The prime factorization of 56 is the process of breaking 56 down into its prime factors. The prime factorization of 56 is 8 x 7, 2 x 2 x 2 x 7, or 2^3 x 7^1.
One way to calculate the prime factorization of 56 is to use a factor tree. To begin, find two numbers that multiply together to equal 56. The two factors that multiply together to equal 56 are 8 and 7. Since 8 and 7 are both prime numbers, they can be written as the prime factors of 56: 56 = 8 x 7.In mathematical terms, the prime factorization of 56 can be expressed as 56 = 2 x 2 x 2 x 7, where 2 is multiplied by itself three times and then multiplied by 7. This is because 56 can also be written as 2 x 2 x 2 x 7, which is the same as 8 x 7.The prime factorization of 56 can also be expressed as the product of the prime exponents: 56 = 2^3 x 7^1. Here, 2 is raised to the third power, and 7 is raised to the first power. This expression is equivalent to 8 x 7.In summary, the prime factorization of 56 is 8 x 7, 2 x 2 x 2 x 7, or 2^3 x 7^1.
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The weights of dogs in a dog show is normally distributed with a mean of 58 pounds and a standard deviation of 17.2 pounds. Use a standard normal distribution curve to find each probability.
8. P(z<-0.8)
9. P(z>1.32)
10. P(-2.8 51)
12. P(35 85)
The solution is, the probability is, 0.5532.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
given that,
P( 31<X<35.7)
P(X>31)= P(Z>(31-μ)/σ)
= P(Z>(31-34.6)/2.8)
= P(Z> -1.2857)
P(X<35.7)= P(Z<(35.7-μ)/σ)
= P(Z<(35.7-34.6)/2.8)
=P(Z< 0.392857)
From z-distribution table
P(Z< -1.29)= 0.09853
p(Z< 0.39) = 0.65173
P( 31<X<35.7)= P(Z<0.39)- P(Z<-1.29)
= 0.65173- 0.09853
=0.5532
Hence, The solution is, the probability is, 0.5532.
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A spinner is divided into six equal parts numbered 1, 2, 3, 4, 5, and 6. In a repeated experiment, Ryan spun the spinner twice. The theoretical probability of both spins being odd numbers is 9/36.
If the experiment is repeated 140 times, predict the number of times both spins will be odd numbers.
140
70
36
35
If the experiment is repeated 140 times, the number of times both spins will be odd numbers, 35.
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
The theoretical probability of both spins being odd numbers is 9/36.
This means that, if the spinner was spun an infinite number of times, 9 out of every 36 spins would result in both spins being odd numbers.
In the repeated experiment, Ryan spun the spinner 140 times.
This means that, based on the theoretical probability, we can expect the number of times both spins will be odd numbers to be approximately
= 140 x 9/36
= 35
The answer is 35, with the expectation that the actual number of times both spins will be odd numbers in 140 trials may not be exactly 35.
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What is number e in MATLAB?
Answer:exp(1)
Step-by-step explanation:
On a trip from Louisiana to Florida, your family wants to travel at least 420 miles in 8 hours of driving. Write and solve an inequality to find what your average speed must be.
The required the average speed must be at least 52.5 mph to travel 420 miles in 8 hours.
What is inequality?A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. A B indicates that a and b are not equal. When a b, an is said to be less than b. A > B indicates that an is superior to b. These two constitute tight inequity.
According to question:Let the average speed of the trip "x" in miles per hour. To find out what the average speed must be, we need to write an inequality based on the given information and then solve it.
The formula for distance, speed, and time is:
distance = speed * time
So, the distance traveled can be written as:
distance = x * 8 hours
And the inequality based on the given information that the distance must be at least 420 miles is:
x * 8 ≥ 420
To solve for x, we need to divide both sides of the inequality by 8:
x ≥ 420 / 8
x ≥ 52.5
So, the average speed must be at least 52.5 mph to travel 420 miles in 8 hours.
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g(x) is a function as defined below 9(x) = 3 If you input 4 into g(x), what do you get for an output? Enter your answer in the simplest form in the space provided below. (If your answer is a decimal number, round it to two decimal places.) Example answer: 42.63
The output of the function g(x) for the given input is 9.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is [tex]g(x)=3^{(\frac{x}{2} )}[/tex].
When we input 4 into g(x), we get
[tex]g(4)=3^{(\frac{4}{2} )}[/tex]
g(4)=3²
g(4)=9
Hence, the output is 9.
