According to the given data in question below given are the separate journal entries for each transaction on the books of Metlock, Inc.
What is entries?"Entries" typically refers to the individual values in a matrix or table. A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns, while a table is an arrangement of data in rows and columns with each intersection representing a single piece of data.
1.On June 10, Metlock, Inc. made an account-based purchase from the Monty Company for $7,400 in goods, FOB shipping point, 3/10, n/30.
Inventory (asset) $7,400
Accounts payable (liability) $7,400
2. On June 11, Metlock, Inc. pays the freight costs of $560:
Freight expense (expense) $560
Cash (asset) $560
3. On June 12, goods totaling $600 are returned to Monty for credit:
Accounts payable (liability) $600
Inventory (asset) $600
4. On June 19, Metlock, Inc pay Monty Company in full, less the purchase discount:
Accounts payable (liability) $7,400
Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]
Cash (asset) $7,178
Note that the purchase discount is calculated as $7,400 x 3%, or $222.
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The information in issue below is taken from Metlock, Inc.'s books, which include separate journal entries for each transaction.
Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]
Cash (asset) $7,178
What is entries?1.On June 10, Metlock, Inc. made an account-based purchase from the Monty Company for $7,400 in goods, FOB shipping point, 3/10, n/30.
Inventory (asset) $7,400
Accounts payable (liability) $7,400
2. On June 11, Metlock, Inc. pays the freight costs of $560:
Freight expense (expense) $560
Cash (asset) $560
3. On June 12, goods totaling $600 are returned to Monty for credit:
Accounts payable (liability) $600
Inventory (asset) $600
4. On June 19, Metlock, Inc pay Monty Company in full, less the purchase discount:
Accounts payable (liability) $7,400
Purchase discounts (contra expense) $222 [($7,400 x 3%) = $222]
Cash (asset) $7,178
Note that the purchase discount is calculated as $7,400 x 3%, or $222.
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The volume of a soap bubble is 1,696.5mm^3. Find the radius and diameter of the soap bubble. Use 3.14 for pie
After solving the question, we can say that diameter of the soap bubble =14.30 mm.
what is sphere ?A sphere, like a ball, is a three-dimensional geometrical object that is completely spherical. It is a symmetrical form with all points on its surface being equidistant from the centre. The radius of a sphere is the distance from its centre to its surface. Spheres can be found in nature in the shape of planets, stars, and bubbles, and they are utilised in a variety of applications including sports equipment, ball bearings, and aesthetic things.
volume of a sphere
[tex]V = (4/3) * \pi * r^3\\ r = (3V / 4 \pi)^(1/3)\\ r = (3 * 1696.5 mm^3 / (4 * 3.14))^(1/3)\\ r = 7.15 mm[/tex]
d = 2r
d = 14.30 mm
diameter of the soap bubble =14.30 mm.
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A survey of all beings on planet Boondin found that 60% preferred hopt
juice to all other juices. If 50 beings were surveyed altogether, how
many of them preferred hopt juice?
label optional
Answer:
If 60% of the beings surveyed preferred hopt juice and 50 beings were surveyed altogether, then we can calculate the number of beings who preferred hopt juice by multiplying the total number of beings surveyed by the percentage that preferred hopt juice: `50 x 0.60 = 30`. So, **30** beings preferred hopt juice.
The table summarizes results from 982 pedestrian deaths that were caused by automobile accidents.
pls help with this question im offering all of my tokens for this
Answer:
34 ft.²
Step-by-step explanation:
We can find the area of this polygon by splitting it into two rectangles.
We can find the area of each individual rectangle, then add their areas to get the area of the entire polygon.
See the attached image for a diagram.
First, we can find the area of the smaller rectangle.
length × width
5 ft. × 2 ft. = 10 ft.²
Next, we can find the area of the larger rectangle.
4 ft. × 6 ft. = 24 ft.²
Finally, we can add the two rectangles' areas together to get the area of the entire polygon.
10 ft.² + 24 ft.² = 34 ft.²
Help me please!!!!!!
Due to its neighbouring perpendicular sides and opposite parallel and equal-length sides, the quadrilateral ABCD is a rectangle.
What are the properties of parallelogram?a) The opposite sides are parallel and equal.
b) The opposite angles are equal.
c) The consecutive or adjacent angles are supplementary.
d) If any one of the angles is a right angle, then all the other angles will be at right angle.
e) The two diagonals bisect each other.
