I NEED HELP ON THIS ASAP!!!

The product of the factors of [tex]65x^2 + 212x - 313[/tex] is equal to the original expression. Lauren may have recognized the expression as a difference of squares and factored it accordingly.

We can first simplify the expression [tex]65x^2 + 212x - 313[/tex] by factoring it:

[tex]65x^2 + 212x - 313 = (13x - 1)(5x + 313)[/tex]

(13x - 1)(5x + 313) = [tex]65x^2 + 212x - 313[/tex]

Therefore, the product of the factors is equal to the original expression.

To see this, we can rewrite the expression as:

[tex]65x^2 - 313 - 212x = (5x)^2 - (2\cdot 5x \cdot 7) + 7^2 - 7^2 - 212x[/tex]

= [tex](5x - 7)^2 - 7^2 - 212x[/tex]

= [tex](5x - 7)^2 - 212x - 49[/tex]

= [tex](5x - 7)^2 - 1^2\cdot 49 - 212x[/tex]

= (5x - 7 - 7)(5x - 7 + 7) - 49 = (5x - 14)(5x) - 49

= 5x(5x - 14) - 49

= 5x(5(x - 2) - 9)

= 5x(5x - 29)

Therefore, the factors of the expression are (5x - 7) and (5x - 29).

Lauren may have recognized the expression as a difference of squares by noticing that the coefficient of the x term (212) is twice the product of the square roots of the first and last terms (sqrt(65) and sqrt(313)), which is a common characteristic of a difference of squares.

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Answer:

72 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

You have a little unclear question with "selects and apple out of the bowl?" I only chose apples (there are 3 of them)

[tex]\frac{3}{12} =\frac{1}{4}[/tex] answer

Step-by-step explanation:

Given,

n(S) = 12

n(A)=3

We have,

P(A) = n(A)/n(S)

= 3 /12

= 1 /4

a. A quartic function with zeroes -5/2, -1, 7/2, and 3 can be written as

f(x) = a(x + 5/2)(x + 1)(x - 7/2)(x - 3), b) Two examples of functions that belong to this family are: f1(x) = 2(x + 5/2)(x + 1)(x - 7/2)(x - 3)

f2(x) = -0.5(x + 5/2)(x + 1)(x - 7/2)(x - 3) and the equation for the member of the family that passes through the point (-2,25) is:

f(x) = (4/275)(x + 5/2)(x + 1)(x - 7/2)(x - 3)

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x.

a) A quartic function with zeroes -5/2, -1, 7/2, and 3 can be written as the product of linear factors with those zeroes:

f(x) = a(x + 5/2)(x + 1)(x - 7/2)(x - 3)

where "a" is a constant that determines the overall scaling of the function.

b) Two examples of functions that belong to this family are:

f1(x) = 2(x + 5/2)(x + 1)(x - 7/2)(x - 3)

f2(x) = -0.5(x + 5/2)(x + 1)(x - 7/2)(x - 3)

Note that these functions differ only in the value of the constant "a".

c) To find the value of "a" that makes the graph of the function pass through the point (-2,25), we can substitute x = -2 and y = 25 into the equation for f(x):

25 = a(-2 + 5/2)(-2 + 1)(-2 - 7/2)(-2 - 3)

Simplifying this expression:

25 = a(5/2)(-1)(-11/2)(-5)

25 = a(6875/4)

a = 100/6875 = 4/275

Therefore, the equation for the member of the family that passes through the point (-2,25) is:

f(x) = (4/275)(x + 5/2)(x + 1)(x - 7/2)(x - 3)

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There were 50 blue box at total in the box.

In mathematics, a cοmbinatiοn is a way οf selecting items frοm a cοllectiοn where the οrder οf selectiοn dοes nοt matter. Suppοse we have a set οf three numbers P, Q and R. Then in hοw many ways we can select twο numbers frοm each set, is defined by cοmbinatiοn.

In smaller cases, it is pοssible tο cοunt the number οf cοmbinatiοns, but fοr the cases which have a large number οf grοup οf elements οr sets, the pοssibility οf a set οf cοmbinatiοn is alsο higher.

The bοx will be represented as (x)

From the question, we form:

White tickets = (1 - 1/10 - 1/2 - 1/4)x = 30

Blue tickets = 3/20 x = 30

Blue tickets =  = 30 x 20 / 3 = 200

Blue tickets = 1/4 x 200 = 50

Thus, There were 50 blue box at total in the box

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Consequently, 15 is the third partial total of the sequence.

