a) you would need $450,332.81 in your account at the beginning. b) the total money that will be pulled out of the account is $600,000.
How to determine How much do you need in your account at the beginninga) To calculate the amount needed in the account at the beginning, we can use the present value formula:
PV = PMT * ((1 - (1 + r)^-n) / r)
Where PV is the present value, PMT is the annual payment, r is the annual interest rate, and n is the number of periods.
Plugging in the values, we get:
PV = 40000 * ((1 - (1 + 0.05)^-15) / 0.05)
PV = $450,332.81
Therefore, you would need $450,332.81 in your account at the beginning.
b) To calculate the total money that will be pulled out of the account, we can simply multiply the annual payment by the number of years:
Total money = PMT * n
Total money = 40000 * 15
Total money = $600,000
Therefore, the total money that will be pulled out of the account is $600,000.
c) To calculate the amount of money that is interest, we can subtract the initial investment from the total money pulled out:
Interest = Total money - Initial investment
Interest = $600,000 - $450,332.81
Interest = $149,667.19
Therefore, $149,667.19 of the money pulled out is interest.
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A rectangular pyramid is shown in the figure.
A rectangular pyramid with a base of dimensions 7 centimeters by 5 centimeters. The two large triangular faces have a height of 7.6 centimeters. The two small triangular faces have a height of 8 centimeters.
What is the surface area of the pyramid?
The surface area of the pyramid is 113 cm².
What is rectangular pyramid?A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.
The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.
To find the surface area of the pyramid, we need to find the area of each face and then add them up.
Area of the base:
The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:
Area of base = length × width = 7 cm × 5 cm = 35 cm²
Area of the four triangular faces:
Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:
Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²
Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²
There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:
Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face
= 2 × 19 cm² + 2 × 20 cm²
= 78 cm²
Total surface area:
Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:
Total surface area = area of base + total area of four triangular faces
= 35 cm² + 78 cm²
= 113 cm²
Therefore, the surface area of the pyramid is 113 cm²
.
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Write 80cm to 2km as rate
One per 2,500 can be used to represent the rate of 80cm to 2km.
Writing measures as a rate.To write 80cm to 2km as a rate, we need to convert the units to the same system. We can convert 80cm to kilometers by dividing by 100,000 (since there are 100,000 centimeters in a kilometer):
80 cm/100,000 = 0.0008 km
Now we can express the rate as:
0.0008 km per 2 km
Or we can simplify it by dividing both the numerator and denominator by 0.0008:
1 per 2,500
Therefore, 80cm to 2km can be expressed as a rate of 1 per 2,500.
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Find the equation of the linear function
represented by the table below in slope-intercept
form.
X: -3,1,5,9
y: -8,0,8,16
By answering the presented question, we may conclude that As a result, the linear function denoted by the table is y = 2x - 2.
what is slope?A line's slope shows how steep it is. A mathematical equation for the gradient is referred to as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of vertical change (rise) to horizontal change between two points (run). The slope-intercept form of an equation is used to represent the equation of a straight line, which is written as y = mx + b. The y-intercept is located where the line's slope is m, b is b, and (0, b). The slope and y-intercept of the equation y = 3x - 7 are two examples (0, 7). The line's slope is m. b is b at the y-intercept, and (0, b).
To obtain the slope and y-intercept of a linear function in slope-intercept form, we must first establish the slope and y-intercept.
With two locations on the line, we can first determine the slope. Let us start with the first and last points in the table:
slope = (y change) / (change in x)
slope = (16 - (-8)) / (9 - (-3))
slope = 24 / 12
slope = 2
We can now use the slope and one of the points to get the y-intercept. Let's take the point (1, 0) as an example:
y = mx + b 0 + b b = 2(1) + b b = -2
Hence the linear function's slope-intercept equation is:
y = 2x - 2
As a result, the linear function denoted by the table is y = 2x - 2.
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A drawer contains 10 blue pens, 12 black pens, and 3 red pens. Without looking, Mr. Lopez is going to take one pen from the drawer, use it, and then put it back into the drawer. Then he is going to take another pen from the drawer to use. What is the probability of Mr. Lopez taking a red pen first and then taking a blue pen?
Answer: 4.8%
Step-by-step explanation: the total amount of pens in the drawer is (10+12+3) = 25
the amount of red pens in the drawer is 3
the probability of picking out a red pen from the drawer = 3/25
the amount of blue pens in the drawer is 10
the probability of picking out a red pen from the drawer = 10/25
the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%
Solve for x.
