TRUE/FALSE. albert deposits $3250 in an account that earns 4.3% interest compounded quarterly. this function models the amount in the account after t years. a =
The given function models the amount in the account after t years is true.
What is compounded quarterly?
The process of calculating the interest earned quarterly on a fixed deposit or investment, computed based on the principal amount plus the interest earned for previous periods, is known as quarterly compounding.
Given:
Albert deposits $3250 in an account that earns 4.3% interest compounded quarterly.
P = $3250
r = 4.3% = 0.043
n = 4
t = t years
So, the function models the amount in the account after t years is,
[tex]A = P(1+\frac{r}{n})^n^t\\ A = 3250(1+\frac{0.043}{4})^4^t[/tex]
This equation is same as the given equation.
Hence, the given function models the amount in the account after t years is true.
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Complete question:
Complete question is attached below.
calculate the (estimated) standard error for the sample mean in this question. round to 3 decimal places (example: 0.123)
Given the following sample of three data points: 3, 6, 9, calculate the (estimated) standard error for the sample mean. Round to 3 decimal places.
s = √((3 - 8)² + (6 - 8)² + (9 - 8)²) / (3 - 1) = 4
2. Calculate the standard error of the sample mean:
SE = s / √n = 4 / √3 = 2.45
3. Round the standard error to three decimal places:
SE = 0.567
The standard error of the sample mean can be calculated by first finding the standard deviation of the sample (s). This is done by taking the sum of the squared differences between each data point and the mean, divided by the number of data points minus one. In this case, the standard deviation is 4. The standard error is then calculated by dividing the standard deviation by the square root of the number of data points, which is 3. The result is 2.45, which can be rounded to 0.567.
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When attempting to do his homework Mark incorrectly uses the addition property of equality below which statement would correct Mark's error?
The addition property of equality states that if two values are equal to a third value, then they are also equal to each other. In this case, 4 is equal to 5+2, so 4 must also be equal to 2+5. However, Mark wrote the equation incorrectly, so the correct statement would be 4 = 5 + 2.
Mark incorrectly uses the addition property of equality, below which statement would correct Mark's error?Mark's statement: 4 = 2 + 5Correct statement: 4 = 5 + 2The addition property of equality is a key concept in mathematics, and it is important to understand and use it correctly. In this case, 4 is equal to 5+2, so the correct statement would be 4 = 5 + 2. This is because the addition property of equality states that if two values are equal to a third value, then they are also equal to each other. Therefore, Mark's statement of 4 = 2 + 5 was incorrect, and the correct statement was 4 = 5 + 2. Understanding and applying the addition property of equality is essential for success in math.
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state university uses thousands of fluorescent light bulbs each year. the brand of bulb it currently uses has a mean life of 1000 hours. a competitor claims that its bulbs, which cost the same as the brand the university currently uses, have a mean life of more than 1000 hours. the university has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the .05 significance level. suppose 64 bulbs were tested with the following results: conduct the test using
Therefore, the solution to the question is T = 2.5 is the test statistic and the manufacturer's claim is supported by the data at the.05 significance level, according to the test's p-value of 0.007 <0.05.
What is test statistics?In statistical hypothesis testing, a test statistic is a statistic that is employed. A hypothesis test is often defined in terms of a test statistic, which is a numerical summary of a data set that can be used to execute the test and reduces the data to one value.
Here,
The test's p-value was 0.007 0.05, indicating that the evidence at the.05 level of significance supports the manufacturer's claim.
1000 hours on average. See if there is more.
We examine the null hypothesis, that is, whether the mean is 1000 hours, by asking:
[tex]H_{0}[/tex]: u=1000
If the mean is greater than1000 hours, we test the alternative hypothesis, which is:
[tex]H_{A}[/tex] : u > 1000
Test statistics:
t= [tex]\frac{X-u}{\frac{S_{d} }{\sqrt{n} } }[/tex]
t= [tex]\frac{X-u}{\frac{S_{d} }{\sqrt{n} } }[/tex]
t=[tex]\frac{1025-1000}{\frac{310 }{\sqrt{1000} } }[/tex]
t=25/9.80
t≈2.5
The test statistic is t = 2.5
P-value for the test and judgment
The right-tailed test's p-value, which has t = 2.5 and 100 - 1 = 99 degrees of freedom, measures the likelihood that a sample mean will be higher than 1025 hours.
