The compound interest rate of the given information for which the annual rate of the bank account is = 3.9%.
What about compound interest?
Compound interest refers to the interest that is earned not only on the principal amount of a loan or investment but also on any interest that has been previously earned. In other words, it is the interest calculated on the initial principal and on the accumulated interest of previous periods. This compounding effect can result in significant growth over time, as the interest earned in each period is added to the principal, and the interest earned in subsequent periods is calculated on the new, larger principal amount. Compound interest is often used in long-term savings and investment accounts, such as retirement funds or fixed deposits, as it can result in a higher return than simple interest over time.
According to the given information:
In this case we know that;
⇒ A = [tex]P(1 + r)^n[/tex]
⇒ A = amount
⇒ P = principal
⇒ r = rate
⇒ n = number of years
⇒ 710.89 = 658.20[tex](1 + r)^2[/tex]
⇒ 710.89/658.20 = [tex](1 + r)^2[/tex]
⇒ 1.08 = [tex](1 + r)^2[/tex]
⇒ ln(1.08) =ln [tex](1 + r)^2[/tex]
⇒ 0.077 = 2ln[tex](1 + r)[/tex]
⇒ 0.077/2 = ln(1 + r)
⇒ ln[tex](1 + r)[/tex] = 0.0385
⇒ 1 + r = 1.039
⇒ r = 1.039 - 1
⇒ r = 0.039
⇒ r = 3.9%
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Find the unknown dimension of a rectangle if its perimeter is 254 meters and one
dimension measures 6 meters. Use labeled sketches and equations to model and
solve this problem. Show your work. Label your answer with the correct units.
The perimeter does indeed equal 254 meters, which confirms that our answer is correct.
What in mathematics is the perimeter?Any two-dimensional closed shape's perimeter is defined as the entire distance encircling it. The perimeter of a rectangle, such as the following: Square perimeter equals the sum of its four edges. Rectangle perimeter equals the sum of its four edges.
Let's call the rectangle's unidentified size x.
P = 2l + 2w, where l is the length and w is the breadth, gives the perimeter of a rectangle.
So that we can create an equation:
254 = 2l + 2(6)
Simplifying the right side:
254 = 2l + 12
Subtracting 12 from both sides:
242 = 2l
Dividing both sides by 2:
121 = l
Consequently, the rectangle's undetermined measurement (length) is 121 metres.
We can compute the perimeter using both variables to confirm our conclusion:
P = 2(121) + 2(6) = 242 + 12 = 254
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right 52.5% as a fraction in simplest form
The fraction in simplest form of 52.5% is 21/40.
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.
Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.`
Steps to convert Decimal to Fraction:
Make a fraction number as the numerator and a 1 as the denominator.Count how many places after decimal point. Consider it as xmultiply denominator by 10x.Change the percentage value as 100 in denominator.Reduce the fraction. Then simplify the answer using basic arithmetic operations.52.5%
=> 525/10%
=> 525/10*100
=> 525/1000
=> 21/40
Therefore, The fraction in simplest form of 52.5% is 21/40.
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A paper drinking have in the shape of a cone has a height of 10 cm in a diameter of 8 cm which of the following is closest to the volume of the cup in cubic centimeters
Step-by-step explanation:
The volume of a cone can be calculated using the formula:
V = (1/3)πr^2h
where r is the radius of the base, h is the height of the cone, and π is a constant approximately equal to 3.14.
In this case, the diameter of the base of the cone is 8 cm, which means the radius is half of that, or 4 cm. The height of the cone is given as 10 cm. Substituting these values into the formula, we get:
V = (1/3)π(4 cm)^2(10 cm)
V ≈ 167.55 cubic centimeters
Therefore, the volume of the paper drinking cone is closest to 167.55 cubic centimeters.
Review the graph of a piecewise function.
The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.
What is a piecewise function ?
A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.
The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.
On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.
On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.
On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.
At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.
The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.
Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.
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Examine the diagram. A triangle has angles 1, 2, 3. Angle 4 is an exterior angle to angle 3. For the angles shown in the diagram, which statements are true? Select all that apply. The sum of m∠3 and m∠4 is 180°. The sum of the measures of the adjacent interior angle and one of the remote interior angles is equal to the measure of the exterior angle. ∠3 is supplementary to ∠1. m∠4 = m∠1 + m∠2. m∠1 + m∠2 + m∠3 = 180°
The statements that are true regarding the diagram given are:
m∠3 + m∠4 = 180° (angles on a straight line)m∠4 = m∠1 + m∠2 (external angle theorem)m∠1 + m∠2 + m∠3 = 180° (triangle sum theorem).What is the Triangle Sum Theorem?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
We have in the diagram that in the diagram given, the statements that are all true are:
m∠3 + m∠4 = 180° (angles on a straight line)
m∠4 = m∠1 + m∠2 (external angle theorem)
m∠1 + m∠2 + m∠3 = 180° (triangle sum theorem).
