Solve the equation by completing the square.
x^2−12x+35=0
After completing the square, the equation is _____, and the solution is x=5,x=7

The identity used to simplify from step 4 to step 5 is the definition of the cosecant function cosecant x = 1/sine x.

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's structure is as follows: Expression is (Number/Variable, Arithmetic Operator, Number/Variable).

                                For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.

 =  the expression 1/sine x

 = 1/sine x + cosine x/sine x

 =  cosecant x + cosine x/sine x

  = cosecant x + cotangent x.

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The sum of the first 50 terms is 3775. Let a be the first term and d be the common difference of the arithmetic sequence.

Then, the tenth term is a + 9d = 28, and the sum of the fifth and seventh terms is 2a + 12d = 32.

Solving these equations simultaneously, we get a = 2 and d = 3.

To find the sum of the first 50 terms, we use the formula for the sum of an arithmetic sequence:

S50 = (50/2)(2a + (50-1)d) = 25(2 + 49(3)) = 3775.

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If lisa is on her way home in her car, she has driven 24 miles so far, which is three-fourths of the way home, Lisa's total drive is 32 miles.

Let's represent the total length of Lisa's drive as x. We know that she has driven 24 miles so far, which is three-fourths of the total length. We can write this information as:

24 = (3/4) x

To find x, we need to isolate it on one side of the equation. We can start by multiplying both sides by 4/3 to get rid of the fraction:

24 * (4/3) = x

Simplifying, we get:

32 = x

We can say that Lisa has already driven 24 miles, which is three-fourths of the total distance. To find the total distance, we use the equation 24 = (3/4) x, where x represents the total distance.

To solve for x, we multiply both sides of the equation by 4/3 to cancel out the fraction, giving us 32 = x. Therefore, Lisa's total drive is 32 miles.

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0.4

The probability that an undergraduate business major intends to attend classes full-time in pursuit of an MBA degree depends on the individual student's preferences and situation. Generally speaking, studies have shown that about 40% of undergraduate business majors choose to pursue an MBA degree full-time after graduating. Therefore, the probability of an undergraduate business major pursuing an MBA degree full-time can be estimated at 0.4.

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[tex]E = 2 + \dfrac{1}{4} \ \text{n}[/tex]

[tex]n = 40[/tex]

[tex]E = 2 + \dfrac{1}{4} (40)[/tex]

[tex]E= 2 + 10[/tex]

[tex]E = 12[/tex]

Elena scored 12 points

Answer:

Step-by-step explanation:

Option A) 2+x+ 5x²-x³ + 2x4 is not in standard form because the terms are not arranged in descending order of exponents.

Option B) x + 5x³ + 6x² + x - 2 also, is not in standard form because like terms are not combined and the terms are not arranged in descending order of exponents.

Option C) 2x + 3x² - 4x³ + 3x² + 2 can be simplified to get: -4x³ + 6x² + 2x + 2. This is not in standard form because the terms are not arranged in descending order of exponents.

Option D) 4x³ + 5x² + 6x6 +7x4-2 can be simplified to get: 6x6 +7x4 + 4x³ + 5x² - 2. This is in standard form because the terms are arranged in descending order of exponents.

Therefore, the polynomial in standard form is option D) 6x6 +7x4 + 4x³ + 5x² - 2.

The modular inverse of 11, modulo 1000 is 901. Expressing the answer in integer form.

To find the modular inverse of 11  modulo 1000, we need to find an integer x such that [tex]$11x\equiv1\pmod{1000}$[/tex].

One way to find the modular inverse is to use the extended Euclidean algorithm. Using this algorithm, we can find the greatest common divisor of 11 and 1000 and express it as a linear combination of 11 and 1000.

We can then use the coefficients of this linear combination to express 1 as a linear combination of 11 and 1000.

Applying the extended Euclidean algorithm, we have:

1000= 11 *90 + 10

11 = 10 *1 + 1

Working backward, we can express 1 as a linear combination of 11 and 1000:

1 =11 - 10* 1

= 11 - (1000 - 11*90)

= 901 * 11 - 1 *1000

Therefore, the modular inverse of 11 modulo 1000 is 901, since

11*901=1 mod{1000}.

