The cannonball will land approximately 20.4 seconds after it was fired.
What is the name of a cannon ball?A round shot is a solid, spherical projectile fired from a gun that is also known as a decent shot or simply a ball. Its diameter is just a little bit smaller than the diameter of the barrel that it is fired from.
A cannon ball's composition.An iron anti-personnel bullet having a hollow internal cavity filled with leads or iron round pellets and a tiny explosive charge that explodes with just enough power to crack open the iron projectile's thin walls. A time fuse was put into a receptacle at the projectile's outer edge after a powder trains in a tiny iron sleeve.
We can use the equations of motion for projectile motion to solve this problem. Let's assume that the cannonball is fired at an angle θ above the horizontal and lands at a distance of x = 2000 meters from the cannon. We also know that the initial speed of the cannonball is 200 m/s.
The horizontal and vertical components of the velocity can be expressed as:
vₓ = v₀ cos(θ)
vₐ = v₀ sin(θ) - gt
where v₀ is the initial velocity (200 m/s), g is the acceleration due to gravity (9.8 m/s²), and t is the time taken for the cannonball to land.
Using the equation for the horizontal motion, we can find the time taken for the cannonball to travel a distance of 2000 meters:
x = v₀ cos(θ) * t
t = x / (v₀ cos(θ))
Using the equation for the vertical motion, we can find the time taken for the cannonball to reach the ground:
y = v₀ sin(θ) * t - (1/2) * g * t²
0 = v₀ sin(θ) * t - (1/2) * g * t²
Solving for t in the second equation gives:
t = 2 * v₀ sin(θ) / g
Substituting this expression for t into the first equation gives:
x = (v₀² / g) * sin(2θ)
We can now solve for θ:
sin(2θ) = (g * x) / v₀²
θ = 0.5 * arcsin((g * x) / v₀²)
Plugging in the given values for g, x, and v0, we get:
θ = 0.5 * arcsin((9.8 m/s² * 2000 m) / (200 m/s)²) ≈ 20.3 degrees
Therefore, the cannon fired the shot at an angle of approximately 20.3 degrees above the horizontal.
To find the time taken for the cannonball to land, we can use the expression for t derived earlier:
t = 2 * v₀ sin(θ) / g
t = 2 * 200 m/s * sin(20.3°) / 9.8 m/s² ≈ 20.4 seconds
Therefore, the cannonball will land approximately 20.4 seconds after it was fired.
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A fast-food restaurant promotes certain food items by giving a game piece with each item.
Advertisements proclaim that "25% of the game pieces are Instant Winners!" To test this claim, a frequent diner collects 20 game pieces and gets only 3 instant winners.
1. Identify the population, the parameter, the sample, and the statistic in this context.
The correct answer of population is all the game pieces and sample is 20.
How to find the percentage of winners?
As we know that a fast-food restaurant promotes certain food items by giving a game piece with each item, and proclaims that 25% of the game pieces are instant winners.
Population is all the game pieces.
Parameter is true proportion of all the game pieces that are winner.
Sample is 20, the game pieces that is collected.
Statistics is the proportion of the sample that are winners i.e. [tex]\frac{3}{20}[/tex]
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sample is the 20 and the statistic is 3/20 .
What is sample space ?A random experiment's sample space is the collection of all possible outcomes. A portion of the sample space is an event that is associated with a random experiment. Any outcome has a probability that is between 0 and 1. All outcomes have probabilities that add up to 1.
he population is all the game pieces that the fast-food restaurant produces.
The parameter is the proportion of game pieces that are instant winners in the population.
The sample is the 20 game pieces that the frequent diner collected.
The statistic is the proportion of instant winners in the sample. In this case, the statistic is 3/20 or 0.15 (15%).
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What is the additive inverse of the polynomial?
The additive inverse of the polynomial -7y² + x²y -3xy - 7x² include the following: A. 7y² - x²y + 3xy + 7x².
What is an additive inverse?In Mathematics and Geometry, an additive inverse can be defined as a number (n) which when added to another number (a) makes it equal to zero (0). This ultimately implies that, an additive inverse is the opposite of another number (a).
Mathematically, an additive inverse can be represented by the following equations:
a + n = 0
a = -n
-7y² + x²y - 3xy - 7x² = -(-7y² + x²y - 3xy - 7x²)
-7y² + x²y - 3xy - 7x² = 7y² - x²y + 3xy + 7x²)
In this context, we can reasonably infer and logically deduce that an additive inverse of -7y² + x²y -3xy - 7x² is 7y² - x²y + 3xy + 7x².
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What value of x makes this equation true 0.6x-5=0.1x+7
Step-by-step explanation:
To solve for x, we'll first need to simplify the equation by combining like terms:
0.6x - 5 = 0.1x + 7
0.6x - 0.1x = 7 + 5
0.5x = 12
x = 12 / 0.5
x = 24
Therefore, the value of x that makes the equation true is 24.
A bookstore manager will randomly select 1 of 5 newly
arrived fiction books and 1 of 4 newly arrived nonfiction
books for a window display. What is the probability that
the manager will select the shortest of the newly arrived
fiction books and the longest of the newly arrived
nonfiction books?
A. 5%
B. 10%
C. 20%
D. 45%
Answer:
Step-by-step explanation:
number of books are 5 so you will have to do 5 by hundred which will lead to twenty percent
The likelihood that the manager will choose the longest just-received nonfiction book and the shortest recently arrived fiction book is 1/20, or 5%.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
The probability of selecting the shortest fiction book is 1/5 and the probability of selecting the longest nonfiction book is 1/4. Since these events are independent, we can multiply their probabilities to find the probability of both events happening:
P(shortest fiction book and longest nonfiction book) = P(shortest fiction book) x P(longest nonfiction book) = 1/5 x 1/4 = 1/20
So the probability that the manager will select the shortest of the newly arrived fiction books and the longest of the newly arrived nonfiction books is 1/20, which is equivalent to 5%.
Therefore, the answer is option A.
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solve with explanation
2(12)-(-4)
Answer:
28
Step-by-step explanation:
2×12-(-4) - and - = +
24+4 + and + = +
28 + and - = -
- and + = -
Calculate the surface area of this right triangular prism.
Total surface area of right triangular prism is 750cm²
Define the term right triangular prism?A right triangular prism is a three-dimensional geometric shape with three rectangular faces connecting the edges of its two parallel, congruent triangular bases.
Area of the two opposite side triangles (A₁) = 2 × ( [tex]\frac{1}{2}[/tex] × 12 × 5)
Area of the two opposite side triangles (A₁) = 60 cm²
Area of upper, lower and side rectangles (A₂) = (5×23) + (12×23) + (13×23)
Area of upper, lower and side rectangles (A₂) = 115 + 276 + 299
Area of upper, lower and side rectangles (A₂) = 690 cm²
Total surface area of right triangular prism = A₁ + A₂
Total surface area of right triangular prism = 60 + 690
Total surface area of right triangular prism = 750 cm²
Therefore, the total area of the right triangular prism is 750cm²
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YZ is tangent to the circle at Z. Find the measure of minor arc WX
.
Step-by-step explanation:
the angle at Y = 1/2 × (arc angle WZ - arc angle ZX).
so,
42 = (arc angle WZ - 51)/2
84 = arc angle WZ - 51
135° = arc angle WZ
the arc angle WX is the remainder of the whole circle to the sum of the arc angles WZ and ZX :
arc angle WX = 360 - 135 - 51 = 174°
Hellpppppp due soon
Answer:21.33 is the right answer for x
WILL GIVE BRAINLIEST
Defense mechanisms
please just check my work, see if u can spot out any errors… thanks :)
Answer:
the is no error in your work
A ramp is being built to ga up a vertical increase of 10 feet. Codes require the angle the
ramp makes with the ground to be no more than 15
. At least how long will the actual
ramp need to be to pass code?
The length of the ramp we need to build should be at least 38.61 feet to pass code.
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.
We can use trigonometry to solve the problem. Let x be the length of the ramp we need to build. Then, the angle the ramp makes with the ground is given by:
sin(theta) = opposite/hypotenuse
where theta is the angle the ramp makes with the ground, opposite is the vertical increase of 10 feet, and hypotenuse is the length of the ramp x.
Solving for x, we get:
x = opposite/sin(theta) = 10/sin(15)
Using a calculator, we can evaluate sin(15) to be approximately 0.2588. Then, we can divide 10 by 0.2588 to get:
x ≈ 38.61
Therefore, the length of the ramp we need to build should be at least 38.61 feet to pass code.
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The entire group of individuals we want information about is called the sample.
The statement is False. The entire group of individuals we want information about is called the population, not sample.
What is sample?In statistics, a sample is a subset of individuals or observations taken from a larger population, which is used to estimate characteristics or parameters of the population.
The goal of statistical analysis is often to make inferences about a population based on information gathered from a representative sample. Therefore, it is important to carefully select a sample that is truly representative of the population of interest.
The sample is a subset of the population that is selected for analysis in order to make inferences about the population.
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The complete question is : The entire group of individuals we want information about is called the sample.
a. True
b. False
A phone company offers two monthly plans. Plan A costs $23 plus an additional $0.12 for each minute of calls. Plan B costs $14 plus an additional $0.16 for each minute of calls.
Help with math problems
The expansion of the multiplication is [tex]-16+12\sqrt{3}[/tex] and [tex]5-13\sqrt{5}[/tex]
What is irrational numbers?Irrational numbers are real numbers that cannot be represented as simple fractions. If N is irrational, it is not equal to p/q, where p and q are integers and q is not equal to zero. [tex]\sqrt{2}, \sqrt{3}[/tex] are two examples.
distributive law
This property states that multiplying the total of two or more addends by a number produces the same result as multiplying each addend separately by the number and then putting the products together.
That is A(B+C)=AB+AC
According to the given information:
[tex](-2\sqrt{3} +2)(\sqrt{3}-5) = -2\sqrt{3}*\sqrt{3} + 10\sqrt{3} +2\sqrt{3} -10[/tex]
=[tex]-6+12\sqrt{3}-10[/tex]
= [tex]-16+12\sqrt{3}[/tex]
[tex](-2-3\sqrt{5})(5-\sqrt{5}) = -10+2\sqrt{5}-15\sqrt{5}+3*5[/tex]
= [tex]-10-13\sqrt{5}+15[/tex]
=[tex]5-13\sqrt{5}[/tex]
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What is the solution of 3x+8/x-4>0
Answer:
Solve the inequality for
x
by finding
a
,
b
, and
c
of the quadratic then applying the quadratic formula.
All real numbers
Interval Notation:
(
−
∞
,
∞
)
Step-by-step explanation:
Can someone pls help me solve this!! Will give brainliest!!
if I said that angle 1 in the diagram below was 122 degrees, how can the angle relationships be used to determine the rest of the angle measures. Include how you can use these angle relationships to prove that lines are parallel.
(add any theorems you would use)
Hello!
1= 122
2= 58
3= 58
4= 122
5= 122
6= 58
7= 58
8= 122
To find angle 2, you subtract 122 from 180 because angles 1 and 2 are supplementary angles. You can find angle 3 by using the vertical angles theorem. This means that angle 2 and 3 are congruent to each other. You can use the same for angle 4, meaning 1 and 4 are also congruent. You can use the alternate interior angles theorem to prove that 3 and 6 are congruent and then use the vertical angles theorem to prove that 6 and 7 are congruent. You can find angles 5 and 8 by proving that 5 is congruent to 4 using the alternate interior angles theorem and then once again using the vertical angles theorem to prove that angle 5 is congruent to angle 8. Let me know if this is too hard to understand, I will happily simplify it.
Which right does the Fair Debt Collection Practices Act (FDCPA) give
borrowers?
OA. The right to negotiate debt
OB. The right to declare bankruptcy
C. The right to verify the amount owed
OD. The right not to receive phone calls
Answer: prohibits debt collection companies from using abusive, unfair or deceptive practices to collect debts from you.
Step-by-step explanation:
prohibits debt collection companies from using abusive, unfair or deceptive practices to collect debts from you.
The right to verify the amount owed is the right the Fair Debt Collection Practices Act (FDCPA) give borrowers The correct option is C.
What is FDCPA?The Fair Debt Collection Practices Act (FDCPA) is a federal law that governs the conduct of third-party debt collectors who attempt to collect debts on creditors' behalf.
Borrowers who are being pursued by debt collectors have several rights under the FDCPA.
One of the rights granted to borrowers by the FDCPA is the right to verify the amount owed.
This means that borrowers have the right to ask the debt collector for written confirmation of the debt, including the amount owed and the creditor's name.
The debt collector is required to provide this information within a reasonable time after receiving the request.
Thus, the correct option is C.
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Simplify the expression.
three tenths squared minus 17 plus the quantity negative 7 divided by the absolute value of 4.3 minus 7.8 end quantity times 2.67
−11.57
−11.60
−21.74
−22.25
I picked b please tell me why i am wrong
Answer:
D. -22.25
Step-by-step explanation:
First, we need to simplify the expression inside the parentheses
|-3.5| = 3.5
Next, we can simplify the expression inside the parentheses:
-7 ÷ |-3.5| = -2
Now we can simplify the entire expression:
3/10^2 - 17 + (-2) x 2.67 = 0.09 - 17 - 5.34 = -22.25
What is the measure!, in degrees in degrees, of angle x?
Answer:23 degrees
Step-by-step explanation:
Ok! I'm a high school student so this is what I can see.
Angles A and the 130 are supper- angles meaning they add up to 180.
So that means A is 50.
Next I noticed by experience that A and B are vertical angles. So that means B is 50 as well.
And since this all have to equal to 360 angles. The equation is
360= 50+130+50+107+x or X= 360- (50+130+50+107)
And that is x=23
Happy Soving
A collection of 50 buttons is in a jar. The probability of reaching into the jar and retrieving a black button is 0.64. What is the probability that you will reach in the jar and retrieve a button that is not black?
Answer: The probability of reaching into the jar and retrieving a black button is 0.64. Therefore, the probability of reaching into the jar and retrieving a button that is not black is the complement of this probability, which is 1 - 0.64 = 0.36.
In other words, the probability of not getting a black button is the same as the probability of getting a non-black button, which includes all the other colored buttons in the jar. Since there are no other details given in the problem regarding the number of non-black buttons or the probability of retrieving each non-black button, we assume that they are all equally likely to be retrieved and simply calculate the probability of not getting a black button as the complement of the probability of getting a black button.
Therefore, the probability of reaching in the jar and retrieving a button that is not black is 0.36 or 36%.
Step-by-step explanation:
PLEASE HELP!! A cylinder has a volume of 128 cubic centimeters and a height of 6 centimeters. What is the volume of a similar cylinder with a height of 9 centimeters?
The volume of cylinder is 191 cubic centimeters.
What is volume?
The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.
Here cylinder with height 6 cm ,
Volume = 128 cubic centimeters.
Now using volume of cylinder formula then,
=> Volume V =
=> 128 = 3.14**6
=> = = 6.79406
=> r = 2.6 cm.
Now volume of cylinder with height 9 cm is ,
=> Volume V = 3.14**9 = 191 cubic centimeters.
Hence the volume of cylinder is 191 cubic centimeters.
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I need help please
(In picture)
The two forms of the expression
[tex] \frac{ {x}^{5} }{ {x}^{10} } [/tex]
when simplified are
[tex] = {x}^{ - 5} [/tex]
x exponents negative 5 and
[tex]\frac{1}{ {x}^{5} } [/tex]
numerator 1 over denominator x exponents 5.
What are the two forms of simplified expression?Given:
[tex] \frac{ {x}^{5} }{ {x}^{10} } [/tex]
When we have the same base but different powers in indices division, one of the bases is chosen and the powers are subtracted.
[tex] = {x}^{5 - 10} [/tex]
[tex] = {x}^{ - 5} [/tex]
[tex] = \frac{1}{ {x}^{5} } [/tex]
Therefore, the simplified expressions are x exponents negative 5 and numerator 1 over denominator x exponents 5.
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how do i find these I’m so confused
Triangles BIG and MOP are similar so, the values of v, w, x, y are 36 cm, 156°, 46.7°, 43.2° respectively.
Describe Triangles?A triangle is a two-dimensional geometric shape that is formed by three line segments that connect three non-collinear points in a plane. These points are called the vertices of the triangle, and the line segments connecting them are called sides.
Triangles are characterized by several properties, including their side lengths, angles, and areas. Based on the lengths of their sides, triangles can be classified into three types:
Scalene triangle: A triangle in which all three sides have different lengths.
Isosceles triangle: A triangle in which two sides have the same length.
Equilateral triangle: A triangle in which all three sides have the same length.
Since triangles BIG and MOP are similar, we know that their corresponding angles are equal and their corresponding sides are proportional.
Let's first find the value of w in triangle BIG. We know that the sum of angles in a triangle is 180 degrees. Therefore, we can find angle BIG as follows:
angle BIG = 180 - angle BGI
= 180 - 24
= 156 degrees
Now we can use the fact that the corresponding sides of similar triangles are proportional to set up the following ratios:
v/42 = 48/v (since BI/IG = GB/BI)
v^2 = 4248
v = sqrt(4248)
v = 36
In triangle MOP, we can use the law of cosines to find the value of angle MOP:
cos(MOP) = (60^2 + 72^2 - y^2) / (26072)
cos(MOP) = (3600 + 5184 - y^2) / 8640
cos(MOP) = (8784 - y^2) / 8640
MOP = acos((8784 - y^2) / 8640)
MOP = 46.7 degrees (approximately)
Now we can use the fact that the corresponding sides of similar triangles are proportional to set up the following ratios:
v/60 = y/72 (since BI/MO = IG/MP)
y = (v/60)*72
y = (36/60)*72
y = 43.2 cm
Lastly, we can use the fact that the sum of angles in a triangle is 180 degrees to find the value of angle POM in triangle MOP:
angle POM = 180 - angle MOP - 126
= 180 - 46.7 - 126
= 7.3 degrees (approximately)
Therefore, we have:
v = 36 cm
w = 156 degrees
x = 46.7 degrees (approximately)
y = 43.2 cm
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Mark was working on the long jump
competition, and he was able to
jump 9 3
4 feet. Chris jumped 7
8
as far as Mark. Write and solve the
equation that will help you figure
out how far Chris jumped.
Explain the steps you took to solve
Chris has jumped 85/8 feet.
What is the distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or an estimate based on other factors in common usage.
Here, we have
Given: Mark was working on the long jump competition, and he was able to jump 9 3/4 feet. Chris jumped 7/8 as far as Mark.
The distance jumped by Mark = 9 3/4 feet
The distance jumped by Chris = 9 3/4 + 7/8
The total distance covered by Chris would be:
= 9 3/4 + 7/8
= 7/8 + 39/4
= 85/8
Hence, Chris has jumped 85/8 feet.
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There are 37 erasers in the receptacle. Each day the students loose 3 erasers. How many erasers are in the receptacle for each of the first 6 days
There will be 34,31,28,25,22,19 erasers after Day 1,2,3,4,5,6respectively.
Define daysDays are units of time that are used to measure the duration of a complete rotation of the Earth on its axis. One day is defined as the time it takes for the Earth to complete one full rotation on its axis, which is approximately 24 hours long.
Starting with 37 erasers, if 3 erasers are lost each day, then the number of erasers in the receptacle for each of the first 6 days can be calculated as follows:
After Day 1: 37 - 3 = 34 erasers
After Day 2: 34 - 3 = 31 erasers
After Day 3: 31 - 3 = 28 erasers
After Day 4: 28 - 3 = 25 erasers
After Day 5: 25 - 3 = 22 erasers
After Day 6: 22 - 3 = 19 erasers
Therefore, there will be 34 erasers after Day 1, 31 erasers after Day 2, 28 erasers after Day 3, 25 erasers after Day 4, 22 erasers after Day 5, and 19 erasers after Day 6.
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Evan sold half his story books and then bought 17 more. He now has 32 books. With how many did he begin?
Evan sold half his story books and then bought 17 more. Evan had thirty bucks.
What is equivalent?
A mathematical statement is known as an equation, and the equal sign ('=') connects two expressions. At least one unknown variable must be determinable. For instance, an equation is 3x - 8 = 16. We achieve x = 8.
We will sοlve the prοblem by fοrming a οne variable equatiοn.
Let's say Evan started out with a lot of problems. Evan gave up half of his regular wares. He split two separate cakes.
He now has (x-x/2)=x/2 straight numbers.
He then gained 17 pounds.
Sο subsequent to purchasing 17 bοοks he has nοw (x/2+17) story bοοks
Given number οf stοry bοοks he has right nοw is 32.
By equating the two, we can construct a equation for one variable.
(x/2+17) = 32 Solving for x will be the equation:
(x/2+17) = 32; x/2 = 32- 17; x/2 = 15; x = 152; x = 30.
According to the initial equation, Evan had 30 books.
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PLSSS Help
Identify the two forms of the simplified expression x^5/x^10
And if you could please give a brief description. Thank you
Both formulations convey the same meaning and represent the same equation mathematical operation: x raised to the power of 5 divided by x raised to the power of 10.
What is the expression?In this format, the expression is shown using exponent notation. The denominator (bottom) of the fraction is x raised to the power of 10, while the numerator (top) of the fraction is x raised to the power of 5. The phrase can therefore be written as x⁵/x¹⁰.
In this method, the division symbol serves to represent the expression. The denominator (bottom) of the fraction is x raised to the power of 10, while the numerator (top) of the fraction is x raised to the power of 5. The expression is therefore (x⁵)/. (x¹⁰).
Therefore, the same mathematical operation is represented by both formulations, which both express the same meaning: x to the power of 5 divided by x to the power of 10.
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PLEASEE HELPP I gotta do my missing assignments tn!! (And pls explain)
Answer:
29°
Step-by-step explanation:
In the first triangle,
46 + 30 + x = 180 (Angle sum property)
76 + x = 180
x = 180 - 76
x = 104
In the second triangle,
47 + 104 + y = 180
151 + y = 180
y = 29
Thus, the required angle is 29°.
Pls like and mark as brainliest!
Answer:
the answer is 29 degrees
Step-by-step explanation:
look at the picture below
Fwam is going to invest in an account paying an interest rate of 5.9% compounded
daily. How much would Fwam need to invest, to the nearest hundred dollars, for the
value of the account to reach $91,000 in 12 years?
In order for the account value to reach $91,000 in 12 years, Fwam would therefore need to invest $39,165.95, to the closest hundred dollars, assuming the interest rate is 5.9% compounded daily.
what is interest ?In exchange for using borrowed funds or assets, a borrower must pay the lender interest. It is charged for a certain duration of time, typically until the loan is fully returned, and is typically stated as a percentage of the amount borrowed. This fee is known as the interest rate. For instance, if a bank lends you $1,000 at a 5% annual interest rate, after a year of borrowing the money you would still owe the bank $50 more in interest. The creditworthiness of the borrower, the risk of the loan, and current market conditions are frequently used to establish the interest rate.
given
We know that Fwam expects the account to be worth $91,000 in 12 years and that the interest rate is 5.9% compounded daily in this situation.
We must convert the interest rate and the time period to the proper units before we can use the formula.
We begin by converting the 5.9% yearly interest rate to a daily rate:
daily rate is equal to (1 + 0.059/365)(365/365)-(1-1) = 0.00015999.
4,380 days in 12 years, or 365 days per year.
We can now enter the values into the formula to find P:
$91,000 = P × 2.3226
P = $39,165.95
In order for the account value to reach $91,000 in 12 years, Fwam would therefore need to invest $39,165.95, to the closest hundred dollars, assuming the interest rate is 5.9% compounded daily.
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what is the answer to 4n – 3?
Step-by-step explanation:
4n - 3 = 0
4n = 0 + 3
4n = 3
[tex]n \: = \frac{3}{4} [/tex]
If o=12, find the sample size to estimate the mean with an error of +4 and 95 percent confidence (rounded to the next higher integer).
Multiple Choice
75
35
58
113
URGENT
We need to round up to the next higher integer, the sample size required to estimate the mean with an error of +4 and 95 Percent confidence is 170.
To find the sample size to estimate the mean with an error of +4 and 95 percent confidence, we need to use the formula:
n = [(z*sigma)/E]^2
Where:
n = sample size
z = z-score for 95% confidence level (which is 1.96)
sigma = standard deviation (unknown in this case)
E = maximum allowable error (which is +4 in this case)
We are given that o=12, which is the population standard deviation. Since we do not have any information about the sample standard deviation, we can use the population standard deviation as an estimate. Therefore, we can substitute o=12 in the above formula to get:
n = [(1.96*12)/4]^2
n = 169.64
Since we need to round up to the next higher integer, the sample size required to estimate the mean with an error of +4 and 95 percent confidence is 170.
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