We can start solving the problem by using a system of equations. Let's call the number of ounces of solution a x and the number of ounces of solution b y. From the problem statement, we know that:
x + y = 150 (because the total amount of the mixture is 150 ounces)
0.6x + 0.9y = 0.65(x + y) (because the mixture is 65% salt, and we can find the amount of salt in the mixture by multiplying the percentage by the total amount)
We can use the first equation to solve for one of the variables in terms of the other:
y = 150 - x
Now we can substitute this expression for y into the second equation:
0.6x + 0.9(150 - x) = 0.65(150)
0.6x + 135 - 0.9x = 97.5
-0.3x = -37.5
x = 125
Now we can use the first equation to find the value of y:
y = 150 - x
y = 150 - 125
y = 25
So the scientist should use 125 ounces of solution a and 25 ounces of solution b to obtain 150 ounces of a mixture that is 65% salt.
The sum of 3 consecutive even integers is 84. What are the 4 integers? Write an equation and solve to determine your answer.
Answer: 27 28 29
Step-by-step explanation:
the length of a shadow of a tree is feet when the angle of elevation of the sun is . approximate the height of the tree.
The approximate height of the tree is feet.
The exact height of the tree cannot be determined without additional information. However, a rough estimate can be made using the following formula:
Height of Tree = Length of Shadow / Tan(Angle of Elevation of Sun)
In this case, the estimated height of the tree would be: Length of Shadow / Tan( ) = feet/tan( ).
The formula to calculate the height of a tree is:
Height of Tree = Length of Shadow * Tan(Angle of Elevation of the Sun)
In this case, Length of Shadow = feet and Angle of Elevation of the Sun
Therefore, the height of the tree can be calculated as follows:
Height of Tree = feet * Tan( )
Height of Tree = feet * 0.839
Height of Tree = feet
Therefore, By the angle of elevation the approximate height of the tree is feet.
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Find the number that belongs
in the green box.
40°
[?]
120°
8
Round your answer to the nearest tenth.
Answer:
10.8
Step-by-step explanation:
using Sine Law
a/sin A = b/sin B = c/sinC
a = 8
A = 40°
b = ?
B = 120
substitute the values and you will get the answer 10.778370842670, rounding to the nearest 10ths.
10.8 is the measure of the value of x to the nearest tenth.
The sine rule formulaThe given diagram is a triangle with side 8 and angles 40 and 120 degrees.
Applying the sine rule, we will have:
x/sin120 = 8/sin40
Cross multiply to have:
8sin120 = xsin40
x = (8sin120)/sin40
x = 6.9282/0.6428
x = 10.8
Hence the measure of the value of x to the nearest tenth is 10.8.
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I asked my daughter how many students are there in her class. She said it is equal to the sum of 3 consecutive natural numbers. Moreover, it is also equal to the sum of the two natural numbers following those 3 consecutive natural numbers. What is the answer to my questions?
Answer: Let's call the smallest of the 3 consecutive natural numbers "n". The other two numbers are "n+1" and "n+2". The sum of these 3 numbers is "3n + 3"
Also, the sum of the two numbers following these 3 consecutive natural numbers is (n+3) + (n+4) = 2n + 7
We know that these two expressions are equal:
3n + 3 = 2n + 7
By solving this equation we can find the value of n.
Subtracting 3 from both sides: 3n = 4
Dividing by 3: n = 4/3
Since n is a natural number, n has to be the integer 1.
So the three consecutive natural numbers are 1, 2, 3 and the sum of the students in the class is 6, which is also the sum of the next two natural numbers 4 and 5.
Therefore, there are 6 students in her class.
Step-by-step explanation:
How many beats are in each of these measures?
JOJ J
OA. 4
OB. 6
OC. 2
OD. 3
Each measure in a 4/4 time signature has four quarter note beats; each measure in a ¾ time signature has three quarter note beats; and each measure in a 2/4 time signature has two quarter note beats.
How many beats are in each of these measures?A 4/4 time signature does not imply that each measure contains simply four quarter notes. It signifies that each measure only contains four beats. These beats may comprise half notes, quarter notes, eighth notes, pauses, or whatever the composer desires, but all note and rest values must add up to no more or less than the time signature’s top number (or numerator).
