We can write the following two linear equations to represent the distance each animal can travel in the race:
d1 = r1 * t
d2 = r2 * t
Let's call the distance that the first animal can travel in a certain amount of time "d1" and the distance that the second animal can travel in that same amount of time "d2". We can write the following two linear equations to represent the distance each animal can travel in the race:
d1 = r1 * t
d2 = r2 * t
where "r1" is the rate of the first animal, "r2" is the rate of the second animal, and "t" is the time that the race lasts. These two equations show how the distance each animal can travel is proportional to their rate and the time that the race lasts.
In this model, the variables are defined as follows:
d1 = distance traveled by the first animal
d2 = distance traveled by the second animal
r1 = rate of the first animal
r2 = rate of the second animal
t = time the race lasts
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i will give you alot of points
Micah withdrew $4.50 from his bank account. Write a rational number to represent this situation
The rational number representation of Micah withdrawing $4.50 from his bank account is -4.5.
How to find the rational number?A rational number is any fraction with non-zero denominators. A rational number can be written as a fraction with a numerator and denominator that are both integers.
In this case, we can write $-4.50$ as the fraction $\frac{-450}{100}$, where the numerator represents the amount of money withdrawn (in cents) and the denominator represents the unit of currency used (in this case, 100 cents = 1 dollar).
So, the rational number representing the amount of money withdrawn from Micah's bank account is {-450} / {100}$ = -4.5.
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A concrete block has a volume of 48 cubic meters and the dimensions show. Find the value of x.
Suppose a license plate must contain 3 letters followed by 4 digits. Letters and digits can be repeated. How many different license plates are possible that end with 5 as the last digit?
There are 17,576,000 possible license plates consisting of 3 letters followed by 4 digits.
Fundamental Counting Principles:
The fundamental counting principle is a rule used to count the total number of possible outcomes in a situation.
When something can be done m different ways and n different ways,
there are then [tex]m*n[/tex] ways to accomplish both.
Based on the given information, since the letters and digits may be repeated, there are:
26 ways to fill in the first letter
26 ways to fill in the second letter
26 ways to fill in the third letter
10 ways to fill in the first digit
10 ways to fill in the second digit
10 ways to fill in the third digit and
1 way to fill in the first digit (as the last digit end with 5)
Thus, by Fundamental Principle of Counting, there are 17,576,000 possible license plates.
26 x 26 x 26 x 10 x 10 x 10 x 1 = 17,576,000
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Which scatter plot represents the data shown in the table?
The diagram of the scatter plot is given in the attached image below.
What is a linear function?The graph of a linear function is a straight line. The following is the form of a linear function.
a + bx = y = f(x).
One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.
The data are shown in the table below:
x y
4 1
5.5 2
7.5 3
9 4
11 5
14 6
From the given choices:
the last diagram of the scatter plot is given in the attached image.
Hence, the scatter plot is given below.
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Write the augmented matrix for the following system of equations 7-6y+8x=0, 6x=-3-2y
The augmented matrix for the system of equations 7-6y+8x=0, 6x=-3-2y is:
| 7 -6 8 | 0 |
| 6 0 -2 | 3 |
This matrix represents the system of equations in a matrix form where the coefficients of the variables are on the left and the constant terms are on the right.
An augmented matrix is a rectangular array that is formed by appending the coefficients of variables and the constant terms of a system of linear equations in a single matrix. It is used as a tool in linear algebra to represent a system of linear equations in a compact form.
The augmented matrix is typically written as:
| a11 a12 a13 | b1 |
| a21 a22 a23 | b2 |
| a31 a32 a33 | b3 |
where aij represents the coefficient of the i-th equation for the j-th variable, and bi represents the constant term for the i-th equation.
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7. A portrait without its frame has
a height 1.5 times its width w,
in inches. Its frame is 4 in. wide
all along its perimeter. What is
an expression for the area of the
framed portrait in terms of w?
