Answer:
B.
Step-by-step explanation:
A bank features a sayings account that has an annual percentage rate of r=2.8% vith interest. compounded semi-atinually. Natalie deposits $7,500 into the aceount. The account batance can be modeted by the exponential formula S(t)=P(1+ T/r ) ^nt , where S is the future value, P is the present value, F is the annual percentage rate, n is the number of times each year that the interest is compounded, and t is the time in years. (A) What values should be used for P,r, and π ? (B) How much money will Natalie have in the account in 9 years? Answer =5 Round answer to the nearest penny
Natalie will have $9,667.81 in her savings account after 9 years.
Given that the bank features a savings account with an annual percentage rate of r = 2.8% with interest compounded semi-annually, and Natalie deposits $7,500 into the account.The account balance can be modeled by the exponential formula:
\(S(t) = P(1 + T/r)^nt,\)
where,
S is the future value,
P is the present value,
r is the annual percentage rate,
n is the number of times each year that the interest is compounded, and
t is the time in years.
(A) Values for P, r, and n are:
P = 7500 (present value)r = 2.8% (annual percentage rate) Compounded semi-annually, so n = 2 times per year
(B) To find out how much money will Natalie have in the account in 9 years, substitute the given values in the exponential formula as follows:
\(S(t) = P(1 + T/r)^nt\)
Where,
t = 9 years,
P = $7,500,
r = 2.8% (2 times per year)
Therefore, S(9) = $7,500(1 + (0.028/2))^(2*9) = $9,667.81 (rounded to the nearest penny). Thus, Natalie will have $9,667.81 in her savings account after 9 years.
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find the area to the right of 23.337 under the chi-square distribution with 12 degrees of freedom. group of answer choices a. 0.025 b. 0.0125 c. 0.0375 d. 0.975
The area to the right of 23.337 under the chi-square distribution with 12 degrees of freedom is 0.0125.
In statistics, the chi-square distribution is a continuous probability distribution that is widely used in inferential statistics. The area to the right of a certain value can be calculated using a chi-square table or a computer program. In this case, we want to find the area to the right of 23.337 under the chi-square distribution with 12 degrees of freedom. Using a chi-square calculator or a chi-square table, we can determine that this area is 0.0125. This means that there is a 1.25% chance of getting a chi-square value greater than 23.337 with 12 degrees of freedom. This type of calculation is often used in hypothesis testing and other statistical analyses.
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Solve the inequality
4x + 1 > 17
X > ?
Step-by-step explanation:
4x > 17
4x > 17 -1
4x > 16
x > 4
. Find the coordinates of the center and the measure of the radius for a circle whose equation is
(x-8)2 + (y+4)² =12 (3 points)
Answer:
Radius is 2√3 units
Center is (8,-4)
Step-by-step explanation:
Compared to the standard form equation of a circle, \((x-h)^2+(y-k)^2=r^2\), then the radius would be \(r=\sqrt{12}=2\sqrt{3}\) and the center would be \((h,k)\rightarrow(8,-4)\).
4.02 Lesson check ! (1)
1. The sequence is an arithmetic sequence with a common difference of d = -200.
2. The sequence is not an arithmetic sequence.
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
For item 1, each term is the previous term subtracted by 200, hence the sequence is in fact an arithmetic sequence with a common difference of -200.
For item 2, the difference between consecutive terms is difference, hence the sequence is not an arithmetic sequence.
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2) The value of y is directly proportional to the value of x. Given y = 12 when x = 36.
What is the value of y when x = 60? Show your work to receive full credit.
Answer:
I believe the answer is 20
Step-by-step explanation:
Practice with Laws of Logic
Provide the valid conclusion to the argument below.
If I am sick, then I will not come to school.
If I do not come to school, then I am sad.
Answer:
if I am sick, then I will not come to school.
Step-by-step explanation:
I need help putting correct answers in the yellow boxes.
