The rational number equivalent to the given expression is 50 5/9.
The given expression is [tex]69\frac{2}{9} -31\frac{1}{9} -(-12\frac{4}{9} )[/tex].
How do add and subtract rational numbers?To add or subtract two rational expressions with the same denominator, we simply add or subtract the numerators and write the result over the common denominator.
Now, [tex]69\frac{2}{9} -31\frac{1}{9} +12\frac{4}{9}[/tex]
[tex]=(69-31+12)(\frac{2}{9}-\frac{1}{9}+\frac{4}{9})[/tex]
=50 5/9
Therefore, the rational number equivalent to the given expression is 50 5/9.
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Compare and contrast the absolute value of a real number to that of a complex number
Answer:
The absolute value of a real number is the distance from 0 on the number line. The absolute value of a complex number is the distance from the origin in the complex plane. Both are distances, and therefore both are positive values. You need to use the distance formula or the Pythagorean theorem to calculate the absolute value of a complex number.
Step-by-step explanation:
Use the distance formula or the Pythagorean theorem to calculate the absolute value of a complex number.
What is a complex number?Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labeled I sometimes known as the imaginary unit, and satisfies the equation i² = 1.
The absolute value of a real number is the distance from 0 on the number line. The absolute value of a complex number is the distance from the origin in the complex plane.
Both are distances, and therefore both are positive values. You need to use the distance formula or the Pythagorean theorem to calculate the absolute value of a complex number.
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what is the prime factorization of 720
if 45 people enrolled in a psychology course but only 35 completed it, what percent of the students completed the course
The volume of a cone is 31.4 cm3 and the radius is 2 cm. What is the height of the cone? Use 3.14 for π. Round to the nearest tenth, if needed.
A) 22.5 cm
B) 7.5 cm
C) 15 cm
D) 41.9 cm
Use the chain rule to find dz/dt. z = xy9 − x2y, x = t2 + 1, y = t2 − 1
The value of dz/dt using the chain rule is [tex]2t[(t^2-1)^9 -2(t^4-1)]+2t[9(t^2+1)(t^2-1)^8-(t^2+1)^2][/tex]
According to chain rule:
[tex]\frac{dz}{dt} = \frac{\delta z}{\delta x} \frac{dx}{dt} + \frac{\delta z}{\delta y} \frac{dy}{dt}[/tex]
Given the following expressions
z = xy⁹ − x²y,
x = t² + 1
y = t² − 1
Get the differentials in the equation
[tex]\delta z/\delta x = y^9-2xy\\dzx/dt = 2t\\\delta z/\delta y =9xy^8-x^2\\dy/dt = 2t[/tex]
Substitute the differentials into the formula
[tex]\frac{dz}{dt} = (y^9-2xy)(2t)+(9xy^8-x^2)(2t)\\\frac{dz}{dt} = 2t[(t^2-1)^9 -2(t^4-1)]+2t[9(t^2+1)(t^2-1)^8-(t^2+1)^2][/tex]
Hence the value of dz/dt using the chain rule is [tex]2t[(t^2-1)^9 -2(t^4-1)]+2t[9(t^2+1)(t^2-1)^8-(t^2+1)^2][/tex]
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What should be done so that the expression will have a value of 10? 4 + 4 2 - 5 × 2
Answer: D NOTHING NEEDS TO BE DONE
Step-by-step explanation: and ANY ONE WHO NEEDS THIS ANSWER LOOK IN THE COMMENTS ON THE QUESTION SO YOU KNOW WHAT IM TALKING ABOUT
A and b alternate rolling a pair of dice, stopping either when a rolls the sum 9 or when b rolls the sum 6. assuming that a rolls first, find the probability that the final roll is made by
a.
The probability of the player for final roll is 25%.
Given data:
To find the probability that the final roll is made by player A, we need to consider the possible outcomes of the game. There are two possible scenarios:
Player A rolls a sum of 9 before player B rolls a sum of 6.
Player B rolls a sum of 6 before player A rolls a sum of 9.
