Using the given principal of $4000, an annual interest of 5.1%, and a time period of 2 years, the amount in a continuously compounded account will be approximately $4483.48 using the formula A = P*e^(rt).
Explanation:In this question, we are asked to find the amount in a continuously compounded account. The formula to calculate this is A = P*e^(rt), where A is the amount, P is the principal, r is the rate, t is the time, and e is the base of the natural logarithm, approximately equal to 2.71828.
In this case, P = $4000, r = 0.051 (5.1% expressed as a decimal), and t = 2.
Substituting these values into the formula, we get: A = 4000 * e^(0.051*2). Using a calculator, we can find this to be approximately $4483.48.
So, after 2 years with an annual interest rate of 5.1%, compounded continuously, the account will contain about $4483.48.
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Which function represents a reflection of f(x) = 5(0.8)x across the x-axis? A. g(x) = 5(0.8)–x B. g(x) = –5(0.8)x C. g(x) = 1/5(0.8)x D. g(x) = 5(–0.8)x
Answer:
2nd option
Step-by-step explanation:
is it always true that trapezoids height is the distance between the 2 bases?
What are the minimum, first quartile, median, third quartile, and maximum of the data set?
12, 6, 8, 3, 10, 15, 18, 7
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE HELP!! WILL GET BRAINIEST IF YOU SHOW WORK
1. Simplify the radical
2. Simplify the radical
3. Simplify the radical
4. Simplify the radical
The simplification of the radical is c/3
What are radicals in math?Radicals in math refer to expressions containing square roots or higher-order roots.
Represented by the radical symbol (√), they involve finding the root of a number. For example, √9 equals 3, as 3 * 3 equals 9.
Simplifying the surd;
√3c²)/√27
= √3 × √c²)/√9 × √3
= √3c/3√3
= c/3
Therefore the simplification of √3c²)/√27 is c/3.
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David wants to rent a movie. He wants to watch either a comedy or a drama. The movie rental store has 18 comedies and dramas available for rent. Seven of the movies are comedies, and eleven of the movies are dramas. David has not seen two of the comedies, and he has not seen four of the dramas. If David selects a movie randomly, what is the probability the movie will be a comedy or a movie that he has not seen?
[tex] |\Omega|=18\\
|A|=7+4=11\\\\
P(A)=\dfrac{11}{18}\approx61\% [/tex]
Identify the pattern for the following sequence. Find the next three terms in the sequence. 5, 2, -1, -4, ____, ____, ____,... a. Subtract 3; -7, -10, -13 b. Add 3; -7, -10, -13 c. Subtract -3; 7, 10, 13 d. Add 3; 1, 4, 7 Please select the best answer from the choices provided
Answer:
A.Subtract 3:-7,-10,-13
Step-by-step explanation:
We are given that a sequence
5,2,-1,-4,...
We have to identify the pattern of the givens sequence and next three terms.
[tex]a_1=5,a_2=2,a_3=-1,a_4=-4[/tex]
[tex]a_2-a_1=2-5=-3[/tex]
[tex]a_3-a_2=-1-2=-3[/tex]
[tex]a_4-a_3=-4-(-1)=-3[/tex]
The difference between two consecutive terms are equal.When the difference between two consecutive terms are equal then the sequence is called arithmetic sequence.Hence, the sequence is arithmetic sequence.
[tex]a_5=a_4-3=-4-3=-7[/tex]
[tex]a_6=a_5-3=-7-3=-10[/tex]
[tex]a_7=a_6-3=-10-3=-13[/tex]
Answer:A.Subtract 3:-7,-10,-13
PLS HELP ME ASAP WITH 1 AND 2, THANK YOU!! SM!!
(Brainliest will be given hopefully!)
(Random answers gets moderated.)
Adrian has been adding 6 cards to his sports card collection each week. He started with 20 cards. Let x be the number of weeks he saves cards. Which inequality would help him find the number of weeks it will take him to have more than 100 cards?
In this mathematical context, the inequality 20 + 6x > 100 can help Adrian find out the number of weeks he needs to continue his weekly addition of 6 cards to his sports card collection to exceed 100 cards in total.
