A value of about 32.9 years. The remaining balance will not reach $3,317 for 33 years, rounded up to the closest year.
What's the point of the example?Interest is often expressed as an annual percentage of the borrowed amount. This percentage represents the loan's interest rate. For instance, a bank will pay interest if you deposit money in an account savings account.
The initial deposit into the personal savings account is denoted by P, and the yearly interest rate is denoted by r. The following formula determines the account balance after t years:
A = Pe^(rt)
P = $1,000, r equals 5.8%, as Well as a is $3,317 in this scenario. To determine how many years it will be for such balance to reach $3,317, apply the following formula:
3,317 = 1,000e^(5.8% * t)
You must isolate t over one portion of the equation to find the solution:
t = ln(3,317 / 1,000) / (5.8% / 100)
That amounts to:
t = ln(3.317) / 0.058
Calculating this yields a result of around 32.9 years. The remaining balance will not reach $3,317 for 33 years, rounded up to the closest year.
Therefore, 33 years are needed to complete the process.
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What fraction form have 6 letters
Answer:
tenth
Step-by-step explanation:
Two scuba divers are swimming below sea level. One diver is located 28 feet below sea level and the other is located 37 feet below sea level. Which expression shows how far apart the divers are?
|−37| − |−28|
|−37| + |−28|
|37| − (−|−28|)
|37| + |28|
Answer:
b. |−37| + |−28|
Step-by-step explanation:
The absolute value of a number is its distance from 0 on the number line. Since the divers are below sea level, both 37 and 28 will be negative numbers.
To find the distance between the two divers, we need to add the absolute values of their depths.
The first diver is at -37 ft and the second diver is at -28 ft, so we can calculate the distance between them as |-37| + |-28| = 37 + 28 = 65 ft
How do you find the long side?
Calculate the length of the longest side of the triangle use following methods :
Pythagoras theorem : (hypotenuse)² = (Base)² + (altitude)²
Sine rule : AB/sin C = AC / sin B = BC / sin A.
As given in the question,
To find the length of the longest side of a triangle use following methods:
a. Triangle is right angle triangle.
In the right angle triangle ,
Hypotenuse is the longest side.
To find the length of the hypotenuse use Pythagoras theorem:
(Hypotenuse)² = (Base)² + (Altitude)²
b. Triangle is not right angle triangle.
Use sine rule:
AB be the longest side in triangle ABC.
Side opposite to ∠A , ∠B , ∠C in ΔABC are BC, AC,AB respectively.
If measure of angles and other sides are given apply sine rule:
AB/sin C = AC / sin B = BC / sin A.
Therefore, the measure of the longest side of the triangle is calculated by :
Pythagoras theorem : (hypotenuse)² = (Base)² + (altitude)²
Sine rule : AB/sin C = AC / sin B = BC / sin A.
The above question is incomplete , the complete question is :
How do you find the long side of the triangle?
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What is they system of inequalities associated with the following graph?
Answer: We can find the inequalities. One inequality has a line with y-intercept 2 and slope -1. The inequality is y >= -x + 2.
Step-by-step explanation:
The internal and external diameters of a hollow hemispherical vessel are 16 cm and 12 cm respectively. If the cost of painting 1 cm² of the surface area is Rs. 5.00, find the total cost of painting the vessel all over. (Use = 3.14)
The surface area of the hemispherical vessel is 715.92 square centimeter and the cost to paint is Rs. 3579.62.
What is surface area?An object's surface area is the total area that all of its surfaces occupy. Different 3D shapes in geometry have various surface areas. There are two groups for the surface area:
Surface area of the lateral Surface that is curved Surface area overall.
Given that the external diameter of the hemispherical vessel is 16cm, hence the radius is 8cm.
The internal diameter of the hemispherical vessel is 12cm, hence the radius is 6cm.
