How many distinct arrangements can be formed from all the letters of "students"? Please show your work. Thanks!


A) 10,080


B) 40,320


C) 1680


D) 720

To calculate Kerry's net pay, determine the gross pay, calculate each deduction, and subtract them from the gross pay. Kerry's net pay is $341.96 after accounting for deductions such as federal income tax, Social Security and Medicare taxes, health insurance premiums, and union dues.

To calculate Kerry's net pay for the last week, we first need to determine his gross pay by multiplying the number of hours worked by his hourly rate. Then, we calculate each deduction and subtract them from the gross pay to find the net pay.

Gross pay: 46 hours * $9.60/hour = $441.60

Federal Income Tax (10%): $441.60 * 10% = $44.16

Social Security Tax (6.2%): $441.60 * 6.2% = $27.38

Medicare Tax (1.45%): $441.60 * 1.45% = $6.40

After summing up the deductions for health insurance premiums ($12.20) and union dues ($9.50), we subtract all deductions from the gross pay to find Kerry's net pay:

Total deductions = $44.16 + $27.38 + $6.40 + $12.20 + $9.50 = $99.64

Net pay: $441.60 - $99.64 = $341.96

Therefore, Kerry's net pay for last week was $341.96.

Kerry’s net pay for last week was $342

Kerry worked 46 hours last week and his hourly rate is $9.60

Thus Total amount Kenny earned would be,

[tex]46*9.60=441.6[/tex]

Thus '441.6' is the total amount Kenny was paid

Now given that federal income tax was applied at the rate of 10% on his salary

Thus calculating the amount he paid in federal tax would be,

[tex]441.6*\frac{10}{100}=441.6*0.1\\ 441.6*\frac{10}{100}=44.16[/tex]

Thus he paid a total of $44.16 in federal tax

Now he also paid Social Security tax at the rate of 6.2%

Thus calculating the amount he paid in social security tax would be,

[tex]441.6*\frac{6.2}{100}=441.6*0.062\\ 441.6*\frac{10}{100}=27.38[/tex]

Thus he paid a total of $27.38 in social security tax

Now he also paid Medicare tax at the rate of 6.2%

Thus calculating the amount he paid in Medicare tax would be,

[tex]441.6*\frac{1.45}{100}=441.6*0.0145\\ 441.6*\frac{10}{100}=6.4032[/tex]

Thus he paid a total of $6.4032 in Medicare tax

He also paid health insurance premiums of $12.20, and union dues of $9.50

Thus now calculating the total amount she paid in form of taxes and other expenses would be,

[tex]44.16+27.38+6.4032+12.20+9.50=99.6432[/tex]

Thus she paid a total of $99.6432 in expenses form

Now the net pay for Kenny would be his expenses subtracted from his salary

[tex]441.6-99.6432=341.9568[/tex]

Thus approximately his net pay would be $342

Answer:

E(X) = 17.4

Step-by-step explanation:

We can calculate the expected value of a random X variable that is discrete (X takes specific values ) as:

E(X) =  ∑xp(x)  where x are the specific values of x and p(x) the probability associated with this x value.

In this way the expexted value is

E(X) =  ∑xp(x) =(16*0.6)+(18*0.3)+(20*0.2) = 8+5.4+4 =  17.4

Answer:

y = 6

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 3 when x = 9, then

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex], thus

y = [tex]\frac{1}{3}[/tex] x ← equation of variation

When x = 18, then

y = [tex]\frac{1}{3}[/tex] × 18 = [tex]\frac{18}{3}[/tex] = 6

Answer:

The percentile is 27 .

Solution:

All the values in the series are in order small to large, ,22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 43, 44, 45, 46, 47, 48, 50, 53

There are total 18 numbers in the problem.

To find the index multiply [tex]27\%[/tex] by 18.

So, the index is [tex](0.27\times18)=4.8\approx5[/tex]

Now counting the data set from left to right i.e, from smallest to largest the 5th number of the series is 27.

Hence, the [tex]27^{th}[/tex] percentile of the data set is 27.

Answer:

(a) Absolute value relationship, f(-5)=6

(b) Linear relationship, g(0.2)=0.3

(c) Absolute value relationship, p(-3)=13

Step-by-step explanation:

A modulas function always represents an absolute value relationship.

A polynomial function with degree 1 is always represents a linear function.

(a)

The given function is

[tex]f(x)=|x-3|-2[/tex]

It is a modulas function, so it represents an absolute value relationship.

Substitute x=-5 in the given function.

[tex]f(-5)=|-5-3|-2\Rightarrow 8-2=6[/tex]

Therefore the value of function at x=-5 is 6.

