Please answer with an exploration


Part A: If (26)x = 1, what is the value of x? Explain your answer. (5 points)


Part B: If (50)x = 1, what are the possible values of x? Explain your answer. (5 points)

A step that is not performed in the process of solving n² - 12n - 10 = 0 by completing the square is: C. Factor n² - 12n - 10 = 0.

In order to solve the given quadratic equation, we would use the completing the square method as follows;

n² - 12n - 10 = 0

By keeping x terms on the left-hand side of the quadratic equation, we would move the constant term to the right-hand side of the quadratic equation by adding 10 on both sides as follows;

n² - 12n - 10 + 10 = 0 + 10

n² - 12n = 10

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

n² - 12n + (12/2)² = 10 + (12/2)²

n² - 12n + 36 = 10 + 36

n² - 12n + 36 = 46

(n - 6)² = 46

By taking the square root of each side, we have:

n - 6 = ±46

n = 6 ±46

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Complete Question:

Which step is NOT performed in the process of solving n² - 12n - 10 = 0 by completing the square?

Add 10 to each side

Add 36 to each side

Factor n² - 12n - 10 = 0

Take the square root of each side

Statistics is a rigorous field that provides a set of tools and techniques for understanding and making decisions based on data. Correct option is C.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. Statistics is used in a wide range of fields, from business and finance to social sciences, engineering, and healthcare.

One of the key goals of statistics is to summarize and make sense of complex data, and this is often done through the use of visualization techniques such as histograms, scatterplots, and box plots.

Statistics also involves techniques such as data mining, which involves the use of algorithms and computational methods to analyze large data sets, and linear regression, which is a technique for modeling the relationship between two variables.

In addition to its practical applications, statistics is also important for understanding the world around us. It can be used to test hypotheses, evaluate the reliability of data, and make predictions about future events. Overall, statistics plays a vital role in modern society by helping us make sense of the vast amounts of data that we encounter every day.

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Complete question is:

Statistics is a rigorous branch of mathematics that deals with

group of answer choices

A. data mining

B. visualization

C. understanding data

D. linear regression

E. all of the above

Answer:

C = 3.14

Step-by-step explanation:

Center of the circle is (h, k)

h = 4,  k = 1

Use the equation of a circle and the given point (4, -4) to find r:

r² = (x-h)² + (y-k)² = (4-4)² + (-4-1)² = 0 + (-5)² = 25

r = √25 = 5

Find circumference, C:

C = 2πr = 2π(5) = 31.4

Brainly doesn't provide drawing tools, but you can easily draw this circle.  Just plot the center point (4, 1), then draw a circle with a radius of 5 around it.  You'll see that this circle passes through the point (4, -4).

The two consecutive integers whose squares have a difference of 279 is 140 and 139.

The uninterrupted series of integers is represented by consecutive meaning in mathematics. It implies that the numbers are continuously following one another in a series. First, we must comprehend the idea of predecessors and successors in order to comprehend the consecutive meaning of consecutive numbers in mathematics. The number that is written immediately before the number is referred to as the predecessor. As opposed to successors, which refer to the number that follows the number. Think about the range 4, 5, 6, and 7. In this case, 4 comes before 5, while 6 comes after 5.

Let us suppose a number = x.

The consecutive number is given as (x - 1)

Two consecutive integers whose squares have a difference of 279, is given as:

x² - (x - 1)² = 279

x² - x² + 2x - 1 = 279

2x - 1 = 279

2x = 280

x = 140

x - 1 = 140 - 1 = 139

Hence, the two consecutive integers whose squares have a difference of 279 is 140 and 139.

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The measured length of DE will be 4 cm.

Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.

Given that AB is 5 cm, BC is 7 cm, and CA is 8 cm in the triangle ABC. The reep midpoints of AB and BC are Ids D and E.

The two triangles ABC and ADE will be similar to each other. The measure of the length DE will be calculated as:-

AC = DE = 7 / 3.5

DE = AC / 2

DE = 8 / 2

DE = 4 cm

Hence, the value of the side DE will be 4 cm.

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From the total of 300 workers in the factory :

a. Number of men = 200 and Women = 100

b. Number of workers works in the morning = 225

c. Number of workers unionized are 150.

d. Number of workers trustworthy are 50.

Total number of workers in the factory are 300.

a. Fraction of men in the factory are ( 2/3)

= 2/3 of 300

= 200

Women

= 300 -200

= 100

b. Number of workers in the morning shift are

= 3/4 of 300

= 225

c. Total number of workers unionized

= 1/ 2 of 300

= 150

d. Number of trustworthy workers

= 1/6 of 300

= 50

Therefore, out of 300 workers in the factory answer of the following questions are:

a. Number of men and women work in the factory are 200 and 100 respectively.

b. Number of workers works in the morning is 225.

c. Unionized workers = 150

d. Trustworthy workers = 50.

