4. One root of a quadratic
equation is 5+i
a. What is the other root?
b.What is the sum of the roots?
c. What is the product of the roots?
d. What is the equation?

The smallest possible value is 44%.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. 

Given that,

If only three persons are running for the office and the third-place candidate received 28 votes and the second-place candidate received 98 votes, the winner could have received only 99 votes.

In this case, the total number of votes cast would be 28 + 98 + 99  =  225 votes.

The percentage for the winning candidate would be:  99 / 225  =  44%

Therefore, the smallest possible value of x is 44%.

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It is impossible to say if the rate of change of the volume changes from positive to negative at a specific time.

It is not possible to determine if there is a time t, for 5 < t < 10, at which the rate of change of the volume of water in the tub changes from positive to negative without any more information. The rate of change of the volume of water in the tub is the derivative of the function representing the volume of water in the tub with respect to time. The information provided does not specify the function or the rate of change of the volume of water in the tub so it is impossible to say if the rate of change of the volume changes from positive to negative at a specific time.

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The equation has no non-real solutions.

An equation of the form ax^2 + bx + c = 0, where a, b, and c are real numbers, can have either no, one, or two solutions. The solutions can be real or non-real (complex).

If the discriminant (b^2 - 4ac) is greater than zero, the equation has two distinct real solutions.

If the discriminant is equal to zero, the equation has one real solution.

If the discriminant is less than zero, the equation has two non-real solutions (complex roots).

In this case, it is given that the equation has one real solution, so that means the discriminant equals zero (b^2 - 4ac = 0). Therefore, the equation has no non-real solutions.

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Answer:

29$

Step-by-step explanation:

1.60+0.75+0.89=3.24 - dollars per one kid
3.24 * 9 = 29.16 - dollars total
round 29.16 to the nearest dollar - 29$

[tex]\tan 40^{\circ} \cot 50^{\circ}-\sec 40^{\circ} \csc 50^{\circ}\\\\=\tan 40^{\circ} \tan 40^{\circ}-\sec 40^{\circ} \sec 40^{\circ}\\\\=\tan^2 40^{\circ}-\sec^2 40^{\circ}\\\\=-1[/tex]

0.6928 or 69.28% is the probability of at least one ace among five cards .

in order to get the probability that at least one of the five cards is an ace, then we implement the use of  complement rule.

as we know this rule states that the probability of an event happening  which is equal to 1 minus the probability of the event  which is not happening.

In this order of situation the event is drawing no aces from the five cards. hence the  probability of drawing no aces is (48/52)^5, as we are having   48 non-ace cards in the deck and the value of the  probability of drawing a non-ace is 48/52.

the calculation to get the probability of drawing at least one ace is:

1 - (48/52)^5 = 1 - (0.9231)^5 = 0.6928

hence  the probability value  of at least one ace among five cards is 0.6928 or 69.28%.  

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Answer:

n = 13

Step-by-step explanation:

n - 26 = - 13 ( isolate n by adding 26 to both sides )

n = - 13 + 26

n = 13

Answer: Change per minute is 26. Water already there is 500.

Step-by-step explanation:

airport administrators take a sample of airline baggage and record the number of bags that weigh more than 75 pounds. then In this situation of statistics , individual is the cases are the bags or each piece of baggage.

What is a case?

In statistics, the word case is used to refer to the individual from which data is collected. For example, in a study about students' performance, the cases are each of the students.

What is the case in this situation?

Considering the administrators will need to weight and record each bag, the cases are each piece of baggage.

A. Number of bags weighing more than 75 pounds.

B. Average weight of the bags.

C. Each piece of baggage.

D. The airport administrators.

Hence airport administrators take a sample of airline baggage and record the number of bags that weigh more than 75 pounds. then In this situation of statistics , individual is the cases are the bags or each piece of baggage.