The area of mathematics known as arithmetic deals with the mathematical study of numbers and the numerous procedures that can be performed on them. Addition, subtraction, multiplication, and division are the fundamental mathematical processes. The icons listed above stand in for these processes.

The given series is an arithmetic series with first term a1 = 2 and common difference d = 3.

To find the third partial sum, we need to add the first three terms of the series:

S₃ = 2 + 5 + 8

S₃ = 15

Therefore, the third partial sum of the series is 15.

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Thus, the following is the rule for the given geometric sequence: [tex]a = 64 * (-2)^(n-1) (n-1)[/tex]. Thus, the solution is (C) a = 64(-2)n-1.

An structured of integers or objects that adhere to a particular pattern or rule is referred to as a sequence in mathematics. The name for each number or item in the sequence is. A series can be explicitly created or defined recursively, and it can be infinite or finite. A method or rule that directly expresses the n - th term of the series in terms of n defines an explicit sequence. For instance, the explicit sequence 2, 4, 6, 8, 10,... has the formula a = 2n, where n is the term's position inside the sequence. A starting value and recursive formula that determines the nth word of the series in terms of the preceding terms describe a recursive sequence.

given

The number sequence is as follows: 64, -128, 256, -512.

We must determine the common ratio between the following terms in order to get the rule for this sequence.

Any term can be divided by its previous term to obtain the common ratio (r). For instance, the result of subtracting the second term (-128) from the first term (64) is

r = (-128) / 64 = -2

The third term (256) divided by the second term (-128) results in:

r = 256 / (-128) = -2

And when the fourth term (-512) is divided by the third term (256), the result is

r = (-512) / 256 = -2

We can observe that for all pairings of following terms, the common ratio is -2.

Now we can apply the following formula to a geometric sequence's general term:

a = a1 * r^(n-1) (n-1)

where r is the common ratio and a1 is the first term.

In place of the values we hold:

[tex]a = 64 * (-2)^(n-1) (n-1)[/tex]

Thus, the following is the rule for the given geometric sequence: [tex]a = 64 * (-2)^(n-1) (n-1)[/tex]. Thus, the solution is (C) a = 64(-2)n-1.

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The following is true of primary data collection: primary data are collected specifically for the research problem at hand.Primary data collection refers to the process of collecting new data or original data that have not been collected before. Primary data are the first-hand data gathered by researchers from original sources.

The following is true of primary data: primary data are collected specifically for the research problem at hand. Primary data are collected to meet specific research objectives and to provide solutions to research problems.Primary data collection methods are affected by the biases of the respondent.

This is because the collection of primary data requires direct contact between the researcher and the respondents or participants. It is important to note that primary data collection methods are relatively more expensive than secondary data. Therefore, researchers should consider the cost implications of primary data collection methods before using them.

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The probability that at least three out of five randomly selected students will possess a GPA in excess of 3.0 is approximately 0.1772.

To solve this problem, we need to use the binomial distribution with n = 5 and the probability of success p = P(GPA > 3.0), which can be found using the normal distribution table:

P(GPA > 3.0) = P(Z > (3.0 - 2.7)/0.7) = P(Z > 0.43) = 1 - P(Z < 0.43) = 1 - 0.6664 = 0.3336

Now we can use the binomial distribution to find the probability that at least three students out of five have a GPA greater than 3.0:

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

Using the binomial formula and the probabilities of success and failure:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

we get:

P(X = 3) = (5 choose 3) * 0.3336^3 * 0.6664^2 = 0.1311

P(X = 4) = (5 choose 4) * 0.3336^4 * 0.6664^1 = 0.0421

P(X = 5) = (5 choose 5) * 0.3336^5 * 0.6664^0 = 0.0040

Therefore:

P(X ≥ 3) = 0.1311 + 0.0421 + 0.0040 = 0.1772

So the probability that at least three out of five students have a GPA greater than 3.0 is approximately 0.1772.

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--The given question is incomplete, the complete question is given

"  The grade point averages (GPAs) of a large population of college students are approximately normally distributed with mean 2.7 and standard deviation 0.7. Suppose that five students are randomly selected from the student body. What is the probability that at least three will possess a GPA in excess of 3.0? "--

Charlie can ensure that each sandwich contains 3 slices of turkey and 3 slices of ham, and can adjust the recipe as needed to suit his family's tastes and preferences.