4. To find the area of a parallelogram, you can follow these steps:
Measure the length of the base of the parallelogram. Let's call this measurement "b".
Measure the height of the parallelogram. Let's call this measurement "h".
Multiply the base length "b" by the height "h" to get the area of the parallelogram.
Therefore, the formula to calculate the area of a parallelogram is:
Area = base length (b) [tex]*[/tex] height (h)
In symbols, this can be written as:
[tex]A = b \times h[/tex]
Alternatively, if the length of both adjacent sides is known, you can use the formula:
A = base length (b) [tex]*[/tex] the length of adjacent [tex]side (a) * sin[/tex](θ)
where theta is the angle between the base and adjacent side.
5. the given vertices on a coordinate plane and see what kind of figure they form.
The figure formed by the vertices A, B, C, and D is a quadrilateral. To determine the precise classification of the quadrilateral, we can use its properties.
To determine if the parallelogram is a rhombus, rectangle, or square, we need to check if the diagonals bisect each other and if the adjacent sides are perpendicular. We can find the midpoint of AC and BD as:
Midpoint of AC: [tex]((2 + 8)/2, (3 + 7)/2) = (5, 5)[/tex]
Midpoint of BD: [tex]((7 + 3)/2, (2 + 8)/2) = (5, 5)[/tex]
The diagonals AC and BD intersect at the midpoint [tex](5,5)[/tex], so they bisect each other.
We can also find the slopes of adjacent sides AB and BC, and we find that they are:
AB: [tex]-1/5[/tex]
BC: [tex]5[/tex]
The product of their slopes is [tex]-1[/tex], so the adjacent sides are perpendicular.
Therefore, the quadrilateral ABCD is a rectangle, because it has opposite sides that are parallel and equal in length, and adjacent sides that are perpendicular.
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How to solve “What is m
Answer: 120
Step-by-step explanation:
The angle measures should add up to 360
110+130+x=360
240+x=360
x=120
A parabola opening up or down has vertex
(-4, -6) and passes through (-14, 13/2)
Write its equation in vertex form.
Answer:
To write the equation of the parabola in vertex form, we use the standard form:
y = a(x - h)^2 + k, where (h, k) is the vertex.
Given that the vertex is (-4, -6), we have:
h = -4 and k = -6
Now, we need to find the value of "a" using the point (-14, 13/2) which lies on the parabola.
Substituting the values in the standard form, we get:
13/2 = a(-14 - (-4))^2 - 6
Simplifying, we get:
13/2 = 100a - 6
100a = 13/2 + 6
a = 19/200
Therefore, the equation of the parabola in vertex form is:
y = (19/200)(x + 4)^2 - 6
Step-by-step explanation:
Complete the table of values for y = x^2 - 2x - 1
Please help ASAP due for tomorrow!!
The values of the quadratic equation; y = x² - 2·x - 1 can be used to complete the table and draw the graph as follows;
(a) x[tex]{}[/tex] -2 -1 0 1 2 3 4
y[tex]{}[/tex] 7 -1 2 -2 -1 2 7
(b) Please find attached the graph of the quadratic equation created with MS Excel
What is the graph of an equation?A graph of an equation is a visual representation of the rule of the equation that shows how the output value changes as the input values is varied.
The table of values in the question can be completed by substituting the x-values in the table into the equation; y = x² - 2·x - 1 as follows;
The values that complete the table are;
y when x = -1 is; y = (-1)² - 2 × (-1) - 1 = 2
y when x = 0 is; y = (0)² - 2 × (0) - 1 = -1
y when x = 3 is; y = (3)² - 2 × (3) - 1 = 2
y when x = 4 is; y = (4)² - 2 × (4) - 1 = 7
The completed table is therefore presented as follows;
x[tex]{}[/tex] -2 -1 0 1 2 3 4
y [tex]{}[/tex] 7 -1 2 -2 -1 2 7
(b) The steps that can be used to draw the graph on the coordinate grid using MS Excel are as follows;
Create a new or existing MS Excel spreadsheetInput the x-values in (for example) column A with values of x from -2 to 4, and in column B the corresponding y-values are obtained using the formula {"=A1^2 - 2*A1 - 1", followed by copying the formula across the cells adjacent to the x-valuesSelect the cells containing the x- and y-values Click on "Insert" tab then click on "Scatter" chart type to select a preferred chartClick on the preferred chart to display the graph of the equation, y = x² - 2·x - 1Please find attached the graph of the quadratic equation, y = x² - 2·x - 1, created with MS Excel
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Which of the following describes the absolute value of a number?
