what kind of number is the discriminate when the two real number solutions to a quadratic equation are rational numbers

The equation of the line passing through (1, 6) and (3, 2) is y = -2x+8

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, a line passes through (1, 6) and (3, 2), we need to find the equation of the line,  

We know that, an equation of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by,

(y-y₁) = (y₂-y₁) / (x₂-x₁) (x-x₁)

Here, (x₁, y₁) and (x₂, y₂) = (1, 6) and (3, 2),

Therefore,

(y₂-y₁) / (x₂-x₁) = 2-6 / 3-1 = -4/2 = -2

Setting the equation,

y-6 = -2(x-1)

y-6 = -2x+2

y = -2x+8

Hence, the equation of the line passing through (1, 6) and (3, 2) is y = -2x+8

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The option that rewrite the expression 1 / 3 + 2  / 5 using commutative law of addition is D.

The commutative property of addition states that a change in the order of the numbers being added does not affect the sum. In other words, when the order of a sum of values is changed, the commutative property of addition states that the sum of the numbers does not affect the sum of the numbers.

Therefore, let's use the commutative law of addition to rewrite 1 / 3 + 2  / 5.

Hence,

[tex]\frac{1}{3} + \frac{2}{5} = \frac{2}{5}+\frac{1}{3} = \frac{6+5}{15} = \frac{11}{15}[/tex]

Therefore, the answer is D.

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The number of revolutions made by larger pulley is,  1032

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

A pulley has a diameter of 8 inches,

And it is belted to a pulley that has a diameter of 12 inches,

the speeds of the pulleys vary inversely to their diameters,

The smaller pulley running at speed of 1,548 revolutions per minute,

The larger pulley running at speed = ?

V α 1/d

Now, it can be written as,

V₁ α  1/d₁

V₂ α 1/d₂

1548 α  1/8

V₂ α 1/12

For removing proportionality sign,

It required to add one constant k,

1548 =  k(1/8)    _____(i)

V₂  = k (1/12)     _____(ii)

Now, by dividing both the equations,

V₂/1548   = k x (1/12)/ k x(1/8)  

V₂/1548 = 8/12

V₂ = 8/12 x 1548

V₂ = 1032

Hence, the RPM of larger pulley is  1032

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The company should adopt the new tread pattern, as the test statistic is lower than the critical value.

For this problem, we will use a one-tailed hypothesis test to determine if the company should adopt the new tread pattern. The null hypothesis (H0) is that the tires will not allow a car traveling at 60 mph to come to a complete stop within an average of 125 feet after the brakes are applied. The alternative hypothesis (H1) is that the tires will allow a car traveling at 60 mph to come to a complete stop within an average of 125 feet after the brakes are applied.

The test statistic used here will be the mean of the sample set, which is 125.33 feet. We need to find the critical value to determine whether or not the company should adopt the new tread pattern. To do this, we will use a one-sample t-test with a significance level of 0.05.

After taking into account the outlier (102 feet), the critical value is 1.711. Since the test statistic (125.33) is lower than the critical value (1.711), we can reject the null hypothesis and conclude that the company should adopt the new tread pattern. The outlier was accounted for by performing a one-tailed hypothesis test rather than a two-tailed hypothesis test. This allowed us to look at the data in the context of a single direction (whether or not the tires meet the objective), so that the outlier did not affect the results.

The company should adopt the new tread pattern, as the test statistic is lower than the critical value.

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To find the value of x for which the function f(x) = -4x^2 + 8x + 10 reaches its global maximum, we need to find its critical points.

First, we find the derivative of the function:

f'(x) = -8x + 8

Next, we set f'(x) = 0 and solve for x:

-8x + 8 = 0

-8x = -8

x = 1

This is the critical point. To determine whether this critical point corresponds to a maximum or a minimum, we look at the second derivative of the function:

f''(x) = -8

Since f''(x) is negative, this critical point corresponds to a maximum.

Therefore, the value of x for which the function f(x) = -4x^2 + 8x + 10 reaches its global maximum is x = 1.

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Answer:

 (4.5, 6)

Step-by-step explanation:

The distance covered is proportional to the rate, so the distance from A to C compared to the distance from B to C will have the same proportion as Phillip's and Bruce's rates.

__

setup

 (C -A)/(B -C) = 7/5 . . . . . distance is proportional to rates

solution

 5(C -A) = 7(B -C) . . . . multiply by 5(B -C)

 12C = 7B +5A . . . . . add 7C+5A

 C = (7B +5A)/12 = (7(7, 6) +5(1, 6))/12 = (49+5, 42+30)/12 = (4.5, 6)

Phillip and Bruce will meet at C(4.5, 6).

Answer:

Step-by-step explanation:

Answer: y = x - 3

Step-by-step explanation:

y-intercept = -3

(0,-3) (4, 1)

m = (x₂ - x₁) / (y₂ - y₁)

m = (4 - 0) / (1 - (-3))

m = 4 / 4

m = 1

y = 1x -3

y = x - 3

Answer:

The individual's body fat percentage of 18.8% indicates that 28.7 pounds of her weight is made up of fat.