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Answer:

-------------------------------------

Simplify each expression and compare with the given answer:

1) 3/8 × 54 = 3/4 × 27 = 81/4 = 20 1/4

2) 5/12 × 26 = 5/6 × 13 = 65/6 = 10 5/6

3) 11/15 × 20 = 11/3 × 4 = 44/3 = 14 2/3,

4) 3/8 × 48 = 3 × 6 = 18

5) 7/12 × 48 = 7 × 4 = 28,

The grouped frequency distribution data is given in the image.

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

Given:

This table shows overall advertising revenue for the American newspaper industry (in billions of inflation-adjusted 2015 dollars) for the years 1980 to 2015.

From the given data,

we can build the grouped frequency distribution data.

And our first class should be 10-19.9.

The table is given in the attached image.

Therefore, the frequency is given in the attached image.

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The polynomials are subtracted to give;

1. 6x²- 5x⁻³ - 8x⁻⁸

2. 5x³+ x - 7x⁻³

3. -2x³ + 10x² -6x + 18

4. 11x³ + 11x² + 8x + 10

5. -2x³ + 12x² - 8x + 10

These are expressions that are composed of terms, coefficients, factors, variables and constants.

They are also composed of mathematical or arithmetic operations such as;

Polynomials are algebraic expression with non-negative integer exponentiation of variables.

From the information given, we have the expressions;

1.{ (-x²) - 5x⁻³} - ( -7x² - 8x⁻⁸)

collect like terms

-x² + 7x² - 5x⁻³ - 8x⁻⁸

Add like terms

6x²- 5x⁻³ - 8x⁻⁸

2. (-2x³ + x) - ( 7x⁻³ - 7x³)

collect like terms

-2x³ + 7x³ + x - 7x⁻³

add like terms

5x³+ x - 7x⁻³

3. (3x³ + 3x² + 9) - (5x³ -7x² +6x - 9)

collect like terms

3x³- 5x³ + 3x² + 7x² -6x + 9 + 9

-2x³ + 10x² -6x + 18

4.5x³ + 5x² + 5 - (-6x³ - 6x² + 8x - 5)

collect like terms

5x³ + 6x³ + 5x² + 6x² + 8x + 5 + 5

11x³ + 11x² + 8x + 10

5. 5x³ + 3x² + 5 - (7x³ - 9x² + 8x - 5)

collect like terms

5x³ - 7x³ + 3x² + 9x² - 8x + 5 + 5

-2x³ + 12x² - 8x + 10

Hence, polynomials are also described as algebraic expressions

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The exact value of a number is often what is meant when the word absolute is used in mathematics.

The absolute value of a number is often what is meant when the word absolute is used in mathematics. For mathematicians, knowing the absolute value is essential. To display a number's absolute value, vertical bars are placed on either side of the number. The absolute value on a number line denotes separation from zero.

The absolute value of a negative number is a positive number. The absolute value of one positive number is equal to that of another positive number. No matter what its sign, a number's absolute value is always its non-negative value. For instance, 5 is also the absolute value of 5, as is the absolute value of -5.

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So, on solving the provided question, we can say that the probability will be P( -1.26 <Z<2.53) => P( Z < 2.53)

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

the probability will be

mean = 10,000

standard deviation = 500

for point a -

n = 40

u = 10,000

P( 9,900 < x < 10,200)

P( -1.26 <Z<2.53)

P( Z < 2.53)

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234 is the sum of the rotcaf of all the even numbers between 1 and 25.To solve this question use the concept of series.

A rotcaf is the sum of the largest factors of the number that is smaller than the number and the number that is obtained by adding two numbers, the rotcaf of 9, for instance, is 9, 3, or 12.

Here given that,

even numbers between 1 and 25 which is: 2,4,6,8,10,12,14,16,18,20,22,24

for finding rotcaf:

(2 + 1) , (4 + 2), (6 + 3), (8 + 4),.....(24 + 12)

Here two series are present:

(1, 3, 5, 7,......23) and (2,4,6,8,......24)

Now, sum of the series is:

= [12 /2 {2+24}] + [12/2 {1 + 12}

= 156 + 78

= 234

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We need to set the function equal to zero.

x² - 3x - 10 = 0

x = 5

x = -2

The answer is -2, 5

Steve has three quarters, three nickels and three pennies. if Steve selects three coins at random and without replacement, then the probability  that the total value is exactly 35 cents is 0.107.