The most popular musical meter is 4/4. Because it is so widespread, it is also known as common time, and the two numerals in the time signature are sometimes substituted with the letter C. The stacking digits in 4/4 indicate that each measure comprises four quarter note beats. To count 4/4 meter, tap the beat every time you tap the beat.
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What is the image of (-10,-4) after dilation by a scale factor of 1/2 centered at the origin?
First, rewrite 2/7 and 3/10
so that they have a common denominator
Answer:
The common denominator will be 70
Step-by-step explanation:
To set the fractions to a common denominator, we need to know what number they both share. In this case, both 7 and 10 share the number 70, since 7 * 10 is 70.
Therefore, we can multiply 2/7 by 10/10 and 3/10 by 7/7:
[tex]\frac{2}{7}[/tex] * [tex]\frac{10}{10}[/tex] = [tex]\frac{20}{70}[/tex]
[tex]\frac{3}{10}[/tex] * [tex]\frac{7}{7}[/tex] = [tex]\frac{21}{70}[/tex]
Answer: Common denominator = 70
Step-by-step explanation: In order to find a common denominator, we need to find what number they have in common. That'd be 70. So, now rewrite the fractions like this:
[tex]\frac{2}{7} = \frac{?}{70}[/tex]
[tex]\frac{3}{10} = \frac{?}{70}[/tex]
Now, we need to find the equivalent fractions on the right. To do that, use this formula for part 1:
Right denominator / left denominator
Then, what you get after dividing those 2, you multiply by the left numerator.
So, let's plug the numbers in:
70 / 7 = 10
10 * 2 = 20
Therefore, [tex]\frac{2}{7} = \frac{20}{70}[/tex]
70 / 10 = 7
3 * 7 = 21
Therefore, [tex]\frac{3}{10} = \frac{21}{70}[/tex]
I hope this helped!
A window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12m, find the dimensions of the rectangle that will produce the largest area of the window.
The dimensions of the rectangle that will produce the largest area of the window are x = (12 - √3) / 2 and y = 3 / √3.
Let x be the length of the rectangle, and y be the width of the rectangle. The perimeter of the window is 12m, and since the triangle is equilateral, we know that all 3 sides of the triangle are equal to x.
Therefore, we can set up the following equation to represent the perimeter of the window: x + y + x = 12
The area expression is:
A = x*y + (x^2 * √3)/4
After substituting x = (12-y)/2, the area expression becomes:
A = [((12-y)/2)*y] + [(12-y)^2 * √3]/16
Which can be simplified to:
A = 6y - 3y^2 + (9-3y)√3 / 4
To find the maximum value of this expression, we can differentiate it with respect to y and set it to zero:
dA/dy = -3y + (9-3y)√3/4 = 0
and solve for y:
-3y + (9-3y)√3/4 = 0
-3y = (3y-9)√3/4
-3y = 3y-9 / 2√3
3y = 9 / 2√3
y = 3 / √3
To find x, we can substitute this value of y back into x = (12-y)/2:
x = (12 - 3 / √3) / 2 = (12 - √3) / 2
So the dimensions of the rectangle that will produce the largest area of the window are x = (12 - √3) / 2 and y = 3 / √3.
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qs 14-12 direct materials used lo p2 use the following information to compute the cost of direct materials used for the current year. assume the raw materials inventory account is used only for direct materials. (assume no indirect materials.) January 1 December 31 Inventories Raw materials inventory Work in process inventory Finished goods inventory 12,000 8,500 6,000 7,500 9,000 5,500 Activity during current year Materials purchased Direct labor Factory overhead $123,500 94,000 39,000 Cost of Direct Material
the cost of direct materials used for the current year i.e the direct material used is $122,000
The computation of the direct material used is shown below:
= Opening raw material inventory + material purchased - ending raw material inventory
January 1 Raw materials inventory $6,000
Add Materials purchased $123,500
Raw material available for production $129,500
($6,000+$123,500)
Less December 31 Raw material Inventory $7,500
Cost of direct materials used $122,000
= $6,000 + $123,500 - $7,500
= $122,000
Hence, the direct material used is $122,000
the cost of direct materials used for the current year i.e the direct material used is $122,000
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In baseball, a ".300 hitter" gets a hit 30% of the time. (For those of you not well-versed in spiritual things like baseball: hitting .300 is pretty good.) Suppose a player has five times at bat in a game.
a) What is the probability of getting at least one hit in a game?
b) What is the probability of getting at least one hit, in ten consecutive games?
