The account with compound interest of 7.2 % quarterly after 5 years is given by A = $ 1,428.75
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the amount after compound interest be represented as A
Now , the equation will be
The initial principal amount = $ 1000
The rate of interest r = 7.2 %
The number of times interest is applied n = 4 ( quarterly )
The number of years b = 5 years
A = P ( 1 + r/n )ⁿᵇ
Substituting the values in the equation , we get
A = 1000 ( 1 + 0.072/4 )⁴ˣ⁵
On simplifying the equation , we get
A = 1000 ( 1 + 0.018 )²⁰
On further simplification , we get
A = 1000 ( 1.018 )²⁰
A = $ 1,428.75
Hence , the amount after 5 years is $ 1,428.75
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Which statement is true?
The true statement is that the y intercept of function A is less than the y intercept of function B.
What is y Intercept?y intercept is the y coordinate of the point on the line where it touches the Y axis. The x coordinate will be 0 there.
Here we have two functions.
Function A is given in the graph and function B is given in the equation form.
From the graph, the y intercept of function A is the y coordinate of the point touching the Y axis.
Line touches the Y axis at the point (0, -3).
So y intercept of function A = -3.
The equation of function B is the slope intercept form.
In the slope intercept form, y = mx + c, c is the y intercept.
From the equation y = 1/2 x + 4, 4 is the y intercept.
So 4 > -3.
Hence the y intercept of B is greater than that of A.
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Which graph has a slope of 4/5?
Answer:
B
Step-by-step explanation:
Rise over run should be 4 rise and 5 to the side run
Answer:
Step-by-step explanation:
The last one (placed below)
Just take two random points (x1,y1) and (x2,y2) from the graph and calculate the slope according to the expression:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
The graph placed below, passes through the points (5,4) and (0,0). So if we replace these coordinates within the formula:
[tex]m=\frac{5-0}{4-0}=\frac{5}{4}[/tex]
In a town the bearing of the swimming pool from the bank is 138 degrees. What is the bearing of the bank from the swimming pool?
The bearing of the bank from the swimming pool is 42 degrees south of west.
What is temperature ?
Temperature is a measure of how hot or cold something is. More specifically, it is a measure of the average kinetic energy of the particles that make up a substance. When the particles in a substance move faster, their kinetic energy increases, and the temperature of the substance goes up.
Temperature is usually measured in degrees Celsius (°C) or degrees Fahrenheit (°F), although in scientific contexts, the International System of Units (SI) unit of temperature is the kelvin (K). The Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C, while the Fahrenheit scale sets the freezing point of water at 32°F and the boiling point at 212°F. The kelvin scale sets the zero point at absolute zero (-273.15°C or -459.67°F), the theoretical temperature at which all molecular motion ceases.
According to given condition:
The bearing of the swimming pool from the bank is 138 degrees.
The bearing is the angle measured clockwise from the north direction.
Therefore, to find the bearing of the bank from the swimming pool, we need to add 180 degrees to the given bearing of 138 degrees and then subtract 360 degrees (a full circle) to get the bearing within the range of 0 to 360 degrees.
So,
Bearing of bank from swimming pool = (138 + 180 - 360) degrees = -42 degrees
Therefore, the bearing of the bank from the swimming pool is 42 degrees south of west.
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How to include fixed effects in regression Stata?
Answer:
Step-by-step explanation:
In Stata, you can include fixed effects in a regression by using the "xtreg" command with the "fe" option. The "xtreg" command is used to fit a linear regression model with panel data, and the "fe" option tells Stata to include fixed effects in the model.
Here's an example of how to run a fixed effects regression in Stata:
xtreg y x1 x2 x3, fe
In this example, "y" is the dependent variable, and "x1", "x2", and "x3" are the independent variables. The "fe" option tells Stata to include fixed effects for each individual in the panel data.
Note that the fixed effects in this example are time-invariant, meaning that they are constant for each individual over time. If you have time-varying fixed effects, you can include them in the regression using the "xtreg" command with the "vce(cluster id)" option, where "id" is the variable indicating the individual in the panel data.
Please help!!!!!Triangle ABC is similar to triangle FGH. Given the following angle measures, find the
missing angle measures.
The measures of angles in similar triangles are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths.
Given that, Triangle ABC is similar to triangle FGH, we need to find the measures of the angles,
The sum of interior angles of a triangle = 180°
Considering Δ ABC,
∠ A + ∠ B + ∠ C = 180°
∠ C = 180°-(22°+75°)
∠ C = 83°
Since, we know that the similar triangles have congruent corresponding angles,
Therefore,
∠ A = ∠ F, ∠ B = ∠ G and ∠ C = ∠ H
Therefore, the measures of angles in Δ FGH are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°
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help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
25%
Step-by-step explanation:
x + 0.25x = y
y - 0.25x = x
If the size of a circle increases by 25% and then decreases back down to it's original size it's going to be the same percentage 25%.