Probability:

Probability is the branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2.

Probability without Replacement:

Probability without replacement means that once you draw an item, you don't put it back into sample space before drawing a second item. In other words, an item cannot be drawn more than once. For example, if he takes one candy out of a box containing nine candies and does not replace the first one, he takes the second one. Of course, the rehearsal room for the second event no longer stays at 9 because we didn't replace the first candy. So the second event has a sample space of 8. That is, the sample space of the second event has changed.

According to the Question:

The only way you can get 35 cents is with 1 quarter and 2 nickels    

There are 3 ways to pick up a quarter  ³C₁

and there are 3 ways you can pick up 2 nickels : ³C₁

Thus,

There are  3× 3 = 9 ways to choose 1 quarters and 2 nickels.

That is 9 favorable outcome.

Now,

there are ⁹C₃ = 84 ways to choose 3 coins from 9  

Therefore,

the probability of picking up 35c is    

9/84

= 3/28

= 0.107  

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The equation for situation 1 is y = 3.5x

The equation for situation 2 is y = 3x

The equation for situation 3 is y = (5/2)x

The equation for situation 4 is  (1/2)x = y

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. It is also known as unit rate and it is usually expressed by k. That is k = y/x

Situation1

A dump truck is hauling loads of dirt to a construction site. After 20 loads, there are 70 square feet of dirt.

k = y/x = 70/20 = 3.5

For every 70 square feet of dirt, there are 2 loads.

y = kx

y = 3.5x

Situation 2

I am making a water and salt mixture that has 2 cups of salt for every 6 cups.

k = 6/2 = 3

This means in every 3 cups there is 1 cup of salt

y = 3x

Situation 3

A store has a "4 for $10" sale on hats.

k = 10/4 = 5/2

This means $5 for 2 hats.

y = (5/2)x

Situation 4

For every 48 cookies I bake, my students get 24.

k = 24/48 = 1/2

This means 1 student gets 2 cookies

y = (1/2)x or (1/2)x = y

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Answer:

Hi Hannah!

there's a little tiny mistake in your question

what's the probability of getting what heart spade etc

you didn't specify it

sorry for bothering but this is my favorite questions

Answer:

Commission Pay =  $2,288
Gross Pay = 4,878

Step-by-step explanation:

Amount of Commission: To calculate the amount of commission earned, multiply the sales by the commission rate. In this case, $57,200 x 4% = $2,288.

Gross Pay: To calculate the gross pay, add the salary to the commission earned. In this case, $2,590 + $2,288 = $4,878.

The inverse variation equation of the rectangle is y = 48/x

The term inverse variation equation in math is defined as the relationships between variables that are represented in the form of

y = k/x

here x and y refers two variables and k is the constant value and it also states if the value of one quantity increases, then the value of the other quantity decreases.

Here we know that the  width of a rectangle varies inversely with the length of the rectangle

Let us consider that x refers the width and y refers the length of the rectangle.

As we all know that the inverse proportion relationship is represented with the equation, y = k/x.

Here we know that the value of width is 4 and length is 12

Then the value of the constant is calculated as,

=> k = (4) x (12)

=> k = 48

Now, we have to write the equation that matches the scenario given, plug in the value of k = 48 into y = k/x, which is written as,

=> y 48/x

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No, it does not mean all real numbers. No solution means that there is no value of the variable that satisfies the equation.

No solution means that there is no value of the variable that satisfies the equation. This means that no matter what value is assigned to the variable, the equation will not be true. Therefore, no solution does not mean all real numbers.

No solution means that there is no value of the variable that satisfies the equation. The equation might be a linear, quadratic, or some other type of equation, but no matter what value is assigned to the variable, the equation will not be true. Therefore, no solution does not mean all real numbers since all real numbers would include the value that would make the equation true. It is possible that all real numbers would be a solution, but no solution does not mean that all real numbers are a solution.

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The total gross earnings are given as follows:

$360.

