Find a degree 3 polynomial with real coefficients having zeros 3 and 3−3i and a lead coefficient of 1. Write P in expanded form.

Answer:

P ( E_1*E_2*E_3*E_4 ) = 0.1055

Step-by-step explanation:

Given:

- 52 cards are dealt in 1 , 2 , 3 , 4 hands.

- Events:

             E_1       Hand 1 has exactly 1 ace

             E_2       Hand 2 has exactly 1 ace

             E_3       Hand 3 has exactly 1 ace

             E_4       Hand 4 has exactly 1 ace

Find:

p =P ( E_1*E_2*E_3*E_4 )

Solution:

Multiplication rule.

- For n ε N and events E_1 , E_2 , ... , E_n:

P ( E_1*E_2*......*E_n ) = P (E_1)*P(E_2|E_1)*P(E_3|E_2*E_1)*......*(E_n|E_1*E_2...E_n-1 )

- So for these events calculate 4 probabilities:-

-  For E_1, is to choose an ace multiplied by the number of ways to choose remaining 12 cards out of 48 non-aces:

                               P ( E_1 ) = 4C1 * 48C12 / 52C13

- For E_2 | E_1 , one ace and 12 other cards have already been chosen. there are 39C13 equally likely hands. The number of different one ace hand 2 is the number of ways to choose an ace from 3 remaining multiplied by the number of ways to choose the remaining 12 from 36, we have:

                               P ( E_2 | E_1  ) = 3C1 * 36C12 / 39C13

                               P ( E_3| E_2*E_1  ) = 2C1 * 24C12 / 26C13

                               P ( E_4 | E_3*E_2*E_1  ) = 1C1*12C12 / 13C13 = 1

- So the multiplication rule for n = 4 is as follows:

     P ( E_1*E_2*E_3*E_4 ) = P (E_1)*P(E_2|E_1)*P(E_3|E_2*E_1)*P ( E_4 | E_3*E_2*E_1  ) = [ 4C1 * 48C12 / 52C13 ] * [ 3C1 * 36C12 / 39C13 ] * [ 2C1 * 24C12 / 26C13 ]

     P ( E_1*E_2*E_3*E_4 ) = [ 4!*48! / (12!)^4 ] / [ 52! / (13!)^4 ]

     P ( E_1*E_2*E_3*E_4 ) = [ 4!*13^4 / (52*51*50*49) ]

    P ( E_1*E_2*E_3*E_4 ) = 0.1055

The probability that each hand in a deck of 52 cards gets exactly one ace is approximately 10.5%.

To determine the probability that each hand in a randomly divided deck of 52 cards has exactly one ace, we use the concept of conditional probability.
Let's find it step by step

Step 1 : consider the event E1 that the first hand has exactly one ace:

There are 4 aces and 52 total cards. The probabilities for drawing an ace for the first hand are affected by the decreasing number of both aces and cards.

The probability of the first hand receiving one ace is calculated as:

P(E1) = (4/52) * (48/51) * (47/50) * ... * (36/39)

Step 2 : consider the event E2 that the second hand receives exactly one ace, given that the first hand already has one:

With one ace already given to the first hand, there are 3 aces remaining and 39 cards left for the second hand.

The probability is calculated as:

P(E2|E1) = (3/39) * (35/38) * ... * (25/26)

Step 3 : Proceed similarly for the third and fourth hands:

P(E3|E1E2) = (2/26) * ... * (12/13)

P(E4|E1E2E3) = 1 (since only one ace remains for the last hand)

Step 4 : Using the multiplication rule, the overall probability P(E1E2E3E4) is calculated by multiplying the individual probabilities:

P(E1E2E3E4) = P(E1) * P(E2|E1) * P(E3|E1E2) * P(E4|E1E2E3)

Step 5 : After performing the calculations, we find:

The combined probability P(E1E2E3E4) = (4/52)*(3/39)*(2/26)(1/13) after simplifying is approximately 0.105 or 10.5%.

