Three consecutive natural numbers ae such that the square of the middle number exceeds the difference of the squares of the other two numbers by 60

Answer: The probability of drawing 5 cards in either ascending or descending order out of the deck of 52 standard playing cards is 0.84%.

Step-by-step explanation: We have the following cards in a deck: 1(ace), 2, 3, 4, 5, 6, 7, 8, 9, 10, 12(Jack), 13(Queen), 14(King) (thirteen different in total). There are 4 copies of each of them yielding 52 cards in total. First to draw all of the cards in the ascending order all of the drawn cards need to be different. Imagine you have 13 piles of 4 identical cards. Let us calculate the number of ways you can select 5 different ones (the order matters). First you select 5 different piles (this secures that each card is different) and this is possible to do in [tex]\frac{13!}{(13-5)!}[/tex] (we use the formula for variations since the order matters). Now, each card in the pile can be selected in [tex]4[/tex] different ways so the total number of sequences with [tex]5[/tex] different cards is [tex]4^5\frac{13!}{(13-5)!}[/tex]. Now we select out of these sequences the clases of those that contain exactly the same cards but in different order. Only 4 of the sequences within the same class will be in ascending order out of 4*5! which is the total number of the sequences within the class! This means that we have to multiply our total number of sequences of 5 different cards by [tex]\frac{4}{4\cdot 5!}=\frac{1}{5!}[/tex] and this yields the final answer of total number of ascending sequences to be

[tex]4^5\frac{13!}{(13-5)!5!}.[/tex]  

The total number of possible ways to draw 5 out of 52 cards is just

[tex]\frac{52!}{(52-5)!}.[/tex]

This yields for the probability

[tex]\frac{4^5\frac{13!}{(13-5)!5!}}{\frac{52!}{(52-5)!}}=0.42\%[/tex]

Exactly the same calculation applies for the descending order. So the probabilty of the cards being in either ascending or descending order is just the sum of these two (the events are mutually exclusive, you cannot have both the ascending and descending order at the same time) yielding the final probability of [tex]0.84\%[/tex].

Answer:

θ ≈ 71.6°

Step-by-step explanation:

The angle between two lines with slopes m₁ and m₂ is:

tan θ = | (m₂ − m₁) / (1 + m₁m₂) |

Here, m₁ = -2 and m₂ = 1.

tan θ = | (1 − (-2)) / (1 + (-2)(1)) |

tan θ = | 3 / -1 |

tan θ = 3

θ ≈ 71.6°

Answer:

Sum = 1,023

Step-by-step explanation:

The given series is:

1 + 2 + 4 + 8 + ........ + a₁₀

The given series is a geometric series.

It is required to find the sum of the first 10 terms

The sum to n terms of a geometric series given by:  [tex]S_{n} = \frac{a(r^n-1)}{r-1}[/tex]

Where: a = the first term = 1

            r = common ratio = 2/1 = 2

           n = number of terms = 10

So,

[tex]S_{n} = \frac{a(r^n-1)}{r-1}[/tex] = [tex]\frac{1*(2^{10} -1)}{2-1} = 2^{10} -1 = 1024 - 1 = 1,023[/tex]

So, the summation of the series = 1,023

Final answer:

To calculate the total number of cherries that the bakery started with, multiply the number of pies by cherries per pie and then add the ones thrown away, resulting in 3026 cherries.

Explanation:

The question asks how many cherries the bakery started with before making the cherry pies. To find the answer, we multiply the number of cherry pies by the cherries used per pie and then add the number of cherries thrown away.

Multiply the number of pies (26) by the number of cherries used for each pie (115).

The result from step 1 gives the number of cherries used to make the pies.

Add the number of cherries thrown away (36) to the result from step 2.

The sum from step 3 is the total number of cherries the bakery started with.

Let's do the calculations:
26 pies × 115 cherries per pie = 2990 cherries
2990 cherries + 36 bad cherries = 3026 cherries

Therefore, the bakery started with 3026 cherries.

To make at least a 25% profit, Cameron should charge a minimum of $1.22 per bag for the mixed candy. The cost per bag is found by adding the total cost of candy corn and M&Ms, then multiplying by 125% and dividing by the number of bags to distribute the cost and profit evenly.

