the length of a rectangle is 3 in. more than its width. The perimeter of the rectangle is 30 in. Find the length and width of the rectangle

Answer:

x = - 26

Step-by-step explanation:

Let the number be x.

According to the question,

\(\frac{x+5}{x-2} = \frac{3}{4}\\\)

Cross multiplying 4 & 3 gives :-

\(4(x+5)=3(x-2)\)

And solving this eqn. gives :-

\(4(x+5)=3(x-2)\\=> 4x+20=3x-6\\=>4x-3x=-20-6\\=>x=-26\)

Verification :-

(putting the value of x = -26 )

\(\frac{x+5}{x-2} \\\\=>\frac{-26+5}{-26-2} \\\\=> \frac{-21}{-28} \\\\=>\frac{21}{28}\)

Reducing  \(\frac{21}{28}\)  by 7 gives  \(\frac{3}{4}\) .

(i) Assumptions of classical linear regression: linearity, independence, homoscedasticity, no perfect multicollinearity, zero conditional mean, and normality. Violation: perfect multicollinearity between X2, X3, and X4.

(ii) Omitted variable bias occurs when X4 is omitted from the model, leading to a biased estimate of β2 compared to α2 if X2 and X4 are correlated.

In the given model, the assumption of no perfect multicollinearity is violated when the regressors X2, X3, and X4 are defined as the log of per capita GDP, the log of the square of per capita GDP, and the proportion of population with graduation, respectively. X3 is a function of X2, and X4 may be correlated with both X2 and X3. This violates the assumption that the independent variables are not perfectly correlated with each other.

Omitted variable bias in β2 compared to α2 occurs when X4 is omitted from the model. This bias arises because X4 is a relevant explanatory variable that affects the dependent variable (Y), and its omission leads to an incomplete model. The bias in β2 arises from the correlation between X2 and X4. If X2 and X4 are not correlated, β2 will equal α2, and there will be no omitted variable bias. However, if X2 and X4 are correlated, omitting X4 from the model will result in a biased estimate of β2 because the omitted variable (X4) affects both Y and X2, leading to a bias in the estimation of the relationship between Y and X2.

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Answer:

hope it helps.............

The modal number of goals scored is 1.

Range of number of goals scored is 3.

Mean of number of goals scored is 2.1

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Here, Modal number of goals scored is 1. (modal number is the value with highest frequency)

Range = Highest term - lowest term

Range = 4 - 1

Range = 3

Mean = ∑xf / ∑f

mean = (1X9 + 2X3 + 3X3 + 4X5) / (9+3+3+5)

mean = 42/20

mean = 2.1

Thus, The modal number of goals scored is 1.

Range of number of goals scored is 3.

Mean of number of goals scored is 2.1.

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Real numbers are the set of all numbers that can be represented on a number line, including rational and irrational numbers. They are used to represent quantities that can be measured or counted.

We are given an operation qb and the rule qb = bº + 2ab. We need to compute 20(103) using this operation.

Step 1: Identify the values of a and b.
In this case, a = 20 and b = 103.

Step 2: Substitute the values of a and b into the rule.
qb = bº + 2ab
20(103) = 103º + 2(20)(103)

Step 3: Solve the equation.
20(103) = 103^1 + 2(20)(103)
20(103) = 103 + 2(20)(103)

Step 4: Perform the calculations.
20(103) = 103 + 2(2060)
20(103) = 103 + 4120

Step 5: Simplify the expression.
20(103) = 4223

The result of the operation 20(103) is 4223. This answer is not among the given options, but please double-check the question and the provided options to make sure there are no errors.

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Answer:

3 indian menus

Step-by-step explanation:

If we assume that the proportions would remain the same then we can use the values provided to calculate the number of indian menus. We can use the Rule of Three in this scenario, since it is a ratio problem and we are given 3 values and a variable. We simply multiply the diagonal values and divide by the remaining value to get the variable.

20 menus   <====>   4 indian menus

15  menus   <====>   x indian menus

(15 * 4) / 20 = x

60 / 20 = x

3 = x

To solve the given problems, we'll use the properties of the normal distribution with mean μ = 100 and standard deviation σ = 10.

a. Probability that X > 85:

To find this probability, we need to calculate the area under the normal curve to the right of 85. We can use the standard normal distribution table or a calculator to find the corresponding z-score and then use the z-table to find the probability.

