The area under the curve between the mean and a z-score
P (Z > - 1.80) - P (Z < - 0.3)1 - P (Z < - 1.80) - P (Z < - 0.3)1 - 0.0359 - 0.3821 = 0.582 = 58.2%What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
1. z = (x[tex]- \mu) /\sigma[/tex]
z= (52350 - 46292)/ 4320
z = 1.40
P(X> 52350 )= P( z> 1.40) = P(z< -1.40)
P(Z>1.40) = 0.0808, which is 8.08%
2. Now, z = (x[tex]- \mu) /\sigma[/tex]
z= (45000- 46292)/ 4320
z = -0.30
and, z = (x[tex]- \mu) /\sigma[/tex]
z= (52350 - 46292)/ 4320
z = 1.40
Then, you must find the area between Z = -0.30 and Z = 1.40
So, P(Z<1.40) - P(Z < - 0.30)
= P(Z > - 1.40) - P(Z < - 0.30)
= 1 - P(Z< -1.40) - P( Z < -0.30)
The area under the curve to the left= 1 - 0.0808 - 0.3821 = 0.5371
3. z = (x[tex]- \mu) /\sigma[/tex]
z= (38500- 46292)/ 4320
z = -1.8
Thus, the area under the curve to the right of Z = - 1.80 and to the left of Z = - 0.3
P (Z > - 1.80) - P (Z < - 0.3)1 - P (Z < - 1.80) - P (Z < - 0.3)1 - 0.0359 - 0.3821 = 0.582 = 58.2%Learn more about Probability here:
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evaluate the integral using integration by parts with the indicated choices of u and dv. (use c for the constant of integration.) xe5x dx; u
Answer:
[tex]\displaystyle \int {xe^{5x}} \, dx=\frac{1}{5}xe^{5x}-\frac{1}{25}e^{5x}+C[/tex]
Step-by-step explanation:
Given Problem
[tex]\displaystyle \int {xe^{5x}} \, dx[/tex]
Make substitutions for IBP
Let [tex]u=x,\,du=dx[/tex] and [tex]v=\frac{1}{5}e^{5x},\,dv=e^{5x}dx[/tex]
Perform IBP
[tex]\displaystyle \int {u} \,dv=uv-\int {v} \, du\\\\\int {xe^{5x}} \, dx=\frac{1}{5}xe^{5x} -\int {\frac{1}{5}e^{5x}} \, dx\\\\\displaystyle \int {xe^{5x}} \, dx=\frac{1}{5}xe^{5x}-\frac{1}{25}e^{5x}+C[/tex]
Find f-1(x) and it’s domain.
For given function f(x) = √x + 9, the inverse function and domain are respectively, f⁻¹(x) = (y - 9)², x ≥ 0 & x ∈ (∞, ∞)
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Given that,
A function,
⇒ f(x) = √x + 9
f⁻¹(x) = ?
the given function is defined for all the values of x,
So domain of the function is real number,
x ∈ (∞, ∞)
Now for f⁻¹(x),
Suppose, f(x) = y
y = √x + 9
y - 9 = √x
squaring both the sides,
(y - 9)² = (√x)²
x = (y - 9)²
And value of x should be greater than zero
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A business office orders paper supplies from one of three vendors, V1, V2, or V3. Orders are to be placed on two successive days, one order per day. Thus, V2V3 might denote that vendor V2 gets the order on the first day and vendor V3 gets the order on the second day. (a) List the sample points in this experiment of ordering paper on two successive days. (Enter your answer in set notation.) (b) Assume the vendors are selected at random each day. What is the probability of each sample point? (Enter your probability as a fraction.) the event that V2 gets at least one order. Find P(A), P(B), P(AUB), and P(ANB) by summing the probabilities of the sample points in these events. (Enter your (c) Let A denote the event that the same vendor gets both orders and probabilities as fractions.) P(A) = P(B) = P(AUB) - P(ANB) =
As a fraction, the probability of each sample point is 8/9.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms.