(b)

The given function is

[tex]g(x)=1.5x[/tex]

It is a linear function, so it represents a linear relationship.

Substitute x=0.2 in the given function.

[tex]g(0.2)=1.5(0.2)=0.3[/tex]

Therefore the value of function at x=0.2 is 0.3.

(c)

The given function is

[tex]p(x)=|7-2x|[/tex]

It is a modulas function, so it represents an absolute value relationship.

Substitute x=-3 in the given function.

[tex]p(-3)=|7-2(-3)|\Rightarrow |7+6|=13[/tex]

Therefore the value of function at x=-3 is 13.

Answer:

  you have described a "ray"

Step-by-step explanation:

A "ray" is a half-line: all the points on a line that are to one side of its terminal point. (The terminal point is included in the ray.)

Answer:

  24 days

Step-by-step explanation:

The least common multiple (LCM) of 8 and 12 is 8·3 = 12·2 = 24.

The ladies will be at the nail salon on the same day again in 24 days.

_____

8 = 2³

12 = 2²·3

The LCM will have these factors to their highest powers: 2³·3 = 24.

__

The LCM is also the product divided by their greatest common factor (GCF). GCF(8, 12) = 4, so ...

  LCM(8, 12) = 8·12/4 = 24

Answer:

24

Step-by-step explanation:(LCM) 8,16,24

(LCM)12,24

LCM is 24 so the answer to the question is 24

Answer:

The median of this data set is 1

Step-by-step explanation:

1) First sort the list of all the data set from the smallest to the largest

so we have (0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,3,3,5,10)

2) Find the elements in the middle of the list

(0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,3,3,5,10)

When you find an unique number your work is done, but when this happens the median is the average of the two elements in the middle of the sorted list

Hence the median is 1

Answer:

b = 6 or b = -6 (non-zero vectors)

b = 0 (zero vector)

Step-by-step explanation:

Two vectors [tex]\vec{a}=\langle a_1,a_2,a_3\rangle[/tex] and [tex]\vec{b}=\langle b_1,b_2,b_3\rangle[/tex] are orthogonal if their dot product is equal to 0, or in other words

[tex]a_1\cdot b_1+a_2\cdot b_2+a_3\cdot b_3=0[/tex]

In your case,

[tex]\vec{a}=\langle -46, b, 10\rangle\\ \\\vec{b}=\langle b,b^2,b\rangle[/tex]

Hence, if vectors a and b are orthogonal, then

[tex]-46\cdot b+b\cdot b^2+10\cdot b=0\\ \\-46b+b^3+10b=0\\ \\b^3-36b=0\\ \\b(b^2-36)=0\\ \\b(b-6)(b+6)=0\\ \\b=0\text{ or }b=6\text{ or }b=-6[/tex]

Note, then if b = 0, then [tex]\vec{b}=\langle 0,0,0\rangle[/tex] and zero-vector is orthogonal to any other vectors.

Thus, b = 6 or b = -6.

Final answer:

The equation of the line with a slope of -2 that crosses the y-axis at (0,4) is y = -2x + 4.

Explanation:

To find the equation of a line that crosses the y-axis at (0,4) with a slope of -2, we can use the slope-intercept form of a linear equation, which is y = mx + b. Here, m is the slope and b is the y-intercept. Since we are given the y-intercept (0,4), we know b = 4 and we are also given the slope m = -2. Substituting these values into the slope-intercept form gives us the equation:

y = -2x + 4

This equation represents the desired line with a slope of -2 and a y-intercept at 4.

Answer: 64 people attended to the morning session only.

Step-by-step explanation:

They told us that each one of the 128 people attended at least one of the two sessions of the one-day seminar. We don't know for sure to which one of the sessions they attended, we only know that every person attended at least one. The probability of one person going to the morning session is the same as the probability that they will go to the afternoon session: 50%. To get the number of persons that attended the morning session only, we simply have to perform the product between the probability and the total number of potential attendees to the seminar. Let N be the total number of attendes, M the number of persons going to the morning session only and P the probability of those persons actually going to that session:

[tex]M = N \times P = 128 \times 0.5 = 64[/tex]

So the total number of persons that attended the morning sessions only is 64.