Preparing food for a day at the beach can be a fun and fulfilling experience. Charlie decided to make sandwiches for his family to snack on when they get hungry. In this case, each sandwich contains 3 slices of turkey and 3 slices of ham.

The first step in making the sandwiches is to gather all the necessary ingredients. Charlie will need bread, turkey slices, ham slices, and any other desired condiments such as mayonnaise, mustard, lettuce, or tomato. He can choose any type of bread, but a sturdy bread such as a ciabatta, sourdough, or French bread would be ideal for a day at the beach.

To assemble the sandwiches, Charlie can follow these simple steps:

1. Lay out the bread slices. Charlie can choose to use one slice of bread per sandwich or two slices for a heartier sandwich.

2. Add a layer of mayonnaise or mustard if desired. Charlie can choose to spread the condiment on one or both slices of bread.

3. Add a layer of lettuce or tomato if desired. This can add some crunch and freshness to the sandwich.

4. Add 3 slices of turkey on one slice of bread, making sure they are evenly distributed. Charlie can choose to overlap the slices or lay them flat.

5. Add 3 slices of ham on top of the turkey slices, again making sure they are evenly distributed.

6. Top the sandwich with the other slice of bread, condiment-side down.

7. If desired, cut the sandwich in half or quarters for easy sharing and eating.

Charlie can repeat these steps for as many sandwiches as needed for his family. He can also customize the sandwiches by adding or subtracting ingredients, such as cheese, bacon, avocado, or pickles.

In terms of nutritional value, the sandwiches provide a good source of protein from the turkey and ham. The bread provides carbohydrates for energy, while the lettuce and tomato provide vitamins and minerals. The mayonnaise or mustard provides some fat and flavor, but can be skipped if desired.

Overall, making sandwiches for a day at the beach is a simple and convenient way to provide nourishing and satisfying food for the family. By following these steps, Charlie can ensure that each sandwich contains 3 slices of turkey and 3 slices of ham, and can adjust the recipe as needed to suit his family's tastes and preferences.

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Charlie's family is going to relax at the beach all day! In preparation, Charlie made s sandwiches for them to eat when they get hungry. Charlie put 3 slices of turkey and 3 slices of ham on each sandwich how does he adjust the situation ?

Answer:

Let Length= x, Width= y

A.t.c.

3x-2=y ...(1)

Area = length × width

= xy = 40

from (1)

[tex]x(3x - 2) = 40 \\ 3 {x}^{2} - 2x = 40 \\ 3 {x}^{2} - 2x - 40 = 0 \\ 3 {x}^{2} - 12x + 10x - 40 = 0 \\ 3x(x - 4) + 10(x - 4) = 0 \\ (3x + 10)(x - 4) = 0 \\ x = - \frac{10}{3} \: or \: 4[/tex]

neglecting -10/3

length = 4

width = 3(4)-2=12-2

= 10

By following these steps, we will have a figure with 4-fold rotational symmetry around the given center point.

To complete the figure with 4-fold rotational symmetry around the center point, follow these steps:
1. Identify the center of rotation:

As mentioned, the given point is the center of rotation.
2. Determine the existing shape or pattern:

Observe the figure and identify the existing shape or pattern to replicate.
3. Divide the circle around the center point into four equal sections (quadrants):

This can be done by drawing two lines that intersect at the center point, dividing the area around it into four equal parts (90 degrees each).
4. Replicate the existing shape or pattern in each quadrant:

Copy the shape or pattern in the first quadrant to the other three quadrants, keeping them equidistant from the center point.
5. Check for symmetry:

Ensure that when you rotate the figure 90 degrees, 180 degrees, or 270 degrees around the center point, it remains identical in appearance.

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Answer: $178.31

Step-by-step explanation:

To calculate Heidi's overtime pay, we first need to find out how many hours she worked overtime and then multiply those hours by her overtime pay rate. The standard workweek in the United States consists of 40 hours, and any hours worked beyond 40 hours are considered overtime.

Step 1: Calculate the number of overtime hours:

Total hours worked = 47.50 hours

Standard workweek = 40 hours

Overtime hours = Total hours worked - Standard workweek = 47.50 - 40 = 7.50 hours

Step 2: Calculate Heidi's overtime pay rate:

Hourly wage = $15.85

Overtime pay rate = Hourly wage * 1.5 (overtime is typically paid at 1.5 times the regular hourly rate) = $15.85 * 1.5 = $23.775

Step 3: Calculate Heidi's overtime pay:

Overtime pay = Overtime hours * Overtime pay rate = 7.50 hours * $23.775 = $178.31 (rounded to 2 decimal places)

Heidi's overtime pay for the week is $178.31.

