Vector A⃗ has magnitude 5.00 and is at an angle of 36.9∘ south of east. Vector B⃗ has magnitude 6.40 and is at an angle of 20.0∘ west of north. Choose the positive x-direction to the east and the positive y-direction to the north. Find the components of A⃗ .

Final answer:

With an expected value of −34% for the state lottery and monthly spending of $40 on tickets, a person can expect to lose $13.60 monthly or $163.20 annually.

Explanation:

If the expected value of playing the state lottery is −34%, and a person spends $40 per month on lottery tickets, we can calculate the expected annual loss as follows:

Firstly, an expected value of −34% means that on average, for every dollar spent, you would expect to lose 34 cents. So for $40 spent in one month, the expected loss would be 34% of $40, which equals $13.60.

Next, we can find the expected loss for a year by multiplying the monthly loss by the number of months in a year:

Therefore, on average, you can expect to lose $163.20 per year if you continue spending $40 on lottery tickets every month.

The problem states:

f(p) is the average number of days a house stays on the market before being sold for price p in $1,000s

So we know:

p is the price in $1000s and

f(p) is the number of days before its sold for p

This means f(275) would be the number of days before its sold for 275,000 (since p is in $1000s).

The answer is:

f(275) represents the average number of days houses stay on the market before being sold for $275,000.

The statement "f(275) represents the average number of days houses stay on the market before being sold for $275,000" best describes the meaning of f(275).

Given,

Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s.

In the given function f(p), the variable p represents the price of a house in thousands of dollars ($1,000s), and f(p) represents the average number of days a house stays on the market before being sold for that price.

Therefore, when you evaluate f(275), it tells you the average number of days houses stay on the market before being sold for $275,000.

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Answer:

[tex]x=\frac{1+\sqrt5}{2}[/tex] and  [tex]x=\frac{1-\sqrt5}{2}[/tex]

and b=[tex]\frac{5}{4}[/tex]

Step-by-step explanation:

We are given that a quadratic equation

[tex]x^2-x-1=0[/tex]

We have to solve the equation by completing square and find the value of b.

[tex](x)^2-2\times x\times \frac{1}{2}+(\frac{1}{2})^2-(\frac{1}{2})^2-1=0[/tex]

[tex](x-\frac{1}{2})^2-\frac{1}{4}-1=0[/tex]

[tex](x-\frac{1}{2})^2-\frac{1-4}{4}=0[/tex]

[tex](x-\frac{1}{2})-\frac{5}{4}=0[/tex]

[tex](x-\frac{1}{2})^2-(\frac{\sqrt5}{2})^2=0[/tex]

[tex](x-\frac{1}{2})^2=(\frac{\sqrt5}{2})^2[/tex]

[tex]x-\frac{1}{2}=\frac{\sqrt5}{2}[/tex] and [tex]x-\frac{1}{2}=-\frac{\sqrt5}{2}[/tex]

[tex]x=\frac{\sqrt5}{2}+\frac{1}{2}=\frac{1+\sqrt5}{2}[/tex]

And [tex]x=\frac{1}{2}-\frac{\sqrt5}{2}=\frac{1-\sqrt5}{2}[/tex]

Therefore,[tex]x=\frac{1+\sqrt5}{2}[/tex] and  [tex]x=\frac{1-\sqrt5}{2}[/tex]

and b=[tex]\frac{5}{4}[/tex]

Final answer:

To complete the square for the equation x²-x-1=0, we add (1/2)² = 1/4 to both sides, resulting in the equivalent equation (x-1/2)² = 5/4, where b is 5/4 or 1.25.

Explanation:

To solve the quadratic equation x²-x-1=0 by completing the square, we need to transform the equation into the form (x+a)² = b. First, we would rearrange the equation to isolate the terms with x: x² - x = 1. The next step is completing the square by adding (1/2 ×-1)² = (1/2)² = 1/4 to both sides of the equation, resulting in x² - x + 1/4 = 1 + 1/4. Therefore, the complete square form is (x-1/2)²= 5/4 and the constant b is 5/4 or 1.25.

Answer:

The answer to your question is: I agree with you, the first option

Step-by-step explanation:

• (0,1) U (1,infinity)  This is the right answer because there are 2 invervals in which the graph decreases, and these intervals are listed in this option.

•(-infinity,-1)U(-1,0)  This option is wrong because from (-∞ , -1) the graph grows up and also from (-1, 0).

•(-infinity,-1)  The graph grows up, this option is incorrect

. (1,infinity) The graph decreases but the option is incomplete.

