The sales of books at a local book fair are shown in the histogram.
A histogram titled Book Sales with the x-axis labeled Number of Books. The x-axis has intervals of 0 to 1, 2 to 3, 4 to 5, 6 to 7, 8 to 9 and 10 to 11. The y-axis is labeled Frequency and starts at 0 with tick marks every two units up to 10. There is a shaded bar above 1 to 3 that stops at 3, above 2 to 3 that stops at 4, above 5 to 6 that stops at 8, above 6 to 7 that stops at 2, above 8 to 9 that stops at 4 and above 10 to 11 that stops at 8.
Which statement best describes the spread and distribution of the data?
The data is almost symmetric, with a maximum range of 11. This might be because the book fair offers fair prices, so most costumers bought books.
The data is skewed, with a maximum range of 14. This might be because many of the customers wanted to stock up before the winter.
The data is bimodal, with a maximum range of 11. This might occur if there is a sale, if you buy 4, or 10 books, you get one free.
The data is symmetric with a maximum range of 10. This might mean that most customers bought less than 3 books because that is all that they could carry.
"The data is skewed, with a maximum range of 14. This could be due to the fact that many customers wanted to stock up before the winter."
What is a histogram?A histogram is a type of graph used in statistics to represent the distribution of a set of continuous data. It consists of a set of adjacent bars, where the area of each bar represents the frequency or relative frequency of observations within a specific interval or "bin" of the data.
The x-axis of a histogram shows the range of values for the variable being measured, divided into intervals or bins. The y-axis shows the frequency or relative frequency of observations within each interval or bin. Histograms are commonly used to show the shape, center, and spread of a distribution of data, as well as any potential outliers or gaps in the data.
In the given question, the histogram shows a skewed distribution, where the majority of book sales occurred in the lower intervals (1-3, 2-3, and 5-6) and the frequency decreases as the number of books sold increases. The maximum range of the data is 14 (from the interval 10-11 to the interval 2-3), which suggests a wide spread of book sales across different intervals.
"The data is skewed, with a maximum range of 14. This could be due to the fact that many customers wanted to stock up before the winter." comes the closest to describing the spread and distribution of the data shown in the histogram.
The other options do not accurately describe the shape or spread of the data shown in the histogram.
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Answer:
C: The data is bimodal, with a maximum range of 11. This might occur if there is a sale, if you buy 4, or 10 books, you get one free.
Step-by-step explanation:
PLEASE HELP!!
Pythagorean Theorem (triangles)
The missing area or side length in the triangles are:
1: Area = 145 units²
2: Area = 17 units²
3: Area = 29 units²
4: Area= 27 units²
5: length = √37 units
6: length = 2√26 units
7: length = 3√11 units
8: length = 5√3 units
How to find the missing area or side length?Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. That is:
c² = a² + b²
Where a and b are the lengths of the legs, and c is the length of the hypotenuse
No. 1
Area (hypotenuse) = 81 + 64 = 145 units²
No. 2
Area (hypotenuse) = 16 + 1 = 17 units²
No. 3
Area (hypotenuse) = 5² + 2² = 29 units²
No. 4
Area (leg) = 36 - 9 = 27 units²
No. 5
length (hypotenuse) = √(6² + 1²) = √37 units
No. 6
length (hypotenuse) = √(10² + 2²) = 2√26 units
No. 7
length (leg) = √(10² - 1²) = 3√11 units
No. 8
length (leg) = √(10² - 5²) = 5√3 units
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Please help me on this!
Answer:
One solution
Step-by-step explanation:
I added a photo of my solution
Answer:
The system has one solution: (0, 4).
Mrs. Perez's class donated 99 different products for the food drive. One-ninth of it was vegetables,2/3 pasta,
and 2/9 was soup. How much of each product did they donate?
Simplifying Mrs. Perez's class donated 11 units of vegetables, 66 units of pasta, and 22 units of soup.
What does the term "simplify expression" mean?The process of solving a math problem is simply known as simplifying an expression. An expression is simplified when it is written in the most straightforward way feasible
vegetables = (1/9) x 99
Simplifying this expression, we get:
vegetables = 11
So the class donated 11 units of vegetables.
Next, we can figure out how much of the donation was pasta. We know that 2/3 of the donation was pasta, so we can set up the equation:
pasta = (2/3) x 99
Simplifying 66 units homemade pasta, 22 units of soup, and 11 units of veggies were all provided by Mrs. Perez's students.