Answer:

the answer is d

Step-by-step explanation:

Answer:

5000 + x = 23600  

Step-by-step explanation:

a car that cost = 23600

down payment = 5000

So he needs to pay: 23600 - 5000 = 18600 more to get the car

Let x represent the amount he needs to pay more, an equation for his situation:

5000 + x = 23600  

Answer:

A. I Only.

Step-by-step explanation:

To begin, we must first be clear that it is the median and that it is the arithmetic mean:

Median is the middle value of a sequence of ordered numbers, for example:

{4,4,4,4,4}, the median is 4 despite being the same numbers.

Now the arithmetic mean is the average value of the samples and is independent of the amplitudes of the intervals.

Then let's analyze each of our options:

I. At least one of the homes was sold for more than $ 165,000.

We know through the flushed:

X1 + X2 +. . . + X7 + (X8 = $130,000) + X9 +. . . + X15 = 15 ∗ 150,000 = $ 2,250,000

Now we will assume the lowest possible value from X1 to X8 = $ 130,000 and from X9 to X15 = X, which is what we want to calculate. That is to say:

X1 = X2 = X3 = X4 = X5 = X6 = X7 = X8 = 130 and X9 = X10 = X11 = X12 = X13 = X14 = X15 = X,

knowing that the total value must be the average of 15, which is equal to $ 2250000 , we have the following equation:

8 ∗ $ 130,000 + 7X = $ 2,250,000

Rearranging:

X = ($ 2,250,000 $ - $ 1,040,000) / 7

X = $ 172,857

Therefore the first statement is true, because at least one house was sold at $ 172,857 which is more than $ 165,000

Evaluating the second option

II. At least one of the homes was sold for more than $ 130,0000 and less than $ 150,000

As the example of the median in the previous case you could have 8 houses that were sold for $ 130,000 or less, therefore here it loses validity, statement II is false.

Evaluating the third option

III. At least one of the homes was sold for less than $ 130,000.

We know that the eighth house sold for $ 130,000, but houses 1 to 7 may also have been sold for that same price. The statement III is false.

Therefore the answer is A. I Only.

Answer:

3.5x + 15 ≥ 55

Step-by-step explanation:

I think the question below contains the missing information.

Josh has a rewards card for a movie theater. - He receives 15 points for becoming a rewards card holder. - He earns 3.5 points for each visit to the movie theatre. - He needs at least 55 points to earn a free movie ticket. Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his firs free movie ticket?

My answer:

Let x is the number of times he visits = 3.5x

Total points = Points received on becoming a member + Points received on x visits

So,

Total Points = 15 + 3.5x

We know the total points must be at least 55 for a free movie ticket.  This can be expressed as:

3.5x + 15 ≥ 55

Answer:

105 miles

Step-by-step explanation:

The question seeks to know the number of miles traveled by Tiera given that she received a certain amount of money in payment.

The total amount of money she received is $147. She receives $7 for every 5 miles traveled. The number of 5 miles traveled is calculated as 147/7 = 21

This means she traveled 5 miles 21 times.

Thus, the total number of miles she had traveled would be 21 * 5 = 105 miles in total

Answer:

8pi feet per second

Or, 25.1 feet per second (3 sf)

Step-by-step explanation:

C = 2pi×r

dC/dr = 2pi

dC/dt = dC/dr × dr/dt

= 2pi × 4 = 8pi feet per second

dC/dt = 25.1327412287

In a cyclic quadrilateral ( a quadrilateral that is inscribed in a circle),

opposite angles add up to 180 degrees. So you can form an equation and solve for x, and thus angle E.

Therefore:

(-2 + 6x) + (7x - 13) = 180

13x - 15 = 180

13x = 195

x = 15

So angle E = 5x

                 = 5 (15)

                 = 75 degrees

Answer:

The required scatterplot is given in attached file.

Step-by-step explanation:

From the scatterplot we see that two study variables are not linearly related. There may be some non-linear relation between the two variables.

The question asks about the relationship between canary chick begging intensity and their relative growth rate. This can be determined by creating and interpreting a scatterplot of the provided data. The relationship would be considered linear if there's a consistent rate of change between begging intensity and growth rate, and non-linear if the rate of change varies.

The question is asking if the relationship between the relative growth rate of canary chicks and the difference in begging intensity is linear or not. By plotting the data on a scatterplot, we would visualize whether there is a consistent, straight-line relationship (linear) or not (non-linear) between these two variables.

