find factors of 5x^3+10x^2+35x
Find a basis for the row space and column space of a matrix and the rank .
Final answer:
To identify a basis for the row and column spaces of a matrix and determine its rank, one uses row reduction to reach REF or RREF. The non-zero rows of the RREF are the basis for the row space, the corresponding columns in the original matrix form the basis for the column space, and the rank is the number of these basis vectors. In statistics, the degrees of freedom for the Test of Independence is calculated as (number of columns - 1)(number of rows - 1).
Explanation:
To find a basis for the row space and column space of a matrix as well as the rank, you follow specific procedures. First, perform row reduction on the matrix to bring it to row echelon form (REF) or reduced row echelon form (RREF). The non-zero rows of the RREF correspond to a basis for the row space. The columns in the original matrix that correspond to the leading 1s in the RREF form a basis for the column space. The rank of the matrix is equal to the number of leading 1s in the RREF form, which is also the number of basis vectors for either the row space or column space since they have the same dimension.
The Test of Independence in statistics uses a contingency table to determine if two categorical variables are independent. The number of degrees of freedom for the test is given by the formula: (number of columns - 1)(number of rows - 1). This is critical when referencing the chi-squared distribution table to determine the p-value for the hypothesis test.
what is the unit rate for $240 for 4 days
you have a standard deck of 52 cards. you pick one card from the deck and then , without putting the first card back , pick a second card . what is the probability that both cards will be 9s??
there are 4 9's in a deck
so first pick = 4/52 reduces to 1/13
second pick there would be 3 9's left and 51 cards so it would be 3/51 reduces to 1/17
probability of both happening = 1/13 * 1/17 = 1/221 (fraction form)
if you need it in decimal it = 1/221 = 0.00452, rounded to 0.005
Which of the following matrices represents the average number of vehicles sold for the two months shown in the table below?
Taylor bought 200 shares of stock for $18.12 per share last year. He paid his broker a fl at fee of $30. He sold the stock this morning for $21 per share, and paid his broker 0.5% commission. a. What were Taylor's net proceeds?
Final answer:
Taylor's net proceeds from the stock transaction are $525, after accounting for the initial purchase cost and broker's commissions on both the buying and selling of the stock.
Explanation:
Taylor bought 200 shares of stock at $18.12 per share and paid a flat brokerage fee of $30. To find the initial cost, we multiply the number of shares by the purchase price and then add the fee:
200 shares × $18.12/share + $30 = $3,654
When Taylor sold his shares at $21 per share, his gross proceeds were:
200 shares × $21/share = $4,200
The broker commission of 0.5% on the selling price is calculated as:
$4,200 × 0.005 = $21
To find Taylor's net proceeds, we subtract both the initial cost and the selling commission from the gross proceeds:
$4,200 - $3,654 - $21 = $525
Therefore, Taylor's net proceeds from the stock transaction are $525.
a light bulb consumes 3600 Watts hours per day. how long does it take to consume 12600 Watts hours?
it would take 84 hours,or 3.5 days,hope this helps
simplify the fraction 48 over 75
48/75
both numbers are divisible by 3
so it simplifies to 16/25
Mr. Yu applies 1/2 ounce of fertilizer to every 5/8 square meter of his lawn. How many ounces of fertilizer does Mr. Yu use per square meter for his lawn? Enter your answer in the box as a fraction in simplest form.
Answer:
[tex]\frac{4}{5} [/tex] ounce
Step-by-step explanation:
We can use rule of three to answer this problem.
The data we have is the following:
fertilizer (ounces) area(m^2)
1/2 ⇒ 5/8
x ⇒ 1
the x represents the unknown quantity of fertilizer that is used in one square meter.
Now we multiply the cross quantities and divide by the remaining value.
[tex]x=\frac{1}{2}*1[/tex] ÷ [tex]\frac{5}{8}[/tex]
[tex]x=\frac{1*8}{2*5} =\frac{8}{10} =\frac{4}{5}[/tex]
He will use 4/5 ounces of fertilizer per square meter.
choose the ratio that you would use to convert 2.5 centimeters to meters please
The ratio which is used to convert 2.5 centimeters to meters is : (d) 1 meter/100 centimeter.
