Based on the table, which statement is true?
A. About 40% of the students prefer Chocolate.
B. About 30% of the students prefer Mint.
C. About 20% of the students prefer Orange.
D. About 50% of the students prefer Orange.

Answer:

Step-by-step explanation:

To find the number of real zeros of a polynomial, we can use Descartes' rule of signs. According to this rule, the number of positive real zeros of a polynomial is equal to the number of sign changes in the coefficients of the polynomial, or is less than that by a multiple of 2. Similarly, the number of negative real zeros is equal to the number of sign changes in the coefficients of f(-x), or is less than that by a multiple of 2.

For f(x) = 3x^5 - 12x^4 + 20x³ - 180x² + 120x+81​, there are 2 sign changes in the coefficients, so the number of positive real zeros is either 2 or 0. To find the number of negative real zeros, we can substitute -x for x in f(x) and simplify:

f(-x) = 3(-x)^5 - 12(-x)^4 + 20(-x)³ - 180(-x)² + 120(-x)+81

= -3x^5 - 12x^4 - 20x³ - 180x² - 120x + 81

There are 3 sign changes in the coefficients of f(-x), so the number of negative real zeros is either 3 or 1. Therefore, f(x) has either 2 or 0 positive real zeros, and either 3 or 1 negative real zeros.

To find the number of imaginary zeros, we can use the complex conjugate root theorem, which states that if a polynomial with real coefficients has a+bi as a root (where a and b are real numbers and i is the imaginary unit), then its conjugate a-bi is also a root. Since the coefficients of f(x) are all real, any non-real roots must occur in conjugate pairs.

Since f(x) has degree 5, it has 5 complex roots (counting multiplicities). If all the real zeros are distinct, then there are 5 distinct complex roots, and hence 5 imaginary zeros (again, counting multiplicities). If there are any repeated real zeros, then there are fewer than 5 distinct complex roots, and hence fewer than 5 imaginary zeros.

In summary, the number of real zeros of f(x) is either 2 or 0 positive zeros and either 3 or 1 negative zeros. The number of imaginary zeros is at most 5 (counting multiplicities).

Answer:

[tex]\\\cos B =\dfrac{8\sqrt{79}}{79}[/tex]

Step-by-step explanation:

How do we find cosine of an angle in a right triangle?
In a right-angled triangle, if one of the angles is θ, then the cosine of θ is the length of the side adjacent to θ, divided by the length of the hypotenuse .

Here we are trying to find cos B

The side adjacent to B is BC with a length of [tex]8[/tex]

The hypotenuse is BD with a length of [tex]\sqrt{79}[/tex]

[tex]\therefore\\\cos B = \dfrac{8}{\sqrt{79}}\\[/tex]

[tex]79[/tex] is a prime number so it cannot be factored

To express in simplest radical form, we have to remove [tex]\sqrt{79}[/tex] from the denominator by  multiplying the numerator and denominator by [tex]\sqrt{79}[/tex]

[tex]\therefore\\\cos B = \dfrac{8}{\sqrt{79}} \times \dfrac{\sqrt{79}}{\sqrt{79}} \\\\= \dfrac{8\sqrt{79}}{79}[/tex]

so after solving, Hence, after 11 minutes, there are 619 litres of water in equation the pond overall.

A assertion that charged objects are equal is known as an equation. Normally, two expressions are connected by the equality symbol (=). A mathematical tool for representing relationships between a number of variables or quantities is an equation. By identifying particular asset(s) of the indeterminate factors that make the equation true, equation may be utilized to solve issues. Many aspects of daily life as well as numerous fields of science, engineering, maths, or other disciplines use equations.

This question is similar to the pipe and cistern problem. The amount of water in the pond (W) after T minutes can be represented by the following equation:

W = 29T + 300

where 29T represents the amount of water added in T minutes and 300 represents the initial amount of water in the pond.

We may simplify the equation by adding T = 11 and finding the total volume of water in the pond after 11 minutes:

W = 29(11) + 300

W = 319 + 300

W = 619

Hence, after 11 minutes, there are 619 litres of water in the pond overall.

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The total amount of water in the pond after 11 minutes of adding water at a rate of 29 liters per minute is 619 liters.

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b.

The equation that relates W (total amount of water in the pond) to T (time in minutes) is:

W = 29T + 300

where 29T represents the amount of water added in T minutes (at a rate of 29 liters per minute) and 300 represents the initial amount of water in the pond.