Without the actual scatterplot, I cannot definitively say if the relationship is linear or not. However, linear relationships typically involve variables moving in the same direction at a constant rate, while non-linear relationships involve variables moving at different rates or directions. Therefore, if the increase in begging intensity is consistently associated with an increase in relative growth rate (and vice versa), the relationship could be considered linear. On the other hand, if increases or decreases in begging intensity inconsistently affect the relative growth rate, the relationship would likely be non-linear.

An important part of this research is the ability to interpret scatterplots and understand the concepts of linear and non-linear relationships in biological data. Interpreting such relationships is integral in the study of animal behavior and understanding how different factors, such as parental care and chick begging, affect survival and growth in bird species like canaries.

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Answer:

D

Step-by-step explanation:

Answer:

Answer in explanation

Step-by-step explanation:

The two laws are mathematical laws which are used in navigating problems which involves triangles. While the Pythagorean theorem is used primarily and exclusively for right angled triangle, the cosine rule is used for any type of triangle.

So, why is the cosine rule a stronger statement? The reason is not far fetched. As said earlier, the cosine rule can be used to resolve any triangle type while the Pythagorean theorem only works for right angled triangle. In fact, we can say the Pythagorean theorem is a special case of cosine rule. The reason why the expression is different is that, for the expression, cos 90 is zero, which thus makes our expression bend towards the Pythagorean expression view.

The explanation regarding the law of cosines is the stronger statement if compared with the Pythagorean theorem is explained below.

The Pythagorean theorem is used when there is the right-angled triangle, while on the other hand, the cosine rule is used for any type of triangle. Here the Pythagorean theorem should be considered for the special case of cosine rule. Due to this the cosine law should be stronger if we compared it with the Pythagorean theorem.

Learn more about cosine here;https://brainly.com/question/16299322

Final answer:

To find the solutions to the system of equations, use the substitution method. The solutions are (1/2, -3/2) and (7, 5).

Explanation:

To find the solutions to the system of equations, we can use the substitution method. First, solve one of the equations for y in terms of x. Let's solve the second equation for y:

y = x - 2

Now substitute this expression for y into the first equation:

x - 2 = 2x^2 - 8x + 5

Now we have a quadratic equation. Rearrange it into standard form:

2x^2 - 9x + 7 = 0

Next, factor the quadratic equation:

(2x - 1)(x - 7) = 0

Set each factor equal to zero and solve for x:

2x - 1 = 0, x - 7 = 0

x = 1/2, x = 7

Now substitute these values of x back into either of the original equations to find the corresponding values of y:

For x = 1/2: y = 1/2 - 2 = -3/2

For x = 7: y = 7 - 2 = 5

So the solutions to the system of equations are (1/2, -3/2) and (7, 5).

Answer:

Step-by-step explanation:

We would apply the formula for

exponential decay which is expressed as

A = P(1 - r)^t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 1,450,000

r = 0.99% = 0.99/100 = 0.0099

t = x years

Therefore, an exponential equation to represent this situation after x years is

A = 1450000(1 - 0.0099)^t

A = 1450000(0.9901)^t

Answer: the height of the melted candies in the pot is 12.2 mm

Step-by-step explanation:

The formula for determining the volume of a square base pyramid is expressed as

Volume = area of base × height

Area of the square base = 12² = 144 mm²

Volume of each pyramid = 15 × 144 = 2160 mm³

The volume of 100 pyramid shaped chocolate candies is

2160 × 100 = 216000 mm³

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Since the pyramids was melted in the cylindrical pot whose radius is 75 mm, it means that

216000 = 3.14 × 75² × h

17662.5h = 216000

h = 216000/17662.5

h = 12.2 mm

Answer:

The height of the melted candies in the pot is 4.07mm

Step-by-step explanation:

H= 100*1/3(12)^2(15)/π(75)^2=64/5π=4.07

Answer:

Option C, SAS Postulate

Step-by-step explanation:

I think that it is option C because it does not give you 3 angles or 3 sides, it gives you 2 angles and 1 side.

Answer:  Option C, SAS Postulate

Answer:

Explanation:

The question is incomplete. The complete question is:

A bag contains 6 red jelly beans, 4 green jelly beans, and 4 blue jelly beans.

