A = $ 1100.76 the amount in a continuously compounded account for the given conditions.
What does compound interest entail?
Compound interest is when you receive interest on both your interest income and your savings. Let's imagine you invest $1,000 (your principal) and it earns 5% once a year in interest or profits (the compounding frequency).principal: $ 1000 annual
interest rate: 4.8%
time: 2 years
We know that continuously compound interest
A = [tex]P_{0} e^{rt}[/tex]
= [tex]1000 e_{(0.048)(2)}[/tex]
= [tex]1000 (e)^{0.096}[/tex]
= [tex]1000 ( 1.10075906 )[/tex]
= 1100 . 75906
A = $ 1100.76
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If AABC AFDE, which of the following statements is true? O ZA ZE O
If ∆ABC and ∆FDE are congruent, then the correct statement among options is ∠C ≅ ∠E.
Congruent figures refers to the figures that can be superimposed on each other. This states that the angles and sides are similar for both the figures being compared. We are given that two triangles are congruent. Same will be true for their sides as well.
Thus, we can interpret that similar angles in the mentioned two triangles will be -
∠A ≅ ∠F
∠B ≅ ∠D
∠C ≅ ∠E
Similarly, the similar sides for both triangles will be -
AB ≅ FD
BC ≅ DE
AC ≅ FE
Therefore, in the congruent triangles ABC and FDE, ∠C and ∠E are congruent.
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A yearly subscription to a monthly magazine costs £42.00. How much does each issue
cost?
Each issue will cost £3.5 if a yearly subscription to a monthly magazine costs £42.00.
Given, a yearly subscription to a monthly magazine costs £42.00 i.e., 12 months to a monthly magazine costs £42.00.
one month will cost £42.00 divide by 12 and let it be x.
we simply calculate the value of x by dividing £42.00 by 12.
x = 42.00/12
x = 3.5
x = £3.5
Therefore, each issue will cost £3.5 if a yearly subscription to a monthly magazine costs £42.00.
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Find the inverse of each function. Determine whether each inverse is a function. f(x)=2 x²-8
The inverse of the function f(x) = y = 2x² - 8 is [tex]y=\pm\sqrt{\frac{x+8}{2} }[/tex].
A function's inverse is a function that reverses the action of a function, say [tex]f[/tex]. If the inverse of f exists, it is denoted by f ⁻¹ and exists only if f is a bijective function.
The domain of a relation's inverse corresponds to the original relation's range. In other words, the inverse's x values are the relation's y values.
Consider the function,
f(x) = y = 2x² - 8
Swapping x and y, to find the inverse.
x = 2y² - 8
Adding 8 on both sides of the equation.
x + 8 = 2y² - 8 + 8
2y² = x + 8
Dividing each side of the equation by 2.
y² = ( x + 8 )/ 2
Taking the square root of the equation.
[tex]\sqrt{y^{2}}=\pm\sqrt{\frac{x+8}{2} }[/tex]
[tex]y=\pm\sqrt{\frac{x+8}{2} }[/tex]
The inverse of the function f(x) = y = 2x² - 8 is [tex]y=\pm\sqrt{\frac{x+8}{2} }[/tex].
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Solve using law of exponents
Graph the inequality. z is less than or equal to 5
Terry was measuring the volume of water on a graduated cylinder but did not notice that the measurements incremented by 2 instead of by 1. As a result he misread the volume of the liquid as 33.0 instead of 36.0. What is his percent error?
We conclude that the percent error in Terry's reading is 8.3 percent.
How to find the percent error?If you did a reading on a value V, and your reading is another value V', the percent error in your reading is given by the formula:
P = 100%*|V - V'|/V
In this case, Terry's reading of the volume of the liquid is V' = 33.0, while the actual value is V = 36.0
Replacing that in the formula for the percent error we get:
P = 100%*|36.0 - 33.0|/36.0 = (3.0/36.0)*100% = 8.3%
We conclude that the percent error in Terry's reading is 8.3 percent.