Which expression should I simplify?
A math difficulty is simply solved by simplifying the expression. When you simplify a phrase, your goal is essentially to make it as simple as you can. There shouldn't be any more multiplication, dividing, adding, or removing to be done at the conclusion.
veggies = 1/9 times 99
When we condense this statement, we get:
eleven vegetables
Hence, the class gave away 11 units of produce.We can then determine what proportion of the contribution was pasta. Given that we know that pasta made up 2/3 of the donation, we can construct the following equation:
spaghetti equals (2/3) x 99
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what is the average time gap between the first cyclists time and each of the remaining cyclists' times (second through fifth) in the 1995 volta a catalunya cycle race if we know the result?
The average time gap between the first cyclist's time and each of the remaining cyclists' times (second through fifth) in the 1995 Volta a Catalunya cycle race is approximately 6 minutes and 7 seconds.
To calculate this, we need to subtract the time of the first cyclist from each of the remaining cyclists' times (second through fifth).The time for the first cyclist was 41:38:33.
The times for the remaining cyclists were as follows:
We can calculate the difference for each cyclist by subtracting the first cyclist's time from their own time:
Adding up all of the times and dividing by four, we get an average of 00:06:07.
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The equation y = -4/7x - 5 has a slope of
find the z-score such that the interval within standard deviations of the mean for a normal distribution contains 87% of the probability.
The Z-score of the interval within standard deviations of the mean for a normal distribution contains 87% of the probability is 1.11 (rounded to two decimal places).
To find the z-score such that the interval within standard deviations of the mean for a normal distribution contains 87% of the probability, we need to use the standard normal distribution table (Z-table) or a calculator that has the inverse normal function.
The standard normal distribution is a normal distribution with a mean of zero and a standard deviation of 1. It is denoted by the letter Z. Z-scores measure the number of standard deviations a data point is from the mean of the data set. A positive Z-score indicates a data point is above the mean, while a negative Z-score indicates a data point is below the mean.
To find the Z-score such that the interval within standard deviations of the mean for a normal distribution contains 87% of the probability, we first need to find the probability that is outside the interval. Since the interval is within standard deviations of the mean, we can use the empirical rule or the 68-95-99.7 rule to find the probability that is outside the interval.
The 68-95-99.7 rule states that 68% of the probability lies within 1 standard deviation of the mean 95% of the probability lies within 2 standard deviations of the mean 99.7% of the probability lies within 3 standard deviations of the mean. Since we are interested in the interval within standard deviations of the mean that contains 87% of the probability, we can assume that the interval is 1 standard deviation away from the mean.
Using the 68-95-99.7 rule, we can find the probability that is outside the interval:
100% - 68% = 32%
Since the probability that is outside the interval is 32%, we want to find the Z-score that corresponds to the probability of 16% on either side of the mean. We use the Z-table or a calculator that has the inverse normal function to find the Z-score that corresponds to a probability of 0.16.
From the Z-table, the Z-score that corresponds to a probability of 0.16 is 1.11 (rounded to two decimal places).
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Find the perimeter of a polygon with
Points A (4,2) B (-4,8) C (-7,4) and D (-1,-4)
The required perimeter is 25+√61 units.
How to find perimeter?We can find the distance between each pair of consecutive points and then add them up to get the perimeter of the polygon.
Using the distance formula, the distance between points A and B is:
[tex]$$AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} = \sqrt{(-4 - 4)^2 + (8 - 2)^2} = \sqrt{100} = 10$$[/tex]
Similarly, the distances between the other pairs of points are:
[tex]$$BC = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2} = \sqrt{(-7 + 4)^2 + (4 - 8)^2} = 5$$[/tex]
[tex]$$CD = \sqrt{(x_D - x_C)^2 + (y_D - y_C)^2} = \sqrt{(-1 + 7)^2 + (-4 - 4)^2} = 10$$[/tex]
[tex]$$DA = \sqrt{(x_A - x_D)^2 + (y_A - y_D)^2} = \sqrt{(4 + 1)^2 + (2 + 4)^2} = \sqrt{61}$$[/tex]
Therefore, the perimeter of the polygon is:
[tex]$$AB + BC + CD + DA = 10 + 5 + 10 + \sqrt{61}$$[/tex]
= 25+√61
Thus, required perimeter is 25+√61.
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the combined score on this test ranges from 400 to 1600. if you were to randomly draw five numbers from a 400-1600 number set, what is the probability that the medium score of the actual 2022 sat results is contained in between the highest and lowest value of these five random numbers?
