Simplify the expression
4 + 3(x + 2)

Answer:

the second one is 46 each

Step-by-step explanation:

360-(88+88)

92/2=46

The weight of the package is 15 pound.

What is an linear equation?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.

Given that the fees for sending a package by media mail

For first pound : $2.41

For the next six pounds: $0.41 per pound

For additional pound: $0.39 per pound

The cost of first 7 pounds is = $(2.41 + (0.41 × 6)) =$4.87

$4.87 < $7.99. Thus the weight of the package is more than 7 pounds

Assume that, the weight of the package is (7 + x) pound.

The fee for (7 + x) pounds package is $(4.87 + 0.39x)

According to the question:

4.87 + 0.39x = 7.99

Subtract 4.87 from both sides:

0.39x = 3.12

Divide both sides by 0.39

x = 8

The weight of the package is (8 + 7) = 15 pounds.

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Answer:

9 and 6

Step-by-step explanation:

Answer:

$150

Step-by-step explanation: 11.25 divided by tax rate of 7.5 % equals 150

Answer:

When we have a rotation about a given point, the distance between the rotated point and the axis of rotation will remain constant, the only thing that changes is the coordinates of the point.

This tell us that the main measures of any rotated shape will not change.

Then the side lengths will remain constant, this implies that the area also remains constant, and this also means that the angle measures should remain the same.

And because the perimeter is equal to the sum of all the side lengths, the perimeter also remains the same.

The only thing that changes will be the coordinates of our polygon.

Answer:

I. 1) 32124, 32456, 32532, 32934, 32983

 2) 62279, 62312, 62345, 62387, 62398

 3) 89123, 90246, 89345, 89534, 89923

 4) 19087, 19216, 19312, 19432, 19910

 5) 31821, 31839, 31861, 31876, 31890

II. 1) 58240, 58204, 58042, 58024

  2) 10908, 10809, 10098, 10089

  3) 85703, 85370, 85307, 85073

  4) 98705, 98570, 98507, 98057

  5) 41810, 41108, 41081, 41018

Step-by-step explanation:

Answer:

Answer:

8b

Step-by-step explanation:

You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:

\(\displaystyle{16b-8b=\left(16-8\right)b}\)

Then evaluate and simplify:

\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)

\(\frac15v+\frac3{10}v=\frac2{10}v+\frac3{10}v=\frac5{10}v=\frac12v\)

Answer:

Bus 1 is traveling faster.

Step-by-step explanation:

The information provided states that Bus 1 travels at 55 miles per hour. The graph shows that Bus 2 travels less than 50 miles per hour. This shows that Bus 1 travels more miles per hour.

Hope it helps!

It is true that the variance is the simplest measure of dispersion and is computed as the difference between the maximum value and the minimum value in the data set.

Variance is a measure of dispersion that, in contrast to range and interquartile range, accounts for the spread of all data points in a data collection. Along with the standard deviation, which is just the square root of the variance, it is the measure of dispersion that is most frequently employed. The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other.

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Answer:

5.048

5.48

5.4871

5.7

Step-by-step explanation:

5.48 is 0.0071 less than 5.4871

Answer:

b≤3

Step-by-step explanation:

For this problem, you want to solve it similarly to linear equations.

We start with 4b+6≤18.

Subtracting 6 from both sides gives 4b≤12.

From there, in order to isolate the b, we must divide both sides by 4, leaving b≤3.

**This content involves solving linear inequalities, which you may wish to revise. I'm always happy to help!

Answer:

The cylinder with maximum volume has a radius of √(20 / 3π) and a height of 0. The maximum volume is V = π(20 / 3π)^2(0) = 0

Step-by-step explanation:

Let's assume the height of the cylinder is also variable and denoted by "h", and the radius of the cylinder is denoted by "r". The surface area of the cylinder is given by:

A = 2πrh + 2πr^2

The cost of the packaging is $0.10 per square cm, and the total cost of packaging should not exceed $4. Therefore, we can write:

0.10(2πrh + 2πr^2) ≤ 4

Simplifying this inequality, we get:

πrh + πr^2 ≤ 20

Now, we want to maximize the volume of the cylinder, which is given by:

V = πr^2h

Using the inequality we derived above, we can express h in terms of r:

h ≤ (20 - πr^2) / πr

Substituting this expression for h in the formula for V, we get:

V = πr^2[(20 - πr^2) / πr]

Simplifying this expression, we get:

V = 20r - πr^3

To find the maximum volume, we need to find the value of r that maximizes V. To do this, we take the derivative of V with respect to r and set it equal to zero:

\(dv/dr\)= 20 - 3πr^2 = 0

Solving for r, we get:

r = √(20 / 3π)

Substituting this value of r back into the inequality we derived earlier, we can find the corresponding value of h:

h = (20 - πr^2) / πr

h = (20 - 20) / (√(3π))

h = 0

Therefore, the cylinder with maximum volume has a radius of √(20 / 3π) and a height of 0. The maximum volume is V = π(20 / 3π)^2(0) = 0

Note that this means the cylinder has no volume and therefore cannot be packaged. In other words, it is not possible to design a cylindrical package with a volume greater than zero that costs less than $4.