Explanation:The subject of this question is Mathematics and it appears to be at a Middle School level. The problem involves understanding and using linear equations and inequalities.
In this situation, Adrian starts with 20 cards and adds 6 more each week. So his total number of cards is represented by the equation 20 + 6x, where x is the number of weeks. If he wants to have more than 100 cards, we set up an inequality like this:
20 + 6x > 100
Thus, the inequality 20 + 6x > 100 allows Adrian to calculate the number of weeks x he needs to continue adding cards to his collection in order to exceed 100 cards total.
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To figure out when Adrian's sports card collection will surpass 100 cards given he is adding 6 cards each week, we can set up the inequality [tex]20 + 6x > 100[/tex]. Solving this gives us that Adrian should wait at least 14 weeks to have more than 100 cards.
Explanation:The subject of this question is Mathematics, specifically, linear algebra and inequalities. Adrian has a sports card collection which began with 20 cards. Every week, he is adding 6 new cards. The statement that relates his ongoing collections would be: 20 + 6x, where x is the number of weeks. Adrian wants to know when his collection will exceed 100 cards. To determine this, we must set up an inequality: [tex]20 + 6x > 100[/tex]. Solving this inequality gives us [tex]x > (100-20)/6[/tex], or [tex]x > 13.33[/tex]. Therefore, Adrian will need to wait at least 14 weeks to have more than 100 cards in his collection given he is adding 6 new cards per week.
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A two digit number with two different digits has a special property when th sum of its digits is added to the product of its digits the result is the number itself
If (-3)^-5=1/x, what is the value x?
The solution is, x = -243 is the value of (-3)^-5=1/x.
What is algebraic identities?The algebraic equations are those which are valid for all values of variables in them are called algebraic identities.
Here we have:
Given that,
(-3)^-5=1/x
now, we have to simplify this expression, to get the value o x .
so, we get,
1/(-3)^5=1/x
or, (-3)^5=x
or, x = -243
Hence the value of the expression (-3)^-5=1/x , is x= -243.
(Note the expression asked is different by minus sign, but generally these questions solved as above. It would be a printing mistake)
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Maria needs to mail 3 letters. Each letter costs $0.41 to mail. How much change will she get back if she gives the clerk $2.00?
Maria has to mail 3 letters, each costing $0.41, totaling to $1.23. She gives the clerk $2.00, so the change she will get back is $2.00 - $1.23 = $0.77.
Explanation:This problem is about simple arithmetic and money management. Maria has to mail 3 letters, each costing $0.41. This means that the total expense that Maria has to pay is $0.41 * 3, which equals $1.23. Maria gives the clerk $2.00, so to find out the change, subtract the total cost of the letters ($1.23) from the amount she gave to the clerk ($2.00). So, the change Maria will get back is $2.00 - $1.23 = $0.77.
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The perimeter of a circle is also known as what?
Factor this trinomial completely.
2x^2 + 10x + 8
A. 2(x + 4)(x + 1)
B. 2(x – 4)(x – 1)
C. 2(x + 4)(x – 1)
D. 2(x – 4)(x + 1)
Help
A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.
Enter your answers in the boxes to complete the two-way table based on the given data.
Answer: The table should look like this
4 9 13
15 8 23
19 17 36
Step-by-step explanation:Happy to help
Based on the complete table, 19 people own a car, 13 people own a truck while 8 people neither own a car nor a truck.
How to complete the table
A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.
own a car Dont own a car Total
Own a trcuk 4 9 13
Dont own a trcuk 15 8 23
Total 19 17 36
Those that own car 15 + 4 =19
those that own truck 9 + 4 = 13
Those that own car and truck 4 (Given)
Those that owns none = 36-15-9 - 4 = 8
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A family of four (two kids and two parents) spend the day at an amusement park. At the end of the day, the family adds up all of the receipts from their meals: $16.25, $17.96, $3.58, $4.61, $5.23. What is the mean and median cost spent? What does the mean cost represent? Why is the mean cost significantly different from the median cost? Which measurement of central tendency is a better representation of the amount of money that the family spent at the amusement park?