First, let's calculate the z-score:

z = (X - μ) / σ

z = (85 - 100) / 10

z = -15 / 10

z = -1.5

Using the z-table or a calculator, we find that the probability of Z > -1.5 is approximately 0.9332.

Therefore, the probability that X > 85 is 0.9332 (rounded to four decimal places).

b. Probability that X < 80:

Similarly, we'll calculate the z-score for X = 80:

z = (X - μ) / σ

z = (80 - 100) / 10

z = -20 / 10

z = -2

Using the z-table or a calculator, we find that the probability of Z < -2 is approximately 0.0228.

Therefore, the probability that X < 80 is 0.0228 (rounded to four decimal places).

c. Probability that X < 90 or X > 130:

To calculate this probability, we'll find the individual probabilities of X < 90 and X > 130, and then subtract the probability of their intersection.

For X < 90:

z = (90 - 100) / 10

z = -10 / 10

z = -1

Using the z-table or a calculator, we find that the probability of Z < -1 is approximately 0.1587.

For X > 130:

z = (130 - 100) / 10

z = 30 / 10

z = 3

Using the z-table or a calculator, we find that the probability of Z > 3 is approximately 0.0013.

Since these events are mutually exclusive, we can add their probabilities:

P(X < 90 or X > 130) = P(X < 90) + P(X > 130)

P(X < 90 or X > 130) = 0.1587 + 0.0013

P(X < 90 or X > 130) = 0.1600

Therefore, the probability that X < 90 or X > 130 is 0.1600 (rounded to four decimal places).

d. 99% of the values are between what two X-values (symmetrically distributed around the mean)?

To find the two X-values, we need to find the corresponding z-scores for the cumulative probabilities of 0.005 and 0.995. These probabilities correspond to the tails beyond the 99% range.

For the left tail:

z = invNorm(0.005)

z ≈ -2.576

For the right tail:

z = invNorm(0.995)

z ≈ 2.576

Now we can find the corresponding X-values:

X1 = μ + z1 * σ

X1 = 100 + (-2.576) * 10

X1 = 100 - 25.76

X1 ≈ 74.24

X2 = μ + z2 * σ

X2 = 100 + 2.576 * 10

X2 = 100 + 25.76

X2 ≈ 125.76

Therefore, 99% of the values are greater than 74.24 and less than 125.76 (rounded to two decimal places).

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Without specific data on the number of students who prefer each option, we cannot calculate the probability.

To determine the probability that a student prefers the zoo or the water park, we need to know the total number of students and the number of students who prefer each option. Without this information, it is not possible to calculate the probability accurately.

To calculate the probability, we would need to divide the number of students who prefer the zoo or the water park by the total number of students. For example, if there are 50 students in total and 30 prefer the zoo and 20 prefer the water park, the probability would be:

P(prefer zoo or water park) = (30 + 20) / 50 = 50 / 50 = 1

However, without specific data on the number of students who prefer each option, we cannot calculate the probability.

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The required, Mmusi borrowed R3000 from Aggie as per the given conditions.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan.

Amount = Principal [1 + rate×time]

Let's call the amount Mmusi borrowed from Aggie "P".

After two years, he has to pay back
= P + P * 18% * 2
= P + 0.18 * P * 2
= P + 0.36P
= 1.36P

So if he has to pay back R4080, we can set up an equation to solve for P:

1.36P = 4080

To find P, we can divide both sides by 1.36:

P = 4080 / 1.36 = 3000

So Mmusi borrowed R3000 from Aggie.

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Answer:

x > - 4

Step-by-step explanation:

5x + 7 > - 13 ( subtract 7 from both sides )

5x > - 20 ( divide both sides by 5 )

x > - 4

Answer:

Step-by-step explanation:

a = 16 inches

NEAREST TENTH: 20

Therefore,Total patients with pneumonia or bronchitis = 25 + 30 - 10= 45Thus, there are a total of 45 patients diagnosed with pneumonia or bronchitis or both.