The student's question involves calculating the minimum selling price for candy bags to achieve a certain profit margin, which is a common type of problem in Mathematics, specifically in the field of algebra and business mathematics.

To find the least price Cameron can charge for each of the thirty bags to make at least a 25% profit, we first calculate the total cost of the candy. Cameron bought twelve pounds of candy corn at 79 cents a pound and eighteen pounds of M&Ms at $1.09 a pound.

Now, we calculate the total cost including the desired 25% profit.

Total cost with profit: $29.10 × (1 + 0.25) = $36.375

Since Cameron is making thirty bags, we divide the total cost with profit by the number of bags.

Minimum selling price per bag: $36.375 / 30 bags = $1.2125

However, as prices are generally rounded to the nearest cent, the minimum charge per bag would be $1.22 to ensure a 25% profit.

Answer:

State A has 27 screens and state B has 21 screens.

Step-by-step explanation:

Let the number of screens in state B be 'x'.

Given:

Number of screens in state A is 6 more than state B

Total number of screens = 48.

Now, as per question:

Number of screens in state A = 6 more than state B.

Framing in equation form, we get:

Number of screens in state A = [tex]6+x[/tex]

Now, total number of screens is the sum of the screens in state A and number of screens in state B. Therefore,

Total number of screens = 48

Number of screens in state A + Number of screens in state B = 48

Substituting the given values, we get:

[tex]6+x+x=48\\\\6+2x=48\\\\2x=48-6\\\\2x=42\\\\x=\frac{42}{2}=21[/tex]

So, state B has 21 screens.

State A has = 6 + 21 = 27 screens.

Therefore, state A has 27 screens and state B has 21 screens.

Answer:

Step-by-step explanation:

#2 the answer is B, -16/9

do 1/4-5/2

to do this, find the least common denominator. it's 4

1/4-10/4=-9/4

then divide 4 by -9/4. This is the same as 4*-4/9. That is -16/9

#3 the answer is A 9x/x-8

first factor the denominator of the first fraction using special products

x^2-6x-16=(x-8)(x+2)

if you look at the first fraction, you can simplify x+2 leaving you with the fraction 1/x+8

multiply that by 9x, and you get 9x/x-8

#4 the answer is C (2x+1)/2x^2

first add x/4 and 1/8

find the least common denominator. its 8

2x/8 + 1/8 is equal to (2x+1)/8

then multiply that by x^2/4 because dividing a fraction is the same as multiplying its reciprocal

you get (2x+1)/2x^2

#5 the answer is C (x-8)/(x+3)

using special products you can factor the numerator

x^2-4x-32 is the same as (x-8)(x+4)

then, using special products you can also factor the denominator

x^2+7x+12 is the same as (x+4)(x+3)

you can see that both the numerator and the denominator is multiplied by (x+4) you can simplify that. That leaves you with (x-8)/(x+3)

#7 the answer is D 3m

in the numerator in the second fraction, you can factor out 5m^2

leaving you with 5m^2(m-6)/5m^2. simplify the 5m^2 and the m-6

after you simplify both of those, you will get 3m

Answer:

The answer is 38.7 kg·m/s

Step-by-step explanation:

Considering the definition of average velocity,

The average speed of an object is defined as the distance traveled divided by the time elapsed.

Therefore, If in the frame of 320, the blue dot appears to be at 0 cm  and 24 frames later (at 344), the blue dot appears to be at 11 cm.  24 frames is 1/10 of a second, so

V = 11cm / 0.10s = 110 cm/s = 1.10 m/s

give or take.

Bonus:  initial system (cart only) momentum

p = mv = 23.8kg * 1.80m/s = 42.8 kg·m/s  

final system (cart+disk) momentum

p = (23.8+11.4)kg * 1.10m/s = 38.7 kg·m/s

Answer:

y/\8

Step-by-step explanation:

(y

4

)

2

​

=y

4⋅2

=y

8

​

This follows from the general rule \left(x^m\right)^{n}=x^{m\cdot n}(x

m

)

n

=x

m⋅n

left parenthesis, x, start superscript, m, end superscript, right parenthesis, start superscript, n, end superscript, equals, x, start superscript, m, dot, n, end superscript.