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A figure has two pairs of parallel sides and four right angles. The figure is translated 4 units down. How many parallel sides does the imagine have?
The number of parallel sides that the translated figure will have is 2 pairs of parallel sides.
What is the result of translation of an Object?
We are given the properties of the figure as;
Number of Parallel sides = Two Pairs
Number of Right Angles = 4
Now, a rectangle is the figure that has two pairs of opposite sides parallel, and four right angles. A square could also have this same properties.
Now, if the figure is translated by 4 units down, according to transformation, that does not change the dimension of the figure and as such it retains same number of parallel sides.
Thus, the number of parallel sides that the translated figure will have is 2 pairs of parallel sides.
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Simplify each expression. (125)⁻²/₃
$10 off $50
Buy-1-Get-1 Half Off
Customers
Spending
More than $30
Customers
Spending
$30 or Less
Which statement best describes how the manager can check if there is an association between the two variables?
The manager must check relative frequencies by row because there are more than two different promotions.
The manager must check relative frequencies by column because there are more than two different promotions
The manager cannot use relative frequencies to look for an association because there are more than two differes
s by now and by column to look for an association.
There are more than two distinct promotions, thus the manager must verify the relative frequencies per column.
The management must examine the relative frequencies by column since there are more than two different promotions, according to the statement that best sums up the relationship between the two variables.
Relative frequency is defined.The ratio of the number of times an event happened to the overall number of events is known as the relative frequency. In essence, it is the frequency ratio between the subgroups and the entire population.
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How do we find the constant rate from two points? (Write yourself step by step
directions to do this)
Step-by-step explanation:
It sounds like you need to find your slope. The equation is y2-y1/x2-x1
Say you have two points, and those two points make a line.
Say those points are (0,0), and (5,5).
To find the slope, we need which is equal to x2-x1/y2-y1 (the two coordinates for the points) which in this case, equals one. That means the constant rate of going up is, 1 each time it moves to the left once.
I hope this answers your problems. If you don't understand anything, I can try to help in the comments!
Solve. Check for extraneous solutions. (5-x)¹/₂=x+1
x = -4 is the extraneous solution of the equation.
The equation is
(5 - x )^1/2 = x + 1
To find the extraneous solution first we need to find the value of x.
So we need to square on both sides of the equation
[tex](\sqrt{5- x})^{2}[/tex] = [tex](x + 1)^{2}[/tex]
5 - x = [tex]x^{2}[/tex] +2x + 1
[tex]x^{2}[/tex] + 3x - 4= 0
[tex]x^{2}[/tex] + 4x - x - 4 = 0
x( x + 4 ) - 1 ( x + 4) = 0
( x + 4)( x - 1) =0
x = -4, 1
Now put both the value of x in the solution in the equation.
x = -4
[tex]\sqrt{5 - (-4)}[/tex] = -4 + 1
[tex]\sqrt{9}[/tex] = -3
3≠ -3
Now put
x = 1
[tex]\sqrt{5 -1}[/tex] = 1 +1
[tex]\sqrt{4}[/tex] = 2
2 = 2
Therefore we get that x = -4 is the extraneous solution of the equation and x = 1 is the solution of the equation.
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Normal curve g has a mean of 50 and a standard deviation of 5. Normal curve h has a mean of 50 and a standard deviation of 10. How do the shapes of these two normal curves compare if they are drawn using the same scale?.
Drawn using the same scale, the shape of the normal curve H will be more spread out than the shape of the normal curve G.
Normal curve, or Gaussian distribution, is a curve that describes data form a variable that has infinite, or very large, number of possible values distributed among the population. It has a symmetric shape, and the distribution rises in the middle, and goes down to the left and to the right. The mean is equal to the mode and median and is located at the middle or top of the curve.
If two normal curves have the same mean, but different standard deviations, then the curve with the larger standard deviation will have a more spread out shape than the other.
If Normal curve H has a standard deviation of 10 and normal curve G has 5, but both has the same mean, then Normal curve H has a more spread out shape than the curve of normal curve G.