Simplify your expression and write
it in standard form.
The expression for the area of the framed portrait in terms of w is: A = [tex]1.5w^{2}[/tex] + 12w + 64.
How to simplify an expression?Simplifying an expression means to write it in its simplest form by combining like terms and removing any redundant or unnecessary elements. There are several techniques you can use to simplify expressions, including:
Combining like terms: Like terms are terms that have the same variable raised to the same power. For example, 2x and 4x are like terms. To simplify an expression, you can add or subtract like terms.
Distributing: Distributing means multiplying a constant or variable by each term within a set of parentheses. For example, if you have the expression 2(x + 3), you can distribute the 2 to each term within the parentheses: 2x + 6.
Factoring: Factoring means finding a common factor among a set of terms and grouping them together. For example, if you have the expression [tex]x^{2}[/tex] + 4x, you can factor out the x: x(x + 4).
Simplifying rational expressions: Rational expressions are expressions that have one fractional term. To simplify a rational expression, you can cancel out common factors in the numerator and denominator.
Let's call the width of the portrait w and the height h. We know that the height of the portrait is 1.5 times its width, so h = 1.5w.
The area of the portrait is the product of its width and height: A = w * h = w * 1.5w = [tex]1.5w^{2}[/tex].
The width of the frame is 4 inches all along its perimeter, so the total width of the framed portrait is w + 4 + 4 = w + 8.
The total height of the framed portrait is h + 4 + 4 = h + 8 = 1.5w + 8.
The area of the framed portrait is the product of its width and height: A = (w + 8) * (1.5w + 8) = (w + 8) * 1.5w + 8 * (w + 8) = 1.5w^2 + 12w + 64.
So, the expression for the area of the framed portrait in terms of w is: A = [tex]1.5w^{2}[/tex] + 12w + 64.
This expression is already in standard form.
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a bag contains 5 red balls and 6 green balls. if two balls are taken out successively, without replacement, what is the probability that green is picked on the first pick given that at least one red is chosen? g
The probability of picking a green ball on the first pick, given that at least one red is chosen, is 11/19.
The probability of picking a green ball on the first pick, given that at least one red is chosen, can be calculated by finding the total number of possible outcomes and then dividing by the number of outcomes that include at least one red ball. In this bag, there are 11 green balls and 5 red balls, for a total of 16 balls. Since two balls are taken out successively without replacement, the total number of outcomes is 16 choose 2, or 120. Of those, there are 10 outcomes that include at least one red ball, so the probability of picking a green ball on the first pick, given that at least one red is chosen, is 11/19. This can be calculated by dividing the number of outcomes that include at least one red ball (10) by the total number of outcomes (120).
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Are x and y common factors?
x and y are not common factors, as they cannot be simplified with themselves.
What are common factors?Common factors in an expression with n terms are the terms that are common to all the terms of an expression.
For example, taking the expression 2 + 4 + 6, we have that 2 is a common factor, as:
4 = 2 x 2.6 = 2 x 3.For variables to be common factors, we have that they must have the same base, with the same or different exponents.
x and y are different bases, hence they are not common factors.
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what is the probability that a randomly selected patient is admitted for something other than coronary care?
The probability that a randomly chosen patient will be admitted for a reason other than coronary care is equal to one less than the likelihood that they will be admitted for that reason.
The likelihood that a randomly chosen patient will be admitted for a reason other than coronary care is equal to 1 less than the likelihood that they will be admitted for that reason. For instance, if the chance of being admitted for coronary care is 0.25, the chance of being admitted for a different reason is 0.75. This is due to the requirement that the total number of outcomes must equal 1. Accordingly, if one outcome has a 0.25 probability, then the chance of every other outcome must equal 0.75. As a result, the likelihood that a randomly chosen patient will be admitted for a reason other than coronary care is equal to 1 minus the likelihood that they will be admitted for that reason.