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Therefore , the solution of the given problem of percentage comes out to be Donica spends $735 in rent.

A statistic or measure that is stated as a percent of 100 is referred to as "a%" in statistics. The terms "pct," "pct," and "pc" are also uncommon. However, it is commonly denoted by the symbol "%". There are no measurements; the proportion of the total sum is flat. Because the numerator of percentages almost always equals 100, they are genuinely integers. Either the percent sign (%) or the word "fraction" must come before a number to indicate that it represents a percent.

Here,

Sales royalty for Donica is calculated as follows:

=>  $12,475 * commission of 4%

=>  $499 commission

Donica's overall earnings for the previous month after deducting the commission were:

Total income equals monthly salary plus commission.

=>  Total income=  $1950 + $499.

=>  $2449 in total profits

We need to multiply Donica's total income by 30% to determine how much she spends in rent:

=>  Rent is 30% of total income.

=>  Rent = 0.3 * $2449 =  $734.70.

When this is rounded to the closest whole integer, we obtain:

=> Rent = $735

Donica thus spends $735 in rent.

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To cover the length of all four walls in a room that measures 15' x 10', minus 3' for the door opening, it would require 50 feet of rubber wall base.

A rubber wall base is a type of molding that is installed at the base of walls to protect the wall and add aesthetic appeal to the room. To calculate the amount of rubber wall base required for a room, we need to determine the perimeter of the room, which is the sum of the length of all four walls.

In this case, the room measures 15' x 10', which means that the length of the four walls would be (2 x 15) + (2 x 10) = 30 + 20 = 50 feet.

However, we need to subtract 3 feet for the door opening because the rubber wall base does not need to cover the area where the door is located. Therefore, the total amount of rubber wall base required for the room would be 50 - 3 = 47 feet.

But, we need to add some extra footage for corner pieces and cuts. Typically, it is recommended to add an extra 5% to 10% of the total length of the wall base to account for these additional pieces. So, adding 5% of 47 feet, we get an additional 2.35 feet, which we can round up to 3 feet.

Therefore, the final answer is 47 + 3 = 50 feet.

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The best estimate for the pike population is 9860, rounded to the nearest whole number.

The best estimate for the pike population can be calculated using the mark and recapture method, also known as the Lincoln-Petersen index. According to this method, the population estimate is given by:

N = (M * C) / R

Where:

N = Population estimate

M = Number of individuals in the first sample

C = Number of individuals in the second sample

R = Number of individuals in the second sample that were tagged in the first sample

Substituting the given values, we get:

N = (770 * 270) / 21

N = 9860

The method used to estimate the pike population is the mark and recapture method, also known as the Lincoln-Petersen index. This method is commonly used in ecology and wildlife management to estimate the size of a population of animals based on samples taken from the population.

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The probability that at least 3 out of 5 businesses have eliminated jobs in the past year is 0.0556.

To find the probability that at least 3 out of 5 businesses have eliminated jobs, we can use the binomial probability formula:

P(X >= 3) = P(X = 3) + P(X = 4) + P(X = 5)

where X is the number of businesses out of 5 that have eliminated jobs, and P(X = k) is the probability of exactly k businesses out of 5 eliminating jobs.

Using the binomial probability formula, we can calculate the probabilities for each possible value of X:

P(X = 3) = (5 choose 3) x (0.13)³ x (0.87)² = 0.0519

P(X = 4) = (5 choose 4) x (0.13)⁴ x (0.87)¹ = 0.0036

P(X = 5) = (5 choose 5) x (0.13)⁵ x (0.87)⁰ = 0.0001

where (n choose k) represents the number of ways to choose k items from a set of n items, and can be calculated using the formula:

(n choose k) = n! / (k! * (n - k)!)

where n! represents the factorial of n.

Now we can add up these probabilities to get the probability of at least 3 out of 5 businesses having eliminated jobs:

P(X >= 3) = 0.0519 + 0.0036 + 0.0001 = 0.0556

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There is only one middle number because the collection has an odd number of numbers. Since six is the midpoint, six represents the median.