We can also see this is correct by expanding the powers.

\begin{aligned} \left(y^4\right)^{2}&=\underbrace{y^4\cdot y^4}_\text{2 times} \\\\\\ &=\underbrace{ \underbrace{y\cdot y\cdot y\cdot y}_\text{4 times} \cdot \underbrace{y\cdot y\cdot y\cdot y}_\text{4 times}} _\text{2 times} \\\\ &=y^{8} \end{aligned}

(y

4

)

2

​

=

2 times

y

4

⋅y

4

​

​

=

2 times

4 times

y⋅y⋅y⋅y

​

​

⋅

4 times

y⋅y⋅y⋅y

​

​

​

​

=y

8

​

Hint #22 / 2

In conclusion, \left(y^4\right)^{2}=y^{8}(y

4

)

2

=y

8

left parenthesis, y, start superscript, 4, end superscript, right parenthesis, squared, equals, y, start superscript, 8, end superscript.

To rewrite the expression, divide the digit term in the numerator by the digit term in the denominator and subtract the exponents. The final expression is y^-1/4.

To rewrite the expression in the form yn, we can use the rules of division of exponentials. In this case, we have 1/y5/4.

To divide, we need to subtract the exponents and divide the digit term in the numerator by the digit term in the denominator.

The digit term in the numerator is 1, and the digit term in the denominator is 1.

So, the expression can be rewritten as y1 - 5/4.

Now, let's simplify the exponent. We have 1 - 5/4 = 4/4 - 5/4 = -1/4.

So, the final expression is y-1/4.

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Answer:

-15x^4y

Step-by-step explanation:

(-3x^3y^2)(5xy^-1)

-15x^4y^2/y

-15x^4y

Answer:

C.  -15x^4y.

Step-by-step explanation:

(-3x^3y^2) (5xy^-1)

= -3*5 x^(3+1)y^(2 - 1)

= -15x^4y.

Answer:

42 liters

Step-by-step explanation:

Set up the ratios as fractions.

6/7 = 36/x

To get the volumes multiply the 6 and the 7 by 6.

This is how you got the 36 for the first volume.

The volume of the second container is 42.

7 x 6 = 42

Answer:

a) The probability is 0.3

b) The probability is 0.1

c) The probability is 0.35

Step-by-step explanation:

Lets call S1 and S2 the events ' he must stop at signal 1 ' and 'he must stop at signal 2' respectively.

a) We know that

0.65 = P(S1 ∪ S2) = P(S1) + P(S2) - P(S1 ∩ S2) = 0.4+0.55-P(S1 ∩ S2) = 0.95 - P(S1 ∩ S2)

Hence P(S1 ∩ S2) = 0.95-0.65 = 0.3

It stops at both signals with probability 0.3

b) Note that, due to the theorem of total probability we have

0.4 = P(S1) = P(S1 ∩ S2) + P(S1 ∩ S2^c) = 0.3 + P(S1∩S2^c)

Where S2^c is the complementary event of S2. Therefore

P(S1∩S2^c) = 0.4-0.3 = 0.1

The probability to stop at the first signal but not at the second one is 0.1

c) The probability of stopping at exactly one signal is equal at the sum of the probabilities of stopping only at the first signal and the probability of stopping only at the second one.

That is P(S1 ∩ S2^c) + P(S1^c ∩ S2) = 0.1 + P(S1^c ∩ S2)

The same way as before:

0.55 = P(S2) = P(S1 ∩ S2) + P(S1^c ∩ S2) = 0.3 + P(S1^c ∩ S2)

Therefore

P(S1^c ∩ S2) = 0.55-0.3 = 0.25

And as a result, the probability of stopping at exactly one signal is 0.25 + 0.1 = 0.35.

The probability that he must stop at both signals 0.30.

The probability to stop at the first signal but not at the second one is 0.1.

The probability that he must stop at exactly 0.35.

Given that,

The probability that he must stop at the first signal is 0.4,

The analogous probability for the second signal is 0.55,

The probability that he must stop at at least one of the two signals is 0.65.