A. 7
B. 4
C. 3
D. 5
The correct option -D. 5; Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.
Explain about the secant of circle:A line that precisely intersects a circle at two points is said to be a secant.
The size of the angle created when two tangents, two secants, or two tangents cross outside of a circle is equal to one-half a positive difference between the sizes of the intercepted arcs.
Using the Theorem:
The square of a length of tangent is equal the the product of such external secant segment and the overall length of the secant if one secant and one tangent both drawn to a circle from a single exterior point:
4(4 + x) = 6²
16 + 4x = 36
4x = 36 - 16
4x = 20
x = 20/4
x = 5
Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.
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Suppose that the functions fand g are defined as follows.
f(x)=2x-1
g(x)=√3x-5
The composite functions (f/g)(x) and (f-g)(x) are (2x-1)/√(3x-5) and (2x-1) -√(3x-5)
Calculating the composite functions (f/g)(x) and (f-g)(x)To calculate (f/g)(x), we need to divide f(x) by g(x):
(f/g)(x) = f(x)/g(x) = (2x-1)/√(3x-5)
The domain of (f/g)(x) is the set of all x-values for which the denominator √(3x-5) is not equal to zero and non-negative
3x-5 ≥ 0, or x ≥ 5/3
Therefore, the domain of (f/g)(x) is x ≥ 5/3.
To calculate (f-g)(x), we need to subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x) = (2x-1) - √(3x-5)
The domain of (f-g)(x) is the set of all x-values for which the expression inside the square root is non-negative:
3x-5 ≥ 0, or x ≥ 5/3
Therefore, the domain of (f-g)(x) is x ≥ 5/3.
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A company is going to make an oil container in the shape of a cylinder. As shown below, the container will have a height of 8 m and a diameter of 10 m. The container will be made from steel (including its top and bottom). Suppose the total cost of the steel will be $13,062.40. How much will the steel cost per square meter? Use 3.14 for it, and do not round your answer.
The per square meter cost of steel will be $32. The solution has been obtained by using the cylinder.
What is a cylinder?
The cylinder, one of the most basic curvilinear geometric shapes, has long been considered to be a three-dimensional solid. It is regarded as a prism with a circle as its basis in elementary geometry.
We are given that the height of cylinder is 8 m and diameter is 10 m.
So, the radius is 5 m.
Now, using the surface area formula, we get
⇒ S = 2πrh + 2π[tex]r^{2}[/tex]
⇒ S = 2π * 5 * 8 + 2π * [tex]5^{2}[/tex]
⇒ S = 2 * 3.14 * 5 * 8 + 2 * 3.14 * 25
⇒ S = 251.2 + 157
⇒ S = 408.2 square meter
Now, it is given that the total cost of the steel will be $13,062.40.
So, per square meter cost will be:
⇒ Cost = [tex]\frac{13,062.40}{408.2\\}[/tex]
⇒ Cost = $32
Hence, the per square meter cost of steel for the cylinder will be $32.
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Chloe claims that Point A=−6 and Point B=1 . Which of the following statements provide support for Chloe's claim? Select ALL that apply. A A<0 because A is to the left of zero B A>0 because A is to the left of zero C A 0 because B is to the left of zero F B>0 because B is to the right of zero
The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.
Describe Comparison Algebra?Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.
Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.
In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.
The statements that provide support for Chloe's claim are:
A. A<0 because A is to the left of zero.
F. B>0 because B is to the right of zero.
Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.
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I need help solving this thank you
The negation is the fourth option.
6 + 3 ≠ 9 or 6 - 3 ≠ 9
How to write the negation?The negation of an equation is an inequality such that we just change the equal sign, by the "≠" sign.
Here we start with the two equations.
6 + 3 = 9 or 6 - 3 = 9
Just change the equal signs for different signs:
6 + 3 ≠ 9 or 6 - 3 ≠ 9
That is the negation, fourth option.
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I need help
A population of bacteria is growing according to the equation p(t)=800e^0.14t Estimate when the population will exceed 1151.
t= ---------
Answer: t=2.59
Step-by-step explanation:
This is a matter of clearing out the equation
set 1151=800e^0.14t
1151/800=e^0.14t
ln(1151/800)/0.14=t
t=2.59
complete the equatiotin 3 over 4 x 6 =
PLEASE HELP
Answer:
1/8
Step-by-step explanation:
If "over" refers to (4 * 6) as a whole,
[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]
If "over" refers to division,
[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]
I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.