The correct option is A which is the function decreasing over the interval (0,1) U(1, infinity).

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

Check all the options:-

Therefore, the correct option is A which is the function decreasing over the interval (0,1) U(1, infinity).

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Answer:

Step-by-step explanation:

x=3(y-b)

or x=3y-3b

3y=x+3b

[tex]y=\frac{x+3b}{3}[/tex]

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\$906.25\\ P=\textit{original amount deposited}\\ r=rate\to 6.25\%\to \frac{6.25}{100}\dotfill &0.0625\\ t=years\dotfill &1 \end{cases} \\\\\\ 906.25=P(0.0625)(1)\implies 906.25=0.0625P\implies \cfrac{906.25}{0.0625}=P \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 14500=P~\hfill[/tex]

B

they have limited (3) common points where the planes meet.

Answer:

b. 60

Step-by-step explanation:

We have been given a formula [tex]5x+10y=800[/tex], where x represents the number of small vehicles and y represents the number of larger vehicles.

To find the number of small vehicles, we will substitute [tex]y=50[/tex] in the given equation as:

[tex]5x+10(50)=800[/tex]

[tex]5x+500=800[/tex]

[tex]5x+500-500=800-500[/tex]

[tex]5x=300[/tex]

[tex]\frac{5x}{5}=\frac{300}{5}[/tex]

[tex]x=60[/tex]

Therefore, 60 small vehicles were washed in total and option 'b' is the correct choice.

Answer:

(on Edge)  1. "The equation of the scenario is p = 55 - 0.5w"

2. "The values of p must be any whole number 45 to 55"

BTW i got number 1 from this user https://brainly.com/profile/Alyssamarie03-2838077

Answer: d. 75% of the screen is occupied by the image  

Step-by-step explanation:

First we have to find a relation between image area and screen area.

Image area is the product of image dimensions.

Screen area is the product of screen dimensions.

We have to divide the major image dimension between the major screen dimension

Major image dim/Major screen dim = 20/5 = 4

Now we have to multiply this relation by the minor screen dimension

Minor screen dim x 4 = 4 x 4 = 16

Then we have found 5/4 = 20/16

Now we can calculate what percent of the screen area is occupied by the image area.

Major image dim x minor image dim/Major screen dim x minor screen dim

Since major image dim = major screen dim, we have:

Minor image dim/Minor screen dim = 12/16 = 0.75 = 75% of the screen

Answer: d. 75% of the screen is occupied by the image

[tex]\textit{\textbf{Spymore}}[/tex]  

Answer:

The total number of students is composite

Step-by-step explanation:

* Lets explain how to solve the problem

- A teacher divides the students into three groups for project

- Each group has the same number of students

- We need to know the total number of students is prime number or

 composite number

∵ The least number of any group is 2 students

∵ There are three groups

∵ The number of students in each group equal

∴ The least number of the students is 6

∵ Any number of students must be multiple of 3 because it will

  divide by 3

∵ Any prime number has only two factors 1 and itself

∵ Any multiple of 3 (except 3) has more than two factors

∵ The class can not be 3 students because when divided to 3

   groups each group will have 1 students and the least number of

   students in a group is 2

∴ The number of the students in the class must be composite

Final answer:

The question deals with evenly dividing students into three groups for a group assignment, indicating that the total number of students is composite, as it is divisible by three.

Explanation:

The question involves dividing a number of students into groups for a group assignment. A key concept here is understanding whether the total number of students is a prime or composite number.

If the students were evenly divided into three groups, this implies that the total number must be divisible by three, making it a composite number.

Examples of group work dynamics include cases where students divide work equally but one ends up doing the most of it, evenly distributing tasks, or each taking on different aspects of a complex problem.

The functions ordered from the least steep slope to the steepest slope are: logarithmic (log(x)), linear (x), quadratic (x²), exponential (eˣ), and cubic (x³).

To compare the steepness of the slopes for different types of functions, we consider the growth or decay rates of each function. The order is determined by the behavior of the functions as x increases.

1. Logarithmic function (log(x)): It grows slowly and approaches infinity as x increases, making it the least steep slope.

2. Linear function (x): It has a constant slope, making it steeper than logarithmic but less steep than quadratic, exponential, and cubic functions.

3. Quadratic function (x²): It increases faster than linear but slower than exponential and cubic functions.

4. Exponential function (eˣ): It grows at an increasing rate, making it steeper than quadratic but less steep than cubic.

5. Cubic function (x³): It has the steepest slope as x increases, making it the most rapidly increasing function.

This order is based on the general behavior of each function type and their rates of growth or decay. Understanding the characteristics of these functions helps in comparing and ordering them in terms of steepness.