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table for y= - 4/7 x - 2
By evaluating the equation we found 3 pairs we can write the table:
x = -7, 0, 7
y = 2, -2, -6
Which represents our equation.
How to get a table for the given relation?We want to get a table of the form:
x: x₁, x₂, x₃, ...
y: y₁, y₂, y₃, ...
To get that, we need to evaluate the given equation in some different values of x, so let's do that.
if we take x = 0, then we get:
y = -(4/7)*0 - 2 = -2
So we have the pair (0, -2)
If x = 7, then:
y = (-4/7)*7 - 2 = -4 - 2 = -6
So we have the pair (7, -6)
If x = -7 then:
y = (-4/7)*-7 - 2 = 4 - 2 = 2
So we have the pair (-7, 2)
So now that we have 3 pairs we can write the table:
x = -7, 0, 7
y = 2, -2, -6
Which represents our equation.
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How do I solve 3/4m - 1/12m = 7/8?? (This is a linear equation problem btw if you didn’t know).
1/4x-2=2x-9
find value for x
Answer:
Add 2 to both sides.
1/4x=2x-7
Multiply both sides by 4
x=8x-28
-8x from each side.
-7x=-28
divide both sides by -7
X=4
Answer: x=4
1. Multiply both sides by 4 to get rid of the denominator, which gives you x-8 = 8x-36
2. Subtract 8x from both sides, which gives you x - 8 - 8x= -36
3. Add 8 to both sides, which gives you x - 8x = -36 + 8
4. Simplify, -7x = -28
5. Divide both sides by -7, x = -28/-7
6. the negative signs cancel and you just get 4
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Every year, the US Census Bureau publishes its Annual Survey of School System Finances. The back-to-back stemplot below shows the 2016 per-pupil expenditure (rounded to the nearest $100) for eastern and western states and the District of Columbia in the United States.
A stemplot titled Per-pupil expenditure for U S States. 7 line 0 means 7,000 dollars per pupil. Eastern States: The values are 87, 88, 88, 89, 92, 98, 92, 92, 102, 113, 114, 117, 121, 132, 141, 142, 147, 153, 154, 155, 156, 179, 184, 190, 191, 223. Western States: The values are 70, 71, 76, 81, 90, 91, 92, 96, 97, 98, 100, 103, 105, 105, 108, 110, 112, 113, 115, 123, 123, 134, 138, 164, 175.
Based on the stemplot, which of the following is a correct comparison of the eastern and western states’ expenditures?
The stemplot gives a correct comparison of eastern and western states’ expenditures as The eastern states have, on average, a higher per-pupil expenditure than the western states.
What does the stemplot show?The Eastern States have expenditure per pupil which are higher in number and in quantity. For instance, they have per-pupil expenditure of $153, $154, $155, and $156. They also have $191, and $190.
When compared to the western states therefore, the eastern states seem to on average, spend more per-pupil.
Options for this question include:
The western states exhibit more variability in their expenditures than the eastern states. The eastern states have, on average, a higher per-pupil expenditure than the western states. The distribution of per-pupil expenditures in the eastern states is more symmetric than the distribution of the western states. The distribution of the western states' per-pupil expenditure is skewed left, while the distribution of the eastern states' per-pupil expenditure is skewed right. Valid conclusions comparing the distributions cannot be made, since there is a different number of states in each group.Find out more on stemplots at https://brainly.com/question/11320163
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Which expression is equivalent to -a times -b?
O a(-b)
O b-a
O (-a)(-b)
O a+b
Answer:
(-a)(-b)
-a ×-b
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Simplify the expression. 6x(3y + 4z)
The algebraic expression 6x(3y + 4z) can be simplified as 18xy + 24xz
the algebraic expression given in the question is a linear equation in three variables that are x , y and z and the simplification of this algebraic expression would also contain all the three variables
To solve this question we have to use the algebraic of distributive property of addition over multiplication
We have to use this algebraic expression which says a(b + c) = ab+ acso, using the above property and substituting the values given in the question we get
6x(3y +4z) = 6x(3y) + 6x(4z)
= 18 xy + 24 xz
Hence, The algebraic expression 6x(3y + 4z) can be simplified as 18xy + 24xz
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There are about 61,000 people at a soccer game. How can 61,000 be written using a power of 10?