The combined score on the 2022 SAT test ranges from 400 to 1600. If you were to randomly draw five numbers from a 400-1600 number set, the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers is approximately 0.004%
How do we find the probability?To find the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers, we need to find the probability of the following event: “the three other random numbers drawn lie between the highest and lowest values.
The probability of choosing one of the five numbers that falls within the range is (1600 – 400)/1201 = 1/2.25.
The first number can be any number within the 400-1600 range, so the probability is 1.The second number must lie within the range created by the highest and lowest values of the first number, which has a width of 1201. Thus, the probability is 1201/3201.
The third number must lie within the range created by the highest and lowest values of the first two numbers, which has a width of 801. Thus, the probability is 801/2401.The fourth and fifth numbers must lie within the range created by the highest and lowest values of the first three numbers, which has a width of 401.
Thus, the probability is 401/1601.Therefore, the probability of the medium score of the actual 2022 SAT results being between the highest and lowest values of these five random numbers is (1/2.25) * (1201/3201) * (801/2401) * (401/1601) * 1 = 0.000038 or approximately 0.004%.
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The coordinates of the vertices of quadrilateral HIJK are H(1,4), I(3,2), J(-1,-4), and K(-3,-2). If quadrilateral HIJK is rotated 270 about the origin, what are the vertices of the resulting image, quadrilateral H’ I’ J’ K’
The vertices of the resulting image, quadrilateral H’ I’ J’ K’ include the following:
H' (4, -1).
I' (2, -3).
J' (-4, 1).
K' (-2, 3).
What is a rotation?In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
In Geometry, rotating a point 270° about the origin would produce a point that has the coordinates (y, -x).
By applying a rotation of 270° about the origin to quadrilateral HIJK, the location of its vertices is given by:
(x, y) → (y, -x)
Ordered pair H (1, 4) → Ordered pair H' (4, -(1)) = (4, -1).
Ordered pair I (3, 2) → Ordered pair I' (2, -(3)) = (2, -3).
Ordered pair J (-1, -4) → Ordered pair J' (-4, -(-1)) = (-4, 1).
Ordered pair K (-3, -2) → Ordered pair K' (-2, -(-3)) = (-2, 3).
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There are 25 pupils in a class who take part in a drinking milk initiative. Pupils have a 210
millilitre glass each. During the break each pupil drinks a full glass of milk. Milk comes in 1000
millilitre bottles. How many bottles of milk are needed?
In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.
Each student in a class of 25 drinks a full 210 millilitre glass of milk, hence the amount of milk consumed overall during the break is:
25 students times 210 millilitres each equals 5250 millilitres.
Milk comes in 1000 millilitre bottles, thus to determine how many bottles are needed, divide the entire amount eaten by the volume of milk in each bottle.
5.25 bottles are equal to 5250 millilitres divided by 1000 millilitres.
We must round up to the nearest whole number because we are unable to have a fraction of a bottle. This results in:
6 bottles in 5.25 bottles
In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.
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What is the contrapositive of the following statement? "If it is not a lion, then it is a cat
The contrapositive of the given statement is "If it is not a cat, then it is a lion."
The contrapositive of the statement "If it is not a lion, then it is a cat" can be obtained by negating the original statement and switching the positions of the antecedent (the "if" part) and the consequent (the "then" part).
The contrapositive takes the form:
"If it is not a cat, then it is a lion."
So, the contrapositive of the given statement is "If it is not a cat, then it is a lion."
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how do you use TAN in equations and what is it?
Answer:
TAN is a mathematical function in trigonometry that stands for tangent. It is used to calculate the tangent of an angle in a right triangle, which is defined as the ratio of the length of the opposite side to the length of the adjacent side.
In equations, you can use TAN to find the value of the tangent of an angle. For example, if you have an angle of 30 degrees in a right triangle and you want to find the value of the tangent of that angle, you can use the TAN function in your calculator or programming language.
The syntax of the TAN function is usually "tan(x)", where x is the angle in radians. If your calculator or programming language uses degrees instead of radians, you may need to convert the angle to radians first using the conversion formula: radians = degrees * (pi/180).
For example, to find the value of the tangent of 30 degrees, you can use the TAN function as follows:
In degrees mode: TAN(30) = 0.57735027
In radians mode: TAN(30*pi/180) = 0.57735027
TAN can be used in various trigonometric equations and identities to solve for unknown sides or angles of a right triangle.
