What two numbers add up to 4 and multiply to -60

The factorization of the given expression is obtained as (x + 1)(x + 5).

In order to factorize an expression first find all the terms that have the common factors. Then, write those terms in the form of product of factors. This is the way to factorize an expression.

The given algebraic expression is (x + 1)²+ 3(x + 1) + x + 1

It can be factorized as follows,

(x + 1)²+ 3(x + 1) + x + 1

⇒ (x + 1)²+ 3(x + 1) + (x + 1)

⇒ (x + 1)²+ 4(x + 1)

In all the three terms the common factor is (x + 1).

Take (x + 1) as common to get,

(x + 1)(x + 1 + 4)

⇒ (x + 1)(x + 5)

Hence, the given algebraic expression can be factorized as (x + 1)(x + 5).

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Answer:

Step-by-step explanation:

The infinite sum of a geometric sequence is given by the formula:

S = a / (1 - r)

where a is the first term of the sequence and r is the common ratio. In this case, a = 4 and r = 4/6 = 2/3. Plugging these values into the formula above, we get:

S = 4 / (1 - 2/3) = 4 / (1/3) = 4 * 3 = 12

Therefore, the infinite sum of the geometric sequence with a = 4 and r = 2/3 is 12.

log[(4)] = 0.60205999132

Answer:

The value of log 4 to the base 10 is 0.6020. In this article, we will discuss the value of log 4 in terms of both natural logarithm and common logarithm in the logarithmic function. Logarithms are inverse of exponential functions.

Here is the value of log 4 with respect to base-10 and base-e.

Step-by-step explanation:

Now, let us discuss finding the value of log 4 using a common and natural log functions. Also, find the log of 4 to the base 2 here.

The graphs and the equations are matched and mentioned above.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph of the function as shown in the image.

The function g(x) = f(x) + 2, is represented by graph [1].

The function h(x) = f(x + 2), is represented by graph [6].

The function k(x) = f(x) - 2, is represented by graph [3].

The function g(x) = f(x - 2), is represented by graph [5].

Therefore, the graphs and the equations are matched and mentioned above.

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In second half of the month it rain by 1/12 of an inch.

Define Algebraic Expression

In mathematics, an expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)

Given,

The rainfall in Georgetown during the first half of the month was = 1/4 inch

The total rainfall for the month was = 1/3 of an inch

To get an answer for this, you need to subtract the amount of rainfall in first half from the total rainfall for the month. This would tell the how much it rained in the second half of the month.

= 1/3 - 1/4

= 4/12 - 3/12

= 1/12

Hence, In second half of the month it rain by 1/12 of an inch.

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The correct answer is O 1:2:3. In a free-falling object, its acceleration due to gravity is constant.

Distance is the physical separation between two points or objects. It is usually measured in miles, kilometers, or meters. Distance can be used to measure the length of a journey, the size of an area, or the difference between two locations. Distance is also used to measure the time taken to travel, the speed of an object, or the strength of a signal. Distance is an important concept in physics and mathematics, and it is fundamental to the understanding of the universe.

This means that the distance covered in each 1-second time interval is directly proportional to the square of the time elapsed. Therefore, the ratio of distances traveled during each 1-second time interval by the object during the first, second, and third seconds of its fall will be 1:2:3.

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The ECOA Valuations Rule requires lenders to issue a copy of the appraisal or written valuation to an applicant. This is true.

Discrimination in any way related to a credit transaction is forbidden by the Equal Credit Opportunity Act (ECOA). It covers all credit extensions, including those given to corporations, partnerships, trusts, and small businesses. The ECOA outlaws discrimination.

According to the ECOA Valuations Rule, you have three business days from the time you receive an applicant's application to inform them that they have the right to a copy of the appraisals. You must provide the applicant with copies of all appraisals and other written valuations as soon as possible.

According to the ECOA Valuations Rule, creditors must inform applicants of their right to obtain copies of appraisals and written valuations

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The ECOA Valuations Rule requires lenders to issue a copy of the appraisal or written valuation to an applicant. True or false.

The equation for the line of best fit in the slope and the intercept form is given as y₁ = 1.91944X₁ - 65.8518

A straight line that minimizes the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

y₁ = mX₁ + b

we have m = 1.91944

b = -65.8518

The question requires us to fill in the values that we have into the corresponding equation.

We will have

y₁ = 1.91944X₁ + (-65.8518)

y₁ = 1.91944X₁ -65.8518

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Answer:

Step-by-step explanation:

The answers are 3, 34, 14 and 16

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

Given are the problems based on equation making and solving,

1) The equation for finding the number of cups will be =

x(8+07.5) = 32

Where x the number of cups.

x = 32/8.75 ≈ 3

Hence, The number of cups is 3

2) Let the number of Red tokens be R and Gold tokens be G, setting up the equation, we get,

R+G = 56

R-G = 12

Adding the equations,

R+R+G-G = 56+12

2R = 68

R = 34

Hence, The number of Red tokens is 34

3) Let the Sally's age be 2x, therefore, Catherine's age is 6+x

Setting the equations,

6+x+2x = 30

3x = 24

x = 8

Therefore, Catherine's age is 8+6 = 14

4) Let the numbers of answers Robert correctly answered be x,

Setting up the equation,

3x-1(20-x) = 44

3x-20+x = 44

4x = 64

x = 16

Therefore, he answered 16 questions correctly.

