Answer:
We should buy at least 19 bonds to have at least a 97% chance of getting 5 or more bonds that do not default.
Step-by-step explanation:
This problem can be solved using the binomial distribution, which can tell us the probability of getting a certain number of successes in a given number of trials, each with a certain probability of success. In this case, the trials are the bonds, the probability of success is 50% (the chance that a bond will not default), and we want to know how many bonds we need to buy to have at least a 97% chance of getting 5 or more successes.
Let X be the number of bonds that do not default. We want to find the smallest value of n (the total number of bonds we buy) such that P(X ≥ 5) ≥ 0.97.
Using the binomial distribution, we can calculate that the probability of getting exactly k successes out of n trials with a probability p of success is:
P(X = k) = (n choose k) * p^k * (1 - p)^(n-k)
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n without regard to order.
To find P(X ≥ 5), we can calculate the probabilities of getting 5, 6, 7, 8, 9, or 10 successes and add them up:
P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
We want this probability to be at least 0.97, so we can set up the following inequality:
P(X ≥ 5) ≥ 0.97
P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) ≥ 0.97
We can then use a spreadsheet or a binomial probability table to find the smallest value of n that satisfies this inequality. For example, using Excel's BINOM.DIST function, we can enter the following formula in a cell:
=BINOM.DIST(4,n,0.5,TRUE) + BINOM.DIST(5,n,0.5,TRUE) + BINOM.DIST(6,n,0.5,TRUE) + BINOM.DIST(7,n,0.5,TRUE) + BINOM.DIST(8,n,0.5,TRUE) + BINOM.DIST(9,n,0.5,TRUE) + BINOM.DIST(10,n,0.5,TRUE)
where n is the number of bonds we want to buy, and TRUE indicates that we want to calculate the cumulative distribution function (CDF) up to the given value of k.
We can then use Excel's Goal Seek tool to find the smallest value of n that makes this formula equal to 0.97. For example, if we set the target value to 0.97 and the "Set cell" to the formula cell, and we vary the "To value" of n, Goal Seek finds that the smallest value of n that satisfies the inequality is 19. Therefore, we should buy at least 19 bonds to have at least a 97% chance of getting 5 or more bonds that do not default.
Find all real x in each of the following
X=(-27)^-2/3
Answer:
Step-by-step explanation:
We can simplify the expression using the rules of exponents:
(-27)^(-2/3) = 1/(-27)^(2/3)
Now, we can use the fact that (-a)^(2/3) = (a^(2/3)) to simplify the expression further:
1/(-27)^(2/3) = 1/(3^3)^(2/3) = 1/3^(3*2/3) = 1/3^2 = 1/9
Therefore, x = 1/9.
prices for used stainless steel side trim for a 1957 chevrolet convertible are $350, $400, $500, $650, $725, $850, and $1700
A.Find the mean to the nearest dollar
B.Find the median
C.Find the four quartiles
D.Find the range(IQR=Q3-Q1)
E. Find the boundary for the lower outliers (Q1-1.5(IQR)).Are there any lower outliers?
F. Find the boundary for the upper outliers(Q3+1.5(IQR)).Are there any upper outliers?
Answer:
Step-by-step explanation:
here are step-by-step explanations for each part of the problem:
A. To find the mean, you add up all of the prices and divide by the number of prices. So:
Mean = (350 + 400 + 500 + 650 + 725 + 850 + 1700) / 7
Mean = 517.86
Rounded to the nearest dollar, the mean is $518.
B. To find the median, you need to put the prices in order from smallest to largest and then find the middle value. In this case, there are seven prices, so the middle value is between the 3rd and 4th prices:
350, 400, 500, 650, 725, 850, 1700
The median is the average of the 3rd and 4th prices, so:
Median = (500 + 650) / 2
Median = 575
The median price is $575.
C. Quartiles divide the data set into four equal parts, so you need to find the values that separate the lowest 25%, the next 25%, the next 25%, and the highest 25% of prices.
To find the quartiles, you can use the following steps:
Put the prices in order from smallest to largest:
350, 400, 500, 650, 725, 850, 1700
Find the median (Q2) as calculated in part B:
Median = $575
Divide the data set into two halves, below and above the median. If the median is included in both halves, exclude it from both.