This p-value is 0.007 according to a t-distribution calculator.
The manufacturer's claim is supported by the data at the.05 significance level, according to the test's p-value of 0.007 <0.05.
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What ratio, a:b, is represented in the table?
a b
1.5 2.5
51 85
99 165
Answers
A 4:54:5
B 2:32:3
C 3:5
The ratio a : b represented in the table of values is (c) 3 : 5
How to determine the ratio a : b represented in the table of values?From the question, we have the following table of values that can be used in our computation:
a b
1.5 2.5
51 85
99 165
Remove the last two entries in the table
So, we have the following representation
a b
1.5 2.5
Express the remaining entries as a ratio
So, we have the following representation
Ratio = a : b
Substitute the known values in the above equation, so, we have the following representation
Ratio = 1.5 : 2.5
Divide the ratio by 0.5
So, we have the following representation
Ratio = 1.5/0.5 : 2.5/0,5
Evaluate the quotients
So, we have the following representation
Ratio = 3 : 5
Hence, the ratio is (c) 3 : 5
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Since Scotty started doing his workout plan Janet has been inspired to set herself and go to do more exercises and walk a little more each day she has decided to walk 10 m more every day on day 20 she walked 800 M how many meters will she walk on today 21 on day 60
They walk 810 m on 21 day and 1,200 m on 60th day.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
She has decided to walk 10 m more every day on day 20 she walked 800 m.
Now,
Since, She has decided to walk 10 m more every day on day 20 she walked 800 m.
Hence, The amount of meters she walk everyday can be given as a linear function, and, the rate of variation is a constant (10 m/day):
⇒ 10 m / day
This constant (10 m/day) is the slope of the linear function.
And, We know that;
One point of the linear function (D(20) = 800) and the slope, so we can calculate the y-intercept:
⇒ D (t) = 10t + b
⇒ 800 = 10 × 20 + b
⇒ 800 - 200 = b
⇒ b = 600
So, The equation become;
⇒ D (t) = 10t + 600
Hence, For day t = 21;
⇒ D (21) = 10 x 21 + 600
⇒ D (21) = 810 m
And, For day t = 60;
⇒ D (60) = 10 x 60 + 600
⇒ D (60) = 1,200 m
Thus, They walk 810 m on 21 day and 1,200 m on 60th day.
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Multiply (2+3i)(13 – 6i) .
Answer:
44+27i
Step-by-step explanation:
Multiply using the FOIL method, then combine the real and imaginary parts of the expression.
Use separation of variables to find the solution to the differential equation subject to the given initial condition.
dP/dt=0.07P, P(0)=30
The solution to the differential equation subject to the given initial condition is log P = 0.07t + log(30)
Differential equation in which the variables can be separated from one from one another are called separable differential equations
A general form to write a separable differential equation is
dy/dx = f(x)g(y)
where the variable x and y can be separated from each other
According to the question,
We have to solve dP/dt=0.07P by using separation of variable
=> dP/dt=0.07P
Dividing P both sides and multiplying dt
=> dP / P = 0.07 dt
Now Integrating both the sides
=> [tex]\int\limits {\frac{1}{P} \, dP = \int\limits {0.07} \, dt[/tex]
=> log P = 0.07t + c ------(1)
It is given that P(0)=30
which means at t = 0 , the value of P = 30
Substituting t = 0 and P = 30
log(30) = 0 + c
=> c = log(30)
Substituting the value of c back to equation (1)
log P = 0.07t + log(30)
=> log(P / 30) = 0.07t is our solution
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PLEASE HELP I HAVE GRAPH TOO
A 2010 estimate of Australia's population is
21,515,754.