Step-by-step explanation:
If < C and < D are supplementary and < C = 5 0 °, find the measure of
< D = °
....
Answer:
<D = 130°
Step-by-step explanation:
Supplementary = 180°
<C = 50°
<D = ?
<C + <D = 180°
180° - 50° = 130°
<D = 130°
The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. The function below shows the relationship between f(x) and x:f(x) = 10(1.3)xWhich of the following graphs best represents the function? (1 point)a Graph of f of x equals 1.3 multiplied by 10 to the power of xb Graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing towards infinityc Graph of f of x equals 10 multiplied by 1.3 to the power of xd Graph of f of x equals 1.3 to the power of x
The graph of an exponential function with an initial value of 10 and a base of 1.3z. Therefore option D is correct.
The function f(x) is an exponential function with a base of 1.3 and an initial value of 10. The graph of an exponential function with a base greater than 1 increases rapidly as x increases. Therefore, option a can be eliminated.
Option b is not a graph of an exponential function, as the function is not continuous and does not approach any asymptote.
Option c shows an exponential function with an initial value of 10 and a base of 1.3/10, which is less than 1. This means that the function would decrease over time, which is not consistent with the problem statement.
Option d shows an exponential function with an initial value of 10 and a base of 1.3, which is consistent with the problem statement. Therefore, option d is the correct answer.
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VERY IMPORTANT DBA !!!
Table C represents a linear relationship that is also proportional. This is because the ratio of the output (y) to the input (x) is always constant, which is a characteristic of proportional relationships.
What is a linear equation?
A linear equation is an algebraic equation that represents a straight line on a graph. In general, a linear equation takes the form:
y = mx + b
A linear relationship between two variables, x and y, is one in which the change in y is directly proportional to the change in x. This means that for any change in x, there is a corresponding change in y that can be expressed as a constant multiple of x.
For example, if we have a linear relationship y = mx + b, where m is the slope of the line and b is the y-intercept, then if we increase x by 1 unit, y will increase by m units. This relationship holds true for all values of x and y along the line.
A proportional relationship, on the other hand, is a special case of a linear relationship in which the ratio of y to x is always the same constant. This means that if we increase x by 1 unit, y will increase by a constant multiple of x. In other words, the relationship between x and y is one of scaling, where the size of y is always a fixed multiple of the size of x.
Therefore, Table C represents a linear relationship that is also proportional. This is because the ratio of the output (y) to the input (x) is always constant, which is a characteristic of proportional relationships.
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Identify the type of sequence 56,49,42,35,28,21
It is Arithmetic Sequence. An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence.
For the given sequence
d= 49-56 = -7
d= 42-49 = -7
Thus, there is -7 as a common difference between the terms.
The distance between succeeding terms in an arithmetic series is always the same. It is often referred to as an arithmetic series or arithmetic progression. The following statement can be used to represent an arithmetic sequence: a, (a + d), (a + 2 d), (a + 3 d),..., where a is the first term and d is the constant difference between values.
To determine the sum of an arithmetic sequence, it is generally simple to add or subtract all the terms in a short series together. An individual can quickly determine the sum of an arithmetic series for a particular number of terms by using the generic formula for the nth term of an arithmetic sequence.
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a ramp 27ft long rises to a platform. the bottom of the platform is 16ft from the foot of the ramp. find , the angle of elevation of the ramp. round your answer to the nearest tenth of a degree.
Angle of elevation of the ramp with a height of 27ft and a platform of 16ft is approximately 59.35°.
The ramp is 27ft long and rises to a platform, the bottom of the platform is 16ft from the foot of the ramp.
We need to find the angle of elevation of the ramp.
The angle of elevation of the ramp is the angle made by the ramp with the horizontal.
Let ABC be the ramp and D be the platform, as shown below: Let AB = 16ft and BC = 27ft.
We need to find the angle ABD.
Consider right-angled ΔABC In right-angled ΔABC,
we have:
tan⁻¹ (BC / AB)
θ = tan⁻¹ (27 / 16)
θ ≈ 59.35°
Hence, the angle of elevation of the ramp is approximately 59.35°.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
180
Step-by-step explanation:
Form an equation
27x+17=180
Solve it for x
x = 6.0recurring
the perimeter is 180
Let me know if it helps
Use Euler’s formula to write in exponential form.