When a dataset is sorted from lowest to highest, the median, a measure of central tendency, reflects the midpoint value of the dataset. The values are first presented from lowest to greatest in order to get the median of a set of data. The median is the middle value when there are an odd number of values. Use the following data set as an example: 5, 7, 24, 3, 6, 4, 4, 30, 19. We first organise the data in order before calculating the median: 3, 4, 4, 5, 6, 7, 19, 24, 30

The dataset contains 9 values, which is strange. The middle value, which is six, is therefore the median.

given

We must first arrange the numbers in ascending order in order to determine the median of the group:

3, 4, 4, 5, 6, 7, 19, 24, 30

The median will be the middle number as there are nine numbers in this collection.

There is only one middle number because the collection has an odd number of numbers. Since six is the midpoint, six represents the median.

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Answer: C - 105

Step-by-step explanation:

75+75=150

360-150=210

210/2=105

The equation of the line of reflection that reflects shape P into shape Q is y = −2x + 12.

To find the equation of the line of reflection that reflects shape P into shape Q, we need to follow some steps:

Step 1: Draw the mirror line. To reflect a point or shape, we must have a mirror line. The mirror line is the line that passes through the reflection and is perpendicular to the reflecting surface. It serves as a reference for reflecting points or shapes.

Step 2: Find the midpoint of PQ. The midpoint of PQ is the point that lies exactly halfway between P and Q.

Step 3: Find the slope of PQ. The slope of PQ is the rise over run or the difference of the y-coordinates over the difference of the x-coordinates.

The slope formula is given by m = (y2 − y1) / (x2 − x1).

Step 4: Find the perpendicular slope of PQ. The perpendicular slope of PQ is the negative reciprocal of the slope of PQ. It is given by m⊥ = −1/m.

Step 5: Write the equation of the line of reflection. The equation of the line of reflection is given by y − y1 = m⊥(x − x1) or y = m⊥x + b, where m⊥ is the perpendicular slope of PQ and b is the y-intercept of the line. To find b, we substitute the coordinates of the midpoint of PQ into the equation and solve for b. Then we substitute m⊥ and b into the equation to get the final answer.

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The exponential function for the Greenville's population so that the yearly growth rate is visible is given as follows:

G(t) = 24000(1.00124)^t.

An increasing exponential function is modeled according to the rule presented as follows:

y = a(1 + r)^t.

In which:

The function for Greenville's population is given as follows:

G(t) = 24000(1.00496)^4t.

Which means that the population grows at a rate of 0.00496 = 0.496% every four years, hence the yearly growth rate is given as follows:

r = 0.00496/4

r = 0.00124.

Then the function is given as follows:

G(t) = 24000(1.00124)^t.

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Fred's Annual pension will be $603.

Average salary = (82000 + 96000 + 105000 + 109000) / 4 = $100,500

Fred's employer will credit him 1.8% of that average for each year he worked, so we can calculate his annual pension as follows:

Annual pension = 0.018 * 4 * 100500 = $7,236

Therefore, Fred's annual pension will be $7,236.

We can simply divide his annual pension by 12:

Annual pension = 7236 / 12 = $603

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Answer:

Step-by-step explanation:

I would say A is the answer! :) It's the only problem that matches up.

Answer:

B. 15

Step-by-step explanation:

its right on edge

Answer: The coordinates of the reflected point are (0.5, -4)

Step-by-step explanation: When a point is reflected across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. So the point (-0.5, 4) reflected across the y-axis will be (0.5, 4).When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. So the point (0.5, 4) reflected across the x-axis will be (0.5, -4).

Answer:

(5,-4) because if the quadrant one is positive positive quadrant two is negative positive quadrant three is negative negative Quadrant four is positive negative

Step-by-step explanation: Hope this helps!! Mark me brainliest! :))

Answer:

61.27

Step-by-step explanation:

Circle perimeter formula: C=2πr

Quarter circle=2πr/4. Given r=11cm

                     2x3.14x11/4=17.27

Rectangle perimeter: C=2(a+b)

                                    =2（2+20）=44

so, total: 17.27+44=61.27

The total students who are going on the field trip are 320 students out of 400 students which has been obtained by using the concept of fractions.