If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red?

The probability that the first jelly bean will be green is the number of green jelly beans divided by the total number of jelly beans:

After chosing the first green jelly bean, there will be 13 jelly beans, from which 6 are red. Thus, the probability that the second jelly bean will be red is:

The probability of the joint events is the product of the two consecutive events:

The probability that the first jelly bean will be green and the second will be red is 12/91.

We start by determining the total number of jelly beans in the bag, which is:

6 red + 4 green + 4 blue = 14 jelly beans.

Step 1: Probability of the first jelly bean being green

The probability of drawing a green jelly bean first is the number of green jelly beans divided by the total number of jelly beans:

P(Green first) = 4/14 = 2/7.

Step 2: Probability of the second jelly bean being red

Once the first green jelly bean is chosen, there are now 13 jelly beans left in the bag, with 6 being red:

P(Red second | Green first) = 6/13.

Step 3: Combined probability

The combined probability of both events happening (first green, then red) is given by multiplying their individual probabilities:

P(Green first and Red second) = (2/7) * (6/13) = 12/91.

Thus, the combined probability is 12/91.

Complete question: A bag contains 6 red jelly beans, 4 green jelly beans, and 4 blue jelly beans. If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red?

Answer:

x = 2

y = 2 +  t

z = -20 -20t

Step-by-step explanation:

First, we are going to find the equation for this parabola. We replace x = 2 in the equation of the paraboloid, thus:

[tex]z = 6-x-x^{2} -5y^{2}[/tex]

if x = 2, then

[tex]z = 6-(2)-2^{2}-5y^{2}[/tex]

[tex]z = -5y^{2}[/tex]

Now, we calculate the tangent line to this parabola at the point (2,2,-20)

The parametrization of the parabola is:

x = 2

y = t  

[tex]z = -5t^{2}[/tex]  since [tex]z = -5y^{2}[/tex]

We calculate the derivative

[tex]\frac{dx}{dt}= 0[/tex]

[tex]\frac{dy}{dt}= 1[/tex]

[tex]\frac{dz}{dt}= -10t[/tex]

we evaluate the derivative in t=2, since at the point (2,2,-20) y = 2 and y = t

Thus:

[tex]\frac{dx}{dt}= 0[/tex]

[tex]\frac{dy}{dt}= 1[/tex]

[tex]\frac{dz}{dt}= -10(2)= -20[/tex]

Then, the director vector for the tangent line is (0,1,-20)

and the parametric equation for this line is:

x = 2

y = 2 +  t

z = -20 -20t

The parametric equation of the tangent line is [tex]L(t)=(2,2+t,-20-20t)[/tex]

The equation of Paraboloid is,

                 [tex]z =6-x-x^{2} -5y^{2}[/tex]

Equation of parabola when [tex]x = 2[/tex] is,

       [tex]z=6-2-2^{2} -5y^{2} \\\\z=-5y^{2}[/tex]

The parametric equation of parabola will be,

     [tex]r(t)=(2,t,-5t^{2} )[/tex]

Now, we have to find Tangent vector to this parabola is,

    [tex]T(t)=\frac{dr(t)}{dt}=(0,1,-10t)[/tex]

We get, the point [tex](2, 2, -20)[/tex] when [tex]t=2[/tex]

The tangent vector will be,

 [tex]T(2)=(0,1,-20)[/tex]

The tangent line to this parabola at the point (2, 2, −20) will be,

     [tex]L(t)=(2,2,-20)+t(0,1,-20)\\\\L(t)=(2,2+t,-20-20t)[/tex]

Learn more about the Parametric equation here:

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Answer:

12cm

Step-by-step explanation:

The scoop of Ice Cream is in the shape of a circular solid which is a Sphere.

For the ice cream to fit into the cone, the volume of the cone must be equal to that of the sphere.

Radius of the Sphere=3cm

Volume of a Sphere = [tex]\frac{4}{3}\pi r^3[/tex]

Volume of a Cone=[tex]\frac{1}{3}\pi r^2h[/tex]

[tex]\frac{1}{3}\pi X 3^2h=\frac{4}{3}\pi X 3^3\\\frac{1}{3}h=\frac{4}{3} X 3\\\frac{1}{3}h=4\\h=4 X 3=12cm[/tex]

The Cone of same radius must be 12cm tall.