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Parallel to the line through (1,-2) (-6,3)
Step-by-step explanation:
A line that is parallel to another line has the same slope but a different y-intercept. The slope of the line through the points (1,-2) and (-6,3) can be found using the slope-point formula:
slope = (y2 - y1) / (x2 - x1) = (3 - (-2)) / (-6 - 1) = 5/7
So, a line that is parallel to this line would have the same slope of 5/7. To find an equation for a line with this slope that passes through a different point, we can use the point-slope formula:
y - y1 = m * (x - x1)
Where m is the slope and (x1, y1) is a point on the line. We can choose any point to use in this formula, but a common choice is the origin (0,0). So, plugging in the values we have:
y - 0 = 5/7 * (x - 0)
y = 5/7 * x
This is the equation for a line that is parallel to the line through the points (1,-2) and (-6,3) and passes through the origin.
you want to enclose a rectangular region with an area of 1200 square feet and a length of 40 feet, 50 feet, or 60 feet. find the perimeter for each possible region.
The circumference is 160 feet for a length of 40 feet. The perimeter is 200 feet for a length of 50 feet. The circumference is 240 feet for a length of 60 feet.
A rectangular region with a 1200 square foot area will have a different perimeter depending on how long it is. The perimeter will be 160 feet if the area is 40 feet long. The length of 40 feet is multiplied by four to get a final measurement of 160 feet. In a similar manner, if the area is 50 feet long, the perimeter will be 200 feet.
The length of 50 feet is multiplied by four to get a final result of 200 feet. Finally, the perimeter will be 240 feet if the area is 60 feet long. The length of 60 feet is multiplied by four to get a final measurement of 240 feet. A rectangular region with an area of 1200 square feet will therefore have a different perimeter depending on its length, with a length of 40 feet resulting in a perimeter of 160 feet, a length of 50 feet resulting in a perimeter of 200 feet, and a length of 60 feet resulting in a perimeter of 240 feet.
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.A circle is inscribed in quadrilateral ABCD. If AB = 4, BC = 5, and CD = 8,
what is DA?
Step-by-step explanation:
I just answered this. how often was that posted ?
the distance of a vertex to its 2 neighboring circle touching points is the same, because tangents emanating from the same point to the same circle must have the same distance to the touching points.
so, AB splits into a (from A to the circle touching point on AB) and b (from the circle touching point on AB to B).
b = AB - a
BC splits into b (from B to the circle touching point on BC) = AB - a, and c (from the circle touching point on BC to C).
c = BC - (AB - a) = BC - AB + a
CD splits into c (from C to the circle touching point on CD) = BC - AB + a, and d (from the circle touching point on CD to D).
d = CD - (BC - AB + a) = CD - BC + AB - a
DA now splits into d (from D to the circle touching point on DA) and ... a (from the circle touching point on DA to A).
a = DA - (CD - BC + AB - a) = DA - CD + BC - AB + a
0 = DA - CD + BC - AB
DA = CD - BC + AB = 8 - 5 + 4 = 7
Answer:
DA = 7
Step-by-step explanation:
You have quadrilateral ABCD with an inscribed circle and side lengths AB=4, BC=6, CD=8, and you want to know the length of DA.
Inscribed circleThe tangents from each vertex of the quadrilateral to the inscribed circle are the same length, so we can work our way around the quadrilateral to find the missing length. The attached figure shows the tangent lengths working counterclockwise from vertex A.
The sum of the tangents from A and D is ...
x + (7 -x) = 7
The length of DA is 7 units.
__
Additional comment
The sum of the lengths of opposite sides is the same in any quadrilateral with an inscribed circle. Here, that sum is 4+8 = 12, so the unknown side is 12-5 = 7.
Evaluate the expression for the given value of the variable.
41 + 5/7t =
t= -1/2
41 + 5.7t= Answer?