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The sample proportion is 0.5507, standard error is 0.0151, margin error is 0.030 and population proportion fall between 0.521<p<0.58

A.

One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

The sample proportion, pcap = 0.5507

b) sample size, n= 1084

The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean.

standard error, SE = [tex]\sqrt{(pcap*(1-pcap)/n)}[/tex]

SE=[tex]\sqrt{(0.5507*(1-0.5507)/1084)}[/tex]= 0.0151

Given Cl level is 95%, hence [tex]\alpha =1-0.95=0.05[/tex]

[tex]\frac{\alpha }{2}= \frac{0.05}{2}= 0.025[/tex]

Zc=Z[tex](\frac{\alpha }{2} )=1.96[/tex]

Margin of errors, in statistics, is the degree of error in results received from random sampling surveys.

Margin of error, ME = zc×SE

ME= 1.96×0.0151

ME= 0.030

c) Cl= (pcap-z×SE, pcap+z×SE)

Cl = (0.5507-1.96×0.0151, 0.5507+1.96×0.0151)

Cl= (0.521, 0.58)

0.521<p<0.58

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The 99% confidence interval to estimate the population proportion of items that are defective is (0.0116, 0.1662).

Sample size , n = 90

defective items , x = 8

Sample proportion = x / n

= 8/90 = 0.0889

= 1- 0.0889 =0.9111

At 99% confidence level the z is ,

α = 1 - 0.99 = 0.01 , α/ 2 = 0.01 / 2

= 0.005

Zα/₂ = Z0.005 = 2.576 ( Using z table )

Margin of error Formula, E = Zα/2× (sqrt(((p-hat× (1 - p-hat)) /n)

= 2.575 ×sqrt((0.0889*0.9111) /90 )

E = 0.0773

A 99% confidence interval is

p-hat - E < p < p-hat + E

=> 0.0889 - 0.0773 < p < 0.0889 +0.0773

=> 0.0116 < p< 0.1662

Hence, confidence interval is (0.0116, 0.1662).

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Answer:

A. 120 degrees.

B. 0 degrees.

Answer:

y = (5/2)x - 18

Step-by-step explanation:

plug in the x, y, and m into the formula y=mx+b, solve for b, and create the formula y = (5/2)x - 18

[tex]y=mx+b[/tex]

We're given:

Plug the slope, [tex]\dfrac{5}{2}[/tex], into [tex]y=mx+b[/tex]:

[tex]y=\dfrac{5}{2}x+b[/tex]

Now, to solve for b, plug in the given point (4, -8):

[tex]-8=\dfrac{5}{2}(4)+b\\\\-8=10+b\\b=-18[/tex]

Plug this into our equation:

[tex]y=\dfrac{5}{2}x-18[/tex]

[tex]y=\dfrac{5}{2}x-18[/tex]

The alpha value is the threshold for statistical significance.

Confidence levels must be decided upon in advance when conducting a survey since they affect the survey's essential scope and error margin. Confidence intervals of 90, 95, and 99% are widely employed in surveys.

A determined statistical result that was based on a sample would likewise hold true for the entire population within the established confidence level if the confidence level were set at 95%.

The probability cutoff for statistical significance is the alpha value. Although p = 0.05 is the most typical alpha value, 0.1, 0.01, and even 0.001 have also been utilized. To choose which alpha value to utilize, it is best to look at the research articles that have been published on your subject.

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Answer:

there is no question here so how can i give you an answer?

Step-by-step explanation:

3/2 is an example of a rational number which can be proved by the properties of rational number.

What is a Rational number?

Rational numbers are numbers which can be expressed as a fraction and also as positive numbers, negative numbers and zero. It can be written as p/q, where q is not equal to zero.

According to the given question:

An example of a rational number can be 3/2. It means integer 3 is divided by another integer 2

Check the following 3 properties of a rational number to determine if it is rational

1. If the number can be written in fraction form

2. If the numerator and denominator of the fraction are integers

3. And the denominator is not equal to zero

If any number satisfies these 3 conditions then it is said to be a rational number

Let's prove for our example that is 3/2

1. 3/2 is a fraction in which 3 is numerator and 2 is denominator

2. 3 and 2 are integers

3. the denominator 2 is not equal to zero.

Hence it is proved that 3/2 is a rational number.

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The probability of winning a prize remains the same for,

e. n = 10 or n=20 or n = 100; the probabilities are the same.

In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment).

From the information we get,

p = 0.5, So, q = 1 - 0.5 = 0.5.

If 70% of 'n' games are won then 30% of n games must be lost.

Let n = 10.

∴ [tex]P(x = 3) = ^{10}C_3p^7q^3[/tex].

