The value of a 10% stake is given as $88.
The formula for the Gordon growth model is:
Stock Price = Dividend / (Required Yield - Growth Rate)
Substituting the given values gives:
Stock price = 1.76 / (0.10 - 0.08) = 1.76 / 0.02 = $88
What are Stocks
Stocks are documents that prove that someone owns a share of the capital of a company. A person who owns shares has the right to some of the company's assets. For example, if a company issues 1000 shares of stock and a person owns 200 shares in that company, that person actually owns 20% of the assets in that company. Majority shareholders will have control rights over a company.
Shareholders also have the right to receive dividends according to the number of shares they own. The acquisition of these dividends usually depends on the profits of the company and has been regulated in accordance with the company's articles of association.
Issuing shares is one way for companies to get fresh funds or capital for long-term business development. Shares themselves can be traded through the Stock Exchange at prices that change according to company conditions and economic conditions.
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find two positive numbers that satisfy the given requirements. the second number is the reciprocal of the first number and the sum is a minimum
The two positive numbers are 1 and 1, depending on the given information.
Let first number be x. So, the second number is 1/x. Now, their sum is minimum, so representing the expression for given information -
Sum (x) = x + 1/x
Rewriting the expression -
Sum (x) = x + [tex] {x}^{-1} [/tex]
Finding the derivative
Sum' (x) = 1 + (-1) [tex] {x}^{-2} [/tex]
Sum' (x) = 1 + (-1)/[tex] {x}^{-1} [/tex]
Sum' (x) = (x² - 1)/x²
Now, to find the minimum -
x² - 1/x² = 0
Multiplying x² on Right Hand Side of the equation
x² - 1 = 0
Rewriting the equation
x = ± 1
As the numbers are positive, so x will be 1.
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Which of the following is equivalent to the rational expression below, where x≠1
?
The equivalent expression is x + 3 + 4/(x - 1)
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(x² + 2x + 1) / (x - 1)
Now,
x² + 2x + 1
= x² + (1 + 1)x + 1
= x² + x + x + 1
= x(x + 1) + 1(x + 1)
= (x + 1)(x + 1)
= (x + 1)²
Now,
(x² + 2x + 1) / (x - 1)
= (x + 1)² / (x - 1)
Now,
x + 3 + 4/(x - 1)
((x - 1)x + 3(x - 1) + 4) / (x - 1)
= (x² - x + 3x - 3 + 4) / (x - 1)
= (x² + 2x + 1) / (x - 1)
Thus,
x + 3 + 4/(x - 1) is the equivalent expression.
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What is the value today of $6,500 that is due in 414
years if the interest rate is 3.96% compounded semi-annually?
Answer:
approximately $4,609,968.67
Step-by-step explanation:
To calculate the future value of a lump sum after compounding over a certain number of years with a specific interest rate, you can use the formula:
FV = PV * (1 + r/n)^(nt)
Where:
FV is the future value
PV is the present value (6500)
r is the annual interest rate (3.96%)
n is the number of times compounded per year (semi-annually, so 2)
t is the number of years (414)
Plugging in the values, you get:
FV = 6500 * (1 + 0.0396 / 2)^(2 * 414)
The future value of $6,500 in 414 years at an interest rate of 3.96% compounded semi-annually is approximately $4,609,968.67.
pls help will mark brainliest asap
The transformed vertices of the ΔABC will be A'(- 2, 0), B'(2, 3)
and C'(0, - 1).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
The given triangle has vertices A(0, 4), B(6, - 4) and C(- 2, 0).
We know a rotation of 90° counterclockwise transforms (x, y) to (- y, x)
and a dilation factor of (1/2) would make it (- y/2, x/2).
Therefore, The vertices of the triangle A'B'C' will be,
A'(- 4/2, 0/2), B'(-(-4)/2, 6/2) and C'(0/2, - 2/2).
A'(- 2, 0), B'(2, 3) and C'(0, - 1).
