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The expression 1.08s +1.02b predicts the end-of-year value of a financial portfolio where s is
the value of stocks and b is the value of bonds in the portfolio at the beginning of the year.
What is the predicted end-of-year value of a portfolio that begins the year with $200 in stocks
and $100 in bonds?
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(a) If θ(1) = 26.0 degree, the angle θ(2) of the emerging beam is 41.3 degree.

(b) The smallest incident angle θ(1) to have total internal reflection at the surface between the medium with n(4) = 1.20 and the medium with n(4) = 1.06 is 62.01.

(a) The path of a beam of light through several layers with different indices of refraction.

Using the Snell's law

n(1) sinθ(i) = n(2) sinθ(r)

The two medium's refractive indices are n(1) and n(2), and the angles of incidence and refraction are θ(i) and θ(r).

The preceding can be revised as

sinθ(r) = sinθ(i)(n(1))/(n(2))

sinθ(r) = sin 26 × 1.60/1.40

sinθ(r) = 0.50

Going from n2 to n3 .

The above calculated will become angle of incidence made with the normal at n(2) and n(3) interface.

The angle of refraction at n(3) medium

sinθ(r3) = sinθ(r) × n(2)/n(3)

sinθ(r3) = 0.50 × 1.40/1.20

sinθ(r3) = 0.58

The angle of incidence for interfaces n(3) and n(4) is now θ(r3).

sinθ(2) = (sinθ(r3) × n(3))/n(4)

sinθ(2) = (0.58 × 1.2)/1.06

sinθ(2) = 0.66

Taking square root on both side, we get

θ(2) = [tex]\sin^{-1}[/tex](0.66)

θ(2) = 41.3 degree

(b) It is possible to calculate the critical angle at the n3 to n4 interface as

θ(c) = [tex]\sin^{-1}[/tex](n(4)/n(3))

θ(c) = [tex]\sin^{-1}[/tex](1.06/1.20)

θ(c) = 62.01

The angle at which 100% internal reflection takes place is known as the critical angle.

Total internal reflection will happen if the beam is incident at an angle of 62.01 at n(3).

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The complete question is:

The figure below shows the path of a beam of light through several layers with different indices of refraction. (Assume n(4) = 1.06.)

(a) If θ(1) = 26.0 degree, what is the angle θ(2) of the emerging beam?

(b) What is the smallest incident angle θ(1) to have total internal reflection at the surface between the medium with n(4) = 1.20 and the medium with n(4) = 1.06?

The approximate solution of the linear system represented by the graph is, (5, 6)

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Given that,

A graph in which two lines are intersecting each other,

basically solution of linear system means where both the lines will intersect,

So, in the graph it can be seen that lines are intersecting around x coordinate 5 and y coordinate 6,

Therefore, the solution is (5, 6)

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The total surface area of the cardboard in square inches is option B. 6 × 5 × 5.

The area of a three dimensional object on it's outer surface is called the surface area of the object.

From the given figure, there are 6 squares with each square having the side length equals 5 inches.

Area of a square = a × a, where a is the length of a side.

Area of a 5 inch square = 5 × 5

There are total of 6 squares.

Total surface area = 6 × 5 × 5

Hence the total surface area of the given figure is option B. 6 × 5 × 5.

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Alexa scored g + 4 goals in the last soccer season.

Expression in mathematics is a combination of symbols, such as numbers and operators, which produces a mathematical result. An expression can involve a single term or multiple terms and usually consists of a combination of constants, variables, operators, functions and parentheses. In an expression, operators are used to perform operations on terms, allowing one to solve equations and other problems. Examples of mathematical expressions include 3 + x = 5, sin(x) + 4, and (x + 2y)^2.

The expression that shows how many goals Alexa scored is: Alexa scored (g + 4) goals.

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The common region to both the inequalities would be the solution region.

Given is the compound inequality as -

–x + y ≤ –1

x + 2y ≥ 4

Refer to the graph of the inequalities attached. The common region to both the inequalities would be the solution region.