We have to determine,

What is the probability that he must stop.

According to the question,

F = Event that a certain motorist must stop at the first signal.

S = Event that a certain motorist must stop at the second signal.

P(S1 ∪ S2) = P(S1) + P(S2) - P(S1 ∩ S2) =0.65

0.4 +0.55 - P(S1 ∩ S2) = 0.65

0.95 - P(S1 ∩ S2) = 0.65

Hence, P(S1 ∩ S2) = 0.95 - 0.65 = 0.30

It stops at both signals with probability 0.30.

The probability that he must stop at both signals 0.30.

P(S1) = P(S1 ∩ S2) + P(S1 ∩ S2^c)

0.4 = 0.3 + P(S1∩S2^c)

Where S2^c is the complementary event of S2. Therefore

P(S1∩S2^c) = 0.4 - 0.3 = 0.1

The probability to stop at the first signal but not at the second one is 0.1.

= P(S1 ∩ S2^c) + P(S1^c ∩ S2)

= 0.1 + P(S1^c ∩ S2)

Then,

= P(S2) = P(S1 ∩ S2) + P(S1^c ∩ S2) = 0.5

= 0.3 + P(S1^c ∩ S2) = 0.5

Therefore,

P(S1^c ∩ S2) = 0.55 - 0.3 = 0.25

And the probability of stopping at exactly one signal is 0.25 + 0.1 = 0.35.

The probability that he must stop at exactly 0.35.

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Answer:

The answer to your question is picture 1

Step-by-step explanation:

- This is a quadratic equation, so we look for a parabola. The four graphs show parabolas.

- We can notice a negative sign before the term (x - 3)², which indicates that it is a down-parabola. We discard the second and the fourth pictures.

- Get the vertex

                         y = -(x - 3)² - 5

                         y + 5 = - (x - 3)²      Vertex = (-5, 3)  

                                                         because we change signs

- With all this information, we conclude that the answer is picture 1 because its vertex is (-5, 3)

Answer:

Step-by-step explanation:

The car's value was $61,412.50  in the year 2006.

x = no. of years since 2000.

Acc. to ques,

100,000 × (0.85)ˣ = 61,412.50

(0.85)ˣ = 0.614125.

ln((0.85)ˣ) = ln(0.614125).

x × ln(0.85) = ln(0.614125).

x = ln(0.614125) / ln(0.85).

x = 5.832 ≈ 6

Step-by-step explanation:

Given  

    2. and w = max (10,w)

From the first equation we get that w= 20

and it also satisfies the second equation.

∴ The value of min(10,w) = min(10,20) ∵w=20

                                        = 10

Considering both conditions, our w value could be 10 or greater. As we are looking for the minimum value between 10 and w, the result of min(10, w) will be 10.

Let's look at the two provided conditions:

Since both conditions suggest that w could be a value 10 or greater, the exponent w in min(10, w) will be at least 10. However, because we're finding the minimum between 10 and w, the value of min(10, w) will be 10.

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Answer:

Step-by-step explanation:

DE*s=BA  24*s=35 s=35/24

(3x+7)35/24=6x-5

35/8x+5/24=6x-5

          -5/24    -5/24

-8bits is equivalent yo 1 byte

-bit is(0 or 1)

So each pixel requires 3 bytes

Primary colors are RGB(red,green and blue),so each color represent one byte.

The frame size is:

1280×1024=1310720 pixels

So that the frame contained 1310720 pixels

The size of the frame buffer is equal to the product of RGB and frame pixels:

=3 × 1310720

=3932160 bytes

The minimum size of the frame buffer to store a frame of 1280 x 1024 pixels, with 8 bits used for each of the three primary colors (red, green, blue) per pixel, is 3932160 bytes.

When calculating the size of a frame buffer, you want to take into account the number of pixels in the frame, the number of bits used to represent each primary color per pixel, and the number of primary colors. In this case, the frame is 1280 x 1024 pixels, and 8 bits are used for each of the three primary colors (red, green, blue) per pixel.

Therefore, the calculation will be as follows:

So, the minimum size of the frame buffer to store a frame in this context would be 3932160 bytes.

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Answer: The limit does not exist.

