Answer:
The polynomial that represents the difference of 12x^3+7x+3 and 3x^7+4x is 12x^3-3x^7+7x-4x.
Mark would like to buy a new guitar that costs $169.00. Mark has saved $55 and receives an allowance of $12 a week. Choose the equation that represents how many weeks, w , it will take for Mark to save enough money to buy the guitar. Responses
With a weekly budget of $12, Mark will need to save money for 9 weeks, 5 days in order to purchase the guitar.
what is equation ?The value is said to be in its simplified form when divided through its smallest equivalent fraction. How to find the most basic form. Find common factors in the denominator and numerators. Verify a minority integer t verify if it qualifies like a prime number. A statement comprising two rotational symmetry and an equal sign in the middle is called an equation in mathematics. The general form of almost any equation contains the degrees of all variables in descending order. The conventional form of something like a linear equation is an x + b = 0. The general form of a mathematical expression with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as identities or conditional solutions. An identity holds true irrespective of the value given to the variables.
given
let the week be x
equation = $55 + 12x = $169.00
55 + 12x = 169
12x = 169 - 55
12x = 114
x = 9.5
With a weekly budget of $12, Mark will need to save money for 9 weeks, 5 days in order to purchase the guitar.
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Which of the following best describes the expression 6(x + 10)? (1 point)
The sum of a constant factor 6 and a 2-term factor x + 10
The product of a constant factor 6 and a 2-term factor x + 10
The sum of constant factors 6 and x + 10
The product of constant factors 6 and x + 10
The best description of the expression 6(x + 10) is given as follows:
The product of a constant factor 6 and a 2-term factor x + 10.
How to describe the expression?The expression for this problem is defined as follows:
6(x + 10).
The 6 before the parenthesis means that the distributive property is applied, meaning that we have a product of two amounts, which are given as follows:
6.x + 10.Meaning that the second option is the correct option.
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The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y < −2x + 10 y < 1 over 2x − 2 coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3 I B A F Question 7(Multiple Choice Worth 1 points) (05.06 MC) A class trip to a ski resort has been planned for your senior trip. The mountain only allows skiing when the temperature is between −10 degrees and 35 degrees. There is room for 38 people on your trip. Write the constraints to represent this real-world problem, where x is the temperature and y is the number of people on your trip. −10 < x < 35 and 0 < y ≤ 38 x < 35 and y > −10 0 < x ≤ 38 and −10 < y < 35 x > −10 and y < 35 Question 8(Multiple Choice Worth 1 points) (05.06 MC) A company dyes two sizes of rugs. A small rug requires 2 hours for dyeing, and a medium-size rug requires 3 hours for dyeing. The dyers need to make at least 15 rugs, and they must do it in less than 60 hours. Let x equal small rugs and y equal medium rugs. Which of the following inequalities can be paired with x + y ≥ 15 to create a system that represents this situation? 2x + 3y < 60 3x + 2y < 60 2x + 3y > 60 3x + 2y > 60 Question 9(Multiple Choice Worth 1 points) (05.06 MC) Solve the following systems of inequalities and select the correct graph: 2x − y < 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB. a dashed line g of x rising left to right that is shaded below and a dashed line f of x that is falling left to right that is shaded above a dashed line f of x rising left to right that is shaded above and a dashed line that is falling g of x left to right that is shaded above a dashed line
The point that is a solution to the system of inequalities y < −2x + 10 and y < 1/2x − 2 is point E at (4, -2). This is because point E satisfies both inequalities.
When we plug in the x and y values of point E into the first inequality, we get -2 < -2(4) + 10, which simplifies to -2 < 2, which is true.
When we plug in the x and y values of point E into the second inequality, we get -2 < 1/2(4) - 2, which simplifies to -2 < 0, which is also true. Therefore, point E is a solution to the system of inequalities.
For question 7, the correct answer is −10 < x < 35 and 0 < y ≤ 38. This is because the temperature must be between -10 and 35 degrees, and there must be between 0 and 38 people on the trip.
For question 8, the correct answer is 2x + 3y < 60. This is because a small rug requires 2 hours for dyeing and a medium-size rug requires 3 hours for dyeing, and the total time must be less than 60 hours.
For question 9, the correct answer is the graph with a dashed line f of x rising left to right that is shaded above and a dashed line that is falling g of x left to right that is shaded above.
This is because the solution to the system of inequalities is the area where both inequalities are true, which is the area where they have shading in common. In this case, it is the area above both dashed lines.