The probability that the mean weight of two fruits picked at random falls between 360 grams and 491 grams is approximately 0.9554 or 95.54%.

To solve this problem, we need to use the formula for the sampling distribution of the sample mean:

x' = μ/√n

where x' is the sample mean, μ is the population mean, and n is the sample size.

Given that the population mean is 443 grams and the standard deviation is 34 grams, we can calculate the standard error of the sample mean:

SE = σ/√n

  = 34/√2

  ≈ 24.04 grams

Now we need to standardize the sample mean to a standard normal distribution using the z-score formula:

z = (x' - μ)/SE

The probability that the sample mean falls between 360 grams and 491 grams is equivalent to the probability that the z-score falls between:

z = (360 - 443)/24.04 ≈ -3.45 and z = (491 - 443)/24.04 ≈ 1.99

Using a standard normal table or calculator, we can find the probability that the z-score falls between -3.45 and 1.99, which is approximately 0.9554.

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Answer:

(a.)  8m

(b.) 12 cm

Step-by-step explanation:

a:

given: area of square = 64m²

formula of area of a square A = s²

We will reverse the formula to find the sum of the sides:

S = √A

S =√64

S = 8

b:

Given: perimeter of a square is 48 cm

formula for a perimeter of a square: P = 4 · s

We will reverse the formula to find the sum of the sides:

S = P ÷ 4

S = 48 ÷ 4

S = 12

The given points can only be represented by an exponential function.

A linear function has the following form = y = f(x) = a bx

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

a is a constant term or y-intercept. This is the value of the dependent variable when x = 0.

b is the coefficient of the independent variable. It is also called the slope and gives the rate of change of the dependent variable.

 We can determine the type of function that can represent the given points by looking at the pattern of y values ​​corresponding to the x values.

Linear Function: A linear function has a constant slope, which means that the difference between any two consecutive values ​​of y must be the same as the difference between  two consecutive values ​​of x. The difference between  two consecutive y values ​​is 9/8, which is not the same as the difference between  two consecutive x values ​​(which is 1). Therefore, the given points cannot be represented by a linear function.  Exponential function: an exponential function has a constant ratio between  two consecutive y-values, meaning that the ratio of any two consecutive y-values ​​must be the same as the ratio of any two consecutive x-values.

The ratio of  two consecutive y values ​​is 2, which is the same as the ratio of  two consecutive x values ​​(which is 1/2). Therefore, the given scores can be represented by an exponential function.  Quadratic function: A quadratic function has a quadratic term, which means that the y-values ​​should show an increasing or decreasing pattern of differences between successive x-values.  The differences between successive y values ​​are 9/8, 3/8, 1/2, and 9. There is no  pattern of increasing or decreasing differences between successive x values, so the given points cannot be represented by a square. function

Therefore, the given scores can only be represented by an exponential function.

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Answer:

  output = -3n +1

Step-by-step explanation:

Given an input/output table for a linear function, you want an expression for the output when the input is n.

The input values count up from 1, so we can consider the output values to be the terms of an arithmetic sequence.

The first term of the sequence is a1 = -2 (when n=1).

The common difference of the sequence is d = (-5 -(-2)) = -3.

The general (n-th) term of an arithmetic sequence is given by the formula ...

   an = a1 +d(n -1)

For the known values of a1 and d, we find the n-th term to be ...

  an = -2 +(-3)(n -1)

  an = -2 -3n +3 . . . . . . . eliminate parentheses

  an = -3n +1 . . . . . . . . collect terms

The term corresponding to an input value of n is ...

  -3n +1

The value of the number is 19

Algebraic expressions are defined as those expressions that are composed of terms, constants, variables, coefficients and factors.

These expressions are also made up of certain mathematical operation, such as;

From the information given, we have;

Let the number be x

Then,

3x + 7

4x - 12

Equate the expressions

3x + 7 = 4x - 12

collect the like terms

7 + 12 = 4x - 3x

add or subtract the values

x = 19

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Answer:

120° and 60°

Step-by-step explanation:

5x - 10 + 3x - 18 = 180

8x = 180 + 10 + 18

8x = 208 / : 8

x = 26

.