Answer: here’s the correct answer

Answer:

Option A is correct.

Step-by-step explanation:

From the dimensions first find the volume of the container and then find the estimate ratio of each cookie on diving the volume by number of cookies.

[tex]i.e. \\ 11 \times 6 \times 3 = 198 \\ = > \: \frac{198}{90} = 2.2 \\ \\ also \: from \: the \: second \: relation \\ 6 \times 6 \times 2 = 72 \\ = > \frac{72}{33} = 2.18 \: ( = approx \: 2.2)[/tex]

Answer:

The answer to your question is below:

Step-by-step explanation:

A number is divisible by 9 if the sum of all the individual digits is evenly divisible by 9.

7,625    example    7 + 6 + 2 +5 = 20  it's not divisible by 9

4,932                      4 + 9 + 3 + 2 = 19 it's not divisible by 9

9,180                                                18  it is divisible

2,969                                                26 it's not divisible by 9

9,180                                                18 it is divisible

4,932                                                18 it is divisible

2,969                                                26 it's not divisible by 9

Answer:

9180 is divisible by 9 .

Step-by-step explanation:

A number is divisible by 9 if the sum of all of it's digits is divisible by 9.

Here, for each of the given numbers, we will find sum of digits then check if the sum of digits is divisible by 9.

For 7,625  :    

 7 + 6 + 2 +5 = 20  ( not divisible by 9)

For 4,932 :                  

 4 + 9 + 3 + 2 = 19 (not divisible by 9)

For 9,180 :  

9+1+8 = 18              ( divisible by 9 )

For 2,969 :

2+9+6+9=26         (not divisible by 9)                                      

Answer:

The answer to your question is: 7 1/3 inches

Step-by-step explanation:

Data

1 inch --------- 15 miles

Distance from Richmond to Washington = 110 miles

Use a rule of three to solve it

        1 inch ----------------- 15 miles

        x    --------------------  110 miles

x = 110x 1 /15

x = 110 / 15   simplify            dividing by 5

x = 22/3

Convert it to a mix number

22/3 = 7 1/3 inches

Final answer:

On the map, 7.6 inches are between the two cities

Explanation:

To find out how many inches are between two cities on a map given the scale and the actual distance. The scale here is that 1 inch represents 15 miles. Therefore, for an actual distance of 110 miles, we simply divide the actual distance by the scale factor to obtain the distance on the map.

By setting up the proportion:
1 inch / 15 miles = x inches / 110 miles, we cross-multiply and solve for x,
which is the number of inches on the map. The calculation would be:
(1 inch / 15 miles) * 110 miles = 110 inches / 15 = 7 3/5 inches or 7.6 inches.

Answer: 8 + 2/3 batches of brownies you can bake.

Step-by-step explanation:

6 1/2 butter  = 6 + 1/2 = (2·6 + 1)/2 = 13/2 sticks of butter, we have this

Since we have 13/2 sticks of butter and each batch of brownies needs 3/4 of a stick of butter, we have to divide the amount of butter we have between the amount of butter we use to bake a batch of brownies.

13/2 butter ÷ 3/4 butter/batch = 13·4/2·3 batches = 52/6 batches = 8 + 2/3 batches

Answer: 8 + 2/3 batches of brownies you can bake.

[tex]\textit{\textbf{Spymore}}[/tex]  

By dividing the total amount of butter (13/2 sticks) by the amount required per batch (3/4 stick), we find that it's possible to make 8 full batches of brownies with 6 1/2 sticks of butter, with some butter left over.

To determine how many batches of brownies you can bake with 6 1/2 sticks of butter, you have to divide the total amount of butter you have by the amount required for one batch. Since each batch requires 3/4 stick of butter, you calculate as follows:

Total sticks of butter: 6 1/2
Required per batch: 3/4

Now convert 6 1/2 to an improper fraction: 6 1/2 = 13/2.

Next, calculate the number of batches by dividing the total butter by the butter per batch:

Number of batches = (13/2) / (3/4) = (13/2) * (4/3) = 52/6

When you simplify 52/6, you get 8 with a remainder, meaning you can make 8 full batches of brownies, and you will have some butter left over.

Answer: a) critical value = 0.0853, b) we reject the null hypothesis.

Step-by-step explanation:

Since we have given that

z = -1.37

And the hypothesis are given below:

[tex]H_0:p=\dfrac{1}{4}=0.25\\\\H_1:p\neq 0.25[/tex]

Since α = 0.01

since critical value = 0.0853

As we can see that 0.853 < 0.25.

so, we reject the null hypothesis.