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What is the value today of $5,100 per year, at a discount rate of 7.9%, if the first payment is received 6 years from today and the last payment is received 20 years from today?
The present value of the cash flows is $30,030.78.
What is the present value?In order to determine the value today of the series of payments, the present value has to be determined. Present value is the sum of the discounted cash flows.
Present value = 5,100 / (1.079)^6 + 5,100 / (1.079)^7 + 5,100 / (1.079)^8 + 5,100 / (1.079)^9 + 5,100 / (1.079)^10 + 5,100 / (1.079)^11 + 5,100 / (1.079)^12 + 5,100 / (1.079)^13 + 5,100 / (1.079)^14 + 5,100 / (1.079)^15 + 5,100 / (1.079)^16+ 5,100 / (1.079)^17 + 5,100 / (1.079)^18 + + 5,100 / (1.079)^19 + + 5,100 / (1.079)^20 = $30,030.78
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i need help with percentage homework
The percentage values are as follows: 75, 135, 60, 50, 245, 105, 175, 315, 450, 60, 125, 140, 280, 150, 320, 150.
What is percent?A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.
Here,
1a. 150% of 50
=1.5*50
=75
1b. 150% of 90
=1.5*90
=135
2a. 100% of 60
=1*60
=60
2b. 50% of 100
=0.5*100
=50
3a. 350% of 70
=3.5*70
=245
3b. 150% of 70
=1.5*70
=105
4a. 350% of 50
=3.5*50
=175
4b. 350% of 90
=3.5*90
=315
5a. 450% of 100
=4.5*100
=450
5b. 200% of 30
=2*30
=60
6a. 250% of 50
=2.5*50
=125
6b. 350% of 40
=3.5*40
=140
7a. 350% of 80
=3.5*80
=280
7b. 150% of 100
=1.5*100
=150
8a. 400% of 80
=4*80
=320
8b. 300% of 50
=3*50
=150
The value of percent are: 75, 135, 60, 50, 245, 105, 175, 315, 450, 60, 125, 140, 280, 150, 320, 150.
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Prove the following vector identities which, among other ideas, extend the chain rule to vector operations. Use index notation. a(x), b(x)-vector functions of position x; ф(x) - scalar function of position NOTE: Begin with the expression on the left and derive the expression on the right. Try not to simply expand both sides and show that they are identical (iii) V - (V xa)-0 (vii) V ab (V aba (Vb)
Vector identities can be derived using index notation. The following vector identities are to be proved: (iii) V - (V xa) = 0, (vii) V ab = (V a)b + a(V b).
Starting with the left-hand side:
V - (V x a) = V + (a x V) (by definition of cross product)
Using the vector triple product, a x (b x c) = (a . c) b - (a . b) c, we get:
V + (a x V) = V + (V . a) a - (V . a) a
= V (since the second term cancels out with the first term)
Thus, V - (V x a) = 0.
(vii) V ab = (V x (b x a))
Starting with the left-hand side:
V ab = V (ab)
Using the scalar triple product, a . (b x c) = (a x b) . c, we get:
V (ab) = (V x b) . (a x a)
= (V x (b x a)) (since a x a = 0)
Thus, V ab = (V x (b x a)).
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Use finite differences to identify the degree of the polynomial that best describes the data.
quintic
quadratic
cubic
quartic
The degree of the polynomial that best describes the data is (c) cubic
How to determine the degree of the polynomial that best describes the data.From the question, we have the following parameters that can be used in our computation:
See attachment
Find the first dfference D1 between the consecutive y-values
D1: 10 28.4 56.4 94
Calculate the second difference
D1: 18.4 28 37.6
Calculate the third difference
D3: 9.6 9.6
The third difference are equal
Hence, the degree is (c) cubic
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_ /12 > 11/12 what is the missing ?
Answer: 12
Step-by-step explanation:
12/12 is greater than 11/12
12/12>11/12
Which of the following is NOT a characteristic of both surveys and experiments?
Data collected about a population is not characteristic of both surveys and experiments. The correct answer would be an option (C).