The above question is incomplete , the complete question is :

The Factory has 300 workers of which 2/3 are men, 3/4 work in the morning, 1/2 are unionized and 1/6 are trusted personnel.

a. How many men work in the factory and how many women?

b. How many workers work in the morning?

c. How many are unionized?

d. How many are trustworthy?

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Answer: 7 + [tex]\frac{B}{5}[/tex] = 3

Step-by-step explanation:

Its pretty simple, just do as the words say. :) the only issue could be "of a number and 5", so you go in order, letting B be the number, it's B/5

a) The connection of the literacy principle to assessments created and used by preceptors and others directly involved in classrooms is fairly straightforward. Less egregious is the connection of the principle to assessments created and assessed by parties outside the classroom. Tradition has allowed and indeed encouraged some assessments to serve responsibility or monitoring purposes without sufficient regard for their impact on pupil literacy.

b) To satisfy the literacy principle, assessment must change in ways consonant with the current changes in tutoring, literacy, and class. In the history, pupil literacy was frequently viewed as a unresistant process whereby scholars flashed back what preceptors told them to flash back . harmonious with this view, assessment was frequently allowed of as the end of literacy. The pupil was assessed on commodity tutored preliminarily to see if he or she flashed back it. also, the mathematics class was seen as a fractured collection of information given meaning by the schoolteacher.

c) The alternate chance gave scholars the occasion not simply to redo the questions on which they were unprofitable in the first stage but, more importantly, to give lesser attention to the essay questions they had little time to address. similar two- stage testing basically formalizes what numerous preceptors of writing do in their courses, giving scholars an occasion to revise their work after the schoolteacher or other scholars have read it and offered suggestions.

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The value of the conversion is;

16, 666. 67 minutes

277.78 hours

Conversion of units is described as the conversion between different units of measurement for the same quantity, using the multiplicative factor.

From the information given, we have;

10⁶ seconds

But, we have to take note of;

60 seconds = 1 min

Then 10⁶ seconds = x min

cross multiply

x = 16, 666. 67 minutes

Also,

60 minutes = 1 hour

Then 16, 666. 67 minutes = x

cross multiply

x = 277.78 hours

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The frequency of each class interval 103 - 107, 108 - 112 and 113 - 117 are 2, 2 and 4 respectively.

A grouped frequency distribution is the distribution of data into various classes with equal width with the frequency being the number of outcomes in that class.

Given are the hottest recorded temperatures (in °F) for eight cities throughout North America.

113   110   108   104   117   116   113   103

The class intervals are 103 - 107, 108 - 112 and 113 - 117.

In the distribution, the frequency of a class is the number of temperatures that class.

The temperatures in the class 103 - 107 are 103 and 104.

Frequency of 103 - 107 = 2

The temperatures in the class 108 - 112 are 108 and 110.

Frequency of 108 - 112 = 2

The temperatures in the class 113 - 117 are 113, 113, 116 and 117.

Frequency of 113 - 117 = 4

Hence the frequency are 2, 2 and 4 for the intervals 103 - 107, 108 - 112 and 113 - 117 respectively.

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From the table, the conclusion can be made that for any value of the input, the value of the output remains the same. Then the correct option is C.

A function is an argument, concept, or regulation that demonstrates an association between two variables. Functions may be located throughout mathematics and are necessary for the expansion of significant linkages.

If the number of values of the variable 'y' is more than one for a given value of 'x', then it is not a function.

The table is given below.

   x         y

 - 5        20

   0        20

   5        20

  10        20

From the table, the conclusion can be made that for any value of the input, the value of the output remains the same. Then the correct option is C.

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The complete question is attached below.

The number of cups of mix that is needed to be used will be 12.8 cups.

Any value assigned to a variable that results in equal outcomes, i.e., tends to equalize the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal, is a solution to a formula. To solve a problem, you must find the formula's workable answer.

For every 2 cups of mix in a lemonade recipe, there should be 3 cups of water. Lemonade made with this recipe makes 5 cups.

Let 'W' be the amount of water in gallons and 'M' be the amount of mix in gallons.

Then the equations are given as,

W / M = 3 / 2            ...1

W + M = 2               ...2

From equations 1 and 2, then we have

(3/2)M + M = 2

(5/2)M = 2

M = 4/5

M = 0.80 gallons

We know that in one gallon, there are 16 cups. Then we have

M = 0.80 x 16

M = 12.8 cups

The number of cups of mix that is needed to be used will be 12.8 cups.