A family of four spent the following for their meals $16.25, $17.96, $3.58, $4.61, $5.23.
Mean cost spent is calculated by:
Total Cost/Number of Meals
(16.25+17.96+3.58+4.61+5.23)/5
47.63/5
$9.53
Mean Cost represents the average amount per meal the family has spent.
Median cost is the cost that in the middle of the five costs which is $5.23.
The mean cost is significantly different from the median cost because it is higher.
Median cost is a better representation of the amount of money that the family spent because, with regard to meal costs, this means that exactly half of the meals in the amusement park are above this price ($5.23) and exactly half are below.
The area of a rectangular garden is given by the trinomial x2 + x – 42. What are the possible dimensions of the rectangle? Use factoring.
The dimensions of the rectangle given by the trinomial (x² + x – 42) are 7 and 6, which are derived by factoring the trinomial and applying the quadratic formula.
Explanation:To find the possible dimensions of the rectangle, we start by factoring the trinomial that represents the area of the rectangle, namely x² + x – 42.
This can be factored as (x + 7)(x - 6), which are the roots of the quadratic equation when set to equal zero.
The roots, or solutions to this equation, can be calculated using the quadratic formula, -b ± √b² - 4ac 2a, which includes squaring the coefficient of the x-term, subtracting four times the product of the remaining coefficients, and dividing the result by twice the leading coefficient.
In this case, the dimensions that correspond to these roots, namely length and width, are 7 and -6. However, since dimensions cannot be negative, we disregard -6. Therefore, the possible dimensions of the rectangle are 7 and 6.
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your mom is looking at he amount of sugar in two different drinks the apple juice has 216 grams sugar for every 8 serving the sprite 234 grams of sugar for every 9 serving which drink has more sugar
Find the probability of drawing a heart or a black card from a standard deck of cards
The probability of drawing a heart or a black card from a standard deck of cards is 3/4.
Explanation:In a standard deck of cards, there are 52 cards in total. However, since we are interested in finding the probability of drawing a heart or a black card, we need to determine how many cards satisfy this condition.
There are 13 hearts in a deck, so the probability of drawing a heart is 13/52 or 1/4. Additionally, there are 26 black cards (13 spades and 13 clubs) in a deck, so the probability of drawing a black card is 26/52 or 1/2.
To find the probability of drawing a heart or a black card, we can add the probabilities together: 1/4 + 1/2 = 3/4.
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Write an equation in intercept form of the parabola that Passes through (-1,40) and x=-5, 4
Select all that are undefined. sec (45°) csc (0°) sec (90°)
Final answer:
The sec(45°) and sec(90°) are defined, but csc(0°) is undefined.
Explanation:
To determine which of the given trigonometric functions are undefined, we need to understand the domains of these functions. In trigonometry, the secant and cosecant functions are undefined for angles where the cosine and sine functions are equal to zero, respectively.
For sec(45°), the cosine of 45° is equal to √2/2, which is not zero. Therefore, sec(45°) is defined.For csc(0°), the sine of 0° is equal to 0, which results in division by zero. Hence, csc(0°) is undefined.For sec(90°), the cosine of 90° is equal to 0, which again leads to division by zero. Thus, sec(90°) is undefined.A quiz consists of two multiple-choice questions. the first question has a total of 7 possible answers followed by the second question which has a total of 3 possible answers. if both questions are answered with random guesses,
A. 0
B. 4
C. 2
D. -2
JK, KL, and LJ are all tangent to circle O. The diagram is not drawn to scale. If JA = 10, AL = 23, and CK = 9, what is the perimeter of ∆JKL
A.84
B.66
C.42
D.38
Answer: the perimeter of JKL is 84
ik this is rlly late but to help anyone else who gets this question:
This is an equilateral triangle, so the adjacent length is gonna be the same value as its corresponding length that was listed
JA = 10
JB = JA, JB is also 10
JA + JB (10+10) = 20
AL = 23
LC = AL, LC is also 23
AL + LC (23+23) = 46
CK = 9
KB = CK, KB is also 9
CK + KB (9+9) = 18
add all those up:
20 + 46 + 18 = 84
Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. x - 2; 4x2 - 3x + 22
Answer:
[tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].