A.
11- 1/2y = 3 + 6x solve for y (literal equation) I'm very confused is it y = 3 + 6x - 11 ×(-2)?
====================================================
Explanation:
Multiply both sides by 2 to clear out the fraction
11 - (1/2)y = 3 + 6x
2* ( 11 - (1/2)y ) = 2*(3 + 6x)
2*11 - 2*(1/2)y = 2*3 + 2*6
22 - y = 6 + 12x
Then let's solve for y
22 - y = 6 + 12x
-y = 6 + 12x-22
-y = 12x-16
y = -(12x-16)
y = -12x+16 is the answer
The final answer is in slope intercept form y = mx+b
m = -12 = slope
b = 16 = y intercept
Hayley and Phoebe have a lemonade stand where they sell cups of lemonade for $0.75 a piece. The function p(c)=0.75c represents the profit p(c) that the girls
earn if they sell c cups of lemonade. The girls have 150 cups.
Find the domain and range. Write your answers as compound inequalities.
The domain of the function is given by: 0 ≤ c ≤ 150
The range of the function is given by : 0 ≤ p(c) ≤ 112.5
The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of domain values.In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).The given statement states that the profit from selling 150 cups of lemonade is denoted by p(c) such that p(c) = 0.75c
Now the girls can sell a maximum of 150 lemonades.
Hence the domain of the values are : 0 ≤ c ≤ 150
at x=0 , p(c) = 0.75 × 0 = 0
at x= 150 , p(c) = 0.75 × 150 = 112.50
Therefore the range of the function is : 0 ≤ p(c) ≤ 112.5
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a contractor buys 8.2 square feet of sheet metal. she used 2.1 square feet so far and has $183 worth of sheet metal remaining. write and solve an equation to find out how much sheet metal costs per foot
1) The equation that shows the cost of sheet metal per foot, s/ft² = $183 ÷ 6.1 ft².
2) The solution of the equation shows that sheet metal costs $30 per foot.
What is an equation?An equation is a mathematical expression that states that two variables are equal.
Equations are stated using the equation symbol (=).
Data and Calculations:The total quantity of sheet metal bought = 8.2 ft²
The total quantity of sheet metal used = 2.1 ft²
The remaining quantity of sheet metal = 6.1 ft² (8.2 ft² - 2.1 ft²)
The value of the remaining quantity of sheet metal = $183
The cost of sheet metal per foot = $30 ($183/6.1 ft²) or ($183 ÷ 6.1 ft²)
Thus, the cost of sheet metal is $30 per foot.
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Identify the place value of the number 8 in 27,893,214
Answer:
Centena de mil, sorry, hundred thousand
Step-by-step explanation:
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On a road map, the distance from Pine Gap to Turkey Trot is 2 inches. The map scale shows inch equals 24
miles. What is the distance, in miles, from Pine Gap to Turkey Trot?
The distance from Pine Gap to Turkey Trot is
miles.
The distance, in miles, from Pine Gap to Turkey Trot is 48 miles.
Here, we are given that on a road map, the distance from Pine Gap to Turkey Trot is 2 inches. The scale of the maps shows that 1 inch is equal to 24 miles.
This simply means that 1 inch on the map is equal to 24 miles in reality. Usually maps use a scale factor to compare the distances as the map is a condensed version of the actual geographical area. Here, the scale factor is 1 inch : 24 yards.
Thus, a distance of 2 inches on the map will be equal to 24 × 2 = 48 miles.
Therefore, the distance, in miles, from Pine Gap to Turkey Trot is 48 miles.
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Write log 150 as a sum or difference of two logarithms. Simplify if possible.
log 150 = log 50 + log 3
∴ log 150 = 2.176
As the base is not mentioned, we will take the base as 10. We will apply the product rule of logarithms to this equation.
log (150) can also be written as log (50×3).