To find the total amount of water after 11 minutes, we substitute T = 11 into the equation:

W = 29(11) + 300

W = 319 + 300

W = 619

Therefore, the total amount of water in the pond after 11 minutes of adding water at a rate of 29 liters per minute is 619 liters.

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The ascending order of the expressions are π/3 , √8/3 , √4/2

Given data ,

Let the expression be represented as A

Now , the value of A is

A = π/3 , √8/3 , √4/2

On simplifying , we get

Now , π > √8

So , the value of π/3 is greater than √8/4 since they have the same denominator

And , the value of √4/2 = 1

Hence , the ascending order is √4/2 , √8/3 , π/3

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The estimate of the expected number of children is 2.88.

To pretend the process of having children until the couple has a girl, we can use the following algorithm:

Start with an empty list of children.

Repeat the following until a girl is born:

1. Firstly create an arbitrary digit from Table A.

2. Then if the digit is 0, 1, 2, 3, 4, or 5,  then add a girl to the list of children.

3. Now, if the digit is 6, 7, 8, or 9, add a boy to the list of children.

After this count total number of children present.

We can repeat this process 25 times using Table A, starting at line 101, and record the number of children in each simulation. Then we can calculate the average number of children as our estimate of the expected number of children.

They are the results of 25 simulations:

9, 3, 3, 7, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1

The average number of children in these simulations is:

(9 + 3 + 3 + 7 + 1 + 1 + 1 + 3 + 3 + 3 + 3 + 3 + 3 + 5 + 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 5 + 1) / 25

= 2.88

thus, our estimate of the anticipated number of children until the couple has a girl is roughly 2.88.

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Molly earned $282.37 - $220.00 = $62.37 in interest at the end of six years.

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

To solve this problem, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(nt) [/tex]

We are given that Molly placed $220.00 in a savings account with an annual interest rate of 4.2%. We are also told that she did not add or take out any money from the account, so the principal remains $220.00. Since we are not given how many times per year the interest is compounded, we will assume it is compounded annually (n = 1).

After 6 years, the formula becomes:

[tex]A = 220(1 + 0.042/1)^{(1*6)}A = 220(1.042)^6[/tex]

A = 220(1.2835)

A = $282.37

Therefore, Molly earned $282.37 - $220.00 = $62.37 in interest at the end of six years.

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The profit earned by Monica per month for the overhead cost of $2,500 is equal to $3,700.

Amount charged by Monica for each hour of time in the studio = $50

Amount paid by Monica per month for her overhead costs to run the studio = $2500

Monica's revenue for the month,

= Multiply the number of hours each client spends in the studio by the hourly rate she charges.

Substitute the values for each client we have,

Client A,

28 hours x $50/hour = $1,400

Client B,

16 hours x $50/hour = $800

Client C,

20 hours x $50/hour = $1,000

Client D,

36 hours x $50/hour = $1,800

Client E,

24 hours x $50/hour = $1,200

Total revenue for the month

= $(1400 + 800 + 1,000 + 1,800 + 1,200 )

=  $6,200

Monica's profit for the month

= subtract her overhead costs from her revenue.

This implies,

Profit = Revenue - Overhead Costs

⇒Profit = $6,200 - $2,500

⇒Profit = $3,700

Therefore, Monica's profit for the month is $3,700.

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The above question is incomplete, the complete question is:

In order to earn money in her new studio, Monica uses her knowledge, experience and expertise to set up a recording studio where she rents studio space to new clients and charges by the hour. She charges her clients $50 for each hour of time in the studio and pays $2,500 per month for her overhead costs to run the studio.

Clients     Hours per month in studio

A                 28 hours in studio

B                  16  hours in studio

C                  20  hours in studio

D                  36  hours in studio

E                   24  hours in studio    

The length of the shadow of the goalpost is 30 feet long

Proportion can be described as an equation in which there are two different ratios that are set equal to each other.

From the information given, we have that;

The goalpost is 12. 5 feet tall

The Coach is 6 feet tall

The coach casts a shadow that is 14. 4 feet lone.

Then,

if 6 feet = 14. 4 long

Then, 12. 5 feet = x

cross multiply the values

x = 180/6

Divide the values

x = 30 feet long

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The lengths of the three rods are given as follows:

The lengths of the rods are obtained applying the proportions in the context of the problem.

The ratio of A to B is:

A/B = 3/2.

Hence:

The ratio of A to C is:

A/C = 2/5.

Hence:

Thus the order, from least to greatest, is:

B, A, C.

