well, we know that a year has 12 months, so 6 months is really just 6/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 2588\\ P=\textit{original amount deposited}\dotfill & \$2500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases}[/tex]
[tex]2588 = 2500[1+(\frac{r}{100})(\frac{1}{2})] \implies \cfrac{2588}{2500}=1+\cfrac{r}{200}\implies \cfrac{647}{625}=\cfrac{200+r}{200} \\\\\\ \cfrac{(200)(647)}{625}=200+r\implies \cfrac{(200)(647)}{625}-200=r\implies \boxed{7.04=r}[/tex]
Determine the eccentricity for r=5/2+1sin theta
0. 5
5
2
1
Determine the equation of the directrix of r=26. 4/4+4. 4 cos theta
X=-6
Y=6
X=6
The eccentricity for r=5/2+1sin theta and the equation of the directrix of r=26. 4/4+4. 4 cos theta is 0.5 and x=6
To find the eccentricity of the polar equation r = 5/2 + 1sin(θ), we first need to convert it to rectangular form:
r = 5/2 + 1sin(θ)
r = 5/2 + 1y/r
r^2 = (5/2)r + y
x^2 + y^2 = (5/2)r + y
x^2 + y^2 = (5/2)√(x^2 + y^2) + y
x^2 - (5/2)√(x^2 + y^2) + y^2 = 0
We can see that this is the equation of a conic section, specifically an ellipse, since the signs of the x^2 and y^2 terms are the same. The standard form of an ellipse centered at the origin is:
x^2/a^2 + y^2/b^2 = 1
Comparing this to our equation, we can see that a^2 = (5/2) and b^2 = 1. The eccentricity of an ellipse is given by:
e = √(1 - b^2/a^2)
Plugging in our values, we get:
e = √(1 - 1/(5/2))
e = √(3/5)
e ≈ 0.5
Therefore, the answer is (A) 0.5.
To find the equation of the directrix for the polar equation r = 26.4/4 + 4.4cos(θ), we first need to convert it to rectangular form:
r = 26.4/4 + 4.4cos(θ)
r = 6.6 + 4.4x/r
r^2 = 6.6r + 4.4x
x = (r^2 - 6.6r)/4.4
We can see that this is the equation of a parabola, since the highest degree of the variable r is 2. The standard form of a parabola with its focus at (0, p) is:
y = (1/4p)x^2
Comparing this to our equation, we can see that p = -6.6/4 = -1.65. The directrix of a parabola is a line perpendicular to the axis of symmetry and located at a distance of |p| from the focus. Since the axis of symmetry is the x-axis, the equation of the directrix is:
y = 1.65
However, since the question asks for the equation of the directrix in terms of x, we can rewrite this as:
x = 0
Therefore, the answer is (C) x = 6.
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What is the remainder when \( f(x)=-6 x^{23}+x^{11}-x^{6}+2 x \) is divided by \( x+1 \) ? The remainder is
The remainder when f(x)=-6x^23+x^11-x^6+2x is divided by x+1 is -7.
Explanation: In this question, we can solve the problem by using the Remainder Theorem. The remainder theorem states that when we divide a polynomial f(x) by x−a then we get a remainder equal to f(a). So, here we can take a=−1 and find the remainder of f(x).
Here is the given polynomial,
()=−6^23+^11−^6+2
We are asked to find the remainder when f(x) is divided by x+1. Using the remainder theorem, we can find the remainder of f(x) by evaluating f(−1).
(−1)=−6(−1)^23+(−1)^11−(−1)^6+2(−1)=6+1+1−2=6
Now, we have the remainder as 6. However, we need the remainder when f(x) is divided by x+1. The relationship between the remainder and the divisor of a polynomial is that when we divide a polynomial f(x) by x−a, we get a remainder of r(x) such that:
()=(−)()+()
where q(x) is the quotient of the division.
So, the question asks us to divide the polynomial f(x) by x+1 and get the remainder. Here is the long division of f(x) by x+1:
The remainder is −7. Therefore, the remainder when f(x) is divided by x+1 is -7.
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4 - 3x = 16
How do you solve this.... I somehow got -4 but I don't think that is right.