Step-by-step explanation:
According to the factor theorem, if [tex]x-a[/tex] is a factor of [tex]p(x)[/tex], then [tex]p(a)=0[/tex].
Let [tex]p(x)=4x^2-3x+22[/tex]. If [tex]x-2[/tex] is a factor of [tex]p(x)=4x^2-3x+22[/tex], then [tex]p(2)=0[/tex].
Let us plug in [tex]x=2[/tex] in to the function to see if it will give us zero.
[tex]p(2)=4(2)^2-3(2)+22[/tex]
We simplify to obtain,
[tex]p(2)=4(4)-3(2)+22[/tex]
[tex]p(2)=16-6+22[/tex]
[tex]p(2)=10+22[/tex]
[tex]p(2)=32[/tex]
Since [tex]p(2)\ne0[/tex], [tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].
According to the Factor Theorem, 'x - 2' is not a factor of the polynomial '4x^2 - 3x + 22'. This determination was made by plugging '2' into the second polynomial and finding that it does not result in zero.
Explanation:For a polynomial P(x), the Factor Theorem states that if you plug a value 'a' into the polynomial and get zero (P(a) = 0), then x-a is a factor of that polynomial. In this case, you are asked to determine whether 'x - 2' is a factor of the quadratic function '4x^2 - 3x + 22'.
To do so, according to the Factor Theorem, plug the value '2' into the second polynomial function, so we have 4*(2)^2 - 3*(2) + 22 = 16 - 6 + 22 = 32. Because this does not equal zero, we can conclude that 'x - 2' is not a factor of the second polynomial '4x^2 - 3x + 22' based on the Factor Theorem.
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evaluate a = log(0.1) and b = ln(e^3)
please help. there is a picture below
What is the minimum value of the graph of y=sin x assumes
Answer:
the answer is
negative one
- 1
Step-by-step explanation:
A set of n = 15 pairs of scores (X and Y values) has SSX = 4, SSY = 25, and SP = 6. What is the Pearson correlation for these data
The graph represents the feasible region for the system:
y<=2x
x + y<=45
x <=30
Minimize the objective function P = 25x + 20y.
The minimum value =?
and occurs when x = ?
and y = ?
We have been given a system of inequalities and an objective function.
The inequalities are given as:
[tex]y\leq 2x\\ x+y\leq 45\\ x\leq 30\\[/tex]
And the objective function is given as:
[tex]P=25x+20y[/tex]
In order to find the minimum value of the objective function at the given feasible region, we need to first graph the region.
The graph of the region is shown below:
From the graph, we can see that corner points of the feasible region are:
(x,y) = (15,30),(30,15) and (30,60).
Now we will evaluate the value of the objective function at each of these corner points and then we will compare which of those values is minimum.
[tex]\text{At (15,30)}\Leftrightarrow P=25\cdot 15+20\cdot 30=975\\ \text{At (30,15)}\Leftrightarrow P=25\cdot 30+20\cdot 15=1050\\ \text{At (30,60)}\Leftrightarrow P=25\cdot 30+20\cdot 60=1950\\[/tex]
Hence the minimum value of objective function is 975 and it occurs at x = 15 and y = 30
Answer:
The minimum value =
975
and occurs when x =
15
and y =
30
Step-by-step explanation:
Edge. 2020
Fifty-eight boys were asked if they play football and/or baseball. Thirty-one of them said they do not play baseball. Sixteen of them said they play football. Twenty of them said they do not play baseball or football. Match the following values to their correct places on the two-way table.
Answer:
5 play Football & Baseball; 22 don't play Football; 11 don't play baseball; 20 don't play either football or baseball. See captures attached. The missing one in your original answer + the one made in Excel.
Step-by-step explanation:
If you fill out the blanks the way explained in the answer, you can prove that the 3 sentences match perfectly. The sum of all of them totals 58.
1. Thirty-one of them said they do not play baseball.
2. Sixteen of them said they play football.
3. Twenty of them said they do not play baseball or football.
By the way, as I mentioned before, I also attached the missing image in your original question.
Have a great day!
Answer:
Here is the answer.