Lower half: 350, 400, 500, 575
Upper half: 650, 725, 850, 1700
Find the median (Q1) of the lower half:
Q1 = (400 + 500) / 2
Q1 = 450
Find the median (Q3) of the upper half:
Q3 = (725 + 850) / 2
Q3 = 787.5
The four quartiles are Q1=$450, Q2=$575 (median), and Q3=$788.
D. The range is the difference between the highest and lowest values in the data set. So:
Range = highest value - lowest value
Range = $1700 - $350
Range = $1350
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). So:
IQR = Q3 - Q1
IQR = $788 - $450
IQR = $338
F. To find the upper boundary for outliers, you add 1.5 times the IQR to Q3. So:
Upper boundary = Q3 + 1.5(IQR)
Upper boundary = $788 + 1.5($338)
Upper boundary = $1282
There are no values above the upper boundary, so there are no upper outliers.
18. A jar contains marbles of different colors. The probability of drawing a red marble at random is 210 .
What is the probability, and the likelihood, that the marble drawn is not red?
The probability and the likelihood, that the marble drawn is not red is high which is 4/5.
What is probability?To determine how likely something is gonna occur, use probability. Several things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty.
It is stated that there is a 2/10 chance of drawing a red marble at random.
We can deduct the likelihood of drawing a red marble from one to determine the likelihood that the drawn marble is not red (since the probability of an event and its complement add up to 1).
So, the probability of drawing a marble that is not red is -
1 - 2/10 = 8/10 = 4/5
Therefore, the probability that the marble drawn is not red is 4/5.
The likelihood of an event is a measure of how plausible it is, given some evidence or knowledge.
In this case, we can say that the likelihood of drawing a marble that is not red is high, since there are more marbles in the jar that are not red than those that are red.
Therefore, the likelihood of drawing a marble that is not red is high.
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Which one is for table ?
Thats the only question im stuck on for this one
Please help me!
The organized list has the following outcomes:
H1 T1
H2 T2
H3 T3
H4 T4
H5 T5
H6 T6
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
Given:
Two events take place.
Let event A be flipping a coin
Let event B be rolling a 6-sided die.
Now, a coin has two faces; one is the head and the other is the tail.
So, the possible outcomes of event A are: {H, T}
H → Head, T → Tail.
Now, a six-sided die has six faces each marked with a number. The numbers marked ranges from 1 to 6.
So, the possible outcomes of event B are {1, 2, 3, 4, 5, 6}
Now, each element of set A should match all the elements of set B.
Now, the tabular form should have a row of outcomes of B and a column of outcomes of event A. Thus,
Outcomes 1 2 3 4 5 6
H H1 H2 H3 H4 H5 H6
T T1 T2 T3 T4 T5 T6
Therefore, the organized list has the following outcomes:
H1 T1
H2 T2
H3 T3
H4 T4
H5 T5
H6 T6
Finally, the correct tree diagram is attached below.
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Complete question:
simplify (6k +5)(5k +5)
Answer:
30k^2+55k+25
Step-by-step explanation:
30k^2+30k+25k+25
=30k^2+55k+25
[tex]30k { }^{2} + 30k + 25k + 25[/tex]
[tex]30k ^{2} + 55k + 25[/tex]
A projectile is fired into the air. The equation below can be used to determine h
, the height of the projectile in feet, after t
seconds.
h(t)=48t−16t2
Which statement best describes the domain of function h(t)
?
The domain of h ( t ) is [0, 3] because the projectile is in the air for 3 seconds.
The domain of h ( t ) is [16, 48] because the projectile can go 48 feet in the air for 16 seconds.
The domain of h ( t ) is [3, 36] because the projectile can go 3 feet in the air for 36 seconds.
The domain of h(t) is [0, 36] because the projectile is in the air for 36 seconds.
