If using the method of completing the square to solve the quadratic equation x2 - 6x – 7 = 0, which number would have to be added to "complete the square"?​

The correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A positive correlation means that as one variable (in this case, happiness) increases, the other variable (GPA) also tends to increase. The magnitude of the correlation coefficient, which ranges from -1 to 1, represents the strength of the relationship. A value of 0.90 indicates a very strong positive linear correlation, suggesting that there is a consistent and significant relationship between happiness and GPA.

This means that as the level of happiness increases among high school students, their GPA tends to be higher as well. The correlation coefficient of 0.90 suggests a high degree of predictability in the relationship between these two variables.

It is important to note that correlation does not imply causation. While a strong positive correlation indicates a relationship between happiness and GPA, it does not necessarily mean that one variable causes the other. Other factors or variables may also influence the relationship between happiness and GPA.

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If the production line breaks down 2 times a week , then the probability that interarrival times between breakdown will be less than 2 days is 0.4060  .

Number of times the production line breaks down is = 2 times ;

We have to find , the probability that interarrival times between breakdown will be less than 2 days ;

Here, the value of λ = 2 and x = 2 ;

the probability can be found by using the Poisson Distribution ;

We know that ;  Poisson's distribution formula ⇒ P(X = x) = [λˣ × \(e^{-\lambda }\)]/x! ;

We have to calculate : P(X < 2) ;

that is P(X < 2) = (2⁰ × e⁻²/0!) + (2¹ × e⁻²/1!)

⇒ P(X < 2) = 0.1353 + 0.2707 ;

⇒ P(X < 2) = 0.4060 .

Therefore , the probability for the time less than 2 days is 0.4060  .

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The given question is incomplete , the complete question is

A manufacturing production line breaks down two times a week on average. What is the probability that the interarrival times between breakdown will be less than 2 days ?

Answer:

i) Area = 25 m²

ii) slope of roof = 36.87°

Step-by-step explanation:

(i)  Let the midpoint of AB = M

Find BC by using Pythagoras' Theorem:  a² + b² = c²

(where a and b are the legs, and c is the hypotenuse of a right triangle)

Legs = MB and MC, hypotenuse = BC

⇒ 1.5² + 2² = BC²

⇒ 6.25 = BC²

⇒ BC = √(6.25) = 2.5

Area of a rectangle = width x length = BC x BE

⇒ area of BCFE = 2.5 x 5 = 12.5

⇒ area of ACFD = area of BCFE = 12.5

Therefore area covered by tiles = 12.5 + 12.5 = 25 m²

ii)

The angle of the slope of the roof will be angle ∠B of the right triangle ΔCMB.

Using sin(A)/a = sin(B)/b = sin(C)/c

sin(90)/2.5 = sin(B)/1.5

0.4 = sin(B)/1.5

0.6 = sin(B)

∠B = 36.87°

Answer:

the odds against Zahra climbing to the top are,

B. 4:1

Step-by-step explanation:

Since she has climbed 7 times in 28 attempts,

the probability of a successful climb is,

P = 7/28

P = 1/4

So, the odds against Zahra climbing to the top are 4:1

Answer:

-1

Step-by-step explanation:

-7=n-6

n=-7+6

n=-1

Please mark me as Brainliest if you're satisfied with the answer.

Answer:

the answer to what?

Step-by-step explanation:

theres no file attached, i think u forgot...

200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.

Forecasted values are as follows: 1,500 and 1,400

Values in actuality: 1,200 and 1,500

Absolute differences:

|1,500 - 1,200| = 300

|1,400 - 1,500| = 100

Now, we calculate the MAD:

MAD = (300 + 100) / 2 = 400 / 2 = 200

Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

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Answer:

I think it is

1: 22.37

2:16.81

3:83.16

Step-by-step explanation:

Answer:

Shape 1: 22.365

Shape 2: 16.81

Shape 3: 83.16

Step-by-step explanation:

I'm going to start with 2, because its the easiest shape to do, which is 4.1*4.1= 16.81. Next is 3, which you find the length by adding 4.1 to 9.1 = 13.2. You then multiply 13.2 by 6.3 = 83.16. Finally for shape 1, you first find the bottom shape,  which you do by dividing 6.3 by 2 so you can get the width of half the triangle. That is 3.15. then you multiply that by 7.1 to get the area of 22.365.

Answer:

\(780\text{ miles}\)

Step-by-step explanation:

Since Pamela's car's MPG (miles-per-gallon) is maintained, we can set up the following proportion:

\(\frac{234}{9}=\frac{x}{30}\), where \(x\) is the number of miles she can drive with 30 gallons of fuel.

Multiply both sides by 30:

\(x=\frac{234\cdot 30}{9},\\x=\boxed{780\text{ miles}}\)

Therefore, Pamela can drive 780 miles with 30 gallons of fuel.