Answer:

The answer to the question is

The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is  (-∞, 4)

Step-by-step explanation:

To apply look for the interval, we divide the ordinary differential equation by (t-4) to

y'' + [tex]\frac{3t}{t-4}[/tex] y' + [tex]\frac{4}{t-4}[/tex]y = [tex]\frac{2}{t-4}[/tex]

Using theorem 3.2.1 we have p(t) =  [tex]\frac{3t}{t-4}[/tex], q(t) =  [tex]\frac{4}{t-4}[/tex], g(t) = [tex]\frac{2}{t-4}[/tex]

Which are undefined at 4. Therefore the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution, that is where p, q and g are continuous and defined is (-∞, 4) whereby theorem 3.2.1 guarantees unique solution satisfying the initial value problem in this interval.

The existence and uniqueness theorems for ODEs determine that the longest interval where the initial value problem has a unique and twice-differentiable solution is (0, 4), avoiding discontinuities at t=0 and t=4.

The initial value problem provided is a second-order linear ordinary differential equation (ODE) of the form:

t(t-4)y"+3ty'+4y=2, with initial conditions y(3)=0 and y'(3)=-1.

To determine the longest interval in which the solution is guaranteed to be unique and twice-differentiable, we need to consider the existence and uniqueness theorems for ODE's, which are predicated on the functions of the equation being continuous over the interval considered. Here, the coefficients of y" and y' are t(t-4) and 3t respectively. The problematic points occur where the coefficient of y" is zero because it will make the equation not well-defined, which occurs at t=0 and t=4. Therefore, the longest interval around the initial condition t=3 that avoids these points is (0, 4). Within this interval, the coefficients are continuous, and hence, the conditions for the existence and uniqueness of the solution are satisfied.

Answer:

(1,-3)

Step-by-step explanation:

the x-axis for A is positive and the y-axis is negative. point A's X value is 1 because it is 1 point away from the origin and the value of the Y is 3 units away from the origin and it has to be negative.

Answer:

16 to the power of 1 over 4 equals 2 to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplied by 1 over 4 equals 2

Step-by-step explanation:

16 to the power of 1 over 4 equals 2 to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplied by 1 over 4 equals 2

(16)^1/4 = (2^4)^1/4

4 cancels 4

2^1 = 2

Answer:

Step-by-step explanation:

The answer is the first one.

[tex]16^{\frac{1}{4}}[/tex]  simplifies down to

[tex](2^4)^{\frac{1}{4}}[/tex]  The power to power rule is that you multiply the exponents together:

[tex]2^{\frac{4}{4}}[/tex]  which is [tex]2^1[/tex]  which is 2

I'm assuming that you are also working with radicals (since radicals and exponents are inverses of each other).  The way to write this is as a radical and simplify it is:

[tex]16^{\frac{1}{4}[/tex]  as a radical is

[tex]\sqrt[4]{16^1}[/tex]

To simplify, try to write the radicand (the number under the square root) so it's a number with a power that matches the index (the number in the "arm" of the radical sign.  Our index is a 4).  

16 is the same as 2⁴:

[tex]\sqrt[4]{2^4}[/tex]

The power on the 2 is a 4, which is the same as the index.  When the power matches the index, you pull out the base as a single number:

[tex]\sqrt[4]{2^4}=2[/tex]

What is the volume of a cylinder, in cubic m, with a height of 5m and a base diameter of 20m? Round to the nearest tenths place.

Answer: 1570.8

The volume of a cylinder with a height of 5m and a base diameter of 20m is approximately 1,570.8 cubic meters when rounded to the nearest tenths place.

To find the volume of a cylinder with a height of 5m and a base diameter of 20m, we will use the formula for the volume of a cylinder: V = πr²h , where V is volume, r is the radius of the base, and h is the height of the cylinder. The radius is half of the diameter, so for a diameter of 20m, the radius is 10m. Substituting these values into the formula gives us V = (π × 10² × 5), which we can calculate as V = 3.1416 × 100 × 5 = 1,570.8 cubic meters, rounded to the nearest tenths place.