The total surface area of the vessel is given by the following formula:
[tex]SA= 2\pi R^2 + 2\pi r^2 + \pi (R^2 - r^2)\\\\SA= 2(3.14)(8)^2 + 2(3.14)(6)^2 + (3.14)(8^2 - 6^2)\\\\SA= 401.92 + 226.08 + 87.92\\\\SA= 715.92[/tex]
The total surface area of the vessel is 715.92 square centimeters.
The cost to paint 1 square centimeter is Rs. 5, hence the cost to paint 715.92 square centimeters is:
C = (715.92)(5)
C = 3579.6
Hence, the cost to paint 715.92 square centimeters is Rs. 3579.62.
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MARKING BRAINLIEST! please help asap
Answer: the answer is negative 5
Step-by-step explanation:
when serenity goes bowling, her scores are normally distributed with a mean of 195 and a standard deviation of 14. what is the probability that the next game serenity bowls, her score will be between 183 and 218, to the nearest thousandth?
The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%
Given that,
Mean = 195
Standard deviation = 14
Thus, the probability between 183 and 218 is the ρ value of z when x = 195
Subtracting by the ρ value of z when x = 183
so, x = 218
z = 218-195/14 = 1.64
when x = 183
z = 183-195/14= -0.85
Thus, z value is 1.64 then the probability is 0.94950 and when z value is -0.85 then the probability is 0.21886
Now, 0.94950 - 0.21886 = 0.73064
Therefore, The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%
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pls help super simple!!!
Answer:
Here are the answers in fraction form.
[tex]x > \frac{1.7}{0.7}[/tex]
[tex]x < - \frac{11.7}{0.7}[/tex]
Here are the answers in decimal form.
[tex]x > 2.43[/tex]
[tex]x < -16.71[/tex]
Step-by-step explanation:
We will have 2 answers.
Answer 1
[tex]0.7x+5 > 6.7[/tex]
Move all terms not containing [tex]x[/tex] to the right side of the inequality.
[tex]0.7x > 6.7-5\\0.7x > 1.7[/tex]
Divide both sides by [tex]0.7[/tex].
[tex]\frac{0.7x}{0.7} > \frac{1.7}{0.7}\\[/tex]
[tex]x > \frac{1.7}{0.7}[/tex]
[tex]x > 2.43[/tex]
Answer 2
[tex]-0.7x-5 > 6.7[/tex]
Move all terms not containing [tex]x[/tex] to the right side of the inequality.
[tex]-0.7x > 6.7+5\\-0.7x > 11.7[/tex]
Divide both sides by [tex]-0.7[/tex].
When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
[tex]\frac{-0.7x}{-0.7} < \frac{11.7}{-0.7}[/tex]
[tex]x < \frac{11.7}{-0.7}[/tex]
[tex]x < -16.71[/tex]
What is the degree of the polynomial 4w - 1?
A. 1
B. 2
C. 3
D. 4
Answer:
Step-by-step explanation:
The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the polynomial is 4w - 1. The highest power of the variable w is 1, so the degree of the polynomial is 1.Therefore, the correct answer is A) 1
Can a function have 2 roots?
A quadratic equation has two roots.
A function can have two roots. A root of a function is a point at which the function's value is equal to zero. This means that the function crosses the x-axis, and two roots means that it crosses the x-axis twice. Depending on the type of function, these two points can be either real or complex numbers. For example, the quadratic equation x2-3x+2 has two real roots, namely x = 1 and x = 2.A quadratic polynomial may have one, two, or zero roots. Quadratic polynomials have a degree of two.
Let's consider a quadratic polynomial
[tex]ax^2+bx+c=0[/tex]
where [tex]a\neq 0[/tex]
The quadratic polynomial is of degree two. Therefore, a quadratic equation has no more than two roots.
There is a formula to find the roots of quadratic polynomials, which is called the quadratic formula.
[tex]x=\frac{-b\frac{+}{-}\sqrt{b^2-4ac} }{2a}[/tex]
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a pulley on a dock is 5 feet above the water level. a rope on the pulley is attached to a boat in the water. the rope is being pulled in at a rate of 3 ft/sec. find the rate of change of the angle of elevation, which is the angle formed by the rope attached to the boat and the horizon, when the boat is 12 feet from the dock. please give an exact simplified answer.
The rate of change of the angle of elevation is -2π/3 radians/second.
We can use the tangent ratio to solve this problem. Since the rope is attached to the boat, we can draw a right triangle with the rope as the hypotenuse. The angle of elevation is the angle formed by the rope and the horizon.
The pulley is 5 feet above the water level, so the length of the opposite side (the side adjacent to the angle) is 5 feet. The length of the hypotenuse is 12 feet, since the boat is 12 feet from the dock.
Using the tangent ratio, we can calculate the angle of elevation:
tan(θ) = opp/hyp = 5/12
θ = arctan(5/12) = 0.927 rad
Now, since the rope is being pulled in at 3 ft/sec, the length of the hypotenuse is decreasing at a rate of 3 ft/sec. Therefore, the rate of change of the angle of elevation is:
rate of change of θ = -(3 ft/sec) / (12 ft) = -2π/3 radians/second
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what does the value of the sample correlation coefficient indicate about the relationship between the admit rate () and the -yr grad. rate ()?
The sample correlation coefficient, is represented as r, measures the strength of correlation and direction of the linear relationship between two variables. It ranges from -1 to 1. The closer the coefficient is to -1, the stronger the negative correlation, the closer it is to 1, the stronger makes the positive correlation reach towards its closer and the closer towards to the expectancy to 0, the weaker the correlation.
The correlation coefficient does not indicate the cause and effect relationship between the variables, just the association between them.
A positive correlation tells us that as one variable increases with respective its the other variable also increases, and a negative correlation means that as one variable increases with respective to its the other variable decreases.
So, the value of the sample correlation coefficient between the rates of admit and the -yr grad rate . rate can indicate if these variables are positively or negatively done as correlated and how strong is this correlation occurs.
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Find the weighted average of the numbers −1 and 1, with weight two-thirds on the first number and one-third on the second number. −0.3 6.2 3 2.8
The weighted average of the numbers −1 and 1 is 0.3. Hence option A is the correct option.
What is the weighted average?
A weighted mean is similar to an average. Rather than contributing equally to the final mean, some data points contribute more "weight" than others. If all of the weights are equal, the weighted mean equals the arithmetic mean (the familiar "average").
Given numbers are -1 and 1.
The first number is -1 and the second number is 1.
Two third of the first number is
= -1 × (2/3)
= -2/3
The one third of second number is
= 1 × (1/3)
= 1/3
The average weight is the sum of two third of the first number and one-third of the second number is -2/3 + 1/3 = -1/3 = -0.33.
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Factorise : 2 5 x x 19x 42 3 2 − − +
Note that after the expression 2x³-5x²-19x+42, has been factorized, we have (x−2)(x+3)(2x−7).
What is factorization?Factorization or factoring in mathematics is the process of expressing a number or any mathematical object as a product of numerous factors, generally smaller or simpler objects of the same sort.
The polynomial 2x³-5x²-19x+42 can be factorized by using the rational root test. To apply this test first we need to find at least one rational zero.
In this case one rational zero is x=2.
This means that we can divide polynomial 2x³-5x²-19x+42 by x−2 (the factor theorem)
That is:
2x³-5x²-19x+42/ x-2
= 2x² - x - 21, this means that
2x³-5x²-19x+42 = (2x² - x - 21) * (x-2)
From the above, our constants are given as:
a = 2, b = -1 and c = 21
Multiply the constant terms by the leading coefficient.
a *x = -42
Find out two number that multiply to a*c = -42 and add b = -1
Next we identify all pairs of numbers with a product of -42. They are:
-1 * 42-2 * 21-3 * 14-6*71 *-422 * -213 * -146 * -7Next we find all factor pair that sum up to b = -1. It is given as 6 +-7 which is identical to item 8 above.
