Answer:
The correct option is (A).
Step-by-step explanation:
If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.
[tex]\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right][/tex]
Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:
[tex]\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right][/tex]
Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.
Thus, the correct option is (A).
Tamar rides her bike 960 feet in 2 minutes. What is her rate of speed?
Answer:
Rate of speed = 480 feet per minutes
Step-by-step explanation:
Given:
Distance covered by bike = 960 feet
Time taken to covered distance = 2 minutes
Find:
Rate of speed = ?
Computation:
⇒ Speed = Distance / Time
⇒ Rate of speed = Distance covered by bike / Time taken to covered distance
⇒ Rate of speed = 960 / 2
⇒ Rate of speed = 480 feet per minutes
Professional basketball coaches may coach at one of three levels: Assistant, Associate, or Head. It is possible to transition from any of these levels (states) to another. Each of these three states is transient because once someone leaves coaching at any level they never return (at least according to our model). On average, annual salary for head coaches is $104,485, for associates is $62,993, and for assistants is $41,389. Using our P matrix, we have solved to find the fundamental matrix (we have called it the (I-Q) inverse matrix): Assist Assoc Head Assist 6 4 2 Assoc 2 6 6 Head 1 2 10 For someone who is a head coach - what is their expected income for the remainder of their professional coaching career?
Answer:
For someone who is a head coach - their expected income for the remainder of their professional coaching career will be
Expected income = 1×$41,389 + 2×$62,993 + 10×$104,485
Expected income = $1,212,225
Step-by-step explanation:
Professional basketball coaches may coach at one of three levels:
AssistantAssociateHeadOn average, the annual salary is given by
Assistant = $41,389Associate = $62,993Head = $104,485Using our P matrix, we have solved to find the fundamental matrix (we have called it the (I-Q) inverse matrix):
Assistant Associate Head
Assistant 6 4 2
Associate 2 6 6
Head 1 2 10
For someone who is a head coach - what is their expected income for the remainder of their professional coaching career?
As per the given P matrix, for someone who is a head coach will be:
Assistant = 1 time
Associate = 2 times
Head = 10 times
Therefore, the expected income will be,
Expected income = 1×$41,389 + 2×$62,993 + 10×$104,485
Expected income = $1,212,225
g(-4)
Please help!!
Answer:
1
Step-by-step explanation:
g(-4) means what is the y value when x is -4.
Find x=-4, and when x=-4. y=1
Answer:
1
Step-by-step explanation:
Solve for a.
ab + c = d
Answer:
a=(d-c)/d
Step-by-step explanation:
ab+c=d
ab=d-c
a= (d-c)/b
Write an equation of a line that is parallel to the line 3y=-x+6 and passes through the point (6,2).
Answer:
y = x+2
y =-x+2 shows 0
We want to show 1 both sides
2y = x+2 shows 2
y = x+2 shows 0 as explained below.
Step-by-step explanation:
3y−x=6
Solve for y.
y=2+x3
Rewrite in slope-intercept form.
y=13x+2.
Use the slope-intercept form to find the slope and y-intercept.
Slope: 13 y-intercept: 2
Any line can be graphed using two points. Select two
x values, and plug them into the equation to find the corresponding y values.
xy 02, 33
Graph the line using the slope and the y-intercept, or the points.
Slope:
13y-intercept: 2x y (0,2) (3,3)
Write the equation of the line parallel to y+4= 1/4(x+5) and passing through the point (8, 20). Write in the format y = mx + b
Answer:
[tex]y=0.25x+18[/tex]
Step-by-step explanation:
So first we take the equation we are given and write it in slope-intercept form (y = mx + b):
[tex]y+4= \frac{1}{4} (x+5)\\\\y+4=0.25x +1.25\\\\y=0.25x-2.75[/tex]
Now we know parallel lines have the same slope, so the line we are looking for has a slope of 0.25.
so we can start to set up our equation:
[tex]y=0.25x+b[/tex]
and then substitue in the point (8,20) to find the y-intercept.
[tex]20=0.25(8)+b\\20=2+b\\b=18[/tex]
So now we have our equation:
[tex]y=0.25x+18[/tex]
Hope this helps!
5.44 Teaching descriptive statistics: A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam. (a) What are the hypotheses for evaluating if the average test scores are different for the different teaching methods?
Answer:
The null hypothesis is that all the different teaching methods have the same average test scores.