What is a survey?The purpose of a survey is to understand populations as a whole by utilizing pertinent questions to collect data from a sample of people.
Data collected about a population is not a characteristic of both survey and experiment because, in an experiment, the researcher typically manipulates one or more variables and measures the effect on another variable, while in a survey, the researcher usually only measures variables and does not manipulate them. As a result, in a survey, the data is typically collected about a sample of the population, rather than the entire population.
Hence, the correct answer would be option (C).
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fill in the blank. because it is typically too expensive and too time consuming, researchers often select a/n___, a group of people that are representative of the larger population.
Because it is typically too expensive and too time consuming, researchers often select a sample, a group of people that are representative of the larger population.
A sample is a smaller group of individuals selected from a larger population for the purpose of studying and making inferences about the population. Sampling is used when studying the entire population is not feasible due to limitations in time, resources, or practicality. The goal is to select a sample that accurately represents the population in terms of key characteristics such as age, gender, education level, etc. The sample must be representative of the population, meaning that it should accurately reflect the characteristics of the population. This is important because any biases or inaccuracies in the sample can lead to incorrect inferences about the population. A well-selected sample should also have a large enough size to provide meaningful results, yet not be so large that it becomes difficult to manage or too expensive to study.
In conclusion, sampling is a crucial step in research because it enables researchers to study a portion of the population, rather than the entire population, in order to make inferences about the larger group.
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a certain statistic will be used as an unbiased estimator of a parameter. let j represent the sampling distribution of the estimator for samples of size 40, and let k represent the sampling distribution of the estimator for samples of size 100. which of the following must be true about j and k ?
The correct statement can identify by using a certain limit theorem.
The correct option is (c).
The sample size of J is 40.
The sample size of K is 100.
As per the central limit theorem, if the population with mean and standard deviation takes a large random sample from the population with replacement, then the distribution of the sample means will be approximately distributed.
Now from the definition of the central limit theorem, both J and K will the same means.
Write the expression for standard deviation.
[tex]s = \frac{\alpha }{\sqrt{n} }[/tex]
From the above expression, the standard deviation is inversely proportional to the sample size.
Thus, the correct statement is the expected values of J and K will be equal, and the variability of J will be greater than the variability of K.
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The complete question is:
A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.
Which of the following must be true about J and K?
a. The expected values of J and K will be equal, and the variability of J will be less than the variability of K.
b. The expected values of J and K will be equal, and the variability of J will be equal to the variability of K.
c. The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.
d. The expected value of J will be greater than the expected value of K, and the variability of R will be greater than the variability of K.
e. The expected value of J will be greater than the expected value of K, and the variability of R will be less than the variability of K.
Consider the following balls-and-bin game. We start with one black ball and one white ball in a bin. We repeatedly do the following: choose one ball from the bin uniformly at random, and then put the ball back in the bin with another ball of the same color. We repeat until there are n balls in the bin. Show that the number of white balls is equally likely to be any number between 1 and n − 1.
The number of white balls is equally likely to be any number between 1 and n−1.
Let W be the number of white balls in the bin after the nth iteration. W can be any number between 1 and n−1. We can calculate the probability of obtaining a specific number of white balls in the bin by considering the number of possible sequences of choices. There are 2^n possible sequences of choices as each choice is either a white ball or a black ball. The number of sequences in which W white balls are selected is (W choose 1)*(n−W choose 1), which is equal to W*(n−W). Therefore, the probability of W white balls in the bin after the nth iteration is P(W) = (W*(n−W))/(2^n).
Since P(W) is equal for all values of W between 1 and n−1, it follows that the number of white balls is equally likely to be any number between 1 and n−1.