Let's calculate the probability for each scenario and determine the probability that the final roll is made by player A.
Scenario 1:
Player A rolls a sum of 9 before player B rolls a sum of 6.
The probability of rolling a sum of 9 with two dice is given by the number of favorable outcomes divided by the total number of possible outcomes.
The number of favorable outcomes for a sum of 9 is 4, as there are four ways to get a sum of 9: (3, 6), (4, 5), (5, 4), and (6, 3).
The total number of possible outcomes when rolling two dice is 36 (6 possible outcomes for each die).
Therefore, the probability of player A rolling a sum of 9 before player B rolls a sum of 6 is 4/36 = 1/9.
Scenario 2:
Player B rolls a sum of 6 before player A rolls a sum of 9.
Similarly, the probability of rolling a sum of 6 with two dice is given by the number of favorable outcomes divided by the total number of possible outcomes.
The number of favorable outcomes for a sum of 6 is 5, as there are five ways to get a sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1).
Therefore, the probability of player B rolling a sum of 6 before player A rolls a sum of 9 is 5/36.
Now, calculate the probability that the final roll is made by player A by adding the probabilities of both scenarios:
Probability that the final roll is made by player A = Probability of Scenario 1 + Probability of Scenario 2
= 1/9 + 5/36
= 4/36 + 5/36
= 9/36
= 1/4
Hence, the probability that the final roll is made by player A is 1/4 or 25%.
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if I fail this I'm gonna fail the quarter. please help
Quadrilateral PQRS is shown below. Which of the following transformations of ΔPTS could be used to show that ΔPTS ≅ ΔQTR ?
A reflection over line segment QS
2) A reflection over line segment PR
3) A reflection over line m
4) A reflection over line l
The transformation that would show triangle PTS is congruent to triangle QTR in quadrilateral PQRS is a reflection over the line segment PR, assuming PQRS is a parallelogram.
Explanation:The question involves identifying which transformation of triangle PTS would show that it is congruent to triangle QTR in quadrilateral PQRS. Without a diagram, it's difficult to provide a specific answer. However, the properties given refer to the symmetric treatment of the sides of a parallelogram and parallel lines. Based on the axioms provided, if PQRS is a parallelogram, then any reflection over the line connecting opposite corners (diagonals) would make two triangles inside the parallelogram congruent. This is because reflections over a line preserve the size and shape of a geometric figure while flipping it over the line. Since PTS and QTR share point T, reflect triangle PTS over the line containing this shared point, which is the line TR or line segment PR, assuming PQRS is a parallelogram.
0.09 is 10 times as much as
Monica wants to make sure that her sentences are easily understood. how long should she make them?
a. an average of 28 words
b. no more than 8 words
c. at least 30 words
d. an average of 20 words
Type the integer that makes the following addition sentence true:
+ 4 = 4
karen sells clothes. after studing her constraints, she knows that she will make $10 profit on each jacket, j, she sells and $6 profit on each shirt, s, she sells. which equation or inequaltiy should she use to show her maximum profit , P?
An investor bought 400 shares of stock, some at $7.00 per share and some at $1.00 per share. If the total cost was $1450.00, how many shares of each stock did the investor buy?
The investor bought 175 shares at $7.00 per share and 225 shares at $1.00 per share.
Explanation:To solve this problem, you can set up a system of equations. Let x be the number of shares bought at $7.00 per share and y be the number of shares bought at $1.00 per share.
From the information given, we know that:
x + y = 400 (equation 1)7x + y = 1450 (equation 2)To solve the system of equations, you can use the substitution method or the elimination method.
Using the elimination method, multiply equation 1 by 7 to make the coefficients of x in both equations equal:
7(x + y) = 7(400)7x + 7y = 2800 (equation 3)Now, subtract equation 2 from equation 3 to eliminate x:
(7x + 7y) - (7x + y) = 2800 - 14506y = 1350y = 225Substitute the value of y into equation 1 to find x:
x + 225 = 400x = 175Therefore, the investor bought 175 shares at $7.00 per share and 225 shares at $1.00 per share.