Any input number of t outside of the range [0, 3] would therefore be meaningless given the circumstances of the issue.
what is equation ?An equation in mathematics is a claim that two expressions are equivalent. Mathematical operations like addition, subtraction, multiplication, division, and exponentiation may be used. It typically includes one or more variables. A connection between two or more variables can be represented by an equation, and it can also be used to determine the value of an unknown variable. Finding the values of the factors that make the equation true is the first step in solving an equation.
given
The projectile is in the air for a maximum of three seconds, so the domain of h(t) is [0, 3], since the equation depicts the projectile's height in feet after t seconds.
Any input number of t outside of the range [0, 3] would therefore be meaningless given the circumstances of the issue.
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The demand equation for a certain item is p=14-x/1000 and the cost equation is c(x)=7000+4x. Find the marginal profit at a production level of 3000 and interpret the result.
Because the cost equation is c(x)=7000+4x, the marginal profit at a production level of 3000 is $9.4 per unit.
what is equation ?An equation in mathematics is a claim made regarding the equivalence of two expressions. It includes one or more variables (unknown values) and describes how those variables and/or constants relate to one another. For instance, the line on a coordinate plane denoted by the equation y = 3x + 5 has a y-coordinate that is equivalent to three times the x-coordinate plus five. Three and five are constants in this equation, while x and y are factors. Finding the value(s) of the dependent variables) that make the equation true is one way to answer an equation. In the example above, we can enter y = 11 into the equation .
given
We must first determine the revenue function, which is provided by, in order to determine the marginal profit at a production level of 3000:
14x - x/1000x = R(x) = xp(x) = 14x - x2/1000
where the demand function is given by p(x) = 14 - x/1000.
The benefit function is next, and it is provided by:
P(x) = R(x) - C(x) = (10x - x2/1000 - 7000) + (4x) = 14x - x2/1000
where the cost function, C(x), equals 7000 plus 4x.
We must take the derivative of the profit function with regard to x and evaluate it at x = 3000 in order to determine the marginal profit:
P'(3000) = 10 - 3/5 = 9.4
Because the cost equation is c(x)=7000+4x, the marginal profit at a production level of 3000 is $9.4 per unit.
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What value of x makes the equation 1+\sqrt{x-1=5} true?
The value of x is -1 and 3 for which x makes the equation.
What is factorization?
Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.
Here, we have
Given: 1 + (x-1)² = 5
We have to solve it for x and find the value of x.
1 + (x-1)² = 5
We solve this equation by factorization and we get
1 + x² - 2x + 1 = 5
x² - 2x + 2 -5 = 0
x² - 2x - 3 = 0
x² + x - 3x - 3 = 0
x(x+1) -3(x+1) = 0
(x+1)(x-3) = 0
x= -1, 3
Hence, the value of x is -1 and 3 for which x makes the equation.
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find the area that is NOT shaded
Answer:
376.8
Step-by-step explanation:
Area of circle: A = πr^2 = π12^2 = 144π
Area of shade: A = (θ/360º) x πr^2 = (60/360) x 144π = 24π
Area not shaded = 144π - 24π = 120π = 120(3.14) = 376.8
I need help please ?!!!??!
Answer: A
Step-by-step explanation:
8.5 inches long. If the actual length of the line is 9.1 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
By answering the above question, we may infer that The inaccuracy, equation when rounded to the closest tenth of a percent, is around 6.6%. The measurement's percent error is 6.6% as a result.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The following formula may be used to get the percent error:
percent error is calculated as follows: 100% divided by (actual value - measured value).
Whereas, "|" stands for absolute value.
In this instance, the measured measurement is 8.5 inches, whereas the real value is 9.1. Hence, by entering these values into the formula, we may obtain:
error = |(9.1 - 8.5) / 9.1| x 100% error = 6.59%
The inaccuracy, when rounded to the closest tenth of a percent, is around 6.6%. The measurement's percent error is 6.6% as a result.
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What is the value of w? W+3/4 =w-2/2
As a result, 7 is the number of w that solves the problem.
What do the denominators mean?In mathematics, a denominator is the lowest integer in a proportion that indicates how many equal portions are split into a whole. It is a fraction's division. In this case, the fraction is 4, so there are four components overall.