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In preparation for the upcoming school year, a teacher looks at raw test scores on the statewide standardized test for the students in her class. Instead of looking at the scores relative to the norms in the state, the teacher wants to understand the scores relative to the students who will be in the class. To do so, she decides to convert the test scores into z-scores relative to the mean and standard deviation of the students in the class. The mean test score in her upcoming class is 202, and the standard deviation is 38.2. The following are the scores for some (not all) of her students. Complete the table using the dropdown menus. The teacher wants to identify those students who may need extra challenge or extra help. As a first cut, she decides to look at students who have z-scores above z = 2.00 or below z = -2.00. Identify the test score corresponding to each of the following z-scores. Round to the nearest whole number. For z = 2.00, test score = .For z - -2.00, test score = .
Z-scores are used to standardize a raw score by converting it into the number of standard deviations it is above or below the mean.
The formula to convert a raw score into a z-score is:
z = (X - Mean) / Standard Deviation
Where X is the raw score, Mean is the mean of the population, and Standard Deviation is the standard deviation of the population.
For z = 2.00:
z = (X - Mean) / Standard Deviation
X = (z * Standard Deviation) + Mean
X = (2.00 * 38.2) + 202 = 238.4 + 202 = 440.4 (rounded to nearest whole number = 440)
For z = -2.00:
z = (X - Mean) / Standard Deviation
X = (z * Standard Deviation) + Mean
X = (-2.00 * 38.2) + 202 = -76.4 + 202 = 125.6 (rounded to nearest whole number = 126)
So for z = 2.00, the corresponding test score is 440, and for z = -2.00, the corresponding test score is 126.
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if x = 3 when y = 6, what is y when x = -2
Answer:
If y=6 when x=3 find y when x =-33.
Step-by-step explanation:
A painting contractor determined the average amount of time needed to paint a house. When 2 painters are used, it takes 15 hours to paint • When 6 painters are used, it takes 5 hours to paint. If p represents the number of painters and h represent the number of hours required to paint the house, which statement is true about this relationship?
The statement that is true about the proportional relationship is that; The time required to paint a house varies directly with the number of painters.
How to find proportional Relationship?The parameters are;
p represents the number of painters.
h represent the number of hours required to paint the house
In this case, the number of hours will be the output variable while the number of painters will be the input variable. Thus, we will have the relationship;
h = kp
where k is the constant of proportionality
When 2 painters are used, it takes 15 hours to paint and as such;
k = 15/2
k = 7.5 hours per painter
When 6 painters are used, it takes 5 hours to paint. Thus;
k = 5/6
k = 0.833 hours per painter
Thus, we can say that the time required to paint a house varies directly with the number of painters.
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suppose x has a geometric distribution with probability 0.3 of success and 0.7 of failure on each observation. the probability that x is 4 is
the probability that x is 4 is given by the formula P(x) = [tex](1 - p)^(x-1) * p[/tex]
The formula for the probability of a geometric distribution is [tex]P(x) = (1 - p)^(x-1) * p[/tex]
Given the probability of success (p) is 0.3, the probability of x being 4 would be:[tex]P(x) = (1 - 0.3)^(4-1) * 0.3[/tex]
P(x) = 0.0729 or 7.29%
The geometric distribution is a probability distribution for the number of failures before the first success in a series of independent trials.
In this problem, the probability of success (p) is 0.3 and the probability of failure (1-p) is 0.7.
Therefore, the probability that x is 4 is given by the formula [tex]P(x) = (1 - p)^(x-1) * p[/tex]
Plugging in the values of p and x, we get:
[tex]P(x) = (1 - 0.3)^(4-1) * 0.3[/tex]
This simplifies to
P(x) = 0.0729 or 7.29%
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the following items are found around the house. they have weight. select the items that are most likely to be measured in ounces. paper bag frying pan can of pop table
The items that are most likely to be measured in ounces are a Paper bag, a can of pop, and a table.
The weight of objects is typically measured in units of mass, such as grams or kilograms, or in units of weight, such as ounces or pounds. In general, smaller and lighter objects are measured in ounces, while heavier objects are measured in pounds or kilograms.
In this case, the paper bag, can of pop, and table are likely to be measured in ounces. These objects are relatively light and can be easily lifted and weighed on a scale, which would make it convenient to use ounces as a unit of measurement. On the other hand, a frying pan is likely to be a heavier object and would typically be measured in pounds or kilograms.
