Consider the polynomial g(x) = 4x³ - x2 - 24x+6
a. List all possible rational zeros of the polynomial. (Assume all numbers shown are both + and -).
O1, 2, 4, 1/2, 1/3, 2/3, 4/3, 1/6
1, 2, 3, 4, 6, 1/2, 3/2, 1/3, 2/3, 4/3, 1/4, 3/4, 1/6
O 1, 2, 3, 4, 6, 1/2, 3/2, 1/4, 3/4
O1, 2, 3, 6, 1/2, 3/2, 1/4, 3/4
b. List all actual zeros of the polynomial (rational, irrational, real, and complex).
Give exact answers, separated by commas as necessary.
Zeros:

The number that we need to add is 1.5^2 = 2.25, we will get the perfect square trinomial:

(w - 1.5)^2 = 352.25

Remember that a perfect square trinomial is:

(a - b)^2 = a^2 - 2ab + b^2

Here we have the quadratic equation:

w^2 - 3w = 350

We can rewrite this as:

w^2 - 2*1.5*w = 350

Then what we need to add and subtract is 1.5^2, then we will get:

w^2 - 2*1.5*w = 350

w^2 - 2*1.5*w + 1.5^2 - 1,5^2 = 350

Grouping the first 3 terms we will get:

(w - 1.5)^2 - 1.5^2 = 350

(w - 1.5)^2 = 350 + 1.5^2

(w - 1.5)^2 = 352.25

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Answer:

To determine how many weeks it will take Clare to save enough money to buy the video game, we need to find the number of weeks it will take for her to save at least $130. Let w be the number of weeks it will take for Clare to save enough money. We can set up the following inequality to represent this situation:

$48 + $5w >= $130

To solve this inequality, we can first add $48 to both sides to get rid of the constant on the left side:

$48 + $48 + $5w >= $130

This simplifies to $96 + $5w >= $130. Subtracting $96 from both sides gives us $5w >= $34. Dividing both sides by $5 gives us w >= 6.8. Since w represents the number of weeks, the solution must be a whole number. Therefore, Clare will need to save for at least 7 weeks in order to have enough money to buy the video game.

The probability that of 300 randomly selected students enrolled in the course, more than 75 of them will earn is 0.9998..

We have given that,

A data of students in a math course offered at northern university will earn .

Total number of randomly selected students enrolled in the course = 300

i.e total number of trials, n = 300

probability of success, p = 35% = 0.35

probability of failure, q = 1-0.35 = 0.65

np = 300× 0.35 =

n(1-p) = 300×0.65 =

both np and n(1-p) are greater than 10 , so we can use normal approximation here.

We have to calculate probability that more than 75 of them will earn an , P(X>75). Using Binomial Probability distribution, X~ Bin(300, 0.35)

P(X= x) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

Now, P(X>75) = 1 - P(X=<75)

but here data is large, that is n= 300, x = 75 so tough to calculate it by hands , thus we use Excel function to find out the required probability. Excel Command: =BINOM.DIST(number_s,trials,probability_s,cumulative)

where, Number_s (required argument) -->the number of successes in trials,i.e "x" Trials (required argument) --> the number of independent trials i.e , "n" must 0≤ n. Probability_s (required argument) --> the probability of success in each trial.

Cumulative (required argument)-->A logical value that determines the form of the function. It can either be: TRUE--> Uses the cumulative distribution function and FALSE--> Uses the probability mass function. Now, for P(X ≤ 75) , the function is look like as

=BINOM.DIST(75,300, 0.35, TRUE) =0.000126081

=BINOM.DIST(75,300, 0.35, FALSE)

= 5.0305E-05

Now, the required probability, P(X> 75)

= 1 - P(X ≤75)

= 1 - 5.03095E-05 = 0.999949691

or using cumulative distribution function,

P(X>75) = 0.999873919

both are give approx. same results

.So, required probability is 0.9998.

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The company can build 5 child bikes and 15 adult bikes in a week.

The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".

Linear Equations are mathematical statements, which can be used to find an unknown quantity or any value in a given problem. Here we use variables like x, y .. etc. to represent unknown values.