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The company profit is decreasing by 1/3 thousand dollars per year.

An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the initial value of y.

Let y represents a company's profit in thousands of dollars, and x represents the time in years.

From the graph, using the point (-3, 4) and (3, 2):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

Substituting:

[tex]y-4=\frac{2-4}{3-(-3)} (x-(-3))\\\\y=-\frac{1}{3}x+3[/tex]

The company profit is decreasing by 1/3 thousand dollars per year.

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To state the null hypothesis and alternative hypothesis for Megan's test, we need to know what type of data she will be collecting and what type of test she will be conducting.

Assuming she will be collecting data on the number of hours of sleep students are getting and conducting a one-tailed hypothesis test, the following are possible null and alternative hypotheses:

a.) Null hypothesis: The average amount of sleep students are getting is equal to or greater than eight hours per night.

Alternative hypothesis: The average amount of sleep students are getting is less than eight hours per night.

b.) Null hypothesis: Less than or equal to 50% of students are getting less than eight hours of sleep per night.

Alternative hypothesis: More than 50% of students are getting less than eight hours of sleep per night.

c.) Null hypothesis: There is no difference in the proportion of students getting less than eight hours of sleep between two groups (e.g., males vs. females, freshmen vs. seniors, etc.).

Alternative hypothesis: There is a difference in the proportion of students getting less than eight hours of sleep between two groups.

d.) Null hypothesis: The number of students getting less than eight hours of sleep is equal to or greater than a certain value (e.g., 30%).

Alternative hypothesis: The number of students getting less than eight hours of sleep is less than the specified value.

Note that in each case, the null hypothesis represents the status quo or the default assumption, while the alternative hypothesis represents Megan's research question or hypothesis. The choice of null and alternative hypotheses depends on the research question, the data being collected, and the type of hypothesis test being conducted.

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The number of seats in each raw by the given graph is 30.

Suppose the considered function whose graph is to be made is

f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values

f(x)

are plotted on the vertical axis.

They are together plotted on the point

(x,y) = (x, f(x))

This is why we usually write the functions as:

y = f(x)

Let the number of rows in the original arrangement be x. Then, the number of seats in each row in original arrangement = x

Total number of seats = x x x = x²

From the given information,

2x(x-10)= x²+ 300

2x²-20x = x²+300

x²-20x-3000

(x-30) (x+10) = 0

x = 30, -10

Since, by the function number of rows or seats cannot be negative. So, x = 30.

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Answer:

lol

Step-by-step explanation:

that sucks

Answer: look at the image for the answer and the solution

Step-by-step explanation:

Answer: a^2 b^2 c^2

Step-by-step explanation:

because that is the pythageoran theorem the rule of it is a^2 + b^2 + c^2 so it's right

Answer:

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

Recall triangle angle sum property, the sum of three interior angles is 180°.

Add up the three angle measures, then solve the equation for x:

Substitute the value of x and find the value of each angle:

375 different combinations of pizza Grayson and his friends can create.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.

The vegetable toppings are mushrooms, broccoli, green peppers, olives, and onions.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

The meat toppings are pepperoni, salami, sausage, chicken, and ground beef.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

They can pick thick, hand-tossed, or deep-dish crust.

Here, n=3 r=1

So, C(n, r) = 3!/1!(3-1)!

= 3

They can also pick garlic, tomato, ranch, pesto, or barbecue sauce.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

Number of ways = 5×5×3×5

= 375

Hence, in 375 ways they can choose pizza.

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Answer:

-2x + 10

Step-by-step explanation:

When you add units you affect the y axis.

Knowing this you can translate it 14 units up by adding 14 + (-4).

The postal cost  is $26

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

twice the weight = 2(40) = 80 kg

volume = 50cm x 50cm x 20cm = 50,000 cm³  = 50 litres

80 + 50  = 130

distance = 200 km

one thousandth = 0.001

one thousandth of the distance = 0.001 * 200 = 0.2

Multiply 130 by 0.2 as given

130*0.2 = 26

The postal cost  is $26

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Answer: 1.5 inches

Step-by-step explanation:

The exponential function that goes through points (0,12) and (2,300) is [tex]y = 12(5)^x[/tex].

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The coordinate points are (0,12) and (2,300).

The exponential function has form [tex]y=ab^x[/tex].

So, the x values are 0,2 and y values are 12,300.

Substitute the first x and y values in the equation -

[tex]12=ab^0[/tex]

a = 12 ...... equation (1)

Substitute the second x and y values in the equation -

300 = ab² ...... equation (2)

Substitute the value of equation (1) in equation (2) -

300 = (12)b²

b² = 300 / 12

b² = 25

b = √25

b = 5

Substitute the values of a and b in exponential function -

[tex]y = 12(5)^x[/tex]

Therefore, the exponential function is [tex]y = 12(5)^x[/tex].