The absolute value of a number is the square root of the
number.
The absolute value of a number is the negative value of the
number.
The absolute value of a number is the square root of the
positive value of the number.
The absolute value of a number is the positive value of the
number.
The absolute value of a number is its negative recicprocal.
Answer: Your answer should be
D
Step-by-step explanation: this is because absolute value makes a number positive, no matter the scenario as long as the number(s) are in the absolute value sign (indicated basically by straight lines) this makes it to where the number can never be negative within the lines.
The first used 20 gal of fuel and the second used 25 gal. The 2 drove 1450 miles and the sum of their fuel efficiencies was 65 miles per gal. What we’re each car fuel efficiency?
Answer: there you go :)
Car 1 consumes 30 gallons of gas.
Car 2 consumes 20 gallons of gas.
Step-by-step explanation:
Let x = gallons consumed by car 1
Let y = gallons consumed by car 2
We set up our equations:
35x+40y = 1850 eq1
x+y = 50 eq2
Substituting eq 2 into eq 1,
35x+40(50-x) = 1850
35x+2000-40x = 1850
-5x+2000 = 1850
-5x = -150
x = 30
Substitute value of x into eq 2.
x+y = 50
30+y = 50
y = 20
Car 1 consumes 30 gallons of gas.
Car 2 consumes 20 gallons of gas.
Ethan sold 2/3 gallons of lemonade.Kayla sold some lemonade too.Together,they sold 1 1/4 gallons.
Who sold more lemonade,Ethan or Kayla? How much more
Answer: Kayla sold 1/12 gallons more than Ethan.
Step-by-step explanation:
Let's start by finding out how much lemonade Kayla sold. We know that together, Ethan and Kayla sold 1 1/4 gallons, which is the same as 5/4 gallons. We also know that Ethan sold 2/3 gallons. Therefore, we can find how much Kayla sold by subtracting Ethan's sales from the total sales:
Kayla's sales = Total sales - Ethan's sales
Kayla's sales = 5/4 - 2/3
To subtract these fractions, we need to find a common denominator. The smallest common multiple of 4 and 3 is 12, so we can rewrite the fractions with 12 as the denominator:
Kayla's sales = (5/4)(3/3) - (2/3)(4/4)
Kayla's sales = 15/12 - 8/12
Kayla's sales = 7/12
Therefore, Kayla sold 7/12 gallons of lemonade. Now, we need to compare this to Ethan's sales. We can convert Ethan's sales to twelfths to make it easier to compare:
Ethan's sales = (2/3)(4/4) = 8/12
Now we can see that Kayla sold more lemonade than Ethan. The difference in sales is:
Kayla's sales - Ethan's sales = 7/12 - 8/12
Kayla's sales - Ethan's sales = -1/12
The result is negative, which means that Ethan sold 1/12 gallons less than Kayla. Therefore, Kayla sold 1/12 gallons more than Ethan.
Consider a random variable X with PDF
fX(x) = (2x/3, if 1 < x ≤ 2,
0, otherwise,
and let A be the event {X ≥ 1.5}. Calculate E[X], P(A), and E[X | A].
By answering the presented question, we may conclude that As a result, variable P(A) = 0.667.
What is a Variable?A variable is something that may be changed in the setting of a math concept or experiment. Variables are often represented by a single symbol. The characters x, y, and z are often used generic symbols for variables. Variables are characteristics that can be examined and have a large range of values. These include things like size, age, money, where you were born, academic status, and your kind of dwelling, to name a few. Variables may be divided into two main categories using both numerical and categorical methods.
To compute E[X], we must integrate the PDF X times over its support:
From x=1 to x=2, E[X] = x fX(x) dx
Because the PDF is only non-zero in the interval (1,2), we have:
[tex]E[X] = x(2x/3) dx between x=1.5 and x=2.E[X] = (2/3) x2 dx between x=1.5 and x=2.E[X] = (2/3) [(2^3)/3 - (1.5)^3]E[X] = (2/3) [8/3 - (27/8)]E[X] = 19/12As a result, E[X] = 1.583.[/tex]
P(A) is calculated by integrating the PDF across the area where X is higher than or equal to 1.5:
[tex]P(A) = fX(x) dx between x=1.5 and x=2.P(A) = (2x/3) dx between x=1.5 and x=2.P(A) = [(2/3)x^2] between x=1.5 and x=2P(A) = (2/3)(2^2 - 1.5^2)P(A) = 2/3As a result, P(A) = 0.667.[/tex]
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Complete question -
Consider a random variable X with PDF fX(x) = (2x/3, if 1 < x ≤ 2, 0, otherwise, and let A be the event {X ≥ 1.5}. Calculate E[X], P(A), and E[X | A].
Trigonometry: Sum and difference Identities
MUST GIVE EXPLANATION:
Will give BRAINLIEST.
Using the sum-to-product formula we get the value as √2 cos(2α)
What is the sum-to-product formula?
The sum-to-product formula is a trigonometric identity that expresses the sum or difference of two trigonometric functions as a product of two trigonometric functions. There are several versions of this formula, depending on the specific functions involved.
We can use the sum-to-product formula to simplify the expression:
cos(2α - π/16) + cos(9π/16 - 2α)
= cos(2α)cos(π/16) - sin(2α)sin(π/16) + cos(9π/16)cos(2α) + sin(9π/16)sin(2α)
= cos(2α)(cos(π/16) + cos(9π/16)) + sin(2α)(-sin(π/16) + sin(9π/16))
= cos(2α)(2cos(5π/16)cos(3π/16)) - sin(2α)(2cos(7π/16)sin(π/16)) (using the sum-to-product formula again)
= 2cos(2α)cos(5π/16)cos(3π/16) - 2sin(2α)cos(7π/16)sin(π/16)
= 2cos(2α)(cos(5π/16)cos(3π/16) - sin(5π/16)sin(3π/16)) (using the product-to-sum formula)
= 2cos(2α)cos(π/4)
= 2cos(2α)/√2
= √2 cos(2α)
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Plot 1 7/8 abd 2 1/2 on the number line
4. The Bagel Factory baked 200 dozen bagels at a cost of R3.60 per dozen. Five dozen bagels become stale and cannot be sold, and 12 dozen are sold at a reduced price of R1.80 dozen. Find the selling price per dozen bagels that will give the bakery their required mark- up of 66% of cost. per
Answer:
R5.98
Step-by-step explanation:
R3.60×66÷100= R2.38 (66% of R3.60)
R3.60+R2.38= R5.98
how to find 66%
R5.98-R3.60
=R2.38÷R3.60
=R0.66×100
=66%
anyone have an idea of what this may be?
The values of the segments A'B' and B'B for the similar triangle ∆ABC area 4 and 4 respectively.
How to calculate the for the segments of the similar triangleThe triangles ABC and A'B'C are similar, this implies that the length A'C of the smaller triangle is similar to the length AC of the larger triangle
so for the segment A'B;
3/9 = A'B'/12
A'B' = (3 × 12)/9 {cross multiplication}
A'B' = 4.
Also for the segment B'B;
3/9 = 2/(2 + B'B)
3(2 + B'B) = 2 × 9 {cross multiplication}
6 + 3B'B = 18
3B'B = 18 - 6
B'B = 12/3
B'B = 4
Therefore, the values of the segments A'B' and B'B for the similar triangle ∆ABC area 4 and 4 respectively.
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what month comes under the 250th day of the year?
Answer:september
Step-by-step explanation:
General solution of sin
Question 1
Write an equation for the surface area of a prism with a length, width, and height of x
inches.
Question 1
Write an equation for the surface area of a prism with a length, width, and height of x
inches.
Answer:
The formula for the surface area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
Since the length, width, and height of the prism in this case are all x inches, we can substitute x for l, w, and h in the formula to get:
Surface Area = 2(x)(x) + 2(x)(x) + 2(x)(x)
Simplifying the equation, we get:
Surface Area = 2x^2 + 2x^2 + 2x^2
Surface Area = 6x^2
Therefore, the equation for the surface area of a prism with a length, width, and height of x inches is:
Surface Area = 6x^2 square inches
What is the measure of a dekaliter?
Answer: Ten liter, or one tenth of a hectoliter (2.6418 gallons liquid measure or 1.135 pecks dry measure): abbrev.dal.
Find a quadratic function of the form y = ax that passes through the point (-2,16).