Therefore, log (150) = log 50 + log 3
We know, log 3 = 0.477log 150 = log 50 + 0.477
Now, we can write log 50 as log (100/2). We will use the quotient rule of logarithms.log 50 = log 100 - log 2
We know, log 100 = 2 and log 2 = 0.301∴ log 50 = 2 - 0.301
log 50 = 1.699 Substituting the value of log 50 = 1.699 in the main equation, log 150 = log 50 + log 3log 150 = 1.699 + 0.477log 150 = 2.176
Therefore, the final answer to the question log 150 = 2.176
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A drawing has a scale of 1:30 On the drawing, a kitchen is a rectangle measuring 12 cm by 27 cm A bedroom has an actual area of 300 000 cm² Which has the bigger actual area, the kitchen or the bedroom? You must show your working.
The actual area of the bedroom is bigger than the actual area of the kitchen.
The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The area of a rectangle is determined by its dimensions. A rectangle's area is essentially equal to the product of its length and breadth.
In the drawing, the kitchen is in the shape of a rectangle with dimensions of 12 cm × 27 cm.
Therefore, the area of the rectangle will be:
Area = Length × Breadth
Area = 12 cm × 27 cm
Area = 324 cm²
Now, the actual area of the bedroom is 300,000 cm².
Then the difference between the area,
difference = bedroom - kitchen
difference = 300,000 - 324 cm²
difference = 299676 cm²
Therefore, the area of the bedroom is bigger than the area of the kitchen.
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The cost to rent an apartment is proportional to the number of square feet in the apartment. An 800 square foot apartment costs $600 per month. What equation represents the relationship between area, A, and cost, C?
The relationship between area and cost is 3/4 means 4 times area gets 3 times cost.
Given the cost to rent an apartment is proportional to the number of square feet in the apartment.
Given the cost of an 800 sqft apartment per month = 600$
By using the given information we can define the relationship between area and cost as below
For 800 sqft = 600 $
for 1 sqft = x
It can be written as
800/1 = 600/x
By cross multiplicating the terms on both sides we get
800 * x = 600
x = 600/800
x = 3/4
The relationship between area and cost is 3/4 means 4 times area gets 3 times cost.
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Solve each equation.
9 x²+6 x=0
The solutions for this quadratic equation is
x = 0 , -2/3
What is quadratic equation ?
A quadratic equation is also known as quadratic function. The quadratic function has the form of equation as ax²+ bx + c, where a, b, and c are the numbers not equal to zero. In mathematics, the quadratic function, the quadratic polynomials , 2nd degree polynomial is a polynomial function with one or more that one variables in which the highest term is of the second degree.
according to question given,
9 x²+6 x=0
take the 3x as common factor, equation is
3x ( 3x + 2) = 0
now, evaluating this expression
3x = 0 , say equation 1
and, 3x +2 =0 say equation 2
from equation 1 , x = 0
and, from equation 2
3x + 2 =0
x = -2 / 3
Thus final solutions for this equation is
x = 0 , -2/3
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS!!!!!!!
Which is an irrational number ??
Answer:
An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio
so the answer would be √13
Step-by-step explanation:
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Answer:
c
Step-by-step explanation:
an irrational number is a number that cannot be written as a number or a fraction
Solve each equation.
log₉3=x
The value of x for log₉3=x is 1/2 or 0.5.
What is log function?An exponent is a logarithm. You may convert any exponential expression to logarithmic form. As an illustration, if 8 = 23, the base is 2, the exponent is 3, and the outcome is 8. This may be represented as 3 = log2 8 in logarithmic notation.
The equation y=logb(x+h)+k shifts the logarithmic function, y=logbx, by k units vertically and h units horizontally.
The equation given is -
log₉3=x
It can be expressed in the form -
3 = 9ˣ
3 = 3²ˣ
As base is same,
1 = 2x
x = 1/2 = 0.5
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