Here we will use Linear Equations to solve the equations.

Here we have

One child bike requires 4 hours to build and 4 hours to test  

Number of hours to build 'c' number of child bikes = 4c

Number of hours to test 'c' number of child bikes = 4c

One adult bike requires 6 hours to build and 4 hours to test.

Number of hours to build 'a' number of adult bikes = 6a

Number of hours to test 'a' number of adult bikes = 4a  

Number of hours taken to build bikes in one week = 120

=> 4c + 6a ≤ 120  --- (1)

Number of hours taken to test the bikes in one week = 100  

=> 4c + 4a ≤ 100 --- (2)  

Assume that

The company can build 5 child bikes and 15 adult bikes in a week

Substitute c = 5 and a = 15 in (1) and (2)

(1) => 4(5) + 6(15) ≤ 120

=> 110 ≤ 120   [ which can be true ]

(2) => 4(5) + 4(15) ≤ 100

=> 80 ≤ 100  [ which can be true ]  

From the above calculations,

Both (1) and (2) are satisfied

Therefore,

The company can build 5 child bikes and 15 adult bikes in a week.

The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".

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The quadratic equation numerically (using tables of x- and y- values).

Correct option: (a). The value of x are x = -1 and x = 3.

A quadratic equation is a second-order polynomial equation in a single variable x with the formula; ax² + bx + c = 0, where a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem. The answer could be simple or complicated.

The given quadratic equation is:

x² - 3 = 2x

or, x² - 2x - 3 = 0

or, x² - 3x + x - 3 = 0

or, x (x - 3) +1 (x - 3) = 0

or, (x - 3) ( x +1 ) = 0

or, x = +3 , -1

The value of x are x = -1 and x = 3.

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The length of each individual piece is x/8

From the question, we have the following parameters that can be used in our computation:

Number of pieces = 8

Length of timber put together = x

The length of each piece of timber is calculated as

The length of each piece = Length of timber put together/Number of pieces

Substitute the known values in the above equation, so, we have the following representation

The length of each piece = x/8

Hence, the length of each piece is x/8

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Solving a system of equations we will see that they need to use:

Let's define the variables:

x = kilograms of the 10% fat-content chocolate.

y = kilograms of the 30% fat-content chocolate.

We know that they want to create 100kg, then:

x + y  =100

And the fat content must be 18%, then we can write the concentration equation:

0.1*x + 0.3*y = 0.18*100 = 18

The coefficients are the percentages in decimal form.

Now we have a little system of equations:

x + y  =100

0.1*x + 0.3*y = 18

Isolating x on the first one we get:

x = 100 - y

Replacing that in the other equation we get:

0.1*(100 - y) + 0.3*y = 18

10 + 0.2*y = 18

0.2*y = 18 - 10 = 8

y = 8/0.2 = 40

They need to use 40kg of the 30% chocolate and 60kg of the 10% chocolate.

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Answer:

The answer is in my screen shot:


Explanation:

It's a geometric sequence with common ratio 3. You can calculate the common ratio by dividing the 240 by 80 or likewise 720 by 240.

Sphere, right cylinder and cube have more than five planes of symmetry.

Symmetry in mathematics means that when one shape is moved, rotated, or flipped, it looks exactly like the other shape. A symmetrical likeness between two halves of an object, when one half is the mirror image of the other, is defined as being proportionate and balanced. As an illustration, many shapes such as square, rectangle, and circle are symmetric along their respective lines of symmetry.

Given,

Sphere and right cylinder have more than five planes of symmetry.

The number of symmetry planes depends on each solid by definition (a figure of three dimensions). The solid is split into two congruent, mirror-imaged parts by the plane of symmetry.

A cube has nine planes of symmetry, a square pyramid has four, hexagonal prims have thirteen, and spheres and cylinders have an infinite number of planes of symmetry, according to the information presented above.