Here,
(a) The sample points in this experiment are:
V1V1, V1V2, V1V3, V2V1, V2V2, V2V3, V3V1, V3V2, V3V3
(b) Since the vendors are selected at random each day, each sample point has the same probability of occurrence. There are a total of 3 * 3 = 9 possible sample points, so each sample point has a probability of 1/9.
(c) Let A denote the event that the same vendor gets both orders, and let B denote the event that V2 gets at least one order.
P(A) is the probability that the same vendor gets both orders, so it is the sum of the probabilities of the sample points V1V1, V2V2, and V3V3. P(A) = 1/9 + 1/9 + 1/9 = 3/9.
P(B) is the probability that V2 gets at least one order, so it is the sum of the probabilities of the sample points V2V1, V2V2, and V2V3. P(B) = 1/9 + 1/9 + 1/9 = 3/9.
P(AUB) is the probability of either A or B occurring, so it is the sum of the probabilities of all 9 sample points. P(AUB) = 9/9 = 1.
P(ANB) is the probability of both A and B occurring, so it is the sum of the probabilities of the sample points V2V2. P(ANB) = 1/9.
So, P(AUB) - P(ANB) = 1 - 1/9 = 8/9.
The probability of each sample point as a fraction is 8/9.
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USE STRUCTURE Explain how you can use Theorem 7.11 to construct a parallelogram by dragging the steps into the correct order. Then construct a parallelogram on a separate sheet of paper using your method.
1. The diagonals bisect each other.
2. The diagonals of parallelogram are perpendicular and equal to each other.
What is Parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
Given:
Using the theorem a quadrilateral whose diagonal bisect each other is a parallelogram.
Then, the diagonals bisect each other then the quadrilateral is a parallelogram.
As, the diagonals of parallelogram are perpendicular and equal to each other then , the parallelogram is a square.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are
x² + (y - 3)² = 36 and x² + (y + 8)² = 36
What is circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
Given equations
⇒ x² + (y - 3)² = 36
comparing with general equation of circle
( x - h )² + ( y - k )² = r²
Center (h , k) = (0 , 3)
Center is on y - axis
Radius r = √36 = 6units
Diameter = 2r = 2×6 = 12units
⇒ x² + (y - 5)² = 6
comparing with general equation of circle
( x - h )² + ( y - k )² = r²
Center (h , k) = (0 , 5)
Center is on y-axis
Radius r = √6 units
Diameter = 2r = 2√6 units
⇒ (x – 4)² + y² = 36
comparing with general equation of circle
( x - h )² + ( y - k )² = r²
Center (h , k) = (4 , 0)
Center is on x-axis
Radius r = √36 = 6units
Diameter = 2r = 2×6 = 12units
⇒ (x + 6)² + y² = 144
comparing with general equation of circle
( x - h )² + ( y - k )² = r²
Center (h , k) = (-6 , 0)
center is on x-axis
Radius r = √144 = 16units
Diameter = 2r = 2×16 = 32units
⇒ x² + (y + 8)² = 36
comparing with general equation of circle
( x - h )² + ( y - k )² = r²
Center (h , k) = (0 , -8)
Center is on y-axis.
Radius r = √36 = 6units
Diameter = 2r = 2×6 = 12units
Hence, equation x² + (y - 3)² = 36 and x² + (y + 8)² = 36 represents the circle with diameter 12 units and a center that lies on y-axis.
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After graduating from college, Carlos receives two different job offers. Both pay a starting salary of $66000 per year, but one job promises a $3300 raise per year, while the other guarantees a 4% raise each year.
Complete the tables below to determine what his salary will be after t years.
