Answer:
5 steps
Step-by-step explanation:
Turn 5/4s into 10/8s and it becomes really easy
The number of steps Erin could paint if he has 5/4 parts of paint, and she needs 2/8 of paint for each stair step, is 5.
What is division?It is a basic operation of mathematics in which you divide a number into smaller parts.
Given:
Erin has 5/4 quarts of paint,
2/8 of paint for each stair-step,
Calculate the number of steps painted as shown below,
Number of steps = total paint / paint required for each step
Number of steps = 5/4 / 2/8
Number of steps =
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Use the inverse matrices to find and (24) ? 7 - 2 2 2 A-1 B-1 = 2 1 3 4 4. 3 4 2 11 (b) (47) b 100 -100 co (24) JUD .11
To find the value of matrix A given A⁻¹ and B⁻¹, we can use the formula A = (A⁻¹)⁻¹ * B⁻¹.
Given A⁻¹ = [[2, 7], [-2, 2]] and B⁻¹ = [[2, 1], [3, 4], [4, 3], [2, 11]], we can calculate A as follows:
Step 1: Calculate the inverse of A⁻¹: (A⁻¹)⁻¹
(A⁻¹)⁻¹ = [[2, 7], [-2, 2]]⁻¹
To find the inverse of a 2x2 matrix, we use the following formula:
[[a, b], [c, d]]⁻¹ = (1 / det([[a, b], [c, d]])) * [[d, -b], [-c, a]]
Step 2: Calculate the determinant of A⁻¹: det([[2, 7], [-2, 2]])
det([[2, 7], [-2, 2]]) = (2 * 2) - (7 * -2) = 4 + 14 = 18
Step 3: Calculate the inverse of A⁻¹: (A⁻¹)⁻¹
(A⁻¹)⁻¹ = (1 / 18) * [[2, -7], [2, 2]] = [[2/18, -7/18], [2/18, 2/18]]
Step 4: Calculate A = (A⁻¹)⁻¹ * B⁻¹
A = [[2/18, -7/18], [2/18, 2/18]] * [[2, 1], [3, 4], [4, 3], [2, 11]]
Performing matrix multiplication, we get:
A = [[2/18 * 2 + (-7/18) * 3, 2/18 * 1 + (-7/18) * 4],
[2/18 * 2 + 2/18 * 3, 2/18 * 1 + 2/18 * 4]]
Simplifying the calculations, we find:
A = [[-1/3, -2/3],
[2/9, 4/9]]
Therefore, the value of matrix A is [[-1/3, -2/3], [2/9, 4/9]].
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Questions are in the image above.
Answer:
hope this helps
you will find all answer in the photo i sent
9) A carton contains 2 litres of tropical juice. The juice consists of 25% mango juice, 30% pineapple juice, and the rest is guava juice. Find how many millilitres of each juice went into the carton of tropical juice.
The carton of tropical juice contains 500 ml of mango juice, 600 ml of pineapple juice, and 900 ml of guava juice.
To find the amount of each juice that went into the carton of tropical juice, we'll calculate the quantities based on the given percentages.
Let's denote the volume of mango juice as M (in milliliters), the volume of pineapple juice as P, and the volume of guava juice as G. Since the total volume of the carton is 2 liters, we have 2000 milliliters as the total volume.
According to the given information, mango juice accounts for 25% of the total volume, pineapple juice accounts for 30%, and the remaining volume is guava juice.
We can express these relationships as equations:
M + P + G = 2000 (Equation 1)
M = 0.25 * 2000 (Equation 2)
P = 0.30 * 2000 (Equation 3)
G = 2000 - (M + P) (Equation 4)
From Equation 2, we have M = 0.25 * 2000 = 500 ml.
From Equation 3, we have P = 0.30 * 2000 = 600 ml.
Substituting these values into Equation 4, we get:
G = 2000 - (500 + 600) = 900 ml.
Therefore, the quantities of each juice that went into the carton of tropical juice are as follows:
Mango juice: 500 ml
Pineapple juice: 600 ml
Guava juice: 900 ml
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please help 6th grade math
Answer:
B
Step-by-step explanation:
A store has 125 scientific calculators.
Brand x sells for $20 each; Brand y sells
for $15 each. If the total selling price
of the calculators is $2,275, how many
of each calculator does the store have?