To solve for w in the equation (W+3)/4 = (W-2)/2, we can start by cross-multiplying to eliminate the denominators:
2(W+3) = 4(W-2)
Expanding the brackets:
2W + 6 = 4W - 8
Simplifying:
2W = 14
W = 7
Therefore, the value of w that satisfies the equation is 7.
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Given that the polynomial [tex]f(x)[/tex] has 9 turning points, which of the following most accurately describes the degree of [tex]f(x)[/tex]?
A. The degree of F(x) is at most 10.
B. The degree of F(x) is at most 8.
C. The degree of F(x) is at least 10.
D. The degree of F(x) is at most 9.
E. The degree of F(x) is at least 9.
F. The degree of F(x) is at least 8.
The correct option is - D. The degree of F(x) is at most 9, shows the largest number of turning points of polynomial function.
Explain about the polynomial functions?Several kinds of polynomial functions exist. They include linear, quadratic, cubic, among many other types.
The idea of turning points, or the points at which a graph shifts from increasing towards decreasing or vice versa, is also present.The quantity of turning points in every polynomial equation is always fewer than or equal to that same degree of the polynomial.The number of rotations is often one smaller than a polynomial's degree.A polynomial function with degree n is provided to us.
The largest number of turning points is what we're looking for.
The most turning points a polynomial function can have are:
n - 1
Thus, the degree of F(x) is at most 9.
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Graph the solution set.
3x - y < 9
2x + y 26
-20
Graph Lay
The solutions of x² - 2x - 4 = -3x + 9 are x = -4.14 and x = 3.14,
which is the x-coordinate of the intersection points of the graphs of y = x² - 2x - 4 and y = -3x + 9
What is quadratic equation?"It is a polynomial equation with degree two."
"The general form of quadratic equation is , where a, b, c are real numbers with a ≠ 0."
here, we have,
For given question,
We have been given an quadratic equation x² - 2x - 4 = -3x + 9
We simplify above quadratic equation.
=> x² - 2x - 4 = -3x + 9
solving we get,
=> x = -4.14 and x = 3.14
Consider the graphs for y = x² - 2x - 4 and y = -3x + 9 as shown below.
Therefore, the solutions of x² - 2x - 4 = -3x + 9 are x = -4.14 and x = 3.14,
which is the x-coordinates of the intersection points of the graphs of y = x² - 2x - 4 and y = -3x + 9
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use traces to sketch and identify the surface 25x²+4y²+z²=100
The surface formed by the equation 25x²+4y²+z²=100 is an ellipse.
What is an ellipse?In mathematics, an ellipse is a planar curve with two focus points, where the total of the two distances from any point on the curve to the focal points is a constant. It generalises the shape of a circle, a unique variety of ellipse in which the two focus points coincide. The eccentricity of an ellipse is used to calculate its length.
We may set one of the variables at a constant value and then plot the resulting 2D curve in the plane created by the other two variables in order to sketch the surface. This procedure can be repeated for various constant values to get a rough surface drawing.
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I need help please! Im not sure how to solve
3x^2 + 4x - 3 = ( 3x -2 ) (x + 2) + 1
What is Remainder Theorem ?
Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn't essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.
Given:- p(x) = 3x^2 + 4x - 3 and g(x) = 3x - 2
p(x) ÷ g(x)
3x^2 + 4x - 3 ÷ ( 3x - 2)
[tex]\frac{3x^2+4x-3}{3x-2} =(x+2 )+ \frac{1}{3x-2}[/tex]
Quotient = x + 2
Remainder = 1
Hence, 3x^2 + 4x - 3 = ( 3x -2 ) (x + 2) + 1
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Please Help me!
Which of the following inequalities would represent the graph shown?
Answer:
f(x)>[tex]\sqrt{1-x}[/tex]
Step-by-step explanation:
because it is above the x axis it is >
Because it is -x is moves to the right
because it is a dotted line and not solid it is >
The question is present in the image
The correct option for the given expression is [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, an expression, [tex]\sqrt[3]{24} \sqrt[4]{32}[/tex], we need to simplify it,
Factoring them,
24 = 2 x 2 x 2 x 3
32 = 2 x 2 x 2 x 2 x 2
Therefore,
[tex]\sqrt[3]{24} = 2\sqrt[3]{3}[/tex]
[tex]\sqrt[4]{32} = 2\sqrt[4]{2}[/tex]
[tex]\sqrt[3]{24} \sqrt[4]{32}[/tex] = [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]
Hence, the correct option for the given expression is [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]
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Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
The coordinates of the fourth vertex are (0, -4).