Answer:
(A) 10e^(i7π/4)
Step-by-step explanation:
You want the exponential form of 5√2 -5i√2.
Complex number notationThere are numerous ways a complex number can be written in "polar form".
The usual choices are ...
a +bi . . . . . . . . . . . . . rectangular form
A(cos(θ) +i·sin(θ)) . . . . a sort of hybrid form
A·cis(θ) . . . . . . . . . . an abbreviation of the above
A∠θ . . . . . . . . . . . . polar form
A·e^(iθ) . . . . . . . . . using Euler's formula
ConversionThe conversion from rectangular form to any of the others makes use of trig identities and the Pythagorean theorem.
A = √(a² +b²)
θ = arctan(b/a) . . . . . with attention to quadrant
ApplicationFor the given number, ...
A = √((5√2)² +(-5√2)²) = (5√2)√(1 +1) = 5·2
A = 10
θ = arctan(-5√2/(5√2)) = -1 . . . in the 4th quadrant
θ = 7π/4
Then the desired exponential form of the complex number is ...
10e^(i7π/4)
__
Additional comment
Spreadsheets and some calculators have an ATAN2(x, y) function that performs a quadrant-sensitive angle conversion.
Solve and then answer the question below.
*MUST SHOW WORK*
Half a number plus eight is fourteen minus a number. How many solutions does this equation have?
To answer the question, this equation has only one solution, which is x = 4.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. It usually consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=).
The expressions on both sides can contain variables, constants, and mathematical operations such as addition (+), subtraction (-), multiplication (*), division (/), exponentiation (^), and others. The goal of an equation is to find the values of the variables that make both sides equal.
by the question.
Let's start by setting up the equation:
[tex]1/2x + 8 = 14 - x[/tex]
where x is the number, we're trying to find.
Now let's simplify the equation by combining like terms:
[tex]3/2x + 8 = 14[/tex]
Subtracting 8 from both sides:
[tex]3/2x = 6[/tex]
Multiplying both sides by 2/3:
[tex]x = 4[/tex]
So, the solution to the equation is x = 4.
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Determine whether the following statement is true or false. If it is false, explain why. The probability that event A or event B will occur is P(A or B)= P(A) + P(B) - P(A or B). Choose the correct answer below. A. True B. False, the probability that A or B will occur is P(A or B)= P(A) middot P(B). C. False, the probability that A or B will occur is P(A or B)= P(A) + P(B). D. False, the probability that A or B will occur is P(A or B)= P(A) + P(B) - P(A and B).
False, the probability that A or B will occur is P(A or B) = P(A) + P(B) - P(A and B).
Define probabilityProbability refers to the measure of the likelihood or chance of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event, and 1 indicates a certain event.
This formula is known as the Addition Rule for Probability and states that to calculate the probability of either event A or event B occurring (or both), we add the probability of A happening to the probability of B happening, but then we need to subtract the probability of both A and B happening at the same time to avoid double counting.
Option A is not the correct answer because it is missing the subtraction of P(A and B), options B and C are incorrect because they omit the subtraction and only add the probabilities of the events. Option D is close, but it is missing the addition of the probabilities of A and B.To know more about event, visit:
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we assume there is sometimes sunny days and sometimes rainy days, and on day 1, which we're going to call d1, the probability of sunny is 0.9. and then let's assume that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance. so, what are the chances that d2 is sunny?
Probability of D2 being sunny = 0.78.
On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.
Therefore, we need to find the chances that D2 is sunny.
There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.
Now, Let us find the probability of D2 being sunny.
We have the following possible cases for D2.
D1 = Sunny; D2 = Sunny
D1 = Sunny; D2 = Rainy
D1 = Rainy; D2 = Sunny
D1 = Rainy; D2 = Rainy
The probability of D1 being sunny is 0.9.
When a sunny day follows a sunny day, the probability is 0.8.
When a sunny day follows a rainy day, the probability is 0.6.
Therefore, the probability of D2 being sunny is given by the formula:
Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.
Therefore, the probability that D2 is sunny are 0.78 or 78%.
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the two sides of a right triangle opposite the non-right angles are called
The two sides of a right triangle opposite the non-right angles are called as adjacent and opposite angle or Legs.
A triangle is a three-sided regular polygon in which the total of any two sides is always larger than the sum of the third side.
A right-angled triangle is one with one of its internal angles equal to 90 degrees, or any angle is a right angle. As a result, this triangle is also known as the right triangle or the 90-degree triangle. In trigonometry, the correct triangle is very significant.
