The amount that should be invested in order to have $2,290 in 16 years is $929.11.
What is compound interest?
The interest on a deposit calculated using both the initial principle and the accrued interest from prior periods is known as compound interest. In other words, compound interest is interest that is earned on interest.
Here, we have
Given: Xin will invest in an account paying an interest rate of 5.8% compounded annually.
Amount to invest = Future value / (1 + r)ᵗ
Where:
r = interest rate
t = time
X = $2,290 / (1 + 0.058)¹⁶
X = 2,290 / 2.46474
X = $929.11
Hence, the amount that should be invested in order to have $2,290 in 16 years is $929.11.
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A 3000-kg truck moving with a velocity of 10 m/s hits a 1000-kg parked car. The impact causes the 1000-kg car to be set in motion at 15 m/s. Assuming that momentum is conserved during the collision, determine the velocity of the truck immediately after the collision.
Answer: The momentum of the truck before the collision is given by the formula:
p_i = m_i * v_i, where m_i is the mass of the object and v_i is its velocity.
The momentum of the truck before the collision is:
p_i (truck) = 3000 kg * 10 m/s = 30000 kg m/s
The momentum of the car before the collision is:
p_i (car) = 1000 kg * 0 m/s = 0 kg m/s
The total initial momentum of the system is the sum of the initial momenta of the truck and car:
p_i (total) = p_i (truck) + p_i (car) = 30000 kg m/s + 0 kg m/s = 30000 kg m/s
After the collision, the final momentum of the system is the sum of the final momenta of the truck and car:
p_f (total) = p_f (truck) + p_f (car)
Let's call the velocity of the truck after the collision v_f (truck). The final momentum of the truck is:
p_f (truck) = 3000 kg * v_f (truck)
The final momentum of the car is:
p_f (car) = 1000 kg * 15 m/s = 15000 kg m/s
Using the conservation of momentum, we can write an equation:
p_f (total) = p_i (total)
30000 kg m/s = p_f (truck) + p_f (car)
30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s
30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s
v_f (truck) = (30000 kg m/s - 15000 kg m/s) / 3000 kg = 7.5 m/s
So, the velocity of the truck immediately after the collision is 7.5 m/s.
Step-by-step explanation:
Are the ratios 4:6 and 2:3 equivalent? Yes or No
Answer:
Step-by-step explanation:
Yes, the ratios 4:6 and 2:3 are equivalent.
To see why, we can compare the proportions of the two ratios by dividing each term by the smaller term in each ratio.
In the ratio 4:6, if we divide both terms by 4, we get:
4/4 : 6/4 = 1 : 3/2
In the ratio 2:3, if we divide both terms by 2, we get:
2/2 : 3/2 = 1 : 3/2
Since both ratios reduce to the same proportion of 1 : 3/2, we can conclude that the ratios 4:6 and 2:3 are equivalent.
Ratios are mathematical expressions that compare two or more quantities. When two ratios are equivalent, it means that they represent the same proportion, even if the numbers in the ratios are different.
To compare the ratios 4:6 and 2:3, we divided each term in each ratio by the smallest term. This is because dividing each term by the same number will keep the proportion of the ratio the same.
For example, in the ratio 4:6, dividing both terms by 4 gave us the proportion of 1 : 3/2, which is the same as the proportion of 2:3 when divided by 2. This means that, even though the numbers in the two ratios are different, they represent the same proportion, and therefore the ratios are equivalent.
It's important to note that when comparing ratios, it's best to reduce the ratios to their simplest form so that the proportions are more easily compared.
find the value of each variable provide proofs
x= 19, y=19
There is a theorem with 45 degrees 45 degrees 90 degrees triangles, it is that the two legs are equal to a and the hypotenuse is equal to a√2
So, since we know the hypotenuse is 19√2, a=19
so x = 19and y = 19
LEVEL 3
Record the letters
in your triangle from
left to right.
Example:
ABCDEFGHI
Enter the correct 9 letter sequence (no spaces) Use all capital letters *
Triangle is a polygon with 3 sides. The record of the letters in your triangle from left to right is EGFBIHDCA.