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Find the standard form of the eclipse with end points of Major Axis (2,2) & (8,2) and minor axis (5,3) & (5,1)
Answer:
Step-by-step explanation:
Pour trouver la forme standard de l'équation d'une ellipse à partir des extrémités des grands axes et des petits axes, nous pouvons utiliser les formules suivantes:
Le centre de l'ellipse est le point (h, k), où h est la moyenne des coordonnées x des extrémités des grands axes et k est la moyenne des coordonnées y des extrémités des petits axes. Donc,
h = (2 + 8) / 2 = 5
k = (3 + 1) / 2 = 2
Donc, le centre de l'ellipse est (5, 2).
La distance a est la moitié de la longueur du grand axe, donc
a = (8 - 2) / 2 = 3
La distance b est la moitié de la longueur du petit axe, donc
b = (3 - 1) / 2 = 1
Maintenant, nous pouvons utiliser ces valeurs pour écrire l'équation de l'ellipse en forme standard:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
En substituant les valeurs trouvées précédemment, nous avons:
(x - 5)^2 / 3^2 + (y - 2)^2 / 1^2 = 1
Ce qui est la forme standard de l'équation de l'ellipse.
PRE-CALCULUS:
Hi! Not really sure how to go about this problem..please help!
Answer:
6
Step-by-step explanation:
the numerator of the fraction is
6(t+h) +1 -(6t +1) = 6h
so the fraction is 6h/h =6
Solve for l if V = 120 w = 5 and h = 4
Answer:
The value of l is 48. The formula to calculate volume (V) is V = l * w * h, so we can rearrange the equation to solve for l, or l = V/(w * h). In this case, l = 120/(5 * 4) = 48.
Answer:
125
Step-by-step explanation:
w
In the expression $c \cdot a^b - d$, the values of $a$, $b$, $c$, and $d$ are 0, 1, 2, and 3, although not necessarily in that order. What is the maximum possible value of the result?
The maximum possible value of the result is 8.
How to solve Linear Equations?
We are given the linear equation;
4x - x = 0
From the linear equation above, seeing that we have an x that is raised to the power of one-third, and we have a single x variable, the first step would be to add x to both sides to get;
The first step to solving the equation is to; C. add x to both sides
The second step to solving the equation is to; C. cube both sides
Solving the equation for x initially yields; C. two possible values
Checking the solutions shows that; D. none are valid solutions
4x - x + x = 0 + x
4x = x
Now, to remove the fraction root, what we will now do as the second step is to cube both sides to get;
(4x)³ = x³
4³x = x³
64x = x³
Divide both sides by x to get;
x² = 64
Take square root of both sides to get;
x = ±√64
x = ±8
Hence, The maximum possible value of the result is 8.
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WILL VOTE 75 POINTSSS
Which of the following can sine squared theta over the quantity 1 plus cosine theta end quantity be simplified to?
cos θ
1 + cos θ
1 − cos θ
sin θ + tan θ
Answer:
The expression "sine squared theta over the quantity 1 plus cosine theta end quantity" can be simplified to "1 - cos θ".
Answer:
1 - cos θ
Step-by-step explanation:
100 points + brainliest!
Answer: D = √2
(please respond if im wrong)
Step-by-step explanation:
The fold is made along BE. A folds onto A′.
A′B = AB =√2 ⇒ A′C = 1
(by Pythagoras)
ΔA′BC
is therefore a right-angled isosceles triangle.
⇒∠BA′C=45∘ ⇒∠EA′D=45∘
⇒ ED = A′D = √2−1
How do I do this? This is confusing..
The points are as selected on the graph.
How to select points on the graph?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
Since f(x) = -9. What this means is that the value of f(x) will always be -9 irrespective of the value of x. That is:
x f(x)
-2 -9
0 -9
2 -9
7 -9
9 -9
Check the attached image for the points on the graph
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Jeremy’s work is below. Determine whether or not he has simplified the ratio 8in/3in correctly. Justify your answer.
The solution is, the total surface area is 92 sq. inches.
What is total surface area?Total surface area refers to the area including the base(s) and the curved part. It is the total area covered by the surface of the object. If the shape has a curved surface and base, then the total area will be the sum of the two areas.
here, we have,
Total paper required = total surface area
Surface area of a cuboid = 2[(l×b) + (l×h) + (b×h)],
Where 'l' is the length, 'b' is the breadth and 'h' is the height
For the box, total surface area = 2[(8×3) + (3×2) + (8×2)]
=2[24 + 6 + 16]
=2[46]
= 92 sq. inches
Hence, The solution is, the total surface area is 92 sq. inches.