Y=
Answer:
y = 4x^2
Step-by-step explanation:
To find a quadratic function of the form y = ax^2 that passes through the point (-2,16), we need to substitute the coordinates of the point into the equation and solve for the coefficient a.
Substituting x=-2 and y=16 into the equation, we get:
16 = a(-2)^2
16 = 4a
a = 4
Therefore, the quadratic function of the form y = ax^2 that passes through the point (-2,16) is:
y = 4x^2
Please I’d love some help with a simple explanation on how you got the answers and the answers (obviously)
Given the above circles,
1) x = 42°
2) x = 29°
3) x = 101°
4) x = 37°
5) x = 31°
6) x = 120°
What is the explanation for the above results?1) x = 42° because the Angles at the circumference of a circle
subtended by the same arc are equal. Since 35° and 103° are two of the three angles in a triangle whose third angle subtends the circumference of the circle along with ∠x, and the third angle = 180 - 35 - 103 = 42° therefore, x = 42°
2) x = 29° because according to the central angle theorem, the angle at the circumference is double the one at the center. Since the angle at the circumference is 61°, the one at the center is 122°. Since the line from the center that couches on both sides of the circumference is the radius, they are equal. Hence, the angles formed at their bases are equal.
Thus, x = (180-122)/2
x = 29°
3) 3) x = 101° because the opposite angles of a cyclic quadrilateral are supplementary.
4) x = 37° based on the angle in the alternate segment theorem.
5) x= 31° is based on the "inscribed angle theorem" or the "theorem of the intercepted arc".
This theorem states that if an angle is inscribed in a semicircle, then the angle is a right angle (i.e., it measures 90 degrees). In other words, if you draw any two chords from the ends of the diameter to any point on the arc of the semicircle, then the angle formed by these two chords at the point on the arc will always be 90 degrees.
6) x = 120° on the basis of the "Tangent-Secant Angle Theorem" or "Tangent-Chord Angle Theorem".
In the problem given above, the angle x is formed by two tangents intersecting at the vertex outside the circle, and the Tangent-Secant (or Tangent-Chord) Angle Theorem is used to find its measure.
The arc formed at the points where the two tangents meet is twice the angle formed inside the circle which is = 30°
Thus, where the rest of the arc traced from the upper point of tangency is traced back to the lower point of tangency is called A,
The measure of arc A is 360° - 60° = 300°.
The measure of angle x is half the difference between the measures of the intercepted arcs, which is (300° - 60°)/2 = 120°.
Therefore, the measure of angle x would be 120°.
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Find the volume of the figure.
Answer:
165inch^3
Step-by-step explanation:
4×7×3=84inch^3
9×3×3=81inch^3
84+81=165inch^3
PLEASE HELP FAST!!
Solve the following system by elimination. CHECK the solution.
- 3x - 6y = - 27
4x - 2y= -4
Answer: -3x - 6y = -27 (Equation 1)
4x - 2y = -4 (Equation 2)
We can use the method of elimination, which involves adding or subtracting the equations to eliminate one of the variables.
In this case, we can start by multiplying Equation 2 by 3 to eliminate the y variable:
-3x - 6y = -27 (Equation 1)
12x - 6y = -12 (Equation 2 multiplied by 3)
Now we can add Equation 1 to Equation 2:
-3x - 6y = -27 (Equation 1)
12x - 6y = -12 (Equation 2 multiplied by 3)
9x = -39
Simplifying this expression, we get:
x = -39/9 = -13/3
Now we can substitute this value of x into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:
-3x - 6y = -27
-3(-13/3) - 6y = -27
13 + 6y = -27
6y = -40
y = -40/6 = -20/3
Therefore, the solution to the system of equations is x = -13/3 and y = -20/3, or (-13/3, -20/3) in coordinate form.
To check the solution, we can substitute the values of x and y into both equations:
-3(-13/3) - 6(-20/3) = -27
4(-13/3) - 2(-20/3) = -4
Simplifying both expressions, we get:
13 + 40 = 27 (which is true)
-52/3 + 40/3 = -4 (which is also true)
Therefore, the solution is correct.
Step-by-step explanation:
"A number decreased cubed by 24"
The expression that represents the sentence "A number cubed decreased by 24" is given as follows:
x³ - 24.
What is the algebraic expression that models the sentence?The sentence for this problem is defined as follows:
"A number cubed decreased by 24".