Therefore, the common region to both the inequalities would be the solution region.

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The required steps to show that circle A is similar to circle B are,
1. Dilate circle A by a scale factor of 0.5.
2. Translate circle A using the rule (x − 5, y − 5).

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

Here,
Circle A = Center of −2, −2 and a radius of 4,
Circle B = Center of 3, 3, and a radius of 2.

Steps to show circle A is similar to circle B
1. Dilate circle A by a scale factor of 0.5

2. Translate circle A using the rule (x − 5, y − 5)

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The paragraph above describes a/an c. controlled experiment.

The participants who drink beer are the b. control group, the participants who drink soda are the a. treatment group.

Flipping a coin to decide which player gets which drink is an example of g. randomization.

A controlled experiment is a type of study in which the researcher manipulates one or more independent variables to observe the effect on a dependent variable. In this case, the independent variable is the type of drink (beer or soda) and the dependent variable is the score achieved in a dart-throwing task.

The purpose of randomly assigning the players to drink either beer or soda is to control for any other factors that could affect the scores, such as the individual's dart-playing ability or the amount of alcohol consumed.

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Complete Question:

A researcher is looking at the effect of drinking alcohol on the ability to play darts. He recruits 20 dart players from the nearby pub and has them come to a lab where he flips a coin for each player. If the coin comes up heads, he has the player drink a pint of beer. If the coin comes up tails, he has the player drink a pint of soda. Each player then throws three darts at a dartboard and the score is recorded. The researcher calculates that the soda-drinkers score, on average, 2.5 points more than the beer-drinkers.

The paragraph above describes a/an _____________.The participants who drink beer are th_____________, the participants who drink soda are the _____________. Flipping a coin to decide which player gets which drink is an example of _____________.

Choose from the list below to fill in the blanks.

a. treatment group

b. control group

c. controlled experiment

d. observational study

e. placebo

f. confounding factor

g. randomization

Answer: A: 9 galloons and then

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{\textbf{B. \$33}}[/tex]

Step-by-step explanation:

To solve this problem, we first need to find the daily rental rate for the midsize sedans. Since the luxury sedans rent for $45 per day and their daily rate is 50% greater than the midsize sedans, we can set up the following equation:

[tex]\Large \boxed{\texttt{45 = 1.5 $\times$ Midsize daily rate}}[/tex]

Now, we can solve for the midsize daily rate:

So, the midsize sedans rent for $30 per day. There are 16 midsize sedans (20 total cars - 4 luxury sedans) and 4 luxury sedans. To find the average daily rental fee for all 20 cars, we can use the following formula:

[tex]\Large\boxed{\texttt{Average daily rental fee} = \frac{\texttt{Total rental fees}}{\texttt{Total number of cars}}}[/tex]

The total rental fees can be calculated as follows:

Now, we can find the average daily rental fee:

So, the average daily rental fee for all 20 cars at this agency is $33, which corresponds to option B.

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The angle that the vector "v = 9i + 8j - 4k" makes with the vector "u = 6i - 4j - k" is Acute Angle .

To determine the angle between two vectors, we need to find the dot product of the vectors and divide it by the product of their magnitudes.

If the result is positive, the angle between the vectors is acute, if it's negative the angle is obtuse, and if it's zero, the angle is a right angle.

In this case, the dot product of vectors "u" and "v" is:

⇒ (6i - 4j - k) . (9i + 8j - 4k) = 54 - 32 + 4 = 26  ;

The magnitude of vector "u" is = √(6² + (-4)² + (-1)²) = √(36 + 16 + 1) = √53

The magnitude of vector "v" is = √(9² + 8² + (-4)²) = √(81 + 64 + 16) = √161

So, the Cosine (Cos) of angle between two vectors "u" and "v" is:

⇒ Cos(θ) = 26/(√37 × √145) = 26/√5365  .