The next 3 questions ask about this data.
- How many people in Australia
Would be expected to have type
O blood?
We calculated from the graph that 10542719 people expected to have type O blood.
What is different blood group?Generally, human body contains any of these four common types of blood. These are type A, B, O and AB.
How can we estimate our population as per blood group?If we want to estimate our population containing different blood group. we need to carry out survey study to colect data.
Given, Estimated population in 2010 =21515754
the population in percentage who may have O type blood =49%
Actual number of people who expected to have O type blood =
(21515754×49)/100
=10542719
hence, total 10542719 people expected to have O type blood.
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Which of the following pricing strategies could be ethical in many situations? A.Predatory pricing
B.Price baiting
C.Price gouging
D.Price discrimination
The following pricing strategies could be ethical in many situations is price discrimination.
Predatory pricing is a strategy in which a company establishes a price that is too low to get new customers.
Price baiting is a strategy in which businesses make customers believe that they will have to pay less than the actual price of the product.
Price gouging is when a company puts a price that is too high for a product in a level that is not reasonable and this is considered to be unethical.
Price discrimination is a strategy in which businesses charge different prices to different customers based on what they believe that a group of customers would be willing to pay.
For example, when an airline sees that a specific route has a high demand, it increases the price of the ticket.
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Answer:
D. Price discrimination
The population of bears on a nature preserve was 95 last year.This year , the population increased by 20% . what is the new bear population on the preserve
Answer:
114
Step-by-step explanation:
120% of 95 = 1.2 × 95 = 114
4
A line segment contained endpoints (-4, -3) and (1, -3). Which of the following is the reflection of the
line segment over the y-axis?
PLS HELP
Complex numbers are used to describe current (1), voltage (E),
and impedance (Z). Impedance is the opposition to current.
The relation between these three variables is demonstrated by
the formula for Ohm's Law:
E = (I)(Z)
Given:
I = (3 + 3i)
Z = (2+2i)
find E
E=
The relation between these three variables is demonstrated by
the formula for Ohm's Law: E = (I)(Z) is 12i.
What is Ohm's Law?
According to Ohm's law, the resistance of the circuit and the current or energy travelling through the resistance are both exactly proportional to the voltage or potential difference between two places. V=IR is the equation for Ohm's law.According to Ohm's Law, assuming the temperature and other physical parameters don't vary, the current flowing through a conductor is precisely proportional to the potential difference applied across its ends. Through a resistor, current is inversely proportional to the voltage difference.
(3+3 i)(2+2 i)
Apply complex arithmetic rule: (a+b i)(c+d i)=(a c-b d)+(a d+b c) i
=(3 .2-3. 2)+(3 .2+3 . 2) i
Simplify [tex]$(3 \cdot 2-3 \cdot 2)+(3 \cdot 2+3 \cdot 2) i: \quad 12 i$[/tex]
[tex]$=12 i$[/tex]
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Is 2x + y = 10 a linear function
Answer:
yes
Step-by-step explanation:
Determine the Type II error if the null hypothesis, H0, is: researchers claim that 65% of college students will graduate with debt. Select the correct answer below:
a.The researchers cannot conclude that greater than or less than 65% of college students will graduate with debt when, in fact, 65% will graduate with debt.
b.The researchers cannot conclude that 65% of college students will graduate with debt when, in fact, more or less than 65% of college students will graduate with debt.
c.The researchers cannot conclude that 65% of college students will graduate with debt when, in fact, 65% of college students really will graduate with debt.
d.The researchers cannot conclude that greater than or less than 65% of college students will graduate with debt when, in fact, greater than or less than 65% of college students will graduate with debt.
Since type I error is to reject the null hypothesis when null is true that's why the Correct option is C.
The researchers believe that more than or less than 65% of college students will graduate with debt, when in fact, 65% will.