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Natasha worked for part of the year before receiving a raise in her hourly rate of pay. The graph below shows the amount of money she has made this year and the hours she has worked since she received the raise. What was the initial amount of money Natasha made?
Answer:
Unfortunately, I cannot see the graph you are referring to since we are communicating through text. However, based on the information given, we can make some general observations.
We know that Natasha received a raise in her hourly rate of pay at some point during the year. Before the raise, she earned some initial hourly rate of pay. Let's call this initial rate of pay "x". Let's also assume that she worked for "h" hours before receiving the raise, and "k" hours after receiving the raise.
We can write an equation to represent the total amount of money she made this year:
Total amount of money = (initial hourly rate of pay x number of hours worked at the initial rate) + (new hourly rate of pay x number of hours worked at the new rate)
Using the variables we defined earlier, we can write:
Total amount of money = (x × h) + ((x + y) × k)
where y is the increase in her hourly rate of pay after the raise.
We also know that she earned a certain amount of money before the raise. Let's call this amount "M". This means that:
M = x × h
Solving for x, we get:
x = M/h
Substituting this expression for x into the first equation, we get:
Total amount of money = (M + yh) + ((M/h + y) × k)
We don't know the values of M, y, h, or k, so we cannot determine the initial hourly rate of pay x or the total amount of money Natasha made this year. However, we have set up an equation that can be used to solve for these values if we have more information.
Suppose a city with population 100,000 has been growing at a rate of 7% per year. If this rate continues, find the population of this city in 19 years.
Answer:b
Step-by-step explanation:
trust it’s b
PLEASE HELP....Dilations
Okay, just think of dilations as scaling the object bigger or smaller. You are just multiplying all points on the shape by a common scalar.
The only other thing is a negative dilation reflects the shape over the origin (which is quite intuitive cause you negate all the coordinates).
Now for question 1 your just trying to find the scale factor given an original point and a dilated point. Since all points are multiplied by the same factor,
(-3,6)x = (-4,8)
x=4/3
For the second question, just check points to see if all follow the same dilation scale factor. For our purposes it suffices to just check the each vertex.
(1,1) -> (2,2) so the scale factor must be 2
(1,4) -> (2,8) good
(5,1) -> (10,2) good
(5,4) -> (10,8) good
So, this transformation describes a dilation. The scale factor is 2.
I need a satisfying conditions question answered thank you sm
The linear function can be written as:
f(x) = -x/3 + 17/3
How to find the linear function?A general linear function can be written as:
f(x) = ax + b
Where a is the slope, and b is the y-intercept.
If we know two points on the line (x₁, y₁) and (x₂, y₂), then the slope of the linear function is:
a= (y₂ - y₁)/(x₂ - x₁)
Here we know the pairs:
f(-4) = 7
f(5) = 4
So we have the points (-4, 7) and (5, 4), then the slope is:
a = (4 - 7)/(5 + 4) = -3/9 = -1/3
Then we can write:
f(x) = -x/3 + b
now we can use one of the given points, like f(5) = 4, replacing that there we will get:
4 = -5/3 + b
4 + 5/3 = b
12/3 + 5/3 = b
17/3 = b
So the function is:
f(x) = -x/3 + 17/3
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Can someone help me
The value of x does not exist.
What is Quadratic equation?
A quadratic equation is a second-degree polynomial equation in a single variable of the form ax^{2} + bx + c = 0, where a, b, and c are constants and x is the variable. The highest exponent of the variable in a quadratic equation is 2, and the equation can be written in standard form, where the coefficient of the squared term (a) is not equal to zero.
The given expression is:
5x² - √3x + 2
This is a quadratic expression in the variable x, which means that it can be written in the form of ax² + bx + c, where a, b, and c are constants. In this case, we have:
a = 5
b = -√3
c = 2
We can use the quadratic formula to find the roots of this expression:
x = [-b ± √(b² - 4ac)] / 2a
Now, putting the values of a, b, and c, we get:
x = [-(-√3) ± √((-√3)² - 4(5)(2))] / 2(5)
Now, Simplifying the expression under the square root, we get:
x = [√3 ± √(-71)] / 10
Since the expression under the square root is negative, there are no real roots to this equation. Therefore, the expression 5x² - √3x + 2 has no real solutions.
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2. The following ordered pairs are found on the graph of the same line.
(0, 4), (1, 7), (2, 10)
Which one of the following points would NOT be found on the line?
A.(5,19)
B.(-1, 1)
C.(-3,-5)
D.(-7,-19)
As a result, the line would not contain the point (5, 19). The right response is A. (5, 19).
What is a graph, exactly?A graph is characterized by a mathematical construct that connects a collection of points to express a specific function. It establishes a pairwise connection between the objects. The graph was made up of nodes (vertices) connected by edges (lines).
We can see that for any two points on a line, the difference between their y- and x-coordinates is always the same. Let's determine this difference for the ordered pairs provided:
(1, 7) - (0, 4) = (1 - 0, 7 - 4) = (1, 3)
(2, 10) - (1, 7) = (2 - 1, 10 - 7) = (1, 3)
As we can see, the difference between the x-coordinates and y-coordinates of any two consecutive points is the same, i.e. 3. Therefore, we can check which of the points given in the options has a difference of 3 between its x-coordinate and y-coordinate.
A. (5, 19): Difference = 19 - 5 = 14
B. (-1, 1): Difference = 1 - (-1) = 2
C. (-3, -5): Difference = -5 - (-3) = -2
D. (-7, -19): Difference = -19 - (-7) = -12
So, we see that option A has a difference of 14 between its x-coordinate and y-coordinate, which is not equal to 3. Therefore, the point (5, 19) would NOT be found on the line. The correct answer is A. (5, 19).
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The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Weights of Dogs in Shelter A
2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 28, and the box ranges from 16 to 20. A line divides the box at 18.
Weights of Dogs in Shelter B
Which animal shelter has the dog that weighs the least?
shelter A
Step-by-step explanation:
The minimum weight for shelter A is not provided in the given information, but we can compare the minimum weight of shelter B with shelter A's box plot.
As per the given information, the whisker of shelter A ranges from 8 to 30, which means the minimum weight in shelter A is 8 pounds. On the other hand, the whisker of shelter B ranges from 10 to 28, which means the minimum weight in shelter B is 10 pounds. Therefore, shelter A has the dog that weighs the least.
Answer:
Your answer is correct, it's shelter A.
Step-by-step explanation:
A sports medicine specialist determines that a
hot-weather training strategy is appropriate for
a 165 cm tall individual whose BSA is less
than 2.0. To the nearest hundredth, what can
the mass of the individual be for the training
strategy to be appropriate?
hom
BSA <2.0
20
1789
Finish
165 cm
^
The mass of the individual can be up to 87.27 kg for the hot-weather training strategy to be appropriate.
How do you solve for the mass of of the individual using the equation provided?Given that the training strategy is appropriate for a BSA less than 2.0, we need to find the maximum mass (M) for the individual with a height (H) of 165 cm. The equation for BSA is:
BSA = √(H x M) / 3600
We can rearrange the equation to solve for M:
M = (BSA^2 x 3600) / H
Since we want the maximum mass for a BSA less than 2.0, we can use BSA = 2.0 as the upper limit:
M = (2.0^2 x 3600) / 165
M = (4 x 3600) / 165
M = 87.27 kg
The above question is in response to the full question as seen in the image;
A sports medicine specialist determines that a hot-weather training strategy is appropriate for a 165 cm tall individual whose BSA is less
than 2.0. To the nearest hundredth, what can the mass of the individual be for the training strategy to be appropriate?
The equation for BSA is BSA = √(H x M)/3600
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
1x
Step-by-step explanation:
Firstly lets expand the brackets for the equation
(x - 7 )2 = 36
If we multiply what's in the brackets by 2 we get this:
2x - 14 = 36
Add 14 to both sides:
2x = 50
Divide both sides by 2:
x = 25
Answer = 1x (Only possible solution
Answer:
The two solutions to the given equation are x = 13 and x = 1.