Generally speaking, arithmetic sequences have the form:

an=a1+(n-1)*d

Where:

an=the nth term in the sequence

a1=the 1st term in the sequence

n=the number of terms in the sequence

d=the difference between consecutive terms (i.e. d=an-an-1=a2-a1=a3-a2, etc.)

The SUM of the terms of an arithmetic sequence, notated Sn, is given by:

Sn=[n/2]*[2a1+(n-1)*d]

So if n=8 then:

a8=a1+7d=63

And if there are 94 terms in the sequence then:

S94=[94/2]*[2a1+93d]=47*(2a1+93d)=94a1+4371d=1000

So this is a system of equations where:

{ a1 + 7d = 63 (Multiply this first equation by -94 on both sides and add to second equation)

{ 94a1 + 4371d = 1000

-94a1 - 658d = -5922 (Add this new equation to second equation)

Therefore:

3713d = -4922

So:

d = -4922/3713

Answer: arithmetic / -30

Step-by-step explanation: This is an arithmetic sequence.

The reason I know that is because the same number is being

added each time to get the next term in the sequence.

In this case, we are adding -30 each time to reach the next term.

So the common difference is -30.

Answer:

268 in ^2

Step-by-step explanation:

SA=2lw+2lh+2hw

width = 4    lenth = 6     height = 11

2(6)(4) + 2(6)(11) + 2 (11)(4)

= 2 (24) + 2(66) + 2 (44)

= 48 + 132 + 88

= 268 in ^2

Answered by G a u t h m a t h

Answer:

y = -3x - 3

Step-by-step explanation:

y = -3x + b

0 = -3(-1) + b

0 = 3 + b

-3 = b

y = -3x - 3

Answer:

Step-by-step explanation:

\((2x -3)(x-1) = 2x(x-1) -3(x-1)\)

                     \(=2x^2 -2x -3x +3\\= 2x^2 - 5x + 3\)

Your parents would need to save approximately $4,467.56 each year to reach their goal of $160,000 by your 18th birthday. your parents would need to save approximately $40,079.89 each year to reach their new goal of $200,000, assuming a five-year saving period.

a. To calculate the amount your parents would have to save each year to reach a goal of $160,000 by your 18th birthday, we can use the future value of an ordinary annuity formula:

FV = P * [(1 + r)^n - 1] / r

Where:

FV = future value ($160,000)

P = annual savings amount

r = interest rate per period (9.5% or 0.095)

n = number of periods (number of years, in this case, 17 since they start saving on your first birthday until your 18th birthday)

Plugging in the values, we have: $160,000 = P * [(1 + 0.095)^17 - 1] / 0.095

Simplifying the equation and solving for P, we find: P ≈ $4,467.56

b. If your parents decide to save for five years instead of four and aim to have $200,000 saved, we can use the same formula to calculate the new annual savings amount: $200,000 = P * [(1 + 0.095)^5 - 1] / 0.095

Simplifying the equation and solving for P, we find: P ≈ $40,079.89

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The probability of AL's number will be a whole number multiple of bill's and bill's number will be a whole number multiple of call's is 1÷ 80

The problem can be solved using Butte force approach

We can solves this in two cases

If Cal's number is :

If Bill's number is , Al’s can be any of 4, 6, 8, 10.

If Bill's number is , Al’s can be any of 6, 9.

If Bill's number is , Al’s can be 8.

If Bill's number is , Al’s can be 10.

Otherwise, Al's number could not be a whole number multiple of Bill's.

If Cal's number is 2 :

If Bill’s number is , Al's can be 8.

Otherwise, Al’s number could not be a whole number multiple of Bill's while Bill’s number is still a whole number multiple of Cal’s.

Otherwise, Bill's number must be greater than , i.e. Al’s number could not be a whole number multiple of Bill’s.

Clearly, there are exactly  cases where Al's number will be a whole number multiple of Bill's and Bill's number will be a whole number multiple of Cal’s. Since there are 10×9×8 possible permutations of the numbers Al, Bill, and Cal were assigned, the probability that this is true is

9÷10×9×8

C = 1÷80

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The table values using function rule y = -10x - 2 is (8,-2,-12,-52)

Given function

y = -10x - 2

From the table

x = -1 , 0 , 1 , 5

substitute x values in function

if x = -1

y = -10x - 2

= -10(-1) - 2

= 10 - 2

y = 8  

if x = 0

y = -10(0) -2

y = -2

if x = 1

y = -10(1) - 2

y  = -12

if x = 5

y = -10(5) -2

y = -52

y values (8,-2,-12,-52)

Table:

x      y

-1     8

0    -2

1     -12

5    -52

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The probability that a plain pencil from the first box and a color pencil from the second box are selected is 3/8.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

A box contains 5 plain pencils and 5 pens.

A second box contains 3 color pencils and 1 crayon.

One item from each box is chosen at random.