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Which of the following equations has no real solutions?
OA. 10(x-6) = 10x - 60
OB.10(x+6)= 10(x + 10)
OC. 10x-6=60x-6
OD. 10x-610x6
Answer:
10x-610x6
The equation 10x-610x6 has no real solutions because it cannot be solved for any value of x. The left side of the equation is 10x-6, and the right side is 10x+6. Since the left side is greater than the right side, no value of x can make the equation true.
Select the correct answer from each drop-down menu. Consider right triangle ABC. A triangle ABC has right angle at B is shown. Base AB has length labeled 40 units. Height BC has length labeled 9 units, and hypotenuse AC has length 41 units.
We know the lengths of the sides opposite and adjacent to angle A, as well as the length of the hypotenuse, then sin(A) = 9/41 and cos(A) = 40/41.
What are trigonometric ratios?
Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.
We can use the following trigonometric ratios:
sin(A) = opposite/hypotenuse
cos(A) = adjacent/hypotenuse
In this case, we know the lengths of the sides opposite and adjacent to angle A, as well as the length of the hypotenuse:
opposite = BC = 9 units
adjacent = AB = 40 units
hypotenuse = AC = 41 units
Using these values, we can calculate the sine and cosine of angle A:
sin(A) = opposite/hypotenuse = 9/41
cos(A) = adjacent/hypotenuse = 40/41
Therefore, we know the lengths of the sides opposite and adjacent to angle A, as well as the length of the hypotenuse, then sin(A) = 9/41 and cos(A) = 40/41.
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Roger will pour concrete to make a sidewalk with the dimensions, in feet, shown in the figure below. He will pour the concrete to a depth of 4 inches. One bag of concrete mix makes 0.6 cubic feet of concrete. What is the least whole number of bags of concrete mix that Roger needs in order to make the sidewalk?
F. 16
G. 44
H. 50
J. 58
K. 67
The least whole number of bags of concrete mix that Roger needs is:
Number of bags = 6
Answer: F. 16
What is Volume?The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
To find the volume of the sidewalk in cubic feet, we first need to convert the dimensions to feet. Since 1 foot = 12 inches, we have:
Length = 24 feet + 6 inches = 24.5 feet
Width = 4 feet + 6 inches = 4.5 feet
Depth = 4 inches = 1/3 feet (since 1 foot = 12 inches, 4 inches = 4/12 feet = 1/3 feet)
The volume of the sidewalk is then:
Volume = Length x Width x Depth
= 24.5 feet x 4.5 feet x 1/3 feet
= 3.25 cubic feet
Since one bag of concrete mix makes 0.6 cubic feet of concrete, the number of bags of concrete mix that Roger needs is:
Number of bags = Volume of sidewalk / Volume per bag
= 3.25 cubic feet / 0.6 cubic feet per bag
= 5.42 bags
Since Roger cannot buy a fraction of a bag, he must buy at least 6 bags of concrete mix. Therefore, the least whole number of bags of concrete mix that Roger needs is:
Number of bags = 6
Answer: F. 16
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32.24 ÷ 2.08 =
What is the answer of this question
Answer:
15.4 is the answer
Stepson
Select the correct answer from each drop-down menu.
Consider right triangle ABC.
A triangle ABC has right angle at B is shown. Base AB has length labeled 40 units. Height BC has length labeled 9 units, and hypotenuse AC has length 41 units.
Answer:
By using trigonometric relations, we will see that:
AC = 15.6 in
AB = 8.4 in.
How to get the measures of the other two sides of the right triangle?
Here we have the right triangle where:
B = 90°
C = 40°
BC = 10 in.
Notice that is the adjacent cathetus to the angle C, then we can use the two relations:
sin(a) = (adjacent cathetus)/(hypotenuse).
tan(a) = (opposite cathetus)/(adjacent cathetus).
Where:
hypotenuse = AC
opposite cathetus = AB.
Then we will have:
sin(40°) = 10in/AC.
AC = 10in/sin(40°) = 15.6 in
tan(40°) = AB/10in
tan(40°)*10in = AB = 8.4 in.
So we can conclude that for the given right triangle we have:
AC = 15.6 in
AB = 8.4 in.
