A laptop has a listed price of $549.98 before tax. If the sales tax rate 9.5%, find the total cost of the laptop with sales tax included. Round your answer to the nearest cent, as necessary

Answer: a. P (x<30) = 0.5276

              b. P (30<x<35) = 0.0555

Step-by-step explanation: An exponential distribution is a distribution of time in which events happens at a constant average rate.

The rate is calculated as

\(\lambda=\frac{1}{\mu}\)

with μ as the mean.

The probability density distribution for this type of distribution is

\(f(x)=\lambda e^{-\lambda x}\)

And probability is calculated as

\(P(X<x)=1-e^{-\lambda x}\)

For tuning of an engine, the rate is

\(\lambda=\frac{1}{40}\)

λ = 0.025

a. Probability of less than 30 minutes:

\(P(X<30)=1-e^{-0.025.30}\)

\(P(X<30)=1-e^{-0.75}\)

P (X < 30) = 0.5276

Probability of tuning in 30 minutes or less is 52.76%.

b. Probability of between 30 and 35 can be described as

\(P(30<X<35)=P(X<35)-P(X<30)\)

\(P(X<35)=1-e^{-0.025*35}\)

\(P(X<35)=1-e^{-0.875}\)

P (X < 35) = 0.5831

P (X < 30) = 0.5276

Then:

\(P(30<X<35)=0.5831-0.5276\)

P (30 < X < 35) = 0.0555

Probability of tuning an engine between 30 and 35 minutes is 5.55%.

Answer:

±94

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

x  (1st consecutive term)

x + 2 (2nd consecutive term)

Step 2: Set up equation

x(x + 2) = 2208

Step 3: Solve for x

Step 4: Identify Consecutive Integers

Possibility 1: x = -48

1st Consecutive Even Term: -48

2nd Consecutive Even Term: -48 + 2 = -46

Possibility 2: x = 46

1st Consecutive Even Term: 46

2nd Consecutive Even Term: 46 + 2 = 48

Step 5: Find sums

Possibility 1: x = -48

-48 + -46 = -94

Possibility 2: x = 46

46 + 48 = 94

Answer:

H0 : μ2004 - μ2000 = 0

Step-by-step explanation:

Given the data:

Year ________: 2000 ___ 2004

Mean ________ 27.34 ___ 48.12

Std. Dev _______10.11 ____ 19.23

Unweighted n 43 54

The hypothesis is to test if there was a significant difference in the average number of hours worked in a week from 2000 to 2004 ;

Hence, the null hypothesis will negate the hypothesis, that is there is no difference in the average hours worked in a week from 2000 to 2004

Null hypothesis ; H0 : μ2 - μ1 = 0

Alternative hypothesis ; H1 : μ2 - μ1 ≠ 0

Null hypothesis suggest that there is no significant relationship exist in the given set of single observed variable.. As the null hypothesis negate the hypothesis. Hence the difference is zero and hypothesis for the given problem is,

\(H_0; (\mu_1-\mu_2)=0\)

\(H_a; (\mu_1-\mu_2)\neq 0\)

For year                     2000         2004

Mean                          27.34          48.12

Standard Deviation   10.11          19.23

Unweighted n             43              54

Null hypothesis suggest that there is no significant relationship exist in the given set of single observed variable.

Now the Analyst want to know if there was a significant difference in the average of hours worked in a week from year 2000 to 2004.

To detect a difference (if there it is) between the average of hours worked in a week from 2000 to 2000, it should be test the null hypothesis that there is no difference between the means against the alternative hypothesis. Therefore,

\(H_0; (\mu_1-\mu_2)=D_0=0\)

Versus

\(H_a; (\mu_1-\mu_2)\neq 0\)

As the null hypothesis negate the hypothesis. Hence the difference is zero and hypothesis for the given problem is,

\(H_0; (\mu_1-\mu_2)=0\)

\(H_a; (\mu_1-\mu_2)\neq 0\)

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9514 1404 393

Answer:

Step-by-step explanation:

The average speed with the wind is (540 mi)/(2 h) = 270 mi/h.

The average speed against the wind is (540 mi)/(3 h) = 180 mi/h.

Let a and w represent the speeds of the airplane and wind, respectively.

  a + w = 270 . . . . speed with the wind

  a - w = 180 . . . . speed against the wind

  2a = 450 . . . . . . sum of the two equations

  a = 225 . . . . . . divide by 2

  w = a -180 = 45

The speed of the airplane is 225 miles per hour; the speed of the wind is 45 miles per hour.

Answer:x/6 + 1 = 4

x= 18

7x+ 4=11

x=1

Step-by-step explanation:

For both questions do  inverse operation.

Look at pic to see how it was solved ;)

hope it helps

Due to length restrictions, we kindly invite to see the explanation of this question to know how to simplify rational numbers to powers with least base.

In this question we have rational numbers to be simplified as powers of least base by means of factor decomposition and algebra properties for rational numbers and powers:

1) 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶

2) 625 = 5 × 5 × 5 × 5 = 5⁴

3) 1 / 9 = 1 / (3 × 3) = (3 × 3)⁻¹ = (3²)⁻¹ = 3⁻²

4) 1 / 16 = 1 / (2 × 2 × 2 × 2) = 1 / 2⁴ = (2⁴)⁻¹ = 2⁻⁴

5) 27 = 3 × 3 × 3 = 3³

6) 0.01 = 1 / 100 = 1 / (2 × 2 × 5 × 5) = 1 / (2² × 5²) = 1 / (2 × 5)² = [(2 × 5)²]⁻¹ = (2 × 5)⁻² = 10⁻²

7) 216 =2³ × 3³ = (2 × 3)³ = 6³

8) 1 / 81 = 1 / 3⁴ = (3⁴)⁻¹ = 3⁻⁴

9) 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁸

10) 1 / 49 = 1 / 7² = (7²)⁻¹ = 7⁻²

11) 1 / 2 = 2⁻¹

12) 1000 = 2 × 2 × 2 × 5 × 5 × 5 = 2³ × 5³ = (2 × 5)³ = 10³

13) 1 / 32 = 1 / (2 × 2 × 2 × 2 × 2) = 1 / 2⁵ = (2⁵)⁻¹ = 2⁻⁵

14) 1 / 25 = 1 / (5 × 5) = 1 / 5² = (5²)⁻¹ = 5⁻²

15) 0.1 = 1 / 10 = 1 / (2 × 5) = (2 × 5)⁻¹ = 10⁻¹

16) 243 = 3⁵

17) (1 / 4)ˣ = [1 / (2 × 2)]ˣ = [1 / 2²]ˣ = (2⁻²)ˣ = 2⁻²ˣ

18) (36)³ˣ = (2 × 2 × 3 × 3)³ˣ = (2² × 3²)³ˣ = [6²]³ˣ = 6⁶ˣ

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Answer:

109

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

because this shapes angle would be out of 360 so you do 360-83-85-69=123 is the answer you get.

hope it make sense:)

Answer:

B

Step-by-step explanation:

a,b and c are the sides of a triangle if it satisfies:

a<b+c  , b<a+c and c<b+a

Here, a=4 and b=7

We have to find c

i.e. all those c which satisfies:

4<7+c , 7<4+c and c<4+7=11

A.3   it is not true since it doesn't satisfies second inequality

B.5   it is true

C.7   it is true

D.9   it is true

E.11   This is clearly false, since it doesn't satisfies inequality third

F.17 This is clearly false, since it doesn't satisfies inequality third

Hence, correct options are:

B.5

C.7

D.9

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Answer:

0.000174

3.5841 x 10^7

4.67  x 10^6

Step-by-step explanation:

1.74 x 10^-4 as an ordinary number

As an ordinary number, the decimal point will be moved 4 times to the left due to the negative power

Hence 1.74 x 10^-4 as an ordinary number

= 0.000174

358.41 x 10^5 in a standard form

In standard form, only one number will be before the decimal point, the number of times the decimal point is moved (to ensure that only the first digit is before the point) is added to the power of ten. Hence

358.41 x 10^5 in a standard form

= 3.5841 x 10^5+2

= 3.5841 x 10^7

4 670 000 in a standard form

As done above, only one digit will be before the decimal

4 670 000 in a standard form

= 4.67  x 10^6

We can say that the domain of f(x) is (-∞, ∞), which means that any real number can be plugged into the function and it will produce a valid output.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

The function f(x) = -x³ + 6x² -10x + 4 is a polynomial function, which means that it is defined for all real values of x. Unlike some functions (such as square roots or logarithms) which have restrictions on their input values, a polynomial function can take any real number as an input.

To express the domain of the function in interval notation, we use the notation (-∞, ∞), which represents all real numbers. The symbol ∞ stands for infinity, and the open interval notation with the parentheses indicates that there are no specific endpoints for the domain; it extends indefinitely in both directions along the real number line.

Therefore, we can say that the domain of f(x) is (-∞, ∞), which means that any real number can be plugged into the function and it will produce a valid output.

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The range of the function is {1,-1,10} for function f(x)=2x³−3x .

A relation is a function if it has only One y-value for each x-value.

In a function what can go into a function is called the Domain. What may possibly come out of a function is called the Codomain. What actually comes out of a function is called the Range.

The given function is f(x)=2x³−3x

The domain is {-1,1,2}

Now f(-1)=2(-1)³-3(-1)

=-2+3=1

f(1)=2(1)³-3(1)=2-3=-1

f(2)=2(2)³-3(2)=16-6=10

Hence, the range of the function is {1,-1,10} for  f(x)=2x³−3x .

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The correct option is; Associative Property of Addition.

For the given question;

The equation formed by the given statement is -

5 + [(-3x) + 4] = [5 + (-3x)] + 4

Observe the stated equation and comparing with the general equation;

The values are arranged in the form of associative addition.

Check the values;

LHS = 5 + [(-3x) + 4] ; simplifying,

5 -3x + 4 = 9 - 3x

RHS =  [5 + (-3x)] + 4 ; simplifying,

5 - 3x + 4 = 9 -3x

As, LHS = RHS and addition is being done.

Thus, the given equation shows the associative property of addition.

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The probability of observing heads when tossing either coin is P(h) = 0.5*P(f) + 0.6*P(b), and the probability of observing tails is P(t) = 0.5*P(f) + 0.4*P(b).

Let's denote the probability of observing heads when tossing the fair coin as P(h|f) and the probability of observing tails when tossing the fair coin as P(t|f). Similarly, we can denote the probability of observing heads when tossing the biased coin as P(h|b) and the probability of observing tails when tossing the biased coin as P(t|b).

In this experiment, the probability of tossing the fair coin is P(f) and the probability of tossing the biased coin is P(b). We can calculate the probability of observing heads as:

P(h) = P(h|f)*P(f) + P(h|b)*P(b)

= 0.5*P(f) + 0.6*P(b).

Similarly, the probability of observing tails is:

P(t) = P(t|f)*P(f) + P(t|b)*P(b)

= 0.5*P(f) + 0.4*P(b).

The probability of observing heads when tossing either coin is P(h) = 0.5*P(f) + 0.6*P(b), and the probability of observing tails is P(t) = 0.5*P(f) + 0.4*P(b).

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Answer:

Alina will get $54

Step-by-step explanation:

132/11 = 12

12x4.5 = 54

The solution to the linear system is c = -6 and d = 3.

To solve the linear system using the elimination strategy, we can eliminate one variable by adding or subtracting the equations. Let's solve the first linear system:

(1) 12c + 28d = 12

(2) -20c + 16d = 168

To eliminate one variable, we can multiply equation (1) by 5 and equation (2) by 3, which will result in opposite coefficients for 'c'. This will allow us to eliminate 'c' when adding the equations together:

(1) 60c + 140d = 60

(2) -60c + 48d = 504

Now, we can add the equations:

(60c + 140d) + (-60c + 48d) = 60 + 504

188d = 564

d = 564/188

d = 3

Substituting the value of 'd' back into equation (1):

12c + 28(3) = 12

12c + 84 = 12

12c = 12 - 84

12c = -72

c = -72/12

c = -6

The solution to the linear system is c = -6 and d = 3.

Now let's analyze the second linear system:

(1) 7x - 3y = 43

(2) 7x - 3y = 13

By comparing the two equations, we can see that they have the same coefficients for both 'x' and 'y', and the constant terms on the right side are different. This means the lines represented by the equations are parallel and will never intersect.

The linear system has no solution.

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Answer:

What's the question?

Step-by-step explanation:

Answer:

3:26 to be on time!

Step-by-step explanation:

If you leave your house at 3:26 am and then walk 34 minutes it will be 4 am

once you get to work.

Answer:

Step-by-step explanation:

13-2x=4x+7                                                                                                          -2x+13=4x+7                                                                                                       (-2x+13)+(-13-4x)=(4x+7)+(-13-4x)                                                                        -2x+13-4x-13=4x+7-13-4x                                                                                

-2x-4x+13-13=4x-4x+7-13                                                                                                  -6x=-6                                                                                                               6x/6=6/6                                                                                                                 x=1                                                                                                    

If the coefficient of determination for any data set is equal to 1, then the sample correlation coefficient for that same data set can be either -1 or +1

The coefficient of correlation is the “R” value which is given in the summary table in the Regression output. R square is also called the coefficient of determination. To find the value of R squared, multiply R by R. In other words, the square of the correlation coefficient is the coefficient of determination. The coefficient of determination is a statistical measurement that examines how differences in one variable can be explained by the difference in a second variable when predicting the outcome of a given event.

Given,

Coefficient of determination= 1

∴ Coefficient of correlation = \(\sqrt{1} = +1 or -1\)

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The value of n, considering the intersecting chords in the circle, is given as follows:

n = 6m.

A chord of a circle is a straight line segment that connects two points on the circle. Specifically, it is a line segment whose endpoints are on the circle. A chord is often denoted by drawing a line segment between the two endpoints, with the segment passing through the interior of the circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Considering the two intersecting chords for the circle in this problem, the value of n is obtained as follows:

5n = 15 x 2

5n = 30

n = 30/6

n = 6m.

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Answer:

Y=-4x 2

Step-by-step explanation:

Answer:

noob dsbhsaghcfddguhfcc

The simplified version of the expression would be 31-w

The numerical part of the expression given is :

Simplifying using Subtraction operation:

Adding the alphabetical part :

Therefore, the simplified form of the expression is 31-w.

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2×y = 2×6= 12 so 2×x = 2×23 = 43 = 113

Step-by-step explanation:

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