H0: μ1 = μ2 = μ3 = μ4 = μ5
The alternative hypothesis is that at least one of the teaching methods have a different mean.
Ha: at least one mean is different. (μ1 ≠ μi)
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For the case above, let μ represent the average test scores for the teaching methods:
The null hypothesis is that all the different teaching methods have the same average test scores.
H0: μ1 = μ2 = μ3 = μ4 = μ5
The alternative hypothesis is that at least one of the teaching methods have a different mean.
Ha: at least one mean is different. (μ1 ≠ μi)
What else would need to be congruent to show that ABC=DEF by SAS?
Answer:
A
Step-by-step explanation:
Answer:
The answer here is A.
A) A is congruent to D.
A=
Step-by-step explanation:
AP E
It’s a math riddle please help Id appreciate it I need this quickly I’ll give additional points... I’d do need an explanation because the question requires it.
The puzzle are: 21, 30, 15, 333.
PuzzleClock:
Clock time=9 o'clock+9 o'clock+3 o'clock
Clock time=21
Calculator:
Calculator 1=1+2+3+4=10
Calculator 2=1+2+3+4=10
Calculator 3=1+2+3+4=10
Calculator=10+10+10
Calculator=30
Bulb:
The 3 bulb has 5 light each which represent the brightness of the 3 bulb.
Bulb=15+(15-15)
Bulb =15+0
Bulb=15
Fourth puzzle
Clock+Calculator×Bulb
9 o'clock+(1+2+2+4)× [3 bulb(3 bulb×4 light)]
9+9×(3×12)
Apply BODMAS
9+9×36
9+324
=333
Inconclusion the puzzle are: 21, 30, 15, 333.
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Determine the number of ways three trumpet players out of 6 are chosen for 1st chair, 2nd chair, and 3rd chair.
Answer:
120 ways
Step-by-step explanation:
There are 3 spots and 6 options
_ _ _
1 2 3
6 ways for 1st chair to be chosen
5 ways for 2nd chair to be chosen (1st chair is chosen already, so there are 5 players left)
4 ways for 3rd chair to be chosen (1st and 2nd are already chosen, only 4 players left)
Multiply 6*5*4 to find the total number of ways (120)
Please answer this correctly
Answer:
10 people
Step-by-step explanation:
Count the x's for more than 1 scarf, which is 2 or 3 scarfs
2 = 9
3 =1
total = 10
Using the data in the table, use the exponential smoothing method with alpha=0.5 and a February forecast of 500 to forecast
sales for May
Month Demand
January 480
February 520
March 535
April 550
May 590
June 630
Answer:
Step-by-step explanation:
The formula to calculate the forecast could be determine by using the exponential smoothing method :
[tex]Ft = F(t-1) + \alpha [A(t-1) - F(t-1)][/tex]
Where ,Ft is the Forecast for period t
F(t-1) is the Forecast for the period previous to t
A(t-1) is the Actual demand for the period previous to t
[tex]\alpha[/tex] = Smoothing constant
To get the forecast for may and june the above formula with [tex]\alpha =0.5[/tex] and april forecast of 500 will be used
For march
[tex]=500+0.5(520-500)\\\\=500+0.5\times20\\\\=500+10\\\\=510[/tex]
For April
[tex]=510+0.5(535-510)\\\\=510+0.5\times25\\\\=510+12.5\\\\=522.5[/tex]
For May
[tex]=522.5+0.5(550-5225)\\\\=522.5+0.5\times27.5\\\\=522.5+13.75\\\\=536.25[/tex]
So forecast for May = 536.25
What’s the correct answer for this question?
Answer:
B:
Step-by-step explanation:
Measure of ARC AFB is 180°
Why?
This is because AB is a diameter.
need answers to 34 35 and 36
Answer:
34) 75
35) 60
36) 210
Step-by-step explanation:
34) Area of a rectangle:
L x B
= 15 x 5
= 75
35) Area of a trapezium :
½ h (sum of || sides)
= ½ x 6 x (12+8)
= 3 x 20
= 60
36) Area of a regular hexagon:
3BH
= 3 x 7 x 10
210
Hope it helps....
Answer:
Step-by-step explanation:
35. 75
area of rectangle : A = b x h
= 15 X 5
= 75
36. 60
area of trapezoid : A = (b1 + b2) x h
2
= (8+12) x 6
2
= 60
37. 210
area of regular polygon : A = P x a (P no. of sides) (a is apothem)
2
= (6 x 10) x 7
2
= 210
Find the value of x.