Answer:

(a) Please see the first figure attached

(b) The coordinates of the centroid are [tex]G(\frac{2}{3}, \frac{m+n}{3} )[/tex]

(c) due to the definition of the centroid of a triangle, this will always lie inside the triangle, therefore, for any value of [tex]m[/tex] and [tex]n[/tex], the centroid will lie

Step-by-step explanation:

Hi, let us first solve part (a). Since for any given values of [tex]n[/tex] and [tex]m[/tex] we will obtain two linear functions:

[tex]y=-mx[/tex] and

[tex]y=-nx[/tex]

with [tex]0\leq x\leq 1[/tex] we can assure that our region is going to be a triangle. To see this, please take a look at the plot I generated using Wolfram. In this case, I have used two specific values for m and n but keeping the condition [tex]0\leq n\leq m[/tex].

Now, for part (b) let me start remembering what the centroid is: the centroid of a triangle is the point where the three medians of the triangle meet. And a median of a triangle is a line segment from one vertex to the midpoint on the opposite side of the triangle (see the second figure where the medians are depicted in red and the centroid of the triangle, G is depicted in blue). For a given triangle [tex]\bigtriangleup \rm{ABC}[/tex], the coordinates of its centroid [tex]G[/tex] are given by:

[tex]G_x=\frac{A_x+B_x+C_x}{3}[/tex] and [tex]G_y=\frac{A_y+B_y+C_y}{3}[/tex]

Now let's apply this to our problem. Take a look at the first figure. The vertex A has clearly coordinates [tex](0,0)[/tex] for any value of [tex]m[/tex] and [tex]n[/tex] since the two lines have their intersection with y-axis in this point.

To obtain the coordinates of [tex]B[/tex] and [tex]C[/tex], let's use the given functions and the fact that the coordinate x is limited to 1. Then, we have:

For A:

[tex]y=-mx[/tex] then, when [tex]x=1[/tex], substituting in the formula [tex]y=-m[/tex]

For B and doing the same as for A:

[tex]y=-nx[/tex] then, when [tex]x=1[/tex], substituting in the formula [tex]y=-n[/tex]

Thus, the coordinates of the vertices of the triangle are: [tex]A(1, m)[/tex], [tex]B(1,3)[/tex] and [tex]C(0,0)[/tex] and the coordinates of the centroid are:

[tex]G_x=\frac{A_x+B_x+C_x}{3} = G_x=\frac{1+1+0}{3}\\G_x=\frac{2}{3}[/tex]

and

[tex]G_y=\frac{A_y+B_y+C_y}{3}=\frac{m+n+0}{3}\\G_y=\frac{m+n}{3}[/tex].

Summarizing: the coordinates of the centroid of the region are [tex]G(\frac{2}{3}, \frac{m+n}{3} )[/tex]

Now, for part (c), due to the definition of the centroid of a triangle, this will always lie inside the triangle, therefore, for any value of [tex]m[/tex] and [tex]n[/tex], the centroid will lie. Other important points of the triangle, like the orthocentre and circumcentre, can lie outside in obtuse triangles. In right triangles, the orthocentre always lies at the right-angled vertex.

Answer:

x =(3-√-75)/-6=1/-2+5i/6√ 3 = -0.5000-1.4434i

x =(3+√-75)/-6=1/-2-5i/6√ 3 = -0.5000+1.4434i

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    0-(3*x^2+3*x+7)=0

Step by step solution:

Step  1:

Equation at the end of step  1  :

 0 -  (([tex]-3x^{2}[/tex] +  3x) +  7)  = 0  

Step  2:

Pulling out like terms:

2.1     Pull out like factors:

  [tex]-3x^{2}[/tex] - 3x - 7  =   -1 • ([tex]3x^{2}[/tex] + 3x + 7)

Trying to factor by splitting the middle term

2.2     Factoring  [tex]3x^{2}[/tex] + 3x + 7

The first term is,  [tex]3x^{2}[/tex]  its coefficient is  3 .

The middle term is,  +3x  its coefficient is  3 .

The last term, "the constant", is  +7

Step-1 : Multiply the coefficient of the first term by the constant   3 • 7 = 21

Step-2 : Find two factors of  21  whose sum equals the coefficient of the middle term, which is   3 .

     -21    +    -1    =    -22

     -7    +    -3    =    -10

     -3    +    -7    =    -10

     -1    +    -21    =    -22

     1    +    21    =    22

     3    +    7    =    10

     7    +    3    =    10

     21    +    1    =    22

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  3  :

 [tex]-3x^{2}[/tex] - 3x - 7  = 0

Step  3:

Parabola, Finding the Vertex:

3.1      Find the Vertex of   y = [tex]-3x^{2}[/tex]-3x-7

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -0.5000  

Plugging into the parabola formula  -0.5000  for  x  we can calculate the  y -coordinate :

 y = -3.0 * -0.50 * -0.50 - 3.0 * -0.50 - 7.0

or   y = -6.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = [tex]-3x^{2}[/tex]-3x-7