What is a triangle?A triangle is a polygon with 3 sides. Also, It has three vertices.
As the example is given to us, ABCDEFGHI is the record of the letters that are when seen from top to bottom, therefore, if we rotate the triangle such that the left side of the triangle is on the upper side, then the triangle we will get is given below.
Thus, the record of the letters in your triangle from left to right is EGFBIHDCA.
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1.28/2.26 step by step explanation
Answer:
approximately 0.567088608.
Step-by-step explanation:
The division of 1.28 by 2.26 can be done as follows:
Divide the whole number part of the dividend (1) by the whole number part of the divisor (2): 1 ÷ 2 = 0 with a remainder of 1.Write the remainder (1) over the dividend, keeping the same decimals: 1.28 ÷ 2.26.Multiply the whole number part of the divisor (2) by the result of the division in step 1 (0) to get 0.Subtract this result (0) from the whole number part of the dividend (1) to get 1.Write the result of step 4 (1) as a decimal over the same number of decimals as the dividend: 1.Repeat steps 3 to 5 using this new number (1) as the dividend until you reach the desired precision.To get the final result, place the decimal point in the result according to the number of decimals in the dividend.Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Equations 4 and 5 are not equivalent to any of the other equations.
What is a equation in math?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
The equations that are equivalent are:
2 + x = 5
Negative 5 + x = negative 2
x + 1 = 4
Subtracting 2 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.
Adding 5 to both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.
Subtracting 1 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.
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Hi! Can someone please help me? Please look in the photo
I would appreciate it a lot thanks :)
Answer:
D
Step-by-step explanation:
Count total dots => 30
Amount of dots under x>=5 => 21
21/30 = 7/10 = 70%
please help as quickly as possible!
On solving the provided question we can say that the quadratic equation is 3x²+15x+9=0
What is quadratic equation ?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
the quadratic equation is 3x²+15x+9=0
by Shridhara Charya formula method, we have
x=−0.697224
x=−4.30278
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what must be added to each term of the ratio 49:64 , so that it becomes 3:4 ?
Answer:
Hence x= 8 should be added to the terms of 49:68 to get the ratio 3:4.
Step-by-step explanation:
have a nice day.
What is the value of r^2 for the following data yo three decimal places ?
The correlation coefficient of the data-set in this problem is given as follows:
C. r² = 0.931.
How to obtain the correlation coefficient for the data-set?The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.
The points from the table in this problem are given as follows:
(3,2), (4,4), (5,5), (7,6), (10,20).
Inserting these points into a calculator, the correlation coefficient is obtained as follows:
r² = 0.931.
Meaning that the correct option is given by option C.
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A typical glass of wine contains about 22 grams of alcohol. Consider a 103-pound woman, with approximately 6 liters (6000 milliliters) of blood, who drinks two glasses of wine. Complete parts (a) and (b) below.
If all the alcohol were immediately absorbed into her bloodstream, what would her blood alcohol content be? (Round to two decimal places as needed.) g/100 mL
Answer: The amount of alcohol the woman consumed can be calculated as follows:
Two glasses of wine * 22 grams of alcohol per glass = 44 grams of alcohol
To convert this amount to milliliters, we need to know the concentration of the alcohol, which is typically around 12% for wine. So, 44 grams of alcohol is equivalent to 44 grams / 0.12 g/mL = 367 mL.
Next, we can calculate the woman's blood alcohol content (BAC) using the following formula:
BAC = (Alcohol consumed in mL) / (Blood volume in mL) * 100%
The blood volume for a 103-pound woman with approximately 6 liters of blood can be estimated as follows:
6 liters * 1000 mL/liter = 6000 mL
So, the BAC can be calculated as follows:
BAC = (367 mL) / (6000 mL) * 100% = 0.0612 * 100% = 6.12%
Therefore, the woman's blood alcohol content would be 6.12% if all the alcohol were immediately absorbed into her bloodstream.
Step-by-step explanation:
Subtract 5m + 11 and m + 8
The expression (m + 8) - (5m + 11) simplifies to -4m - 3.