Answer:
Step-by-step explanation:
so there’s 25 and 25 it’s kinda like counting money divide it into 4 pieces 25 , 50 , 75 , 100
Answer:
The answer would be x=3
Step-by-step explanation:
Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication a at what time will you need to stop the infusion
Answer:
6 PM
Step-by-step explanation:
125 mg --- 300 mL
500 mg --- x mL
x = 500*300/125 = 1200 mL solution contains 500 mg
rate = 100 mL/h
1200 mL* 1h/100 mL = 12 h
6AM + 12 h = 6 PM
You need to stop infusion at 6 PM
It is found that You need to stop infusion at 6 PM.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication.
125 mg = 300 mL
500 mg = x mL
x = 500*300/125
x = 1200 mL
Here solution contains 500 mg
The rate = 100 mL/h
1200 mL* 1h/100 mL = 12 h
6AM + 12 h = 6 PM
Therefore, You need to stop infusion at 6 PM.
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Which table represents a linear function?
Answer:
Top right option
Step-by-step explanation:
work out the weekly mean number of 50 kg bags of flour used in these 5 weeks
Kim is a baker, she buys flour in 50kg bags.
weeks 1 2 3 4
NO of bags of flour 7 14 8 13
Kim will make 2400 loaves in week 5
Each of these loaves will need 250g of lour
Kim works out weekly mean number of 50kg bags of flour used in these 5 weeks.
she will use the figure for future orders.
Answer:
Weekly Mean Number of 50-kg bags =10.8 bags
Step-by-step explanation:
In Week 1, Kim uses 7 50kg bags of flour
In Week 2, Kim uses 14 50kg bags of flour
In Week 3, Kim uses 8 X 50kg bags of flour
In Week 4, Kim uses 13 X 50kg bags of flour
In Week 5, Kim will make 2400 loaves.
Each of these loaves will need 250g of flour.
Total Mass of flour that will be used =2400 X 250=600,000 grams
[tex]600,000$ grams=600,000 \div 1000$ kg =600kg\\Number of 50-kg bags =600 \div$ 50 =12 bags[/tex]
In Week 5, Kim will use 12 bags.
Therefore:
Weekly Mean number of 50kg bags of flour used in these 5 weeks.
[tex]=\dfrac{7+14+8+13+12}{5}\\\\ =\dfrac{54}{5}\\\\=10.8 \\ \approx 11$ bags[/tex]
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
Volume of cylinder = πr²h
= (3.14)(4)(0.75)
= 9.4
Since she'll fill it half so
Amount of water to be filled = 4.7
Q5. Calculate the median value of this data set. 24 -8 -17 32 -1 -28
Answer:
The median value in this set is -4.5
Step-by-step explanation:
Reorder the numbers from least to greatest
-28,-17,-8,-1,24,32
Then, since there is 6 digits in this data set there is no defined median value. In the numbers 1 to 8 there are 8 different numbers, the middle of 1 to 8 is 4.5. Then since were using the numbers -8,-1 the middle is -4.5
Which of the following expressions shows the correct amount of sales tax for the computer at Store A? Select all that apply. 6%($1,200) 0.6($1,200) 0.06($1,200) 1/6($1,200) 3/50($1,200)
Answer:
1, 3,5
Step-by-step explanation:
Answer:
1,3,5
Step-by-step explanation:
TIMED PLEASE HELP When f = 2 and g = 8, n = 4. If n varies jointly with f and g, what is the constant of variation?
1/4
1/2
4
64
The Answer is 1/4
Step-by-step explanation:
The required constant of variation for given data is k = 1/4
The correct option is (a)
What is constant of variation?In a direct variation, the product of two variables; in an inverse variation, the ratio of two variables, is called constant of variation
Formula:
k = [tex]\frac{n}{fg}[/tex]
How calculate constant of variation?Here we have given that n = 4, f = 2 and g = 8
Substitute the given values into above formula
k = [tex]\frac{4}{2(8)} =\frac{1}{4}[/tex]
The required constant of variation is 1/4
Therefore the correct option is (a)
This is the conclusion to the answer.
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What’s the correct answer for this question?