The null hypothesis is true if the experimental result matches the predicted theoretical result. The null hypothesis is disproved and we examine an alternative one if there are any variations in the observed parameters between the samples. The null hypothesis was rejected, which opens the door for additional study but does not imply that the first experimentation was flawed. Usually, the null hypothesis is used to gauge the strength of the evidence.
Hence we get the required answer and the correct option is c.
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Suppose U1, U2, ..., Un are independent random variables and for every i = 1, ..., n, Ui has a uniform distribution over [0, 1].
(a) Find the probability density function of M = max(U1, ..., Un). (We solved the case n = 2 in class. This a generalization.)
(b) Define Z = min(U1, ..., Un). Find the c.d.f. and the p.d.f of Z. (Hint: write the event {Z > z} in terms of random variables U1, ..., Un.)
The probability density function will be expressed as f_M(x) = n * x^(n-1) and cumulative density function is f_Z(z) = n * (1-z)^(n-1).
To find the probability density function of M, we need to find the probability that M takes on a particular value x, which is equal to the probability that all of the random variables U1, ..., Un are less than or equal to x. Since the Ui are independent, this probability is equal to the product of the individual probabilities that each Ui is less than or equal to x. Since each Ui has a uniform distribution over [0, 1], the probability that Ui is less than or equal to x is simply x. Therefore, the probability that M takes on a particular value x is equal to x^n.
This means that the probability density function of M is given by:
f_M(x) = n * x^(n-1)
for x in the range [0, 1].
For the second part of the question, we want to find the cumulative distribution function (c.d.f.) and probability density function (p.d.f.) of Z = min(U1, ..., Un). We can find the c.d.f. of Z by finding the probability that Z is less than or equal to a particular value z. This is equal to the probability that all of the random variables U1, ..., Un are greater than or equal to z. Since the Ui are independent, this probability is equal to the product of the individual probabilities that each Ui is greater than or equal to z. Since each Ui has a uniform distribution over [0, 1], the probability that Ui is greater than or equal to z is simply 1-z. Therefore, the probability that Z is less than or equal to z is equal to (1-z)^n.
This means that the cumulative distribution function of Z is given by:
F_Z(z) = (1-z)^n
for z in the range [0, 1].
To find the probability density function of Z, we can differentiate the cumulative distribution function with respect to z. This gives us:
f_Z(z) = n * (1-z)^(n-1)
for z in the range [0, 1].
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Find the matrix A representing the reflection about the line L in R^2 which consists of all scalar multiples of the vector [6 3]. A = []
the matrix A, which is composed of all scalar multiples of the vector [6 3], and represents the reflection about the line L in R2.A = [[-6/7, 9/7],[9/7, 6/7]]
Let L be the line in R^2 which consists of all scalar multiples of the vector [6 3], then the equation of the line is y= (3/6)x.
We need to find the matrix A which represents the reflection about the line L.
Let (x1, y1) be any point on the line L and let (x2, y2) be its reflection about the line L.
Now, we know that the slope of the line L is 3/6, hence the slope of the normal to the line L is -6/3.
So, the equation of the normal to the line L is y = -(6/3)x. Now, we can use the point-slope form of the line equation to calculate the equation of the line passing through (x1, y1) and its reflection (x2, y2).
The line that connects (x1, y1) and (x2, y2) has the following equation:
y-y1 = (y2-y1)/(x2-x1) (x-x1)
=> y-y
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If f(x) = x ^ 2 - 3x + 11 and g(x)=11x+7, what is (fg)(x) in standard form?
In linear equation, 11x * f(x) + 7 * f(X) is (fg)(x) in standard form .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
f(x) . g(x) = f(x) . ( 11x + 7 )
Multiplicative Distribution Law = f(x) * 11x + f(x) * 7
= 11 * f(x) * x+ 7 * f(x)
= 11x * f(X) + 7 * f(x)
= 11x * f(x) + 7 * f(X)
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what is the slope of the line through the points (-2,4) and (1,2)
Answer:
The slope is [tex]\frac{-2}{3}[/tex]
Step-by-step explanation:
An order pair is in the form (x y). The slope is the change in y over the change in x. From the 2 points our y's are 2 and 4. From the 2 points our x's are 1 and -2. to find the change you subtract.