Hope this helps and be sure to mark this as brainliest! :)
ii) The door is 0.9 m wide and 2.1 m high. Each of the four windows is 1.5 m wide and 1.2 m high work out the toral area of the door and the four windows
Answer: The area of the door can be calculated as:
Area of door = width x height
= 0.9 m x 2.1 m
= 1.89 square meters
The area of one window can be calculated as:
Area of window = width x height
= 1.5 m x 1.2 m
= 1.8 square meters
Since there are four windows, the total area of the four windows is:
Total area of four windows = 4 x Area of window
= 4 x 1.8 square meters
= 7.2 square meters
Therefore, the total area of the door and the four windows is:
Total area = Area of door + Total area of four windows
= 1.89 square meters + 7.2 square meters
= 9.09 square meters
Hence, the total area of the door and the four windows is 9.09 square meters.
Step-by-step explanation:
The expression 12x +8 is equivalent to the expression a(bc+c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4). Which statement best explains whether the students answer is correct or incorrect
The student's is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).
What is expression?Expression is the communication of emotion or ideas through words, art, music, or other forms of communication. It is the way in which a person or artist conveys their thoughts and feelings in a creative and meaningful way. Expression can be seen in the form of art, writing, music, dance, and other creative outlets. Expression is a powerful tool that can be used to communicate a message or to evoke a feeling in the audience. Expression can be used to inspire, educate, motivate, and even to heal. Expression is a way to connect people and cultures, and a way to share stories and experiences. It is a way to express oneself in a meaningful and powerful way.
This is because 12z+8 can be written as 2z(6x+4), where the greatest common factor of 12 and 8 (2z) is factored out.
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Complete Question:
The expression 12z+8 is equivalent to the expression a (bx + c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4).
Which statement best explains whether the student's answer is correct or incorrect?
OA. The student's answer is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).
OB. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4z, so the correct expression is 4z (3x+2).
C. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4, so the correct expression is 4 (3x+2).
OD. The student's answer is incorrect because the greatest common factor of 12 and 8 is 8, so the correct expression is 8 (4x+1).
Calculate Volume of Air passing through Filter HEPA Filter 100ft/min *- Airflow 4ft 2ft Volume = Filter Area x Airflow Velocity
The volume of air passing through the filter is 800 cubic feet per minute. It is calculated by multiplying the air flow speed (100ft/min) by the area of the filter (8ft²).
Explanation:The volume of air passing through the HEPA filter can be calculated using the formula for the speed of air flow multiplied by area. The speed of the air flow is given as 100ft/min and the area of the filter is given as 4ft x 2ft, which equals 8 square feet. Therefore, the volume of the air passing through the filter can be calculated as 8ft2 x 100ft/min = 800 cubic feet per minute.
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1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping
and sprinkles. How many different sundaes can you make when you order one flavor of ice
cream, one topping and one color of sprinkles from the chart below? Show all possible
outcomes in a tree diagram.
Ice Cream
Chocolate
Vanilla
Strawberry
Topping
Fudge
Marshmallow
Sprinkles
Chocolate
Rainbow
How many sample spaces are there? HINT: How many possible combinations?
b. P (Chocolate, Fudge, Rainbow)
Answer:
Step-by-step explanation:
Answer:
You can make 12 possible sundaes with these toppings.
Step-by-step explanation:
Chocolate, Vanilla, and Strawberry all have 4 possible outcomes:
1. Fudge & Chocolate Sprinkles
2. Fudge & Rainbow Sprinkles
3. Marshmallow & Chocolate Sprinkles
4. Marshmallow & Rainbow Sprinkles
-------------------------------------------------------------------------------------------------------------
4 x 3 will equal 12, the total possible sundaes you can make with these toppings and ice cream flavors.
find the area and perimeter of each figure below.
Answer:
finding the perimeter, you sumthe distance all round that is 7+7.5+17.8+6=38.3
38.3 is the perimeter
What is the perimeter of the triangle?
Answer:
40 units
Step-by-step explanation:
a = 8
b = 15
To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]8^{2} +15^{2} =x^{2}[/tex]
64 + 225 = c^2
289 = c^2
c = 17
a + b + c = perimeter
8 + 15 + 17 = 40
Answer:
40 units
Step-by-step explanation:
You want the perimeter of the triangle shown in the graph.