Step-by-step explanation: The limit of a piecewise function f(x) as it approaches "a" will exist if and only if the value of the limit of f(x) as x approaches "a" from the left is the same with the value of the limit of f(x) as x approaches "a" from the right.

From the given question the value are not the same. We have 5 (limit from the left) and -3 (limit from the right). So, we can conclude that the limit of f(x) as x approaches "a" does not exist.

Answer:

It's descriptive.

Step-by-step explanation:

inferential statistic, means we are inferring based on a sample of our population. Many times we need to infer because the data we need to collect is too large, i.e. the population is too large e.g. the average age of high school students in the US. so we take a sample, a portion of this population and we calculate their mean age. If our sample is random enough, we can "infer" to a certain degree of accuracy the mean

But descriptive statistics, describes the data. They are numbers used to summarise and describe a data. 60% describes the data.

Answer:

The answer to your question is below

Step-by-step explanation:

f(x) = 2x + 5

To solve letter a, just multiply each term of f(x) by 3 and subtract 2.

a) 3f(x) - 2 = 3(2x + 5) - 2

                 = 6x + 15 - 2

               = 6x + 13

To f(x) subtract twice g(x)

b) f(x) - 2g(x) = 2x + 5 - 2(x² - 3x + 2)

                    = 2x + 5 - 2x² + 6x - 4

                    = -2x² + 8x + 1

Multiply 5 by each term of f(x) and divide it by g(x)

c)      [tex]\frac{5f(x)}{g(x)} = \frac{5(2x + 5)}{x^{2} - 3x + 2}[/tex]  

                = [tex]\frac{10x + 25}{x^{2}-3x + 2}[/tex]

Answer:

P(A' U B) = 84/100

Step-by-step explanation:

We have, P(A) = 86/100

P(B) = 79/100

P(A') = 7/50

P(A U B) = 95/100

-: P(A intersection B) = P(A) + P(B) - P(A U B)

P(A intersection B) = 86/100 + 79/100 - 95/100

P(A intersection B) = (86+79-95)/100 = (165-95)/100

P(A intersection B) = 70/100

Now, P(A' U B) = P(A') + P(A intersection B)

P(A' U B) = 7/50+70/100

P(A' U B) = (7*2+70)/100 = (14 + 70)/100

P(A' U B) = 84/100

The object's position function is y = 2.5t² - 2t derived using kinematic equations. The speed at time t is |-2 + 5t| m/s where t is the time.

This is a problem of mechanics related to the motion of the object under the influence of a force. First, we need to calculate the acceleration using the formula F=ma. This gives us the acceleration as a = F/m = 20N/4kg = 5m/s². The object is moving upwards so this force is in the positive y direction.

The initial velocity vector is given as vs0d − i2j. The i-component represents the x-direction, and the j-component represents the y-direction. Thus, the initial speed is sqrt((0d)² + (−2)²) = 2 m/s. However, given that this velocity is in the negative y-direction, we determine its initial speed to be -2 m/s.

Now, we can determine the position function for the y-direction using the equation y = y0 + v0y*t + 0.5*a*t², where y0 represents the initial position (origin), v0y is the initial velocity in the y-direction (-2m/s for this case), a is the acceleration (5 m/s²), and t is time. Substituting these values, the equation becomes y = 0 – 2t + 0.5*5t² = 2.5t² - 2t.

For the speed at time t, you can utilize the velocity's magnitude in the y-direction using v = v0y + a*t = -2 m/s + 5t The magnitude ||v|| = sqrt((0)² + (-2 + 5t)²) = |-2 + 5t| m/s as speed is always positive.

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We determined the object's position function to be [tex]\[ \matbf{r}(t) = -t \mathf{i} + 2t \mathf{j} + \frac{5t^2}{2} \mathf{k} \][/tex] and its speed at time t to be |v(t)| = [tex]\sqrt{5 + 25t^2}[/tex]. The calculations involved using Newton's second law and integrating the acceleration and velocity.

To find the position function and speed of the object under the given conditions, we need to use the principles of Newtonian mechanics. Let's break it down step-by-step.