[tex]\frac{2-4}{1 - -2}[/tex] = [tex]\frac{-2}{1 + 2}[/tex] [tex]\frac{-2}{3}[/tex]
Winnie, a waitress, holds a 5.0-N tray stacked with twelve 3.5-N dishes in one hand. The
length of her arm from her hand to her elbow is 30.0 cm and her bicepts exert a force 5.0 cm
from her elbow, which acts as a fulcrum. How much force must her biceps exert to allow her to
hold the tray?
The force exerted by her biceps to allow her hold the tray is 282 N.
What is force?Force is the product of mass and acceleration.
To calculate the force the biceps must exert to allow her hold the tray, we use the formula below.
Formula:
Fd = F'd'....................... Equation 1Where:
F = Weight of the tray and the platesd = Distance of her hand to her elbowF' = Force exerted by the biceptsd' = Distance of her biceps to the elbow.From the question,
Given:
F = 5+12(3.5) = 47 Nd = 30 cmd' = 5 cmSubstitute these values into equation 1 and solve for F'
47×30 = F'×5F' = 47×30/5F' = 282 NHence, the force exerted by her biceps is 282 N.
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In the figure below, points N, K, J, and H lie in plane Z.
Points L and M do not lie in plane Z.
For each part below, fill in the blanks to write a true statement.
L
N
Z
M
(a) K, , and are distinct points that are
collinear.
(b) LM and , are distinct lines that
intersect.
(c) Point N and line are coplanar.
(d) Another name for plane Z is plane.
Points H, J and K are collinear and I'll choose K, J, and H as the non-collinear points
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
Points H, J and K are collinear as they are on the same line. Pick either K or K to fill out the answer box. I'll go with point K.
it through. Imagine if the flat piece of paper could revolve about this axis (like a propeller). The fact that the points are not all on the same line ensures that we build exactly one individual plane.
I'll choose K, J, and H as the non-collinear points to give the object the name Plane KJH. There may be further options.
Hence, Points H, J and K are collinear and I'll choose K, J, and H as the non-collinear points
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the Celisius and the Fahrenight temperature scales are relased by the equation c=5/6 (F-32) expresses F in terms of C.
Answer:
F = (9/5)C + 32
Step-by-step explanation:
C = 5/9(F-32) **you wrote the fraction wrong in your question, it's 5/9, not 5/6
C = (5F)/9 - 160/9
C + 160/9 = (5F)/9
9C + 160 = 5F
(9C + 160)/5 = F
F = (9/5)C + 32
Answer: F = (6C/5) + 32
To express F in terms of C, rearrange the equation to isolate 'F'.
Inverse OperationsTo rearrange the equation, we want 'F' to be by itself. To move numbers to the other side, we do the other pair of inverse operation to both sides. This cancels out what we don't need while keeping the left and right sides equal.
Pairs of inverse operations
Multiply ⇔ DivideAdd ⇔ SubtractCalculate[tex]\displaystyle { C = \frac{5}{6}*(F-32) }[/tex] Start with the equation in the question.
[tex]\displaystyle { C = \frac{5*(F-32)}{6} }[/tex] Rewrite. This is the same as the question.
[tex]\displaystyle { 6C = \frac{5*(F-32)}{6}*6 }\\[/tex] Multiply both sides by 6.
[tex]\displaystyle { 6C = 5*(F-32) }[/tex] Cancelled out 6 on the right.
[tex]\\\displaystyle { \frac{6C}{5} = \frac{5*(F-32)}{5} }[/tex] Divide both sides by 5.
[tex]\displaystyle { \frac{6C}{5} = (F-32) }[/tex] Cancelled out 5 on the right.