Since the value of Cos(θ) is positive, the angle between the vectors is acute. This means the vectors "u" and "v" are pointing in somewhat similar directions, but not exactly the same direction.

The given question is incomplete , the complete question is

Determine whether the angle vector "v" makes with vector "u" is acute, obtuse, straight, a right angle, or whether "v" is a vector in the same direction as "u" . u=6i-4j-k  and  v=9i+8j-4k .

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answer: b = 9metres

l = 19metres

Answer:

Dimensions are L=19, w=9, or L=9, w=19

Step-by-step explanation:

Perimeter P=2(L+W)

So,  56=2(L+W)

       28=L+W

        L=28-W

Area         A=L*W

Because A=171, so 171=L*W

Substituting the expressions: put L=28-w, to 171=L*W,

So, 171=(28-W)W

     171=28w-w²

     W²-28W+171=0

      (W-9)(W-19)=0

      W=9, or W=19

We got L=28-W before, so when w=9, put to L=28-W, so, L=19

Dimensions are L=19, w=9, or L=9, w=19

16 is the number which is one-fifth of a number when one-fourth of that same number is 20.

As per the given data:

One-fourth of the number is resulted to 20.

Here we have to determine the result of one-fifth of the same number from the given options.

An expression for a portion of a whole is a fraction.

For any real numbers, the fractional component of x is defined.

Let the number be X.

One-fourth of a number is 20 which means:

Multiply the one-fourth fraction with an unknown number which results in the number 20.

[tex]$\frac{1}{4}[/tex]  (X) = 20

X = 20 × 4

X = 80

Now we have to determine that one-fifth of the same number.

Multiply the one-fifth fraction by 80.

We get:

= [tex]$\frac{1}{5}[/tex] (80)

= [tex]$\frac{1}{5}[/tex]   × 5 × 16

= 16

One-fifth of the number 80 is 16

Therefore Option (D) - 16 is the correct answer.

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Answer: the only clear answer i can think of would be, NO, the work she did was not clear i would say she did 4/10days she needed to work

Step-by-step explanation:

The equation of the parabola graphed is given as follows:

(x - 3)² = 5(y + 1)

The equation of a vertical parabola is given as follows:

(x - h)² = 4p(y - k)

In which:

The vertex is at the coordinate (3,-1), hence the parameters h and k are given as follows:

h = 3, k = -1.

The directrix is at the coordinate y = -2.25, hence the value of p is obtained as follows:

-1 - p = -2.25

p = 1.25.

Meaning that the equation of the parabola is given as follows:

(x - 3)² = 5(y + 1)

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Answer:

The expression "84 × 7 = ( + 4) × = 80 × || + 28 + x 7" is not a valid mathematical equation and has errors in syntax. I suggest rephrasing it to a clear and well-formed equation for me to help solve.

If vector B is added to vector A and the resultant is a null vector then A and B are equal and have opposite directions

We are given two vectors, vector A and vector B.

Now, vector B is added to vector A and it is said that the resultant of this addition is a null vector. It can be written as

vector B + vector A = 0

It can also be written as

vector A = 0 - vector B

vector A =  - vector B

We can see that the magnitude of both the vectors, vector A and vector B are equal. The minus sign here represents that the direction of vector B is opposite to vector A

Hence, we can conclude that if vector B is added to vector A and the resultant is a null vector then A and B are equal and have opposite directions

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The given expressions in the expanded form are 2x² + 6x + 4, 8x² + 28x + 24 and x² + 24x + 144.

a. (x + 1)(2x + 4) =

Expanding the product:

2x² + (2 × 1 + 4 × 1)x + 4 × 1 = 2x² + 6x + 4

b. (2x + 3)(4x + 8) =

Expanding the product:

8x² + (4 × 3 + 8 × 2)x + 8 × 3 = 8x² + 28x + 24

c. (x + 12)² =

Expanding the square:

x² + 2 × x × 12 + 12² = x² + 24x + 144

So, for each expression, the expanded form is given by ax² + bx + c.