Hence, a) critical value = 0.0853, b) we reject the null hypothesis.

Answer:

The answer is: small+large.

Step-by-step explanation:

If the variable of the smaller sheetrock is stored in small:

var small.

And the variable of the larger sheetrock is stored in large:

var large.

The length of the wall will be the sum of the two pieces of sheetrock:

For example:

var small = 5;

var large = 10;

small+large = 5 + 10 = 15 is the length of the wall.

Final answer:

To calculate the total length of a wall made with two sheets of sheetrock, use the expression 'small + large'. The correct unit for measuring large objects like walls is often feet, and including units is essential for clarity in measurements.

Explanation:

The question asks for an expression to calculate the total length of a wall built with two pieces of sheetrock with lengths stored in the variables small and large. Since the total length of the wall will be the sum of the lengths of the two pieces of sheetrock, the expression you would write is small + large. This will give you the length of the entire wall when you substitute in the numerical values for the lengths represented by the two variables.

When measuring large objects like walls, the appropriate unit of measure is often feet, as inches would be too small and miles or kilometers would be excessively large. It's important to always include units in your measurements to avoid confusion and to ensure that the measurements are useful for practical applications, such as buying fabric or building materials.

The volume of a cylinder is changing at a rate of 256π cm³/min when the height of the cylinder is 12 cm, the radius is 4 cm, the circumference of the cylinder is increasing at a rate of π4 cm/min, and the height of the cylinder is increasing four times faster than the radius.

The primary equation you need for this problem is the volume of a cylinder, which is V = πr²h. Given the height h of the cylinder is increasing four times faster than the radius r, if we use dh/dt for the rate of change of the height and dr/dt for the rate of change of the radius, we have dh/dt = 4dr/dt.

Also, the rate at which the circumference of the cylinder is increasing is d(2πr)/dt=2πdr/dt = π4 cm/min. Hence we can set up an equation as 2πdr/dt = π4. Solving for dr/dt, we get dr/dt = 2 cm/min.

Substituting this into the previous equation, we find that dh/dt = 8 cm/min. Now, if we take the derivative of the volume equation with respect to time, we get dV/dt = πr²dh/dt + 2πrh*dr/dt.

With the values r = 4cm, h = 12cm, dr/dt = 2 cm/min, and dh/dt = 8 cm/min, replacing in the equation above gives us: dV/dt = π*4²*8 + 2π*4*12*2 = 256π cm³/min. So, the volume of the cylinder is changing at a rate of 256π cm³/min.

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Answer:

A. 52°

Step-by-step explanation:

All interior angles of ANY quadrilateral sum up to 360°; corresponding base angles sum up to 180°, therefore the m∠A is 52°.

I am joyous to assist you anytime.

Answer:

The answer is below

Step-by-step explanation:

Data

Winter =    234

Spring =    673

Summer = 843

Fall =         425

Total =     2175

Then

Winter                2175 -------------------------  100%

                             234 -----------------------    x

                   x = 234(100)/2175 = 10.8 %

Spring               2175 ------------------------   100%

                           673 -----------------------    x

                   x = 673(100)/2175 = 30.9 %

Summer            2175 ------------------------   100%

                          843  ------------------------     x

                    x = 843(100) /2175 = 38.8 %

Fall                   2175 ------------------------   100%

                           425 ----------------------      x

                    x = 425(100)/2175 = 19.5%

Total = 10.8 + 30.9 + 38.8 + 19.5 = 100%

Answer:

  see below

Step-by-step explanation:

3. The answers in the image below are in "interval notation". In set notation, they might be ...

  increasing: {x∈ℝ: -2 < x < 0 ∪ 2 < x}

  decreasing: {x∈ℝ: 0 < x < 2}

  positive: {x∈ℝ: -4 ≤ x < 1.5 ∪ 3 < x}

  negative: {x∈ℝ: 1.5 < x < 3}

  domain: {x∈ℝ: x ≥ -4}

  range: {x∈ℝ: x ≥ -3}

  y-intercept: y ∈ {2}

  x-intercepts: x ∈ {1.5, 3}

  relative minimum: (x, y) ∈ {(2, -3)}

  relative maximum: (x, y) ∈ {(0, 2)}

__

4. Answers are in the image below.

The function is increasing where its slope is positive, decreasing where its slope is negative. Where the slope changes sign, there may be a point where the slope is 0 or undefined. The function is neither increasing nor decreasing there, so those points are not part of the intervals for increasing or decreasing.