How to subtract the expresisonsFrom the question, we have the following parameters that can be used in our computation:
Subtract 5m + 11 and m + 8
To subtract (5m + 11) from (m + 8), we need to distribute the negative sign to each term inside the first set of parentheses:
(m + 8) - (5m + 11)
Open the brackets
= m + 8 - 5m - 11
Evaluate the like terms
= -4m - 3
Hence, (m + 8) - (5m + 11) simplifies to -4m - 3.
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Find the average rate of change, problem in picture
The average rate of change of the function over the interval (-1, 2) is 3.
What is Average Rate of Change of a Function?Average rate of change of a function is defined as the rate at which the value of the function is changing with respect to the change in the input values.
Difference quotient of a function over an interval is also the same concept as the average rate of change of a function.
Average rate of change of a function f(x) over an interval (a, b) is [tex]\frac{f(b) - f(a)}{b-a}[/tex].
Given interval is (-1, 2).
From the graph, f(-1) = -4 and f(2) = 5
Average rate = [tex]\frac{f(2) - f(-1)}{2--1}[/tex] = (5 - -4) / (3) = 9/3 = 3
Hence the given function has an average rate of change over the interval (-1, 2) at 3.
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the perimeter of this triangle is 32,
write down the equation in terms of x
The value of x in the triangle is 5 units.
How to find the perimeter of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The perimeter of a triangle is the sum of the whole three sides of the triangle.
Hence,
x + 2x + 3 + x + 9 = 32
4x + 12 = 32
subtract 12 from both sides of the equation
4x + 12 = 32
4x + 12 - 12 = 32 - 12
4x = 20
divide both sides of the equation by 4
x = 20 / 4
x = 5
Therefore,
x = 5
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For 5days, Kareem put 4 into his savings account each day. His parents also added a certain amount of money to the account each day. In the end, there was a total of 40 in the account. How much money did Kareem's parents add each day?
Answer:
both Kareem and his parents added 4 each, to the ACC for five days
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To encourage bulk buying, a company reduces the list price of $4,000 per unit by
three cents times the number of units bought. Write a function statement for the
company's revenue (R) from a particular distributor that buys x units.
R(x) =
The expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased and multiplying by x gives the total revenue from selling x units at that price.
What is revenue?
Revenue can be defined as the total amount of income generated by the sale of goods and services related to the primary operations of the business.
The revenue (R) from a particular distributor that buys x units can be calculated using the following function statement:
R(x) = (4000 - 0.03x) * x
Where
4000 is the original list price per unit 0.03 is the discount per unit per unit purchased x is the number of units purchasedThe expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased, and multiplying by x gives the total revenue from selling x units at that price.
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Find the value of x for the following
Answer:
x = -4°
Step-by-step explanation:
We know that,
→ Sum of angles of straight line is 180°.
Now we have to,
→ Find the required value of x.
Forming the equation,
→ (54°) + (7x + 154°) = 180°
Then the value of x will be,
→ 7x + 154° + 54° = 180°
→ 7x + 208° = 180°
→ 7x = 180° - 208°
→ 7x = -28°
→ x = -28° ÷ 7
→ [ x = -4° ]
Hence, the value of x is -4°.
Answer: I think x = -4
Step-by-step explanation: I used a calculator.
Select the graph of y = 2 sinz+2
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The graph of y = 2 sin(x) + 2 is given by the following option:
Graph A.
How to graph the sine function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The function in this problem has an amplitude of 2, meaning that before the vertical shift, it oscillates between -2 and 2.
Due to the vertical shift, the function is going to oscillate between 0 and 4, with a period of 2π and no phase shift, crossing the midline of y = 2 at the origin, hence Graph A is the correct graph.
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If Z₁=3-2i
Z2=-2+3i
Z3=4+2i
Evaluate Z₂ Z3/Z₁
Answer:
32/13
Step-by-step explanation:
To evaluate the expression Z₂ * Z3 / Z₁, we first need to find the complex numbers Z₂ * Z3 and Z₁.