Answer:
Brand x: 80
Brand y: 45
Step-by-step explanation:
x + y = 125
20x + 15y = 2275
-20x - 20y = -2500
(+) 20x + 15y = 2275
--------------------------------
-5y = -225
y = 45
x + y = 125
x + 45 = 125
x = 80
Answer:
Brand x: 80
Brand y: 45
If an augmented matrix [ A b ] is transformed into [ C d ] by elementary row operations, then the equations Ax = b and Cx = d have exactly the same solution sets.
true false
If an augmented matrix [ A b ] is transformed into [ C d ] by elementary row operations, then the equations Ax = b and Cx = d have exactly the same solution sets is true.
Elementary row operations are specific operations that can be performed on the rows of a matrix. These operations include:
Swapping two rows.Multiplying a row by a non-zero scalar.Adding a multiple of one row to another row.When we apply elementary row operations to an augmented matrix [ A b ], we are essentially performing the same operations on the corresponding system of linear equations Ax = b. The purpose of these operations is to simplify the matrix or system of equations, but they do not change the solution set.
Each elementary row operation corresponds to an equivalent algebraic operation on the system of equations. For example, swapping two rows corresponds to rearranging the order of equations, multiplying a row by a scalar corresponds to multiplying both sides of the equation by the same scalar, and adding a multiple of one row to another row corresponds to adding or subtracting equations.
Since elementary row operations preserve the equivalence between the matrix and the system of equations, any solution that satisfies the original system Ax = b will also satisfy the transformed system Cx = d. Similarly, any solution that satisfies Cx = d will also satisfy Ax = b.
Therefore, the solution sets of the original system Ax = b and the transformed system Cx = d are exactly the same.
Therefore, If an augmented matrix [ A b ] is transformed into [ C d ] by elementary row operations, then the equations Ax = b and Cx = d have exactly the same solution sets is true.
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Use the figure to find the measures of the numbered angles. PLZZZ HELPPPP
angle 1 = 90°
angle 2 = 90°
angle 3 = 90°
angle 4 = 90°
angle 5 = 90°
angle 6 = 90°
angle 7 = 90°
Answer:
All of them are 90 degrees.
Step-by-step explanation:
a
252 cm sq.
b
324 cm sq.
c
144 cm sq.
d
21 cm sq.
HeLp I yEaH i HaVe AsKeD fOr LiKe 20 AnsWeRs BuT i NeEd ThEm AnSwErEd Or I fAiL AhAhA but please help even if you just answer one question
Answer:D
Step-by-step explanation:
Convert: 76 ounces = _____ pounds _____ ounces
Answer:
4 pounds 12 ounces
Step-by-step explanation:
there are 16 ounces in 1 pound so 76/16 = 4.75 and .75 is equal to 12 ounces.
76 ounces is equal to 4 pounds and 12 ounces.
To convert 76 ounces to pounds and ounces, we need to consider that 1 pound is equal to 16 ounces.
Here's how to proceed:
Divide the total number of ounces by 16 to find the number of pounds:
76 ounces ÷ 16 ounces/pound = 4.75 pounds
Since 4 pounds = 4 x 16 pounce/ pound
= 64 ounces ,we subtract this amount from the total of 76 ounces to determine the remaining ounces:
= 76 ounces - 64 ounces
= 12 ounces
Therefore, 76 ounces is equal to 4 pounds and 12 ounces.
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Jenica bowls three games and scores an average of 116 points per game. She scores 105 on her first game and 128 on her second game. What does she need to score on her third game to get a mean score of 116?
Answer:
115 points on her third game.
Step-by-step explanation:
To find the answer add the first and second games together.
128 + 105 = 233 ÷ 2 = 116.5 (then divide by two because there is two games).
This is the average of two games. To find the average of THREE games try different numbers to see which number works.
233 + 110 = 343 ÷ 3 = 114.3
(so we have to try a higher number than 110).
233 + 112 = 345 ÷ 3 = 115 on average (still not enough).
233 + 115 = 348 ÷ 3 = 116. (we found the answer!)
233 + 115 = 348 ÷ 3 = 116
Find the number of subsets in the set (x l x is a day of the week)
a. 124
b. 256
c. 127
d. 128
please tell me where to drag the numbers! thank you!
Answer:
1. 7
2. 3
3. 2 and 2
Step-by-step explanation:
first is 7
second is 3
third is 2 and 2
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Have a great day, be safe and healthy
Thank u
XD
The average low temperature in Tobermorey in October is 5 C. In February it is 23 C lower. What is the average low temperature in Tobermorey in February?
please show your answer
(It’s a math question about negative numbers and positive numbers on the number line)
Answer:
-18 C
Step-by-step explanation:
we have to do this operation
5 - 23
we can proceed like this
if we do 5-5 we reach the 0
23 - 5 = 18
now we have to do 18 steps to the left of the zero, that it means reach -18, that is the answer of the question
Convert: 24 yards = _____ feet
72 feet
48 feet
76 feet
8 feet
Answer:
24 yards = 72 feet
Step-by-step explanation:
3 feet per yard
24 x 3 = 72
Can someone help me with this. Will Mark brainliest.
Answer:
1. True
2. True
3. True
An author of a book gets 3% of the price of each book sold. He received $24,380. How many copies of the book were sold, if each book was sold for $32.00?
Please Explain
divide the number by 32 then divide what you get by 3 and last times 100 equals 25,395.83333333 round it if you want to to 25,395.8
Solve the linear congruence 2x + 6 = 4(mod 8).
The solution to the linear congruence 2x + 6 ≡ 4 (mod 8) is x ≡ 3 (mod 8).To solve the linear congruence 2x + 6 ≡ 4 (mod 8), we need to find the values of x that satisfy the congruence equation.
First, let's simplify the equation:
2x + 6 ≡ 4 (mod 8)
Subtracting 6 from both sides:
2x ≡ 4 - 6 (mod 8)
2x ≡ -2 (mod 8)
Next, we can simplify -2 (mod 8) by adding 8 to it:
-2 ≡ 6 (mod 8)
Now the congruence equation becomes:
2x ≡ 6 (mod 8)
To solve for x, we need to find the multiplicative inverse of 2 modulo 8. The multiplicative inverse of 2 is 4, as 2 * 4 ≡ 1 (mod 8).
Multiplying both sides of the congruence equation by 4:
4 * 2x ≡ 4 * 6 (mod 8)
8x ≡ 24 (mod 8)
Simplifying the equation:
8x ≡ 24 (mod 8)
x ≡ 3 (mod 8)
Therefore, the solution to the linear congruence 2x + 6 ≡ 4 (mod 8) is x ≡ 3 (mod 8).
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Chloe has a bag of marbles with 5 blue marbles, 1 white marbles, and 3 red marbles.
Find the following probabilities of Chloe drawing the given marbles from the bag if the first marble(s) is(are) returned to the bag after they are drawn.
a) A Blue, then a red =
b) A red, then a white =
c) A Blue, then a Blue, then a Blue =
a) The probability of Chloe drawing a blue marble, then a red marble, with replacement is (5/9) * (3/9) = 15/81 ≈ 0.185.
b) The probability of Chloe drawing a red marble, then a white marble, with replacement is (3/9) * (1/9) = 3/81 ≈ 0.037.
c) The probability of Chloe drawing three blue marbles in a row, with replacement, is (5/9) * (5/9) * (5/9) = 125/729 ≈ 0.172.
For each probability, we multiply the probabilities of drawing each marble consecutively, taking into account that the marble is returned to the bag after each draw. The denominator is 9 because there are a total of 9 marbles in the bag. The numerators reflect the number of marbles of each color in the bag.
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From Monday through Friday Sydney works in the bookstore on one day and in the tutoring center where on another doing on Saturday and Sunday Sydney cooks food 50% of the days how many days does Sidney work in a week what percent of Monday through Friday does Sidney work
Answer: The other 50%
Step-by-step explanation:
A veterinarian says you should feed a 5-year-old beagle
2/3 cup of dog food twice a day. According to the veterinarian, how much food should the beagle eat in a 30 days?
Answer:
40 cups of food
Step-by-step explanation:
First, you would multiply 2/3 by 2, which gives you 4/3. That means the beagle will eat 1 and 1/3 of a cup a day. If you multiply that by 30, you get 40.
A paint color is made using 4 drops of red and 5 drops of blue for each 5 gallons of paint. How many gallons of paint are being colored when 45 drops of color are used?
Use a known Maclaurin series to obtain a Maclaurin series for the given function. f(x) = xe^7x [infinity]
f(x) = ∑
n=0
Find the associated radius of convergence, R. R =
Using the known Maclaurin series expansion for e^x: e^x = 1 + x + (x^2 / 2!) + (x^3 / 3!) + ...
We can obtain the Maclaurin series for the function f(x) = xe^(7x) by multiplying the Maclaurin series for e^x by x:
f(x) = x(1 + 7x + (7x)^2 / 2! + (7x)^3 / 3! + ...)
Simplifying further:
f(x) = x + 7x^2 + (49x^3 / 2!) + (343x^4 / 3!) + ...
Therefore, the Maclaurin series expansion for f(x) is:
f(x) = x + 7x^2 + (49x^3 / 2!) + (343x^4 / 3!) + ...
The associated radius of convergence, R, can be determined by applying the ratio test. In this case, we have an infinite power series with terms involving powers of x. The ratio test states that if the limit of |a_(n+1) / a_n| as n approaches infinity is L, then the radius of convergence is R = 1 / L.
In our case, applying the ratio test yields a limit of 0 as n approaches infinity. Therefore, the radius of convergence R is infinite, indicating that the Maclaurin series for f(x) converges for all values of x.
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May someone please help me with this :)
Answer: It would be option D :)
Step-by-step explanation: the formula for volume in a cylinder is π r squared times height. You plug those in and that’s your answer!
simplify the expression ((-1)^5/(-2)-3)^2
Answer:
Sure! Let's simplify the expression step by step:
((-1)^5/(-2)-3)^2
= (-1/2 - 3)^2 // Since (-1)^5 = -1
= (-7/2)^2
= 49/4
Therefore, ((-1)^5/(-2)-3)^2 simplifies to 49/4.
Ashley got 18 out of 42 questions correct on the test. How many more questions would she have
needed to get comect to receive a 70% on the testi
Consider the following. x=3cos(θ),y=4sin(θ),−π/2≤θ≤π/2 (a) Eliminate the parameter to find a Cartesian equation of the curve.
The Cartesian equation of the curve is 4x² + 3y² = 36.
We can eliminate the parameter θ by using the trigonometric identity cos²(θ) + sin²(θ) = 1, which gives us:
x²/9 + y²/16 = cos²(θ) + sin²(θ) = 1
Multiplying both sides by 16 to get rid of the fraction, we have:
16(x²/9 + y²/16) = 16
4x² + 3y² = 36
Therefore, the Cartesian equation of the curve is 4x² + 3y² = 36.
The Cartesian equation 4x² + 3y² = 36 represents an ellipse centered at the origin with semi-axes lengths of 2√3 and 2√2. The standard form for the equation of an ellipse centered at the origin is:
(x²/a²) + (y²/b²) = 1
where a and b are the semi-axes lengths of the ellipse. To convert the given equation to this standard form, we need to divide both sides by 36:
(4x²/36) + (3y²/36) = 1
Simplifying:
x²/9 + y²/12 = 1
Comparing with the standard form, we have:
a² = 9 and b² = 12
Therefore, the semi-axes lengths are √9 = 3 and √12 ≈ 3.464.
So, the equation 4x² + 3y² = 36 represents an ellipse centered at the origin with semi-axes lengths of 3 and approximately 3.464.
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The total cost (in dollars) of producing x food processors is C(x)=2500+20x-0,1x². (A) Find the exact cost of producing the 71st food processor. (B) Use the marginal cost to approximate the cost of producing the 71st food processor.
(A) The exact cost of producing the 71st food processor is $3415.90. (B) Using the marginal cost approximation, the cost of producing the 71st food processor is approximately $5.80.
The cost of producing the 71st food processor can be found by substituting x = 71 into the cost function C(x) = 2500 + 20x - 0.1x². (A) The exact cost of producing the 71st food processor is C(71) = 2500 + 20(71) - 0.1(71)² = 2500 + 1420 - 504.1 = $3415.90.
The marginal cost represents the change in cost when one additional unit is produced. It can be approximated by calculating the difference between the cost of producing x+1 units and x units and dividing it by the change in quantity. In this case, the marginal cost is the derivative of the cost function, which is given by C'(x) = 20 - 0.2x. To approximate the cost of producing the 71st food processor using the marginal cost, we can evaluate C'(x) at x = 71. (B) C'(71) = 20 - 0.2(71) = 20 - 14.2 = $5.80. Therefore, the approximate cost of producing the 71st food processor using the marginal cost is $5.80.
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PLEASE GRAPH THE ANSWER AND HAVE A PICTURE ATTACHED. I WILL REALLY APPRECIATE IT :)
-Also no links please...
Answer:
The first is (-1, 1) and the second is (2, -2)
Step-by-step explanation:
Soon Yee was putting together her notebook after the first day of
school. She bought a pack of 200 sheets of loose-leaf notebook
paper and some dividers. She wanted to put the same amount of
paper in each of the four sections for her core subjects: math,
history, English and science. She figured that herſtwaelective
courses (art and music) each only needed half bf the amount of
paper that a core subject needed. How many sheets of paper did
she put into the art section of her notebook?
Answer: Since her art and music sections each only had half the number of sheets of paper as a core subject, together the two sections had the same amount of paper as a core subject. Therefore, it is almost like her notebook had five core subjects, rather than four core subjects and two electives. If she divided the 200 sheets equally among the five core subjects, there would be 200 ÷ 5 = 40 sheets in each section. Now we can see that art would actually have half of this amount, or 20 sheets of paper.