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The expressions are evaluated to 7 and -6

Algebraic expressions are mathematical expressions comprising of terms, coefficients, variables, constants and factors.

These expressions are also comprised of mathematical or arithmetic operations. These operations are;

From the information given, we have that;

a. -4d + 3

b. k - m

Given that d= ,-1. k = 4 and m = -10

Now, substitute the values, we get;

a.-4(-1) + 3

expand the bracket

4 + 3 = 7

b. k - m

4 - 10

-6

Thus the values are 7 and -6

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If dropped from a height of 20 feet, the ball will travel a vertical distance of 39 feet.

We know that a ball if dropped will bounce back to 95% of its original height.

This means that when a ball is dropped from a distance of 100 m, it will travel 95 meters up.

Here we have been given that the ball is dropped from a height of 20 feet.

Hence, it will bounce back to a height of

95% of 20 = 19 feet.

Hence, the total vertical distance traveled by the ball is

The height at which it was dropped from + distance it bounced back to

20 feet + 19 feet

= 39 feet.

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Step-by-step explanation:

a) h−¹(x) = (x-13)/ (5x+7)

b) h-¹(x) cannot be found when x = 7.

At 25 mph, stopping distance = 22.56 feet

At 110 mph, stopping distance = 436.81 feet

Now, According to the question:

Let d represents the stopping distance required by an alfa romeo.

The stopping distance is proportional to the square of velocity is equivalent to the equation,

[tex]d = kv^2[/tex]

Here, k is proportionality constant.

We have,

d = 177 feet and v = 70 mph.

So, proportionality constant

[tex]k =\frac{177}{(70mph)^2}[/tex] ≈ 0.0361

Thus, the stopping distances required by an alfa Romeo going at 25 mph and at 110 mph,

[tex]d_2_5=0.0361[/tex] × [tex](25mph)^2[/tex] = 22.56 feet

[tex]d_1_1_0[/tex] = 0.0361 × [tex](110mph)^2[/tex] = 436.81 feet

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Answer:

To find the volume of a prism, use the formula V = A * h, where A is the area of the base of the prism and h is its height. For example, for the first prism, the area of the base is 8 and the height is 4, so the volume is 8 * 4 = 32. For the second prism, the area of the base is 6 and the height is 9, so the volume is 6 * 9 = 54. The first prism has a volume of 32 and the second prism has a volume of 54.

Here, the degree of the numerator, 2, is equal to the degree of the denominator, 2, so r(x) has a nonzero horizontal asymptote

Asymptote is a line taken in relation to curve. The line is always far apart from the curve irrespective of distance. Taking the definition in sense of curve, then the curve tries to reach this line while moving towards infinity. Horizontal asymptote indicates the behaviour of function at graph edge.

The equation to be considered for formation of horizontal asymptote is y = mx + b, where u is y-axis, m is slope, x is axis and b is constant. If the two values, that are numerator and Denominator are equal, then y = b.

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Answer:

  1/3

Step-by-step explanation:

You want to find x in a Venn diagram with regions labeled (x(x-5)), x, 2x, and 20, when the total is ε = 100. And you want to know the probability that a British stamp is from the 20th century.

The whole is the sum of the parts:

  ε = x(x-5) +x +2x +20

  100 = x² -2x +20 . . . . . . . . simplify

  81 = x² -2x +1 . . . . . . . . . subtract 19 to make a complete square

  81 = (x -1)²

  9 = x -1 . . . . . . . positive square root

  x = 10 . . . . . . . . add 1

Now we know ...

P(B) = (x +2x)/ε = 30/100 = 0.3

P(T&B) = x/ε = 10/100 = 0.1

The probability that a British stamp is from the 20th century is ...