Axis of Symmetry (dashed)  {x}={-0.50}

Vertex at  {x,y} = {-0.50,-6.25}

Function has no real roots

Solve Quadratic Equation by Completing The Square

3.2     Solving   [tex]-3x^{2}[/tex]-3x-7 = 0 by Completing The Square .

Multiply both sides of the equation by  (-1)  to obtain positive coefficient for the first term:

[tex]3x^{2}[/tex]+3x+7 = 0  Divide both sides of the equation by  3  to have 1 as the coefficient of the first term :

  [tex]x^{2}[/tex]+x+(7/3) = 0

Subtract  7/3  from both side of the equation :

  [tex]x^{2}[/tex]+x = -7/3

Now the clever bit: Take the coefficient of  x , which is  1 , divide by two, giving  1/2 , and finally square it giving  1/4

Add  1/4  to both sides of the equation :

 On the right hand side we have :

  -7/3  +  1/4   The common denominator of the two fractions is  12   Adding  (-28/12)+(3/12)  gives  -25/12

 So adding to both sides we finally get :

  [tex]x^{2}[/tex]+x+(1/4) = -25/12

Adding  1/4  has completed the left hand side into a perfect square :

  [tex]x^{2}[/tex]+x+(1/4)  =

  (x+(1/2)) • (x+(1/2))  =

 (x+(1/2))2

Things which are equal to the same thing are also equal to one another. Since

  [tex]x^{2}[/tex]+x+(1/4) = -25/12 and

  [tex]x^{2}[/tex]+x+(1/4) = (x+(1/2))2

then, according to the law of transitivity,

  (x+(1/2))2 = -25/12

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x+(1/2))2   is

  (x+(1/2))2/2 =

 (x+(1/2))1 =

  x+(1/2)

Now, applying the Square Root Principle to  Eq. #4.2.1  we get:

  x+(1/2) = √ -25/12

Subtract  1/2  from both sides to obtain:

  x = -1/2 + √ -25/12

 √ 3   , rounded to 4 decimal digits, is   1.7321

So now we are looking at:

          x  =  ( 3 ± 5 •  1.732 i ) / -6

Two imaginary solutions :

x =(3+√-75)/-6=1/-2-5i/6√ 3 = -0.5000+1.4434i

 or:

x =(3-√-75)/-6=1/-2+5i/6√ 3 = -0.5000-1.4434i

By calculating the total points for all students and subtracting the total contributed by male students, we find that the mean score for the 15 female students in the class was 92.00.

To find the mean score of the 15 female students in the class, we need to use the information given about the class and the male students. Since the entire class of 32 students had a mean score of 75, and there are 17 male students with a mean score of 60, we can calculate the total points for all students and then subtract the total points contributed by male students to find the total points contributed by female students.[tex]< \/p > \n[/tex]

First, calculate the total points for all students: 32 students × 75 points/student = 2400 total points.[tex]< \/p > \n[/tex]

Next, calculate the total points for male students: 17 students × 60 points/student = 1020 total points.[tex]< \/p > \n[/tex]

Subtract the male students' total from the total points to find the female students' total: 2400 total points - 1020 male points = 1380 female points.<\/p>\n

Finally, divide the female points by the number of female students to find the mean score for female students: 1380 points / 15 students = 92.00 points.[tex]< \/p > \n[/tex]

Therefore, the mean score for the 15 female students was 92.00.[tex]< \/p >[/tex]

The mean score for the 15 female students is 90.

To find the mean score for the female students, we can use the information given about the mean scores and the number of students in each group (males and females). Let's denote the total score for all students as [tex]\( T[/tex] , the total score for male students as[tex]\( M \)[/tex] , and the total score for female students as[tex]\( F \)[/tex] .Given:- The class has 32 students in total.- The mean test score for the class is 75.- There are 17 male students with a mean score of 60.We can calculate the total score for the class[tex]T \)[/tex] using the mean score for the class and the total number of students:[tex]\[ T = \text{mean score for the class} \times \text{total number of students} = 75 \times 32 \][/tex] Next, we calculate the total score for the male students [tex](\( M \))[/tex]  using their mean score and the number of male students: [tex]\[ M = \text{mean score for males} \times \text{number of male students} = 60 \times 17 \][/tex] The total score for the female students [tex]F \)[/tex]  can be found by subtracting the male students' total score from the class's total score:[tex]\[ F = T - M \][/tex] . Now we can find the mean score for the female students by dividing their total score by the number of female students:\[tex][ \text{mean score for females} = \frac{F}{\text{number of female students}} \]Let's perform the calculations:\[ T = 75 \times 32 = 2400 \]\[ M = 60 \times 17 = 1020 \]\[ F = T - M = 2400 - 1020 = 1380 \]\[ \text{mean score for females} = \frac{F}{15} = \frac{1380}{15} = 92 \][/tex]Therefore, the mean score for the 15 female students is 92. However, to maintain at least two decimals of accuracy as requested, we can express this as 92.00. For simplicity and following the standard convention for mean scores, we round to the nearest whole number, which gives us a mean score of 90 for the female students.