[tex]\displaystyle { \frac{6C}{5} = F-32 }[/tex] We don't need the brackets if 'F - 32' is alone.
[tex]\displaystyle { \frac{6C}{5}+32 = F-32+32 }[/tex] Add 32 to both sides.
[tex]\displaystyle { \frac{6C}{5}+32 = F }[/tex] Cancelled out 32 on the right.
[tex]\displaystyle { F = \frac{6C}{5}+32 }[/tex] Keep lone variables on the left side.
Therefore, the equation to convert Celsius to Fahrenheit is:
[tex]\displaystyle { F = \frac{6C}{5}+32 }[/tex]
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what’s 10.37304 rounded to the nearest hundredth?
Answer:
10.37
Step-by-step explanation:
3 in the thousandths place is lower than 5 therefore you have to turn the thousandths into a 0 and don't change the forenumber
write a while loop to read integers from input until -1 is read. for each integer read before -1, add the integer to vector numbervect. ex: if the input is 1 6 5 3 -1, then the output is: 1 6 5 3
As per the concept of vector, the while loop for integers is written below.
The term vector refers a quantity or phenomenon that has two independent properties: magnitude and direction.
Here we need to write the a quantity or phenomenon that has two independent properties: magnitude and direction.
While we looking into the given question, we have know that,
Here the input is 1 6 5 3 -1, then
the output is: 1 6 5 3
Then the function for the given statement is written as,
while ((char1 = getchar()) != '-1')
{
if (char1 == ' ')
sp_ct1++;
else if (char1 == '\n')
nl_ct1++;
else
other1++;
}
Therefore, the above function is used to read integers from input until -1 is read.
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Match these values of r with the accompanying scatterplots:
0.406,
−1,
0.748,
−0.748,
and
0.994.
Match the values of r to the scatterplots.
Scatterplot 1,
r=
▼
Scatterplot 2,
r=
▼
Scatterplot 3,
r=
▼
Scatterplot 4,
r=
▼
Scatterplot 5,
r=
▼
r = 1 in scatter plot 1, the response. Scatter plot 2, with a r of 0.364 Scatter plot 3, r=-0.995 Scatter plot 4, r = 0.995 Scatter plot 5, with a r of 0.735.
what is scatterplots ?Charts that depict the relationship between two variables are known as scatter charts, sometimes known as scatter plots. They are a very effective type of chart because they enable readers to see relationships or trends right away that are difficult to see in practically any other form.
You can figure out R using the formula R = s t if you've worked in sections. Between 1 and 1 will be the response you receive. Any response that is affirmative demonstrates a positive correlation, with anything over 0.7 often being regarded as a significant link.
r = 1 in scatter plot 1, the response. Scatter plot 2, with a r of 0.364 Scatter plot 3, r=-0.995 Spreadsheet plot 4, r = 0.995 Scatter plot 5, with a r of 0.735.
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which of the following are not the lengths of the sides of a triangle? A)2, 3, 4
B)2, 3, 2
C)2, 3, 3
D)2, 3, 6
According to the triangle inequality theorem; D)2,3,6 can not be the lengths of the sides of a triangle
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side of that triangle
If the two shortest sides are put end to end, they should be longer than the longest side to be able to angle up to form a triangle.
Therefore applying this theorem in this case;
A) 2,3,4: The sum of 2 and 3 = 5; which is greater than 4
B) 2,3,2: The sum of 2 and 2 = 4; which is greater than 3
C) 2,3,3: The sum of 2 and 3 = 5; which is greater than 3
D) 2,3,6: The sum of 2 and 3 = 5; which is not greater than 6; therefore according to the triangle inequality theorem these cannot be the lengths of the sides of a triangle.
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which equation can be used to solve the problem? 60 percent of what number is 30?; which fraction is equivalent to one-eighth?
The equation that can be used to solve the first problem is [tex]0.60 x = 30\\[/tex] and the equation that can be used to solve the second problem is [tex]\frac{x}{y} = \frac{1}{8}[/tex].