Linda bought 6 pounds of rice for 4$ How many dollars did she pay per pound of rice
Answer: 24
Step-by-step explanation: 6*4=24
4+4+4+4+4+4=24
Answer:
she paid $1.50 / 1lb
Step-by-step explanation:
6lbs divided by $4 = 1.50 or $1.50 / 1lb
give example discrete variable
Discrete variables are a subset of variables that have a limited range of values. A variable that counts how many kids a family has, for instance, can only be a whole number, such as 0, 1, 2, etc.
Discrete variables, like integers or categories, are a form of variable that can only take specified, distinct values. For instance, a discrete variable is the number of siblings a person has because it can only be 0, 1, 2, 3, etc.Discrete variables are a subset of variables that have a limited range of values. A continuous variable, on the other hand, can accept any value within a range.Whole numbers like 0, 1, 2, 3, and so forth are frequently used as discrete variables. The number of kids in a household, the number of products in a shopping cart, or the number of individuals in a room are all examples of discrete variables.
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I don’t understand the questions
The solutions to the expressions using laws of exponents are;
17) y^(19/28)
18) 1/a^(5/9)
How to use Laws of Exponents?The product rule of exponents states that "To multiply two expressions with the same base, add the exponents while keeping the base the same". Thus;
y² × y³ = y²⁺³
= y⁵
17) y^(3/7) × y^(1/4)
Applying product rule of exponents gives;
y^(³/₇ + ¹/₄)
= y^(19/28)
18) The negative exponent rule states that: To convert any negative exponent into positive exponent, the reciprocal should be taken." Thus;
x⁻³ = 1/x³
Thus;
a^(-5/9) = 1/a^(5/9)
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A student noticed different gas prices as she drove around town. Find the first quartile. Round your answer to the nearest cent. $3.31 $3.28 $3.42 $3.35 $3.31 $3.26 $3.38 $3.32 $3.34
Answer: $3.32
Step-by-step explanation:
First arrange the given discrete values in ascending order.
$3.26, $3.28, $3.31, $3.31, $3.32, $3.34,$3.35, $3.38, $3.42
we will use the formula 1/2 x (n +1), where n is total number of discrete values which in this case is 9.
This formula doesn't give the answer of the second quartile, it tells which nth term in the arranged set will be the second quartile.
1/2 (9+1) = 5.
Now we will choose the 5th term of the ascending order set.
Second quartile is same as the median, that means you need the mid value.
What are the measures of the angles? Please help 55 points.
Answer: 5
Step-by-step explanation:
Opposite angles of parallelograms are always equal, thus resulting in the equation, 20 + 2x = 6x simplified to 20 = 4x, so x is equal to 5. Hope this helps!
Answer:
The answer is a) 5
Step-by-step explanation:
8)
Determine the measure
of angle 8.
G.8.B
Answer:
140 ° , because it is vertically opp to angle 4 and angle 4 is corresponding 8 .
Julian and Nikhil are making paper cones to hold popcorn
to hand out at parent math night. They want the cones to
hold 28.26 (about 9) cubic inches of popcorn. What are
two different possible values for height h and radius r for
the cones?
The possible values for radius r and height h of the cone will be 2 and 2.1485 respectively.
What exactly is a cone?
A cone is a shape formed by connecting a single point known as the apex or vertex to all of the points of a circular base using a series of line segments (which does not contain the apex). The distance from the vertex to the base is the cone's height. The circular base's radius has been measured. The slant height is the length of the cone from the peak to any point along the base's perimeter. The height, radius of base, and slant height of the cone in the figure define it.
Volume of cone=1/3πr²h, where r=base radius and h=cone height
Curved surface area=πrL, where L is the slant height.
Now,
Given Volume of cone to hold popcorn=9 inch³
i.e. 1/3πr²h=9
r²h=9*3*7/22
r²h=8.5943
let r=2
then h=8.5943/4
h=2.1485
Hence,
The possible values for radius r and height h of the cone will be 2 and 2.1485 respectively.
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What does x equal pls my grade is depending on this
please answer the question below!
The values of x in f(x)=2x g(x)=2^x is x=2 and x=0.77.
What is the solution for an equation?