Answer:
40.6428571429
Step-by-step explanation:
To evaluate the expression for the given value of the variable when t = -1/2, we just need to substitute the value of t into the expression:
41 + 5/7 * (-1/2) = 41 - 5/14
41 - 5/14 = 40.6428571429
So the answer is 40.6428571429.
Solve the equation. n/-1.5 = -1.2 N=?
Answer:
1.8
Step-by-step explanation:
The equation we are given is [tex]\frac{n}{-1.5} = -1.2[/tex]. We can multiply both sides by -1.5 to get n = 1.8.
Answer:
N = 1.8
Step-by-step explanation:
You do cross multiplication
n*1 = -1.5 * -1.2
1n = 1.8
To check it, we plug in 1.8
1.8/-1.5 = -1.2
What is important to know when solving problems that contain exponents? How can you improve at this skill?
When solving problems that contain exponents, we must know the value of both elements for the result to be correct. This ability can be improved by knowing how to multiply very well.
What is an exponent?An exponent is a mathematical expression that tells us that a value must be multiplied by itself a certain number of times, the most common exponent is the square in which a value must be multiplied by itself once, for example:
4² = 4 * 4 = 16To improve in problems with exponents we must know how to multiply very well because this is the basic operation that is most related to solving exponents.
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find the area of shaded region
The area of the shaped portion of the given diagram(circle) would be = 153.86cm²
How to calculate the area of a circle?The formula which is used to calculate the area of a circle = πr²
where π = 3.14
radius = 7 cm
Therefore the area of the shaded part of the circle ;
= 3.14 × 7²
= 3.14 × 49
= 153.86cm²
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Casey buys a bracelet. She pays for the bracelet and pays $0.72 in sales tax. The sales tax rate is %6, percent.
What is the original price of the bracelet, before tax?
The original price of the bracelet, before tax $0.68
What is the original price of the bracelet, before tax?From the question, we have the following parameters that can be used in our computation:
Amount = $0.72
Sales tax = 6%
Using the above as a guide, we have the following:
Amount = Original amount * (1 + Sales tax)
Substitute the known values in the above equation, so, we have the following representation
0.72 = Original amount * (1.06)
So, we have
Original amount = 0.68
Hence, the original amount = 0.68
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PLEASE HURRY The table displays data collected, in meters, from a track meet. 1/3 2 4 1 7 2/3 4/5 5/2 what is the median of the data collected? 1 1.5 2 2.5
The median of the data collected is 1.5. Option B
How to determine the median of the dataIt is important to note that the median of a given set of data is the middle number or the sum of the pair of numbers arranged in the order from the least to the greatest value.
From the information given, we have the data set;
1/3 2 4 1 7 2/3 4/5 5/2
Arrange the values in an ascending order from the least to the greatest value
1/3, 2/3, 4/5, 1, 2, 5/2, 4, 7
Since the total number is odd, take the two middle number and divide by 2, we get;
1 + 2/2
add the values
3/2
Divide the values
1. 5
Hence, the value is 1.5
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HELP ME SOLVE THIS PLEASEEEE!!! HURRY!
The missing angles in the figure are:
∠XVR = 125°
∠RVS = 55°
∠WVS = 125°
∠RST = 110°
∠RSV = 70°
∠VSU = 110°
∠UST = 70°
∠TUS = 39°
How to find the missing angles?
Angle geometry is a branch of mathematics that deals with the study of angles and their properties in two-dimensional figures such as circles, triangles, and polygons.
∠XVW + ∠XVR = 180° (sum of angles on a straight line is 180° )
Thus, ∠XVR = 180 - 55 = 125°
∠RVS = 55° (vertically opposite angles are equal)
∠WVS = 125° (vertically opposite angles are equal)
∠RST = 55 + 55 = 110° (exterior angle of a triangle)
∠RSV = 180-55-55 = 70° (sum of angles in a triangle is 180°)
∠VSU = 110° (vertically opposite angles are equal)
∠UST = 70° (vertically opposite angles are equal)
∠TUS = 180 - 70 -71 = 39° (sum of angles in a triangle is 180°)
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20% of the student population likes the turkey Sandwich.How many students do not like the turkey sandwich?