The total gross earnings are obtained applying the proportions in the context of this problem, first obtaining the total number of hours and then multiplying by the rate.

The hours are given as follows:

After November 14, the hours are given as follows:

Hence the total number of hours is obtained as follows:

3.5 + 2 + 3.5 + 4 + 5 + 5.5 + 4.5 + 4 = 32 hours.

The rate is of $11.25 per hour, hence the total earnings are given as follows:

11.25 x 32 = $360.

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The equation for the number of white dots is a(n) = 2n - 1 while the equation for the number of black dots is a(n) = (n - 1)²

The pattern for the number of black and white dots is depicted in the attached picture.

Refer to the the picture, the sequence of the white dots are:

n = 1  number of white dots = 1

n = 2  number of white dots = 3

n = 3  number of white dots = 5

n = 4  number of white dots = 7

Notice that the number of white dots form an arithmetic sequence, with:

first term = a = 1

common difference = d = 3 - 1 = 2

Hence, the equation for the nth term is:

a(n) = a + (n - 1) d

a(n) = 1 + (n - 1) x 2

a(n) = 2n - 1

Now look at the black dots.

n = 1  number of black dots = 0

n = 2  number of black dots = 1

n = 3  number of black dots = 4

n = 4  number of black dots = 9

Notice that the number of black dots is a quadratic sequence starting from 0.

We can write:

n = 1  number of black dots = 0 = (1 - 1)²

n = 2  number of black dots = 1  = (2 - 1)²

n = 3  number of black dots = 4 = (3 - 1)²

and so on. Hence, the equation of the nth term for the number of black dots is:

a(n) = (n - 1)²

The picture in your question was missing, but most likely it was like in the attached picture.

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Answer:

70% of the data points

Step-by-step explanation:

To calculate the percentage of data points that fall within one standard deviation of the mean, you can follow these steps:

Calculate the mean of the data set: (55+54+66+38+53+56+57+66+45+65)/10 = 55

Calculate the standard deviation of the data set: √ (((55-55) ²+(54-55) ²+(66-55) ²+(38-55) ²+(53-55) ²+(56-55) ²+(57-55) ²+(66-55) ²+(65-55)²)/9) = 7.8

Determine the range for data points within one standard deviation of the mean: Mean ± 1 * standard deviation = 55 ± 1 * 7.8 = [47.2, 62.8]

Count the number of data points that fall within this range: 55, 54, 53, 56, 57, 45, and 65 fall within this range.

Calculate the percentage of data points that fall within this range: (7/10) * 100 = 70%

Therefore, 70% of the data points in the given data set fall within one standard deviation of the mean.

The roots of the polynomial are:

2, -9 (with a multiplicity of 4), and -14

Remember that for a polynomial of degree N with the roots:

{x₁, ..., xₙ}

Can be written as:

P(x)= (x - x₁)*(x - x₂)*...*(x - xₙ)

Here the polynomial given is:

P(x) =(x+2)(x-9)^4(x-14)

We can expand this as:

P(x) =(x + 2)*(x - 9)*(x - 9)*(x - 9)*(x - 9)*(x - 14)

Then the roots are:

2, -9, and -14

(where the -9 has a multiplicity of 4).

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Answer:

The scatter plot provided shows a relationship between the independent variable (x) and the dependent variable (y) that appears to be non-linear. The data points seem to be scattered around the graph. The best fit line would be a polynomial equation, the degree of the equation depends on the shape of the data points. It is not possible to give an exact equation of the line of best fit without knowing the data points.

(a) It is not possible to give an approximate equation of the line of best fit without knowing the data points or a more detailed information of the graph.

(b) Without a clear equation to predict values, it is not possible to predict the value of y for x = 10.

Answer:

a) Let x be the number of bags of snacks supplied, and y be the number of beverages supplied.

b) We know that the total number of items supplied is the sum of the number of bags of snacks and the number of beverages, so we can write:

x + y = 400

We also know that the number of beverages supplied is 50 more than the number of bags of snacks, so we can write:

y = x + 50

Therefore, the system of equations for the situation is:

x + y = 400

y = x + 50