The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
We are given that;
f(x) 2x and g(x)=2^x
Now,
To graph the functions on the same coordinate plane, we can plot some points and connect them with a line:
f(x) = 2x
(0, 0), (1, 2), (2, 4), (3, 6), ...
g(x) = 2^x
(0, 1), (1, 2), (2, 4), (3, 8), ...
To find the solutions to the equation f(x) = g(x), we need to set the two expressions equal to each other and solve for x:
2x = 2^x
x=2, 0.77
Therefore, the answer of the given equation will be x=2, 0.77
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Can someone help me with this please
The sides of the rectangle are
1. (x - 1)2. (x + 6)3. (x - 5)4. (x + 1)the codes are CFID
How to find the unknow part of the rectangleThe unknown part of the rectangle is solved using division of polynomial and the check is completed by multiplication of the polynomial involved
checking for the correct answers
1. 2(x + 5)(x - 1) = (2x + 10)(x - 1)
2x² - 2x + 10x - 10
2x² + 8x - 10
2. 3(x - 1)(x + 6) = (3x - 3)(x + 6)
3x² + 18x - 3x - 18
3x² + 15x - 18
3. 2(x + 1)(x - 5) = (2x + 2)(x -5)
2x² - 10x + 2x - 10
2x² - 8x - 10
4. 5(x - 1)(x + 1) = (5x -5)(x + 1)
5x² + 5x - 5x - 5
5x² - 5
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Complete the table.
f(x) = -5|x - 9|
X |f(x)
0 |
2 |
4 |
6 |
The table of values is
X |f(x)
0 | -45
2 | -35
4 | -25
6 | -15
Hwo to complete the table of valuesFrom the question, we have the following parameters that can be used in our computation:
f(x) = -5|x - 9|
We have the x values to be
x = 0, 2 4 and 6
Substitute the known values in the above equation, so, we have the following representation
f(0) = -5|0 - 9| = -45
f(2) = -5|2 - 9| = -35
f(4) = -5|4 - 9| = -25
f(6) = -5|6 - 9| = -15
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Currently, 2 out of 195
countries celebrate
Groundhog Day. How many
celebrations
could we expect
if there were 950 countries?
If there were 950 countries, we could expect celebrations from 10 countries.
What was the Groundhog Day all about?Groundhog Day is a popular North American tradition celebrated on February 2 in the United States and Canada. It is based on the Pennsylvania Dutch superstition that if a groundhog emerges from its burrows on this day and sees its shadow due to clear weather, it will retreat to its burrow and winter will last six weeks longer.
In our calculation, as 2 out of 195 celebrate the day, we need know how many celebrations we could expect if there were 950 countries.
950 / 195 = 4.87179487179 = 4.87. We will multiply 4.87 by 2 country giving us 9.74, approximately 10 countries.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answer:
Option 2 Is Correct
Step-by-step explanation:
The following statements are true about the function and its graph:
The graph of the function is a parabola.
The graph contains the point (0, 0).
The graph does not contain the point (20, -8).
Option 1 is true because the function is a quadratic function, and all quadratic functions have a parabolic graph.
Option 2 is true because the y-intercept of the function is (0,0).
Option 3 is false because the function opens upwards
Does someone mind helping me with this problem? Thank you!
Answer:3y +=7
=>3y-7-x
=>y=(7-x)/3 Step-by-step explanation:Solve for 'y' means, solve the equation to get the value of y and in terms of ,x means value of y not necessarily in pure constant form,but in the form of x.
A candle maker is ordering wax. Each small candle uses 12 ounces of wax. Each large candle uses 18 ounces of wax. The candle maker wants to make 42 small candles and 38 large candles.
Which answer is the most reasonable estimate of the total amount of wax needed?
Answer:
1188
Step-by-step explanation:
12x42 + 18x38 = 1188
Mr. Yu applies 12 ounce of fertilizer to every 58 square meter of his lawn.
How many ounces of fertilizer does Mr. Yu use per square meter for his lawn?
Enter your answer in the box as a fraction in simplest form.
ounces per square meter
Answer: 0.20689655
Step-by-step explanation: because you take 12 divided by 58
Find the solution of the system of equations
3x+7y=-17
-3x+9y=-15
Answer: The solution of the system of equations is (x, y) = (-1, -2).
Step-by-step explanation:
We can solve this system of equations by using either elimination or substitution method. Here, we'll use elimination:
Adding the two equations, we get:
(3x + 7y) + (-3x + 9y) = -17 - 15
Simplifying the left side and right side:
16y = -32
Dividing both sides by 16:
y = -2
Now we can substitute y = -2 into either of the original equations and solve for x. Let's use the first equation:
3x + 7(-2) = -17
Simplifying:
3x - 14 = -17
Adding 14 to both sides:
3x = -3
Dividing both sides by 3:
x = -1
Here is an equation: x + 3y = 6.
