The augmented matrix of a system of linear equations AX = B was reduced to upper-triangular form so that 2 1 0 1 2 [AB] 0 -1 31 0 0 mln where m and n are real numbers. State all values of m and/or n such that the following statements are true. (a) Matrix A is invertible. (b) The system AX = B has no solutions. (c) The system AX = B has an infinite number of solutions. (d) Columns of the augmented matrix (AB) are linearly independent. (e) The system AX = 0 has a unique solution. (f) At least one eigenvalue of the matrix A is zero. (g) Columns of the matrix A form a basis in R3.
Answers
a. Matrix A is invertible when |A| = -m ≠ 0 then statement true.
b. The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.
c. The system AX = B has an infinite number of solutions when m = n = 0 then statement true.
d. Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.
e. The system AX = 0 has a unique solution when m ≠ 0 then statement true.
f. At least one eigenvalue of the matrix A is zero when m = 0 then statement true.
g. Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.
Given that,
The augmented matrix of a system of linear equations AX = B was reduced to upper-triangular form so that
[A|B] = \(\left[\begin{array}{ccc}2&1&0 \ | \ 2\\0&-1&3 \ | \ 1 \\0&0&m \ | \ n\end{array}\right]\)
Where m and n are real numbers.
We know that,
a. We have to prove matrix A is invertible.
For A to be invertible.
|A| ≠ 0
|A| is the determinant of the matrix A.
|A| = 2(-m) -1(0) + 0(0) = -m
Here, m is the real number.
So, |A| = -m ≠ 0
Therefore, Matrix A is invertible when |A| = -m ≠ 0 then statement true.
b. We have to prove the system AX = B has no solution.
When Rank[A|B] > Rank[A]
m = 0 and n ≠ 0 has a real number
Therefore, The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.
c. We have to prove the system AX = B has an infinite number of solutions.
When m = n = 0, and Rank[A] < 3
Therefore, The system AX = B has an infinite number of solutions when m = n = 0 then statement true.
d. We have to prove columns of the augmented matrix (AB) are linearly independent.
When m ≠ 0 and m∈R and n= 0
Therefore, Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.
e. We have to prove the system AX = 0 has a unique solution.
When \(\left[\begin{array}{ccc}2&1&0 \\0&-1&3 \\0&0&m \end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}0\\0\\0\end{array}\right]\)
The equation are 2x + y = 0, -y + 3z = 0 and mz = 0
m ≠ 0 should be any real number except zero.
Therefore, The system AX = 0 has a unique solution when m ≠ 0 then statement true.
f. We have to prove at least one eigenvalue of the matrix A is zero.
When λ = 2, 1, m
m = 0 then eigen value is zero
Therefore, At least one eigenvalue of the matrix A is zero when m = 0 then statement true.
g. We have to prove columns of the matrix A form a basis in R³.
When m ≠ 0
Therefore, Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.
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Related Questions
Under what circumstances should the chi-square statistic not be used: Question 15 options: if the expected frequencies are >5 for any cell if the expected frequencies are <5 for any cell if the expected frequencies
Answers
The chi-square statistic should not be used under certain circumstances, specifically when the expected frequencies in any cell of the contingency table meet certain criteria.
The two conditions that indicate when the chi-square statistic should not be used are if the expected frequencies are greater than 5 for any cell or if the expected frequencies are less than 5 for any cell. When the expected frequencies are greater than 5, it implies that the sample size is large enough, and the chi-square test can be considered valid and reliable. However, when the expected frequencies are less than 5, it may lead to unreliable results and less accurate statistical inference. In such cases, the assumptions underlying the chi-square test may not hold, and alternative methods or tests should be considered, such as Fisher's exact test or Monte Carlo simulation. Using the chi-square test with expected frequencies that do not meet these criteria can lead to inflated type I error rates and unreliable conclusions. Therefore, it is important to assess the expected frequencies in each cell of the contingency table before applying the chi-square test and consider alternative approaches if the conditions are not met.