Step-by-step explanation:
To solve the given equation (x - 7)² = 36, begin by square rooting both sides:
[tex]\implies \sqrt{(x-7)^2}=\sqrt{36}[/tex]
[tex]\implies x-7=\pm6[/tex]
Now add 7 to both sides of the equation:
[tex]\implies x-7+7=\pm6+7[/tex]
[tex]\implies x=7\pm6[/tex]
Therefore, the two solutions are:
[tex]\implies x=7+6=13[/tex]
[tex]\implies x=7-6=1[/tex]
What is the area of a rectangle with a length of 3 1/3 feet and a width of 1 2/3
0 2 7/9 ft
0 3 2/9 ft²
0 5 5/9 ft²
0 8 1/3 ft²
Answer:
[tex]5 \frac{5}{9} \: {ft}^{2} [/tex]
Step-by-step explanation:
[tex]a \: (length) = 3 \frac{1}{3} \: ft[/tex]
[tex]b \: (width) = 1 \frac{2}{3} \: ft[/tex]
[tex]a \: (rectangle) = a \times b[/tex]
[tex]a = 3 \frac{1}{3} \times 1 \frac{2}{3} = \frac{10}{3} \times \frac{5}{3} = \frac{50}{9} = 5 \frac{5}{9} {ft}^{2} [/tex]
Write the absolute value equations in the form |x-b|=c that have the following solution sets: One solution: x=<5
IN EQUATION FORM NOT SIMPLIFIED.
Answer:
|x-5|=0
Step-by-step explanation:
That was easy.
Find the slope of the line.
A decreasing line that has a Y intercept of zero and passes through the point, four, negative 3.
How do I get domain for (x-7)(x-1) over (x+3)(x-1)
Answer:
To find the domain of the function f(x) = (x-7)(x-1)/(x+3)(x-1), we need to consider the values of x that make the denominator zero since division by zero is undefined.
In this case, the denominator (x+3)(x-1) is zero when x = -3 and x = 1. Therefore, we need to exclude these values from the domain.
So, the domain of f(x) is all real numbers except x = -3 and x = 1.
In interval notation, we can write the domain as (-∞, -3) U (-3, 1) U (1, ∞).
Can the sides of a right triangle have lengths 5, 15, and √250? Explain.
A triangle must have a third side that is bigger than the sum of any two of its sides. There cannot be a triangle with these side lengths because in this instance, 5 + 15 = 20 is not greater than 250.
Application of Pythagoras theoremTo check whether the given lengths can form the sides of a right triangle, we need to check if they satisfy the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's label the sides of the triangle as a, b, and c, where c is the hypotenuse. Then, the Pythagorean theorem can be written as:
a^2 + b^2 = c^2
Plugging in the given values, we get:
5^2 + 15^2 = (√250)^2
Simplifying the left-hand side, we get:
25 + 225 = 250
This is not true, since 25 + 225 = 250 does not hold. Therefore, the given lengths cannot form the sides of a right triangle.
In fact, we can see that the given lengths violate the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side. In this case, 5 + 15 = 20 is not greater than √250, so a triangle with these side lengths cannot exist.
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How do l do this help
Answer:
130
Step-by-step explanation:
Answer: y=130 x=130
Step-by-step explanation:
I will mark you brainiest!
The value of M is
A) 14
B) 18
C) 20
D) 28
Answer:
I got 28
Step-by-step explanation:
use the formula k=y/x. 6/8=0.75
21/0.75=
Find the coordinates of the point 13
of the way from A to B.
If you know the coordinates for points between A and B, that you can use this method to determine the dimensions of the spot that is located (0, 1/3) between A and B.
What do coordinates number mean?A set of integers called coordinates are used to locate a spot or a shape in a two-dimensional plane. The x-coordinate as well as the y-coordinate are two integers that describe a point's location on a [tex]2D[/tex] plane.
To find the coordinates of the point that is [tex]1/3[/tex] of the way from point A to point B. we can use the midpoint formula, which states that the coordinates of the midpoint of the line segment joining two points [tex](x1, y1)[/tex]and [tex](x2, y2)[/tex] are:
[tex]((x1 + x2)/2, (y1 + y2)/2)[/tex]
In this case, let's assume that point A has coordinates (x1, y1) and point B has coordinates (x2, y2). Then the point that is 1/3 of the way from A to B has coordinates:
[tex]((2/3) × x1 + (1/3) × x2, (2/3) × y1 + (1/3) × y2)[/tex]
Therefore, So if you have the coordinates of points A and B, you can plug them into this formula to find the coordinates of the point 1/3 of the way from A to B.
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20 POINTS ANSWER FOR BRAINLIST SHOW WORK
Subtract. Express the answer in standard Form.