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Pretest: Unit 2
Question 3 of 20
Determine the number of solutions for the equation shown below.
4x+6=4x+6
A. 2
B. 0
C. Infinitely many
D. 1
SUBMIT
Answer:
infinitely many
Step-by-step explanation:
this equation is true for each and every value.
so its solutions are infinite
RECT is a square (not drawn to scale). RA = 13^2 -3x-3 inches and AC = x(x+2).
A. Find the length of ET to the nearest tenth
B. Find the length of RT to the nearest tenth
The length of ET and the length of RT to the nearest tenth will be 268.3 units and 198.7 units, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
RECT is a square (not drawn to scale).
RA = 13² - 3x - 3
AC = x(x + 2)
The diagonals of the square will be RC and ET. And "A" is the intersection point. Then the equation is given as,
RA = AC
13² - 3x - 3 = x(x + 2)
169 - 3x - 3 = x² + 2x
x² + 5x - 166 = 0
x = [- 5 ± √(5² - 4 × 1 × (-166))] / (2 × 1)
x = 10.62, -15.62
Then the length of AC is given as,
AC = 10.62 (10.62 + 2)
AC = 134.13 units
The diagonals of the square are congruent. Then we have
ET = RC
ET = 2 AC
ET = 2 x 134.13
ET = 268.3 units
Then the length RT is given as,
RT = ET / √2
RT = 198.7 units
The length of ET and the length of RT to the nearest tenth will be 268.3 units and 198.7 units, respectively.
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Given the rate per compounding period, find r, the annual rate.
0.425% per month
Answer:
Step-by-step explanation:
To find the annual rate given the rate per compounding period, we need to convert the rate from the compounding period to the annual period. In this case, the rate is given as 0.425% per month.
One way to convert the rate is to multiply it by the number of compounding periods in a year:
r = 0.425%/month * 12 months/year
r = 5.1%/year
Therefore, the annual rate, r, is 5.1%.
what is The equation of The line
Answer:
y = (2/3)x + 10
Step-by-step explanation:
To find the equation of the line in slope-intercept form, y=mx+b, we need to know the slope and the y-intercept. The slope, or m, is rise over run. To find slope, we need to look at 2 points. For this question, I will be using the points (0,10) and (30,30). The rise, or change in y value, is 20, while the run, or change in x value, is 30. This means our rise over run in 20/30, or 2/3. Now that we have established the slope, or m, let's find the y-intercept, or b. To do this, you just need to look at where the line passes through the y-axis. In the image, you can see the line passes through the y-axis as x=10, making our y-intercept, or b, 10. Using this information, we can now find the equation of the line:
y = mx + b
m = slope, 2/3
b = y-intercept, 10
y = (2/3)x + 10
So, the equation of the line is y = (2/3)x + 10
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Solve the problem below. Be sure to show all calculations. Explanations given to justify your solutions must be given in complete sentences.
Given the figure to the right and the fact that m∠ABD= 133°, find the measurements of the angles below.
m∠ABC=___ m∠BCD=___ m∠ACB=___
The angle measures for this problem are given as follows:
m∠ABC = 112º.m∠BCD = 34º.m∠ACB = 34º.How to obtain the angle measures?ADC is an isosceles triangle, with an angle of 44º, hence the base angles have the measure given as follows:
2x + 44 = 180. (sum of the internal angles of a triangle).
2x = 136
x = 136/2
x = 68º.
Hence the measure of angles ACB and BCD is of 34º, as the bisection divides the angle into two angles of equal length.
Considering the two base angles of 34º, the measure of angle ABC is given as follows:
m < ABC + 2 x 34 = 180
m < ABC = 112º.
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HELP ASAPPPPPPPPPPP DUE IN TWO HOUR
The graph shows a function of the form f(x) = ab^x.
Use the drop-down menus to complete the statements about the function, and then write an equation that represents this function.