The function is positive when it is above the x-axis, negative when it is below the x-axis. The function is neither positive nor negative where it is on the x-axis or where it is undefined.

The domain is the horizontal extent of the function. Any points where the function is undefined are excluded.

The range is the vertical extent of the function, all of the y-values where the function output is defined. Here, m(2) is not defined, so y=-7 is not an output at that point. However, y=7 is an output for m(-14 2/3). Likewise, m(9) does not have an output of 0, but m(3) does, so 0 is part of the range.

X- and y-intercepts are where the graph intersects the x- or y-axis, respectively. M(x) is undefined at (9, 0), so there is no x-intercept there.

A relative minimum is any point where the y-values increase on either side of the point. For m(x), the function is undefined at its relative minima, so it cannot be said to have any.

A relative maximum is any point where the y-value decreases on either side of the point. M(x) has one at the vertex of the parabolic segment.

Answer:

i * i = -1

Step-by-step explanation:

W hen you multiply an imaginary number or i number by another imaginary pure number, the answer is going to be a negative number, due that i *i= -1. The joke is funny because if you do what the recording is saying there you won't have a pure imaginary number and if you dial again, the same would happen again and again.

Answer:

When we work with imaginary numbers, we have that

i = √(-1)

then, we have that i*i = √(-1)*√(-1) = -1

An imaginary number is a number of form A + B*i, where A and B are real numbers.

Now, a purely imaginary number is a number of the form B*i, where B is a real number.

Then, if we multiply this number by i, we have that:

B*i*i = B*(-1) = -B

now we have a real number.

The joke is that now you can "reach" a real number.

Answer:  0.1010052

Step-by-step explanation:

Given : Significance level : [tex]\alpha=0.01[/tex]

Alternative hypothesis : [tex]H_1:\ p\neq\dfrac{3}{4}[/tex]

The test statistic value : [tex]z=-1.64[/tex]

Since , the alternative hypothesis is two-tailed, so the test is a two-tailed test.

Using standard normal distribution table for z, we have

The P-value of two-tailed test will be :-

[tex]2P(z>|-1.64|)=2P(z>1.64)\\\\=2(1-P(z\leq1.64))\\\\=2(1-0.9494974)\\\\=0.1010052[/tex]

Hence, the P-value = 0.1010052

Answer:

-1/32.

Step-by-step explanation:

(-1/2)^3 * (-1/2)^2

= -1/8 * 1/4

= -1/32.

Answer:

  B.  3

Step-by-step explanation:

"k" represents the number of units of upward translation between f and g. Since g is translated 3 units upward from f, we must have k=3.

Answer:

2 .

length of ,XY= a-6

length of ,YZ =3a+11

total length of ,XZ =41

Since,Point X,Y,Z lies in same straight line XZ..

So,

XZ= XY+ YZ

41= a-6 + 3a+11

41= 4a +5

41-5 = 4a

36/4 = a

a= 9

putting value of a in lengths XY and XZ we get,

XY= 9-6

= 3

YZ = 3*9 + 11

=27 + 11

=38

Length of XY = 3

Length of YZ = 38

Answer of 3 and 4 are as similar of above solved examples..

No, Jessica he will not have enough to buy the jacket. She would have saved $32, not $35.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Lets x represent the number of weeks it will take to save enough money. If she saves $11 each week, then in x weeks she will save 11x dollars.

Also, Add this to the 107 she has already saved, and at the end of 11 weeks she will have 11x + 107 dollars.

We want the amount saved to be equal to the price of the bike, so our equation;

11x + 107 = 173

Now we solve the equation.

Subtract 107 from both sides ;

11x = 66

Divide both sides by 11;

x = 6

No, Jessica he will not have enough to buy the jacket. She would have saved $32, not $35.

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Answer:

5!!

Step-by-step explanation:

When writing the polynomial in standard form, we have:

5X⁴ - 2X + 1

The leading coefficient is 5, since it's part of the term with the highest degree.

Final answer:

The leading coefficient of the polynomial 1 - 2x + 5x⁴ in standard form is 5, as standard form requires terms to be in descending powers of x.

Explanation:

The question asks to identify the leading coefficient of a polynomial when written in standard form. The given polynomial is 1 - 2x + 5x⁴. The standard form of a polynomial requires the terms to be written in descending powers of x. Therefore, the standard form of the given polynomial is 5x⁴ - 2x + 1. The leading coefficient is the coefficient of the term with the highest power of x, which in this case is 5 for the term 5x⁴.