Next, replace the middle term -1x with 6x-7x to get:
(2x² −x−21) * (x-2) =(2x² +6x−7x−21) * (x-2)
If we thus apply factoring by grouping, and factor 2x out of the first group and -7 out of the second group, we have: (2x-7) (x+3) (x-2).
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Full Question:
Factorise 2x³-5x²-19x+42
you are interested in the number of english-speaking people on the planet who want to play a new kind of online video game. you asked 300 college students if they were interested in playing video games, 100 said yes, and of them 20 preferred your game to an existing game that is widely used. how many people were in the sample? select one: a. the number of english-speaking people on the planet who want to play a new kind of online video game. b. 300 c. 200 d. 100 e. 20
b. Total Sample = 300 college students
The question is asking how many people were in the sample of 300 college students that were asked if they were interested in playing video games. The answer is option B: 300.
To answer this question, we must first understand the context of the question. It is asking about the number of English-speaking people on the planet who want to play a new kind of online video game. To answer this, 300 college students were asked if they were interested in playing video games. Of those 300 students, 100 said yes, and 20 of those students preferred this new game to an existing game that is widely used. Therefore, the sample size was 300.
The sample size is 300 college students. From the 300 college students, 100 said yes to playing video games. Of these 100, 20 preferred the new game to an existing game. Therefore, the sample size is 300 college students.
Total Sample = 300
No. of Yes = 100
No. of Prefers new game = 20
So, Total Sample = 300 college students
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From the set {10, 18, 21}, use substitution to determine which value of x makes the inequality true.
To use substitution to determine which value of x makes the inequality true, we need to have an inequality with x as one of the variables. Without more information on the inequality, it is not possible to determine which value of x makes the inequality true. The set {10, 18, 21} does not contain any variable x.
Solve for x. Round to the nearest tenth, if necessary.
By using trigonometric relations, we can see that the angle x on the right triangle is:
x = 62.96°
How to find the value of x on the right triangle?On the image, we can see a right triangle, and we want to find the value of x, which is the measure of an angle on the right triangle.
On the given triangle we can see that the hypotenuse measures 77 units, and the adjacent cathetus to the angle has a measure of 35.
Then we can use the trigonometric relation:
cos(x) = (adjacent cathetus)/(hypotenuse)
Replacing the values that we know:
cos(x) = 35/77
Now we can apply the inverse cosine function in both sides:
Acos(cos(x)) = Acos(35/77)
x = Acos(35/77) = 62.96°
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The record lowest temperature in Fraser, Colorado (which is disputedly known as the icebox of the nation) was -54°. There is a 14° difference warmer between the lowest temperature in Fraser and the lowest temperature in International Falls, Minnesota. (They also lay claim to the title of icebox of the nation.)
What was the lowest temperature recorded in International Falls?
The lowest temperature recorded in International Falls is - 40°.
What are some alternative names for arithmetic operations?Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
Given, The lowest temperature in Fraser, Colorado is - 54°, and the difference between the lowest temperature in Fraser, Colorado, and the lowest temperature in International Falls, Minnesota is 14°.
There the lowest temperature recorded in International Falls is,
- 54° + 14°. (as stated warmer we put a positive sign)
= - 40°.
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I will choose your answer brainliest!
Question is:
The function f is defined by F (x) = x + 1.
Find f ( y - 3 ).