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Substituting the given parameters into the midpoint of a line segment formula, the midpoint of the diagonal is given by;
Midpoint = [(3 - 6)/2, (6 - 6)/2]
Midpoint = [-3/2, 0/2]
Midpoint = (-1.5, 0).
For the fourth vertex, we have:
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
(-1.5, 0) = [(-3 + x₂)/2, (4 + y₂)/2]
-3 + x₂ = 2(-1.5)
x₂ = -3 + 3
x₂ = 0.
4 + y₂ = 0
y₂ = -4.
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Simplify expression 6+(-4)(2-3)^2=
Step-by-step explanation:
=6+(-4)(2-3)²
=6+(-4)(-1)²
=6-4×1
=2
Please help with this thank you
The slope of the linear function is given as follows:
3/2.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.
The slope represents the rate of change of a linear function, meaning that it is calculated as the change in y divided by the change in x.
Considering points (-4,-4) and (-2, -1), we have that when x increases by 2, y increases by 3, hence the slope is given as follows:
m = 3/2.
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estion
The graph shows the quadratic function f, and the table shows the quadratic
function g.
-4 -2
f(x)
44
2
2
4
➜
2
4
x
x
-5 -4 -3 -2 -1
g(x) 10 7 6 7
6 7 10 15 22
0 1
Answer:
look in the comments and have a good day
29 cents using 5 coins
Answer:
20 + 5 + 2 and two 1 cents will make 29 Euro cents.
20 + 5 + 2 and two 1 cents will make 29 Euro cents.
20 + 5 + 2 and two 1 cents will make 29 Euro cents.
20 + 5 + 2 and two 1 cents will make 29 Euro c
Step-by-step explanation:
Answer: A quarter and 4 pennies
Step-by-step explanation:
25+4=29
The equation c = 2b + 6 represents the total cost c of b sets of beads and one necklace string. Graph the relationship on the coordinate plane.
To show how c and b are related, we can draw a line through these points. A positive sloped straight line should appear on the graph.
What equation describes the graph?Identifying the slope and y-intercept is necessary before putting the equation in y-intercept (y=mx+b) form and figuring out the equation of a graphed line. The slope is the y-to-x change ratio.
Plotting points on the coordinate plane with values for b and calculating the appropriate values for c is necessary to graph the equation c = 2b + 6.
Let's pick some b values and determine the matching c values:
c = 2(0) + 6 = 6 when b = 0.
If b = 1, then c = 2(1) + 6 = 8.
c = 2(2) + 6 = 10 when b = 2
These points can be used to plot the graph:
Set the scene (0, 6)
Set the scene (1, 8)
Set the scene (2, 10)
Now we may illustrate the relationship between c and b by drawing a line across these locations. A positive sloped straight line should appear on the graph.
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A business sets up a sinking fund so they will have a $61,000.00 to pay for a replacement piece of equipment in 9 years when the current equipment will be sold for scrap. If they make deposits at the end of every 2 months for 9 years in the investment that pays 5.9% compounded every 2 months, what size should each payment be?
The every 2 months payments are $
.
The size of each payment for the sinking fund must be $1586.87.
What is sinking fund?A sinking fund is a collection of funds that have been put up or saved to pay off bonds or debts. A corporation that issues debt will eventually have to pay that loan back, and the sinking fund lessens the burden of a significant outflow of revenue. The corporation creates a sinking fund so that it may make contributions to it in the years before the bond matures.
The sinking fund formula is given as:
A = P * ((1 + r/n)ⁿˣ - 1) / (r/n)
61000 = P * ((1 + 0.009833/6)⁽⁶⁽⁹⁾ ⁻ ¹⁾/ (0.009833/6)
61000 = P * 38.4647
P = 1586.87
Hence, the size of each payment for the sinking fund must be $1586.87.