Answer:
80 percent of people don't like the turkey sandwich because 80 plus 20 equals 100 so think about it as a subtraction equation
Answer: 80% of students don't like turkey sandwiches.
Any population, P, for which we can ignore immigration, satisfies dP/dt = Birth rate - Death rate. For organisms which need a partner for reproduction but rely on a chance encounter for meeting a mate, the birth rate is proportional to the square of the population. Thus, the population of such a type of organism satisfies a differential equation of the form dP/dt = aP^2 - bP with a, b > 0. This problem investigates the solutions to such an equation. Sketch a graph of dP/dt against P. Note when dP/dt is positive and negative. dP/dt < 0 when P is in dP/dt > 0 when P is in
As a result, on a graph of dP/dt vs P, the curve would be concave down for P b/a and concave up for P > b/a. The curve would reach its maximum when P = b/a, with dP/dt equal to zero.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.
Here,
The equation dP/dt = aP² - bP represents the rate of change of the population P over time t.
When dP/dt is positive, the population is increasing. When dP/dt is negative, the population is decreasing.
To find when dP/dt is positive and negative, we need to find the critical points where dP/dt = 0.
Solving the equation dP/dt = aP² - bP = 0, we get:
aP² - bP = 0
aP(P - b/a) = 0
This equation has two solutions: P = 0 and P = b/a.
For P < b/a, dP/dt is negative (the population is decreasing). For P > b/a, dP/dt is positive (the population is increasing).
So, on a graph of dP/dt against P, the curve would be concave down for P < b/a and concave up for P > b/a. At P = b/a, the curve would have a maximum and dP/dt = 0.
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Miguel buys a dozen (12) bagels for $9.99. How much money did he spend on each bagel?
Miguel buys a dozen (12) bagels for $9.99. How much money did he spend on each bagel?
Answer:.83
Multiply. Write your answer as a fraction in simplest form. 4x 4/15
Answer:
1 1/15
Step-by-step explanation:
4 x 4/15 = 4/1 x 4/15 = 16/15 = 1 1/15
Actors competing in a 42 mile bicycle race he’s already completed 18 miles of the racing is traveling at a constant speed of 12 mph when one starts the race what is traveling at a constant speed for 16 mph. Our constant speed could want to travel to catch up with Hector at the finish line explain.
In 4 hours, and 30 minutes (or 4.5 hours), Wanda will catch up to the hector.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Hector competing in a 42-mile bicycle race he’s already completed 18 miles of the racing and is traveling at a constant speed of 12 mph.
Let x = the hours needed for Wanda to catch up to Hector.
Hector has already completed 18 miles. Hector travels at 12 miles per hour.
After x more hours, Hector will travel
18 + 12x miles
Wanda travels at 16 miles per hour. In x hours, she travels
16x miles
If Wanda catches up to Hector, then
16x = 18 + 12x
4x = 18
x = 4.5 hours
Therefore, Wanda will catch up to the hector at 4 hours, 30 minutes (or 4.5 hours).
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Complete question:
Factorize 4x^4 – 20x^2 + 25 using the Perfect Square Method
Answer:
see below
Step-by-step explanation:
4x^4 – 20x^2 + 25
= (2x-5)²
so the factor is 2x-5
Farmer McDonald has 14 chickens for every 3 geese on his farm. If there are 15 geese, how many chickens are there?
Step-by-step explanation:
14 for every 3 would be the same as 14/3
If we make that equal to x/15, what follows...