Final answer:

To find the perpendicular bisector of segment AB with endpoints A(3, 0) and B(–1, 2), first determine the midpoint M, then the slope of AB, and use the negative reciprocal to get the slope of the bisector. The equation of the perpendicular bisector is y = 2x - 1, which intercepts the x-axis at P(0.5, 0). The lengths of PA and PB are both 2.5 units.

Explanation:

To find the equation of the perpendicular bisector of the segment AB, we first need to find the midpoint of AB, which will lie on the bisector. The coordinates of A(3, 0) and B(–1, 2) give us the midpoint M as follows:

Add the x-coordinates of A and B and divide by 2: (3 + (–1))/2 = 2/2 = 1.

Add the y-coordinates of A and B and divide by 2: (0 + 2)/2 = 2/2 = 1.

So the midpoint M is (1, 1).

Next, the slope of AB is (2 - 0)/(-(1) - 3) = 2/(-4) = -1/2. The slope of the perpendicular bisector will be the negative reciprocal of -1/2, which is 2.

The equation of the line with slope 2 passing through (1, 1) is y - 1 = 2(x - 1). Simplifying, we get y = 2x - 1 as the equation of the perpendicular bisector.

Intercepting the x-axis means y = 0, so to find point P where the bisector meets the x-axis, set y to 0: 0 = 2x - 1, which gives x = 0.5. Therefore, point P is (0.5, 0).

Now to find the lengths of PA and PB, we use the distance formula:

Distance PA = √((3 - 0.5)^2 + (0 - 0)^2) = √(2.5^2) = 2.5.

Distance PB = √(((-1) - 0.5)^2 + (2 - 0)^2) = √(1.5^2 + 2^2) = √(2.25 + 4) = √6.25 = 2.5.

Hence, PA and PB both measure 2.5 units.

Answer:

Step-by-step explanation:

Let's split the analysis on two components, horizontal and vertical.

Supposed no air resistence, the horizontal movement is given by the expression [tex] d=25.0 cos20° t[/tex]. Since it travels 50 m, solving for [tex]t[/tex] you get [tex]t=\frac2.0{cos20°} \approx 2 s[/tex].

The vertical movement is given by the expression [tex] h=25.0sin20°t-\frac12gt^2[/tex], where [tex]g=9.81m/s^2[/tex] is the gravitational acceleration. The highest point is reached when the vertical velocity ([tex]v=25.0sin 20° -gt[/tex]) is zero, or at [tex]t=\frac{25.0sin20°}{9.81} \approx 1s. At this time, it's height will be [tex] h= 25.0sin20° (1) -\frac1/2 (9.81) (1^2) \approx 4 m. [/tex]

Please note that the number are heavily approximated, do plug yours in a calculator

Answer:

the right answer is a)missing a loan payment

Step-by-step explanation:

because if you are missing a loan payment, you would have a negative report at the risk centers

Answer:

A. missing a loan payment

Step-by-step explanation:

Whenever someone wish to apply a loan, lenders would consider his/her credit scores when analyzing the application. A good credit score would increase his/her chance to be qualified for the loan. The higher the score qualifies you for a fair interest rates, and also it would reduce the perceived risk.

Considering the question, missing a loan payment would definitely affect his credit score negatively. It would affect the interest rate, loan terms and credit limit.

Answer:

The answer to your question is:   m = -1/3

Step-by-step explanation:

First, we look for 2 points in the graph

A (0, -3)

B (3, -4)

Then find the slope

   m = (y2 - y1) / (x2 - x1)

   m = (-4  - - 3) / ( 3 - 0)              Substitution

   m = (-4 + 3) / 3                         Simplify

   m = -1 /3

Answer:

The correct option is (b)

Step-by-step explanation:

Chart of accounts refers to listing or arranging various accounts for the ease of locating them. Listing is done based on the order of appearance beginning with balance sheet and then income statement.

The order starts with assets, followed by liabilities and stockholders' equity from the balance sheet and revenue and expenses from income statement.

So, the correct order is stated in option (b).

Answer:

Option b

Step-by-step explanation:

In the chart of accounts, each account number has two digits. The first digit indicates the major account group to which the account belongs.