(8s ^2 − 3s − 3) − (−4s ^2 + s − 13)
Answer:
To subtract the second polynomial from the first, we need to distribute the negative sign to all terms inside the second set of parentheses, and then combine like terms:
(8s^2 - 3s - 3) - (-4s^2 + s - 13)
= 8s^2 - 3s - 3 + 4s^2 - s + 13 (distributing the negative sign)
= 12s^2 - 4s + 10 (combining like terms)
The resulting polynomial is already in standard form because the terms are arranged in descending order of degree. Therefore, the final answer in standard form is:
12s^2 - 4s + 10
The perimeter and the length of the base of an isosceles triangle are 25cm and 9cm respectively. Calculate the area of the triangle. (Ans: 29.76cm²)
Answer:
Let's denote the length of the equal sides of the isosceles triangle by "x". Then the perimeter of the triangle can be expressed as:
Perimeter = 2x + 9
But we also know that the perimeter of the triangle is 25cm, so we can set these two expressions equal to each other and solve for x:
2x + 9 = 25
2x = 16
x = 8
Therefore, the length of each of the equal sides is 8cm. Now, we can use the formula for the area of a triangle:
Area = (base × height) / 2
Since the triangle is isosceles, we know that the height is also the perpendicular bisector of the base, dividing it into two equal parts of length 4.5cm each. Now we can find the height of the triangle using the Pythagorean theorem:
h² + 4.5² = 8²
h² + 20.25 = 64
h² = 43.75
h ≈ 6.61
Substituting these values into the formula for the area of the triangle, we get:
Area = (9 × 6.61) / 2
Area ≈ 29.76 cm²
Therefore, the area of the isosceles triangle is approximately 29.76 cm².
In PQR, PQ= 5.4, QR= 3.6, and PR=6.2. To the nearest Tenth, what is M∠R
Therefore , the solution of the given problem of angles comes out to be M∠R measured at 45.4 degrees, to the closest tenth.
An angle meaning is what?The intersection of the lines that form a skew's ends determines the size of its biggest and smallest walls. There's a possibility that two paths will intersect at a junction. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by placing two line beams in various configurations between their ends.
Here,
To determine the size of angle R in triangular PQR, we can apply the Law of Cosines:
=> cos(R) = (PQ₂ + PR₂ - QR₂) / (2 * PQ * PR)
=> cos(R) = (5.4₂ + 6.2₂ - 3.6₂) / (2 * 5.4 * 6.2)
=> cos(R) = 0.6960917
When we calculate the inverse cosine of both sides, we obtain:
=> R = cos⁻¹(0.6960917)
=> R equals 45.4 degrees
Angle R in triangle PQR is therefore measured at 45.4 degrees, to the closest tenth.
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Identify as a direct variation, inverse variation or neither. Y+x=10
Answer:
y=x10 is a direct variation, because everything you do to y will result in a similar change in x .
5. You throw a water balloon into the air and its path is modeled by
h =-d² + 4d + 5 where h is the height in feet and d is the horizontal
distance in feet.
a. When the horizontal distance is 1 (d=1), what is the height of
the balloon?
b. Your arch nemesis (enemy) is standing about 33 feet away from
you, does the water balloon hit them? (Explain your answer)
Step-by-step explanation:
Your POST does not match the picture....I will use the equation in the picture
h = - 1/8 d^2 + 4d + 5
a) when d = 1 find 'h' by putting '1' in the equation for 'd'
h = -1/8 *(1^2) + 4(1) + 5 = 8 8/9 ft high
b) when d = 33
h = -1/8 ( 33^2) + 4 (33) + 5 = .875 ft = 7/8 ft high
yah...it will probably hit your enemy
The diameter of a circle is 5 miles. What is the circumference?
Answer: Circumference, C = 15.71 miles
Step-by-step explanation:
The formula for the circumference of a circle is C = 2*pi*r, where C is the circumference and r is the radius. (Value of pi = 3.1415)
In this case, the diameter, d = 5 miles = 2*r, so we can substitute that into the formula:
C = pi*d = 3.1415*5
C = 15.7079 miles
Therefore, the circumference of the circle is approximately 15.71 miles, if we round to two decimal places.
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Can somebody find me a pencil to write please
Try going to the store and they should be surprisingly cheap.
Answer: here it is.
Step-by-step explanation:
I need help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation: 1. is Yes 2 is no 3. is all 4 is Y and 50 5 is yes and -1