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The second situation costs less by

The cost of the first situation is

Adult = 8 * 2 = 16

drink = 2 * 2 = 4

popcorn = 2 * 2 = 4

Total = $24

Second situation

rent a video = $3.50

buy a 2 liter of cola = $1.60

a bag of microwave popcorn = $1.98.

Total = $7.03

The second situation costs less by

$24 - $7.03

= $16.92

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Answer: y = x(x+1)(x-4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,y=x^3-3x^2-4x

taking x commonly

y=x(x^2-3x-4)

y=x(x^2+x-4x-4)

y=x[x(x+1)-4(x+1)]

y=x(x+1)(x-4)

the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people is approximately 0.000008, or about 0.0008%

The problem of calculating the probability of a certain pattern of birthdays among a group of people can be approached using the techniques of combinatorics and probability. To calculate the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people, we can use the following steps: First, we need to choose which 4 months will have exactly 2 birthdays and which 4 months will have exactly 3 birthdays. There are 12 months to choose from, so the number of ways to make these choices is given by the binomial coefficient: C(12, 4) × C(8, 4). This is the number of ways to choose 4 months out of 12 to have exactly 2 birthdays, multiplied by the number of ways to choose 4 months out of the remaining 8 to have exactly 3 birthdays. Next, we need to assign the people to the months. To do this, we can use the principle of inclusion-exclusion, which states that the number of ways to assign the people to the months so that each of the chosen months has the correct number of birthdays is: N = (20!/(2!²× 3!⁴)) × (4¹² - 6 × 3¹² + 4 × 2¹²). This expression counts the number of ways to distribute the 20 people among the 12 months so that the chosen months have the correct number of birthdays, and subtracts the cases where one or more of the chosen months have too many or too few birthdays. The factor (20!/(2!⁸ × 3!⁴)) accounts for the fact that we are counting distinguishable arrangements of people. Finally, we can calculate the probability of the desired pattern of birthdays by dividing the number of favorable outcomes (N) by the total number of possible outcomes, which is simply the total number of ways to assign the people to the months, given by: 12²⁰. Putting it all together, we get: P(4 months with 2 birthdays, 4 months with 3 birthdays) = N / 12²⁰. Evaluating this expression gives: P(4 months with 2 birthdays, 4 months with 3 birthdays) ≈ 0.000008. Therefore, the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people is approximately 0.000008, or about 0.0008%.

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Using the unit conversions, the height of the tree in yards is 126.33 yd

Let h be the height of the tree.

It is given that the Height of the tree is 379 feet and we need to find the height of the tree in yards.

From the given statement, Hyperion is the tallest tree in the park, with a height of approximately 379 feet,

We need to convert the height of the tree from feet to yards. So, We divide the height of the tree by three for the yard.

So, for one foot: h = (1/3) yd

For, 379 feet: h = 379/3 yd

                         = 126.33 yd

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The length, L (in miles), that is left to be paved after d days is given by the following function L = 205 - 9d.

In this function, 205 represents the total length of the road that needs to be paved, and 9 represents the number of miles that the crew paves each day. The variable d represents the number of days that the crew has been working on the road.

To find the length of the road that is left to be paved after a certain number of days, we can substitute the value of d into the function and solve for L. For example, if the crew has been working on the road for 10 days, we can find the length of the road that is left to be paved as follows:

L = 205 - 9d

L = 205 - 9(10)

L = 205 - 90

L = 115

Therefore, after 10 days, the crew still has 115 miles of road left to pave.

This function can be useful for the construction crew to keep track of their progress and plan their work accordingly. It can also be used by project managers and other stakeholders to monitor the project and ensure that it is on track to be completed within the desired timeframe.

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The amount of money in the account after 2 years is $573.04.

What is compound interest?

Compound interest is the interest earned on an initial principal deposit as well as on the accumulated interest from previous periods. In other words, it is interest on interest.

To calculate the amount of money in the account after 2 years, we can use the formula for compound interest:

A = P(1 + r/n)ⁿᵗ

where A is the final amount, P is the principal amount (the initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period (in years).

In this case, P = $500, r = 0.07 (7%), n = 1 (compounded annually), and t = 2.

Plugging these values into the formula, we get:

A = 500(1 + 0.07/1[tex])^{(1 \times 2)}[/tex]

A = 500(1.07)²

A = $573.04

Therefore, the amount of money in the account after 2 years is $573.04.

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