A right-angled triangle is a triangle in which one of the angles is 90 degrees. The total of the other two angles is 90 degrees. The sides that include the right angle are perpendicular and form the triangle's base. The third side is known as the hypotenuse, and it is the longest of the three sides.
The three sides of the right triangle are connected. Pythagoras' theorem explains this relationship. This theorem states that in a right triangle,
Perpendicular² + Base² = Hypotenuse²
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Work out the recipricol of 0.5
Answer:
the answer is 2
Step-by-step explanation:
this answer will be 200⁰0000000000⁰00000⁸⁰643367897⁶43677443⁵=5.0
Write the expression in complete factored
form.
3p(a - 1) - 2(a - 1)
Help!
Answer:
(a - 1)(3p - 2)
Step-by-step explanation:
3p(a - 1) - 2(a - 1) ← factor out (a - 1) from each term
= (a - 1)(3p - 2)
QUESTION 3
A pan of brownies is cut into eight equal rows. Two thirds of one of those rows is what fraction of the whole pan.
Answer:
1/12
Step-by-step explanation:
Each row would be 1/8 of the whole pan. Now multiply 1/8 by 2/3.
Multiply the numerators: 1*2=2
Multiply the denominators: 8*3=24
Your answer: 2/24 or 1/12 simplified (dividing both top and bottom by 2)
Hope this helps. :)
Answer:
[tex]\frac{1}{11}[/tex]
Step-by-step explanation:
[tex]\frac{2}{22}[/tex] = [tex]\frac{1}{11}[/tex]
I drew a pan when I divided into 8 rows. Then I divided that up inot 2/3. In the first row that is divided into 3 parts, I want one of those 2 parts. The total parts are 22. 2/22
A number subtracted from 80 gives — 30. Find the number
The number which, when subtracted from 80, results in -30 is equal to 110.
To solve this problem, we can use algebraic equations to represent the given information. Let x be the number that we want to find.
According to the problem, when we subtract x from 80, we get -30:
80 - x = -30
To solve for x, we can isolate it on one side of the equation by adding x to both sides, and then simplify:
80 - x + x = -30 + x
80 = -30 + x
Next, we can isolate x by subtracting -30 from both sides:
80 - (-30) = x
Simplifying the right-hand side:
80 + 30 = x
110 = x
Therefore, the number that was subtracted from 80 and gave -30 as the result is 110.
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For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are [1 - 20x + 150x^2 + cx^3 ]. find c?
Using binomial theorem we can expand the equation but We are not given the value of a or n, so we cannot determine c exactly.
What is the difference between real and integer?Integers are real numbers that only comprise positive and negative whole integers as well as natural numbers. Because of rational and irrational numbers, real numbers may include fractions, whereas integers cannot.
What's a real number?A real number is a quantity in mathematics that may be expressed as an infinite decimal expansion. Real numbers, as opposed to natural numbers such as 1, 2, 3,..., which are generated from counting, are used in measures of continually changing quantities such as size and time.
by applying the binomial theorem:
[tex](1 + ax)^n = C(n, 0) + C(n, 1)(ax) + C(n, 2)(ax)^2 + C(n, 3)(ax)^3 + ...[/tex]
where C(n, k) is the binomial coefficient, which equals[tex]n!/(k!(n-k)!).[/tex]
The first few terms of this expansion are:
[tex](1 + ax)^n = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]
Comparing with the given expression [1 - 20x + 150x^2 + cx^3], we have:
[tex]1 - 20x + 150x^2 + cx^3 = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]
Equating coefficients of [tex]x^3[/tex] on both sides, we get:
[tex]c = n(n-1)(n-2)(a^3/6)[/tex]
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PLS HELP MEEEEEEE ASAP
Answer:
[tex]{ \sf{a = { \blue{ \boxed{{53 \: \: \: \: \: \: \: \: }}}}} \: cm}[/tex]
Step-by-step explanation:
[tex] { \mathfrak{formular}}\dashrightarrow{ \rm{4 \times side \: length}}[/tex]
Each side has length of a?
[tex]{ \tt{perimeter = a + a + a + a}} \\ \dashrightarrow{ \tt{ \: 212 = 4a}} \\ \\ \dashrightarrow{ \tt{4a = 212}} \: \\ \\ \dashrightarrow{ \tt{a = \frac{212}{4} }} \: \: \\ \\ { \tt{a = 53 \: cm}}[/tex]