Z₂ * Z3 = -2 + 3i * 4 + 2i = (-8 + 14i) + (-6 + 6i) = -8 + 8i
Z₁ = 3 - 2i
So, Z₂ * Z3 / Z₁ = (-8 + 8i) / (3 - 2i)
We can simplify this expression by multiplying the numerator and denominator by the complex conjugate of the denominator, which is (3 + 2i).
Z₂ * Z3 / Z₁ = (-8 + 8i) / (3 - 2i) * (3 + 2i) / (3 + 2i) = (-8 + 8i) * (3 + 2i) / (3 - 2i) * (3 + 2i)
Z₂ * Z3 / Z₁ = ((-8 * 3 + 8 * 2i) + (8 * 3 + 8 * 2i)) / (3^2 + (-2i)^2) = (16 + 16i) / 13
Therefore, Z₂ * Z3 / Z₁ = (16 + 16i) / 13.
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-13) = 20 B. g(0) = 2 C. g(7) = -1 D. g(-4) = -11
Answer: It is not possible to determine the truth of these statements without further information about the function g. The information given only provides the domain and range of the function and the values of g at two specific points, 0 and -9. To determine the value of g at other points, we would need to know the equation for the function g.
Step-by-step explanation:
Mann Park is the shape of a triangle.
On a map, it has borders that measure 5 inches inches, 7 inches
and 9 inches. If the shortest border of Mann Park is
1000 meters long, how long in meters, is its longest
border?
The longest border of the Mann's park is 228.6 meter.
What is Triangle inequality theorem ?The Triangle Inequality It is a basic principle of geometry that the lengths of any two sides of a triangle must add up to more than the length of the third side. In other words, the longest side of any triangle must be shorter than the total length of the other two sides.
In this case, the shortest side of Mann Park measures 5 inches, and the two longer sides measure 7 inches and 9 inches.
So, the sum of the lengths of the two longer sides is:
' 7 inches + 9 inches = 16 inches.
Since 5 inches is less than 16 inches, we know that the 5-inch side is the shortest side, and the 9-inch side is the longest side.
One inch is approximately equal to 0.0254 meters, so we have:
= 9 inches x 0.0254 meters/inch
= 0.2286 meters
Since the shortest side is 1000 meters long, the longest side is:
= 1000 meters x 0.2286 meters/inch
= 228.6 meters long.
Therefore, the longest border of Mann Park is approximately 228.6 meters long.
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Multiply
-1/5. (-2/7)
Write answer in simplest form.
Answer:
2/35
Step-by-step explanation:
[tex](-\frac{1}{5})(-\frac{2}{7}) = \frac{2}{35}[/tex]
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For students majoring in Hospitality Management, it was determined that 5% have visited 1–10 states, 16% have visited 11–20 states, 45% have visited 21–30 states, 19% have visited 31–40 states, and 15% have visited 41–50 states. Suppose a Hospitality Management student is randomly selected. What is the probability that the student has visited 21 or more states?
A. 0.15
B. 0.21
C. 0.45
D. 0.79
The probability is 0.79 that a randomly chosen student has visited 21 or fewer states.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
from the given data we get,
The categories are mutually exclusive, so we have ...
P(≥21) = P(21-30) +P(31-40) +P(41-50)
= 45% +19% +15%
P(≥21) = 79%
=0.79
The probability is 0.79 that a randomly chosen student has visited 21 or fewer states.
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Describe the transformation given to the parent function f(x)=sin(x) given the graph of the equation g(x)=sin(3x)-4
A:The graph is vertically stretched by a factor of 1/3 and shifts up 4 units.
B:The graph is vertically stretched by a factor of 1/3 and shifts down 4 units.
C:The graph is horizontally compressed by a factor of 1/3 and shifts up 4 units.
D:The graph is horizontally compressed by a factor of 1/3 and shifts down 4 units.
The transformation given to the parent function f(x)=sin(x) given the graph of the equation g(x)=sin(3x)-4 will be C. The graph is horizontally compressed by a factor of 1/3 and shifts up 4 units.
How to explain the transformationThe parent function f(x) = sin(x) has been transformed by replacing x with 3x in the argument of the sine function.
This results in a horizontal compression of the graph by a factor of 1/3. In addition, the graph of g(x) = sin(3x) is shifted upward 4 units, as indicated by the subtraction of 4 from the value of the sine function.
The correct option is C.
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10 inches in 6 hours
80 inches in 2 days
The relation is a direct variation
How to determine if the relation is a direct variationFrom the question, we have the following parameters that can be used in our computation:
10 inches in 6 hours
80 inches in 2 days
Convert 2 days to hours
So, we have the following representation
10 inches in 6 hours
80 inches in 72 hours
For the relation to be a direct variation, the following must be equal
6/10 = 72/80
Evaluate
0.6 = 0.6
Hence, the relation is a direct variation
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Complete question
Determine if the following relation represents a direct variation
10 inches in 6 hours
80 inches in 2 days
Graph h(x)=−x2+3.
Use the parabola tool then choose the vertex followed by one point on the parabola.
Answer: I do not have the capability to create a graph. However, I can tell you how to graph the parabola h(x) = -x^2 + 3.
A parabola is defined by its equation in the form y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = -1, b = 0, and c = 3.
The vertex of the parabola is the highest or lowest point on the graph and is given by the coordinates (-b/2a, c - b^2/4a). For this parabola, the vertex is (0, 3), since b = 0 and a = -1.
To find another point on the parabola, you can plug in any x-value and use the equation of the parabola to find the corresponding y-value. For example, if you plug in x = -2, you get:
h(-2) = -(-2)^2 + 3
h(-2) = 4 + 3
h(-2) = 7
So the point (-2, 7) is also on the parabola.
With the vertex and one other point on the parabola, you can now graph the parabola.
Step-by-step explanation:
What is the slope of line p? on a coordinate plane, a straight line goes through (negative 3, negative 2), (0, 0), and (3, 2).
Slope line formula is used for determining the slope of a line. Based on the given points, the slope of line is 2/3.
To find the slope of the line passing through the given points, we can use the slope formula, which states that the slope of a line passing through two points (x1, y1) and (x2, y2) is given by the expression:
slope = (y2 - y1) / (x2 - x1)
Using this formula, we can calculate the slope of the line passing through the three given points as follows:
slope = (2 - (-2)) / (3 - (-3)) = 4/6 = 2/3
Therefore, the slope of the line passing through the given points is 2/3.
Alternatively, we can observe that the three points are collinear and lie on the same straight line. We can use this fact to find the slope of the line by computing the rise over run between any two of the points. For example, using the points (0,0) and (-3,-2), we have a rise of 2 and a run of 3, so the slope is 2/3. This confirms that the slope of the line passing through the given points is 2/3.
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(4,−2) and (−8,−1) slope intercept form
If the figure below is reflected over the y-axis, what are the coordinates of c’? I need IT ALL!
Given diagram drawn on the graph is parallelogram.
For find out 4th coordinate of parallelogram.
We must know the basics of graph.
Graph can defined as pictorial representation using data or point in the organized manner.
Graph having x-coordinate and y-coordinate.
For find out the location of point.
We must know how to locate coordinates.
For find X-point , parallel distance from y-axis.
For find Y-point , parallel distance from x-axis.
Observe the given diagram.
Find out the parallel distances of x-axis and y-axis.
4th coordinate of parallelograms is c(2,-5).
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Identify true statements about set membership and subsets
The statement that are true are :
a. Z is an element {y,z}
b. {6,7,8 } is a subset of {1,2,3,4......}
c. 3 is an element of {2,3}
d. r is not an element of {s,t,u}
What is set?
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
The objects in a set are called the elements (or members ) of the set; the elements are said to belong to the set (or to be in the set), and the set is said to contain the elements.
The following statements are true about the set
a. Z is an element {y,z}
b. {6,7,8 } is a subset of {1,2,3,4......}
c. 3 is an element of {2,3}
d. r is not an element of {s,t,u}
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