Round your answers to the nearest dollar.
t
t
years 1 5 10 15 20
Salary with $3300 raise per year
t
t
years 1 5 10 15 20
Salary with 4% raise per year
Answer:
Salary with $3300 raise per year:
t (years) Salary
1 $69300
5 $82600
10 $95900
15 $1092000
20 $1225000
Salary with 4% raise per year:
t (years) Salary
1 $68640
5 $83833
10 $102219
15 $124869
20 $152947
Note: The calculations for the 4% raise are done as follows:
Year 1: 66000 * 1.04 = $68640
Year 5: 66000 * 1.04^5 = $83833
Year 10: 66000 * 1.04^10 = $102219
Year 15: 66000 * 1.04^15 = $124869
Year 20: 66000 * 1.04^20 = $152947
Step-by-step explanation:
Find the perimeter of the triangle whose vertices are (−3,−5)
, (5,−5)
, and (5,1)
. Write the exact answer. Do not round.
For the use of a test for a certain disease, the sensitivity is 0.92, the specificity is 0.93, and the prevalence is 0.01. a. Given that a test is positive, find the probability that a random patient has the disease. b. Draw a tree diagram for a typical sample of patients. c. Of the cases that are positive, explain why the proportion in error is larger if the prevalence is lower.
Step-by-step explanation:
a. Given a positive test result, the probability that a random patient has the disease is called the positive predictive value (PPV). The PPV can be calculated using the following formula:
PPV = Sensitivity * Prevalence / (Sensitivity * Prevalence + (1 - Specificity) * (1 - Prevalence))
Plugging in the values given in the question, we get:
PPV = 0.92 * 0.01 / (0.92 * 0.01 + (1 - 0.93) * (1 - 0.01)) = 0.087
So, the probability that a random patient has the disease given a positive test result is 0.087 or 8.7%.
b. A tree diagram for a typical sample of patients with a positive test result would look something like this:
+-----------+-----------------+
| Test Result| Positive (TP + FP) |
+-----------+-----------------+
| | TP (Disease) |
| | 0.92 * 0.01 |
| | FP (No Disease)|
| | 0.08 * 0.99 |
+-----------+-----------------+
c. If the prevalence is lower, the proportion of positive test results due to false positives (FP) increases compared to true positives (TP). This is because the positive predictive value (PPV) decreases as the prevalence decreases, meaning that a larger proportion of positive test results are due to false positives. This is why the proportion in error is larger if the prevalence is lower.
100%
At 11:00 A.M. the temperature was 37 °F. At 11:00 P.M. the temperature was -6 °F.
What was the change in temperature between 11:00 A.M. and 11:00 P.M.?
A. 6°F
OB. 31 °F
C. 37 °F
OD. 43 °F
The change in temperature between 11.00am and 11.00pm would be = 43°F. That is option D.
What is temperature?Temperature is defined as the scalar quantity that shows or measure the degree of hotness or coldness of a medium.
The temperature of a medium at 11.00am = 37°F
The temperature of a medium at 11.00 pm = -6°F
The difference between the both given temperature = 37-(-6) = 37+6 = 43°F.
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3. Write the expression as a simplified rational expression. Show your work.
Answer:
5/1/6+ 1/X + 1
Answer:
(1/x)+31
Step-by-step explanation:
To simplify the expression
5/(1/6) + 1/X + 1,
we need to first simplify the fraction 5/(1/6):
5/(1/6) = 5 * 6/1 = 30
Now we can substitute this value back into the expression:
30 + 1/X + 1
To combine the last two terms, we need to find a common denominator, which is X:
30X/X + 1/X + X/X
Simplifying the numerator:
30X + 1 + X
Combining like terms:31X + 1
so the simplified rational expression is (1/x)+31
Plsss can you give me all th fractions of percentages but I don’t want something like 20/100 plsss give me fractions like 1/2=50 and I almost forgot when you give me the fractions plss also give me the percentages
Answer:
Here are some fractions and equivalent percentages.