The answers are 0.8319, 0.1588, but I don`t understand how the textbook got them.
Step-by-step explanation:
a) The probability of getting at least one hit in a game can be found by using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.
In this case, the event of getting at least one hit in a game is the complement of getting no hits in a game.
To get no hits in a game, the player must get 0 hits out of 5 at bats.
The probability of getting no hits in a game is (1-.3)^5 = 0.168.
Therefore, the probability of getting at least one hit in a game is 1 - 0.168 = 0.832
b) The probability of getting at least one hit in ten consecutive games is found by multiplying the probability of getting at least one hit in one game by itself ten times.
So it would be (0.832)^10 = 0.1588
Alternatively, we could use the binomial distribution formula, where probability of getting a hit k times out of n trials is given by
P(k) = (n choose k) * p^k * (1-p)^(n-k)
If we want to find the probability of getting at least one hit in ten games, we need to find the probability of getting 0 hits in all ten games and subtract it from 1.
1 - (1 - 0.832)^10 = 0.1588
So the probability of getting at least one hit in ten consecutive games is 0.1588.
Part 1 of 2
K
The salary of members of two governing bodies in 2008 was $166.3 thousand, and has increased
by approximately $2 thousand per year since then.
Complete parts a. and b.
B
Points: 0 of 1
(a) Complete the following table to help find an expression that stands for the salary (in
thousands of dollars) of members of the two governing bodies t years since 2008.
Number of years and salaries of members
of the two governing bodies.
Years
Salary
since 2008 (thousands of dollars)
0
1
2
3
4
t
(Do not simplify.)
Save
(2.
(2.
(2.
(2.
x
The starting pay was $ 168.6 and has climbed by $ 3,000 annually since 2008 at a consistent rate.
What is the salary ?Since it is a percent increase, they will receive a 2% salary raise in year two, which will amount to $30,000. As a result, it would be 1.2, and we'll now try to identify a pattern. We know that the pay will be 30,000 because of the 2% increase because the power in this situation is one and the salary is in the eleventh year.
At this moment, I would have accepted ten times the 2% rise. During the first year, it would not have occurred. If you want to proceed, divide it by one less than 1.2 to get the temperature. After we calculate it, we'll receive a value for their entire compensation for the next 10 years.
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h+2k=3
3h+6k=9
Solve the system of liner equations using elimination by multiplication
Answer:
H = 3
K = 0
Step-by-step explanation:
To solve the system of linear equations using elimination by multiplication, we can first multiply the first equation by 3. This gives us:
3(H+2k)=3*3=9
3H+6k=9
Now we have the same coefficient (6k) on the second variable in both equations. We can now subtract the first equation from the second equation to eliminate the second variable:
3H+6k=9
-3H-6k=-9
0H=0
This tells us that the system of equations is consistent and has infinitely many solutions. To find the specific solution, we can use either equation and substitute in a value for one of the variables. For example, we can use the first equation and substitute in H=3. This gives:
3+2k=3
2k=0
k=0
Now we can substitute this value for k back into either equation to find the value of H. For example, using the first equation:
H + 2(0) = 3
H = 3
So the solution to the system of equations is:
H = 3, k = 0
The temperature for the previous two days were 62 degrees and 58 degrees. Find the temperature for the third day such that average daily temperature for the three days is 64 degrees.
Logan read a total of 54 pages of the geology and math textbooks. They read 39 pages in the geology textbook. How many pages did Logan read in the math textbook?
Connections Pool Service needs to fill up a neighborhood pool in
Lakewood. They use a cylindrical tank on the truck to transport water
from the warehouse to the pool.
The tank is completely filled with water and then drains completely into the pool. The volume of the cylindrical tank is V = 36πr, where r, is the radius of the tank in feet.
The volume of the neighborhood pool is V₂ = 1/2(4/3pi r3 2) where r₂ is the radius of the pool.
a. Since V₁=V₂, write an equation that shows r1 as a function of r2.
[Hint: set them equal and solve for r₁.]
Using the concept of change of subject of formula, we can express the radius r₁ and r₂ as r₁ = r₂² / 18π
What is Volume of CylinderThe formula of volume of a cylinder is given as;
V = πr²h
r = radius of cylinderh = height of cylinderThe equation for the volume of the cylindrical tank is V1 = 36πr₁ and the equation for the volume of the neighborhood pool is V2 = 1/2(4/3πr₂²).
Since V₁ = V₂, we can set the two equations equal to each other and solve for r₁:
36πr₁ = 1/2(4/3πr₂²)
To solve for r₁, we can first multiply both sides of the equation by 2/4/3, which gives:
18πr₁ = r₂²
Then we can divide both sides of the equation by 18π to get:
r₁ = r₂² / 18π
So we can say that r₁ is a function of r₂ because it can be expressed in terms of r₂.
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the side length of the following square can be expressed by the equation 1=√A , where A represents the area of the square.A=AZ+12in^2/ell=xin. What is the side length of the square if the area is 4x+12in^2
The side length of the square will be 1 unit.
What is a square?
A square is a two-dimensional plane figure with four equal sides and all the four angles are equal to 90 degrees. The properties of rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.
The most important properties of a square are listed below:
All four interior angles are equal to 90°All four sides of the square are congruent or equal to each otherThe opposite sides of the square are parallel to each otherThe diagonals of the square bisect each other at 90°The two diagonals of the square are equal to each otherThe square has 4 vertices and 4 sidesThe diagonal of the square divide it into two similar isosceles trianglesThe length of diagonals is greater than the sides of the square.Now
As given
1=√A (A=area)
Hence,
A=1
Now because A=side^2
Therefore,
Side=√1
side=1
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suppose the length of a certain rectangle is 8 meters more than twice its width and the perimeter is 46 meters. Find it's area
The area of the rectangle is A = 172.5 m^2
The area of a rectangle can be found by using the formula A = lw, where l is the length and w is the width. In this case, we are given that the length is 8 meters more than twice the width, so we can let l = 2w + 8. We are also given the perimeter, which is the sum of the length and width multiplied by two, or 2l + 2w. We can set this equal to 46 and solve for w:
2(2w + 8) + 2w = 46
4w + 16 = 46
4w = 30
w = 7.5
Therefore, the width of the rectangle is 7.5 meters and the length is 2(7.5) + 8 = 23 meters. The area of the rectangle can then be found by substituting these values into the area formula:
A = lw
A = (23)(7.5)
A = 172.5 m^2
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Calculate the trade discount for 15 boxes of computer paper if the unit price is $14.26 and a single trade discount rate of %45 is allowed.
So, the trade discount for 15 boxes of computer paper if the unit price is $14.26, and a single trade discount rate of 45% allowed is $96.255.
Trade discount refers to the reduction in list price known as a discount, allowed by a supplier to the consumer while selling the product generally in bulk quantities to the concerned consumer to increase the sales of the business as more customers are attracted when the discount is given on the list price of the product.
We have to calculate the trade discount for 15 boxes of computer paper.
the unit price of computer paper is $ 14.26, and a single trade discount rate is 45% allowed.
The trade discount on one unit computer paper is.
= 45%×14.26
= $6.417
now, trade discount on 15 unit of computer paper box is.
=6.417×15
=$96.255.
So, the trade discount for 15 boxes of computer paper if the unit price is $14.26, and a single trade discount rate of 45% allowed is $96.255.
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enrique says 0.44444444 is a rational number. which of the following best describes whether enrique is correct and why? enrique is correct. repeating decimals are rational numbers because they can be written as fractions. the number is actually equivalent to 4/9. enrique is correct. repeating decimals are rational numbers because they can be written as fractions. the number is actually equivalent to 4/10. enrique is not correct. repeating decimals are never rational numbers. enrique is not correct. some repeating decimals are rational numbers, but this one is not.
Repeating decimals are never rational numbers. Hence the statement of enrique that "0.44444 is a rational number" is incorrect.
Rational numbers are those which can be expressed as the ratio of two integers, but the denominator should not be zero. Rational numbers can be expressed in p/q form. Rational numbers are never repeating decimals. For example 10/2, 3/2, 2/1 are rational numbers.
Irrational number are those which cannot be written in the form of p/q. They are repeating decimal and recurring decimals. The best example of irrational number is the value of π(pie). The value of π is 3.1415...with no repeating pattern of decimals.
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Polynomial Arithmetic
Polynomial 1: 2x2
+ 3x − 6
Polynomial 2: x2
− 4x + 2
Question 1
What is the sum of the two polynomials?
Responses
A x2
− x − 4x 2 − x − 4
B 3x2
− x + 43 x 2 − x + 4
C 3x2
− x − 43 x 2 − x − 4
D x2
− x + 2x 2 − x + 2
Question 2
What is the product of the two polynomials?
Responses
A 4x4
− 5x3
− 14x2
+ 30x + 124 x 4 − 5 x 3 − 14 x 2 + 30x + 12
B 2x4
− 5x3
+ 7x2
+ 15x + 122 x 4 − 5 x 3 + 7 x 2 + 15x + 12
C 2x4
− 5x3
− 14x2
+ 30x − 122 x 4 − 5 x 3 − 14 x 2 + 30x − 12
D 8x4
− 5x3
+ 14x2
+ 45x − 12
Answer:
Sum of two polynomials:
[tex]3x^2 - x - 4[/tex] Choice C (read explanation carefully)
Product of the two polynomials:
[tex]2x^4-5x^3-14x^2+30x-12\\\\[/tex] Choice C (read explanation carefully)
In both cases, your answer choice copy/paste messed up the formatting. I looked at the coefficients and came up with the choices.
You should compare the actual terms with the choices I have provided to make sure they match
Step-by-step explanation:
The two polynomials are
2x² + 3x - 6
and
x² - 4x + 2
Addition
To add these two polynomials together group like terms and add their coefficients:
(2x² + 3x - 6) + (x² - 4x + 2)
= 2x² + 3x - 6 + x² - 4x + 2
= (2x² + x²) + (3x -4x) + (-6 + 2)
= 3x² - x - 4
Your answer choices have lost formatting during copy paste. You will have to compare and choose the right one. I think it is C because it has a 3x² term and the last term is - 4
Multiplication
[tex]\left(2x^2\:+\:3x\:-\:6\right)\cdot \left(x^2-4x\:+\:2\right)\\\\\\[/tex]
Distribute the parentheses - multiply each term in the second polynomial by each term in the first polynomial and simplify
[tex]\left(2x^2\:+\:3x\:-\:6\right)\cdot \left(x^2-4x\:+\:2\right)\\\\= 2x^2x^2+2x^2\left(-4x\right)+2x^2\cdot \:2+3xx^2+3x\left(-4x\right)+3x\cdot \:2-6x^2-6\left(-4x\right)-6\cdot \:2\\\\= 2x^4-8x^3+4x^2+3x^3-12x^2+6x-6x^2+24x-12\\\\\textrm{Add similar terms}\\=2x^4 +(-8x^3+3x^3)+ (4x^2-12x^2-6x^2) + (6x+24x) -12\\\\[/tex]
[tex]=2x^4-5x^3-14x^2+30x-12\\\\[/tex] (Answer)
Again your answer choices have lost formatting but my best guess from looking at the coefficients is that it is choice C
An aircraft seam requires 23 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.) (a) If 19% of all seams need reworking, what is the probability that a rivet is defective? 0.9920x (b) How small should the probability of a defective rivet be to ensure that only 8% of all seams need reworking? 0.8530 X Need Help?Read It Talk to a Tutor
The probability using the same formula as before: P(X>=3) = 1 - P(X<=2), which gives us 1 - 0.8530p = 0.08, or p = 0.0934.
Let p be the probability of a rivet being defective. In order for 19% of all seams to need reworking, at least 4 of the 23 rivets must be defective. This means that the probability of at least 4 of the rivets being defective must be 0.19. We can calculate this probability using the formula P(X>=4) = 1 - P(X<=3), where X is a binomial random variable with parameters n = 23 and p = p. This gives us 1 - 0.9920p = 0.19, or p = 0.1984.
To ensure that only 8% of all seams need reworking, at least 3 of the 23 rivets must be defective. This means that the probability of at least 3 of the rivets being defective must be 0.08. We can calculate this probability using the same formula as before: P(X>=3) = 1 - P(X<=2), which gives us 1 - 0.8530p = 0.08, or p = 0.0934.
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Without dividing, choose <, >, or = to make each statement true.
We can conclude that -
f(x) < g(x), means that expression f(x) is less than g(x) {for given (x)}.f(x) > g(x), means that expression f(x) is greater than g(x) {for given (x)}.f(x) = g(x), means that expression f(x) is equal to g(x) {for given (x)}.What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the inequality signs as : >, < and =.
An inequality is used to make unequal comparisons between two numbers or expressions.
f(x) < g(x), means that expression f(x) is less than g(x) {for given (x)}.f(x) > g(x), means that expression f(x) is greater than g(x) {for given (x)}.f(x) = g(x), means that expression f(x) is equal to g(x) {for given (x)}.Therefore, we can conclude that -
f(x) < g(x), means that expression f(x) is less than g(x) {for given (x)}.f(x) > g(x), means that expression f(x) is greater than g(x) {for given (x)}.f(x) = g(x), means that expression f(x) is equal to g(x) {for given (x)}.To solve more questions on inequalities, visit the link below -
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8. Solve 9*² = 3³x-2
Answer:
To solve the equation 9x² = 3³x-2, we can follow these steps:
First, we need to simplify the right side of the equation. 3³ = 27, so we can replace 3³ with 27. The equation now becomes: 9x² = 27x - 2
Next, we'll want to get all the x terms on one side of the equation and all the constants on the other side. To do this, we'll add 2 to both sides of the equation: 9x² = 27x - 2 + 2 = 27x. This gives us: 9x² = 27x
Next, we'll divide both sides of the equation by 9. This will give us x² = 3x.
Finally, we can divide both sides by 3. This will give us x = 1.
So the solution is x = 1
jason had $32. he spent all the money buying four cds for x dollars each and two magazines for y dollars each. if jason had bought five cds and two magazines, he would have run short by $4. the following system of equations models this scenario: 4x 2y
Step-by-step explanation:
The given system of equations models the scenario where Jason spent all of his money on buying CDs and magazines, and that if he had bought one more CD, he would have run out of money. The system of equations is:
4x + 2y = 32 (Equation 1)
5x + 2y = 36 (Equation 2)
The first equation represents the total amount of money Jason spent on 4 CDs (x dollars each) and 2 magazines (y dollars each). The second equation represents the total amount of money Jason would have spent if he had bought one more CD. By subtracting equation 1 from equation 2, we get:
x = 4 (Equation 3)
This equation tells us that each CD costs $4.
By substituting this value into equation 1, we get:
4(4) + 2y = 32
16 + 2y = 32
2y = 16
y = 8 (Equation 4)
This equation tells us that each magazine costs $8.
So, Jason spent $4 for each CD and $8 for each magazine.
What is the solution for the system of linear equations shown in the graph?
a coordinate grid with one line that passes through the points 0 comma 0 and 1 comma negative 3 and another line that passes through the points 0 comma 2 and negative 1 comma 1
negative one half comma three halves
one half comma one half
three halves comma three halves
negative three halves comma one half
The solution of the system of equations is:
(-3/2, 1/2)
What is the solution of the system of equations?
Here we have two lines of the form:
y = a*x + b
one passes through (0, 0) and (1, -3)
For the first point we know that the constant is 0, and replacing the values of the second point we get:
1 = a*-3
1/-3 = a
The line is:
y = (-1/3)*x
The second line passes through (0, 2) and (-1, 1) from the first point we can see that:
y = a*x + 2
And replacing the values of the second point we get:
1 = a*-1 + 2
1 - 2 = -a
-1 = - a
1 = a
This line is y = x + 2
Then the system of equations is:
y = x + 2
y = (-1/3)*x
We can replace use the substitution method to write:
x + 2 = (-1/3)*x
x + 1/3*x = -2
(4/3)*x = -2
x = -2*(3/4)
x = -3/2
And the y-value is:
y = -3/2 + 2
y = 1/2
The solution is (-3/2, 1/2)
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7. Higher Order Thinking Joel counts back
from 79. He stops at 65. Cross out the
numbers that Joel does not count.
77 72 70 82
70 82 67 62 80
On applying higher-order thinking skills, it can be seen that Joel does not count the numbers 82 82 62 80 while counting backwards from 79 to 65.
What is Higher-Order Thinking?
Higher-order thinking is a concept of educational reform based on learning taxonomies (like Bloom's taxonomy). Higher-order thinking skills are also known as higher order thinking skills (HOTS). The theory holds that some forms of learning have more universal advantages while requiring more cognitive effort than others.
Joel counts back from 79 to 65.
The numbers in descending order from 79 to 65 is -
79 78 77 76 75 74 73 72 71 70 69 68 67 66 65
The numbers go from right to left on a number line.
The options for the numbers are -
77 72 70 82 70 82 67 62 80
After applying HOTS the numbers which do not lie in between 79 and 65 when counting backwards is -
82 82 62 80
Therefore, the numbers which can be eliminated are 82 82 62 80.
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The lithosphere is..
a. the rigid outer part of the earth, consisting of the crust and upper mantle.
b. the layer above crust mostly made up of gasses.
Selected:c. the lower part of the mantle where convection starts.This answer is incorrect.
d. a safe space for everyone.
The lithosphere is: a. the rigid outer part of the earth, consisting of the crust and upper mantle.
What is the Lithosphere?The Lithosphere is the solid outer shell of the Earth that forms the Earth's surface, including the continents and the ocean floor. It is the uppermost layer of the Earth's solid surface, composed mostly of the minerals, such as silicon and oxygen, that form rocks like granite and basalt.
The lithosphere is composed of the Earth's crust and the uppermost part of the Earth's mantle. It is broken up into tectonic plates that are in constant motion and are responsible for the earthquakes, volcanoes, and the creation and destruction of land masses. The lithosphere is also the layer that supports all life on Earth.
Therefore, we can state that the correct description of the lithosphere is: a. the rigid outer part of the earth, consisting of the crust and upper mantle.
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Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 7 hours of burning, a candle
has a height of 23.2 centimeters. After 26 hours of burning, its height is 15.6 centimeters. What is the height of the candle after 25 hours?
The height of the candle after 9 hours can be written as 23.4 cm.
What is a linear relationship?
The linear relationship is the relationship between two variables such that it follows a straight line.
As it is given that the height of the candle is linear to the amount of time. Now, let's the time be on the x-axis and the y-axis be the height of the candle. therefore, the slope of the linear relationship can be represented as,
Point1 of the slope, (x₁, y₁) = (6, 24.6)
Point2 of the slope, (x₂, y₂) = (21, 18.6)
Now, since we know the two points of the linear relationship, therefore, the slope can be written as,
m = (y2 - y1)/(x2-x1)
m = (18.9 - 24.6) / (21 - 6)
m = -0.4
Thus, the slope of the linear relationship is -0.4.
Now, the equation of the linear relationship can be written as,
y = mx + c
y1 = mx1 + c
24.6 = (-0.4 * 6) + c
24.6 = -2.4 + c
Thus, the Linear relationship of the candle height and the amount of time can be written as y = -0.4x + C.
Now, In order to calculate the height of the candle after 9 hours, we will substitute the value of the x as 9.
y = -0.4x + 27.
y = -0.4(9) + 27.
y = -3.6 + 27.
y = 23.4
Hence, the height of the candle after 9 hours can be written as 23.4 cm.
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How do you solve this problem: you have a random number generator that in each trial generates a number in {1,2,…,n} uniformly at random. What’s the expected number of trials to see all of the n values at least k times? Specifically for k=log(n)
A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.
How do you explain logarithm?
The exponent or power that must be added to a base to produce a particular number is called the logarithm. If bx = n, then the mathematical expression for x is x = logb n, where x is the logarithm of n to the base b. For instance, since 23 = 8, 3 is the logarithm of 8 in base 2, or 3 = log2 8.
The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to obtain a number x is hence the logarithm of a number x to the base b. For instance, since 1000 = 103, log10 of 1000 is 3, or log10 = 3.
Common logarithms, with a base of 10, binary logarithms, with a base of 2, and natural logarithms, with a base of e 2.71828, are the four most popular varieties of logarithms.
Say you have n=4 and k=2. (Next, we might look at n=8 and k=3). Let f[(x-list_),y] be the expected value of the number of random trials needed to get from a list of thus and so many hits already, to completion with y or more hits in every slot. We want f[(0,0,0,0),2].
Note that f[anylist,0]=0, and that f[(0),1]=1.
Now f[0000,2]=1+f[0001,2], because the first random number has to go somewhere and whichever one it lands on is symmetric to the case where it lands on 4.
Next, f[0001,2]=1+(1/4)f[0002,2]+(3/4) f[0011,2]=1+(1/3)f[000,2]+(3/4)f[0011,2], the second step because once one slot is filled, it just takes 4/3 times as long to finish because 1/4 of your shots will be wasted on the saturated target.
By and by, you’ll encounter f[1111,2] among other situations, and this will be equal to f[0000,1].
It’s a finite calculation, it can be written up as a recursive program, and you’ll be able to get an exact answer for any f[(however many zeros), (whatever value counts as saturation)]. The calculation will, unfortunately, run into geometric expansion of time and space as there are going to be a lot of subcases to consider even for f[00000000,3]. Still, it’s nice to have the actual exact answer for a number of representative small cases.
As to the long term situation, once you’ve fired, say, n log n shots, you theoretically might be done, having `wasted no shots’. But consider the number of hits that “1” has got. This is a binomial distribution, with the probability of k hits out of n log n shots each at odds 1/n of hitting being Binomial[n log n, k](1/n)^k((n-1)/n)^(n log n-k). This should work out to roughly a Poisson distribution, with density something like (x/log n)e^{-x/log n} being the probability that you got x hits. The saturated targets would be the ones with x greater than log n, and you’d expect a typical target would need ( log n - x ) e x / log n dx further hits.
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according to government data, 22 percent of children in the united states under the age of 6 years live in households with incomes that are classified at a particular income level. a simple random sample of 300 children in the united states under the age of 6 years was selected for a study of learning in early childhood. if the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (note: z represents a standard normal random variable.)
The probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level is approximately 0.04.
What is the binomial distribution?
In a binomial distribution, the probability of getting success must remain the same for the trials we are investigating. For example, when tossing a coin, the probability of flipping a coin is ½ or 0.5 for every trial we conduct, since there are only two possible outcomes.
To approximate the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level, we can use a normal approximation to the binomial distribution.
The sample size is n = 300 and the proportion in the population is p = 0.22. The standard deviation of the sample proportion is:
[tex]\sigma_{p}[/tex] = √(p(1-p)/n) = √(0.22(1-0.22)/300) = 0.0115
We can use the standard normal distribution to approximate the probability that the sample proportion is at least 0.27:
[tex]P(p_{hat} > = 0.27) \approx P( (p_{hat} - p) / \sigma_{p} > = (0.27 - 0.22) / 0.0115 )[/tex]
P(z >= 1.74)
where z is the standard normal variable.
We can use a standard normal table or calculator to find the probability for z >= 1.74 is about 0.04.
Hence, the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level is approximately 0.04.
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