Answer:
107 meters
Step-by-step explanation:
Central angle = 123°
In radians
123° = 123π/180
123° = 2.147 radians
Putting in formula
S = r∅
S = (50)(2.147)
S = 107 meters
"The chance that a person selected at random has blue eyes is 16%. Two people are chosen at random (and are independent of each other). Find the probability at least one of them does not have blue eyes. Round your answer to 4 decimal places."
Answer:
[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]
And replacing we got:
[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=2, p=1-0.16=0.84)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we can find this probability:
[tex] P(X \geq 1)[/tex]
And we can solve this probability like this:
[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)[/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]
And replacing we got:
[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]
A fast food hamburger restaurant uses 3,500 lbs. of hamburger each week. The manager of the restaurant wants to ensure that the meat is always fresh i.e. the meat should be no more than two days old on average when used. How much hamburger should be kept in the refrigerator as inventory
Answer:
The peak inventory will be 2 sales days of hamburguers, which is equivalent to 7,000 lbs. As they are consumed in 2 days, the average inventory is 3,500 lbs.
Step-by-step explanation:
If the meat should be no more than two days old on average when used, the stock of hamburguer in the refrigerator has to be at most the equivalent to 2 day of sales.
The "2 days old" represents the inventory turnover.
If we use all the hamburguers in the refrigerator and refill inmediatly, the average inventory is:
[tex]\bar I=\dfrac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\\\\\\bar I=\dfrac{2*3,500+0}{2}=3,500[/tex]
The peak inventory will be 2 sales days of hamburguers, which is equivalent to 7,000 lbs. As they are consumed in 2 days, the average inventory is 3,500 lbs.
For a particular diamond mine, 78% of the diamonds fail to qualify as "gemstone grade". A random sample of 106 diamonds is analyzed. Find the mean μ.
Answer:
Mean of the binomial distribution μ = 82.68
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 106 diamonds
The probability that the diamonds fail to qualify as "gemstone grade
p = 78% =0.78
We will use binomial distribution
Mean of the binomial distribution
μ = n p
μ = 106 × 0.78
μ = 82.68
conclusion:-
Mean of the binomial distribution μ = 82.68
Tyson’s puppy weighed 8 pounds 3 ounces last year.
In one year the puppy gained 2 pounds 4 ounces.
How much does Tyson’s puppy weigh now in ounces?
Last year- 8 lbs 3 ounces
Add 2 lbs and 4 ounces
Which is 10 lbs 7 ounces
10 lbs in onces is 160 ounces
Then you add the other 7 ounces so the final answer is 167 ounces
Tyson’s puppy weighs 167 ounces!
Good luck please mark me as braniliest!!!!!!
A plane intersects the prism perpendicular to the base, intersecting opposite sides of the base. Which best describes the cross section?
Answer:
Step-by-step explanation:
For a rectangular prism, a plane intersecting this prism produces a two dimensional figure as its cross section and in this case the cross section is a rectangle.
For a triangular prism, a plane intersecting this prism produces a two dimensional figure as its cross section and in this case the cross section is a triangle.
A tank contains 60 kg of salt and 1000 L of water. A solution of a concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min. The solution is mixed and drains from the tank at the same rate. Let y be the number of kg of salt in the tank after t minutes. Write the differential equation for this situation
Answer:
[tex]\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg[/tex]
Step-by-step explanation:
Volume of water in the tank = 1000 L
Let y(t) denote the amount of salt in the tank at any time t.
Initially, the tank contains 60 kg of salt, therefore:
y(0)=60 kg
Rate In
A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.
[tex]R_{in}[/tex] =(concentration of salt in inflow)(input rate of solution)
[tex]=(0.03\frac{kg}{liter})( 9\frac{liter}{min})=0.27\frac{kg}{min}[/tex]
Rate Out
The solution is mixed and drains from the tank at the same rate.
Concentration, [tex]C(t)=\dfrac{Amount}{Volume} =\dfrac{y(t)}{1000}[/tex]
[tex]R_{out}[/tex] =(concentration of salt in outflow)(output rate of solution)
[tex]=\dfrac{y(t)}{1000}* 9\dfrac{liter}{min}=0.009y(t)\dfrac{kg}{min}[/tex]
Therefore, the differential equation for the amount of Salt in the Tank at any time t:
[tex]\dfrac{dy}{dt}=R_{in}-R_{out}\\\\\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg[/tex]
The radius of a circle is 2.6 in. Find the circumference
to the nearest tenth.
Answer:
16.
Step-by-step explanation:
since given the radius and the formula of the circumference of a circle is 2pie*r