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Answer: 98*

Alternate exterior angles are equal

Answer: 98 degrees

Step-by-step explanation:

98 degrees and x are alternate exterior angles.

The complete solution to the given ordinary differential equation (ODE)is:

\(y(x) = y_h(x) + y_p(x) = 5e^{6x} - 2e^{-2x} + 10e^{-2x} = 5e^{6x} + 8e^{-2x}\)

To solve the second-order ordinary differential equation (ODE) using the method of undetermined coefficients, we assume a particular solution of the form:

\(y_p(x) = A e^{-2x}\)

where A is a constant to be determined.

Next, we find the first and second derivatives of \(y_p(x)\):

\(y_p'(x) = -2A e^{-2x}\\y_p''(x) = 4A e^{-2x}\)

Substituting these derivatives into the original ODE, we get:

\(4A e^{-2x} - 4(-2A e^{-2x}) - 12(A e^{-2x}) = 10e^{-2x}\)

Simplifying the equation:

\(4A e^{-2x} + 8A e^{-2x} - 12A e^{-2x} = 10e^{-2x}\)

Combining like terms:

\((A e^{-2x}) = 10e^{-2x}\)

Comparing the coefficients on both sides, we have:

A = 10

Therefore, the particular solution is:

\(y_p(x) = 10e^{-2x}\)

To find the complete solution, we need to find the homogeneous solution. The characteristic equation for the homogeneous equation y'' - 4y' - 12y = 0 is:

r² - 4r - 12 = 0

Factoring the equation:

(r - 6)(r + 2) = 0

Solving for the roots:

r = 6, r = -2

The homogeneous solution is given by:

\(y_h(x) = C1 e^{6x} + C2 e^{-2x}\)

where C1 and C2 are constants to be determined.

Using the initial conditions y(0) = 3 and y'(0) = -14, we can solve for C1 and C2:

y(0) = C1 + C2 = 3

y'(0) = 6C1 - 2C2 = -14

Solving these equations simultaneously, we find C1 = 5 and C2 = -2.

Therefore, the complete solution to the given ODE is:

\(y(x) = y_h(x) + y_p(x) = 5e^{6x} - 2e^{-2x} + 10e^{-2x} = 5e^{6x} + 8e^{-2x}\)

The question is:

Use the method of undetermined coefficients to solve the second order ODE y'' - 4 y' - 12y = 10\(e ^{- 2x}\), y(0) = 3, y' (0) = - 14

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The probability that Zack randomly selects 4 chocolate pastries out of 8 pastries from a population of 20 pastries, of which 12 are chocolate, is approximately 0.206 or 20.6%.

The hypergeometric distribution can be used to calculate the probability of selecting a certain number of objects with a specific characteristic from a population of objects with and without the characteristic, without replacement.

The probability of Zack selecting 4 chocolate pastries out of 8 randomly chosen pastries from a population of 20 pastries, of which 12 are chocolate.

The probability mass function of the hypergeometric distribution is:

\(P(X = k) = (C(N_1,k) \times C(N_2,n - k)) / C(N,n)\)

where:

X is the random variable representing the number of pastries that are chocolate in the sample of 8

k is the number of chocolate pastries in the sample of 8 (in this case, k = 4)

N₁ is the number of chocolate pastries in the population (in this case, N₁ = 12)

N₂ is the number of non-chocolate pastries in the population (in this case, N₂ = 20 - 12 = 8)

n is the sample size (in this case, n = 8)

N is the total number of pastries in the population (in this case, N = 20)

Plugging in the values, we get:

\(P(X = 4) = (C(12,4) \times C(8,8 - 4)) / C(20,8)\)

\(P(X = 4) = (495 \times 70) / 167,960\)

P(X = 4) ≈ 0.206

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Answer:

True

Step-by-step explanation:

At hour 9, the temperature recorded was = 75 degrees

At hour 13, the temperature recorded was = 95 degrees

The rate of change = Change in the temperature / Change in the time

⇒ The rate of change = 95 - 75 degrees / 13 - 9 hour

⇒ The rate of change = 20 degrees / 4 hours

⇒ The rate of change = 5 degrees per hour

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In the inpatient setting, a CPT code (Current Procedural Terminology) would typically be assigned by the hospital for a procedure code to accurately bill for the services provided during the patient's stay.

This code is used to describe the specific medical service or procedure performed, such as a surgery or diagnostic test. It is important for hospitals to accurately assign CPT codes to ensure proper billing and reimbursement for the services provided. Additionally, the use of standardized CPT codes helps to facilitate communication and record-keeping across different healthcare providers and facilities.

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Answer: A range of values, created using sample, within which population parameter has a certain probability of occurring.

Reason: E.g. P(a<x>b) = 0.95

confidence interval is A range of values, is created using a sample, within a population parameter that has a certain probability of occurring.