Answer:
f(y - 3) = y - 2
Step-by-step explanation:
to find f(y - 3) , substitute x = y - 3 into f(x) , that is
f(y - 3) = y - 3 + 1 = y - 2
in 6 years the age of my sister and her three children will be 90 years what will it in 4 years
The age of my sister and her three children in 4 years will be 70 years
How to find the age in 4 yearsThe age is added in 6 years to get 90 years> the addition is done as follows
Sister + 6 + Child1 + 6 + Child2 + 6 + Child3 + 6 + Child4 + 6 = 90 years
Sister + Child1 + Child2 + Child3 + Child4 + 6 + 6 + 6 + 6 + 6 = 90
Sister + Child1 + Child2 + Child3 + Child4 + 6 * 5 = 90
Sister + Child1 + Child2 + Child3 + Child4 = 90 - 30
Sister + Child1 + Child2 + Child3 + Child4 = 60
In 4 years the age will be
Sister + Child1 + Child2 + Child3 + Child4 + 4 * 5 = 90
Sister + Child1 + Child2 + Child3 + Child4 = 90 - 20
Sister + Child1 + Child2 + Child3 + Child4 = 70
in 4 years the ages will be 70 years
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A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a(t) = cos t . At time t = 0, its position Is x = 3.
(a) Find the velocity and position functions for the particle.
(b) Find the values of t for which the particle is at rest.
a) The velocity and position functions are given as follows:
Velocity: v(t) = sin(t).Position: s(t) = -cos(t) + 3.b) The particle is at rest when: t = kπ, k = ± 1, ± 2, ± 3, ...
How to obtain the functions?The acceleration function for this problem is defined as follows:
a(t) = cos(t).
The velocity function is the integral of the acceleration function, hence it is given as follows:
v(t) = sin(t).
(as the integral of cos(t) is sin(t).)
The particle will be at rest when:
v(t) = 0.
Hence:
sin(t) = 0
t = arcsin(0)
t = kπ, k = ± 1, ± 2, ± 3, ...
The position function is the integral of the velocity function, hence it is given as follows:
s(t) = -cos(t) + 3.
As:
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How to turn the coordinates (-3,5) (4,-4) into y=mx+b
Answer:
y = -[tex]\frac{9}{7}[/tex] + [tex]\frac{8}{7}[/tex]
Step-by-step explanation:
Answer:
y = [tex]-\frac{9}{7} x +\frac{8}{7}[/tex]
Step-by-step explanation:
To turn the coordinates into y=mx+b, you first need the slope, m.
To find that you would use [tex]m = \frac{y2 - y1}{x2 - x1}[/tex],
Let (-3, 5) = (x2, y2)
and (4, -4) = (x1, y1)
[tex]m = \frac{5 - (-4)}{-3 -4}[/tex]
or, [tex]m = -\frac{9}{7}[/tex].
Now you have the slope, you will need the y-intercept, b, which you will need to use the point-slope formula (y - y2) = m(x - x2) and plug one of the points and slope into the equation (It does not matter which point you use).
So, (y - 5) = [tex]-\frac{9}{7}[/tex](x - (-3) or (y - 5) = [tex]-\frac{9}{7}[/tex](x + 3)
Then you would distribute the -9/7 to the (x + 3),
which turns into
(y - 5) = [tex]-\frac{9}{7}x[/tex] + ([tex]-\frac{9}{7}[/tex])3
y - 5 = [tex]-\frac{9}{7} x -\frac{27}{7}[/tex]
After that , add 5 from both sides,
y - 5 = [tex]-\frac{9}{7} x -\frac{27}{7}[/tex]
+ 5 +5
--------------------------------
y = [tex]-\frac{9}{7} x +\frac{8}{7}[/tex]
And that should be in y=mx+b form!
Hope it helps!
Given an a -valve of 2 an d a vertex at (3,-1),write an equation in vertex form for the quadratic function f(x) = a (x-h)²+k
The quadratic equation written in the vertex form is:
y = 2*(x - 3)^2 - 1
How to write the quadratic equation?We know that for a leading coefficient a, and a vertex (h, k), we can write the quadratic equation as:
f(x) = a*(x - h)^2 + k
Here we know that the leading coefficient is 2, and the vertex of our quadratic equation is (3, -1)
Then the values that we have are:
a = 2
h = 3
k = -1
Then we can write the quadratic equation in the vertex form as:
y = 2*(x - 3)^2 - 1
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Carol has three times as many 10 dollar bills as 5 dollar bills. she has a total of $350.
how many five dollar bills does carol have? how many 10 dollar bills?
x • 2/5 = 4 what is X standing for?
[tex] \sf \frac{2x}{5} = 4 \\ \sf \: 2x = 4 \times 5 \\ \sf \: 2x = 20 \\ \sf \therefore \: x = 10[/tex]
Answer: X stands for 10
Step-by-step explanation:
If we subsitute X for 10, and convert 2/5 to 0.4 we get, 10x0.4 = 4
To convert a fraction to a decimal, you simply divide the numerator by the denominator.
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answer:
Sin A / A = Sin B / B Law of Sines
Sin 73 / X = Sin 59 / 18 Application of Law of Sines
X = Sin 73 / Sin 59 * 18 = .956 / .857 * 18 = 20.1
Properties of Real Numbers Use properties of real numbers to write the expression without parentheses.
By using the properties of real numbers the given expression can be written as -8y.
What is solving an expression?
Another word for "solving a math problem" is "simplifying an expression." When you simplify an expression, your goal is essentially to make it as simple as you can. There shouldn't be any additional multiplying, dividing, adding, or subtracting to be done at the conclusion.
Given:
The given expression is, [tex]\frac{4}{3}(-6y)[/tex]
According to the distributive property of real numbers, if a, b, c are three real numbers the,
a(bc) = (ab)c
Using the associative property of multiplication, the given expression can be written as,
[tex]\frac{4}{3}(-6y) = (\frac{4}{3}*(-6))*y \\\frac{4}{3}(-6y) = (\frac{-24}{3} )*y\\\frac{4}{3}(-6y) = -8y[/tex]
Hence, by using the properties of real numbers the given expression can be written as -8y.
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Solve for X, Leave in simplest radical
Simplest radical form means the radical form of a number or algebraic expression in simplest terms.
Solve for X, Leave in simplest radical?The simplest radical form of the square root of 16 is √16. Generally, the radical form of the square root of a number can be written, if we know the prime factorization of a number. Thus, the prime factorization of 16 is 2×2×2×2.
Square root of 16 is +4 or -4. Since -4 is not a natural number, the square root can be described as an integer.
16 (sixteen) is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Two car owners are in need of car repairs. Lacey will need to pay the mechanic $3 per minute for labor, plus $398 to cover the cost of new parts. Sebastian will need to pay $466 for parts and $1 per minute for labor. Depending on how long each repair takes, the two jobs might end up costing the same amount. How much time would that take? How much would Lacey and Sebastian each have to pay?
Answer:
Step-by-step explanation:
x=#of minutes
y= cost
Laceys equation: y=3x+398
Sebastions equation: y=x+466
intersection (34, 500)
itll take 34 minutes and cost $500
Joe and Tim observed two points, P, and Q, on a number line.
Joe said that the absolute values of the numbers represented by the two points are different.
Tim said that the absolute values of the numbers represented by the two points are the same.
Which of the following explains who is correct? How did you get your answer?
Joe, because the points have different signs
Tim, because each point is fraction 3 over 8 unit away from 0
Tim, because the distance between the points is fraction 3 over 8 unit
Joe, because the points are at different locations
Points P and Q are 3/8 unit away from 0, and because absolute values cannot be zero, the absolute values are the same. Tim is the correct one here, and the correct argument is the second answer option.
Absolute values are numbers that are either zero or positive. They can never be negative, since it is the very definition of absolute values. If a given number is negative, then you only need to change the sign to positive so that you get the absolute value of the number. For example, the absolute value of - 0.001 is 0.001.
Points P and Q are equally 3/8 unit away from 0, but P is negative and Q is positive. The distance of both are not 3/8 unit but twice as that. Even though - 3/8 and 3/8 are not the same because of the different signs, they have the same absolute value, which is 3/8. Therefore, Tim is the correct one.
This question refers to the image attached.
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