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Select all the correct answers.
Given: m/WOZ = 90°
m/ZOB = 45°
Prove: m/AOW = 45°
What evidence in the proof supports the statement that 45° +mZAOW = 90°?
Statements
1. m/WOZ =
90°
2. m/ZOB = 45°
3. ZZOB ZXOA
4. m/XOA 45°
5. ZXOW + ZWOZ = 180°
6. m/XOW 90°
|7.m/XOA + mZAOW
=
Reasons
1. given
2. given
3. vertical angle theorem
4. definition of congruence
5. linear pair theorem
6. subtraction property of equality
= m/XOW 7. angle addition postulate
The correct answers are:
vertical angle theorem
angle addition postulate
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
The evidence in the proof that supports the statement that m/AOW = 45° is:
Statement 3: ZZOB ZXOA. This means that ZOB and ZOA are vertical angles, which means they are congruent.
Statement 4: m/XOA = 45°. This is the measure of ZOA, which is congruent to ZOB.
Statement 7: m/XOA + m/AOW = m/XOW. This is the angle addition postulate, which states that the sum of the measures of the angles in a triangle is 180°.
So, combining these pieces of evidence, we have:
m/XOA = 45° and m/XOA + m/AOW = m/XOW,
therefore m/AOW = m/XOW - m/XOA
= 90° - 45°
= 45°.
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Answer:7, 4, 6,
Step-by-step explanation:
Prove: DFBE is a parallelogram
The proof of the parallelogram is given as follows:
A parallelogram is a quadrilateral with the following properties:
Opposite sides are parallel: The opposite sides of a parallelogram are equal in length and parallel to each other.Opposite angles are equal: The opposite angles of a parallelogram are equal in measure.Consecutive angles are supplementary: The sum of the measures of the consecutive angles in a parallelogram is equal to 180 degrees.Diagonals bisect each other: The diagonals of a parallelogram bisect each other and are equal in length.The opposite sides of a parallelogram are equal in length.These properties make parallelograms useful for studying transformations and in solving problems in geometry, physics, engineering, and other fields.
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Examine the following sequence 1,4,9, 16, 25 Why is 36 the next number in the sequence? Because the pattern is:
a. Add the next even number
b. Square the number of the next term, n
c. Cube the number of the term, n
d. Add 2 + the number of the term, n
Answer:
b. Square the number of the next term, n
Step-by-step explanation:
You want to know the pattern of the sequence 1, 4, 9, 16, 25, ... and why it tells you the next number is 36.
PatternUsually we look for a common difference or a common ratio when we're trying to identify a sequence as arithmetic or exponential. This sequence has neither, as the differences are 3, 5, 7, 9, and the ratios are 4, 9/4, 25/16.
Neither of these are constant sequences. However, we do notice that the sequence of differences has a common difference of 2. The fact that "second differences" are common (all the same) means the sequence can be described by a second-degree polynomial.
Looking at the sequence values, we see they are ...
1 = 1², 4 = 2², 9 = 3², 16 = 4², 25 = 5²
so we expect the 6th term to be the square of 6, 6² = 36. This is in line with the predicted next number.
The pattern is ...
square the number of the next term, n
solving systems by substitution WS
3x-8(5x-3)=24
PLEASE HELP
Which angle is formed by a secant and tangent line?O ANGO GSEO EGSO NGL
The angle is formed by a secant and tangent line is GSE.
NS is a secant, whereas SE is a tangent line. Thus, they combine to form the angle GSE.
Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent crosses it, is perpendicular to the tangent. Any curved form can be considered a tangent. Tangent has an equation since it is a line. A line that touches a circle just once is said to be tangent to it. A point to circle can only have one tangent. The intersection of the tangent and the circle is known as the point of tangency.
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7 times the sun of 6 and 5
can some one help me..
Answer:
77
Step-by-step explanation:
here, you're multiplying 7 by the "sum of 6 and 5", which just means to add 6 and 5
so, you're multiplying 7 by 11
7*11=77
How do you calculate interior painting cost?
The interior painting cost is calculated according to the cost of the paint and the area that to be painted.