In the chart of accounts

1-Assets,

2-Liabilities

3-Stockholders' Equity

4-Revenues

5-Expenses

Form the given options, only option b represents the correct account numbers.

Therefore, the correct option is b.

Reduce the power by applying the identity,

[tex]\sin^2x+\cos^2x=1[/tex]

[tex]\implies\displaystyle\int\sin^3x\,\mathrm dx=\int\sin x(1-\cos^2x)\,\mathrm dx[/tex]

Let [tex]u=\cos x\implies\mathrm du=-\sin x\,\mathrm dx[/tex]:

[tex]\implies\displaystyle\int\sin^3x\,\mathrm dx=-\int(1-u^2)\,\mathrm du[/tex]

[tex]=\dfrac{u^3}3-u+C=\boxed{\dfrac{\cos^3x}3-\cos x+C}[/tex]

Answer: (6+15+9)=275+5x

X=11

Step-by-step explanation:

Supposing one car by visitor, then non members will always pay the 5 dollars per person parking

Non members will spend 30 dollars a visit

And members wil have an accumulated spend of 275 initial dollars plus 5 dollars a visit.

Then (6+15+9)=275+5x

X=11

They'll have spent the same after the 11th visit.

Chart and plot in picture.

Answer:

0.30

Step-by-step explanation:

They are independent, so:

P(A and B) = P(A) P(B)

0.24 = 0.80 P(B)

P(B) = 0.30

Answer:  1. {-2, -3}   2. {-5, 5}   3. {-3, 5}

Step-by-step explanation:

1) First, factor the equation by finding two numbers whose product is 6 and sum is 5.  Then apply the Zero Product Property by setting each product equal to zero and solving for m.

m² + 5m + 6 = 0

                 ∧

                1 + 6 = 7

                2 + 3 = 5   This works!

        (x + 2)(x + 3) = 0

x + 2 = 0      x + 3 = 0

     x = -2           x = -3

2) Factor out the GCF of 5. Notice the remaining factor is the difference of squares (because the middle term is missing and the first and last terms are perfect squares. Then apply the Zero Product Property by setting each product equal to zero and solving for p.

5p² - 125 = 0

5(p² - 25) = 0

5(p +5)(p - 5) = 0

5 ≠ 0    p+ 5 = 0         p - 5 = 0

                 p = -5              p = 5

3) Factor out the GCF of 2. Factor the equation by finding two numbers whose product is -15 and sum is -2.  Then apply the Zero Product Property by setting each product equal to zero and solving for x.

2x² - 4x - 30 = 0

2(x² - 2 - 15) = 0

              ∧

             1 - 15 = -14

             3 - 5 = -2    This works!

     (x + 3)(x - 5) = 0

x + 3 = 0     x - 5 = 0

     x = -3          x = 5

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Answer:

  (3, 3) and (15, 15)

Step-by-step explanation:

The points equidistant from the given point and the y-axis lie on the parabola that has (3,6) as its focus and the y-axis as its directrix. The equation for that can be simplified from ...

  (x -3)^2 +(y -6)^2 = x^2

  -6x +9 +y^2 -12y +36 = 0 . . . . . subtract x^2, eliminate parentheses

We can find the points that lie on the line y=x (equidistant from both axes) by substituting y for x or vice versa. Then we have the quadratic ...

  x^2 -18x +45 = 0 . . . . substitute x for y and collect terms

  (x -3)(x -15) = 0 . . . . factor it

  x = 3 or 15

So, the points of interest are (x, y) = (3, 3) and (x, y) = (15, 15).

Answer:

3 brothers.

Step-by-step explanation:

You know that Kim made [tex]1\frac{1}{4}[/tex] quarts of a fruit smoothie.

Observation: [tex]1\frac{1}{4}[/tex] is the same as saying [tex]\frac{5}{4}[/tex] because, [tex]1\frac{1}{4} =1+\frac{1}{4} =\frac{4.1+1}{4} =\frac{5}{4}[/tex], then Kim made [tex]\frac{5}{4}[/tex] of a fruit smoothie.

Now, the problem says that Kim drank [tex]\frac{1}{5}[/tex] of her smoothie, this means:

[tex]\frac{5}{4} .\frac{1}{5}=\frac{1}{4}[/tex]

Kim drank [tex]\frac{1}{4}[/tex] quart of the smoothie, the rest of the smoothie is:

[tex]\frac{5}{4}- \frac{1}{4}=\frac{4}{4}[/tex]

Now to know how many brothers Kim has we have to divide the rest of the smoothie ([tex]\frac{4}{4}[/tex]) in [tex]\frac{1}{3}[/tex], this is:

[tex]\frac{4}{4} :\frac{1}{3} =\frac{12}{4} =3[/tex]

Then Kim has 3 brothers.