  P(T|B) = P(T&B)/P(B) = 0.1/0.3

  P(T|B) = 1/3

Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem! (see explanation)

Step-by-step explanation:

[tex]\frac{x-4}{3} \leq 5[/tex]

[tex]\frac{1}{3}x + \frac{-4}{3} \leq 5[/tex]

[tex]\frac{1}{3}x+ \frac{-4}{3} + \frac{4}{3} \leq 5+ \frac{4}{3} \\\frac{1}{3}x\leq \frac{19}{3}[/tex]

[tex]3*\frac{1}{3}x\leq 3*( \frac{19}{3} )[/tex]

Answer:

x [tex]\leq[/tex] 19

(Hope this helped!)

(see image for number line graph)

The interquartile range of the given data using R is 13.3

As per the given data,

The midterm scores of an algebra class of 20 students;

69, 84, 52, 93, 81, 74, 89, 85, 88, 63, 87, 64, 67, 72, 74, 55, 82, 91, 68, 77

We have to find the interquartile range using R.

Interquartile Range;-

The interquartile range includes the second and third quartiles or the middle half of your data set (IQR). The range gives the spread of the full data set, whereas the interquartile range gives the range of the middle half of the data set.

Interquartile range = [tex]Q_{3} -Q_{1}[/tex]

[tex]Q_{1}[/tex] is the lower quarter

[tex]Q_{3}[/tex] is the upper quarter

[tex]Q_{2}[/tex] is the median

Here,

[tex]Q_{2}[/tex] = 63 +  [tex]$\frac{87}{2}[/tex]

[tex]Q_{2}[/tex] = [tex]$\frac{150}{2}[/tex]

[tex]Q_{2}[/tex] = 75

[tex]Q_{1}[/tex] = 81 + [tex]$\frac{74}{2}[/tex]

[tex]Q_{1}[/tex] = 77.5

[tex]Q_{3}[/tex] = 74 + [tex]$\frac{55}{2}[/tex]

[tex]Q_{3}[/tex] = 64.5

Then,

Interquartile range = [tex]Q_{3} -Q_{1}[/tex] = - (64 . 5 - 77.5) = 13.3

That is,

The interquartile range for the given data set is 13.3.

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Answer:um it dose not show the thing i downloded  the file if u  try again i will anser it for  tho

Step-by-step explanation:

The angular velocity in rpm of a point on its rim is equals to the 4224 rad/min.

We have, a cylinder with Radius , R = 6 inch. Spining velocity, S = 24 miles per hour

We have to calculate the the angular velocity in rpm of a point on its rim. To calculate Angular and Linear Speed from Linear velocity :

Step 1: Identify which speed we are asked to calculate and Identify the radius and the velocity. We already identified all this in above.

Step 2: To calculate the angular speed when the linear speed and the radius of the circular object use : angular velocity = linear velocity/radius

First, we need to reconcile the unit of the radius of the wheel/rim and the unit of the speed of the car. Also, we are asked to give the answer in radians per minute. So, let's convert the speed to inches per minutes. So, the linear velocity of spining = 24 miles per hour × 5280 ft. per miles× 12 inches per ft. × 1 hour / 60 minutes

= 25,344 inches per minute

Now, the angular velocity is written as

angular velocity = linear velocity /radius

= 25,344 inches per minute / 6 inches

= 4224 /min. Hence, the angular velocity of the rim is 4224 rad/min.

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If a cylinder with a 6 in. radius is spinning at 24 mph, The angular velocity of a point on the rim of the cylinder is 672.27 rpm.

Angular velocity is a measure of the speed at which an object is rotating around a central axis. It is measured in units of radians per second (rad/s) or revolutions per minute (rpm). To find the angular velocity of a point on the rim of the cylinder, we need to first convert the linear velocity (24 mph) to linear velocity in feet per second (ft/s). We can use the formula:

where v is the linear velocity, r is the radius of the cylinder, and ω is the angular velocity.

Due to the 6 in. = 0.5 feet,

ω = v χ 1 r = 24 miles hr 1 0.5 ft χ 5280 ft mile = 253,440 (rad) hr

Then, 672.27 rpm at 253,440 (rad) hr  1 2pi rev rad  1 60 hr min

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