Among 50 patients admitted to a clinic, 25 are diagnosed with pneumonia, 30 with bronchitis, and 10 with both pneumonia and bronchitis. The number of patients with pneumonia or bronchitis (or both) can be determined as follows:Let A denote the number of patients diagnosed with pneumonia and B denote the number of patients diagnosed with bronchitis.

According to the inclusion-exclusion principle, the total number of patients with pneumonia or bronchitis is given by:Total patients with pneumonia or bronchitis = \(A + B - (A ∩ B)\)where A ∩ B represents the intersection of the sets A and B.In this case, A = 25, B = 30, and A ∩ B = 10.

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Answer:

Option D.

Step-by-step explanation:

We have the function:

f(x) = -a*(x + b)^(1/2)

Where:

a > 0

b > 0

Now, as a is positive and we have the coefficient "-a", we will have that the function is always negative.

Why? because (x + b)^(1/2) is always positive.

then: -a*(x + b)^(1/2) is always negative.

We also should see that the domain is not the set of all real numbers, because if:

x + b < 0, then we have the square root of a negative number, and we know that this is a complex number.

The only option that meets these two conditions is option D.

Answer

C

Step-by-step explanation:

Got it mf wrong

Answer:

x=-2

Step-by-step explanation:

Answer:

A pentagon, any side with 5 sides is a pentagon.

Step-by-step explanation:

Answer:

118

Step-by-step explanation:

33+29 = 62

180 - 62 = 118

Answer:

Step-by-step explanation:

Corresponding angles and sides of ΔMNP and ΔUVW are congruent:

The triangles are congruent by SAS. One side and angle marked as congruent and another side is congruent as common to both.

Corresponding sides are congruent:

Given ∠C ≅ ∠D

In order to prove the congruence of ΔAED and ΔBEC by ASA we need another angle and the included side to be congruent.

We can observe ∠AED ≅ ∠BEC as vertical angles.

Additional information we need is:

Triangles ABC and ADC are congruent by SAS:

Therefore corresponding sides BC and CD are also congruent

Perimeter of ABCD is:

Answer:

Free to use your own personal information ℹ to help you find the best deal for the your business in the word of the day you free to do it and you can get a ghost 500k for your invitation or your personal life to make a name for your family and your family Merry Christmas and Happy New Year to you and your family Merry are you the

Answer: its 18, x=18

Answer:

Step-by-step explanation:

\(Selling \:price = 3000gh Cedis\\Profit \% = 25\%\\Cost\:price =?\\\\CP =\frac{ ( Selling\:price \times 100 )}{ ( 100 + percentage profit)} \\\\C.P = \frac{3000\times 100 }{100+25}\\\\ C.P = \frac{300000}{125} \\\\Cost\: Price = 2400gh Cedis\)

Answer:

The number Gavin was thinking of is -78.

Step-by-step explanation:

-78 +1= -77

-77/7 = -11

To solve I did:

-11 * 7

-77

-77-1= -78

When throwing a pair of dice, there are a total of 6 sides on each die, which gives us 6 x 6 = 36 possible outcomes. The total number of spots (the sum of the numbers on the dice) can range from 2 to 12.

When a pair of dice are thrown, there are three possible outcomes for the total number of spots: 1) The sum of the spots on both dice is less than 7. This occurs when the first dice lands on a number between 1 and 6, and the second dice lands on a number that will make the total less than 7 (e.g. if the first dice lands on 3, then the second dice must land on a number less than or equal to 3).  2) The sum of the spots on both dice is exactly 7. This occurs when the first dice lands on a number between 1 and 6, and the second dice lands on the number that will make the total equal to 7 (e.g. if the first dice lands on 2, then the second dice must land on 5).  3) The sum of the spots on both dice is greater than 7. This occurs when the first dice lands on a number between 1 and 6, and the second dice lands on a number that will make the total greater than 7 (e.g. if the first dice lands on 4, then the second dice must land on a number greater than 3).