1/4 = 1/4 x 100 = 25%
1/8 = 1/8 x 100 = 12.5$
3/8 = 3/8 x 100 = 300/8 = 37.5%
3/4 = 3/4 x 100 = 75%
1/3 = 1/3 x 100 = 33.33% (rounded to 2 decimal places)
54% = 54/100 = 27/50
Here are some percentages and equivalent fractions:
54% = 54/100 = 27/50
36% = 36/100
45% = 9/20
20% = 1/5
30% = 3/10
Step-by-step explanation:
To convert a fraction to a percentage, multiply by 100
To convert a percentage to a fraction, divide by 100 and reduce to lowest fractional form
Examples:
1/4 = 1/4 x 100 = 25%
1/8 = 1/8 x 100 = 12.5$
3/8 = 3/8 x 100 = 300/8 = 37.5$
3/4 = 3/4 x 100 = 75%
1/3 = 1/3 x 100 = 33.33% (rounded to 2 decimal places)
Similarly,
54% = 54/100 = 27/50
36% = 36/100
dividing by 4 both numerator and denominator gives
36% = 36/100 = 9/20
45% = 45/100 = 9/20 (divide by 5)
20% = 20/100 = 1/5
Estimate the local maximum of y=2x3+x2−7x−6.
Answer: (-1.25, 0.41)
Step-by-step explanation:
What is the surface area?
29 in
36 in
5 in
square inches
Answer:
The surface area of a rectangular prism can be calculated by adding the area of each of its six faces. The formula for the surface area of a rectangular prism with length l, width w, and height h is:
Surface Area = 2lw + 2lh + 2wh
So for a rectangular prism with length 29 inches, width 36 inches, and height 5 inches, the surface area can be calculated as follows:
Surface Area = 2 * 29 * 36 + 2 * 29 * 5 + 2 * 36 * 5
= 2,612 + 290 + 360
= 3,262 square inches
Therefore, the surface area of the rectangular prism is 3,262 square inches.
What is the surface area? 23 yd 23 yd 23 yd square yards
Based on the information, it can be inferred that the area of a surface with sides 23 yards and base 23 yards is 529 square yards.
How to calculate the surface area of this figure?To calculate the surface area of this figure we must perform the following procedure:
We know the side and the base of this figure measure 23 yards, so we must apply the following formula.
Area = side * baseArea = 23 yards * 23 yardsArea = 539 square yardsSo we can infer that the area of this surface would be 534 square yards.
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2000 Paul was twice as old as his brother Biko. In 2008 Paul was only four years older than his brother. In what year was Biko born ? Select one: a. 1996 b. 1990 c. 1992 d. 1998 e. 2000
Answer:
a. 1996
Step-by-step explanation:
Let Paul's age in 2000 be P
Let Bilko's age in 2000 be B
Statement: Paul was twice as old as his brother Biko in 2000 means
P = 2B (1)
In 2008 Paul was only four years older than his brother.
Since 2008 is 8 years from 2000, both Paul and Bilko have aged 8 years
Paul's age in 2008 = P + 8
Bilko's age in 2008 = B + 8
Statement: In 2008 Paul was only four years older than his brother means
P + 8 = B + 8 - 4
P = B + 4 (2)
Given these two equations (1) and (2)
Substitute P = 2B from (1) in (2):
2B = B + 4
==> 2B - B = 4
==> B = 4
Therefore in 2000, Paul was 8 years old and Bilko was 4 years old
Bilko's year of birth = 2000 - 4 = 1996
After biking 5/12 miles, Jada has traveled 2/3 of the length of her trip. How long (in miles) is the entire length of her trip? Write an equation to represent the situation, and find the answer using your preferred strategy.
The entire length of the trip is 9/12 miles.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
After biking 5/12 miles,
Jada has traveled 2/3 of the length of her trip.
Let x be the entire length of the trip.
The equation is,
x = 1/3 + 2/3
x = 1/3 + 5/12
x = 9/12
Therefore, the distance is 9/12 miles.
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If y varies directly as x, and y=6 when x=15, find y when x=2.