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Answer nah the correct answer is cylinders cubes and cones

Step-by-step explanation:

seen it irl on edgennuitiy

Answer:

year 1: 90% × 245000 = 220500

year 2: 90% × 220500 = 198450

year 3: 90% × 198450 = 178605

∴ the car price after 3 years is 178605

explanation:

the value of car decreases 10%. that means the car price is 90%

The price of the car after 3 years will be 178605

We can calculate the value in the following way

Rate of decrease in car's price: 10%

Current price of the car: 245000

Value after 1 year, say value1= current value-10% of current value

[tex]value1=245000-\frac{10*245000}{100}[/tex]

=245000-24500

=220500

After 1 year, the next decrement in the price will be based on the value of the car in that year. In other words, we calculate the value after the second year by decreasing by 10% of value1.

Value of car after 2 years, say value2= value1- 10% of value1

[tex]value2=220500- (\frac{10*220500}{100})[/tex]

=220500-22050

=198450

Similarly,

Value of car after 3 years, say value3= value2- 10% of value2

[tex]value3=198450- (\frac{10*198450}{100})[/tex]

=198450-19845

=178605

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The standard deviation of p^ is approximately 0.00012.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.

The formula for standard deviation S.D is given below:

By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the more the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.

Calculation:

The formula for standard deviation S.D is given below:

Here,P = 3% = 0.03 and N = 240

∴ S.D = √0.03(1 - 0.03)/240

∴ S.D = 0.00012.

The standard deviation of p^ is approximately 0.00012.

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a) The type of function for each case is given as follows:

b) The functions for each house are given as follows:

c) The value of each house after 25 years is given as follows:

There is a significant difference in these valuations, as an exponential function increases faster than a linear function.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

Hence House 1 is an exponential function, as:

312519.92/303417.40 = 303417.40/294580 = 1.03.

And the definition is given as follows:

294580(1.03)^x.

The value of the house after 25 years is given as follows:

294580(1.03)^25 = $616,785.10.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

Hence House 2 is a linear function, as each year, the value of the house is increased by 9000.

Then the definition is given as follows;

295000 + 9000x.

The value of the house after 25 years is given as follows:

295000 + 9000(25) = $520,000.

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Answer:

Possible changes —

(i) Increase farmland

(ii) Sow healthy strawberry seeds

(iii) Choose a nutrient-rich, suitable plot of land

Answer:

Jolie will get 45.85 change

Step-by-step explanation:

34.67+19.48=54.48

100.00-54.15=45.85

Step-by-step explanation:

The dance committee expects attendance to number within 25 of last year's 87 students can be expressed using an inequality involving absolute value as:

|x - 87| <= 25

This inequality states that the absolute difference between the number of students attending the dance (x) and 87, which was the number of students attending last year, must be less than or equal to 25. This means that the number of students attending the dance this year must be within 25 of the number of students attending last year.

Answer:

Equation 2: y=750-100x

Step-by-step explanation:

Part (A) = Paired, Part (B) = Not Paired, Part (C) = Paired, Part (D) = Paired

Part A:

Compare pre- (beginning of the semester) and post-test (end of the semester) scores of students

Paired, as a subject are the same in both.

Score

A score is a group of 20 (often used in combination with a cardinal number, i.e. fourscore to mean 80), but also often used as an indefinite number.

Part B:

Assess the gender-related salary gap by comparing the salaries of randomly sampled men and women.

Not paired.

Sample

A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample. The possible values and the likelihood of each are determined by the random variable's probability distribution.

Part C:

Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.

Paired, as a subject are the same in both.

Vitamin E

Vitamin E is a fat-soluble vitamin with several forms, but alpha-tocopherol is the only one used by the human body.

Part D:

Assess the effectiveness of a diet regimen by comparing the before and after weights of subjects.

Paired, as a subject are the same in both.

Weight

The weight of an object refers to the force of gravity that is acting on the object. Furthermore, its calculation is mass times the acceleration of gravity, w = mg. The SI unit of weight is the newton because weight is a force.

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Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.

Paired, as a subject are the same in both.

Vitamin E

Vitamin E is a fat-soluble vitamin with several forms, but alpha-tocopherol is the only one used by the human body.

Yes, because no x values repeat.

The correct answer is option D. The covariance between securities a and b is 195.

To calculate the covariance between securities a and b, we can use the formula:

covariance = correlation coefficient * standard deviation of security a * standard deviation of security b

Plugging in the given values, we get:

covariance = 0.65 * 12 * 25 = 195

Therefore, the answer is (d) 195.

The covariance between two securities measures the extent to which the two securities tend to move together. A positive covariance indicates that the securities tend to move in the same direction, while a negative covariance indicates that the securities tend to move in opposite directions.

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Answer:

0 is the answer

Step-by-step explanation:

0*5=0

0=0*5  ==> use Zero property of multiplication

This property states that any number multiplied by 0 equals 0.

Answer:

7.8125%

Step-by-step explanation:

(4200/3200-1)/4 the difference for every month

so this would result to 7.8125% every month

Answer:

Rate = (Percentage/Base)/Time

Rate =(1 000/3 200)/4

Rate = 0.3125/4

Rate = 0.078125       (convert to percent)

Rate = 7.9%        (nearest tenth)

Step-by-step explanation:

Answer:

B, E

Step-by-step explanation:

The number of hours taken by plane in cases 1 and 2 will be 7.5 hours and 2.48 hours, respectively.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

2 planes left a similar air terminal simultaneously. One is going at 422 mph straight east, the other is voyaging 384 mph straight west.

If the distance between them is 6045 miles. Then the time is calculated as,

T = 6045 / (384 + 422)

T = 6045 / 806

T = 7.5 hours

2 planes left a similar air terminal simultaneously. One is going at 422 mph straight NORTH, the other is voyaging 384 mph straight WEST.

If the distance between them is 1997 miles. Then the time is calculated as,

T = 1997 / (384 + 422)

T = 1997 / 806

T = 2.48 hours

The number of hours taken by plane in cases 1 and 2 will be 7.5 hours and 2.48 hours, respectively.

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......,,........,.....-.......

The median would best describe the centre of the distribution for a highly skewed right histogram of US household income.  The correct option is A.

The median is the value that separates the distribution into two equal parts and is less influenced by extreme values than the mean.

Since a highly skewed right distribution has a long tail on the right side, the mean is likely to be pulled towards that tail, making it an unreliable measure of the centre.

The mode, or most frequently occurring value, may not be useful for describing the centre of a skewed distribution. The variance is a measure of the spread or dispersion of the data, not its centre.

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Answer:

Since angle 9 is 110 degrees, that means that angle 10 must be 70 degrees, because the angle is on a straight line, so the angles must add to be 180 degrees, because they are supplementary angles.  Since p ll q (p is parallel to q), that means that angle 1 is 110 degrees and angle 2 is 70 degrees.  Because angles 1, 2, 5, and 6 have to add to be 360 degrees and angles 1+2 equals 180 degrees, that means that 5+6 equals 180 degrees as well.   Angle 6 equals 110 degrees so that means angle 5 is 70 degrees.  On the other side, angle 8 is 70 degrees, and since the two angles are the same, p and q are the same.

The system of equations is x + y = 16 and y = 2x - 2

The number of shirts and pairs of pants Sylvia brought are 10 and 6, respectively

From the question, we have the following parameters that can be used in our computation:

When the statements are interpreted, we have the system of equations to be

x + y = 16

y = 2x - 2

In (a), we have

x + y = 16

y = 2x - 2

This gives

x + 2x - 2 = 16

Evaluate the like terms

3x = 18

Divide

x = 6

Recall that

y = 2x - 2

So, we have

y = 2 x 6 - 2

y = 10

Hence, the number of shirts she packed is 10

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Answer: the answer to a is 50% chance the answer to b is also 50% chance

Step-by-step explanation:

The original price is $1049 and the amount saved is $321

From the question, we have the following parameters that can be used in our computation:

Cost after discount = $728

Discount = 30% off

The original price is calculated as

Cost after discount = Original price * (1 - Discount)

So, we have

Original price = Cost after discount/(1 - Discount)

This gives

Original price = 728/(1 - 30%)

Evaluate

Original price = 1049

Here, we have

Amount saved = Original price - Cost after discount

So, we have

Amount saved = 1049 - 728

Evaluate

Amount saved = 321

Hence, the amount saved is $321

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