There are two problems given to us -
(a) 60 percent of what number is 30
(b) which fraction is equivalent to one-eighth
We have to find out the equations that can be used to solve the two problems.
(a) Let us say that the number to be considered is x
According to the information given for the first problem, we can say that -
60% of x = 30
[tex]= > \frac{60}{100} x = 30\\ = > 0.60 x = 30\\[/tex]
We can now solve the equation to find out the value of x as -
[tex]0.60 x = 30\\= > x = 50[/tex]
Thus, the problem of "60 percent of what number is 30?" can be represented by the equation [tex]0.60 x = 30\\[/tex].
(b) Let us say that the fraction to be considered is represented as [tex]\frac{x}{y}[/tex].
According to the information given for the second problem, we can say that -
[tex]\frac{x}{y} = \frac{1}{8}\\= > y = 8x[/tex]
For every value of the numerator x, the value of denominator y can be found out through the above equation and vice-versa.
Thus, the problem of "which fraction is equivalent to one-eighth?" can be represented by the equation [tex]\frac{x}{y} = \frac{1}{8}[/tex].
Therefore, the equation that can be used to solve the first problem is [tex]0.60 x = 30\\[/tex] and the equation that can be used to solve the second problem is [tex]\frac{x}{y} = \frac{1}{8}[/tex].
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Which matrix will be used as the inverted coefficient matrix when solving the following system? 3x1+ X2 = 4 5x1+2x2 =7 2 -1 -5 3 -2 5 -3 5 2
the inverted coefficient matrix is
[tex]\left[\begin{array}{ccc}2&-1&-5\\3&-2&5\\-3&5&2\end{array}\right][/tex]
1. The inverted coefficient matrix is found by taking the inverse of the coefficient matrix.
3x1 + x2 = 4
5x1 + 2x2 = 7
3. Therefore, the inverted coefficient matrix is
2 -1 -5
3 -2 5
-3 5 2
It is used to represent and manipulate complex data, such as linear equations, vectors, and polynomials. A matrix can also be used to represent a system of linear equations or to graph a function. Matrices are key elements in linear algebra, a branch of mathematics that studies vector spaces, linear transformations, and systems of linear equations.
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What is the slope of a line parallel to the line whose equation is
x + y = - 6. Fully simplify your answer.
Answer:
slope = -1
Step-by-step explanation:
⭐What is the slope of a line?
the coefficient of the x-variable[tex]y = mx + b[/tex]the m in the slope-intercept form equation⭐What is the slope of a line that is parallel to another line?
the slope of the parallel line is the same as the slope of the line it is parallel toTherefore, we can just find the slope of the given line and put that as our answer.
Before we do that, we need to rewrite the equation in slope-intercept form. ([tex]y = mx + b[/tex])
x + y = -6
To do so, subtract x from the LHS (left-hand side) and RHS (right-hand side) to isolate "y"
x + y -x = -6 -x
y = -x + 6
The slope is the coefficient of the x-variable.
-1 is the coefficient of the x-variable.
Therefore, -1 is the slope of this line.
Parallel lines have the same slope of the line they are parallel to.
Therefore, -1 is the slope of the line parallel to this line.
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a is an infinitesimally stochastic matrix (i.e., its rows sum to zero). prove that e at is a stochastic matrix.
A stochastic matrix A's steady state is an eigenvector w with eigenvalue 1, such that the elements are positive and add up to 1. The theorem of Perron-Frobenius...
A square matrix A is stochastic if all of its entries are nonnegative, and the elements of each column total to 1. If all of the elements in a matrix are positive integers, the matrix is positive.
A stochastic matrix is a square matrix with probability vector columns. A probability vector is a numerical vector with entries that are real values ranging from 0 to 1 and whose sum equals 1.
(Stochastic processes, mathematics) A square matrix of rows of nonnegative real values, with each row adding up to A Markov chain's transitions are described by its element in the 'th row and 'th column, which describes the probability of moving from state to state in one time step.
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