Step-by-step explanation:

The information I provided is based on the formula for calculating body fat percentage, which is body fat weight divided by total body weight multiplied by 100.

Answer:

Step-by-step explanation:

x weight         131

----           = -------------

18.8%             100%

Cross multiply and get 24.6 pounds

The 85% confidence interval for the mean time at lunch is (25.01, 31.79) minutes.

In a random sample of eighteen people, the mean time at lunch was 28.4 minutes.

Standard deviation of 8.2 minutes.  

A common method to calculate the confidence interval for the mean of a normal distribution is to use the Z-score. For a 85% confidence interval, the Z-score is 1.44. Therefore, the confidence interval can be calculated as:

The confidence interval formula in statistics is used to describe the amount of uncertainty associated with a sample estimate of a population parameter.

Where,

n= Number of terms

[tex]$\overline{\mathrm{x}}[/tex]= Sample Mean

[tex]$\sigma[/tex]=Standard Deviation

[tex]$z_{\alpha / 2}[/tex]= Value corresponding to a2 in z table

[tex]$t_{\alpha / 2}[/tex]= Value corresponding to a2 in t table

[tex]$\alpha[/tex]=(1 - Confidence Level /100)

So for the given data, the confidence interval would be:

=28.4 ± 1.44 * 8.2 / √18

=28.4 ± 1.44 * 8.2 / 4.24

=28.4 ± 3.39

=(25.01, 31.79)

Therefore, the 85% confidence interval for the mean time at lunch is (25.01, 31.79) minutes.

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In rare instances, the numerical value of the standard deviation might be 0. The standard deviation, defined as the square root of the variance, is a measure of the dispersion of a collection of data. A collection of data's variance is the average of the squared departures from the mean.

The standard deviation represents the average level of variation in your dataset. It informs you how far each number deviates from the mean on average. A high standard deviation implies that values are spread out from the mean, whereas a low standard deviation shows that values are close to the mean. The standard deviation quantifies the data's dispersion around the mean value. It is useful for comparing data sets that have the same mean but a different range. The mean of the following two numbers, for example, is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. The second, on the other hand, is plainly more dispersed.

Here,

When all of the data points in a collection are equal, the deviations from the mean are all 0, and so the variance is likewise zero. When the variance is zero, the square root of the variance (the standard deviation) is likewise zero. As a result, the standard deviation can only be 0 if all of the data points in the collection are equal.

In other words, the standard deviation is 0 when there is no fluctuation or dispersion in the data.

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Answer:

6.1

Step-by-step explanation:

6.1 / 6.1 = 1

The unit rate of the typed words is 78 words per minute

An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic

Unit rate is the ratio of two different quantities. The denominator for a unit rate is always equal to one.

Gordon types 2,886 words in 37 minutes. The unit rate is the ratio of the total words typed to total time taken. Hence:

Unit rate = 2,886 words / 37 minutes = 78 words per minute

The unit rate is 78 words per minute

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Answer:

x = 2.29cm

Step-by-step explanation:

From the picture below we are given a right angle triangle and asked to find the value of x. We can use the SOHCAHTOA principle to find the side x.

Base on the angle given the adjacent side of the triangle is x while the hypotenuse is given as  4 cm. Let's find the value of x .

cos 55° = adjacent/hypotenuse

cos 55° = x/4

cross multiply

x = 4 cos 55°

x = 4 × 0.57357643635

x = 2.2943057454

x ≈ 2.29 cm

The percentage of votes that were in favour of the new speed limit is 30%.

William's town voted on a new speed limit.

Total votes in town = 10

Total votes in favour = 3

Total votes not in favour = 10 - 3 = 7

We are asked to determine the percentage of votes that were in favour of the new speed limit.

the percentage of votes that were in favour of the new speed limit can be calculated using the formula:

% of votes in favour of speed limit = (Total votes in favour/Total votes in town) x 100

% of votes in favour of speed limit = (3/10) x 100

% of votes in favour of speed limit = 30 %

Hence, the percentage of votes that were in favour of the new speed limit is 30%.

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Answer:

A

Step-by-step explanation:

y = 3.8 − 0.4x.

y =  − 0.4x + 3.8

so slope = -0.4 negative slope

intercept = 3.8

The sample size for Simulation A is greater than then the sample size for Simulation B and the variability of Simulation A will be less then the variability of Simulation B.  

What is sampling distribution ?

An example of a sampling distribution is a probability distribution of a statistic that is derived from repeated sampling of a particular population.            

                         It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.

Given,

Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325.

Simulation A will consist of 1500 trials with a sample size of 100.

Simulation B will consist of 2000 trials with a sample size of 50.

Center for Simulation A and Simulation B will be roughly equal.  

Overall Sample size of Simulation A will be

  = 1500 * 100  = 150000

Overall Sample size of Simulation B will be

 = 2000 *  50  =  100000

Hence, the sample size for Simulation A is greater than then the sample size for Simulation B and the variability of Simulation A will be less then the variability of Simulation B.  

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The complete question is -

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

The length of the segment is approximately 2.2.

The length of the segment can be found using the Pythagorean theorem.