Use the whole numbers 0-6 without repeating to create two (x, y) coordinate pairs that are solutions and one that is not.
The two solutions of the linear equation are:
(0, 2)
(3, 1)
And a coordinate pair that is not a solution is:
(0, 5)
How to find the coordinate pairs?Here we have the linear equation:
x + 3y = 6
And we want to find two ordered pairs that are solutions.
To find them,wecan evaluate in two values of x and then find the correspondent values of y.
if x = 0
0 + 3y = 6
y = 6/3 = 2
if x = 3
3 + 3y = 6
3y = 6 - 3
3y = 3
y = 3/3 = 1
So the two solutions are (0, 2) and (3, 1)
And a point that is not a solution can be one with the same x-value than one of the above ones but a different y-value, like (0, 5)
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Which values of x make the following statement true? Choose all correct
answers.
x-9.5 = a negative number
X = 9
X = -9.5
x = -9
x = 10
X = -10
x = 10.5
The values of x make the statement true are x = 9 X = -9.5 x = -9 and x = -10
Which values of x make the statement true?From the question, we have the following parameters that can be used in our computation:
x-9.5 = a negative number
Using the above as a guide, we have the following:
x - 9.5 < 0
Make x the subject
x < 9.5
This means that the values of x are less than 9.5
From the options, we have:
x = 9 X = -9.5 x = -9 and x = -10
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Which equations support the fact that rational numbers are closed under addition?
Select each correct answer.
A. √2+√2=2√2
B. √6+(-√6)=0
C. √9+√9=2√9
D. 1/3+1/3=2/3
Answer:
Step-by-step explanation:
None of the given equations support the fact that rational numbers are closed under addition, because they all involve irrational numbers or fractions, which are not necessarily rational.
Option (A) involves the irrational number √2.
Option (B) involves adding the irrational number √6 with its negative, which results in a rational number, but it doesn't prove that all additions of rational numbers are also rational.
Option (C) involves the perfect square 9, but the square root of a non-square integer is generally an irrational number.
Option (D) involves the addition of two rational numbers, which is a valid example of the closure property of rational numbers under addition.
Therefore, the correct answer is (D) 1/3+1/3=2/3.
How many quart in a cubic feet ?
The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot.
So the volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.
The quantity of cubic feet can be multiplied by 29.9220779 to get the conversion to quarts. For instance, if you have a container with a 2 cubic foot volume, the quantity of quarts in that container would be:2 cubic feet multiplied by the US liquid quart density of 29.9220779 gives 59.8441558 US quarts. The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.
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please help me solve this
Answer:
1) 108 2) 72 3) 11
Step-by-step explanation:
1) since the angle of PNM is the same as PLM, then we can simply add 42 and 66 to get 108 degrees
2)since the total angle in parallelogram is 360, we can take away the two angles we do know. Those are PLM and PNM which are 108 each.
360-108-108=144
with the last two corners having the same angle, the remaining degrees are distributed evenly giving us 144/2 = 72
3)since the length of LM and PN are the same then we get the equation
2d = 22 which gives us d = 11
3c^2 - 20c + 12 factorise by splitting the middle
Answer:
(3c - 2)(c - 6)
Step-by-step explanation:
Quadratic Formula:
ax^2 + bx + c
a = 3 and c = 12
a * c --> 3 * 12 = 36
b --> -20
Two numbers that multiply to get 36 and added together get -20 are -18 and -2.
-18(-2) = 36
-18 + (-2) = -20
[tex]\frac{-18}{3c} = \frac{-6}{c}[/tex], [tex]\frac{-2}{3c}[/tex]
(c - 6)(3c - 2) = 3c^2 - 20c + 12
PLEASE HELP!!!! Which of the following statements are equivalent to the statement the price decreased by 1/2%. Choose all the correct answers
A) The price doubled
B) The price is 150% of the price before
C) The price was reduced by a quarter of what it was before
D) The price is half of what it was before
E) The price is now 1.5 times greater than what it was before
F) The price now is 66 2/3% of what it was before
G) The price now is 200% of what it was before
H) The price is 75% of what it was before
The equivalent to the statement the price decreased by 1/2% will be 0.995x. Thus, all options are incorrect.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Let the price be 'x'. Then the equivalent to the statement the price decreased by 1/2% is given as,
⇒ (1 - 0.5 / 100) x
⇒ 0.995x
The equivalent to the statement the price decreased by 1/2% will be 0.995x. Thus, all options are incorrect.
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