Answer:
yes you are right
Step-by-step explanation:
move 4 to other side so its -3x=12
divide 12 by -3
x=-4
PLEASE HELP!! I ONLY NEED HELP WITH THE LAST PART (ASKING AVERAGE SPEED)
Answer:
429
Step-by-step explanation:
At the shelter 0.6 of the animals are dogs, If there are 260 totally animals how many are not dogs?
Answer: 104
Step-by-step explanation:
If .6 or 60% of the animals in the shelter are dogs, then we can multiply .6 by 260 to get how many are dogs.
.6 times 260 is 156.
260-156=104.
b. If there are 440 towers, how many customers does the company have? Write a proportion you can use to solve. Choose the correct proportion.
Answer:
What's your question
Step-by-step explanation:
How many customers in each tower
You spend a $5 per turn on a fair game to win $15 for each winYou lose the first round but win the next two rounds. What was the net payoff ?
If you spend a $5 per turn on a fair game to win $15 for each win and you lose the first round but win the next two rounds, then the net payoff is $15
Since you spend $5 per turn and play three rounds, your total cost is $5 x 3 = $15.
If you win a game, you receive $15, so winning two games will give you $15 x 2 = $30.
However, since you lost the first round, you only won two out of three rounds. Therefore, your net payoff is:
= $30 - $15
Subtract the numbers
= $15
Therefore, your net payoff is $15
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Challenge A store is giving out cards labeled 1 through 10 when customers enter the store. If the card is an even number, you get a 10% discount on your purchase that day. If the card is an odd number greater than 6, you get a 30% discount. Otherwise, you get a 25% discount. The table shows the results of 200 customers. What is the relative frequency for each discount? Use pencil and paper. If the manager of the store wants approximately half of the customers to receive the 25% discount, does this seem like an appropriate method? explain
Answer: To find the relative frequency for each discount, we need to divide the number of customers who received each discount by the total number of customers.
Discount Number of customers Relative Frequency
10% 70 0.35
25% 99 0.495
30% 31 0.155
To determine if it is appropriate for the manager to want approximately half of the customers to receive the 25% discount, we can calculate the relative frequency for the 25% discount and compare it to 0.5 (or 50%).
Relative frequency for 25% discount = 99/200 = 0.495
Since the relative frequency for the 25% discount is already very close to 0.5, it seems like an appropriate method to achieve the manager's goal. However, it's worth noting that this method may not be the most effective in terms of maximizing profits or customer satisfaction. It's always important for businesses to carefully consider their pricing strategies and discount policies.
Step-by-step explanation:
Which of the following rectangles has an area that can be represented by the algebraic expression 9x+9
?
Responses
Image with alt text:
Image with alt text:
Image with alt text:
Image with alt text:
Answer: we can't see the images
Step-by-step explanation:
Answer:
Step-by-step explanation:
be can not see the pictures sir do better ni***
A mixture of 50 liters of paint is 25% red tint, 30% yellow tint and 45% water.
5 liters of yellow tint are added to the original mixture.
The percent of yellow tint in the new mixture is ____?
Answer must be correct to 1 decimal place
From the given information provided, the percent of yellow tint in the new mixture is 36.4%.
The total amount of yellow tint in the original mixture is:
0.30 × 50 liters = 15 liters
When 5 liters of yellow tint are added to the mixture, the total amount of yellow tint becomes:
15 + 5 = 20 liters
The total amount of new mixture is:
50 + 5 = 55 liters
To find the percentage of yellow tint in the new mixture, we divide the amount of yellow tint by the total amount of the mixture and multiply by 100:
(20/55) × 100 = 36.4%
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Isabel left her home at 11. 30 A. M. She took 45 minutes to jog to the park.
After exercising for 1 hour 55 minutes, she jogged home. She reached home at 3 P. M.
How long did she take to jog home? Explain how you got to this answer
Answer: 1 hour 50 minutes
Step-by-step explanation: it took her 2 hours to get home
she left home at 11:30 am it took her 45 minutes to jog to the park by the time she got to the park it was 12:15 pm she exercised for 1 hour and 55 minutes by the time she was done her work out it is 1:10 if she finished at 3 pm it took her 1 hour 50 minutes to get home
The expression (1 - 2x)4 can be written in the form 1 + px + qx^(2) - 32x^(3) + 16x^(4) By using the binomial expansion, or otherwise, find the values of the integers p and q.
