The equation as a single logarithm is log(4x)^3)/(4y)^2
What is logarithm and some of its useful properties?When you raise a number with an exponent, there comes a result.
Lets say you get
a^b = c
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Some properties of logarithm are:
[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) \times log_b(c) = \log_a(c)[/tex]
Log with base e = 2.71828... is written as
[tex]\ln(x)[/tex]
Log with base 10 is written as
[tex]\log(x)[/tex]
Given;
Equation=3log4x-2log4y
=log(4x)^3-log(4y)^2
=log(4x)^3)/(4y)^2
Therefore, the answer of logarithm will be log(4x)^3)/(4y)^2
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If a and b are nonzero digits, then the number of digits (not necessarily different) in the sum of the three whole numbers is
9 8 7 6
A 3 2
B 1 (A). 4 (B). 5 (C). 6
(D). 9
(E). Depends on the values of A and B
If a and b are nonzero digits, the number of digits (which may or may not be different) in the sum of the three whole numbers is determined by the values of A and B that is option E.
What is digit?In mathematics, digits are single numbers that are used to represent values. In math, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used in various combinations and repetitions to represent all of the values. A digit is a symbol that can represent any of the ten numbers from 0 to 9. If a and b are nonzero digits, the number of digits (which may or may not be different) in the sum of the three whole numbers is determined by the values of A and B. A digit can be any of the following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A number is a measurement of something. It can be written with one, two, three, or more digits.
Here,
If a and b are nonzero digits, the number of digits (which does not have to be the same) in the sum of the three whole numbers is determined by the values of A and B that is option E.
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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:
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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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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What is the image of (-10,-4) after dilation by a scale factor of 1/2 centered at the origin?
Step 2 The admission price increased by 50%. Complete the bar diagram that represents 150% of the price 5 years ago. price 5 years ago = $3 So, the current admission price is current price = + or --- increase 150%
The bar diagram representing 150% of the price 5 years ago would be a bar with a height of $4.50.
What is the percentage?
Percentage is a way to express a number as a fraction of 100. It is often used to describe the relationship between two quantities, or to express a rate or change in a quantity over time. The symbol for percent is "%".
For example, if a pizza is marked up by 20%, it means the price has increased by 20/100 or 1/5 of the original price. If a student scores 80% on a test, it means they got 80 out of 100 questions correct. If a stock's value increases by 10%, it means the value has gone up by 10/100 or 1/10 of the original value.
The current admission price is $3 + $3 * 50% = $3 + $1.50 = $4.50.
150% of the price 5 years ago is $3 * 150% = $3 * 1.5 = $4.50.
So, the bar diagram representing 150% of the price 5 years ago would be a bar with a height of $4.50.
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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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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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Starting at home, Malavika walks 3 blocks west, then 6 blocks east, and finally 11 blocks west.
a) How many blocks is she from home?
b) How many blocks has she traveled?
Answer:
she is 0 blocks away from home because you said she started at home
Answer:
a) Malavika is 8 blocks west from home
b) Traveled 20 blocks total
Step-by-step explanation:
a) According to a compass: 3 west (left), then 6 east (right) and that puts you at 3 east (right). Then back 11 west (left) puts you at 8 west (left)
b) Add up all blocks traveled: 3 + 6 + 11 = 20
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
Dirk purchased a bike horn. He paid $5.33 and received $4.18 in change. How much did the bike horn cost?
$1.15
Step-by-step explanation:Let's call the cost of the bike horn "x".
Dirk paid $5.33 and received $4.18 in change, so he must have paid x + $4.18 = $5.33.
Solving for x, we get x = $5.33 - $4.18 = $1.15.
Therefore, the bike horn cost $1.15.
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
For each of the indefinite integrals below, choose which of the following substitutions would be most helpful in evaluating the integral. Enter the appropriate letter (A,B, or C) in each blank. DO NOT EVALUATE THE INTEGRALS.A. x = 4tanθB. x = 4 sin θC. x = 4 sec θ1. ∫√(x^²-16) dx2. ∫(x^² dx)/√(16-x^2) dx3. ∫ dx / (16+x^2)^34. ∫ (x^2 – 16)^(5/2) dx5. ∫ dx / (16 – x^2)^(3/2)
For equation 1, substitution x=4tanθ is the most helpful. For 2, substitution x=4sinθ is the most helpful. For 3, substitution x=4secθ is the most helpful. For 4, substitution x=4sinθ is the most helpful. For 5, substitution x=4tanθ is the most helpful.