Answer:
-5 ± √5² - 4 · 1 · 4
2 · 1
Step-by-step explanation:
ax²+bx+c=0 (quadratic equation)
x= -b ± √b² - 4ac
2a
a= 1
b= 5
c= 4
-5 ± √5² - 4 · 1 · 4
2 · 1
What is the sum of
1
2
+
1
4
? Use the fraction strip to HELP?
A.
2
8
B.
2
6
C.
4
8
D.
6
8
Answer:
B. 26 should be pretty simple math
The measures of two interior angles of a triangle are 108° and 54°. What is the measure of the third angle?
A. 18°
B. 38°
C. 54°
D. 108°
Answer:
Answer is 18 degree as per the question
Answer: A. 18°
Step-by-step explanation:
Your formula is 108°+54°+X=180°
To find X, add 108° & 54°. The sum is 162°.
Next you need to subtract your sum from 180°.
180°-162°=18°
X=18°
A circular dining room table top has a radius of 22 inches. What is the
diameter of the table top?
What is the circumference of the table top? Write your answer using m.
Show your work.
How much simple interest would Alexis earn if he deposits $2450 in a savings account with a simple interest rate of 12% for 15 years.
Answer:
4410
Step-by-step explanation:
The solution of m2 − 14m + 49 = 0 is
Answer:
49/12 or 4 1/12 or 4.083 (all the same answer in different forms)
Step-by-step explanation:
2m-14m+49=0
-12m+49=0
-12m+-49
m=49/12
Answer: m=7
Step-by-step-explanation:
m^2-14m+49=0
(m-7)^2=0
m-7=0
m=7
Pls helppp due today!!!!!!
Answer:
i think it might be 25350¹⁷
or 2⁵x3⁴x5⁴x13⁵
angle a and angle b are complementary angles. if m angle a =5x-2 and m angle b = 3x +4 what is the value of x
What is the equation, in point-slope form, of the line that is
perpendicular to the given line and passes through the
point (-4, 3)?
y-3 = -2(x + 4)
Y-3 = -
2(x+4)
y-3 = {(x + 4)
Y-3 = 2(x + 4)
Answer:
y=1/2x+5
Step-by-step explanation:
the perpendicular line equation's slope is a negative reciprocal, so the new equation's slope is 1/2. so now you have y=1/2x+b plug in (-4,3) to find b. so you will do 3=1/2(-4)+b. 3=-2+b and then you solve for b. you would get b=5. so, the new equation is y=1/2x+5
(-3,0) m = 2
Finde slope intercept form
Answer: y = 2x + 6
Step-by-step explanation:
Slope-Intercept form is represented by y = mx + b, whereas m represents the slope and b represents the y-intercept.
m = 2 is the slope (up 2 units, over 1 unit) and the line goes through 6 on the y-axis, which is where + 6 comes in.
The line also goes through (-3, 0) using the slope.
3. Let f(t)=√2-21 + t. a. Solve for f'(t). b. Solve for f"(t). c. Find f(3), f'(3), and f"(3).
a. The derivative of f(t) is f'(t) = 1.
b. The second derivative of f(t) is f''(t) = 0.
c. f(3) is undefined, f'(3) = 1, and f''(3) = 0.
a. To find the derivative of f(t), we can apply the power rule for differentiation and the derivative of a constant:
f(t) = √2-21 + t
Using the power rule, the derivative of √(2-21) is 0 since it is a constant.
The derivative of t is 1.
Therefore, the derivative of f(t) is:
f'(t) = 0 + 1 = 1
b. To find the second derivative of f(t), we differentiate f'(t) with respect to t:
f'(t) = 1
The derivative of a constant (1 in this case) is 0.
Therefore, the second derivative of f(t) is:
f''(t) = 0
c. To find f(3), f'(3), and f''(3), we substitute t = 3 into the expressions for f(t), f'(t), and f''(t):
f(t) = √2-21 + t
f(3) = √2-21 + 3
f(3) = √(-19) + 3 (since 2-21 = -19)
f(3) is undefined since the square root of a negative number is not defined in the real number system.
f'(t) = 1
f'(3) = 1
f''(t) = 0
f''(3) = 0
Therefore, f(3) is undefined, f'(3) = 1, and f''(3) = 0.
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A baker uses a coffee mug with a diameter of 8\text{ cm}8 cm8, start text, space, c, m, end text to cut out circular cookies from a big sheet of cookie dough.
What is the area AAA of each cookie?
Give your answer in terms of pi.
A=A=A, equals
\text{cm}^2cm
2
start text, c, m, end text, squared
Answer:
Step-by-step explanation:
Since the cookies is circular in nature, we will use the formula for calculating the area of circle to calculate the area if each cookies.
Area of each cookies = πd²/4
Given diameter d = 8cm
Area of the cookies = π(8)²/4
Area of the cookies = 64π/4
Area of the cookies = 16π cm²
Answer:
16 pi ^2
Step-by-step explanation:
um yes
find the slope of the line graphed
Answer:
THERES NO PIC I CANT SEE
Step-by-step explanation:
Question 3 of 10
Classify the following triangle. Check all that apply.
11.9 , 7,6,11.9
A.Scalere
B. Right
C. Isosceles
D. Equilateral
E. Obtuse
F .Acute
Answer:
Step-by-step explanation:
An isosceles triangle is a one that has two of its sides equal. Hence option (c) is correct because here two sides have length of 11.9.
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The vectors
[-4] [ -3 ] [-4]
u =[-3], v = [ -3 ], w = [-1]
[ 5] [-11 + k] [ 7]
are linearly independent if and only if k ≠
The vectors u, v, and w are linearly independent if and only if k ≠ -8.
To understand why, let's consider the determinant of the matrix formed by these vectors:
| -4 -3 -4 |
| -3 -3 -11+k |
| 5 -11+k 7 |
If the determinant is nonzero, then the vectors are linearly independent. Simplifying the determinant, we get:
(-4)[(-3)(7) - (-11+k)(-11+k)] - (-3)[(-3)(7) - 5(-11+k)] + (-4)[(-3)(-11+k) - 5(-3)]
= (-4)(21 - (121 - 22k + k^2)) - (-3)(21 + 55 - 55k + 5k) + (-4)(33 - 15k)
= -4k^2 + 80k - 484
To find the values of k for which the determinant is nonzero, we set it equal to zero and solve the quadratic equation:
-4k^2 + 80k - 484 = 0
Simplifying further, we get:
k^2 - 20k + 121 = 0
Factoring this equation, we have:
(k - 11)^2 = 0
Therefore, k = 11 is the only value for which the determinant becomes zero, indicating linear dependence. For any other value of k, the determinant is nonzero, meaning the vectors u, v, and w are linearly independent. Hence, k ≠ 11.
In conclusion, the vectors u, v, and w are linearly independent if and only if k ≠ 11.
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What are parallel lines
Answer:
Parallel lines are lines in the same plane that do not intersect, like lines on notebook paper.
The "in the same plane" requirement is important! Take a look at the attached image. Lines AD and DC don't intersect, but they are not in the same plane (face of the rectangular solid). We don't call those parallel, we call them skew lines.
The diameter of a circle is 6 cm find the circumference to the nearest tenth
Answer:
28.3
Step-by-step explanation:
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Answer:
18.85 cm
Step-by-step explanation:
what is the slope intercept form for 2y-6=0
Answer: y=3
Step-by-step explanation: 2y=6 y=3
Answer:
Step-by-step explanation:
y = mx + b
0x + 2y - 6 = 0 ⇒ y = 0x + 3 ⇒ y = 3
I need explanation and help me plz !!!!
Answer:
52
Step-by-step explanation:
There are a total of 380+240+110 people. (730)
0.52 are in stage 3.
0.33 in stage 2.
0.15 in stage 1.
52 people from stage 3 should be in the group.
An architect builds a scale model of a building, where 1 cm = 0.5 m. If the scale model is 15 cm tall, how tall will the actual building be, in meters, written as a decimal?
Answer:
The actual building will be 7.5 m tall
Step-by-step explanation:
Given the scale model value of the building, we want to find the actual height of the building
From the scale model;
1 cm = 0.5m
Thus 15 cm will be 15 * 0.5 = 7.5 m
Use the confidence level and sample data to find the minimum sample size. (Round your answers to whole number). An Airlines operation manager wants to estimate the percentage of the passengers who prefer aisle seats. How many air passengers must be surveyed? Assume - in order to be 95% confident that the sample percentage is in error by no more than four percentage points - nothing is known about the passengers who prefer aisle seats. a. 424
b. 306
c. 12
d. 601
The minimum sample size required to estimate the percentage of passengers who prefer aisle seats with a 95% confidence level and an error margin of no more than four percentage points is 601. The correct option is d. 601.
To determine the minimum sample size needed to estimate the percentage of passengers who prefer aisle seats with a 95% confidence level and an error margin of no more than four percentage points, we can use the formula for sample size calculation:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level
p = estimated proportion (0.5 in this case, assuming no prior knowledge)
E = desired margin of error (0.04 or 4% in this case)
Using the given information, let's calculate the minimum sample size:
Z = Z-score for a 95% confidence level is approximately 1.96 (standard normal distribution)
p = 0.5 (since nothing is known about the passengers who prefer aisle seats)
E = 0.04 (4% margin of error)
n = (1.96^2 * 0.5 * (1-0.5)) / 0.04^2
n = (3.8416 * 0.25) / 0.0016
n = 0.9604 / 0.0016
n = 600.25
Since the sample size must be a whole number, we need to round up the result:
n = ceil(600.25) = 601
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in how many ways can 4 different physics books, 3 different mathematics books, and 2 psychology books be arranged on a bookshelf if the physics books must be together and the mathematics books must be together?
Since the physics books must be together and the mathematics books must be together, There are 1728 ways to arrange the books.
What is fundamental counting principle?The basic counting principle is a method for keeping track of all the potential outcomes in a situation. According to this statement, there are n m n times m n ways to carry out both of these actions if there are n ways to perform one action and m ways to perform another action after that. How selection is made based on options is determined by the Fundamental Principle of Counting. The approach of selection, taking into account all of the potential options and their combinations for calculating the probability, is made simpler by the Fundamental Principle of Counting.
Here,
There are 3 book,
3!=6
3 different mathematics books,
3!=6
4 different physics books,
4!=24
2 psychology books
2!=2
by fundamental counting principle,
6*6*24*2=1728
There are 1728 different ways to arrange the books because the mathematics and physics books must be together.
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During British History from 1550-1650. What was going on in Britain during the time just before, during and just after Shakespeare lived? Who were the rulers? What was the political atmosphere? What were the people concerned about? How did the people live?
Answer:
What was going on in Britain during the time just before Shakespeare lived?
Elizabeth had settled the religious question by establishing the Church of England as the official religion of the country, insisting on church services in English, the English Bible and prayer book in churches etc, but not going as far in extreme Protestantism as, for instance, the Puritans would have liked her to do.
Step-by-step explanation:
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The period from 1550-1650 in British history was a time of significant political, social, and cultural change.
What is British History?England, which had absorbed Wales under Henry VIII in the 16th century, merged with Scotland in 1707 to form a new sovereign state known as Great Britain.
Here are some key events and factors that were happening during the time just before, during, and just after Shakespeare lived:
Queen Elizabeth I reigned as Queen of England from 1558 until her death in 1603.Religious strife: The 16th century in England saw religious strife, with tensions between Catholics and Protestants leading to violence and persecution.Political unrest: Throughout the 17th century, England experienced a number of political conflicts and upheavals, including the English Civil War between royalists and parliamentarians.Economic changes: Significant changes occurred in the English economy during the 16th and 17th centuries, including the expansion of international trade and the rise of capitalism.Early modern England's daily life was marked by significant social stratification and inequality.Thus, the period from 1550-1650 was a time of significant change and upheaval in England, with political, religious, and economic developments shaping the lives of its people.
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