The number is unknown, hence the variable that represents the number is given as follows:
x.
The cube of the number is given as follows:
x³.
The number is then decreased by 24, hence we subtract the expression x³ by 24 to obtain the algebraic expression as follows:
x³ - 24.
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The following images are some basic limits on graphs , please answer them.
The piecewise function formed by two functions and a point is not continuous at x = 1.
How to determine limits in a piecewise function
In this problem we find the case of a piecewise function formed by three expressions in three corresponding intervals: two functions and a point. These expressions are defined in the images attached below. The x-value is on the horizontal axis and the y-value is on the vertical axis.
According to the first figure, the y-value of the function is getting closer to 2 as x approaches 1 from the left side.
According to the second figure, the y-value of the function is getting closer to 3 as x approaches 1 from the left side.
According to the third figure, the y-value of the function is equal to 0.5 when x is equal to 1.
Therefore, the piecewise function is not continuous at x = 1.
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log19(53.875) to base 10
Log base 19 of 53.875 is approximately 0.97212 when converted to base 10.
To convert log base 19 of 53.875 to base 10, we can use the formula:
log base b of x = log base a of x / log base a of b
where a: current base and b: desired base.
So, in this case, we want to convert log base 19 of 53.875 to base 10. We can use the formula above with a = 19 and b = 10:
[tex]log base 10 of 53.875 = log base 19 of 53.875 / log base 19 of 10[/tex]
Log base 19 of 10 is equal to 1/log base 10 of 19, since the logarithm of 10 to any base is equal to 1. Using a calculator, we can determine that the log base 10 of 19 is roughly 1.278753.
Substituting:
log base 10 of 53.875 = log base 19 of 53.875 / 1.278753
To find the value of log base 19 of 53.875, we can use a calculator to evaluate log base 19 of 53.875, which is approximately 1.244036.
Substitute to equation:
log base 10 of 53.875 = 1.244036 / 1.278753
Simplify to get:
log base 10 of 53.875 = 0.97212
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Helpppp pleaseee
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
To find the annual rate of change between 1992 and 2006, we can use the formula:
r = [tex](V_2/V_1)^{1/n}-1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.
=>r = -0.0839
Therefore, the rate of change between 1992 and 2006 is -0.0839.
To express the rate of change in percentage form, we can multiply the result from part A by 100:
=>r = -0.0839 x 100
=> r = -8.39%
Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.
To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.
From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:
where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.
=>V = 11792.51
Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).
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Factor the trinomial completely
64x² +8x+1/4
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(Factor completely. Simplify your answer. Use integers or fractions for any numbers in the expression)
A. 64x² + 8x + =
B. The polynomial is prime.
A.Factorizing the polynomial is (8x + 1/2)².
B.The polynomial 64x² + 8x + 1/4 is not prime.
define factorizationFactorization is the process of expressing a mathematical expression, such as a number or a polynomial, as a product of its factors or simpler components.
To factorize 64x² + 8x + 1/4, we can use the factoring formula for a quadratic trinomial:
a² + 2ab + b² = (a + b)²
In this case, we have 64x² + 8x + 1/4, so we can rewrite it as:
(8x)² + 2(8x)(1/2) + (1/2)²
Notice that the first and last terms are perfect squares, so we can apply the factoring formula to get:
(8x + 1/2)²
Therefore, the factorization of 64x² + 8x + 1/4 is:
64x² + 8x + 1/4 = (8x + 1/2)²
The polynomial 64x² + 8x + 1/4 is not prime.
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Question 7 (5 points) Simplify the expression. (4 + )(7 – ) Question 7 options: 28 – 4 + 7 – 28 + 4 + 7 – 28 – 4 + 7 + 28 + 4 + 7 +
The simplified expression is 28 - 4 using distributive property.
To simplify the expression (4 + )(7 – ), we can use the distributive property of multiplication over addition.
First, we have to multiply the 4 by both the terms inside parentheses:
(4 + )(7 – ) = (47) + (4- )
Next, we distribute negative sign to second term inside parentheses:
(47) + (4- ) = 28 - 4
The simplified expression = 28 - 4.
In other words, the phrase is the outcome of adding 4 to an unknown quantity, taking it out of 7 after that, and then taking the outcome of that subtraction out of 28. The operation's outcome is simplified to 24, which can be used in additional calculations or problem-solving.
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