Substitutions are often used to simplify indefinite integrals. For example, in the first integral ∫√(x^2-16) dx, substitution x=4tanθ is the most helpful. This is because it will allow us to simplify the expression under the radical. After substituting, we have ∫√(16tan^2θ-16) dθ. The 16tan^2θ can be factored to give 16(tan^2θ-1), which is equal to 16sec^2θ-16. This simplifies the integral, making it easier to integrate. In a similar way, substitution can also be used to simplify the other integrals. For example, for the fourth integral ∫(x^2 – 16)^(5/2) dx, substitution x=4sinθ is the most helpful. After substituting, we have ∫(16sin^2θ-16)^(5/2) dθ. This simplifies the integral, making it easier to integrate. In general, the substitutions chosen for each integral should be the ones that simplify the expression the most, allowing for easier integration.
1. A. x = 4tanθ
2. B. x = 4sinθ
3. C. x = 4secθ
4. B. x = 4sinθ
5. A. x = 4tanθ
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1.The angles of a quadrilateral are m,3m, 2m and 3m in that order. a Write an equation in m. Find m. C Find the angles of the quadrilateral. d Make a sketch of the quadrilateral. e What kind of quadrilateral is it? 2.Calculate the size of each angle of a e regular octagon.3. In Figure 6.25: Find the value of x. a b Find the unknown angles in the hexagon. 117⁰ 1319 2x 3x 142⁰
Answer:
=> A/Q,
m + 3m + 2m+ 3m 360° =
9m = 360°
m = 360/9
m = 40°
Angle A = m = 40°
Angle B = 3m = 120°
Angle C 2m = 80° =
Angle D = 3m = 120°
Given: ΔABC, AB=√2, M∈AC, AM=1, BM=1, and BC=2
Find: m∠ABC
The measure of the angle ∠ABC is given by 45°
What is the Pythagoras theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².
Given here: ΔABC with AB=√2, AM=1,BM=1 and BC=2
Now in ΔABM we have two sides equal AM=1,BM=1
and AB=√2
Thus AM²+BM²=AB²
Thus the triangle must be a right angled triangle with AB as its hypotenuse
let ∠B=Ф then we have TanФ=1/1
⇒ Ф=45°
Hence, The measure of the angle ∠ABC is given by 45°
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Please help (Geometry)
PICTURE INCLUDED
Answer: ASA postulate
Step-by-step explanation:
There is a congruent side included between two pairs of congruent angles.
If one side of a rectangle is 8 centimeters and the another side of the rectangle is 12 centimeters, what is the area of the rectangle?
A) [tex]96cm^{2}[/tex]
B) [tex]40cm^{2}[/tex]
C) 96 cm
D) 40 cm
Answer:
Your answer is: A) [tex]96cm^{2}[/tex]
Step-by-step explanation:
The area of the rectangle having a length of 12 cm and a width of 8 cm
is 96 cm².
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know the area of a rectangle is (length×width).
Given, one side of a rectangle is 8 cm and the other side of the rectangle is 12 cm.
Therefore, The area of this rectangle is,
= (12×8) cm².
= 96 cm².
So, the area of the rectangle is 96 cm².
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What is the rational function?
If a polynomial can be expressed as a polynomial divided by a polynomial, that function is deemed rational. x is 3, the sole zero in the denominator.
A rational function can be found in what way?The numerator and denominator degrees are frequently used to distinguish rational functions.If a polynomial can be expressed as a polynomial divided by a polynomial, that function is deemed rational. A rational function's domain is the collection of all numbers except the zeros in the denominator since polynomials are defined everywhere. f(x) Equals x in Example 1. (x - 3). x = 3, the sole zero in the denominator.Whenever the denominator polynomial is not equal to zero, a rational function is the ratio of two polynomial functions. R(x) = P(x)/Q(x) is a common representation, with P(x) and Q(x) being polynomial functions.To learn more about rational function refer to:
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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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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?
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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Without evaluating each expression, determine which value is the greatest. Explain how you know.
1.7 % -9
2. (-7)+(-93)
3. (-72).9 3/
4. (-75) ÷ (-9)
The value of 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex] is the greatest. The solution is obtained by using the arithmetic operations.
What are arithmetic operations?
In mathematics, mainly there are four basic operations upon which all the calculations are done. The operations are:
1. Addition(‘+’) wherein the sum of the numbers is obtained.
2. Subtraction(‘-’) wherein the difference of the numbers is obtained.
3. Multiplication(‘×’) wherein the product of the numbers is obtained.
4. Division(‘÷’) wherein the quotient of the numbers is obtained.
We are given first expression as 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex]
The answer for this expression can be a positive or a negative number depending on the fact which of the terms is greater.