[tex] \frac{chickens}{geese} = \frac{14}{3} = \frac{x}{15} [/tex]
If we cross multiply
[tex]3x = 14(15)[/tex]
[tex]3x = 210[/tex]
And lastly we divide by 3
[tex]x = 70 \: chickens[/tex]
The height of a ramp, y, is proportional to the
horizontal distance along the ramp, x. Both
lengths are measured in feet. The equation
that relates the two is:
y=1/4x
Produce a graph of this relationship on the grid
provided. Explain how you made your graph.
This line represents the proportional relationship between x and y, as described by the given equation.
What is Equation?An equation is a physical and mathematical statement the describing physical phenomen or describe the relationship between different physical quantities. It typically consist of two or more variables which are symbol representing physical quantities and an equal sign the variable may be quantities such as force velocity your energy and the question describe how this quantities relate to each other.
To graph this relationship, I first plotted the origin (0,0) on the grid. Then, I made a table of values for x and y, using the given equation. I placed x values from 0 to 10 on the x-axis and the corresponding y values from 0 to 2.5 on the y-axis. Finally, I plotted each point on the graph to create a straight line. This line represents the proportional relationship between x and y, as described by the given equation.
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9 A hollow metal tube is made using a 5 mm metal sheet. The tube is 35 cm long and has an exterior diameter of 104 cm.
a. Draw a rough sketch of the tube and add its dimensions
b.Write down all the calculations you will have to make to find the volume of metal in the tube.
C. Calculate the volume of metal in the tube. d How could you find the total surface area of the outside plus the inside of the tube?
On solving the provided question, we can say that value of the total surface area of the outside plus inside of the tube will be (1033+1143) = 2176 cubic cm
what is surface area ?An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).
Volume is 704cm3
Total Surface area is 2176
Cylinder volume is calculated as follows: cylinder volume = π * radius² * height.
Length of metallic tube, h = 35 c
Radius (R) = 5.2 cm
inner Radius (r) = 4.7cm
Volume of metal =
3.14*(27.04-22.09)*35
704 cm cubic
Surface area inside
2*22/7*4.7*35
1033 cubic cm
Surface area outside
2*22/7*5.3*35
1143 cubic cm
Value of the total surface area of the outside plus inside of the tube will be (1033+1143) = 2176 cubic cm
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true or false? z-score helps to determine how far a particular value is from the mean relative to the data setâs standard deviation.
Answer:
True
Step-by-step explanation:
True. A z-score, also known as a standard score, is a statistical measure that helps to determine how far a particular value is from the mean relative to the data set's standard deviation.
A z-score is a dimensionless quantity that expresses the distance between a particular value and the mean of a distribution in terms of the number of standard deviations that the value is from the mean. A positive z-score indicates that the value is above the mean, while a negative z-score indicates that the value is below the mean.
To calculate the z-score for a given value, the formula is: z = (x - μ) / σ where z is the z-score, x is the value being considered, μ is the mean of the data set, and σ is the standard deviation of the data set.
For example, if the mean of a data set is 50 and the standard deviation is 10, and we are interested in finding the z-score for a value of 65, the calculation would be: z = (65 - 50) / 10 = 1.5. This indicates that the value of 65 is 1.5 standard deviations above the mean of the data set.
Z-scores are useful for comparing values across different data sets or for identifying extreme values in a data set. Values with high positive or negative z-scores are typically considered to be outliers, indicating that they are further from the mean than most other values in the data set.
In summary, the statement "z-score helps to determine how far a particular value is from the mean relative to the data set's standard deviation" is true. Z-scores are a statistical measure that help to express the distance between a particular value and the mean of a distribution in terms of the number of standard deviations that the value is from the mean.
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Pls help me solve from example 3 to 5 with steps I m really confused rn and there’s no one to explain me
The value of the exponents will be (x²)³ = x^6 and the value of 7² will be 49.
How to calculate the exponentThe exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
The value of (x²)³ will be:
= x^(2 × 3)
= x^6
The value of 7² will be:
7 × 7
= 49
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