(5x - 10)° = (5 × 26 - 10)° = 120°

(3x - 18)° = (3 × 26 - 18)° = 60°

Answer:

The probability of selecting an orange chew is 25/62, and the probability of selecting a peach chew is 13/62. To find the probability that the next chew Lydia removes from the bag will be orange or peach, we add these probabilities:

P(orange or peach) = P(orange) + P(peach) = 25/62 + 13/62 = 38/62

To express this probability as a percent, we divide the numerator by the denominator, then multiply by 100:

P(orange or peach) = 38/62 = 0.6129...

0.6129... × 100 ≈ 61

Therefore, the probability that the next chew Lydia removes from the bag will be orange or peach, expressed as a percent to the nearest whole number, is 61%

Step-by-step explanation:

he sold the house for 180000, which is 24% more than the amount he paid.

180000 = x + 0.24x

Simplifying this equation, we get:

1.24x = 180000

x = 180000 / 1.24

x ≈ 145161.29

Chengbo paid approximately 145161.29 yuan for the house.

Answer:

Step-by-step explanation:

To find the diameter of the Andromeda galaxy in miles, we can use the given information:

Diameter of Andromeda galaxy = 2.2 X 10^5 light-years

1 light-year = 5.9 X 10^12 miles

So, we can use dimensional analysis to convert light-years to miles:

2.2 X 10^5 light-years * 5.9 X 10^12 miles/light-year = 1.298 X 10^18 miles

Therefore, the diameter of the Andromeda galaxy in miles is approximately 1.298 X 10^18 miles.

Step-by-step explanation:

A  =  S + 2

L = A + 10 =   S+2   + 10  = S + 12

S  = S

Summed , they equal 83

S+2     +  S+12   + S  = 83

3S = 69

S = 23  messages  

The length of the line that has the coordinate pairs of (-4 1/2,5) and (8 2/3, 5) is 12.16 units.

If two points of coordinates are given then we calculate the distance between them by using the following formulae

To find the length of the line is nothing but the calculation of the distance between two points that are given in the question.

[tex]d = \sqrt{(x_{2} - x_{2} )^{2} +(y_{2} - y_{1} )^{2} }[/tex]

d is the distance between two points.

(x1, x2) and (y2, y1) are the two endpoints of the line.

We can put all the values into the distance formulae and find the length of the line segment.

x1 = -4 1/2 = -3.5, y1 = 5

x2 = 26/3 = 8.6667, y2 = 5

[tex]d = \sqrt{(8.6667-(-3.5))^{2} +(5 - 5)^{2}\\[/tex]

= 12.16

Therefore, the length of the line segment is approximately 12.16 units.

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To calculate the number of possible passwords, we need to find the total number of combinations of lowercase letters and digits for each character of the password.

Then raise that number to the power of 9 (since there are 9 characters in the password and replications are allowed). There are 26 lowercase letters and 10 digits (0 to 9), so the total number of options for each character is 26+10=36.

Therefore, the number of possible passwords is[tex]36^9[/tex], which is equal to 1.0333862 ×[tex]10^16[/tex] (rounded to two decimal places in scientific notation). In other words, there are over 10 quadrillion possible combinations of passwords, making it very difficult for someone to guess or hack into the system by trying different combinations.

This highlights the importance of choosing a strong and secure password that is difficult for others to guess or brute-force.

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After solving the linear equation Lillian is farther along in the book than Khadija after 4 days.

A linear equation is an algebraic equation of the form:

y = mx + b

where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope represents how steep the line is, and the y-intercept is the point at which the line intersects the y-axis.

As we know, Lillian was on 40 pages and Khadija was on 10 pages. So, the equation is,

And Let L represent the page of the book that Lillian is on at the end of t days into the month, and let K represent the page of the book that Khadija is on at the end of t days into the month.

[tex]L(t) = 40 + 15t[/tex]   Lillian's progress after t days

[tex]K(t) = 10 + 20t[/tex]  Khadija's progress after t days

After solving the linear equation, we will get the rate of the reading page.

Let's say t=4,

[tex]L(4) = 40 + 15(4) = 100[/tex]

[tex]K(4) = 10 + 20(4) = 90[/tex]

Therefore, after 4 days, Lillian is farther along in the book than Khadija.

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Answer:

real and rational roots

Step-by-step explanation:

The discriminant of the given equation is [tex]7^2-4(2)(6)=1[/tex].

Since the discriminant is a perfect square, the equation has real and rational roots.