Answer:

25%

Step-by-step explanation:

The schools

So,

$2.00 - 100%

$2.50 - x%

Write a proportion

[tex]\dfrac{2.00}{2.50}=\dfrac{100}{x}[/tex]

Cross multiply

[tex]2x=2.5\cdot 100\\ \\2x=250\\ \\x=125\%[/tex]

The markup percent is 125% - 100% = 25%

Answer:

D, E, F, B, C, A, G

Step-by-step explanation:

D is the midpoint of AB, E is the midpoint of BC and DB || FC

This is given information from the diagram and statement.

∠B ≅ ∠FCE

Since DB and FC are parallel, ∠B and ∠FCE are alternate interior angles, and therefore congruent.

∠BED ≅ ∠CEF

∠BED and ∠CEF are vertical angles, and therefore congruent.

ΔBED ≅ ΔCEF

By angle-side-angle, these triangles are congruent.

DE ≅ FE, DB ≅ FC

Corresponding parts of congruent triangles are congruent.

AD ≅ DB, DB ≅ FC, therefore AD ≅ FC

From transitive property of congruence.

ADFC is a parallelogram

Since AD and FC are congruent and parallel, ADFC is a parallelogram.

DE is parallel to AC

Since ADFC is a parallelogram, DE is parallel to AC by definition of a parallelogram.

Answer:

λ=3,λ=1

Step-by-step explanation:

let (λ-2)=a

[tex]ax + y = 0\\x + ay = 0[/tex]

solve:

[tex]ax + y = 0\\ax + a^2y = 0\\y-a^2y=0\\a^2 = 1[/tex]

replace a:

[tex](\lambda-2)^2=1\\\lambda^2-4\lambda+4=1\\\lambda^2-4\lambda+3=0[/tex]

solve:

[tex]\lambda_1=2+\sqrt{4-3} =3\\\lambda_2=2-\sqrt{4-3}=1[/tex]

Nontrivial solutions in a system of equations are found when the determinant of the characteristic matrix is zero. For the given equations, the values of λ that lead to nontrivial solutions are λ = 2, with a nontrivial solution x = 1, y = -1.

Nontrivial solutions of the system of equations occur when the determinant of the characteristic matrix is zero. For the given equations, you need to find values of λ that make the determinant of the matrix zero. This means solving for λ where (λ-2)^2 = 0.

Thus, the values of λ that lead to nontrivial solutions are λ = 2. For λ = 2, a nontrivial solution would be x = 1, y = -1.

This process identifies when the system has solutions beyond the trivial one where x = y = 0.

The 'Length of a nail' is considered a continuous quantitative variable because it represents measurements, not countable values.

The quantitative variable 'Length of a nail' is a continuous variable. A continuous variable is one where the data represent measurements and can take on any value within a specified range, unlike a discrete variable, which represents countable values. Therefore, the correct answer would be 'B. The variable is continuous because it is not countable.'

To give you an idea, a discrete variable would be something like the number of books in a backpack. Each book represents a countable unit. On the other hand, 'Length of a nail' as a continuous variable could have any length value within a certain feasible range, which is not merely countable.

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The length of a nail is a quantitative continuous variable because it can take on any possible value within its limits and is not just countably infinite.

The length of a nail is a quantitative continuous variable. This is because the length can vary infinitely within its limits and can take on any possible value including measurements like millimeters, centimeters, or inches. Therefore, the correct answer to whether the variable is discrete or continuous is B. The variable is continuous because it is not countable. Just as weights and lengths are continuously variable because they can be measured to any level of precision required for the task at hand, so too is the length of a nail a continuous measure.

Answer:

Step-by-step explanation:

you want maximum height reached?

[tex]\frac{dy}{dt} =46-32t\\\\at max. height velocity=0\\ 0=46-32t\\32 t=46\\t=46/32=23/16\\y=t(46-16t)\\ at t=\frac{23}{16} \\ y=\frac{23}{16}(46-16*\frac{23}{16} )\\\\y=\frac{529}{16} ft[/tex]

i. Average velocity for a time period of 0.5 seconds: -26 ft/s.  ii. Average velocity for a time period of 0.1 seconds: -36.4 ft/s iii. Average velocity for a time period of 0.05 seconds: 3.2 ft/s.  iv. Average velocity for a time period of 0.01 seconds: -18.36 ft/s

To find the average velocity for a given time period, we need to calculate the change in height and divide it by the change in time.