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Look at the stem-and-leaf plot of scores on a science test. Stem 6 7 8 9 10 Leaf 4,7 0, 0, 0, 3, 6, 9, 9 2, 2, 5, 8 1, 4, 4, 7, 7 0, 0, 0, 0 Key 6 4 = 64 How many students scored more than 70 but less than 80?
The number of students who scored more than 70 but less than 80 is zero.
What is the stem-and-leaf diagram?A stem-and-leaf diagram is a quantitative analysis of a collection of data points that are separated into a "stem" (the first digit of the number) and a "leaf" (the remainder of the number) (the last digit of the number).
To find the number of students who scored more than 70 but less than 80, we need to look at the stem-and-leaf plot and count the number of leaves that fall within this range.
Stem 7 has a leaf of 6, which represents a score of 76. Therefore, at least one student scored between 70 and 76.
The stem 8 has leaves of 2, 5, and 8, which represent scores of 82, 85, and 88, respectively. Therefore, no students scored between 76 and 80.
Therefore, the number of students who scored more than 70 but less than 80 is zero.
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Josslyn's workout consists of swimming and practicing yoga. While swimming she burns 7 calories per minute, and while practicing yoga she burns 5 calories per minute. Josslyn wants to burn at least 500 calories each day.
Let x be the number of minutes she spend swimming and let y be the number of minutes she spends practicing yoga. Write an inequality that models this situation.
Answer:
Step-by-step explanation:
Josslyn burns 7 calories per minute while swimming and 5 calories per minute while practicing yoga. Let x be the number of minutes she spends swimming and y be the number of minutes she spends practicing yoga.
The total number of calories burned, C, is given by:
C = 7x + 5y
To burn at least 500 calories each day, we can write the inequality:
7x + 5y ≥ 500
This inequality states that the total number of calories burned from swimming and practicing yoga, 7x + 5y, must be greater than or equal to 500. Josslyn can achieve this goal by spending a combination of x minutes swimming and y minutes practicing yoga.
1. 10¹ =
please someone tell me the answer.
Answer: 10
Step-by-step explanation: any number to the first power is the number being multiplied
Answer: 10
Step-by-step explanation: Any number to the first power equals the same number, for example: 4 to the first power is 4, or in this case 10 to the first power = 10.
Which of the following expressions is equivalent to 2 to the power of 3x − 4?
the quantity 1 to the power of x end quantity over 8
the quantity 3 to the power of x end quantity over 4
the quantity 6 to the power of x end quantity over 8
the quantity 8 to the power of x end quantity over 16
The quantity 8 to the power of x end quantity over 16
What is equivalent expression?
In mathematics, two expressions are said to be equivalent if they have the same value for all possible values of the variables involved. In other words, equivalent expressions represent the same mathematical object or concept, but they may be expressed in different forms or notations.
Equivalent expressions are expressions that have the same value for all possible values of the variables involved, and they can be used to simplify or manipulate algebraic expressions.
Then we have;
8^x/16
= 2^3(x)/2^4
Then we use the laws of exponents;
2^3x - 4
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Write a verbal sentence to represent 5n/n+3=n-8
For this equation our term is root of -24
What is verbal sentence ?
Verbal sentences consist of a verb + subject + object or adverbial phrase. The subject and object can be either nouns or pronouns.
After solving the equation we get square of n which is equal to three times of eight
If the subject is a pronoun, it is always a suffix; and if the object is pronoun, it is always a dependent pronoun. When the subject is a pronoun, the word order is normal, meaning that the subject follows the verb and precedes the object.
If the subject is a noun and the object is a dependent pronoun, the pronoun object is before the noun subject.
The dative has a special place in the word-order of verbal sentences. It is expressed by the preposition n in addition to a noun or pronoun referring to a person, if the subject is a pronoun. It assumes a third place following the verb and its subject. However, if the subject is a noun, the dative is allocated a forward position and occurs before the subject.
If the subject is a noun and the object is a pronoun and the sentence consists of a dative, the word order is thus:
Verb + dative + dependent pronoun (object) + subject
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