To convert 2.5 centimeters to meters, we choose the ratio that relates centimeters to meters,
The correct ratio to use in this case is 1 meter/100 centimeters,
This ratio states that there are 100 centimeters in 1 meter.
To convert centimeters to meters, we divide the given measurement (2.5 centimeters) by the ratio of 1 meter/100 centimeters.
Using this ratio, we have:
2.5 centimeters × (1 meter/100 centimeters) = 2.5/100 meters
2.5/100 = 0.025 meters,
So, 2.5 centimeters is equal to 0.025 meters.
Therefore, The correct answer is (d) 1 meter/100 centimeter.
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use the remainder therom to find the remainder when x^4-3x^2-9x+4 is divided by x-3
Final answer:
To find the remainder when dividing x^4-3x^2-9x+4 by x-3, substitute x=3 into the polynomial and calculate the expression.
Explanation:
To find the remainder when dividing x^4-3x^2-9x+4 by x-3, we can use the Remainder Theorem. According to the theorem, if we substitute the opposite of the divisor into the polynomial, the remainder will be the value we get.
So, substitute x = 3 into the polynomial:
3^4 - 3(3)^2 - 9(3) + 4
Calculating this expression, we find that the remainder is 142.
What is the end behavior of the graph of the polynomial function f(x) = 2x^3 – 26x – 24?
The end behavior of the function f(x) = 2x³ – 26x – 24 can be described as:
As x → -∞, y →-∞ and as x→∞, y →∞.
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
To determine the end behavior of the polynomial function f(x) = 2x³ – 26x – 24, we need to examine the degree of the polynomial and the sign of its leading coefficient.
The degree of the polynomial is 3, which means it is an odd-degree polynomial.
The sign of the leading coefficient is positive (+2). These two pieces of information tell us that the end behavior of the graph will be as follows:
As x becomes very large in the positive direction, the values of the function will also become very large in the positive direction.
As x becomes very large in the negative direction, the values of the function will become very large in the negative direction.
Therefore, as x → -∞, y →-∞ and as x→∞, y →∞.
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How can you display data in a Histogram?
Answer:
You can display data in a histogram by labeling the x and y axis with your numbers provided. Then you put in the amount of numbers.
Answer:
Sample response: To create a histogram, first label the x-axis and choose the interval. Then calculate the frequency of each interval. Next, label the y-axis and determine the scale. Now create the bars. Draw bars the height of the frequency for each interval. Last, give the graph a title.
Step-by-step explanation:
forty more than twice malia's age is 64
Solve the equation below for x by graphing. x ≈ -2.50 x ≈ 2.50 x ≈ -0.50 x ≈ -6.00
Answer:
The answer is A. -2.50
Step-by-step explanation:
Angela uses 2/3 cup strawberries to make 5/6 of a liter of smoothies what is unit rate in cups of strawberry per liter
Answer:
[tex]\frac{4}{5}\frac{cup}{liter}.[/tex]
Step-by-step explanation:
The problem says that Angela uses 2/3 cup strawberries to make 5/6 liter of smoothies. Then, to find the unit rate in cups of strawberrry per liter, that is cup/liter we need to divide both fractions:
[tex]\frac{\frac{2}{3}cup}{\frac{5}{6}liter} = \frac{2*6}{3*5}\frac{cup}{liter} = \frac{12}{15}\frac{cup}{liter}= \frac{4}{5}\frac{cup}{liter}.[/tex]
Then, the unit rate in cups of strawberry per liter is [tex]\frac{4}{5}\frac{cup}{liter}.[/tex] That is, Angela uses 4/5 cups of strawberry to do 1 liter of smoothie.
A club orders 124 T-Shirts at a cost of $18 each. Which is the best estimate of the total cost of the order?