If you want to learn more about right triangles:
Step-by-step explanation:
The scrap value of a machine at the end of its useful life is given by S(n)=C(1-r), where C is the original cost, n is the useful life
of the machine in years, and r is the constant annual percentage of value lost. Find the scrap value of the following machine.
Original cost, $41,000; life, 10 years; annual rate of value lost, 13%
Answer:
$ 2,484.23
Step-by-step explanation:
The formula for scrap value is
S(n) = C( 1- r)ⁿ
where
S(n) = scrap value after n years
C = original cost
r = rate of value lost in decimal
n = number of years
First convert r to a decimal by dividing by 100
r = 13/100 = 0.13
S(10) = 10,000(1 - 0.13)¹⁰
= 10,000 x (0.87)¹⁰
= 10000 x 0.248423
= $ 2,484.23
2 Select the correct answer. A circle with radius 5 and center A. The coordinates of the center of the circle are (-3, 12). What is the general form of the equation of the given circle with center A? A. x2 + y2 + 6x − 24y − 25 = 0 B. x2 + y2 − 6x + 24y + 128 = 0 C. x2 + y2 + 6x – 24y + 128 = 0 D. x2 + y2 + 6x − 24y + 148 = 0 Reset Next
The correct equation is D. x2 + y2 + 6x − 24y + 148 = 0.
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.
This equation is the general form of a circle with center A and radius 5. The equation can be derived from the coordinates of the center A and the radius of the circle. The center of the circle is located at (-3, 12). To get the equation, first calculate the distance between the center A and a point on the circumference of the circle, which is the radius of the circle, 5. Then, use the Pythagorean theorem to calculate the equation of the circle: x2 + y2 + 6x – 24y + 148 = 0.
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Just need help with this question..
Graph appears to intersect the X axis in between 20 and 22 and algebraically the estimate of zero is 21.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Given a linear function which represents the profit of Bethany, y after x hours of dog walking.
(a) From the graph, we have to estimate the zero.
The graph seems to intersect the X axis in between 20 and 22, approximately 21.
(b) To solve this algebraically, we have the profit function,
y = 23x - 480
When y = 0,
23x - 480 = 0
23x = 480
x = 20.87 ≈ 21
Hence the graphical method gives the same estimate as the algebraic method.
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A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle. Let s be the side length of the polygon, let r be the hypotenuse of the right triangle, let h be the height of the triangle, and let n be the number of sides of the regular polygon. Polygon area = n(12sh).
Here, we let n be the number of sides of the regular polygon. Polygon area = n(12sh). As n increases, h approaches r so that rh approaches r² and hence, this statement is true. So, option 4 is the correct option.
When ns equals circumference or 2r, the polygon will turn into a circle.
A polygon must be converted into a circle.
Let s represent the polygon's side length, r represent the hypotenuse of the right triangle,
Let n be the regular polygon's number of sides and h be the height of the triangle.
The polygon's area is now specified as polygon area = n(1/2sh).
Now, we must suppose that the polygon's sides are infinite in order to obtain a circle. In order to do this, we must assume that the polygon's perimeter is the same as the circle's perimeter.
That's why when the number of sides of the polygon will increase its perimeter will become closer to 2πr and its area will become close to a circle.
The complete question that you might be looking for is-
A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle. Let s be the side length of the polygon, let r be the hypotenuse of the right triangle, let h be the height of the triangle, and let n be the number of sides of the regular polygon. polygon area = n(12sh) Which statement is true?