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To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer:

4x+3y-23=0

Step-by-step explanation:

4x+3y-23=23-23

4x+3y-23=0

Answer:

m = 2

Step-by-step explanation:

∠ GLI = 90°

∠ GLH + ∠ HLI = ∠ GLI , that is

9m + 25m + 22 = 90

34m + 22 = 90 ( subtract 22 from both sides )

34m = 68 ( divide both sides by 34 )

m = 2

Then

∠ HLG = 9m = 9 × 2 = 18°

Answer:

Somebody once told me the world is gonna roll me

I ain't the sharpest tool in the shed

She was looking kind of dumb with her finger and her thumb

In the shape of an "L" on her forehead

Well the years start coming and they don't stop coming

Fed to the rules and I hit the ground running

Didn't make sense not to live for fun

Your brain gets smart but your head gets dumb

So much to do, so much to see

So what's wrong with taking the back streets?

You'll never know if you don't go

You'll never shine if you don't glow

Hey now, you're an all-star, get your game on, go play

Hey now, you're a rock star, get the show on, get paid

And all that glitters is gold

Only shooting stars break the mold

It's a cool place and they say it gets colder

You're bundled up now, wait 'til you get older

But the meteor men beg to differ

Judging by the hole in the satellite picture

The ice we skate is getting pretty thin

The water's getting warm so you might as well swim

My world's on fire, how about yours?

That's the way I like it and I'll never get bored

Hey now, you're an all-star, get your game on, go play

Hey now, you're a rock star, get the show on, get paid

All that glitters is gold

Only shooting stars break the mold

Hey now, you're an all-star, get your game on, go play

Hey now, you're a rock star, get the show, on get paid

And all that glitters is gold

Only shooting stars

Somebody once asked could I spare some change for gas?

I need to get myself away from this place

I said, "Yup" what a concept

I could use a little fuel myself

And we could all use a little change

Well, the years start coming and they don't stop coming

Fed to the rules and I hit the ground running

Didn't make sense not to live for fun

Your brain gets smart but your head gets dumb

So much to do, so much to see

So what's wrong with taking the back streets?

You'll never know if you don't go (go!)

You'll never shine if you don't glow

Hey now, you're an all-star, get your game on, go play

Hey now, you're a rock star, get the show on, get paid

And all that glitters is gold

Only shooting stars break the mold

And all that glitters is gold

Only shooting stars break the mold

Step-by-step explanation:

Answer:

B. √x.

Step-by-step explanation:

That would be B - the square root of x.

The particular solution to the given differential equation is y^2 = x^2 + y0^2, where y0 is the initial value of y at x = 0.

The given differential equation is dy/dx = x/y, where y cannot equal 0. It is a separable differential equation that can be solved by rearranging terms and integrating both sides.

To solve the differential equation dy/dx = x/y, we can begin by rearranging the equation to separate the variables. Multiplying both sides by y and dx, we get y dy = x dx. Now, we can integrate both sides:

∫y dy = ∫x dx

Integrating, we obtain (1/2)y^2 = (1/2)x^2 + C, where C is the constant of integration. Simplifying this equation, we have y^2 = x^2 + C.

To find the particular solution, we need an initial condition. Let's assume that at x = 0, y = y0. Substituting these values into the equation, we get y0^2 = 0^2 + C, which gives C = y0^2.

Therefore, the particular solution to the given differential equation is y^2 = x^2 + y0^2, where y0 is the initial value of y at x = 0.

It's important to note that the solution is valid as long as y ≠ 0, as division by zero is undefined.

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The inequalities will be 2t + s ≤ 50 and 3t + 5s ≤ 150

We are given that,

It costs her $3 to make one T-shirt

and

it costs her $5 to make each sweatshirt

number of T-shirts = 3t

number of sweatshirts = 5s

her budget for the month is given to be $150 for materials for shirts

thus, according to the question,

we have

3t + 5s ≤ 150

we are also given that

it takes Amanda 2 hours to sew a t-shirt

and

it takes Amanda 1 hour to sew the sweatshirt,

but because she is booked with other projects for the month she only has 50 hours to sew the shirts.

2t + s ≤ 50

thus the inequalities will be 2t + s ≤ 50 and 3t + 5s ≤ 150

What are inequalities?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality.

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Answer:

You can use the distance formula to find the slope. The distance formula is Y2-Y1/X2-X1. So, -16-(-8)/-8-(-10)=-8/2=-4. The slope of the line is -4.

:)