A.) 4/5
B.) 4
C.) 5
d.) 5/4
Answer:
Option A: 4/5
Step-by-step explanation:
If y varies directly as x written as y ∝ x, this can be written as an equation:
y = kx where k is a constant
Since y = 6 when x = 15:
6 =k · 15
6 = 15k
15k = 6
k = 6/15 = 2/5
The equation beocmes
y = (2/5) x
Therefore when x = 2,
y = (2/5) x 2 = 4/5
Option A: 4/5
A swimming pool has 500 gallons in it and is leaking. The change in the amount of water in the pool is -3 gallons per hour. How many gallons would the pool contain after 6 hours?
Amount of gallons of water after 6 hours is 482 gallons.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given that,
Initial volume of the swimming pool = 500 gallons
The change in the amount of water in the pool is -3 gallons per hour.
Each hour, the volume of the pool is decreasing by -3 gallons.
Change in the amount of water in 1 hour = -3 gallons
Change in the amount of water in 6 hours = -3 × 6 = -18 gallons
After 6 hours,
Volume of the pool = 500 - 18 = 482 gallons
Hence there will be a volume of 482 gallons of water after 6 hours.
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Taylor invested PhP 100,000 at a rate of 5.8%. If the rate is compounded yearly, how much investment should she have after 3.5 years?
What is the Formula for mean of sample distribution sample proportions
For large samples, the sample proportion is approximately normally distributed, with mean μˆP=p. and standard deviation σˆP=√pqn
Taken from stats.libretexts.org btw^^
Please helppp i really need it noww!!!
Graph the numbers that are solutions to both x + 1 < 9 and 4x ≤ 8 .
Answer:
It is graphed in the picture.
Step-by-step explanation:
Answer:
See the attached graph
Step-by-step explanation:
Take each inequality and isolate x for each
x+1 < 9
==> x + 1 - 1 < 9 -1 add 1 both sides
==> x < 8
4x ≤ 8
==> 4x/4 ≤ 8/4 divide by 4 both sides
==> x ≤ 2
So we have two inequalities to satisfy
To graph,
Graph each inequality separatelyChoose a test point to determine which side of the line is to be shaded or simply use a graphing calculator to automatically shadeThe solution to the system of equations is the area where the two shadings overlap i.e. values which satisfy both inequalitiesTo graph the first inequality, draw a vertical line at x = 9 parallel to the y-axis. This line should be dotted to show it is a < inequality. Everything to the left of this line satisfies x < 8
To graph the second inequality, x ≤ 2, draw a vertical line at x = 2 parallel to the y-axis. This line should be solid to show it is a ≤ inequality. Everything to the left of this line satisfies x ≤ 2
The common points for both lines are shown in dark purple in the graph where the two shaded areas overlap
If you just wanted it on the number line that would be the second image
Mimi had 8,630 blueberries. She baked 22 pies using an equal number of blueberries in each pie. How many blueberries did Mimi use in each pie.
392
8630 divided by 22. = 392.272727... cant be decimal so round down
100 POINTS WILL PLEASEEEEEE HELP
Answer:
The $30,000 in revenue should be entered as a credit in the journal entry.
Step-by-step explanation:
In accounting, revenues are recorded as credits, which means that they increase the credit side of the accounting equation (revenues increase equity, which is a credit account). Debits, on the other hand, are used to record expenses and decreases in assets.Therefore, the journal entry to record $30,000 in revenue for the business on October 1 would be:Date
Account Account Number Debit Credit
1 - Oct Revenue 4050 30,000Since revenue is being credited, there is no debit amount entered in this entry. The credit amount of $30,000 is entered in the credit column, as shown above.