The probability that a plain pencil from the first box and a color pencil from the second box are selected,

= 5/10 x 3/4

= 3/8

Therefore, the probability is 3/8.

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The option (c)  all patients in a local hospital makes up the population

Surveys are a commonly used method for collecting data in various fields, including healthcare. They can provide valuable insights into patients' experiences, opinions, and preferences, which can help healthcare providers improve their services.

In this case, the survey was conducted among patients in a local hospital, and the results showed that 62.42% of the respondents believed that healthcare providers needed to spend more time with each patient.

The answer is not immediately obvious, but we can make some inferences based on the information given. However, we cannot generalize the results to all patients in the area or the entire population.

Third, surveys cannot account for all the factors that may influence the results, such as demographic characteristics, health status, or cultural background.

Therefore, we can conclude that the population under study is "patients in a local hospital" who participated in the survey.

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To solve this problem, we need to use the standard deviation and the concept of normal distribution.

(a) To find the maximum score of the lowest 15%, we need to find the score at which only 15% of the students scored lower. We can use a z-score table to find the corresponding z-score.

First, we calculate the z-score for the mean of 9.3:

z = (x - μ) / σ
z = (0 - 9.3) / 1.6
z = -5.81

Next, we use the z-score table to find the area to the left of z = -5.81, which is approximately 0.

Since we want the lowest 15%, we need to find the score that corresponds to the area to the right of 0.15 (1 - 0.15 = 0.85).

Using the z-score table again, we find that the corresponding z-score is approximately 1.04.

Now we can solve for x:

1.04 = (x - 9.3) / 1.6
x = 11.0

Therefore, the maximum score of the lowest 15% is 11.

(b) To find the minimum score of the highest 85%, we can use the same approach as before.

First, we need to find the z-score for the mean of 9.3:

z = (x - μ) / σ
z = (0 - 9.3) / 1.6
z = -5.81

Next, we use the z-score table to find the area to the left of z = -5.81, which is approximately 0.

Since we want the highest 85%, we need to find the score that corresponds to the area to the right of 0.85.

Using the z-score table again, we find that the corresponding z-score is approximately 1.04 (we could also use the table to find the z-score that corresponds to 0.15 and then subtract it from 0).

Now we can solve for x:

1.04 = (x - 9.3) / 1.6
x = 10.68

Therefore, the minimum score of the highest 85% is 11.

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The number of 11-inch softballs ordered is 70 and the number of 12-inch softballs ordered  is 50

a + b = 120 equation 1

2.50a + 3.50b = 350 equation 2

Where:

The elimination method would be used to determine the number of each size of softball ordered.

Multiply equation 1 by 2.5

2.5a + 2.5b = 300 equation 3

Subtract equation 3 from equation 2

b = 50

Substitute for b in equation 1

a + 50 = 120

a = 120 - 50

a = 70

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Triangles with the provided side lengths of 3.5, 3.5, and 9 cannot be formed.

According to the Properties of triangle, the length of the third side of a triangle must be greater than the sum of any two of a triangle's sides.

Given the side lengths are 3.5, 3.5 and 9;

Sum of two sides = 3.5 + 3.5 = 7 cannot exceed 9

Thus, it is clear that a triangle cannot be formed using the specified side lengths of 3.5, 3.5, and 9.

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The population mean of the data is 6.

The population has n = 16 scores.

The sum of all of the scores is equal to 96.

Therefore, the population mean can be found as follows:

The population mean is the mean or average of all values in the given population.

The population mean is represented mathematically as follows:

population mean = sum of terms / number of terms

Therefore,

sum of terms = 96

number of terms = 16

Hence,

population mean =  = 96 / 16

population mean =  6

Therefore, the population mean of the data is 6.

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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The equation representing this function is y = tan(x)

The equation which represents a tangent function with a domain of all real numbers such that x is not equal to pi over 4 plus pi over 2 times n comma where n is an integer is:y = tan(x)The tangent function is one of the six trigonometric functions, which is abbreviated as tan. The inverse of the cotangent function is the tangent function. It is also referred to as the inverse tangent, arctan, or tan^-1.

It is defined by the ratio of the opposite side to the adjacent side of a right triangle. The tangent function is a periodic function with a period of π radians or 180°. Its value alternates between negative and positive infinity over each period.The tangent function is not defined at odd multiples of π/2, that is, (2n+1)π/2 for all integers n. This is because the denominator in the tangent function becomes zero, causing a vertical asymptote.
For example, the values of the tangent function for π/2, 3π/2, 5π/2, etc. are undefined. Therefore, the domain of the tangent function is all real numbers except for odd multiples of π/2. The notation for the domain is (-∞, -π/2) U (-π/2, π/2) U (π/2, 3π/2) U (3π/2, ∞).However, in this case, the domain is all real numbers except π/4 + nπ/2, where n is any integer.

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