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the 9th term of an arithmetic sequence is 29 and the 27th term is 83 find a and d
Answers
Answer:
Hope you understand
a=5 and d=3
A sequence begins with −15. Each term is calculated by adding 6 to the previous term. Which answer correctly represents the sequence described?
Answers
The answer that correctly represents the sequence described is:
-15, -9, -3, 3, 9, ...
What does a sequence mean?In mathematics, a sequence is an ordered list of numbers, called terms, that follow a certain pattern or rule. The terms of a sequence are usually indexed by natural numbers, starting from some fixed initial value.
A sequence can be either finite or infinite. A finite sequence has a fixed number of terms, while an infinite sequence goes on indefinitely. Sequences can be defined in many ways, such as explicitly giving the formula for each term or defining a recursive formula that describes how to calculate each term from the previous ones.
According to the given informationThe sequence described in the problem can be generated by starting with -15 and repeatedly adding 6 to the previous term. So the first few terms of the sequence are:
-15, -15 + 6 = -9, -9 + 6 = -3, -3 + 6 = 3, 3 + 6 = 9, ...
In general, we can write the nth term of the sequence as:
aₙ = aₙ₋₁ + 6
where a₁ = -15 is the first term.
Using this recursive formula, we can find any term in the sequence by adding 6 to the previous term.
Therefore, the answer that correctly represents the sequence described is:
-15, -9, -3, 3, 9, ...
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Russel runs 9/10 mile in five minutes .At this rate, how many miles can he run in one minute?
Answers
Answer:
Including results for russell runs 9/10 mile in five minutes .at this rate, how many miles can he run in one minute?.
Step-by-step explanation:
The state of a spin 1/2 particle in Sx basis is defined as (Ψ) = c+l + x) + i/√7 l - x) a) Find the amplitude c+ assuming that it is a real number and the state vector is properly defined. b) Find the expectation value . c) Find the uncertainty △SX.
Answers
1) The amplitude c+ is c+l
2) The expectation value is 0
3) The uncertainty ΔSX is √(3/7) c+.
Now, we know that any wave function can be written as a linear combination of two spin states (up and down), which can be written as:
Ψ = c+ |+> + c- |->
where c+ and c- are complex constants, and |+> and |-> are the two orthogonal spin states such that Sx|+> = +1/2|+> and Sx|-> = -1/2|->.
Hence, we can write the given wave function as:Ψ = c+|+> + i/√7|->
Now, we know that the given wave function has been defined in Sx basis, and not in the basis of |+> and |->.
Therefore, we need to write |+> and |-> in terms of |l> and |r> (where |l> and |r> are two orthogonal spin states such that Sy|l> = i/2|l> and Sy|r> = -i/2|r>).
Now, |+> can be written as:|+> = 1/√2(|l> + |r>)
Similarly, |-> can be written as:|-> = 1/√2(|l> - |r>)
Therefore, the given wave function can be written as:Ψ = (c+/√2)(|l> + |r>) + i/(√7√2)(|l> - |r>)
Therefore, we can write:c+|l> + i/(√7)|r> = (c+/√2)|+> + i/(√7√2)|->
Comparing the coefficients of |+> and |-> on both sides of the above equation, we get:
c+/√2 = c+l/√2 + i/(√7√2)
Therefore, c+ = c+l
The amplitude c+ is a real number and is equal to c+l
The expectation value of the operator Sx is given by: = <Ψ|Sx|Ψ>
Now, Sx|l> = 1/2|r> and Sx|r> = -1/2|l>
Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= -i/√7(c+l*) + i/√7(c+l)= 2i/√7 Im(c+)
As c+ is a real number, Im(c+) = 0
Therefore, = 0
The uncertainty ΔSX in the state |Ψ> is given by:
ΔSX = √( - 2)
where = <Ψ|Sx2|Ψ>and2 = (<Ψ|Sx|Ψ>)2
Now, Sx2|l> = 1/4|l> and Sx2|r> = 1/4|r>
Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= 1/4(c+l* + c+l) + 1/4(c+l + c+l*) + i/(2√7)(c+l* - c+l) - i/(2√7)(c+l - c+l*)= = 1/4(c+l + c+l*)
Now,2 = (2i/√7)2= 4/7ΔSX = √( - 2)= √(1/4(c+l + c+l*) - 4/7)= √(3/14(c+l + c+l*))= √(3/14 * 2c+)= √(3/7) c+
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An artist sold 128 pieces of jewelry. Of the pieces of jewelry sold, 32 were rings. What percent of the pieces of jewelry sold were rings?