The second expression is (-7[tex]\frac{5}{6}[/tex] ) + (- 9[tex]\frac{3}{4}[/tex])
The answer for this expression will be a negative number because addition of two negative numbers is always negative.
The third expression is (-7[tex]\frac{5}{6}[/tex] ) . 9[tex]\frac{3}{4}[/tex]
The answer for this expression will be a negative number because multiplication of one negative number and one positive number is always negative.
The fourth expression is (-7[tex]\frac{5}{6}[/tex] ) ÷ (- 9[tex]\frac{3}{4}[/tex])
The answer for this expression will be a positive number because division of two negative numbers is always positive. But, dividing two numbers will give us value close to 1 because the numbers 7 and 9 are very close to each other.
Hence, the value of 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex] is the greatest.
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the inverse of resistance is 1.0 / resistance. the following program computes the inverse of a measurement of resistance and then outputs the inversed value. the code contains one or more errors. find and fix the error(s). ex: if the input is 0.500, then the output should be: the inverse of resistance
The incorrect code contained two errors. The first was that the variable 'resistance' was initialized with a string value from the prompt, and the second was that the inverse value was not rounded off to two decimal places.
// incorrect code
//
// let resistance = prompt("Enter the resistance: ");
// inverse = 1.0 / resistance;
// console.log("The inverse of resistance is " + inverse);
// correct code
let resistance = parseFloat(prompt("Enter the resistance: "));
let inverse = 1.0 / resistance;
console.log("The inverse of resistance is " + inverse.toFixed(2));
1. In the incorrect code we have a variable 'resistance' that is initialized with a string value from the prompt. To fix this we have used the parseFloat function to convert this string to a float value.
2. In the incorrect code the inverse value is not rounded off to 2 decimal places. To do this we have used the toFixed(2) method to round off the inverse value to 2 decimal places.
The incorrect code contained two errors. The first was that the variable 'resistance' was initialized with a string value from the prompt, and the second was that the inverse value was not rounded off to two decimal places. To fix these errors, the parseFloat function was used to convert the string value of 'resistance' to a float value, and the toFixed(2) method was used to round off the inverse value to two decimal places.
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In 2003, the price of a certain automobile was approximately with a depreciation of 1,750 per year. After how many years will the cars value be $11,250? A) write an equation to model the problem. Let the represent the number of years after 2003. For example, the year 2005 would be represented by t=2. B)Solve the equation to find the answer to the question above.
The number of years after 2003 that the car's value will be $11,250 is t = 7.5 years.
In 2003, the price of a certain automobile was approximately with a depreciation of 1,750 per year. After how many years will the cars value be $11,250 A) write an equation to model the problem. Let the represent the number of years after 2003.
A) The equation to model the problem is:
Price in year t = 2003 Price - (t - 1)(1,750)
B) To solve the equation for t, we can rearrange it to isolate t:
t = (2003 Price - 11,250) / 1,750
Therefore, the number of years after 2003 that the car's value will be $11,250 is t = 7.5 years. This means that the car's value will be $11,250 in the year 2010.5.
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One number is 7 more than another number. If the smaller number is doubled and added to 3 times the larger number, the sum is 86. Find the two numbers.
Smaller number =
Larger number=
(Type the integers or decimals.)
Smaller number = 7
Larger number = 14
How to solve algebraic equation?An algebraic equation can be solved in a variety of ways.
The method you use to solve an equation depends on the type of equation and the information you are given.
Some of the most common methods to solve algebraic equations include using factoring, using the quadratic formula, completing the square, graphing, and using the substitution method.
This question uses the algebraic equation solving technique.
Step 1: Create an equation that relates the two numbers.
Let x = the smaller number
Let y = the larger number
2x + 3y = 86
Step 2: Substitute the given information into the equation.
We know that y = x + 7, so we can substitute that into the equation.
2x + 3(x + 7) = 86
Step 3: Solve the equation.
2x + 3x + 21 = 86
5x + 21 = 86
5x = 65
x = 13
Step 4: Substitute the value for x into the expression for y.
y = x + 7
y = 13 + 7
y = 20
Therefore, the two numbers are 7 and 14.
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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.
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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use letters and number if needed to create a word problem and solve it:
look at image to create one
ex) Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?
Answer:
Cayley earned per day: 4 x 5 = 20
: Her earning per week- 3 x 20 = 60
: Her earning for 8 weeks- 8 x 60 = 480
Cayley earns $480 per week.
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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