what is 6% sales tax on $4929.00

[tex]|\Omega|={_{53}C_3}\cdot 45=\dfrac{53!}{3!50!}\cdot45=\dfrac{51\cdot52\cdot53}{2\cdot3}\cdot45=1054170\\|A|=1\\\\P(A)=\dfrac{1}{1054170}\approx0.00000095\%[/tex]

The residual for the newborn is -0.9148 kg, indicating he is lighter than what the model predicts for his length.

To calculate the residual for the newborn's weight, we first use the least squares regression line equation, which is weight = -5.33 + 0.1926 * length. We then input the newborn's length of 48 cm into the equation to predict the weight.

Predicted weight = -5.33 + (0.1926 * 48) = -5.33 + 9.2448 = 3.9148 kg

The residual is the difference between the actual weight and the predicted weight, so for this newborn, the residual = actual weight - predicted weight = 3 kg - 3.9148 kg = -0.9148 kg.

The negative residual indicates that the newborn weighs less than what the regression model predicts for a boy of 48 cm in length. This could suggest that the child is lighter than average for his length

For this case we must factor the following expression:

[tex]4x ^ 2 + 23x-72[/tex]

We rewrite the middle term as a sum of two terms whose product is [tex]4 * (- 72) = - 288[/tex] and whose sum is 23. These numbers are -9 and +32. So:

[tex]4x ^ 2 + (- 9 + 32) x-72\\4x ^ 2-9x + 32x-72[/tex]

We factor the highest common denominator of each group.

[tex]x (4x-9) +8 (4x-9)[/tex]

We factor taking into account the common term [tex](4x-9):[/tex]

[tex](4x-9) (x + 8)[/tex]

Finally, the factored expression is:

[tex](4x-9) (x + 8)[/tex]

Answer:

Option D

Answer:

The correct answer option is D. (4x – 9)(x + 8).

Step-by-step explanation:

We are given the following polynomial and we are to find its factored form:

[tex]4x^2+23x-72[/tex]

Finding factors of (-72 * 4 = ) -288 such that when added they give a result of 23 and when multiplied it gives a product of -288.

[tex] 4 x ^ 2 + 3 2 x - 9 x - 7 2[/tex]

[tex] 4 x ( x + 8 ) - 9 ( x + 8 ) [/tex]

[tex] ( 4 x - 9 ) ( x + 8 )[/tex]

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given a situation that

If an increase in one variable causes a decrease in another​ variable,

Then, there is inverse relationship.

When one variable is increased whereas other variable falls.

There will be inverse relationship.

Since inverse relation has negative relation.

Then, there is a negative relationship.

Hence, Option 'A' is correct.

An increase in one variable causing a decrease in another indicates a negative relationship between the two variables, characterized by opposite directional movements and graphically represented by a line with a negative slope.

When discussing the correlation between two variables, it is important to consider the direction and type of relationship they share. If an increase in one variable causes a decrease in the other variable, this is defined as a negative relationship. In a negative relationship, the two variables move in opposite directions, meaning that as one variable increases, the other decreases and vice versa.

The relationship is depicted graphically as a line with a negative slope on a graph, where the line descends as it moves from left to right. This situation should not be confused with dependent, direct, or independent relationships, which describe different aspects of variable interaction.

Answer: 0.6767

Step-by-step explanation:

Given : Mean =[tex]\lambda=2[/tex] errors  per page

Let X be the number of errors in a particular page.

The formula to calculate the Poisson distribution is given by :_

[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex]

Now, the probability that a randomly selected page does not need to be retyped is given by :-

[tex]P(X\leq2)=P(0)+P(1)+P(2)\\\\=(\dfrac{e^{-2}2^0}{0!}+\dfrac{e^{-2}2^1}{1!}+\dfrac{e^{-2}2^2}{2!})\\\\=0.135335283237+0.270670566473+0.270670566473\\\\=0.676676416183\approx0.6767[/tex]

Hence, the required probability :- 0.6767

In the attachement, there is what I came up with so far. I think that finding 'a' is non-trivial, if possible at all.

[tex]A_c[/tex] - the area of a circle

[tex]A_{cs}[/tex] - the area of a circular segment

Answer:

- the area of a circle

- the area of a circular segment

Answer:

[tex]2.39\%[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=4\ years\\ P=\$10,000\\A=\$11,000\\ r=?\\n=4[/tex]  

substitute in the formula above  

[tex]11,000=10,000(1+\frac{r}{4})^{4*4}[/tex]  

[tex]1.1=(1+\frac{r}{4})^{16}[/tex]  

Elevated both sides to (1/16)

[tex]1.005975=(1+\frac{r}{4})[/tex]  

[tex]0.005975=\frac{r}{4}[/tex]  

[tex]r=0.005975*4=0.0239[/tex]  

Convert to percent

[tex]0.0239*100=2.39\%[/tex]  

Step-by-step explanation:

The average rate of change of a function f(x) over an interval [a, b] is:

(f(b) − f(a)) / (b − a)

(f(4) − f(0)) / (4 − 0)

(7/17 − -1/5) / 4

(52/85) / 4

13/85

Answer:

yes thank you so much i was struggling so much with this tysm

Step-by-step explanation:

Answer:

  30 connections

Step-by-step explanation:

20 switches with 3 connections each will have a total of 20×3 = 60 connections. That counts each connecting link twice, so only 30 connecting links are required.

Answer:

30 Connections!

Step-by-step explanation:

I did this on AoPs :)

Answer: The required proportion is [tex]\dfrac{172}{523}[/tex] in fraction and [tex]0.329[/tex] in decimals.

Step-by-step explanation:

Since we have given that

Number of suspected criminals is drawn = 523

Number of criminals were captured = 172

We need to find the proportion of people who were caught after being on the 10 Most wanted list.

So, Proportion of people who were caught is given by

[tex]\dfrac{172}{523}\\\\=0.3288\\\\\approx 0.329[/tex]

Hence, the required proportion is [tex]\dfrac{172}{523}[/tex] in fraction and [tex]0.329[/tex] in decimals.

The estimated proportion of suspected criminals caught after being on the FBI's 10 Most Wanted list is 0.329, or 32.9%, based on a sample where 172 out of 523 individuals were captured.

To estimate the proportion of people who were caught after being on the FBI's 10 Most Wanted list, we can use the sample data provided. In the sample, 523 suspected criminals were monitored and 172 were captured. The estimated proportion of individuals caught is calculated by dividing the number of people captured by the total number in the sample.

To find this proportion, we perform the following calculation:

Proportion = Number of people captured / Total number of suspected criminals

Proportion = 172 / 523

Proportion = 0.329 (rounded to three decimal places)

So, the estimated proportion of people who were caught after appearing on the list is approximately 0.329, or 32.9%.

ANSWER

The value of this function at x=-1 is 1

EXPLANATION

The given function is

[tex]f(x) = 3x + 4[/tex]

We want to find the value of this function at x=-1.

We substitute x=-1 into the function to obtain:

[tex]f( - 1) = 3( - 1)+ 4[/tex]

We multiply out to obtain:

[tex]f( - 1) = - 3+ 4[/tex]

[tex]f( - 1) = 1[/tex]

Therefore the value of this function at x=-1 is 1.

Answer:  [tex]f(-1)=1[/tex]

Step-by-step explanation:

Given the linear function f(x):

[tex]f(x)=3x+4[/tex]

By definition. a relation is a function if each input value has only one output value. In this case you need to find the output value for the input value [tex]x=-1[/tex]. In order to do this, you need to substitute this value of the variable "x" into the linear function given.

Then:

When [tex]x=-1[/tex]:

[tex]f(-1)=3(-1)+4[/tex]

Remember the multiplication of signs:

[tex](+)(-)=-\\(+)(+)=+\\(-)(-)=+[/tex]

Then, the value of f(x) when [tex]x=-1[/tex] is:

 [tex]f(-1)=-3+4[/tex]

 [tex]f(-1)=1[/tex]

Answer:

  3x -4y = 2

Step-by-step explanation:

A plot of the points makes it clear that the longest diagonal is BD. The 2-point form of the line through those points can be found by filling in ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (4 -(-2))/(6 -(-2))(x -(-2)) +(-2) . . . . . fill in points B and D

  y = (6/8)(x +2) -2

  4y = 3(x +2) -8 . . . . . .  multiply by 4

  3x -4y = 2 . . . . . . . . . . add 2-4y

Answer: Hence, a) 0,  b) 2, and  c) 0

Step-by-step explanation:

As we know that If the difference of sum of odd places values and sum of even places value is divisible by 11, then the number is itself divisible by 11.

(a) 362,375,__35

Sum of odd places values : 3+2+7+5+x=17+x

Sum of even places values : 6+3+5+3=17

Difference between them is 17+x-17=x

So, x should be 0 to get divisible by 11 as 0 is divisible by 11.

(b) 82,919,__21

Sum of odd places values : 8+9+9+2=28

Sum of even places values : 2+1+x+1=4+x

Difference between them is 28-(4-x)=24-x

So, x should be 2 so, that it becomes 24-2=22 which is divisible by 11.

(c) 57,13__,473

Sum of odd places values : 5+1+x+7=13+x

Sum of even places values : 7+3+4+3=17

Difference between them is 17-(13+x)=4-x

So, x should be 4 so that it becomes 4-4=0 which is divisible by 11.

Hence, a) 0,  b) 2, and  c) 0

Answer:

a) 1/2 = 50%

b) 3/4 = 75%

c)  1 / 52 or 1,9%

Step-by-step explanation:

In a standard deck of cards, there are 52 cards in total:

13 are hearts, 13 are diamonds, 13 are clubs and 13 are spades.

​(a) Compute the probability of randomly selecting a club or spade

How many cards are a club or a spade?

C = 13 clubs + 13 spades = 26 cards

Out of the 52 total, that means that:

P (club or spade) = 26/52 = 1/2 = 50%

​(b) Compute the probability of randomly selecting a club or spade or heart. ​

How many cards are a club or a spade?

C = 13 clubs + 13 spades  + 13 hearts = 39 cards

Out of the 52 total, that means that:

P (club or spade or heart) = 39/52 = 3/4 = 75%

(c) Compute the probability of randomly selecting a two or diamond.

There's only ONE two of diamond in  regular deck of cards, so...

P(2 of diamond) = 1 / 52 or 1,9%

Answer:

3x+5y+2

Step-by-step explanation:

remove the 0

Answer:

  C. zeros below the diagonal

Step-by-step explanation:

Upper echelon form (zeros below the diagonal) corresponds to a system of equations that has one equation in one variable, one equation in two variables, and additional equations in additional variables adding one variable at a time.

The single equation in a single variable is easily solved, and that result can be substituted into the equation with two variables (one of which is the one just found) to find one more variable's value. This back-substitution proceeds until all variable values have been found.

The process of producing such a matrix is called Gaussian Elimination.

__

The back-substitution process effectively makes the matrix be an identity matrix (diagonal = ones; zeros elsewhere) and the added column be the solution to the system of equations.

To solve a system of equations using the matrix method, you transform the augmented matrix to have zeros below the diagonal through Gaussian elimination. Then, you substitute back into the equations to find the solution.

To solve a system of equations using the matrix method, you use elementary row operations to transform the augmented matrix into one with zeros below the diagonal. This is achieved through a method called Gaussian elimination. The goal is to reduce the matrix to its row-echelon form, which leaves zeros below the diagonal. After this reduction, you can then proceed to substitute back into the equations to find the solution.

For example, let's take the system of equations:
x+2y=7
3x-4y=11
This can be represented as an augmented matrix:
[1 2 | 7]
[3 -4 | 11]
Using Gaussian elimination, we can eliminate the '3' below the diagonal by subtracting 3x the first row from the second, getting you:
[1 2 | 7]
[0 -10 | -10]
By substituting, we then find the solutions for the system of equations.

https://brainly.com/question/31978592

#SPJ2

Answer:

88 ft²

Step-by-step explanation:

Area of larger square

10 × 8 = 80

10 × 8 because 10 is the length and 8 because the 6 and 2 rectangle is missing so it wouldn't be 10 × 10

4 × 2 = 8

4 × 2 = 8 because we need to work out the area of the smaller rectangle

80 + 8 = 88

ANSWER

The relation is not a function.

EXPLANATION

The relation is not a function because we have an x-coordinate mapping on to more than one y-coordinate.

This occurs at x=1.

The ordered pairs (1,1) and (1,3) disqualify the relation from being a function.

Hence the relation is not a function.

The coefficient of variation (CV) is calculated as the standard deviation divided by the mean, expressed as a percentage. Calculate the mean and standard deviation for each set of data, then use these to calculate the CV. Round to one decimal place.

The coefficient of variation (CV) is a measure of relative variability. It's calculated as the ratio of the standard deviation to the mean, and it's often expressed as a percentage. We first need to calculate the mean and standard deviation for both sets of data, A and B.

Let's take Set A as an example: Add all the values together and divide by the count (the total number of values) to get the mean. Next, subtract each value by the mean and squared it, then sum all those squared differences. Divide that by the count minus one to get the variance. The standard deviation is the square root of the variance. Finally, the CV is (standard deviation / mean) x 100.

Repeat these steps for Set B.

Remember to always round to one decimal place as requested in the question.

https://brainly.com/question/30883513

#SPJ3

Answer:

The correct option is 2.

Step-by-step explanation:

Let A be the event that the college student belongs to a health club and B be the event that the college student lives off-campus.

The probability that a college student belongs to a health club is 0.3.

[tex]P(A)=0.3[/tex]

The probability that a college student lives off-campus is 0.4.

[tex]P(B)=0.4[/tex]

The probability that a college student belongs to a health club and lives off-campus is 0.12.

[tex]P(A\cap B)=0.12[/tex]

The probability that a college student belongs to a health club OR lives off-campus is

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

[tex]P(A\cup B)=0.3+0.4-0.12[/tex]

[tex]P(A\cup B)=0.58[/tex]

The probability that a college student belongs to a health club OR lives off-campus is 0.58. Therefore the correct option is 2.

Answer:

Step-by-step explanation:

Since we want twice as much Mocha as Decaf, we can create a "bag" that contains 2 lbs of Mocha (at 11.50 each) and 1 lb of Decaf (at 10). The value of this "bag" is then 2×11.50 +10.00 = 33.00. For 181.50, we can buy ...

  181.50/33.00 = 5.5

"bags". This amount is ...

  11 lbs of Arabian Mocha and 5.5 lbs of Columbian Decaf

The answer is A, 71°.

180-109=71

Since m and n are parallel, angles 4 and 6 will add up to 180 degrees - just like angles 4 and 2. Remember that 180 degrees is a straight line: if angles 4 and 6 are put together, they will make a straight line.

Answer:

  A)  -2

Step-by-step explanation:

The form is indeterminate at x=0, so L'Hopital's rule applies. The resulting form is also indeterminate at x=0, so a second application is required.

Let f(x) = x·sin(x); g(x) = cos(x) -1

Then f'(x) = sin(x) +x·cos(x), and g'(x) = -sin(x).

We still have f'(0)/g'(0) = 0/0 . . . . . indeterminate.

__

Differentiating numerator and denominator a second time gives ...

  f''(x) = 2cos(x) -sin(x)

  g''(x) = -cos(x)

Then f''(0)/g''(0) = 2/-1 = -2

_____

I like to start by graphing the expression to see if that is informative as to what the limit should be. The graph suggests the limit is -2, as we found.

Answer:

[tex]F_{yx}=3x^{2} cos(xy)- yx^{3} sin(xy)[/tex]

Step-by-step explanation:

We need to find out the partial differential [tex]F_{yx}[/tex] of [tex]F(x,y)=x^{2}sin(xy)[/tex]

First, differentiate [tex]F(x,y)=x^{2}sin(xy)[/tex] both the sides with respect to 'y'

[tex]\frac{d}{dy}F(x,y)=\frac{d}{dy}x^{2}sin(xy)[/tex]

Since, [tex]\frac{d}{dt}\sin t =\cos t[/tex]

[tex]\frac{d}{dy}F(x,y)=x^{2}cos(xy)\times \frac{d}{dy}(xy)[/tex]

[tex]\frac{d}{dy}F(x,y)=x^{2}cos(xy)\times x[/tex]

[tex]\frac{d}{dy}F(x,y)=x^{3}cos(xy)[/tex]

so, [tex]F_y=x^{3}cos(xy)[/tex]

Now, differentiate above both the sides with respect to 'x'

[tex]F_{yx}=\frac{d}{dx}x^{3}cos(xy)[/tex]

Chain rule of differentiation: [tex]D(fg)=f'g + fg'[/tex]

[tex]F_{yx}=cos(xy) \frac{d}{dx}x^{3} + x^{3} \frac{d}{dx}cos(xy)[/tex]

Since, [tex] \frac{d}{dx}x^{m} =mx^{m-1}[/tex] and [tex] \frac{d}{dt} cost =-\sin t[/tex]

[tex]F_{yx}=cos(xy)\times 3x^{2} - x^{3} sin(xy)\times \frac{d}{dx}(xy)[/tex]

[tex]F_{yx}=cos(xy)\times 3x^{2} - x^{3} sin(xy)\times y[/tex]

[tex]F_{yx}=3x^{2} cos(xy)- yx^{3} sin(xy)[/tex]

hence, [tex]F_{yx}=3x^{2} cos(xy)- yx^{3} sin(xy)[/tex]

Answer:

Overall final score = 77.75% ; Grade = C.

Step-by-step explanation:

The approach to solve this question is to realize that the marks have to be converted into the respective percentages of the whole course. This means that the marks of all the components have to be normalized according to the grading breakdown.

Project Marks = 97/100. Weightage = 15%. So 97*15/100 = 14.55/15.

This means that the student received 14.55 marks in the project out of 15.

Similarly for other components:

Mid-Term Marks = 83/100. Weightage = 15%. So 83*15/100 = 12.45/15.

Homework Marks = 82/100. Weightage = 35%. So 82*35/100 = 28.7/35.

Finals Marks = 63/100. Weightage = 35%. So 63*35/100 = 22.05/35.

After the conversion process, add up the normalized marks, which are now acting as the percentages earned in all the components.

Aggregate Percentage = 14.55 + 12.45 + 28.7 + 22.05 = 77.75%.

According to the grade scale, the student receives a C because 70 is less than 77.75 and 77.75 is less than 80.

Summarizing, the student receives a C at 77.75%!!!

The student gets the Grade 'C' because the aggregate percentage is greater than 70 and less than 80 and this can be determined by using the given data.

Given :

A student's project marks are 97 out of 100 but the weightage of the project marks is 15%. That is:

[tex]=\dfrac{97\times 15}{100}[/tex]

[tex]=14.55[/tex]

So, the project marks are 14.55 out of 15.

A student's homework assignments marks are 82 out of 100 but the weightage of the project marks is 35%. That is:

[tex]=\dfrac{82\times 35}{100}[/tex]

= 28.7

So, homework assignments marks are 28.7 out of 35.

A student's midterm marks are 83 out of 100 but the weightage of the project marks is 15%. That is:

[tex]=\dfrac{83\times 15}{100}[/tex]

= 12.45

So, midterm marks are 12.45 out of 15.

A student's final exam marks are 63 out of 100 but the weightage of the project marks is 35%. That is:

[tex]=\dfrac{63\times 35}{100}[/tex]

= 22.05

So, final exam marks are 22.05 out of 35.

So, the aggregate percentage is given by:

Aggregate Percentage = 14.55 + 12.45 + 28.7 + 22.05 = 77.75%

The student gets the Grade 'C' because the aggregate percentage is greater than 70 and less than 80.

For more information, refer to the link given below:

https://brainly.com/question/22687297

Answer:

5.(3)

Step-by-step explanation:

5.(3)=16/3

Answer:

d

Step-by-step explanation:

Answer:

Quincy

Step-by-step explanation:

Each student is assigned a two digit number, so let's split the random number line into two digit numbers:

59, 78, 44, 43, 12, 15, 95, 40, 92, 33, 00, 04, 67, 43, 18, 02, 61, 05, 73, 96, 16, 84, 33, 84, 54

Now let's identify the numbers between 00 and 29.

59, 78, 44, 43, 12, 15, 95, 40, 92, 33, 00, 04, 67, 43, 18, 02, 61, 05, 73, 96, 16, 84, 33, 84, 54

So the fifth student in the list is #18, or Quincy.

Answer:

Quincy is the answer

Step-by-step explanation:

Answer: 0.7619

Step-by-step explanation:

Given : Mean : [tex]\mu=45.0 [/tex]

Standard deviation : [tex]\sigma =8.0[/tex]

Sample size : [tex]n=9[/tex]

We assume that the variable is normally distributed.

The value of z-score is given by :-

[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

a) For x= 46.9 years

[tex]z=\dfrac{46.9-45.0}{\dfrac{8}{\sqrt{9}}}=0.7125[/tex]

The p-value : [tex]P(z<0.7125)=0.7619224\approx0.7619[/tex]

Hence, the  probability that the average age of those doctors is less than 46.9 years =0.7619

The question relates to probability in a normally distributed population. We calculated the standard error and z-score, then used the z-table to find that there is approximately a 76.11% chance that the average age of 9 randomly chosen doctors from this hospital will be less than 46.9 years.

The subject of this question pertains to Probability and Statistics, specifically the application of the Normal Distribution in the context of calculating the probability of a particular outcome in a real-world scenario. We'll apply the rule for the Central Limit Theorem (CLT) since the sample size is reasonably large (n = 9).

The first step is to calculate the standard error (SE). The SE of the mean can be calculated by dividing the standard deviation by the square root of the number of doctors:

SE = 8.0/sqrt(9) = 8.0/3 = 2.67.

Next, you would calculate the z-score. The z-score of 46.9 is obtained by subtracting the population mean from 46.9 and then dividing by the SE:

Z = (46.9 - 45.0)/2.67 = 0.71.

To determine the probability that the average age is less than 46.9 years, you will want to look up the z-score of 0.71 in a z-table, which gives a value of 0.7611, or 76.11%. So there is approximately a 76.11% chance that the mean age of the 9 doctors chosen will be less than 46.9 years old.

https://brainly.com/question/27342429

#SPJ11

Answer:

  0.74

Step-by-step explanation:

P(A∪B) = P(A) + P(B) - P(A∩B) = 0.57 + 0.17 - 0

P(A∪B) = 0.74

The probability of A∩B is zero because the classes are mutually exclusive.