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).

If 4 out of 5 students are going on the field trip, then the fraction of students going on the field trip is 4/5.

To find out how many students are going on the field trip, we can multiply this fraction by the total number of students:

Number of students going on the field trip = (4/5) x 400

Number of students going on the field trip = 320

Therefore, 320 students are going on the field trip.

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By function, The fact that this number is 1/2 indicates the half-life of the substance is 1 year.

How would you define a function in plain English?

A function is described as a relationship between a set of inputs and one output for every one of them. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output.

                             Every function has an associated domain, codomain, or range. A mathematical function is a rule that, given the values of one or more independent variables and the dependent variable, determines the value of the dependent variable.

300 represents the initial amount of the substance, the amount present at t=0.

0.5 is the fraction of substance remaining at the end of each year. The fact that this number is 1/2 indicates the half-life of the substance is 1 year.

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Answer:49 = 7×7; 64 = 8×8; Difference Square is the answer. where a =7u; b = 8v. Hope that you carry out the rest Bianca,.. Jung Tran

Step-by-step explanation:

Answer:

1.75a + 8b

Step-by-step explanation:

0.75a + 10b + a - 2b ← collect like terms

= (0.75 + 1a) + (10b - 2b)

= 1.75a + 8b

Answer:

1.75a+8b

Step-by-step explanation:

Given here, 0.75a + 10b + a – 2b = 0.75a+a+10b-2b

                                                     =1.75a+8b

Hence, The required equivalent expression is 1.75a+8b

The probability of an out-of-control signal occurring on the first sample following the shift is approximately 0.0026 or 0.26%.

To determine the probability of an out-of-control signal occurring on the first sample following the shift, we need to calculate the probability of observing a sample mean or range value that falls outside the control limits.

For the X-bar chart:

New process mean (after the shift) = 702.00

Standard deviation (constant) = 1.738

Sample size (n) = 6

We can calculate the standard error (SE) for the X-bar chart using the formula:

SE = Standard deviation / √(sample size)

SE = 1.738 / √(6) ≈ 0.709

Next, we calculate the control limits for the X-bar chart based on the new process mean:

New UCL = New process mean + 3 × SE

= 702.00 + 3 × 0.709

= 704.127

New LCL = New process mean - 3 × SE

= 702.00 - 3 × 0.709

= 699.873

Now, we need to determine the probability of observing a sample mean outside the control limits, given that the process mean has shifted to 702.00. We can assume a normal distribution for the sample means.

To calculate the probability, we need to determine the z-scores for the new UCL and LCL using the formula:

z = (X - μ) / SE

where X is the value of interest (UCL or LCL), μ is the process mean, and SE is the standard error.

For the UCL:

z = (New UCL - μ) / SE

= (704.127 - 702.00) / 0.709

= 2.999

For the LCL:

z = (New LCL - μ) / SE

= (699.873 - 702.00) / 0.709

= -2.999

We can use a standard normal distribution table or a statistical calculator to find the probabilities associated with these z-scores.

Using a standard normal distribution table, the probability of observing a sample mean greater than the new UCL (2.999 z-score) is approximately 0.0013 (or 0.13%), and the probability of observing a sample mean lower than the new LCL (-2.999 z-score) is also approximately 0.0013 (or 0.13%). Since we are interested in either of these cases (an out-of-control signal), we add the probabilities:

Probability of an out-of-control signal = 0.0013 + 0.0013 ≈ 0.0026 (or 0.26%)

Therefore, the probability of an out-of-control signal occurring on the first sample following the shift is approximately 0.0026 or 0.26%.

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Complete question =

Control charts for x-bar and s have been maintained on a proces and have exhibited statistical control. The sample size is n=6. The control chart parameters are as follows:

X-bar: UCL = 708.20, Center line = 706.00, LCL = 703.80

R chart: UCL = 3.420, Center line = 1.738, LCL = 0.052

natural tolerance limits for the process are ±5.214.

the estimated standard deviation is 1.738.

d) Suppose the process mean shifts to 702.00 while the standard deviation remains constant. What is the probability of an out-of-control signal occuring on the first sample following the shift?

Answer:

See below!

Step-by-step explanation:

a) 1, 2, 3, 4, 5

The possible outcomes are all the options that there are on the spinner

b) 2

There are only 2 even numbers!

c) [tex]\frac{2}{5}[/tex] or 0.4

There are 2 out of 5 numbers are even on the spinner so that must be the solution!

d) 1

The spinner has only one multiple of 3, so the possible outcome should also be 1.

e) [tex]\frac{1}{5}[/tex] or 0.2

There are only 1 out of 5 options which are multiples of 3, so that would be our solution

f) 4

There are 4 prime numbers in the spinner (1, 2, 3, 5), so that would be a possible outcome.

g) [tex]\frac{4}{5}[/tex] or 0.8

The spinner has 4 out of 5 prime numbers, so our answer would be that!

Hope this helps, have a lovely day! :)

The rectangular prism is 3 inches by 4.75 inches by 20.5 inches, has a total surface area of 346.25 in².

We need to find the surface area of an object, the surface area of a solid three-dimensional object is the area of the boundary surface of the object and its surroundings, therefore:

The dimensions of the rectangular prism will be as follows:

Let the length of the rectangular prism = 3 inches

Let the width of the prism = 4.75 inches

Let the height of the prism = 20.5 inches

Therefore, the surface area, A, of a rectangular prism can be found using the formula:

A = 2 × Length × Width + 2 × Length × Height + 2 × Height × Width

Therefore, the surface area of the rectangular prism in the question is found as follows:

Area, A = 2 × 3 × 4.75 + 2 × 3 × 20.5 + 2 × 20.5 × 4.75 = 346.25

The total surface area of the rectangular prism is 346.25 in².

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Answer:

346.25

Step-by-step explanation:

took the test :)

Brad needs to score between 72 and 79 on the fourth test in order to get a C for the semester.

To explain why this is so, we need to first understand how the grade for the semester is calculated.Since the final course grade depends entirely on the average of four equally weighted 100-point tests, this means that each test will count for 25% of Brad’s final grade. Therefore, Brad needs to get an average score of 70-79 (inclusive) on the four tests combined in order to get a C for the semester.

In order to calculate what range of scores Brad needs to get on the fourth test in order to get a C for the semester, we need to look at the scores he has already obtained on the first three tests. Brad has scored 87, 89 and 78 on the first three tests. This gives him a total score of 254 (87+89+78=254). This means that Brad needs to get a score of between 70 and 79 on the fourth test in order to reach a total score of between 280-309 (inclusive), which will result in an average score of between 70-79 (inclusive), and give Brad a C for the semester.

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Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:

[tex]$ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}[/tex]

it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm.

1. Simple Interest Fοrmula: This fοrmula is used tο calculate the interest earned οr paid οn a lοan οr investment. It is calculated as:

[tex]\rm I = P \times r \times t[/tex]

Where I is the interest earned οr paid, P is the principal amοunt, r is the interest rate, and t is the time periοd.

2. Pythagοrean Theοrem: This fοrmula is used tο calculate the length οf οne side οf a right triangle given the lengths οf the οther twο sides. It is calculated as:

[tex]\rm a^2 + b^2 = c^2[/tex]

Where a and b are the lengths οf the twο legs οf the right triangle, and c is the length οf the hypοtenuse.

3. Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:

[tex]$ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}[/tex]

Where a, b, and c are cοefficients οf the quadratic equatiοn ax² + bx + c = 0, and x is the sοlutiοn.

4. Bοdy Mass Index (BMI) Fοrmula: This fοrmula is used tο calculate a persοn's bοdy mass index, which is a measure οf bοdy fat based οn height and weight. It is calculated as:

BMI = (weight in kilοgrams) / (height in meters)²

A BMI οf 18.5 tο 24.9 is cοnsidered healthy, while a BMI οf 25 tο 29.9 is cοnsidered οverweight, and a BMI οf 30 οr higher is cοnsidered οbese.

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Complete question:

Describe some common or unique mathematical formulas that you use in your life.