Determine where there are carpets in your house. Increase this by four times. For example, multiply 500 square feet of carpet by four to get 20000 square feet. Find out the current rate per square foot that your painter charges. For instance, depending on the scenario, painters may charge anywhere between Rs 26 and Rs 30 per square foot. Consequently, your expense would be 27 x 2000, or Rs 54,000. This figure is on the high side. After taking measurements, the painter would provide you with a final statement outlining the specific amount of work performed. This is how interior painting cost is calculated.
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questions. Show your work.
1
If a company has 48 full-time employees (40 hours per week for
50 of the 52 weeks in a year) and 12 part-time employees who work
24 hours per week (for 50 weeks), how many labor hours are in the year?
If the company has experienced 6 recordable injuries, what is the IR?
The solution is, : d) 255 ≤ f(x) ≤ 340.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
The function
f(x)= 8.5x
represents the amount of money that Steve earns given the number of hours, x, he works.
The dependent variable is the total amount that he earns, f(x) while the independent variable is the number if hours, x that he works. The range is the possible values of the dependent variable that satisfies the equation.
Steve works between 30 and 40 hours per week.
This means that the lowest amount that he earns is 8.5×30 = $255
The highest amount that he earns is 8.5× 40 = 340.
Therefore, the range is
255 ≤ f(x) ≤ 340
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The temperature falls from 0 degrees to -12 degrees in 3 hours. Which expression finds the change in
temperature per hour?
7 49
24
49.7
49 7
Answer:
Step-by-step explanation:
The change in temperature over the three hours is -12 - 0 = -12 degrees. To find the change in temperature per hour, divide the total change by the number of hours:
-12 / 3 = -4 degrees per hour
So, the change in temperature per hour is -4 degrees. The answer is -4.
need answer shortly pleaaaaaaaaaase
Which expressions are equivalent to the one below? Check all that apply.
log 2-log 6
A. log 3
B. log 2
C. log(2) + log
-log()
□ D. log()
Equivalent expression for the expression ( log 2 - log 6 ) is,
⇒ - log 3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ log 2 - log 6
Now, Simplify the expression by using logarithmic rule as;
⇒ log 2 - log 6
⇒ log 2 / 6
⇒ log 1/3
⇒ log 3⁻¹
⇒ - log 3
Therefore, We get;
Equivalent expression for the expression ( log 2 - log 6 ) is,
⇒ - log 3
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Feb 09, 6:13:08 PM
Watch help video
If f(x) = 2x³ - 11x² - 20x - 7 and f(7) = 0, then find all of the zeros of f(x)
algebraically.
Answer: x =
Submit Answer
?
DELL
M =
The zeroes of the polynomial f(x) = 2x³ - 11x² - 20x - 7 are - 1, - 1/2, and 7.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, A cubic polynomial f(x) = 2x³ - 11x² - 20x - 7.
Now, If f(7) = 0 then (x - 7) is a factor of the polynomial f(x).
Therefore, f(x) = (x - 7)(2x² + 3x + 1).
Now, 2x² + 3x + 1 = 0.
2x² + 2x + x + 1 = 0.
2x(x + 1) + 1(x + 1) = 0.
(x + 1)(2x + 1) = 0.
x = - 1 or x = - 1/2.
So, The zeros are - 1, - 1/2, and 7.
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two similar solids have base areas of 47cm2 (smaller solid) and 199cm2 (bigger solid) the smaller solid is 350cm3 volume
calculate volume of larger solid
The graph represents the distribution of the number of
questions answered correctly on a 50-question math
test.
24
28
Math Test Scores
32
36
40
44
48
X
What is the standard deviation of the data?
04
08
O 12
O 24
The standard deviation of the given data is 8.
Option B is the correct answer.
What is the standard deviation?To calculate the standard deviation of the given data, we can use the following formula:
σ = √ [Σ(xi - μ)² / N
where σ is the standard deviation, xi is each data point, μ is the mean of the data, and N is the total number of data points.
We have,
The mean of the data:
μ = (24 + 28 + 32 + 36 + 40 + 44 + 48) / 7
= 36
Now,
We can calculate the sum of squared differences from the mean.
Σ(xi - μ)²
= (24 - 36)² + (28 - 36)² + (32 - 36)² + (36 - 36)² + (40 - 36)² + (44 - 36)²
+ (48 - 36)²
= 144 + 64 + 16 + 0 + 16 + 64 + 144
= 448
And,
We can substitute these values into the formula for the standard deviation.
So,
σ = √ [Σ(xi - μ)² / N]
= √[448 / 7]
= 8.13
= 8
Therefore,
The standard deviation of the given data is 8.
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I’m not sure what the answer is or how to solve.
The correct statements regarding the ordered pairs are given as follows:
A. f(0) = 3.D. f(4) = 6.How to define the ordered pair and how it relates to the numeric value?The general format of an ordered pair is given as follows:
(x,y).
The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.
The two pairs on this problem are given as follows:
(0,3) and (4,6).
Hence the numeric values are given as follows:
A. f(0) = 3.D. f(4) = 6.More can be learned about ordered pairs at brainly.com/question/1528681
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Study Guide and Intervention The Quadratic Formula and the. ... Thediscriminant is a perfect square, so the equation has 2rational roots.
The value of the discriminant for the equation "2x² + 5x + 3" is 1 , and the it has 2 real and rational roots .
The Discriminant of a quadratic equation of the form of ⇒ "ax² + bx + c" is calculated by the expression "b² - 4ac" .
the values of the variables "a", "b" and "c" ; for quadratic equation "2x² + 5x + 3" ,
the value of a is = 2, b is = 5, and c is = 3.
substituting values ;
So , the discriminant is ⇒ b² - 4ac
⇒ 5² - 4×2×3 ;
⇒ 25 - 24
⇒ 1
Since , the discriminant is (1)positive, which means that the equation has 2 real roots. and since, discriminant is a perfect square, that means the roots are rational numbers.
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The given question is incomplete , the complete question is
Find the value of the discriminant for the equation 2x² + 5x + 3 , and then describe the number and type of roots for the equation .
how to calculate hexagon sum of interior angles
Answer:
Step-by-step explanation:
The sum of the interior angles in a polygon can be calculated using the following formula:
(n - 2) * 180 degrees
where n is the number of sides in the polygon.
To understand why this formula works, let's consider a single interior angle in the polygon. Each interior angle is split into two equal angles that form a straight line. The sum of these two angles is 180 degrees. Now, if we look at all the interior angles in the polygon, we can see that they are divided into (n - 2) pairs of angles that form straight lines. This means that the sum of all the interior angles in the polygon is (n - 2) * 180 degrees.
For a hexagon, which has 6 sides, we can plug in n = 6:
(6 - 2) * 180 = 4 * 180 = 720 degrees
So, the sum of the interior angles in a hexagon is 720 degrees.
what is the common name of the rectangular vessel where the solution to be analyzed by uv-vis spectrometry is poured into?
A cuvette or spectrophotometer cell is the conventional term for the rectangular container into which the solution to be examined by UV-Vis spectrometry is put.
A cuvette is a tiny, square or rectangular container that can be constructed of glass, plastic, or quartz and is used to hold little amounts of liquid samples.
It features two clear sides that are parallel to one another and is optically transparent.
The spectrophotometer measures the light that travels through the sample on these faces.
The cuvette's design guarantees consistent sample thickness and interference-free light transmission.
A more broad phrase, "spectrophotometer cell," can apply to any sort of cell or container used to store a sample for spectrophotometer examination, including cuvettes and other containers like test tubes or vials.
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the product of 7 x 2/21
Answer: The product of 7 and 2/21 is equal to 2/3.
Step-by-step explanation:
To multiply 7 by 2/21, we can first simplify 2/21 to its lowest terms by finding the greatest common factor of 2 and 21, which is 1. Then we can multiply 7 by 2 and divide the result by 21:
7 x 2/21 = (7 x 2) / 21 = 14 / 21
The fraction 14/21 can also be simplified to its lowest terms by dividing both the numerator and denominator by the greatest common factor, which is 7:
14/21 = (2 x 7)/(3 x 7) = 2/3
What are the 3 types of integers?
Answer: In summary, all integers can be classified as either positive, negative, or zero.
Step-by-step explanation:
There are three types of integers: positive integers, negative integers, and zero.
Positive integers: Positive integers are numbers greater than zero, such as 1, 2, 3, 4, and so on.
Negative integers: Negative integers are numbers less than zero, such as -1, -2, -3, -4, and so on.
Zero: Zero is an integer that is neither positive nor negative. It is the only integer that is neither positive nor negative, and it is often referred to as the "origin" on a number line.
In summary, all integers can be classified as either positive, negative, or zero.
Answer: The three types of integers are Zero (Neutral Integers), Negative Integers, and Positive Integers.
