The amount of money that Nora would need to invest is $25913.
How to determine the value of P?In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where:
A represents the future value.n represents the number of times compounded.P represents the principal.r represents the interest rate.T represents the time measured in years.By substituting the given parameters into the formula for compound interest, we have the following;
[tex]72,000 = P(1 + \frac{0.064}{365})^{365 \times 16}\\\\72,000 = P(1 + 1.75 \times 10^{-4})^{5,840}\\\\72,000 = P(1.000175)^{5,840}[/tex]
P = 72,000/2.77849825425152
Principal, P = $25913.28 ≈ $25913
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125-foot redwood tree is leaning 20° off vertical. How long will its shadow be when the angle the sunlight makes with the ground is 68°?
Answer:
To solve this problem, we can use trigonometry. Let's call the length of the shadow "s" and the height of the tree "h". Since the tree is leaning, we can't just use the height of the tree directly as one leg of a right triangle. Instead, let's draw a diagram of the situation and see if we can find a way to use trigonometry.
|\
| \
| \ h
|20\
| \
| \
________|____\
s
In this diagram, the angle between the ground and the sunlight is 68 degrees, and the angle between the tree and the ground is 70 degrees (since the tree is leaning 20 degrees off vertical). We can use the tangent function to relate these angles to the lengths of the sides of the triangle:
tan(68) = h / s
tan(70) = h / (s + 125)
We can solve for "h" in terms of "s" using the second equation:
h = (s + 125) * tan(70)
Then we can substitute this expression for "h" into the first equation and solve for "s":
tan(68) = [(s + 125) * tan(70)] / s
s * tan(68) = (s + 125) * tan(70)
s * tan(68) = s * tan(70) + 125 * tan(70)
s = 125 * tan(70) / [tan(68) - tan(70)]
s ≈ 318.8 ft
Therefore , the shadow will be approximately 318.8 feet long.
Step-by-step explanation:
7. Based on an exponential model of the data, what is the predicted value of Variable 2 when
Variable 1 = 2?
Round your answer to the nearest whole number.
Variable 1:
10
20
30
40
50
60
70
80
90
100
variable 2:
100
80
52
40
35
25
17
11
10
7
Answer:
128
Step-by-step explanation:
You want a prediction for x=2 when the given data is modeled by an exponential model.
x = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100y = 100, 80, 52, 40, 35, 25, 17, 11, 10, 7ModelA graphing calculator's exponential regression function models this data with the formula ...
y = 135.7 · 0.9711^x
y = 137.7 · 0.9711^2 ≈ 127.94 . . . . when x=2
This model gives a value for variable 2 of approximately 128 when variable 1 = 2.
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1. Have you immersed yourself in an unfamiliar environment and if so, what feelings did
you experience-vulnerability, loneliness, uncertainty?
2. How will globalization change your organization's mix of customers and products? How
will you need to grow and adapt to lead in the future state of the organization?
3. How high is your GQ? What concrete actions can you take to raise it?
1. When people find themselves in an unfamiliar environment, it is common to feel vulnerable, lonely, and uncertain.
2. Globalization can change the mix of customers and products for an organization by creating new markets and opportunities for growth.
3. You can improve your GQ by practicing mindfulness and meditation
What are the feelings that you have?Businesses may need to concentrate on creating new goods and services that appeal to a global market as well as modifying their business models to satisfy the needs of clients in various regions of the world if they want to be leaders in the organization's future state.
In order for them to be more adaptable and receptive to changes in the global marketplace, they might also need to invest in technology and tactics.
Globalization can significantly impact an organization's mix of customers and products. The organization must adapt to this by investing in research and development to create new products.
By applying mindfulness, the GQ can be adequately raised for the organization.
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Question 10(Multiple Choice Worth 10 points) (04.05 MC) Davenport University claims to accept 63% of applicants. In a random sample of 1,000 Davenport University applicants, 602 were accepted. Calculate the 95% confidence interval and evaluate whether Davenport's claim seems accurate.
The confidence interval using the 95 percent level of significance is given as CI = (0.57, 0.63)
How to solve for the confidence levelSolve for the sample proportion
= 602/1000 = 0.602
z* is the critical value from the standard normal distribution at the 95% confidence level = (1.96)
n = sample size (1000)
CI = 0.602 ± 1.96√((0.602(1-0.602))/1000)
CI = 0.602 ± 0.032
0.602 - 0.032 , 0.602 + 0.032
CI = (0.57, 0.63)
Hence the confidence interval using the 95 percent level of significance is given as CI = (0.57, 0.63)
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In △ABC, we are told that a=17, ∡B=70∘, and ∡C=48∘. Solve for b and c.
Answer: b=18.1 and c=14.3
Step-by-step explanation:o solve for the lengths of the sides b and c in triangle ABC, we can use the law of sines, which relates the lengths of the sides of a triangle to the sines of the angles opposite those sides. Specifically, the law of sines states that:
a/sin(A) = b/sin(B) = c/sin(C)
where A, B, and C are the angles of the triangle opposite sides a, b, and c, respectively.
Given that a = 17, B = 70°, and C = 48°, we can write:
b/sin(70°) = 17/sin(A)
c/sin(48°) = 17/sin(A)
To solve for b and c, we need to find sin(A). We can do this by using the fact that the angles of a triangle sum to 180°:
A + B + C = 180°
A = 180° - B - C
A = 180° - 70° - 48°
A = 62°
Now we can substitute sin(A) = sin(62°) into the equations above and solve for b and c:
Approximate e^-0.11 to 4 decimal places
Answer: 0.8958
Step-by-step explanation:
A radioactive element has decayed to 1/32 of its original concentration in 10 yrs. What is the half-life of this element?
The half-life of this radioactive element is approximately 2 years.
We have,
The decay of a radioactive element follows an exponential decay model of the form:
[tex]N = N_0 e^{-kt}[/tex]
where:
N0 is the initial concentration of the radioactive element
N is the concentration after time t
k is the decay constant
We are given that the element has decayed to 1/32 of its original concentration, which means that its current concentration is 1/32 times its initial concentration:
N/N0 = 1/32
Taking the natural logarithm of both sides and rearranging, we get:
ln(N/N0) = ln(1/32) = -3.465
Now we can use the formula for half-life, which relates the decay constant to the half-life t1/2:
t1/2 = ln(2) / k
We can solve for the decay constant k by using the information that the element has decayed to 1/32 of its original concentration in 10 years:
ln(N/N0) = -kt
-3.465 = -k x 10
k = 0.3465
Substituting this value of k into the formula for half-life, we get:
t1/2 = ln(2) / k = ln(2) / 0.3465 = 2.0 x 10^0 years = 2 years.
Therefore,
The half-life of this radioactive element is approximately 2 years.
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In a paddock of goats and chickens, there are 67 heads and 166 legs. How many goats are there?
Find the volume of rectangular prism. (You should have at least 2 steps shows in your work!)(show all decimal places or a fraction)
Answer:
[tex]3 \frac{3}{4} \times 4 \frac{1}{2} \times 5 = \frac{15}{4} \times \frac{9}{2} \times 5 = \frac{675}{8} = 84\frac{3}{8} [/tex]
The volume is 84 3/8 cubic meters = 84.375 cubic meters.
Find the missing side of the triangle 12, 34° and 90°
Answer:
To find the missing side of a right triangle given an angle and a side, you can use trigonometric functions. In this case, we have the angle opposite the missing side, so we can use the sine function.
The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, we can set up the following equation:
sin(34°) = opposite / 12
To solve for the opposite side, we can multiply both sides by 12:
opposite = 12 * sin(34°) ≈ 6.60
Therefore, the missing side of the triangle is approximately 6.60 units long.
Step-by-step explanation:
I need help finding 1=cos(8π)+isin(8π) but it has to be divided by 6. I will give 20 points to whoever answers it.
Answer: 1/6 = cos(8π)/6 + i*sin(8π)/6
Step-by-step explanation: In the context of complex numbers, the division of 1 by 6 can be accomplished by employing a straightforward procedure that involves dividing both the real and imaginary components by 6.
The mathematical expression 1/6 may be represented in academic prose via the complex number format (cos(8π)/6 + i*sin(8π)/6).
NEED ANSWER ASAP PLEASE
Answer:
second one
the y intercept is 8, the slope is -6/8, reduced -3/4
Step-by-step explanation:
equation if a line in slope intercept form is y=mx+
Please help with my geometry.
Find the area of the shaded region.
Answer:
192pie
Step-by-step explanation:
To find the area of a circle, it is pie (3.14) times r². The radius is 24, so it is 24² times pie. The area is 576 pie. Now to find the area of the shaded, you would do 1/3 times the area. 1/3 of 576 is 192. The answer is 192pie
During certain time periods at a hospital, patients arriving at the emergency room have waiting times that are uniformly distributed between 0 and 7 minutes. Assume that a patient is randomly selected, and find the probability that the waiting time is less than 0.75 minutes. (Round to three decimal places)
Since the waiting times are uniformly distributed between 0 and 7 minutes, the probability density function (PDF) of the waiting time is:
f(x) = 1/7 for 0 ≤ x ≤ 7
0 otherwise
To find the probability that the waiting time is less than 0.75 minutes, we need to integrate the PDF from 0 to 0.75:
P(X < 0.75) = ∫[0,0.75] f(x) dx
P(X < 0.75) = ∫[0,0.75] 1/7 dx
P(X < 0.75) = [1/7 * x] [0,0.75]
P(X < 0.75) = 1/7 * 0.75
P(X < 0.75) = 0.1071
Therefore, the probability that the waiting time is less than 0.75 minutes is 0.1071 (rounded to three decimal places).
Muriel translated the phrase below into an algebraic expression and then evaluated it for n = 4.
the product of a number and 8
Which of the following contains the correct expression and value?
Answer:
[tex]8n=32[/tex]
Step-by-step explanation:
Muriel's algebraic expression for the phrase "the product of a number and 8" would be 8n, where n represents the number. When n = 4, the value of 8n would be 8 times 4, which is 32. Therefore, the correct expression and value is 8n = 32 when n = 4.
Answer:
8n=32
Step-by-step explanation:
got it right on homework
A bottle of water has a diameter of 3 inches and a height of 8 inches, and a mass of 1250 g. What is the volume and density?
The volume of the bottle is 56.52 cubic inches, and the density is 22.12 g/in³.
What is the volume and density of the bootle water?The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 ).
Density is expressed mathematically as;
p = m / v
Where m is mass and v is volume.
Given that:
Diameter = 3 in
Radius r = diameter/2 = 3/2 = 1.5 in
Height h = 8 in
Mass m = 1250 g
Find the volume:
V = π × r² × h
V = 3.14 × (1.5 in )² × 8in
V = 56.52 in³
Find the density:
p = m / v
p = 1250g / 56.52 in³
p = 22.12 g/in³
Therefore, the density is 22.12 g/in³.
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Melissa drew a right triangle.
The perimeter of the triangle is 9+√41.
The hypotenuse is of length ✓41.
Using this information, what is the length of the other
two sides of the triangle?
Answer:
Let's denote the two legs of the right triangle as a and b, and the hypotenuse as c. We know that c = √41, so we can use the Pythagorean theorem to relate a and b to c:
c^2 = a^2 + b^2
Substituting c = √41, we get:
(√41)^2 = a^2 + b^2
41 = a^2 + b^2
We also know that the perimeter of the triangle is:
perimeter = a + b + c = 9 + √41
Substituting c = √41, we get:
a + b + √41 = 9 + √41
a + b = 9
Now we have two equations with two unknowns (a and b):
a^2 + b^2 = 41
a + b = 9
We can solve this system of equations by substitution. Solving the second equation for a, we get:
a = 9 - b
Substituting this into the first equation, we get:
(9 - b)^2 + b^2 = 41
81 - 18b + 2b^2 = 41
2b^2 - 18b + 40 = 0
b^2 - 9b + 20 = 0
(b - 4)(b - 5) = 0
So we have two possible solutions: b = 4 and b = 5. We can find the corresponding value of a using a = 9 - b:
a = 5 and b = 4 or a = 4 and b = 5
Therefore, the two legs of the right triangle are 4 and 5.
PLEASE HELP (WILL GIVE BRAINLIEST
Answer:
V = 62.8 m[tex]^{3}[/tex]
Step-by-step explanation:
V = pi × (radius)[tex]^{2}[/tex] × height
V = [tex]\pi[/tex] × [tex]r^{2}[/tex] × h
V = (3.14 × [[tex]2^{2}[/tex]]) × 5
V = (3.14 × 4) × 5
V = 12.56 × 5
V = 62.8 m[tex]^{3}[/tex]
The first text message was sent on December 3, 1992. Two decades later, texting has become one of the most popular methods of communication. The number, in millions, of SMS messages sent per year in the United Kingdom is given in the table below. In 2012, the first decrease occurred in the number of SMS messages in the UK and was attributed to the unveiling of Apple’s iMessage on June 6, 2011. Find an exponential model for the number of SMS messages sent annually for years before 2012.
Year 2003 2005 2007 2009 2010 2011
SMS 24086 39751 66331 104358 128462 150651
in
millions
An exponential model for the number of SMS messages sent annually for years before 2012 is [tex]y = 12421e^{0.2325x}[/tex].
How to determine the equation of line of best fit?In this scenario, the year would be plotted on the x-axis (x-coordinate) of the scatter plot while the SMS messages would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the year and SMS messages, an exponential equation for the line of best fit is given by
[tex]y = 12421e^{0.2325x}[/tex]
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I REALLY NEED HELP LIKE ASAP PLS PLS I HAVE A LOT OF HOMEWORK TO DO PLS ANSWER
5(3n+4n+3) = -125
solve for the value of n pls.
Answer:
n=-4
Step-by-step explanation:
5(3n+4n+3) = -125
First, combine like terms:
5(7n+3) = -125
Then, distribute the 5:
35n+15 = -125
Then, get n by itself:
35n= -140
Then, divide by 35 to get n by itself:
n = -140/35
Simplify
n = -4
solve the inequality and graph the solution on the line provided.
5x - 15 < 10
Answer: x < 5, see attached for the graph.
Step-by-step explanation:
To solve, we will isolate the variable.
Given:
5x - 15 < 10
Add 15 to both sides of the equation:
5x < 25
Divide both sides of the equation by 5:
x < 5
For the graph, we will use an open circle because this is only less than (<), not less than and equal to.
Then, since x is all values less than 5, we will shade our arrow to the left of 5. See attached.
Find the value of $x$ . Write your answer in simplest form. 9 squared 2
The value of the expression 9 squared will be 81.
How to explain the expressionIn Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The value will be:
= 9²
= 9 × 9.
= 81
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In circle N with � ∠ � � � = 12 4 ∘ m∠MNP=124 ∘ and � � = 13 MN=13, find the area of sector MNP. Round to the nearest hundredth.
If circle with center N with m∠MNP=124 ∘ and MN=13, the area of sector MNP is approximately equal to 194.86 square units.
To find the area of a sector of a circle, we need to use the formula:
Area of sector = (central angle/360°) x πr²
Where r is the radius of the circle.
In this problem, we know that the central angle m∠MNP is 124° and MN, which is also the radius of the circle, is 13. So we can substitute these values into the formula:
Area of sector = (124/360) x π(13)²
Area of sector ≈ 194.86
Therefore, the area of sector MNP is approximately equal to 194.86 square units.
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I needed help with this one can some help me
A graph of quadrilateral M'N'O'P' after a vertical translation is shown below.
What is a translation?In Mathematics and Geometry, the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
By translating the pre-image of quadrilateral MNOP vertically downward 4 units, the coordinates of quadrilateral M'N'O'P' include the following:
(x, y) → (x, y - 4)
M (-2, 5) → (-2, 5 - 4) = M' (-2, 1).
N (-3, 2) → (-3, 2 - 4) = N' (-3, -2).
O (-5, 2) → (-5, 2 - 4) = O' (-5, -2).
P (-6, 5) → (-6, 5 - 4) = P' (-6, 1).
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answer:
[tex]\sqrt{2}[/tex]
Step-by-step explanation:
When t = 0, the velocity is:
[tex]\begin{aligned}\vec{v}(t)&=3^t \vec{i}+e^{6t} \vec{j}\\\\t=0 \implies \vec{v}(0)&=3^0 \vec{i}+e^{(6 \cdot 0)} \vec{j}\\ &=1 \vec{i}+1 \vec{j} \end{aligned}[/tex]
Speed is the magnitude of the velocity of the object.
[tex]\boxed{\text{A vector $\binom{x}{y}$ has magnitude $\sqrt{x^2+y^2}$}}[/tex]
Therefore, the particle's speed at time t = 0 is:
[tex]\begin{aligned}\implies |v|&=\sqrt{1^2+1^2}\\&=\sqrt{1+1}\\&=\sqrt{2}\end{aligned}[/tex]
please help me with this. I know the answer for the first one, but I'm just confused about the second one.
Answer: 20
Step-by-step explanation:
because Juanita has a aquarium that is 5 feet LONG, 4 feet WIDE, and 2 feet DEEP, in part b it asks what if the water is 1 foot DEEP so what they're trying to say is what if you replace the original 2 feet DEEP with 1 foot DEEP?
so it would be length x width x depth
5x4x1=20
so the volume is 20ft^3
Find the missing exponent 82/256=3/4
The missing exponent of the expression is determined as 4.
What is the value of the missing exponent?The value of the missing exponent is calculated as follows;
The given function is;
81/256 = (3/4)ˣ
To determine the value of the missing exponent, we will apply the power law of indicial equation as follows;
From base of the exponential function, we will determine the value of x;
3⁴/4⁴ = (3/4)x
(3/4)⁴ = (3/4)ˣ
4 = x
Thus, the missing value of the exponential function is determined by applying rules of exponent.
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The complete question is below:
Find the missing exponent 81/256 = (3/4)ˣ
I need help with this pre calculus question , i understand how to find the period i just don’t understand this graph
The period of the function in the graph is 2π
What is period of a function?Period represents the distance across horizontally located between successive duplicates of an equivalent outline within a graphed function.
In other words, we can say that period is the distance to complete an oscillation where this distance is counted in time. Hence period is measured is seconds
In the graph, the period can be calculated using the points
2π and 0 OR -π and πThese points shows a complete oscillation.
Using from 2π to 0
= 2π - 0
= 2π
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Thank you for the help!
Answer:
c 57
Step-by-step explanation:
Brainliest and points if answered correct!!!!
The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 24 and 6 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is 6, which means that the swimmer will finish the race after 6 minutes.
The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
The slope of the line is negative one fourth, which means that the swimmer completes a lap in one fourth of a minute.
since i don't see the graph ill go with... B The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
-24/6 = -4
Step-by-step explanation:
The slope of the line can be found using the formula:
slope = (change in y) / (change in x)
In this case, we can use the two given points on the line: (0, 24) and (6, 0).
Change in y = 0 - 24 = -24
Change in x = 6 - 0 = 6
Therefore, slope = -24/6 = -4
This means that for every minute that passes, the swimmer completes four laps. The swimmer's pace is steady and consistent throughout the race, gradually decreasing the number of laps remaining until they finish at 0 after six minutes.
Answer:
The slope of the line represents the rate of change in the number of laps remaining per unit of time (in this case, per minute). In other words, it tells us how quickly the swimmer is completing laps.
Since the slope of the line is -4, this means that the swimmer is completing 4 laps every minute. This could be interpreted as the swimmer's pace or speed in the race. The negative sign indicates that the number of laps remaining is decreasing over time, which is expected as the swimmer completes more and more laps.
It's worth noting that the slope is constant throughout the race, meaning that the swimmer is maintaining a consistent pace. This information could be useful for the swimmer and their coach in terms of planning and pacing the race.