Answers
Step-by-step explanation:
when you have a problem you can tell me please follow
The dot plot shows the number of raffle tickets bought by each person.
Number of Raffle Tickets Bought
A dot plot going from 0 to 5. 0 has 4 dots, 1 has 0 dots, 2 has 4 dots, 3 has 6 dots, 4 has 3 dots, 5 has 5 dots.
Where is the peak of the dot plot?
1
3
5
6
Answers
Answer:it’s B aka 3
Step-by-step explanation:
Answer:
3 AKA B
Step-by-step explanation:
if you look at it 3 is the highest peak
Find a given that: a P(2, 3) and Q(a, -1) are 4 units apart b P(-1, 1) and Q(a, -2) are 5 units apart c X(a, a) is √√8 units from the origin d A(0, a) is equidistant from P(3, -3) and Q(-2, 2).
Answers
Answer:
To solve this problem, we can use the Pythagorean Theorem to solve for a.
For part (a), we know that P(2, 3) and Q(a, -1) are 4 units apart, so we can use the Pythagorean Theorem to calculate a:
(a - 2)² + (-1 - 3)² = 4²
Solving for a, we get:
a = 7
For part (b), we know that P(-1, 1) and Q(a, -2) are 5 units apart, so we can use the Pythagorean Theorem to calculate a:
(a + 1)² + (-2 - 1)² = 5²
Solving for a, we get:
a = 4
For part (c), we know that X(a, a) is √√8 units from the origin, so we can use the Pythagorean Theorem to calculate a:
a² + a² = 8
Solving for a, we get:
a = 2√2
For part (d), we know that A(0, a) is equidistant from P(3, -3) and Q(-2, 2), so we can use the Pythagorean Theorem to calculate a:
(3 - 0)² + (-3 - a)² = (-2 - 0)² + (2 - a)²
Solving for a, we get:
a = -1
Therefore, the value of a that satisfies all conditions is a = -1.
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What is the equation of a circle with a radius of 6 and a center at ( -2 , 3 )?
Answers
(x-p)^2+(y-q)^2=r^2
The radius is given (r=6), as well as the centre of the circle (-2;3).
"p" and "q" represent the coordinates of the centre of the circle.
So it would look like this -
(x-p)^2+(y-q)^2=r^2
p=x-coordinate (-2)
q=y-coordinate (3)
r=6
(x-(-2))^2+(y-(3))^2 =6^2
(x+2)^2 + (y-3)^2 = 36
***"^" means "to the power of"
Hope this helped~
Answer:
Solution given:
centre(h,k)=(-2,3)
radius(r)=6 units
we have
equation of a circle is:
(x-h)²+(y-k)²=r²
(x+2)²+(y-3)²=6²
(x+2)²+(y-3)²=36 is required equation of a circle.
Using the Bohr equation to calculate the frequency, in Hz, of a
C5+ photon. The photon moves from n=6 to n=2. Have your answer in 3
significant figures.
Answers
the frequency of the C5+ photon is approximately 7.31 x 10^14 Hz, rounded to three significant figures.
The frequency of a photon can be calculated using the Bohr equation. In this case, we are considering a C5+ ion transitioning from energy level n=6 to n=2. The Bohr equation is given by:
ν = R_H * (1/n_f^2 - 1/n_i^2)
where ν is the frequency of the photon, R_H is the Rydberg constant (approximately 3.29 x 10^15 Hz), n_f is the final energy level, and n_i is the initial energy level.