The difference in length between the longest rod and the shortest rod is 55 cm, hence the length of rod A is obtained as follows:

C - B = 55

2.5A - 0.6666A = 55

A = 55/(2.5 - 0.6666)

A = 30 cm.

Then the lengths of B and C are given as follows:

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The measure of the angle ∠SQR is 34°. Then the measure of arc RQ will be 68°.

Given that:

arcYQ = 80°

∠RQY = 106°

The central angle is double the angle at the periphery that was subtended by the same chords.

∠RQY + ∠RSY = 180°

106° + ∠RSY = 180°

∠RSY = 74°

∠QSY = 1/2 arc QT

∠QSY = 1/2 x 80°

∠QSY = 40°

∠SQR + ∠QSY = ∠RSY

∠SQR + 40° = 74°

∠SQR = 34°

arc RQ = 2 x ∠SQR

arc RQ = 2 x 34°

arc RQ = 68°

The measure of the angle ∠SQR is 34°. Then the measure of arc RQ will be 68°.

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The requried water in Juan's body weight is 57.13 kilograms or 117.13 pounds

To find out how much water is in Juan's body weight, we need to multiply his body weight by the percentage of his weight that is water:

Water weight = Body weight × Percentage of body weight that is water

First, we need to convert Juan's weight from pounds to a more convenient unit for the calculation, such as kilograms:

185 pounds = 84.09 kilograms

Now we can calculate the water weight:

Water weight = 84.09 kg x 68/100 = 57.13 kg

Therefore, the water in Juan's body weight is 57.13 kilograms or 117.13 pounds

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The end behavior of a function is determined by the degree of the highest-order term in the function. Thus, the answer is Option 4: as x→∞, y→−∞ and as x→−∞, y→−∞.

It is a rule that assigns an output value to each input value. In other words, a function is an equation that describes a relationship between two sets of values.

In this case, the highest-order term is 3x⁴, which has a degree of 4. Since the degree of the highest-order term is even, the end behavior of f(x) is that as x→∞, y→−∞ and as x→−∞, y→−∞.

To further explain, the degree of the highest-order term determines the direction of the end behavior of the function.

If the degree of the highest-order term is even, the end behavior of the function is that as x approaches either positive or negative infinity, the value of the function will approach negative infinity. If the degree of the highest-order term is odd, the end behavior of the function is that as x approaches either positive or negative infinity, the value of the function will approach positive infinity.

In this case, the degree of the highest-order term is 4, which is even, so the end behavior of f(x) is that as x→∞, y→−∞ and as x→−∞, y→−∞.

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For a sample of two proportions, the 98% confidence interval for the difference in two proportions is equals to ( 0.087, 0.211).

We have a random sample of customers completely satisfied with their local telephone service. Number of southern residents in sample, [tex] n_1[/tex] = 620

Number of northeastern residents in sample, [tex] n_2[/tex] = 720

The first proportion of southern residents who are completely satisfied with their local telephone service, [tex] \hat p_1[/tex] = 35% = 0.35

The second proportion of northeastern residents who are completely satisfied with their local telephone service , [tex] \hat p_2[/tex]= 50% = 0.50

We have to determine the 98% confidence interval for the difference in two proportions.

Confidence level = 98%

Level of significance = 1 - 0.98 = 0.02 or a/2 = 0.01

Now, using the distribution table value of z-score for 98% or 0.01 confidence level is equals 2.326. The confidence interval formula, [tex]CI = ( \hat p_1 - \hat p_2) ± z^* \sqrt{ \frac{\hat p_1( 1 - \hat p_1)}{n_1} + \frac{ \hat p_2( 1 - \hat p_2)}{n_2}} \\ [/tex]

Substitute all known values in above formula, [tex]CI = ( 0.35 - 0.50 ) ± (2.326)\sqrt{ \frac{0.35( 1 - 0.35)}{620} + \frac{0.50( 1 - 0.50)}{720}} \\[/tex]

[tex] = ( -0.15) ± (2.326)\sqrt{ \frac{0.35( 0.65)}{620} + \frac{0.50( 10.50)}{720}} \\ [/tex]

[tex]= ( -0.15) ± 2.326×0.027 \\ [/tex]

= ( 0.087, 0.211)

Hence, required value is ( 0.087, 0.211).

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Approximately 68% of the observations fall between the values ​​302 and 338 where the mean of a normal probability distribution is 320; the standard deviation is 18.