Step-by-step explanation:
Negative Integers are the ones that has a value less than zero, examples of these are -7, -8, -9.
Positive integers, on the other hand. Are the ones that has a value more than zero, examples of these are 10, 11, 12, 13.
Note: The key difference between Negative Integers and Positive Integers is that a negative integer has a "-" sign, while a positive integer does not.
Zero are the neutral integers which means that it's the integer that's in the middle of the positive and negative integers, it has neither a positive sign or a negative sign.
Another note: Integers do not include fractions or decimals, only whole numbers.
A cylinder has volume 78 cm. What is the volume of a cone with the same radius and height? A. 156cm3 B. 234cm3 C. 39cm3 D. 26cm3
The volume of a cone with the same radius and height is D. 26 cm³.
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h and the volume of a cone is (1/3)πr²h.
Therefore, The volume of a cone of the same radius and height is one-third the volume of a cylinder.
Given, A cylinder has a volume of 78 cm³.
Therefore, The volume of a cone with the same radius and height is,
= (78/3) cm³
= 26 cm³.
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What is 4 Ounces (4oz) in Pounds (lb)?
4 ounces is equal to 0.25 pounds. Since 1 pound is equal to 16 ounces, to convert ounces to pounds, you need to divide the number of ounces by 16. So, 4 ounces divided by 16 equals 0.25 pounds.
One pound is equivalent to 16 ounces. To convert 4 ounces to pounds, you need to divide 4 by 16. This gives the result of 0.25 pounds, since 4 ounces is one-quarter of a pound. The conversion factor between ounces and pounds is useful when working with small weights, as ounces are commonly used to express small quantities of weight, while pounds are used for larger quantities. Knowing the conversion factor can help in many situations, such as when cooking, measuring ingredients or mailing a package, where it may be necessary to convert between different units of weight.
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The Drama club is selling tickets to a play for x dollars each for each ticket they sell the school receives x dollars and the drama club receives the remaining amount the drama club sells 108 tickets for a total of (108x+972) how much money does the drama club receive for each ticket they sell i need to show work thanks !!! your are the best
Answer:
The drama club receives $9 for each ticket they sell.
Step-by-step explanation:
The total amount of money the drama club receives from selling 108 tickets is the difference between the total amount collected and the amount donated to the school.
Total amount collected = 108x + 972
Amount donated to the school = 108x
Amount received by the drama club = (108x + 972) - 108x = 972
Therefore, the drama club receives a fixed amount of $972 for selling 108 tickets.
To find how much money the drama club receives for each ticket sold, divide the total amount received by the number of tickets sold:
972/108 = $9
Therefore, the drama club receives $9 for each ticket they sell.
This season, the probability that the Yankees will win a game is 0.59 and the probability that the Yankees will score 5 or more runs in a game is 0.45. The probability that the Yankees lose and score fewer than 5 runs is 0.33. What is the probability that the Yankees would score fewer than 5 runs when they lose the game? Round your answer to the nearest thousandth.
Suggested: Needed in Decimal form (Regular outcome)
The probability that the Yankees scored fewer than 5 runs is 0.805.
What is probability?It is the chance of an event occurring from a total number of outcomes.
The formula for probability is:
Probability = Number of required events / Total number of outcomes.
We have,
We will use conditional probability.
P(A/B) = P(A∩B) / P(B)
The probability that the Yankees won a game.
= 0.59
This means,
The probability that the Yankees lost a game.
P(A) = 1 - 0.59 = 0.41
The probability that the Yankees scored 5 or more runs.
= 0.45
P(B) = The probability that the Yankees scored fewer than 5 runs.
So,
The probability that the Yankees lose and score fewer than 5 runs.
P(A ∩ B) = 0.33
Now,
The probability that the Yankees scored fewer than 5 runs.
P(B/A) =P(A∩B) / P(A)
So,
= 0.33 / 0.41
= 0.8048
= 0.805
Thus,
The probability that the Yankees scored fewer than 5 runs is 0.805.
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The amount of wheat exported by a country
increased exponentially each year between
2006 and 2015.
In 2011, the country exported 240,000 tonnes
of wheat.
In 2015, the country exported 685,464 tonnes
of wheat.
Work out how much wheat the country
exported in 2006.
Give your answer to the nearest tonne.
PLEASE HELP ME!!
Answer:
2011 2016 685,4632 thousand
Step-by-step explanation: