Now say you invest the $7,500 and the highest interest rate you can find is 4.5% compounded annually, but you would have to leave the investment in the account for a minimum of 4 years. If you decide to wait 4 years to buy the car, how much more money will you have to save to buy a car at the $9,500 price? Use the compound interest formula A = P (1 + i)n. (Round final answer to the nearest cent, but otherwise don’t round any intermediate values)
The amount of money that you will have to save to buy a car at the $9,500 price is $556.11 ($9,500 - $8,943.89).
How is the amount of money needed determined?The amount of money needed can be determined by calculating the future value of $7,500 invested at 4.5% for 4 years.
Then, the result, which is the future value, $8,943.89, is deducted from the $9,500 price, to determine the additional savings required.
The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.
Where:
A = future value
P = Present value of investment
i = interest rate
n = number of periods.
The future value can also be determined using an online finance calculator, as follows.
Data and Calculations:N (# of periods) = 4 years
I/Y (Interest per year) = 4.5%
PV (Present Value) = $7,500
PMT (Periodic Payment) = $0
Results:
FV = $8,943.89
Total Interest = $1,443.89
Thus, the amount of money that you will have to save to buy a car at the $9,500 price is $556.11.
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Find an equation for the line below
I have been staying up studying all night i and have ming so mich trouble with this will someone help
Answer:
may be like this
its 32cm³
What percent of 128.6 is 4?
Answer:
3.11%
Step-by-step explanation:
4/128.6=0.0311
multiply by 100
3.11%
find the surface area of composite figure. use 3.14 for π. round to the nearest tenth
Answer:
334 in^2.
Step-by-step explanation:
The surface area = area of the top prism + area of the bottom - 2 * area of the base of the top smaller prism
= 2(5*3 + 5*3 + 3*3) + 2(9*7 + 9*5 + 7*5) - 2* 3*5
= 2* 39 + 2*143 - 30
= 334
REALLY HARD QUESTION HELPPPP
Drag the tiles to the correct boxes to complete the pairs.
∆ABC and ∆PQR are similar. ∆ABC is dilated by a scale factor of 1.25 and rotated 45° counterclockwise about point B to form ∆PQR. The side lengths of ∆ABC are AB, 5 units; BC, 4.2 units; and AC, 4 units. Match each side of ∆PQR to its length.
Answer:
Step-by-step explanation: I did the test and the answer should be A
hope this helps :)
Hey can someone help me with this?
Answer:
Step-by-step explanation:
A. a = $1350 b. b= 89%
B. 1350(.89)^t = 675
t = 5.9 years
Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference
2. Also, let b1, b2, b3, ... be a sequence of positive integers in geometric progression with common
ratio 2. If a1 = b1 = c, then the number of all possible values of c, for which the equality
2(a1 + a2 + ⋯ + an
) = b1 + b2 + ⋯ + bn
holds for some positive integer n, is _____
Since [tex]a_1,a_2,a_3,\cdots[/tex] are in arithmetic progression,
[tex]a_2 = a_1 + 2[/tex]
[tex]a_3 = a_2 + 2 = a_1 + 2\cdot2[/tex]
[tex]a_4 = a_3+2 = a_1+3\cdot2[/tex]
[tex]\cdots \implies a_n = a_1 + 2(n-1)[/tex]
and since [tex]b_1,b_2,b_3,\cdots[/tex] are in geometric progression,
[tex]b_2 = 2b_1[/tex]
[tex]b_3=2b_2 = 2^2 b_1[/tex]
[tex]b_4=2b_3=2^3b_1[/tex]
[tex]\cdots\implies b_n=2^{n-1}b_1[/tex]
Recall that
[tex]\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n[/tex]
[tex]\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]
It follows that
[tex]a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n + n(n-1)[/tex]
so the left side is
[tex]2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n[/tex]
Also recall that
[tex]\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}[/tex]
so that the right side is
[tex]b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)[/tex]
Solve for [tex]c[/tex].
[tex]2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}[/tex]
Now, the numerator increases more slowly than the denominator, since
[tex]\dfrac{d}{dn}(2n(n-1)) = 4n - 2[/tex]
[tex]\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2[/tex]
and for [tex]n\ge5[/tex],
[tex]2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2[/tex]
This means we only need to check if the claim is true for any [tex]n\in\{1,2,3,4\}[/tex].
[tex]n=1[/tex] doesn't work, since that makes [tex]c=0[/tex].
If [tex]n=2[/tex], then
[tex]c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0[/tex]
If [tex]n=3[/tex], then
[tex]c = \dfrac{12}{2^3 - 6 - 1} = 12[/tex]
If [tex]n=4[/tex], then
[tex]c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N[/tex]
There is only one value for which the claim is true, [tex]c=12[/tex].
Find the cofactors of each entry in the first row of the matrix . ac11 = ac12 = ac13 =
The cofactors of each entry in the first row of the matrix exist
[tex]$$Ac_{11 }= -13[/tex]
[tex]Ac_{12} = 44[/tex]
[tex]Ac_{13} = 27[/tex]
We have to estimate the cofactors of each entry in the first row of the matrix.
What is the matrix?A set of numbers exists arranged in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix.
Thus the cofactors of each entry in the first row of the matrix exist
[tex]$$Ac_{11 }= -13[/tex]
[tex]Ac_{12} = 44[/tex]
[tex]Ac_{13} = 27[/tex]
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can someone solve this step by step pls
The solutions to the quadratic equation -t² + 7t = 0 are 7 and 0.
Hence, x = 7, 0.
What are the solutions to the quadratic equation?Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given the equation;
-t² + 7t = 0
Comparing with the standard form.
a = -1b = 7c = 0We substitute into the quadratic formula.
x = (-b±√(b² - 4ac)) / (2a)
x = (-7±√( (7)² - ( 4 × -1 × 0) ) / (2 × -1)
x = (-7±√( 49 - 0) ) / (-2)
x = (-7±√49 ) / (-2)
x = (-7±7 ) / (-2)
x = (-7-7 ) / (-2), (-7+7 ) / (-2)
x = -14/(-2), 0/(-2)
x = 7, 0
The solutions to the quadratic equation -t² + 7t = 0 are 7 and 0.
Hence, x = 7, 0.
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does someone mind helping me with this question? Thank you!
Answer:
[tex]\frac{263}{999}[/tex]
Step-by-step explanation:
The midpoint of K is M(-3, -1). One endpoint is J(-12, -11). What are the coordinates of endpoint K?
K=
Answer:
K(6, 9)
Step-by-step explanation:
Let the K coordinates be (x, y)
Mid-point formula:
[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]
Applying formula:
[tex]\sf (-3,\:-1) = (\:\dfrac{-12+x}{2} ,\: \dfrac{-11+y}{2} )[/tex]
Comparing expression:
[tex]\sf \dfrac{-12+x}{2} = -3 \quad and \quad \dfrac{-11+y}{2} = -1[/tex]
[tex]\sf -12+x = 2(-3) \quad and \quad -11+y = 2(-1)[/tex]
[tex]\sf x = -6 + 12 \quad and \quad y = -2 + 11[/tex]
[tex]\sf x = 6 \quad and \quad y = 9[/tex]
So, coordinates of K is (6, 9)
Find the missing side. Round your answer to the nearest tenth.
What are the steps to finding missing sides
Answer:
23.6
Step-by-step explanation:
→ Identify length not given
Opposite
→ Find a formula without opposite
Cos = Adjacent ÷ Hypotenuse
→ Rearrange
Adjacent = Cos × Hypotenuse
→ Substitute
cos 38 × 30 = 23.6
Answer:
[tex]x = 23.6[/tex]
Step-by-step explanation:
To find the missing side of a right-angled triangle, first look at the given angle, and notice its relationships with the given and required sides.
In this case:
• The side adjacent to the given 38° angle is [tex]x[/tex] (required).
• The hypotenuse is 30 units.
The trigonometric ratio that relates the adjacent side and hypotenuse of a triangle is cosine (cos), where:
[tex]\boxed{cos \space\ \theta = \frac{adjacent}{hypotenuse}}[/tex].
Substituting into the formula:
[tex]cos (38^{\circ}) = \frac{x}{30}[/tex]
⇒ [tex]x = cos(38^{\circ}) \times 30[/tex]
⇒ [tex]x = 23.6[/tex]
Plot a graph for the following data recorded for an object falling from rest
A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.
In this exercise, you're required to plot a graph for the data (velocity and time) recorded for an object that is falling from rest.
Based on the graph for the data (see attachment), we can logically deduce the following points:
The kind of curve obtained is linear.The relationship between the variables is direct variation.After 4.5 seconds, I expect the velocity to be equal to 140 ft/s.The amount of time required for the object to attain a speed of 100 ft/s is 3.2 seconds.Read more on graphs here: brainly.com/question/25875680
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Complete Question:
Plot a graph for the following data recorded for an object falling from rest
a. What kind of a curve did you obtain?
b. What is the relationship between the variables?
c. What do you expect the velocity to be after 4.5 s?
d. How much time is required for the object to attain a speed of 100 ft/s?
Rajani is making smoothies. Each smoothie uses 3/5 cup of yogurt. How much yogurt
does she need to make 13 smoothies?
Answer:
Rajani needs 7.8 (39/5) cups of yogurt to make 13 smoothies.
Step-by-step explanation:
3/5 = 0.6
The amount of cups of yogurt needed to make 13 smoothies = 13 x 0.6
This equals to 7.8 cups or 39/5 cups of yogurt to make 13 smoothies.
Hope this helps!
1. Find the midpoint of the line segment with endpoints (-7, 3) and (3,-7).
Step-by-step explanation:
the coordinates of a midpoint are
x = (x1 + x2)/2
y = (y1 + y2)/2
with (x1, y1) and (x2, y2) being the endpoints.
so, our midpoint here is
((-7 + 3)/2, (3 + -7)/2) = (-4/2, -4/2) = (-2, -2)
Mrs. Wood is a librarian at Westside Library. In examining a random sample of the library's book collection, she found the following. 716 books had no damage, 68 books had minor damage, and 43 books had major damage. Based on this sample, how many of the 36,500 books in the collection should Mrs. Wood expect to have major damage? Round your answer to the nearest whole number. Do not round any intermediate calculations.
Using proportions, it is found that Mrs. Wood should expect 1,898 books out of the 36,500 to have major damage.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
For this problem, the proportion of books with major damage is:
43/(716 + 68 + 43) = 0.051995.
Hence, out of 36,500 books, the expected amount of books with major damage is:
0.051995 x 36,500 = 1898.
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1. Solve for x.
12
10
X
5
The sum of two consecutive even integers is 26. What is the product of the two integers?
A) 168
B) 160
C) 132
D)120
A hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp?
The area of the trapezoidal tarp in the hotel is 47.3 square inches.
What is a trapezoid?A trapezoid is a quadrilateral having one pair of parallel opposite sides. It can have right angles (a right trapezoid) and congruent sides (isosceles), but neither is needed.How do determine the area of the trapezoid?
The area of a trapezoid is calculated using:Area = 0.5 × (Sum of parallel sides) × HeightFrom the complete question, the parallel sides are 10ft and 12ft.
So, Area = 0.5 × (10 + 12) × hEvaluate,
Area = 11 × hThe height (h) is computed using the cosine function shown below:
cos(120 - 90) = h/5This gives
cos(30) = h/5Make h the subject:
h = 5cos(30)Evaluate:
h = 4.3So, we get:
Area = 11 × 4.3Evaluate:
Area = 47.3Therefore, the area of the trapezoidal tarp in the hotel is 47.3 square inches.
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The complete question is given below:
A hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp?
to find the height. first find that d is 60,45, or 120. this means the height of the trapezoid is approximately 2.5,4.3, or 3.5 feet. so the area of the tarp is approximately 47.3,30.0 or 38.5 square feet.
Could I get some help with this?
Answer:
Step-by-step explanation:
base=b=7.2yd
height =h=7yd
area of parallelogram = b x h
. =7.2yd x 7yd
=50.49[tex]yd^{2}[/tex]
Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range:
The five number summary can be calculated as follows:
lower quartile(Q₁) = 54 + 56 / 2 = 55
Median = 63.5
Upper quartile(Q₃) = 74
Maximum = 80
Interquartile range = Q₃ - Q₁ = 74 - 55 = 19
How to find the five number summary ?The five number summary can be found as follows;
48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80
minimum = 48
lower quartile(Q₁) = 54 + 56 / 2 = 55
The median is the middle number when the data is arranged in ascending or descending order.
Median = 63 + 64 / 2 = 127 / 2 = 63.5
Upper quartile(Q₃)= 74 + 74 / 2 = 148 / 2 = 74
Maximum = 80
Interquartile range = Q₃ - Q₁ = 74 - 55 = 19
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In which two ways can a scrum master exemplify characteristics of a servant leader?
There are 10 common characteristics attributed to servant leadership: active listening, empathy, healing, awareness, persuasion, conceptualization, foresight, stewardship, commitment to the growth of people, and community-building.
How does a Scrum Master demonstrate servant leadership?A Scrum Master is a servant-leader whose focus is on the needs of the team members and those they serve (the customer), with the goal of achieving results in line with the organization's values, principles, and business objectives.
1. Active listening: Active listening is the practice of preparing to listen, observing what verbal and non-verbal messages are being sent.
2. Empathy: the ability to understand and share the feelings of another.
3. Healing: the process of making or becoming sound or healthy again.
4. Awareness: knowledge or perception of a situation or fact.
5. Persuasion: A belief or set of beliefs, especially religious or political ones.
6. Conceptualization: The action or process of forming a concept or idea of something.
7. Foresight: The ability to predict or the action of predicting what will happen or be needed in the future.
8. stewardship: The job of supervising or taking care of something, such as an organization or property.
9. Commitment: The state or quality of being dedicated to a cause, activity, etc.
10. Community-building: Community building is a field of practices directed toward the creation or enhancement of community among individuals within a regional area or with a common need or interest.
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A laptop is on sale for 45% off the regular price. If the sale price is $299.75, what was the original price?
The original price of the laptop is calculated as $545
How to find the original Price?We are given;
Sales Price of Laptop = $299.75
Now, the laptop is on sale for 45% off regular price.
If original price is x, then we can express that;
(100% - 45%) * x = 299.75
Thus;
55%x = 299.75
0.55x = 299.75
x = 299.75/0.55
x = $545
Thus, the original price of the laptop is calculated as $545
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Which of the following is the domain and range of the ellipse with equation 4x2 + 25y2 – 8x + 100y + 4 = 0?
The domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]
How to determine the domain and the range of the ellipse?The equation of the ellipse is given as:
4x^2 + 25y^2 – 8x + 100y + 4 = 0
Next, we plot the graph of the ellipse
See attachment for the graph of the ellipse
The domain
From the attached graph the minimum and the maximum values of x are:
Minimum = -4
Maximum = 6
So, the domain of the ellipse is [-4. 6]
The range
From the attached graph the minimum and the maximum values of y are:
Minimum = -4
Maximum = 0
So, the range of the ellipse is [-4. 0]
Hence the domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]
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Which numbers below are part of the domain for this graph? Select all that apply.
The numbers which are a part of the domain for the graph are: 6, 1 and 2.
Which numbers are part of the domain?The domain of a graph is a set of all possible input, x-values. Consequently, since the domain of the graph given ranges over intergers, 1 to 10, it follows that numbers which are part of the domain are; 6, 2, and 1.
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Write an inequality
greater than (-3) but less than or equal to 3
meaning x
An inequality greater than (-3) but less than or equal to 3 is as follows:
- 3 < x ≤ 3
What is an inequality?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.
An inequality have the following signs:
<>≤≥Therefore, an inequality greater than (-3) but less than or equal to 3 can be represented as follows:
Note the value we are comparing is x.
Hence,
- 3 < x ≤ 3
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1. Find the length of a.
if g(x)=4x^2-16 were shifted 9 units to the right and 1 down, what would the new equation be?
The answer is g'(x) = 4x² - 72x + 307.
If shifted 9 units right, substitute (x - 9) in place of x.
g'(x) = 4(x - 9)² - 16If shifted 1 unit down afterwards, subtract 1.
g'(x) = 4(x - 9)² - 16 - 1g'(x) = 4(x - 9)² - 17g'(x) = 4x² - 72x + 324 - 17g'(x) = 4x² - 72x + 307Answer:
h(x)=4(x-9)^2-17
Step-by-step explanation:
Find sin(2x), cos(2x), and tan(2x) from the given information. sin(x) = 5 13 , x in quadrant i
The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.
According to the statement
We have given that the sin(x) = 5/13 , x in quadrant iii
And we have to Find the value of cos x using the following:
So, For this purpose, we know that the trigonometry terms are:
sin2(x) + cos2(x) = 1;
or cos2(x) = 1-sin2(x)
And
cos2(x) = 1-(-5/13)2 =
cos2(x) = 144/169;
We know that the
In quadrant III both the sin and cos are negative so
cos(x) = -12/13 (after taking square roots).
And
Then tan(x) = sin(x)/cos(x) = (-5/13)/(-12/13) = 5/12.
Now you can use the angle addition formulas to find sin(2x), cos(2x), and tan(2x).
Now
sin(x + x) = sinx * cosx + cosx * sinx
= (-5/13)*(-12/13) + (-12/13)(-5/13) = 120/169
And
cos(x + x) = cosX * cos(x) - sinx*sinx
= (-12/13)(-12/13) - (-5/13)(-5/13)
= 119/169
So,
You could use the tan double angle formula, but it is easiest to use
tan(2x) = sin(2x)/cos(2x) = (120/169) / (119/169)
= 120/119.
So, The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.
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