Accounting ◆ QUESTION: 2 The information below relates to Winelands Ltd for the year ended 28 February 2021.The company was registered with an authorised share capital of 1 000 000 shares. 600 000 of these shares were in issue on 1 March 2020, the beginning of the current financial year. 13 NSC Grade: 12 (TERM: 1) COMPANIES LEDGER ACCOUNTS REQUIRED: 2.1. Prepare the following accounts in the General Ledger. - Ordinary share capital >> Retained income NOTE: Close off all these accounts correctly at the end of the year. INFORMATION: A. Balances in the ledger on: Ordinary share capital Retained income Shares 28 February 2021 R ? 28 February 2020 R 2 100 000 737 100 - On 31 August 2020 all the unissued shares were issued at 500 cents per share. On 30 November 2020 the directors repurchased 120 000 shares at 620 cents per share from a retired shareholder. This shareholder originally purchased his shares on the JSE at various times and at different prices over the past years.
Showing this information in a ledger is given below":
The Ledger AccountOrdinary Share Capital:
28 February 2021: 1,000,000 authorized shares * 500 cents per share (for the shares issued on 31 August 2020) = R500,000
28 February 2020: 600,000 issued shares * R35 (2,100,000 / 60) = R21,000
Retained Income:
28 February 2021: R500,000 (Ordinary Share Capital) - R21,000 (Ordinary Share Capital) + R120,000 (repurchased shares at 620 cents per share) = R599,000
28 February 2020: R737,100 (Retained Income)
Note: The R35 per share in 28 February 2020 was calculated by dividing the total ordinary share capital of R2,100,000 by the number of shares in issue (600,000).
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a = [1 0 -4 0 3 -2 -2 6 3] b = [4 1 -4] Denote the columns of A by a1, a2, a3, and let W = Span {a1, a2, a3,}. is b in {a1, a2, a3,}? how many vectors are in {a1, a2, a3,}? is b in W? How many vectors are in W? Show that a1 is in W.[ hint: row operations are unneceassary.]
a. there are three vectors in {a₁, a₂, a₃}.
b. There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.
c. we have that a₁ is in the W.
What is matrix?A matrix is a set of integers arranged in rows and columns. The rows and columns of integers are arranged in a rectangular matrix. The matrix A, for instance, contains two rows and three columns. The elements of the matrix, also known as the entries, are the integers. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics.
a. The vector b is not in {a₁ ,a₂, a₃} since b is not equal to any of the column vectors of A. Clearly, there are three vectors in {a₁, a₂, a₃}.
b. Vector b is in W if the augmented matrix [a₁, a₂, a₃ b] is consistent.
The augmented matrix is:
[tex]\left[\begin{array}{cccc}1&0&-4&4\\0&3&-2&1\\-2&6&3&-4\end{array}\right] \sim \left[\begin{array}{cccc}1&0&-4&4\\0&3&-2&1\\0&6&-5&4\end{array}\right] \sim \left[\begin{array}{cccc}1&0&-4&4\\0&3&-2&1\\0&6&-1&2\end{array}\right][/tex]
Thus, since the system is consistent we have that b must be in W.
There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.
c. since [tex]\left[\begin{array}{c}1\\0\\-2\end{array}\right] = 1. \left[\begin{array}{c}1\\0\\-2\end{array}\right] + 0. \left[\begin{array}{c}1\\0\\-2\end{array}\right] + 0. \left[\begin{array}{c}1\\0\\-2\end{array}\right][/tex] we have that a₁ is in the W.
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a. there are three vectors in {a₁, a₂, a₃}.
b. There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.
c. we have that a₁ is in the W.
What is matrix?A matrix is a set of integers arranged in rows and columns. The rows and columns of integers are arranged in a rectangular matrix. The matrix A, for instance, contains two rows and three columns. The elements of the matrix, also known as the entries, are the integers. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics.
a. The vector b is not in {a₁ ,a₂, a₃} since b is not equal to any of the column vectors of A. Clearly, there are three vectors in {a₁, a₂, a₃}.
b. Vector b is in W if the augmented matrix [a₁, a₂, a₃ b] is consistent.
No, b is not in {a1, a2, a3}.
There are 3 vectors in {a1, a2, a3}.
Yes, b is in W.
There are infinitely many vectors in W.