DimensionsYou can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.
The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:
c² = a² +b²
c² = 8² +15² = 64 +225 = 289
c = √289 = 17
The long side of the triangle is 17 units.
PerimeterThe perimeter of the triangle is the sum of the lengths of its sides:
P = 8 + 15 + 17 = 40
The perimeter is 40 units.
__
Additional comment
A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...
{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}
You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.
The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)
Help please i dont know
The histogram should be modified as follows:
The bin from 6 to 15 should be increased by 2.The bin from 16 to 25 should be increased by one.The bin from 26 to 35 should be increased by one.The bin from 46 to 55 should be increased by one.What is shown by an histogram?A histogram is a type of graphical representation that displays the distribution of a dataset. It is a bar graph-like chart where the data is divided into intervals, called "bins", which are represented by adjacent rectangular bars of varying heights.
Then the height of the histogram gives the number of observations into each data interval.
Hence the histogram should be modified as follows:
The bin from 6 to 15 should be increased by 2. -> two measures of 12.The bin from 16 to 25 should be increased by one. -> measure of 16.The bin from 26 to 35 should be increased by one. -> measure of 26.The bin from 46 to 55 should be increased by one. -> measure of 48.More can be learned about histograms at https://brainly.com/question/25983327
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Help corrections due in 3 hours! giving 25 points and brainlist
The value of GH in the right angle triangle, given FH and Angle FHG is 22.46 inches.
How to find the value of GH ?Since we have the adjacent side (FH) and want to find the hypotenuse (GH), we can use the cosine function.
cos(35°) = adjacent side (FH) / hypotenuse (GH)
We know that FH = 18.4 in. So, we can write the equation as:
cos(35°) = 18.4 / GH
GH = 18.4 / cos(35°)
GH = 18.4 / 0.81915
= 22.46 inches
So, the length of GH, the hypotenuse, is approximately 22.46 inches.
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On the Y axis, we have the profit from the trucking company and on the X axis, we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
Answer:
B.
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
the description is very confusing and lacks any hint about the behavior of the curve before the change.
but ok, let's assume that the curve (line ?) is in general going up. in other words, if the traveled miles go up, so does the profit.
I also don't know how they could drive the miles without paying the driver, but again, let's assume they did.
now they pay the driver. $0.25 per mile.
this has to come out of their profit.
so, the Y (profit) values all go down by 0.25.
therefore, the y-intercept is going down too.
that eliminates C. and D.
for this to be true they have to have some overhead costs that apply even if there are 0 miles traveled (which is the meaning of the y-intercept : the y-value when x = 0).
so, the line must be in a form
y = ax + b
with "b" <> 0.
and since we assumed the line to go up (positive slope), a "sinking" line means that the x-intercept (the break-even point, where the line goes from below the x-axis and therefore negative (y) profit up into positive profit) will move to the right (become greater).
because now that they have additional costs (paying the driver), it takes longer (more driven miles) to make a positive profit.
and that eliminates A, leaving B. as the right answer.
(a) What is the value of x? Show your work.
(b) What is the measure of angle C? Show your work.
In triangle ABC
a) The value of x = 29⁰
b) The angle c equal to 93⁰
What is a triangle?A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.
According to the given informationIn a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.
We know that:
angle a = 35⁰
angle b = 52⁰
angle c = 3(x+2)⁰
Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:
angle a + angle b + angle c = 180
Substituting the values we know, we get:
35 + 52 + 3(x+2) = 180
Simplifying the equation, we get:
87 + 3x + 6 = 180
3x + 93 = 180
3x = 87
x = 29
Therefore, x = 29⁰
To find angle c, we can substitute the value of x into the equation we were given for angle c:
angle c = 3(x+2)
angle c = 3(29+2)
angle c = 3(31)
angle c = 93
Therefore, angle c is equal to 93⁰.
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Peanuts sell for Php 10.00 per gram. Cashews sell for Php 8.00 per gram. How many grams of cashews should be mixed with 12 g of peanuts to obtain a mixture that sells for Php 9.00 per gram?
PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]
Answer:
Phn10x12
Step-by-step explanation:
PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]
) Rewrite as an exponential equation.
log8 1/64 =2
(b) Rewrite as a logarithmic equation.