A sampling method's degree of certainty or uncertainty is measured by confidence intervals. In statistics, the probability that a population parameter will fall between a set of values for a certain percentage of the time is referred to as a confidence interval. Confidence intervals that contain either 95% or 99% of expected observations are frequently utilized by analysts. To comprehend the statistical significance of their estimates, inferences, or predictions, statisticians and other analysts employ confidence intervals.

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To find the sum of fractions, we need to have a common denominator. In this case, the common denominator is 7 * (-11) * 21 * 22 = -230,514.

Now we can add the fractions:

\(\displaystyle \frac{3}{7} + \frac{6}{-11} + \frac{-8}{21} + \frac{5}{22} = \frac{3 \cdot (-11) \cdot 21 \cdot 22}{7 \cdot (-11) \cdot 21 \cdot 22} + \frac{6 \cdot 7 \cdot (-21) \cdot 22}{-11 \cdot 7 \cdot (-21) \cdot 22} + \frac{-8 \cdot 7 \cdot (-11) \cdot 22}{21 \cdot 7 \cdot (-11) \cdot 22} + \frac{5 \cdot 7 \cdot (-11) \cdot 21}{22 \cdot 7 \cdot (-11) \cdot 21}\)

Simplifying the fractions:

\(\displaystyle \frac{-1386}{-230514} + \frac{1848}{-230514} + \frac{-1936}{-230514} + \frac{1155}{-230514}\)

Combining the fractions:

\(\displaystyle \frac{-1386 + 1848 - 1936 + 1155}{-230514}\)

Simplifying the numerator:

\(\displaystyle \frac{-319}{-230514}\)

Dividing the numerator and denominator:

\(\displaystyle \frac{319}{230514}\)

Therefore, the sum of the fractions 3/7, 6/-11, -8/21, and 5/22 is 319/230514.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The slope of the regression line predicting y from x is 0.30.

Given that,

x              y

29          215

62          225

75          173

99         129

108        111

So, the coordinate points are (29, 215) and (62, 225)

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here, slope = (225-215)/62-29)

= 10/33

= 0.30

Therefore, the slope of the regression line predicting y from x is 0.30.

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Answer:

8

Step-by-step explanation:

Answer: C: 4/5

Step-by-step explanation: You can use the bar in the fraction as a dividing symbol.

Answer:  C, four fiths, 4/5

Step-by-step explanation:

The equation of the tangent line to the astroid at the point (-3√3, 1) is: y = -(3√3)^(1/3)x - 3(3√3)^(1/3) + 1

To find the equation of the tangent line to the astroid at the point (-3√3, 1), we need to first find the slope of the tangent line.

We can do this by taking the derivative of the equation of the astroid with respect to x, and then evaluating it at the point (-3√3, 1).

Taking the derivative of x²/³ + y²/³ = 4 with respect to x, we get:

(2/3)x^(-1/3) + (2/3)y^(-1/3) * dy/dx = 0

Solving for dy/dx, we get:

dy/dx = (-x^(1/3))/y^(1/3)

Substituting x = -3√3 and y = 1, we get:

dy/dx = (-(-3√3)^(1/3))/(1^(1/3)) = -(3√3)^(1/3)/1

So the slope of the tangent line at the point (-3√3, 1) is -(3√3)^(1/3).

Now we can use the point-slope form of the equation of a line to find the equation of the tangent line. The point-slope form is:

y - y1 = m(x - x1)

Substituting x1 = -3√3, y1 = 1, and m = -(3√3)^(1/3), we get:

y - 1 = -(3√3)^(1/3)(x + 3√3)

Simplifying, the equation of the tangent line to the astroid at the point (-3√3, 1) is:

y = -(3√3)^(1/3)x - 3(3√3)^(1/3) + 1

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Answer:

13

Step-by-step explanation:

There are 2 rearrangements of abcd in which no two adjacent letters are also adjacent letters in the alphabet.

What is letter arrangements?

A sorting technique that allows the person to arrange alphabets as conditioned according to the question. Then total arrangements are calculated to know the result.

According to the given question:

Using XXXX as stencil for letters arrangement

We can't put B in either of the middle positions, as there would only be the far end at which to put both A and C and we can't put two things in one slot. That is, XBXX would require A and C to both be in the red X in order to avoid putting them next to B...can't do that, so B can't go in the middle.

Similarly, we can't put C in either of the middle positions, as there would only be the far end at which to put both B and D and we can't put two things in one slot.

So, B and C must go on the ends.

BXXC can only be filled in as BDAC.

CXXB can only be filled in as CADB.

Hence there are 2 such arrangements.

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The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.

Given that the population mean, \(\mu\) = 90 wpm

The standard deviation of the population ,\(\sigma\) = 10

Sample size, n = 12

Sample mean, \(\bar x\) = 95

The reading rate of students follows the normal distribution.

Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)

        = \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)

        = 1.732

Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)

                                                                                       = P(z>1.732)

                                                                                       = 1- P(z<1.732)

                                                                                       = 0.4582

[The value 0.4582 found from the area under the normal curve using tables].

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