Yes, a1 is in W because it can be expressed as a linear combination of the vectors in W. This is shown by the equation a1 = 1(a1) + 0(a2) + 0(a3). The coefficients of the vectors in the linear combination are all integers and this equation shows that a1 is in the span of the vectors in W.
Thus, since the system is consistent we have that b must be in W.
There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.
c. since we have that a₁ is in the W.
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Here is a data set: 27 39 14 36 43 20 29 27 47 38 13 24 24 23 17 29 37 26 20 33 16 41 27 17 12 24 14 17 24 20 You are examining the data with a stem-and-leaf plot. Here is the start of the plot. Finish the plot.
Answer:
Stem | Leaf
-----|-----
1 | 2 7 7 2 4
2 | 9 8 7 6 3 0 9 7
3 | 7 6 4 3 1 7
4 | 3 6
-----|-----
Step-by-step explanation:
To create a stem-and-leaf plot, we first divide each data point into two parts: the stem, which is the first digit or digits, and the leaf, which is the final digit or digits.
For this data set, the stem for each data point would be the tens digit, and the leaf would be the units digit.
Here's how the plot would look like:
Stem | Leaf
-----|-----
1 | 2 7 7 2 4
2 | 9 8 7 6 3 0 9 7
3 | 7 6 4 3 1 7
4 | 3 6
-----|-----
Note that the stems are listed in increasing order, and the leaves for each stem are listed in order within that stem. This helps to give an overall sense of the distribution of the data, such as the range and the concentration of data points in certain regions.
Kelsey’s neighborhood has a straight road with stop signs at both ends and a fire hydrant at its midpoint. On a map, the fire hydrant is located at (12,7) and one of the stop signs is located at (3,11). Where on the map is the other stop sign located?
The coordinate of the other stop sign located will be (21, 3).
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
Kelsey’s neighborhood has a straight road with stop signs at both ends and a fire hydrant at its midpoint. On a map, the fire hydrant is located at (12,7) and one of the stop signs is located at (3,11).
Then the coordinate of the other stop sign located is given as,
(12, 7) = [(x₁ + 3) / 2, (y₁ + 11) / 2]
(24, 14) = [x₁ + 3, y₁ + 11)
(21, 3) = (x₁, y₁)
(x₁, y₁) = (21, 3)
The coordinate of the other stop sign located will be (21, 3).
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Find the length of side x.
Give your answer to 1 decimal place.
13 cm
98°
X
17 cm
[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ x = \sqrt{13^2+17^2~-~2(13)(17)\cos(98^o)} \implies x = \sqrt{ 458 - 442 \cos(98^o) } \\\\\\ x\approx\sqrt{519.51}\implies x\approx 22.8[/tex]
Make sure your calculator is in Degree mode.
I need help with this question
Answer:
684π
Step-by-step explanation:
It is two parts: half of a sphere and one cylinder.
Sphere volume formula: V=4/3πR³, r=12/2=6, r³=216
v=4/3π216
v=288π
Half of sphere: 288π/2=144π
Cylinder volume: V=πr²h, r=12/2=6, r²=36, h=15,
V=π*36*15=540π
So, total is 144π+540π=684π
consider the matrix below. are the column vectors of this matrix linearly independent or linearly dependent? show all explanations or computations.| 1 0 5 || -2 1 -6 || 0 2 8 |
The column vectors of this matrix are linearly independent, meaning they are not dependent upon one another, and the determinant is not equal to 0.
The given matrix is:
| 1 0 5 |
| -2 1 -6 |
| 0 2 8 |
We must compute the matrix's determinant in order to determine if the matrix's column vectors are linearly independent or linearly dependent.
A scalar value that can be used to assess linear dependency or independence is the determinant of a matrix.
The determinant of the matrix is:
det(A) = 1(-68) - 0(18) + 5(-2*2) = -6 + 0 - 20 = -26
Since The column vectors of this matrix are linearly independent, meaning they are not dependent upon one another, and the determinant is not equal to 0.
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