Two cargo trains each leave their respective stations at 1:00 p.m. and approach each other, one traveling west at 6 miles per hour and the other on separate tracks traveling east at 14 miles per hour. The stations are 40 miles apart. Find the time when the trains meet and determine how far the eastbound train has traveled.
A). 3 p.m, 28 mi
B). 12 p.m., 20 mi
C). 2 p.m., 18 mi.
D). 1 p.m., 15 mi
let x = hours
6x + 14x = 40
20x=40
x = 40/20 = 2 hours
1 pm + 2 hours = 3 pm
eastbound trains is going 14 miles per hour, 14 mph x 2 hours = 28 miles
Answer is A. 3 pm and 28 miles
The eastbound train has traveled 28 miles and they met at 3:00 pm
Speed is the ratio of total distance to total time taken. It is given by:
Speed = distance / time
Let both cargo trains meet each other at time t.
For the train traveling west:
6 = d₁ / t
d₁ = 6t
For the train traveling east:
14 = d₂ / t
d₂ = 14t
Since both trains are 40 miles apart, hence:
d₁ + d₂ = 40
6t + 14t = 40
20t = 40
t = 2 hours
t = 3:00 pm (1:00 pm + 2 hours)
Distance travel by east bound train = d₂ = 14t = 14(2) = 28 miles
The eastbound train has traveled 28 miles and they met at 3:00 pm
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The outside diameter of a pipe is 5 and 7/32 inches. The walls of the pipe are 5/32 inches thick whats the inside diameter
James has 875 feet of rope. There are 13 teams of hikers. If James gives an equal amount of rope to each team how much rope will each team receive
Answer:
67.307 feet of rope per team
Step-by-step explanation:
A cereal bar contains 4000 milligrams of protein. How much protein does it contain in grams
Samantha puts an initial $500 into a savings account. The account has a 4% annual compound interest rate. What is the function that best represents Samantha's account and how much does she have in savings after 5 years? Round your answer to the nearest dollar. Hint: Use the formula, f(x) = P(1 + r)x. (5 points)
Answer: The answer is y = 500(1.04) x
Step-by-step explanation: The formula is y = P (1 + r) x
So, given that P which is the initial value 500(1+0.4) x
f(x)=500(1.04) x
draw or write to explain why 1 hundred 4 tens and 14 tens name the same amount
Tony buys a CD that is priced at $13.59. He has a coupon for $1.85 off. He pays with a $20 bill. Which is the best whole number estimate of how much change he gets? $8
Use the inequality -4t - 8 ≤ 12 to fill in the missing numbers.
a) t ≥ ?
b) t + 4 ≥ ?
c) t - ? ≥ 0
d) t + 10 ≥ ?
e) 3t ≥ ?
f) t/? ≥ -5
If p(a) = 0.62, p(b) = 0.47, and p(a or
b.= 0.88, then p(a and
b.= _____
Probabilities are used to determine the chances of an event
The value of P(a and b) is 0.21
The given parameters are:
P(a) = 0.62
P(b) = 0.47
P(a or b) = 0.88
P(a and b) is calculated using the following formula
P(a and b) = P(a) + P(b) - P(a or b)
So, we have:
P(a and b) = 0.62 + 0.47 - 0.88
P(a and b) = 0.21
Hence, the value of P(a and b) is 0.21
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plez help me and show your work
0.7/10 = 0.07
1.05 / 15 = 0.07
1.40 / 20 =0.07
1.75/25 = 0.07
yes it is proportional ( they all equal the same when divided)
proportion = 0.07
Part B) y = 0.07x
you work for a dress maker and your boss sends you to the fabric store to buy blue fabric she tells you to buy the best deal what's is the best deal
20 yards for $30.00
40 yards for $45.00
50 yards for $70.00
65 yards for $85.00
Which rows represent when (p ∧ q) ∨ (p ∧ r) is true?\
Answer:
The answer is B. A, B, and C
Step-by-step explanation:
Just took the test on edg
Which equation is equivalent toy- 6 = -12(x+ 4)? (1 point)
a. y=-6x-48
b. y=6x-48
c. y=-12x-42
d. y=-12x-54?