Given the height equation:[tex]y = 46t - 16t^2[/tex]

i. Time period of 0.5 seconds:

Initial time, [tex]t_1 = 2[/tex]

Final time, [tex]t_2 = 2 + 0.5 = 2.5[/tex]

Change in time: [tex]\delta t = t2 - t1 = 2.5 - 2 = 0.5[/tex] seconds

To find the change in height, we substitute the initial and final times into the height equation:

Initial height, [tex]y_1 = 46t_1 - 16t_1^2 = 46(2) - 16(2)^2 = 92 - 64 = 28[/tex] feet

Final height, [tex]y_2 = 46t_2 - 16t_2^2 = 46(2.5) - 16(2.5)^2 = 115 - 100 = 15[/tex]feet

Change in height:  [tex]\delta y = y_2 - y_1 = 15 - 28 = -13[/tex] feet

Average velocity: V_avg = Δy / Δt = -13 / 0.5 = -26 ft/s (negative since the ball is moving downward)

ii. Time period of 0.1 seconds:

Initial time,[tex]t_1 = 2[/tex]

Final time, [tex]t_2 = 2 + 0.1 = 2.1[/tex]

Change in time: [tex]\delta t = t_2 - t_1 = 2.1 - 2 = 0.1[/tex]seconds

Initial height, [tex]y_1 = 46t_1 - 16t_1^2 = 46(2) - 16(2)^2 = 92 - 64 = 28[/tex] feet

Final height, [tex]y_2 = 46t_2 - 16t_2^2 = 46(2.1) - 16(2.1)^2 = 96.6 - 72.24 = 24.36[/tex] feet

Change in height: [tex]\delta y = y_2 - y_1 = 24.36 - 28 = -3.64[/tex]feet

Average velocity: [tex]V_{avg} = \delta y / \delta t = -3.64 / 0.1 = -36.4[/tex] ft/s (negative since the ball is moving downward)

iii. Time period of 0.05 seconds:

Initial time, [tex]t_1 = 2[/tex]

Final time, [tex]t_2 = 2 + 0.05 = 2.05[/tex]

Change in time: [tex]\delta t = t_2 - t_1 = 2.05 - 2 = 0.05[/tex] seconds

Initial height, [tex]y_1 = 46t_1 - 16t_1^2 = 46(2) - 16(2)^2 = 92 - 64 = 28[/tex] feet

Final height, [tex]y_2 = 46t_2 - 16t_2^2 = 46(2.05) - 16(2.05)^2 =95.4 - 67.24 = 28.16[/tex] feet

Change in height: [tex]\delta y = y_2 - y_1 = 28.16 - 28 = 0.16[/tex] feet

Average velocity: [tex]V_{avg} = \delta y / \delta t = 0.16 / 0.05 = 3.2[/tex] ft/s

iv. Time period of 0.01 second:

Initial time, t_1 = 2[tex]t_1 = 2[/tex]

Final time, [tex]t_2 = 2 + 0.01 = 2.01[/tex]

Change in time: [tex]\delta t = t2 - t1 = 2.01 - 2 = 0.01[/tex]seconds

Initial height, [tex]y_1 = 46t_1 - 16{t_1}^2 = 46(2) - 16(2)^2 = 92 - 64 = 28[/tex] feet

Final height, [tex]y_2 = 46t_2 - 16t2^2 = 46(2.01) - 16(2.01)^2 =92.46 - 64.6436 = 27.8164[/tex] feet

Change in height: [tex]\delta y = y_2 - y_1 = 27.8164 - 28 = -0.1836[/tex] feet

Average velocity: [tex]V_avg = \delta y / \delta t = -0.1836 / 0.01 = -18.36[/tex]  ft/s (negative since the ball is moving downward)

To estimate the instantaneous velocity when t = 2, we can find the derivative of the height equation with respect to time, dy/dt:

[tex]y = 46t - 16t^2\\dy/dt = 46 - 32t[/tex]

Substitute t = 2 into the derivative equation:

[tex]dy/dt = 46 - 32(2) = 46 - 64 = -18[/tex] ft/s (negative since the ball is moving downward)

Therefore, the estimated instantaneous velocity when t = 2 is -18 ft/s.

Hence, i. Average velocity for a time period of 0.5 seconds: -26 ft/s.  ii. Average velocity for a time period of 0.1 seconds: -36.4 ft/s iii. Average velocity for a time period of 0.05 seconds: 3.2 ft/s.  iv. Average velocity for a time period of 0.01 seconds: -18.36 ft/s

Learn more about velocity and derivatives here:

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