As h increases, s approaches r so that rh approaches r². As r increases, h approaches r so that rh approaches r². As s increases, h approaches r so that rh approaches r². As n increases, h approaches r so that rh approaches r².Learn more about polygons on
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An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 35, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 15 graded projects, (a) What is the probability that exactly 10 of these are from the second section? (Round your answer to four decimal places.) (b) What is the probability that at least 10 of these are from the second section? (Round your answer to four decimal places.) (c) What is the probability that at least 10 of these are from the same section? (Round your answer to four decimal places.) (d) What are the mean value and standard deviation of the number among these 15 that are from the second section? (Round your mean to the nearest whole number and your standard deviation to three decimal places.) mean projects standard deviation projects (e) What are the mean value and standard deviation of the number of projects not among these first 15 that are from the second section? (Round your mean to the nearest whole number and your standard deviation to three decimal places.) mean projects standard deviation projects Need Help? Read It Watch It Master it Submit Answer TO.2/1.2 Points] DETAILS PREVIOUS ANSWERS DEVORESTAT9 3.E.072. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A personnel director interviewing 9 senior engineers for five job openings has scheduled seven interviews for the first day and two for the second day of interviewing. Assume that the candidates are interviewed in a random order. (a) What is the probability that x of the top five candidates are interviewed on the first day? 0 hộ; 2, 5, 9) Ohx; 2, 9, 5) OhN; 7, 9, 5) Ohx; 7,5,9) (b) How many of the top five candidates can be expected to be interviewed on the first day? (Round your answer to two decimal places.) candidates Need Help? Read it 1-/3 Points] DETAILS DEVORESTAT9 3.E.078. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y, (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.382 for this random variable. (Round your answers to three decimal places.) (a) What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals? exactly 3 intervals at most 3 intervals (b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
(a) The probability that exactly 10 of the first 15 graded projects are from the second section can be calculated using the binomial probability formula:
P(X = 10) = (15 choose 10) * (35/60)^10 * (25/60)^5 = 0.0361
(b) The probability that at least 10 of the first 15 graded projects are from the second section can be calculated by summing the probabilities for 10, 11, 12, 13, 14, and 15:
P(X >= 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.0361 + 0.0132 + 0.0035 + 0.0007 + 0.0001 + 0.0000 = 0.0536
(c) The probability that at least 10 of the first 15 graded projects are from the same section can be calculated by summing the probabilities for 10, 11, 12, 13, 14, and 15 from both sections:
P(X >= 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.0361 + 0.0132 + 0.0035 + 0.0007 + 0.0001 + 0.0000 + 0.0019 + 0.0003 + 0.0000 + 0.0000 + 0.0000 + 0.0000 = 0.0556
(d) The mean value and standard deviation of the number among these 15 that are from the second section can be calculated using the formulas for the mean and standard deviation of a binomial distribution:
mean = np = 15 * (35/60) = 8.75
standard deviation = sqrt(np(1-p)) = sqrt(15 * (35/60) * (25/60)) = 1.568
(e) The mean value and standard deviation of the number of projects not among these first 15 that are from the second section can be calculated using the formulas for the mean and standard deviation of a binomial distribution, with n = 45 (the remaining number of projects) and p = 35/60 (the probability of a project being from the second section):
mean = np = 45 * (35/60) = 26.25
standard deviation = sqrt(np(1-p)) = sqrt(45 * (35/60) * (25/60)) = 2.714
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Precision Engineering Factory consumes 12,500 units of a component in every three- month period. The ordering, receiving and handling costs are TZS 3 per order while the trucking costs are TZS 12 per order. Further details are as follows: deterioration and obsolescence cost TZS 0.04 per unit per year, interest cost, TZs 0.06 per unit per year, storage cost TZS 1,000 per year for 50.000 units, a) Calculate the total cost of matenal (ignore decimals and show working clearly).
If Precision Engineering Factory consumes 12,500 units of a component in every three- month period. the total cost of material is TZS 6,060 per year.
How to find the total cost of material?The annual demand for the material can be calculated as follows:
Annual demand = (12,500 units/3 months) x (4 quarters/year) = 50,000 units/year
Ordering cost = TZS 3 per order
Number of orders = (50,000 units/year) / (12,500 units/order) = 4 orders/year
Ordering cost per year = (4 orders/year) x (TZS 3/order) = TZS 12/year
Trucking cost = TZS 12 per order
Trucking cost per year = (4 orders/year) x (TZS 12/order) = TZS 48/year
Deterioration and obsolescence cost = TZS 0.04 per unit per year
Deterioration and obsolescence cost per year = (50,000 units/year) x (TZS 0.04/unit/year) = TZS 2,000/year
Interest cost = TZS 0.06 per unit per year
Interest cost per year = (50,000 units/year) x (TZS 0.06/unit/year) = TZS 3,000/year
Storage cost = TZS 1,000 per year for 50,000 units
Storage cost per unit per year = (TZS 1,000/year) / (50,000 units) = TZS 0.02/unit/year
Storage cost per year = (50,000 units/year) x (TZS 0.02/unit/year) = TZS 1,000/year
Total cost of material = Ordering cost + Trucking cost + Deterioration and obsolescence cost + Interest cost + Storage cost
Total cost of material = TZS 12/year + TZS 48/year + TZS 2,000/year + TZS 3,000/year + TZS 1,000/year
Total cost of material = TZS 6,060/year
Therefore, the total cost of material is TZS 6,060 per year.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The correct sketch is B
What is the liquid range of water?The liquid range of water refers to the temperature range at which water exists as a liquid. At standard atmospheric pressure (1 atm), the liquid range of water is from 0 degrees Celsius to 100 degrees Celsius, or from 32 degrees Fahrenheit to 212 degrees Fahrenheit.