3 0=1
a) the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}[/tex]
b) the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
What is exponential equation?
An exponential equation is one in which the exponent contains a variable.
(a) We can rewrite the logarithmic equation as an exponential equation by using the definition of logarithms. The logarithmic equation
log8 1/64 = 2
means that 8 raised to the power of 2 is equal to 1/64:
[tex]8^2 = 1/64[/tex]
Thus, we can write the exponential equation as:
[tex]1/64 = 8^{(-2)}[/tex]
Therefore, the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}.[/tex]
(b) We can rewrite the exponential equation as a logarithmic equation by using the definition of logarithms. The exponential equation
[tex]3^0 = 1[/tex]
means that the logarithm of 1 to the base 3 is equal to 0:
log3 1 = 0
Therefore, the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
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Help Please...
You have 67 coins consisting of half-dollars and quarters. The number of quarters is 7 more than three times the number of half-dollars.
How many quarters do you have?
How many half -dollars do you have?
There are 52 quarters and 15 half-dollars
To solve this problem
Let's represent the number of half-dollars as "x" and the number of quarters as "y".
From the problem statement, we know that:
x + y = 67 (because there are a total of 67 coins)
y = 3x + 7 (because the number of quarters is 7 more than three times the number of half-dollars)
We can use substitution to solve for x:
x + (3x + 7) = 67
4x + 7 = 67
4x = 60
x = 15
So there are 15 half-dollars. We can use this to find the number of quarters:
y = 3x + 7
y = 3(15) + 7
y = 52
So there are 52 quarters.
Therefore, there are 52 quarters and 15 half-dollars.
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50pts!!!!
Many investors use interest-only loans to buy shares or property. For such loans the principal stays constant and only the interest is paid back each month.
She buys an investment property for $300 000 and borrows the full amount at 7% p.a. simple interest. She rents out the property at $1500 per month and pays $3000 per year in rates and other costs to keep the property.
Find the amount of interest she needs to pay back every month.
Find her yearly income from rent.
By considering the other costs in keeping the property, calculate her overall loss in a year.
she hopes that the property’s value will increase enough to cover any loss she is making. By what percentage of the original price will the property need to increase in value per year?
Step-by-step explanation:
to find the interest she needs to pay back every month, we need to use this formula:
I = PRT/12
in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:
I = (300,000)(7)(1)/12 = $17,500 in interest every month
to find her yearly income from rent, we have to multiply the monthly rent by 12
1500 × 12 = $18,000
to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000
she said that she hopes the property's value will increase to cover the loss she made.
to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as
Percentage increase = (difference in increase/Original price) × 100
so
percentage increase = (15000/300000) × 100 = 5%
so the property needs to increase in value by at least 5% per year to cover the loss.
The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.
Explanation:First, let's calculate the monthly interest she needs to pay. 7% of $300,000 is $21,000 for a year. To find the monthly interest, we divide this by 12, resulting in $1750.Her yearly income from rent is $1500 multiplied by 12, giving us $18,000.To calculate her overall loss, we add the yearly interest and the costs to keep the property, then subtract the yearly rent income. So, $21,000 + $3000 - $18,000 = $6000 loss per year.Lastly, to find out by what percentage the property value needs to increase, we divide the loss by the original price and multiply by 100, giving us 2% increase per year.Learn more about Interest and Profit Calculation here:https://brainly.com/question/32651816
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whats the answer to 102-38x14 divided by 7+162= help plss
Answer:
-2.5
Step-by-step explanation:
follow BIMDAS.
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Find an equation of the osculating plane and an equation of the normal
plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1).
The equation of the normal plane is 4y = 4π, or equivalently, y = π.
What is osculating plane?The word osculate comes from the Latin osculatus, which is a past participle of the verb osculari, which means "to kiss." Thus, an osculating plane is one that "kisses" a submanifold.
To find the osculating plane and normal plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1), we need to follow these steps:
Find the first and second derivatives of the curve with respect to t.Evaluate the derivatives at t = π to get the velocity, acceleration, and curvature vectors at the point (0, π, 1).Use the velocity and acceleration vectors to find the normal vector of the osculating plane.Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.Use the curvature vector to find the normal vector of the normal plane.Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.Step 1: Find the first and second derivatives of the curve with respect to t.
x' = 2cos2t
y' = 1
z' = -2sin2t
x'' = -4sin2t
y'' = 0
z'' = -4cos2t
Step 2: Evaluate the derivatives at t = π.
x'(π) = 2cos2π = 2
y'(π) = 1
z'(π) = -2sin2π = 0
x''(π) = -4sin2π = 0
y''(π) = 0
z''(π) = -4cos2π = -4
So the velocity vector at the point (0, π, 1) is v = ⟨2, 1, 0⟩, the acceleration vector is a = ⟨0, 0, -4⟩, and the curvature vector is κv = ⟨0, 4, 0⟩.