For a standard probability distribution with mean μ and standard deviation σ, about 68% of the observations lie within one standard deviation of the mean, between μ - σ and μ + σ. 

In this case, the mean is 320 and the standard deviation is 18. therefore,

μ - σ = 320 - 18 = 302

μ + σ = 320 + 18 = 338

Therefore, approximately 68% of the observations fall between the values ​​302 and 338. 

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We use percentage to compare one quantity against another, with the second quantity rebased to 100.

The most basic application of percentages is to compare one quantity against another, with the second quantity rebased to 100.

We can represent "a% of b" as -

a% of b = a/100 x b

a% of b = ab/100

So, a% of b = ab/100

Therefore, we use percentage to compare one quantity against another, with the second quantity rebased to 100.

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Answer:48.6805998746%, you can round this.

Step-by-step explanation:

In order to solve this, you need to divide the smaller number by the larger number, creating a fraction. This will give you a decimal number. In order to get the percent, you need to take the decimal, and move the decimal point 2 digits TO THE RIGHT. This will give you 48.6805998746%.

To check this, you can use the answer, and use a calculator such as desmos to calculate 48.6805998746% of 659470.53

This provides you with 321034.21, which means that this is the correct percent. You can round this to get something like 48.7%

a) The interest on the loan using exact interest and ordinary interest is as follows:

b) The difference between exact interest and ordinary interest amounts is d. $10.38.

Exact Interest is interest based on a period of 365 days.

Ordinary interest is interest based on a period of 360 days.

Loan amount = $35,000

Loan period = August 6 to December 14 (130 days)

Interest rate = 6%

Interest = $35,000 x 6% x 130/365

= $747.95

Interest = $35,000 x 6% x 130/360

= $758.33

Difference = $10.38 ($758.33 - $747.95)

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Answer:

A = 4 cm^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the length of the base and h is the height

A = 1/2 ( 4) (2)

A = 4 cm^2

Answer:

[tex]4 {cm}^{2} [/tex]

Step-by-step explanation:

Formula for the area of a triangle= 1/2*base*height

[tex] \frac{1}{2} \times 4 \times 2 \\ = 4[/tex]

[tex]therefore \: the \: area \: = 4 {cm}^{2} [/tex]

— reading 189 pages in 63 minutes is a page of 3 pages in one minute

To find the inverse function, we need to switch x and y and solve for y. So, g(x) = (x-2)/5 is the inverse of f(x) = 5x+2.

The variable in the equation is y.

y = 5x + 2

Now, we need to switch x and y and solve for y.

x = 5y + 2

x - 2 = 5y

y = (x - 2)/5

So, the inverse function of f(x) is g(x) = (x-2)/5. To show that this is the inverse of f(x), we need to verify that g(f(x)) = x and f(g(x)) = x for all values of x.

g(f(x)) = g(5x+2) = (5x+2-2)/5 = x

f(g(x)) = f((x-2)/5) = 5(x-2)/5 + 2 = x - 2 + 2 = x

Therefore, g(x) = (x-2)/5 is the inverse function of f(x) = 5x+2.

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In case of different values of cofficient of determination, r² during training and validation represents our regression model is overfitting, so increase the parameter alpha. So, option(a) is right.

The regression model using the normal L₁ technique is called Lasso Regression, and the model using L2 is called Ridge. Ridge regression reduces all regression coefficients to zero. We have a ridge regression training model, during data training, regression coefficient R² = 1

during data validation, regression coefficient R² = 0

R-squared is a suitable measure for linear regression models. This analysis shows the percentage of variance in the variable that the independent variables explain together. Here, R² = 1, shows model is good to fit but R² = 0, shows model is not fit to good. If the R²(test) ≪R²(training), then it indicates that your model does not generalize well. Then we can say model is overfitting state. So, option (b) represents right step to do.

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Complete question:

you train a ridge regression model, you get a R^2 of 1 on your training data and you get a R^2 of 0 on your validation data; what should you do?

a) Your model is underfitting, so increase the parameter alpha.

b) Your model is overfitting, so increase the parameter alpha

c) Your model is under fitting; so perform a polynomial transform

d) Nothing, your model performs flawlessly on your validation data

Answer:

13 units²

Step-by-step explanation:

Area = L x W

Area = 3 1/4 x 4             (3 1/4 = 3.25)

Area = 3.25 x 4

Area = 13                

or

Area = L x W

Area = 3 1/4 x 4

Area = 13

For a Dot plot of time taken in math class by students in a 7th grade, the mean commute time is equal to the 23.75 minutes.