This means that water can exist as a liquid within this temperature range, but if the temperature falls below 0 degrees Celsius or rises above 100 degrees Celsius, it will freeze into a solid or boil into a gas, respectively.
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If you invest $9,500 per period for the following number of periods, how much would you have?
13 years at 10 percent.
50 years at 9 percent.
The accrued amounts are $32,796.58 and $706,396.44.
Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
x = P (1+r/n[tex])^{rt}[/tex]
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
(a) If you invest $9,500 per period for 13 years at 10 percent.
First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 9,500.00(1 + 0.1/1[tex])^{13}[/tex]
A = 9,500.00(1 + 0.1[tex])^{13}[/tex]
A = $32,796.58
(b). If you invest $9,500 per period for 50 years at 9 percent,
First, convert R as a percent to r as a decimal
r = R/100
r = 9/100
r = 0.09 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 9,500.00(1 + 0.09/1[tex])^{50}[/tex]
A = $706,396.44
Therefore, the amounts are$32,796.58 and $706,396.44.
To learn more about the compound interest rate;
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A water company uses the function T = 35 + 0.003w to calculate each customer’s monthly water bill, T, where w is the number of gallons of water used. Which statement describes the slope of the function?
Customers are charged $35.00 each month.
Customers are charged $0.003 per gallon of water used.
Customers are charged 0.003 of a cent each month.
Customers are charged $35.003 per gallon of water use
IF YOU SPAM I WILL REPORT YOU IMMEDIATELY AND I PERSONALLY WILL BAN YOU IMIDEATLEY IF CORRECT I WILL GIVE THE BRAINLIEST. GOOD Luck.
Answer:
Customers are charged $0.003 per gallon of water used.
Step-by-step explanation:
In the given function, T = 35 + 0.003w, the coefficient of w (which is 0.003) represents the rate at which the total cost (T) increases per unit increase in the amount of water used (w). In other words, it is the cost per gallon of water used.
Therefore, the slope of the function is 0.003, and it represents the rate of change of the cost with respect to the amount of water used. Each additional gallon of water used will increase the monthly bill by $0.003.
What are the x-coordinates to the solutions of the system of equations:
x + y + 10 = 0
x ^ 2 + y - 2 = 0
A) x = - 4, -3
B) x= 4, 14
C) x= -3, 4
D) x= -3, -7
Answer:
C
Step-by-step explanation:
x + y + 10 = 0 ( subtract x + 10 from both sides )
y = - x - 10 → (1)
x² + y - 2 = 0 → (2)
substitute y = - x - 10 into (2)
x² - x - 10 - 2 = 0
x² - x - 12 = 0 ← in standard form
(x - 4)(x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 4 = 0 ⇒ x = 4
The conjugate of 145+ 145/3
Answer:
193 1/3
Step-by-step explanation:
First, we need to convert [tex]\frac{145}{3}[/tex] into a mixed number.
[tex]\frac{145}{3}[/tex] = [tex]48[/tex] [tex]\frac{1}{3}[/tex]Now, we can add them together:
[tex]145 +48\frac{1}{3} = 193 \frac{1}{3}[/tex]Therefore, the answer is [tex]193\frac{1}{3}[/tex].
[7] Which country is known as the ‘Land of Thunderbolts’?
(A) China
(B) Bhutan
(C) Mongolia
(D) Thailand
IAS CHINADU KUMAR KHAN
Answer: CHINA
Step-by-step explanation:
IAS CHINADU
Answer:
Bhutan is the answer.
help i need to fisinsh some work for my geometry class because teacher is mean
Answer:
5pi (use the pi character button on your screen)
Step-by-step explanation:
Arc length formula is the shortest formula in all of all math!
Arc length = r•theta
r is the radius. In your question, it is 6.
"theta" is the angle in radians, which was given in your question as 5pi/6.
Fill in these given values to the formula.
Arc length
= r • theta
= 6 • 5pi/6
Simplify (the 6's cancel)
= 5pi
HELPPPPP
i need the answer for this today
Answer:
Below
Step-by-step explanation:
The quations are both equal to 'y' so the equations are equal
5x-10 = -3x+ 14
8x = 24
x = 3 <====== use this value of 'x' in one of the equations to calculate y
y = 5x-10
y = 5(3)-10 = 5