Substituting the values into the equation, we have:
ν = 3.29 x 10^15 Hz * (1/2^2 - 1/6^2)
Simplifying the equation further, we get:
ν = 3.29 x 10^15 Hz * (1/4 - 1/36)
Calculating the value, we find:
ν = 3.29 x 10^15 Hz * (8/36)
ν ≈ 7.31 x 10^14 Hz
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find parametric equations for the line. (use the parameter t.) the line through (−4, 2, 3) and parallel to the line 1 2 x
Answers
The parametric equations for the line are:
x = -4 + t
y = 2 + 2t
z = 3 + xt where t is the parameter that represents the position along the line.
To find the parametric equations for the line through the point (-4, 2, 3) and parallel to the line with direction vector (1, 2, x), we can use the following approach:
Let's denote the parametric equations as:
x = x₀ + at
y = y₀ + bt
z = z₀ + ct
We know that the line is parallel to the vector (1, 2, x). Since the line is parallel, the direction ratios (a, b, c) will be the same as the direction ratios of the given vector.
So, we have:
a = 1
b = 2
c = x
Now, we need to determine the initial point (x₀, y₀, z₀) on the line. Since the line passes through (-4, 2, 3), we can assign these values as the initial point:
x₀ = -4
y₀ = 2
z₀ = 3
Therefore, the parametric equations for the line are:
x = -4 + t
y = 2 + 2t
z = 3 + xt
where t is the parameter that represents the position along the line.
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Hannah needs to calculate the cotangent of an angle. She uses the ratio
opposite leg
for her calculation. Did Hannah correctly calculate the cotangent of the angle?
adjacent leg
A
B.
Yes, Hannah correctly calculated the cotangent of the angle.
adjacent leg
No, Hannah should have used the ratio
opposite leg
hypotenuse
No, Hannah should have used the ratio
opposite leg
O c.
D.
No, Hannah should have used the ratio
adjacent leg
hypotenuse
Answers
Answer:
B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)
Step-by-step explanation:
✍️The formula for calculating cotangent of an angle is given as:
\( cot = \frac{adjacent}{opposite} \).
The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.
Therefore, Hannah did not calculate the cotangent of the angle correctly.
She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.
15 +(12+18a) simplify the expression
I NEED THE ANSWER ASAP PLEASE
Answers
Answer:
27+18a
Step-by-step explanation:
Select all expressions that are squares of linear expressions.ap2 – 6p + 99x2 – 36x2 + 6x + 36Ex+4)2(2d + 8)(2d - 8)x2 + 36
Answers
Part a
p2 – 6p + 9
we know that
p2 – 6p + 9=(p-3)^2
so
the given expression is a square of linear equation
Part b
9x2 – 36=(3x-6)(3x+6)
the given expression is not a square of linear equation
Part c
x2 + 6x + 36
the given expression is not a square of linear equation
Part d
(1/2x+4)^2
he given expression is a square of linear equation
The five-number summary for the number of stylists employed by each hair salon in Jamesville is shown in the following table:
Min= 7
Q1= 9
Median= 12
Q3= 15
Max= 18
The five-number summary suggest that about 75% of salons in Jamesville have fewer than how many stylists employed?
Answers
Answer:
I think its 4
Step-by-step explanation:
don't really know how to but its simple really
The five-number summary suggests that about 75% of salons in Jamesville have fewer than 15 stylists.
How does a boxplot show the data points?A box plot has 5 data descriptions.
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called the second quartile.The last line of the box shows the third quartile.Since the Q₁, Median(Q₂), and Q₃ divide the data into 4 parts such that each part represents 25% of the data. Therefore, The five-number summary suggests that about 75% of salons in Jamesville have fewer than 15 stylists, this is represented by the third quarter.
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Where is the gap in the data?
Number of Patients Per Hour Who Waited Longer than 15 Minutes
A dot plot going from 0 to 5. 0 has 8 dots, 1 has 6 dots, 2 has 1 dot, 3 has 5 dots, 4 has 0 dots, and 5 has 3 dots.
0
2
4
8
Answers
Answer:
4 hours
Step-by-step explanation:
I don’t work with data points too much but I believe the gap is at 4 because it is where no one waited that long and where the date kind of stops and then start back up at 5 hours
Hopes this helps
4. Add. 2a + 8 + 4b + 5
Answers
Answer:
Step-by-step explanation:
2a + 4b + 8 + 5
2a + 4b + 13
HELP find the missing side!!!
Answers
Answer: 12.96 and 8.87 units respectively
Step-by-step explanation:
The sine rule states that the ratio between a side of a triangle and the sine of the angle opposing the side will be equal for all three sides of the same triangle.
For Q20, we can get the equation \(\frac{19}{sin(90)} = \frac{x}{sin(43)}\) and from here we can solve for x which is 12.96 so the answer to Q20 is 12.96 units.
For Q21, the angle opposite of x can be found by summing up the two known angles and subtracting that from 180° to get 43°. From here, we can get the equation \(\frac{13}{sin(90)} = \frac{x}{sin(43)}\) and solve for x which is 8.87 so the answer to Q21 is 8.87 units
Can you help me please???
Which expressions are equivalent to (3w - 4x)4? Select TWO correct responses.
A. 4(-1wx)
B. 12 w -16 x
C. 7w -8x
D. -16 x +12w
Pick 2
Answers
Combine the like terms to create an equivalent expression:
-n+(-4)-(-4n)+6
Answers
Step-by-step explanation:
-n + (-4) - (-4n) + 6 = -n - 4 + 4n + 6 = 3n + 2
Answer:
3n+2
Step-by-step explanation:
-n+(-4)-(-4n)+6
= -n-4+4n+6
= 3n-4+6
= 3n+2
what is 750.0 ml expressed in l? a. 0.750 l b. 75,000 l c. 7,500 l d. 750,000 l
Answers
750ml is equal to 0.750 l.
To convert from milliliters (ml) to liters (l), we can use the liter scale. The liter scale shows that 1 liter is equal to 1000 milliliters. Therefore, to convert from milliliters to liters, we can divide the number of milliliters by 1000.
In this case, we have 750.0 ml. To convert this to liters, we can divide by 1000:
750.0 ml / 1000 = 0.750 l
Therefore, 750.0 ml is equal to 0.750 l, and the correct answer is a. 0.750 l.
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does the equator cross the northen or southern part of south america south america is mostly located
Answers
Answer:
It crosses the northern part of south America! The equator is an imaginary line around the middle of a planet or other celestial body. It is halfway between the North Pole and the South Pole
Step-by-step explanation:
Answer:
Step-by-step explanation:
Please look up "equator" on the internet. You'll see that the equator passes through the South American country Ecuador. Ecuador is in the northern part of South America and the equator crosses mainly that part of the continent.
On average, 4 customers per hour use the public telephone in the sheriff's detention area, and this use has a Poisson distribution. The length of a phone call varies according to a negative exponential distribution. with a mean of 5 minutes. The sheriff will install a second telephone booth when an arrival can expect to wait 3 minutes or longer for the phone
a. By how much must the arrival rate per hour increase to justify a second telephone booth?
b. Suppose the criterion for justifying a second booth is changed to the following: install a second booth when the probability of having to wait at all exceeds 0.6 Under this criterion, by how much must the arrival rate per hour increase to justity a second booth?
Answers
A. The arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone boothe.
B. The arrival rate per hour must increase by at least 1.6 customers per hour to justify a second telephone booth under the new criterion.
How to calculate arrival rateTo get the how much arrival rate must increase, we must get the expected waiting time for a customer.
Assuming;
X is the number of customers who arrive per hour
Y is the length of a phone call in minutes.
Then, X follows a Poisson distribution with λ = 4 (since 4 customers per hour use the phone on average)
Y follows a negative exponential distribution with mean μ = 5 (since the mean length of a phone call is 5 minutes).
Total time is given as sum of waiting time and length of call;
T = W + Y
The waiting time W is the difference between the time a customer arrives and the time that the phone becomes available. waiting time follows a uniform distribution where mean= 1/λ (since the arrivals follow a Poisson process);
Then we have;
E(W) = 1/(2λ) = 1/8 hours
The expected total time T that a customer spends at the phone booth is:
E(T) = E(W) + E(Y) = 1/8 + 5/60 = 11/48 hours
For a second telephone booth to be justifiable, new customer that arrives must wait 3 minutes or longer for the phone.
E(W) ≥ 1/20
To get λ,
1/(2λ) ≥ 1/20
λ ≤ 10
This means that, the arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone booth.
b. Getting how much the arrival rate per hour must increase to justify a second telephone booth under the new criterion,
we need to find the probability that a customer has to wait at all.
Let P(W > 0) be the probability that a customer has to wait.
P(W > 0) = 1 - P(W = 0)
The waiting time W follows a uniform distribution with mean 1/λ, so we have:
P(W = 0) = 1 - λ/4
The length of a phone call Y follows a negative exponential distribution with mean 5 minutes = 1/12 hours, so we have:
P(Y > t) = e^(-μt) = e^(-t/12)
The probability that a customer has to wait is given as;
P(W > 0) = 1 - P(W = 0) = λ/4
To justify a second telephone booth, the probability of having to wait at all must exceed 0.6. so we have;
P(W > 0) > 0.6
λ > 2.4
The arrival rate per hour must increase by at least 2.4 - 4 = 1.6 customers per hour to justify a second telephone booth under the new criterion.
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Find the slope of the line going through the points (-2,3) and (3,6). Put your answer in simplest fraction fo.
"
Answers
The slope of the line passing through the points (-2, 3) and (3, 6) is 3/5.
To find the slope of a line passing through two points, we use the slope formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Given the points (-2, 3) and (3, 6), we can substitute the values into the formula:
m = (6 - 3) / (3 - (-2))
= 3 / 5
The resulting slope is 3/5.
The slope represents the rate at which the line rises or falls as we move horizontally along the line. In this case, a slope of 3/5 indicates that for every 5 units of horizontal movement to the right, the line rises by 3 units vertically.
Alternatively, for every 5 units of horizontal movement to the left, the line falls by 3 units vertically. This indicates a positive slope, meaning the line has an upward trend from left to right.
The slope is a measure of the steepness of the line. In this case, a slope of 3/5 indicates a moderately steep incline. It means that for every 5 units of horizontal distance, the line rises by 3 units.
Understanding the slope of a line helps us analyze its direction, steepness, and relationship between the x- and y-coordinates. It is a fundamental concept in mathematics and has numerous applications in various fields, such as physics, engineering, and economics.
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Help the perimeter is about _ units_
Answers
The perimeter of the given polygon is about 16.4 units.
How to find the perimeter of the polygon?We want to find the perimeter of the polygon whose vertices are (-3, 2), (2, 2) and (-1, -3).
The perimeter will be equal to the sum of the distances between the vertices, and remember that the distance between two points (x₁, y₁) and (x₂, y₂) is:
d = √( (x₂ - x₁)² + (y₂ - y₁)²)
The distances are:
between (-3, 2) and (2, 2)
d = √( (-3 - 2)² + (2 - 2)²) = 5
between (-1, -3) and (2, 2)
d = √( (-1 - 2)² + (-3 - 2)²)
d = √( 9 + 25) = 6
between (-1, -3) and (-3, 2)
d = √( (-1 + 3)² + (-3 - 2)²)
d = √29 = 5.4
Then the perimeter is:
5.4 + 6 + 5 = 16.4
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work out the value of x
Answers
x + 3x + 90° = 360°
4x = 360° - 90°
4x = 270°
4x/4 = 270°/4
x = 67.5°
Hope it helps! Make me brainliest if it’s correct.
Estimate the difference to the nearest tenth.
0.8 – 0.638
A) 1.3
B) 0.13
C) 0.2
D) 0.1
Answers
Answer:
C) 0.2
Step-by-step explanation:
To estimate the difference between 0.8 and 0.638 to the nearest tenth, we can simply subtract the two numbers and round the result to the nearest tenth.
0.8 - 0.638 = 0.162
Rounding 0.162 to the nearest tenth gives us:
0.2
Therefore, the estimated difference between 0.8 and 0.638 to the nearest tenth is 0.2.
To estimate the difference between 0.8 and 0.638 to the nearest tenth, we need to subtract 0.638 from 0.8:
\(0.8 - 0.638 = 0.162\)To round this to the nearest tenth, we look at the tenths place, which is 6. Since 6 is greater than 5, we need to round up. Therefore, the answer is:
\(0.8 - 0.638 \approx \fbox{0.2}\)\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)
the student lockers at olympic high are numbered consecutively beginning with locker number 1. the plastic digits used to number the lockers cost two cents a piece. thus, it costs two cents to label locker number 9 and four cents to label locker number 10. if it costs $137.94 to label all the lockers, how many lockers are there at the school?
Answers
The number of lockers in the school, given that each locker costs two cents, would be 2, 001 lockers.
How to find the number of lockers ?The number of lockers can be found by finding the cost of the first 9 lockers to be :
= 2 x 9 lockers
= 18 cents
The next 90 lockers till 99 locker:
= 4 x 90
= $ 3.60
Then 100 lockers till 999 lockers :
= 6 cents x 900
= $ 54
Then 1, 000 lockers to 1, 999 lockers :
= 8 cents x 1, 000
= $ 80
This gives :
= 0. 18 + 3. 60 + 54 + 80
= $ 137. 78
We are left with 16 cents to reach $ 137. 94 which means that there are 2 more lockers with 4 digits:
= 1, 999 + 2
= 2, 001 lockers
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Help please dont understand
Answers
Answer:
The total area is 72 and A is the correct answer.
Step-by-step explanation:
Here is how they used the formula in A:
60 = 5/6 x A (do 5/6 x A/1 = 5A/6)
60 = \(\frac{5A}{6}\)(multiply both sides of the equation by 6 to get rid of the denominator)
60 x 6 = \(\frac{5A}{6}\) x 6
360 = 5A (divide both sides of the equation by 5)
360 / 5 = 5A/5
72 = A
You want to find the probability, p, that the average of 150 random points independently drawn from the interval (0, 1) is within 0.02 of the midpoint of the interval. Give an estimate for the probability p.
Answers
The estimate for the probability p, that the average of 150 random points drawn from the interval (0, 1) is within 0.02 of the midpoint, is 0.7998.
What is the probability?The standard deviation of the original population.
Since the interval (0, 1) has a range of 1 and a mean of 0.5, the standard deviation can be calculated as:
σ = (b - a) / √12
= (1 - 0) / √12
≈ 0.2887
The standard error of the mean is given by:
SE = σ / √n
= 0.2887 / √150
≈ 0.0236
The probability that the average of the 150 random points falls within 0.02 of the midpoint (0.5) of the interval.
P(0.48 < X < 0.52)
The z-score formula is used to standardize this range:
z = (X - μ) / SE
For the lower bound, z = (0.48 - 0.5) / 0.0236 ≈ -0.8475
For the upper bound, z = (0.52 - 0.5) / 0.0236 ≈ 0.8475
Using a calculator, we can find the cumulative probabilities associated with these z-scores:
P(-0.8475 < Z < 0.8475) ≈ 0.7998
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