Step 1: Find the acceleration

Given:

- Force ( F = 20 N ) upward

- Mass  (m = 4 kg)

Using Newton's second law (F = ma) , we can find the acceleration:

[tex]\[ \mthbf{a} = \frac{\mahbf{F}}{m} \][/tex]

Since the force is acting directly upward (which we'll take as the ( z )-direction):

F = 20k

Thus,

[tex]\[ \mahbf{a} = \frac{20 \matbf{k}}{4} = 5 \mahbf{k} \][/tex]

So, the acceleration is:

a = 5k

Step 2: Find the velocity function

The initial velocity is given as:

[tex]\[ \matbf{v}(0) = -\matbf{i} + 2\matbf{j} \][/tex]

Acceleration is constant, so we can integrate to find the velocity function:

[tex]\[ \matbf{v}(t) = \mathf{v}(0) + \mathf{a} t \][/tex]

Substituting the known values:

[tex]\[ \mathf{v}(t) = (-\matbf{i} + 2\matbf{j}) + 5 t \mahbf{k} \][/tex]

Thus,

[tex]\[ \matbf{v}(t) = -\matbf{i} + 2\matbf{j} + 5t \mthbf{k} \][/tex]

Step 3: Find the position function

To find the position function, integrate the velocity function:

[tex]\[ \mahbf{r}(t) = \mathf{r}(0) + \int \mathf{v}(t) \, dt \][/tex]

Given that the object starts at the origin:

r(0) = 0

Integrating the velocity function:

[tex]\[ \mathf{r}(t) = \int (-\mathf{i} + 2\matbf{j} + 5t \mathf{k}) \, dt \][/tex]

[tex]\[ \mahbf{r}(t) = (-\matbf{i}t) + (2\matbf{j}t) + \left( \frac{5t^2}{2} \matbf{k} \right) \][/tex]

Thus, the position function is:

[tex]\[ \matbf{r}(t) = -t \mathf{i} + 2t \mathf{j} + \frac{5t^2}{2} \mathf{k} \][/tex]

Step 4: Find the speed at time ( t )

Speed is the magnitude of the velocity vector:

[tex]\[ \mathb{v}(t) = -\mathf{i} + 2\matbf{j} + 5t \mathb{k} \][/tex]

Calculate the magnitude:

[tex]\[ \text{Speed} = |\mathbf{v}(t)| = \sqrt{(-1)^2 + (2)^2 + (5t)^2} \][/tex]

[tex]\[ \text{Speed} = \sqrt{1 + 4 + 25t^2} \][/tex]

[tex]\[ \text{Speed} = \sqrt{5 + 25t^2} \][/tex]

Answer:

D itll go from 87.5 to 70, so it'll drop by 17.5

Step-by-step explanation:

Answer:

The answer is actually D

Step-by-step explanation:

This is true because when you add the scores together you get 350 and then you divide that number by however many data numbers there are in the set.

86+84+90+90=350

because there are 4 numbers in the data set you so divide 350 by 4 which equals 87.5

Then he scores a 0 on the quiz, it will indeed affect the mean.

You add the numbers 86+84+90+90+0 still equals 350, however, instead of 4 numbers in the data set it's 4 because of the zero.

Instead of dividing by 4, you divide by 5

350 divided by 5 equals 70.

the original MEAN was 87.5 and now it is 70, so that means that it decreased by 17.5. there's is your answer. The answer is D 17.5

Answer: c. sampling error

Step-by-step explanation:

Since, the sample is a subset of population , so there are chances for unavoidable variation in sample mean from the population mean that varies from sample to sample .

This variation is known as sampling error.

∴ The difference between the value of the sample statistic and the value of the corresponding population parameter is called the sampling error .

Hence,the correct answer is c. sampling error .

The difference between the sample statistic and the population parameter is known as the sampling error. This error occurs due to the sample selected being unrepresentative of the entire population.

The difference between the value of the sample statistic and the value of the corresponding population parameter is referred to as the sampling error. This definition directly fits the option c. Listed among the given options. A sampling error is a discrepancy that occurs due to an unrepresentative selection of observations from the whole population. The nature of statistical sampling means there will always be some level of uncertainty or error because we are making estimates based on a sample from a larger population, rather than the entire population itself.