The function shown in the graph must be the function f(x)=2×4ˣ
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: f(x)=abˣ and when x is equal to 0 then f(0)=2
also if x increases by the functions gets multiplied by 4
Thus if f(0)=2 then f(1)= 8 , f(2)=32
or the function can be rewritten as f(x)=2×4ˣ
Thus f(0)=2×4⁰
=2
f(1)=2×4¹
Hence, The function shown in the graph must be the function f(x)=2×4ˣ
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u can get brainliest just help me out asap
Which of the following results in the expression 0.86 x 22
0.22 of 86%
22% of 0.86
86% of 22
0.86 of 22%
86% of 22 is the correct answer
} problem 9. (10 pts) determine which of the following subsets of r 3 are subspaces of r 3 . you should use the subspace test from the lectures to show that a given subset is a subspace, or, if it is not a subspace, exhibit one of the axioms of a vector space that fails to be satisfied. (a) a
Options C and D are subsets of R³, which are {(-5x,4x,3x)| x arbitary} and {(x,y,z)| x+y+x=0}
A) Correct. We have to check whether the potential subspace containing the zero vector is a great place to start on these sorts of problems. No zero vector so this is not a subspace.
B) This is a subspace. The set of solutions of a homogeneous linear system is always a subspace it is known as a "null space" of some corresponding linear transformation.
Let, [tex]M=\left[\begin{array}{ccc}2&9&0\\8&0&-5\\\end{array}\right][/tex] then the set in B) is just Null(M). Again, Nullspaces are always subspaces.
Alternatively, you could solve the corresponding system Mx=0 and find the elements of that set [tex]x=\left[\begin{array}{c}5/8&-5/36&1\\\\\end{array}\right][/tex] for any choice of z∈R. So this
can be a set in the span of [tex]x=\left[\begin{array}{c}5/8&-5/36&1\\\\\end{array}\right][/tex]
C) Correct. we can see a subspace because the elements are just multiples of (−5,3,4) and again spans are subspaces.
D) Correct. This can be a subspace for the same reasons as part B.
E) Correct. Not a subspace. An easier counter-example: (1,1,1) is in there. But (−1)(1,1,1)=(−1,−1,−1) is not.
F) Not a subspace. (0,0,0) is not in there.
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Plot the following inequality on the number line. −2
The number line of x <-2 is added below
How to plot the inequality on a number lineFrom the question, we have the following parameters that can be used in our computation:
x < -2
For the inequality x < -2:
All real numbers that are less than -2 satisfy the inequality.
So, we can represent the solution set of the inequality using the interval (-∞, -2)
When represented on a number line, we have:
-∞ -3 -2 -1 0 1 2 ∞
--------------------------------------------------------------------------
. <- o . . . . .
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Simplify
6 (2x^2-5)=
x= -3
The value of the expression for x=-3 is 78.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 6(2x²-5).
Here, x=-3
Substitute x=-3 in the expression 6(2x²-5), we get
6(2(-3)²-5)
= 6(18-5)
= 78
Therefore, the value of the expression is 78.
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A rectangular prism has a base of 19 ft by 8 ft and a diagonal of 25 ft. Identify its height. Round to the nearest tenth.
Answer:
14.1
Step-by-step explanation:
To find the height of the rectangular prism, use the formula for the length of a diagonal of a right rectangular prism.
d=l2+w2+h2−−−−−−−−−−√
Substitute 8 for l, 19 for w, and 25 for d
Then solve for h
25=82+192+h2−−−−√
Simplify.
25=64+361+h2−−−−√
Square both sides.
625=425+h2
Subtract 425 from both sides.
200=h2
Take the positive square root of both sides.
200−−−√=h
Round to the nearest tenth.
14.1≈h
Therefore, the height of the rectangular prism is about 14.1ft
Click on all the values that are equivalent to
-(2/3).
A.-2/-3
B.2/-3
C.-2/3
D.-3/-2
E.-3/2
F.3/-2
Answer:
-2/-3
Step-by-step explanation: Because -2/-3=2/3.