One half of a number y is more than 22
Answer:
Inequality: [tex]\frac{y}{2}>22[/tex]
Solution: [tex]y>44[/tex]
Step-by-step explanation:
We are supposed to write and solve an inequality for the given verbal description.
One half of a number y would be y divided by 2: [tex]\frac{y}{2}[/tex].
Since one half of a number y is more than 22, so we can set an inequality as:
[tex]\frac{y}{2}>22[/tex]
Multiply both sides by 2:
[tex]\frac{y}{2}*2>22*2[/tex]
[tex]y>44[/tex]
Therefore, the solution to our given inequality is any value of y greater than 44.
which formula can be used to describe the sequence? 1.2, 3, 7.5, 18, 7.5, ...
Answer:
Option A) [tex]1.2(2.5)^{x-1}[/tex]
Step-by-step explanation:
We are given a series:
[tex]1.2, 3, 7.5, 18.75, ...[/tex]
We know that the given series is a geometric series as
[tex]\displaystyle\frac{3}{1.2} = \frac{7.5}{3} = \frac{18.75}{7.5} = 2.5[/tex]
Geometric Series:
A geometric series is a series with a constant ratio between successive terms. The first term is represented by aIn the given series a = 1.2The common ratio is denoted by rFor the given series r = 2.5The [tex]n^{th}[/tex] term of a geometric series is given by:
[tex]a_n = a(r)^{n-1}[/tex]
[tex]a_1= 1.2\\a_2 = 1.2(2.5)^{2-1} = 3\\a_3 = 1.2(2.5)^{3-1} = 7.5\\a_4 = 1.2(2.5)^{4-1} = 18.75[/tex]
Thus, the general term of the given series can be formulated with the help of [tex]f(x) = 1.2(2.5)^{x-1}[/tex]
Option A) [tex]1.2(2.5)^{x-1}[/tex]
How many 7/8 yard long scarves can I make from 156 feet of fabric
Which expression shows the result of applying the distributive property to 3(2x−6) ?
A. 2x−18
B. 6x−18
C. 6x−6
D. 5x−3
How to write one hundred seventy five and one hundred fifty five thousandth in standard form
There are eight rooms in Fern's home . Two of them are used for her office space. What percentage of the home's rooms is not used for the office space?
Please help me will pick brainliest answer with more info!!!
What is 20% of 1630?
Francois baked just enough cookiesto fill all the orders at his bakery. While the cookies were cooling, a kitchen assistant knocked over a cooling rack and spilled 12 percent of the cookies onto the floor. Francois had to bake 36 more cookies to replace them.
How many cookies were ordered in total? And please explain.
I NEED HELP NOW PLEASE!!!!!!!!
Josiah, the manager of a pet store, bought 72 oz of water conditioner to use in his fish tanks. His small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner. He made a sketch to show the line representing the different combinations of tanks he could put the water conditioner into. The x-axis represented the number of small tanks and the y-axis represented the number of large tanks. The manager labeled only the intercepts.
Which points did the manager label?
(0, 6) and (2, 0)
(0, 12) and (36, 0)
(6, 0) and (0, 2)
(0, 36) and (12, 0)
Find the slope of the graph of the function y=5x/x-2 at (3,15). Then find an equation for the line tangent to the graph at that point.
The slope of the graph at the point (3,15) is -10. The equation of the tangent line at that point is y = -10x + 45.
Explanation:To find the slope of the graph, we need to differentiate the equation y=5x/(x-2). Using the quotient rule, the derivative of this equation is (5(x-2) - 5x)/(x-2)². Simplifying this further, we get -10/(x-2)². Now, substitute the x-coordinate of the point (3,15) into the derivative to find the slope at that point. Substituting x=3, we get a slope of -10/1 = -10.
To find the equation of the tangent line at the point (3,15), we use the point-slope form of a line, y - y1 = m(x - x1). Substituting the slope (-10) and the coordinates of the point (3,15) into this equation, we get y - 15 = -10(x - 3). Simplifying further, we get y - 15 = -10x + 30. Rearranging the equation, we get y = -10x + 45. Therefore, the equation of the tangent line to the graph at the point (3,15) is y = -10x + 45.
there is 4/5 lb of sand in the class science supplies. if one scoop of sand weighs 1/20 lb, how many scoops of sand can maria get from the class supplies and still leave 1/2 lb in the supplies
what inequality represents the verbal expression? 8 less than a number n is less than 11
The inequality representing the verbal expression '8 less than a number n is less than 11' is written as 'n < 19'. This is found by adding 8 to both sides of the inequality 'n - 8 < 11'.
Explanation:The inequality that represents the verbal expression '8 less than a number n is less than 11' can be translated into a mathematical inequality as follows. First, '8 less than a number n' means you take 8 away from n, which is written as n - 8. Then, this quantity being 'less than 11' is represented by the inequality n - 8 < 11. To find the range of values for n, we solve this inequality.
Step 1: Add 8 to both sides of the inequality to isolate n -
n - 8 + 8 < 11 + 8
Step 2: Simplify -
n < 19
Therefore, the inequality symbol that represents the verbal expression is n < 19.
The inequality that represents the verbal expression '8 less than a number n is less than 11' is 8 < n < 11. The symbol '<' represents 'less than' and since the number n is between 8 and 11, we use the inequality symbol '<' twice.
The inequality that represents the verbal expression '8 less than a number n is less than 11' is 11 > n - 8 > 8.
Explanation:The inequality that represents the verbal expression '8 less than a number n is less than 11' is 11 > n - 8 > 8. This inequality states that the number n, decreased by 8, is greater than 8 and less than 11.
A culture of 2.4×10^11 bacteria is in petri dish A. A culture of 8×10^9 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
The number of bacteria in petri dish A is 30 times greater than the number in petri dish B. This is calculated by dividing 2.4 × 10^11 by 8 × 10^9.
To determine how many times greater the number of bacteria in petri dish A is compared to petri dish B, we need to divide the number of bacteria in petri dish A by the number in petri dish B.
Given:
Petri dish A: 2.4 × 10^11 bacteriaPetri dish B: 8 × 10^9 bacteriaThe calculation is:
2.4 × 10^11 / 8 × 10^9 = 3 × 10^1 = 30
Therefore, the number of bacteria in petri dish A is 30 times greater than in petri dish B.
Using this example, estimate the traffic flow for a roundabout presented below. the graphical model shows the number of cars per hour that are entering or leaving a roundabout. if the portion of the roundabout between a and b has an estimated traffic flow of from 6[e] to 8[a] cars per hour, what is the estimated traffic flow between c and a, and between b and c?
We have three equations that we can use for this problem.
X1 − X3 = 35
X2 − X1 = 50 X3 – X2 = 15 To solve for C and A. We’ll take the first equation and put 23 for X1. X1 − X3 = 35 23 − X3 = 35 −X3 = 35 - 23 −X3 = 12 The estimated traffic flow for C and A is 12 cars per hour. Now, to solve for B and C, we’ll take the second equation and put 23 for X1 as well. X2−X1=50 X2− (23) =50 X2 = 50 + 23 X2 = 73 The estimated traffic flow for B and C is 73 cars per hour.f(x) = 2x^2 + 3 and g(x) = x^2 - 7, find (f-g)(x)
A) 3x^2 - 10
B) x^2 - 4
C) x^2 + 10
D) 3x^2 - 4
Let's solve for a.y=2x2+3andgxStep 1: Flip the equation.3adgnx+2x2=yStep 2: Add -2x^2 to both sides.3adgnx+2x2+−2x2=y+−2x23adgnx=−2x2+yStep 3: Divide both sides by 3dgnx.3adgnx3dgnx=−2x2+y3dgnxa=−2x2+y3dgnx answer :a=−2x2+y3dgnx
121 bricks in 16.5 minutes 22 brings in m minutes