[tex]P(x = 3) = ^{10}C_3(0.5)^7(0.5)^3[/tex].

P(x = 3) = 120×0.0078×0.125.

P(x = 3) = 0.117 Or 11.7% chance.

Now, Changing the value as all the 'n's are multiple of 10 and we'll have the same probability.

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Applying the triangle sum theorem, the measures of the angles are:

m∠1 = 30°

m∠1 = 60°

The triangle sum theorem states that we will always have a sum of 180 degrees when we add all interior angles of a triangle.

Therefore:

m∠2 = 180 - 90 - 30 [triangle sum theorem]

m∠2 = 60°

Angle 1 and Angle 2 are complementary angles, therefore:

m∠1 + m∠2 = 90

Substitute

m∠1 + 60 = 90

m∠1 = 90 - 60

m∠1 = 30°

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The area of the given pyramid will be 144.53 ft² thus option (B) is correct.

With a base that is a polygon and sides that are three or more triangles that converge at the top.

A pyramid is a three-dimensional object in which three triangles intersect in such a way that the base side becomes a triangle.

As per the given pyramid,

Total surface area = 2 x(1/2)6 x 8 + 2 x (1/2)7 x 7.79 + 7 x 6

Total surface area = 24 + 27.265 + 42 = 144.53 ft²

Hence "The supplied pyramid will have a surface area of 144.53 feet²".

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The number of balls in the basket at first is 35.

A basket contained 4 times as many blue balls as red balls.

Therefore,

let

x = red balls

Hence,

number of blue balls = 4x

After 21 blue balls were taken away, there were twice as many red balls as blue balls.

2(4x - 21) =  x

8x - 42 = x

subtract 8x from both sides of the equation

8x - 42 = x

8x - 8x - 42 = x - 8x

-42 = - 7x

divide both sides by -7

x = -42 / -7

x = 6

Therefore,

red balls = 7

blue balls = 4(7) = 28

Total balls = 35

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Answer:

35

Step-by-step explanation:

don't ask

Without more information, it is not possible to determine how long it took for Mr. Jones to have 50 mg or less of the medicine left in his body. Factors such as the type of medicine, the dosage Mr. Jones was taking, and his metabolism can all affect the amount of time it takes for the medicine to be metabolized and eliminated from his body. It is important for Mr. Jones to follow the instructions given to him by his doctor and to consult with his doctor if he has any questions or concerns.

We know that,

With the help of example,

5/3

Numerator= number of equal parts of remaining

Denominator=total number of equal parts.

According to question.

Given data in the question,

Multiply the whole number by the denominator.

7×4=28………………. (1)

Adding 1 in numerator

28+1=29

Divide by 4 in denominator

29 divided by 4

7.25

the decimal form of 7 1/4% is 7.25

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After changing 7 1/4 percent into decimal we get, 7.25.

In mathematics, decimals can be used as an alternative to fractions. You can express a fraction in decimal form, such as 0.5, rather than writing it out as 1/2, with zero in the place of the one and five in the place of the ten. Decimus, which means tenth in Latin, is the root of the word decimal. The decimal system is also known as a base-10 system because it uses 10 as its fundamental unit.

Decimal refers to any number in the decimal system. They are employed in the expression of both whole numbers and fractions. A "." (known as a decimal point) is inserted to demarcate the whole number from the fraction. The space between the digit in the ones place and the digit in the tenth place is known as the decimal point, and it serves as the separator between them.

Given that 7 1/4 %

in proper form it will be written as

=(7×4)+1 /4

= 29/4

now dividing 29 by 4 we get

7.25

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Three sets of two-thirds can be created since each whole produces a two-thirds and one half of another two-thirds.

The number 0.666 is 2/3 in decimal notation.Consequently, there are a total of 5 components to distribute. (2+3=5) Consequently, you divide the value you want to share by five.Consequently, there are a total of 5 components to distribute. 2 + 3 = 5, therefore you divide the value you want to distribute by 5.

The two most frequent splits are 2-for-1 and 3-for-1, meaning that a stockholder receives two or three shares, respectively, for each share they currently own. When a corporation divides the number of shares that stockholders own, the market price rises in proportion.

Sixteen twenty-fourths (16/24) is a fraction that is equal to two thirds (2/3).

He cut the soap into two equal pieces, making it weigh 0.333333333 pounds.

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Answer: 1/4

Step-by-step explanation:

To find the probability that Robbie will pull a blue marble out of the bag, we need to first determine the total number of marbles in the bag. Since there are 2 blue marbles, 4 red marbles, and 2 yellow marbles, the total number of marbles in the bag is 2 + 4 + 2 = 8.

Next, we need to determine the number of blue marbles in the bag. Since there are 2 blue marbles, the number of blue marbles in the bag is 2.

Finally, we can use these numbers to calculate the probability that Robbie will pull a blue marble out of the bag. The probability is equal to the number of blue marbles divided by the total number of marbles, which is 2 / 8 = 1/4. Therefore, the probability that Robbie will pull a blue marble out of the bag is 1/4.