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Answer:

x = 6.

Step-by-step explanation:

Because the the 2 angles are equal

4 / (x + 2) = 3 / (9-3)

4/(x+2) = 3/6

4 / (x + 2) = 1/2

x + 2 = 4*2 = 8

x = 8 - 2 = 6.

Answer: T may hold either L or L2

Step-by-step explanation: Going by Landlord and Tenant's law, when L leases a property to T and afterwards assigns his or her own interest to L2. T can either hold L or L2 when a paramount title holder X ejects T from the property.

According to the Law, L (in this case can be referred to as the Landlord) can actually assign all of his or her own rent rights and reversion to L2 (can be referred to as Landlord 2 or assignee). Whatever agreements or contracts made between L and T according to the lease of the property automatically ropes in L2. In this case, T is ejected by X who is a paramount title holder. This goes against the contract agreement between L and T, and therefore gives T the right to hold either L or L2.

I hope this helps.  

Answer:

x³ − x² + 9x − 9 = 0

Step-by-step explanation:

Imaginary roots come in conjugate pairs.  So if 3i is a root, then -3i is also a root.

(x − 1) (x − 3i) (x − (-3i)) = 0

(x − 1) (x − 3i) (x + 3i) = 0

(x − 1) (x² − 9i²) = 0

(x − 1) (x² + 9) = 0

x (x² + 9) − (x² + 9) = 0

x³ + 9x − x² − 9 = 0

x³ − x² + 9x − 9 = 0

To find a third-degree polynomial equation with rational coefficients that has the given roots, we consider the conjugate of the complex root. The equation can be written as (x - 1)(x - 3i)(x + 3i) and simplified to x^3 - x^2 + 9x - 9.

To find a third-degree polynomial equation with rational coefficients that has the given roots of 1 and 3i, we need to consider the conjugate of 3i, which is -3i. Therefore, the roots of the equation are 1, 3i, and -3i.

To find the polynomial equation, we start by noting that the polynomials with rational coefficients will have complex conjugate pairs of roots. Thus, we can write the equation as (x - 1)(x - 3i)(x + 3i). Simplifying, we get (x - 1)(x^2 + 9). Expanding further, the equation is x^3 - x^2 + 9x - 9.

Therefore, the desired third-degree polynomial equation with rational coefficients is x^3 - x^2 + 9x - 9.

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Answer:

the choice of consumers regarding what to purchase to satisfy their wants and the choice of producers regarding what to produce to maximize profits.

Step-by-step explanation:

Answer:

[tex]Down\ payment = 7,344[/tex]

Step-by-step explanation:

Let x be the amount of 15% of gross income.

Given:

Jessica gross income = 48,960.00

She decided to use 15% amount as down payment.

We need to find the amount of 15% of gross income.

Solution:

Using percentage formula.

[tex]percentage = (\frac{Value}{Total\ value})\times 100[/tex]

Now we substitute 15 in the place of percentage and 48,960 in the place of Total value.

[tex]15=(\frac{x}{48960})\times 100[/tex]

Now, we apply cross multiplication rule.

[tex]x= \frac{48960\times 15}{100}[/tex]

[tex]x=48960\times 0.15[/tex]

[tex]x =7,344[/tex]

Therefore: Down payment is 7,344.

Final answer:

Jessica allocated $7,344 for the down payment on a house based on her 15% gross income allocation.

Explanation:

The budget that Jessica allocated for her down payment on a house is calculated as follows:

Calculate 15% of Jessica's gross income: 15% of $48,960 is $48,960 * 0.15 = $7,344.

Therefore, the budget that Jessica allowed for the down payment on a house is $7,344.

Answer:

168 members are on the marching band but not part of the percussion.

Step-by-step explanation:

Given:

The high school marching band has 196 members,and 28 of them are a part of the percussion.

Now, to find the members on the marching band but not part of the percussion.

Total members of marching band = 196.

Members of them who part of percussion = 28.

So, to get the members of the marching band who are not the part of the percussion we subtract members of them who part of percussion from total members of marching band:

[tex]196-28[/tex]

[tex]=168.[/tex]

Therefore, 168 members are on the marching band but not part of the percussion.