Answer:It depends

Step-by-step explanation:

Answer:

40/13

The decimal form is going to be 3.076

Answer:

B. 1 1/7

Step-by-step explanation:

-9 2/7-(-10 3/7)

=-9 2/7+10 3/7

=1 1/7

Therefore, B. 1 1/7

Answer:

The answer is B

Step-by-step explanation:

B. 1 1/7

Answer: $406

Step-by-step explanation:

Answer: she earned $406 last week.

Step-by-step explanation:

Last week, she worked 2 hours on Monday, 10 hours on Tuesday, and 9 hours on Wednesday. This means that the number of hours that she worked for the first three days is

2 + 10 + 9 = 21 hours

She had Thursday off, and then she worked 8 hours on Friday. Therefore, the total number of hours that she worked for the week is 21 + 8 = 29 hours.

If Nanette earns $14 per hour, then the total amount of money that Nanette earned in all last week is

29 × 14 = $406

Answer: kg*m^2 / s^3

​

Answer:

Answer: kg*m^2 / s^3

Step-by-step explanation:

Answer:

(96π + 160) cm2

Step-by-step explanation:

Answer:

(a) [tex]P(X < 12)=0.26[/tex]

(b) [tex]P(X=2)=0.15[/tex]

Step-by-step explanation:

Question a

This is a Poisson distribution. The average/mean, μ = 14

So, probability that fewer than 12 field mice are found on a given acre is:

[tex]P(X < 12) = e^{-14}(\frac{14^{0}}{0!} +\frac{14^{1}}{1!} + \frac{14^{2}}{2!} + \frac{14^{3}}{3!} +\frac{14^{4}}{4!} + \frac{14^{5}}{5!} +\frac{14^{6}}{6!}+\frac{14^{7}}{7!}+\frac{14^{8}}{8!} +\frac{14^{9}}{9!}+\frac{14^{10}}{10!}+\frac{14^{11}}{11!})\\ \\P(X < 12) = e^{-14}(1+14+98+457.33+1600.67+4481.87+10457.69+20915.38+36601.91+56936.31+79710.83+101450.15)\\\\P(X < 12) = 8.315*10^{-7}(312725.1248)=0.26 \\\\P(X < 12)=0.26[/tex]

Question b

This is a Binomial distribution with:

Probability of success, p = 0.26

n = 3

[tex]P(X=2)= (3C2)p^{2}(1-p)=\frac{3!}{2!(3-2)!}*(0.26^{2})*(1-0.26)\\ \\P(X=2)=3(0.0676)(0.74)=0.15\\\\P(X=2)=0.15[/tex]

Final answer:

To find the probability that fewer than 12 field mice are found on a given acre and on 2 of the next 3 acres inspected, use the cumulative distribution function (CDF) of the Poisson distribution and the binomial distribution.

Explanation:

To find the probability that fewer than 12 field mice are found on a given acre, we need to use the cumulative distribution function (CDF) of the Poisson distribution. The average number of field mice per acre is 14, so the parameter of the Poisson distribution is also 14.

(a) To find the probability that fewer than 12 field mice are found on a given acre, we calculate P(X < 12) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 11), where X is the number of field mice found on a given acre

(b) To find the probability that fewer than 12 field mice are found on 2 of the next 3 acres inspected, we calculate P(X < 12) for each acre and use the binomial distribution to determine the probability of 2 successes out of 3 trials.

Answer:

b = [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

period = [tex]\frac{2\pi }{b}[/tex], that is

b = [tex]\frac{2\pi }{period}[/tex] = [tex]\frac{2\pi }{\frac{3\pi }{4} }[/tex] = 2π × [tex]\frac{4}{3\pi }[/tex] = [tex]\frac{8}{3}[/tex]

Answer:

f(x) = 4cos(8/3)x - 3.

The missing space is 8/3.

Step-by-step explanation:

The general form is  f(x) = Acosfx + B    where A = the amplitude, f = frequency and B is the vertical shift..

Here A is given as  4,  B is - 3 and the frequency f = 2 π / period  =

2π / (3π/4)

= 8/3.

So the answer is f(x) = 4cos(8/3)x - 3.