Given points (x1,y1) and (x2,y2), the length of the segment between them is given by:

√((x2-x1)^2 + (y2-y1)^2)

Plugging in the given points:

√((-3-(-4))^2 + (3-1)^2) = √(1^2 + 2^2) = √5

Rounding to the nearest tenth:

√5 ≈ 2.2

So the length of the segment is approximately 2.2.

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ChatGPT Jan 30 Version. Free Research Preview. Our goal is to make AI systems more natural and safe to interact with. Your feedback will help us improve.

Initial value is 1, The base, or rate of change, is 1/3 and the domain is All real Numbers.

Two or more expressions with an Equal sign is called as Equation.

Consider the function:

[tex]y=a(1\pm r)^{m}[/tex]

where m is the number of times this growth/decay occurs,

a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, then there is exponential growth happening by r fraction or 100r %

From the graph of the exponential decay function.

The initial value is 1.

The base, or rate of change, is 1/3.

The domain is All real Numbers.

Hence,  initial value is 1, The base, or rate of change, is 1/3 and the domain is All real Numbers.

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The given question is incomplete, the complete question is Analyze the graph of the exponential decay function.

The initial value is:

The base, or rate of change is:

The domain is:

Answer:

−6+4y−10m

Step-by-step explanation:

Answer: 15

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

If 15 baseballs weigh 75 ounces, then 1 baseball weighs 75/15 = 5 ounces.

So, 15 ounces is equal to 15/5 = 3 baseballs.

The pairs of sample size n and population proportion p would produce the greatest standard deviation is D) n = 100 and p is close to 0

The entire group about whom you want to make conclusions is referred to as a population.

The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole.

We know, The standard deviation for a population proportion is, [tex]\sigma_p = \sqrt\frac{p(1-p)}{n}[/tex].

Now, The pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p is when n = 100 and p is close to 0 let's say we took

n = 100 and p = 0.1 then [tex]\sigma_p = \sqrt\frac{p(1-p)}{n}[/tex] will be = 0.09 and when n = 100 and

p = 0.5 then [tex]\sigma_p = \sqrt\frac{p(1-p)}{n}[/tex] = 0.05.

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A closed-ended question is one that doesn't permit many different answers.

Closed-ended questions are those that can only be answered by choosing one of a small number of possibilities. These questions are typically multiple-choice with a single-word response, such as "yes" or "no," or they can use a rating system (e.g. from strongly agree to strongly disagree).

Close-ended questions, such as "yes/no" or multiple choice questions with predetermined answers, are questions that demand a certain response from the respondent. Closed-ended inquiries are frequently used to collect quantitative data from respondents.

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Since Point A is an element of a direct variation, the other points that are elements of this direct variation include the following:

B. [-2, -8].

E. [2, 8].

In Mathematics, a direct variation is also referred to as direct proportion and it can be modeled by using the following mathematical expression or function:

y = kx

Where:

In direct proportion, the value of x represent an independent variable while the value of y represents the dependent variable. Therefore, an equation that models the situation is given by:

-4 = -k

k = 4

y = 4x

When x = 8, the equation y = 4x is given by:

y = 4(8) = 32.

When x = -2, the equation y = 4x is given by:

y = 4(-2) = -8 (True).

When x = 4, the equation y = -4x is given by:

y = 4(4) = 16.

When x = 2, the equation y = 4x is given by:

y = 4(2) = -8 (True).

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The ratio notation and decimal notation to describe the relationship between the number of double basses and the total number of instruments in the string section are:

4 : 44 and 0.01.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The number of instruments in the string section.

= 7 cellos + 4 double basses + 11 first violins + 11 second violins + 11 violas

= 7 + 4 + 11 + 11 + 11

= 44

Now,

The number of double basses.

= 4

Now,

Ratio notation to describe the relationship between the number of double basses and the total number of instruments in the string section is.

= 4 : 44

The decimal notation to describe the relationship between the number of double basses and the total number of instruments in the string section is.

= 4/44

= 1/11

= 0.01

Thus,

The ratio notation is 4:44.

The decimal notation is 0.01.

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2. The angle measures of the triangle are given as follows: 30º, 60 and 90º.

3. The value of x is given as follows:

[tex]x = 5\sqrt{2}[/tex]

The three trigonometric ratios are defined as follows:

For item 2, we have an angle of 90º, along with two different side lengths, hence the angles cannot be equal.

For item 3, we have that:

[tex]\sin{45^\circ} = \frac{x}{10}[/tex]

Hence:

[tex]\frac{\sqrt{2}}{2} = \frac{x}{10}[/tex]

[tex]2x = 10\sqrt{2}[/tex]

[tex]x = 5\sqrt{2}[/tex]

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Answer: the original price was around $84.07

I don’t know the exact answer but here’s how I did it, I also checked and it’s around the same savings so somewhere around 84.07 makes sense

Answer:

No.

Step-by-step explanation:

No, the equality ||u + v|| = ||u|| + ||v|| does not hold for all vectors u and v in 3D. This equality is known as the Triangle Inequality, and it states that the length of the sum of two vectors is always less than or equal to the sum of their individual lengths. Hence, ||u + v|| <= ||u|| + ||v||.