Step 3: Use the velocity and acceleration vectors to find the normal vector of the osculating plane.
The normal vector of the osculating plane is given by the cross product of the velocity and acceleration vectors:
n = v × a = ⟨2, 1, 0⟩ × ⟨0, 0, -4⟩ = ⟨4, 0, 0⟩
Step 4: Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.
The equation of the osculating plane is given by:
4(x - 0) + 0(y - π) + 0(z - 1) = 0
Simplifying, we get:
4x - 4 = 0
So the equation of the osculating plane is 4x = 4, or equivalently, x = 1.
Step 5: Use the curvature vector to find the normal vector of the normal plane.
The normal vector of the normal plane is given by the curvature vector:
n' = κv = ⟨0, 4, 0⟩
Step 6: Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.
The equation of the normal plane is given by:
0(x - 0) + 4(y - π) + 0(z - 1) = 0
Simplifying, we get:
4y - 4π = 0
So, the equation of the normal plane is 4y = 4π, or equivalently, y = π.
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Problem 7: Find the surface area and round to the nearest tenth.
Answer:
1629.24m
Step-by-step explanation:
starting with the easy ones
1) Rectangle 1:
Surface area of rectangle=Length x width
SAR= 24x21
= 504m
2) Rectangle 2:
SAR= 19x21
=399
3) Rectangle 3
SAR= 21x8
=168
4) Rectangle 4:
SAR= 21x11
=231
*because the top and bottom are trapeziums the formular for it is
A=1/2(a+b)h
although those trapeziums don't have h(Height)
it needs to be broken down into two triangles and a rectangle. to find the height*
5) side/height of triangle A:
formula: C squared= a squared + b squared
in this case we already have C and A. meaning we have to rearrange the formula to:
x = c^2 - a^2
x = 8^2 - 2.5^2
x = sqrt 57.75
x = 7.61
6) Trapezium
SA= 1/2(a+b)h
SA= 1/2(19+24)7.61
=163.62
7) add all surface area together
which should equal 1629.24m
Prove: DC = 6 units
A
6 units
D
Statements
AD || BC
ZDAC ZBCA
C
?
DC BA
DC = BA
given
alternate interior angles theorem
AC AC
reflexive property of congruence
ZDCA ZBAC alternate interior angles theorem
DC = 6 units
Which step is missing?
B
O A. ADAC
OB. ADCA
O C. ADCA
Reasons
?
CPCTC
definition of congruent sides
substitution property of equality
ABCA by SAS
ABCA by ASA
ABCA by SAS
The missing step in the proof is: D. ADCA
What is the missing step and reason of the proof?In the statements, we are given that AD || BC and ZDAC = ZBCA (alternate interior angles theorem), so we can conclude that triangle ADCA is similar to triangle BCA (by AA similarity criterion).
Therefore, we have the following proportional sides:
DC/AC = AC/BC
Given that DC = BA (given statement), we can substitute BA for DC in the proportion:
BA/AC = AC/BC
Now, we can cross-multiply to get:
BA * BC = AC²
Using the given statement that AC = AC (reflexive property of congruence), we can substitute AC for AC in the equation:
BA * BC = AC * AC
Use the definition of congruent sides to replace BA with DC:
DC * BC = AC * AC
And finally, use the substitution property of equality to replace BC with 6 units (given statement):
DC * 6 = AC * AC
From this equation, we can see that DC = 6 units, which completes the proof. Therefore, the missing step is statement D. ADCA.
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Find the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum.
Answer: The formula for compound interest is:
A = P(1 + R/100)^t
where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.
Here, P = Rs. 3,500, R = 8%, and t = 2 years.
So, the amount after 2 years will be:
A = 3,500(1 + 8/100)^2
= 3,500(1.08)^2
= 3,892.32
Therefore, the compound interest for 2 years will be:
CI = A - P
= 3,892.32 - 3,500
= 392.32
Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.
Step-by-step explanation: