)

Step-by-step explanation:

Given:

(9x² - 2x + 1) - (3x² + 5x - 8)

Find:

Value of equation

Computation:

(9x² - 2x + 1) - (3x² + 5x - 8)

(9x² - 2x + 1 - 3x² - 5x + 8)

(6x² - 7x + 9)

Answer:

2

Step-by-step explanation:

-4 x -2 is 8. -4 -2 is -6. 8-6 is 2.

Answer:

8-4-2=2

It was +8 because the multiplication of two negatives will give u a positive

Step-by-step explanation:

The sampling technique that ensures that every person in the target population has an equal chance of being selected is probability sampling. To produce accurate results, this technique guarantees that every member of the target population has an equal chance of being selected.

A random process is used in probability sampling to select participants. It is the most robust sampling technique that can be used in a research study, with the potential for producing reliable findings. There are different types of probability sampling, including simple random sampling, systematic sampling, stratified sampling, and cluster sampling.Long answer:Probability sampling is a sampling technique that ensures that every person in the target population has an equal chance of being selected. This technique is utilized to produce accurate results by ensuring that every member of the target population has an equal chance of being selected. Probability sampling employs a random process to select participants, and it is the most robust sampling technique that can be used in a research study.

Researchers randomly choose groups or clusters and select participants from each group.Cluster sampling has several advantages over other types of probability sampling. For instance, it is less expensive than other forms of probability sampling, and it allows researchers to include participants who may not be available in other types of sampling techniques. However, it is critical to note that cluster sampling also has several disadvantages. For instance, it may result in larger sampling errors than other types of sampling techniques, and it may be less representative of the population of interest.

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The solution is Option B.

The equation of line is given by y = ( -3/4 )x + 4 , where the rate of change is the slope m = ( -3/4 ) and the initial value is 4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

A line is graphed that passes through the y-intercept at 4 and through the point P ( 4 , 1 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

Substituting the values in the equation , we get

y = mx + 4   be equation (1)

when y = 1 , x = 4

1 = 4m + 4

Subtracting 4 on both sides of the equation , we get

4m = -3

Divide by 4 on both sides of the equation , we get

m = -3/4

So , the slope of the line is m = -3/4

Therefore , the equation of line is y = ( -3/4 )x + 4

Now , the initial value of the equation is when x = 0

So ,

y = ( -3/4 ) ( 0 ) + 4

y = 4

So , the initial value of f ( 0 ) = y = 4

Hence , the equation of line is y = ( -3/4 )x + 4

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The expression ********** can be represented as 3333333333 in base four, 4444444444 in base five, and 7777777777 in base eight, according to the respective numerical systems.

a) In base four, each digit can have values from 0 to 3. The symbol "*" represents the value 3. Therefore, when we have ten "*", we can express it as 3333333333 in base four.

b) In base five, each digit can have values from 0 to 4. The symbol "*" represents the value 4. Hence, when we have ten "*", we can represent it as 4444444444 in base five.

c) In base eight, each digit can have values from 0 to 7. The symbol "*" represents the value 7. Thus, when we have ten "*", we can denote it as 7777777777 in base eight.

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Answer:

18/40

Step-by-step explanation:

Answer: 47

Step-by-step explanation:

simply substitute the constants with 5 and 3.

(5)^2 + 9(3) - 5 = 47

Answer:

C and D

Step-by-step explanation:

You can just divided the numerator by the denominator and find which answers are the same as 9/10

Answer:

See below.

Step-by-step explanation:

Solving :-

#1

#2

They both have the numerator in both solutions to be 5 and -3 respectively. I believe this is because both equations have the constant term, c, to be -15 and 5 and -3 are factors of -15.

Answer:

Explanation:

The statement "Suppose that 14% of people own dogs," implies that the probability of owning a dog is given as;

Therefore, if two people are selected randomly for owning dogs, they would have the same probability attached to them.

We can then combine both probabilities by using the "and" symbol. which implies "multiplication."

Workings

Answer:

the third and fourth one is correct

The coterminal angle for the -4π/5  are -14π/5 , 6π/5 and reference angle is π/5 respectively.

Two different angles that have the identical starting and ending edges termed coterminal angles however, since one angle measured clockwise and the other determined counterclockwise, the angles' terminal sides have completed distinct entire rotations.

We have an angle:

-4π/5

To find the coterminal angle, add and subtract by 2π in the angle -4π/5

Coterminal angle:

= -4π/5 - 2π

= -14π/5

= -4π/5 + 2π

= 6π/5

Reference angle:

= π - 4π/5  (as the angle lies in the second quadrant)

= π/5

Thus, the coterminal angle for the -4π/5  are -14π/5 , 6π/5 and reference angle is π/5 respectively.

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Answer:

I think the answer is 1

Step-by-step explanation:

-(-2)-1

=1

Answer:

4 legs from the bed and 4 from the chair im guessing since not all have 4

Hope This Help

Answer:

4 legs from the bed and 4 from the chair

Step-by-step explanation:

im a math wizard fr

So, the probability of ending up with a three-digit number that is divisible by 4 is 1/24.

To find the probability of ending up with a three-digit number that is divisible by 4 when spinning the spinner three times, we need to consider the possible outcomes that satisfy this condition and divide it by the total number of possible outcomes. Let's analyze the given spinner and its possible outcomes:

Spinner: [1, 2, 3, 4, 5, 6]

To form a three-digit number, the hundreds digit will be determined by the first spin, the tens digit by the second spin, and the units digit by the third spin. A number is divisible by 4 if the last two digits (tens and units digits together) form a number divisible by 4. Therefore, we need to find the number of possible outcomes for the tens and units digits that satisfy this condition.

Possible outcomes for the tens digit: [2, 4, 6]

Possible outcomes for the units digit: [2, 4, 6]

Combining the possible outcomes for the tens and units digits, we have a total of 9 (3 possibilities for the tens digit multiplied by 3 possibilities for the units digit) favorable outcomes. The total number of possible outcomes for each spin is 6 (since there are 6 numbers on the spinner). Since we are spinning the spinner three times independently, the total number of possible outcomes for spinning it three times is 6^3 = 216. Therefore, the probability of ending up with a three-digit number divisible by 4 is:

Probability = favorable outcomes / total outcomes

Probability = 9 / 216

Probability = 1 / 24

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Answer:

O I, II & III

Step-by-step explanation:

(2, 3) and (1, 1)

m = (3 - 1)/(2 - 1) = 2

y = 2x + b

1 = 2(1) + b

b = -1

The equation of the line is

y = 2x - 1

I) y = 2(x - 2) + 3 = 2x - 4 + 3 = 2x - 1   Yes

II) y = 2x - 1   Yes

III) y = 2(x - 1) + 1 = 2x - 2 + 1 = 2x - 1   Yes

Answer: O I, II & III

Answer:

C.

Step-by-step explanation:

The square root of 8 is 2.828427....

But if you don't have a calculator, just think of the "perfect square" closest to that. The square root of 9 is 3, so you know the square root of 8 is close to that, but a little less.

A few "perfect squares":

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25