Mean is a statistical measures. It is calculated by the addition of all data values divided by number of data values. It is denoted by [tex]\bar X[/tex].

That is [tex]\bar X = \frac{ \sum X_i}{ n}[/tex], where

We have a Dot plot which represents time it takes students in a 7th grade math class to get to school every morning. We have to determine mean of compete time in minutes. See the above figure carefully, and concluded the value,

Time students

5 4

10 0

15 4

20 4

25 2

30 2

35 5

40 2

45 1

Using above mean formula, [tex]\bar X = \frac{ (4×5+ 0 ×10+ 15×4 + 20×4 + 25×2 + 30×2 + 35×5 + 40×2 + 45× 1)}{24}[/tex]

= 23.75

Hence, mean value is 23.75 minutes.

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Complete question:

The above figure complete the question

the dot plot below represents how long it takes students in a 7th grade math class to get to school every morning. commute time commute time minutes what was the mean commute time? minutes

The required equation of the graph is f(x) = x²- 4. Option B is correct.

Given information,
The graph of F(x), shown, has the same shape as the graph of g(x) = x².

In the graph, it can be seen clearly that the graph is obtained by the trasformation of the graph g(x) by 4 units down. So the equation of the graph shown is given as:

f(x) = g(x) - 4

f(x) = x²- 4

Thus, the required equation of the graph is f(x) = x²- 4. Option B is correct.

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.

(1) 24.15% of the students take more than 260 minutes (2) Approximately 22 students take more than 260 minutes. (3) 69.15% of the students take between 220 and 260 minutes to make the desserts. (4) Approximately 62 students take between 220 and 260 minutes to make the desserts.

1)To find the percentage of students who take more than 260 minutes, we need to find the area to the right of 260 on the normal distribution curve. Using a standard normal table or calculator, we find that this area is 0.1587 or 15.87%.

2) To find the number of students who take more than 260 minutes, we need to multiply the percentage from part 1 by the total number of students: 0.1587 x 90 = 14.28. Rounding to the nearest whole number, we get 14 students.

3) To find the percentage of students who take between 220 and 260 minutes, we need to find the area between these two values on the normal distribution curve. Using a standard normal table or calculator, we find that this area is 0.4772 or 47.72%.

4) To find the number of students who take between 220 and 260 minutes, we need to multiply the percentage from part 3 by the total number of students: 0.4772 x 90 = 42.95. Rounding to the nearest whole number, we get 43 students.

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The completee question is :

The time it takes Culinary Arts students to make a sponge cake, 100 powders, and 10 flans is normally distributed with a mean of 240 minutes and a standard deviation of 20 minutes. The culinary arts teacher has 90 students.

1. What percentage of the students take more than 260 minutes to make the desserts?

2. How many students take more than 260 minutes to make the desserts?

3. What percentage of the students take between 220 and 260 minutes to make the desserts?

4. How many students take between 220 and 260 minutes to make the desserts?

Answer:

triangle is it

Step-by-step explanation:

C goes to C'

(5,-6)    goes to (-6,-5)     this is a 90 degree rotation clockwise

( x, y)   changed to   (y,-x)   <====== clockwise rotation  90 degrees

The distance between the lines with the given equations is : 2.21 units.

We have the equation of line:

3x + y = 1

y + 6 = -3x

To find the distance between the lines.

Now, According to the question:

Convert both equations to slope-intercept form of y = mx + b:

3x + y = 1 ⇒ y = - 3x + 1

y + 6 = - 3x ⇒ y = - 3x - 6

And, we can see that both slopes are same.

So these are parallel lines, and the distance between parallel lines is:

We use the formula:

[tex]d = \frac{|b_1-b_2|}{\sqrt{1+m^2} }[/tex]

where b₁, b₂ - y-intercepts, m- slope

Substitute the values and calculate them.

[tex]d = \frac{|1+6|}{\sqrt{1+(-3)^2} } =\frac{7}{\sqrt{10} }=2.21[/tex]

Hence, The distance between the lines with the given equations is : 2.21 units.

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The surface area of the pyramid is determined as 435.60 mm².

The surface area of the pyramid with pentagon base is calculated as follows;

S.A = 5/2 b(a + s)

where;

The slant height is calculated as follows;

l = √(15.4² + 7.2²)

l = 17 mm

The surface area of the pyramid is calculated as follows;

S.A = 5/2 x 7.2 (7.2 + 17)

S.A = 435.60 mm²

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