Using the binomial expansion theorem, the values of integers p and q are -8 and 24, respectively
Expanding an expression using the binomial theoremFrom the question, we are to use the binomial expansion to expand the given expression and determine the values of p and q.
We can expand (1 - 2x)^4 using the binomial theorem as follows:
(1 - 2x)^4 = 1^4 - 4(1^3)(2x) + 6(1^2)(2x)^2 - 4(1)(2x)^3 + (2x)^4
= 1 - 8x + 24x^2 - 32x^3 + 16x^4
Now, we will compare this expression to the given expression
Comparing the expression to the given expression, 1 + px + qx^2 - 32x^3 + 16x^4
We see that:
p = -8
q = 24
Hence, the values p and q are -8 and 24, respectively.
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A = 1/2bh or A = bh/2
Area: 256.5 cm2
base: 27cm
What is the height?
help would be appreciated
A group of Physicians must build an addition to their existing private clinic. They are considering three different sized additions; a small addition, a medium addition and a large addition. If the medical demand is high (there is a favorable market for the addition) they would realize a net profit of $100,000 with a large addition, a net profit of $40,000 with a medium addition and a net profit of $10,000 with a small addition. If the medical demand is low (there is an unfavorable market for the addition) they would realize a net loss of $40,000 with the large addition, a net loss of $10,000 with the medium addition and a net profit of $5,000 with the small addition. The Physicians were also able to assign the following utility preference values to each of the potential payoffs they could encounter. Utility of $100,000 is 1.0, U ($40,000) is 0.9, U ($10,000) is 0.6, U ($5,000) is 0.5, U ($-10,000) is 0.4, and U ($-40,000) is 0.0. The physicians also have a reliable forecast indicating a 40% probability of the high medical demand. Using expected monetary value theory, what should they do and what is the expected value of that decision? Using expected utility theory, what should they do and what is the expected utility of that decision?
Therefore , the solution of the given problem of probability comes out to be the medium addition because it has the greatest expected utility (0.72).
What is probability, exactly?The primary goal of the structures within a methodology expression known as criteria is to provide an indication of the probability that the assertion is true or that a specific event will occur. Any number between zero and one, at which 0 is frequently indicated as a possibility and 1 has frequently used to denote a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability diagram.
Here,
The following formula can be used to determine each option's anticipated financial value:
=> EMV of big addition = (0.4 * $100,000) plus (0.6 * -$40,000) for a total of $16,000.
=> EMV of the middle addition is
= (0.4 * $40,000) plus (0.6 * -$10,000) for a total of $14,000.
=> EMV of a minor addition = (0.4 * 10,000) plus (0.6 * 5,000), which equals $6,000
The large addition should be chosen by the physicians as it has the greatest expected financial value of $16,000.
dividing each outcome's usefulness value by its likelihood, then adding the results:
=> (0.4 * 1.0) + (0.6 * 0.0) = 0.4 is the EU of the big addition.
=> (0.4 * 0.9) + (0.6 * 0.6) = 0.72 is the EU of medium addition.
Smaller EU = (0.4 * 0.5) + (0.6 * 0.6) = 0.58
The doctors should choose the medium addition because it has the greatest expected utility (0.72), according to expected utility theory.
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What will be the coordinates of point G after
a 90° counterclockwise rotation about the
origin?
So, if we have the original coordinates of point G, we can swap the x and y values and negate the new y-value to find the coordinates of point G after a 90° counterclockwise rotation about the origin.
To perform a 90° counterclockwise rotation about the origin, we can use the following transformation:
x' = -y
y' = x
This means that the new x-coordinate (x') will be the negative of the original y-coordinate (y), and the new y-coordinate (y') will be the original x-coordinate (x).
If we have the coordinates of point G, we can apply this transformation to find the new coordinates after the rotation.
Let's say that the coordinates of point G are (x, y). Then, the new coordinates (x', y') after the rotation will be:
x' = -y
y' = x
So, the new coordinates will be (-y, x). Therefore, if we want to find the new coordinates after a 90° counterclockwise rotation, we just need to swap the x and y values and negate the new y-value. This gives us the following coordinates for point G after the rotation:
G' = (-y, x)
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There are 2 boys and 2 girls working on an art project. They are sharing 10 ounces of paint equally. How much paint should each child get?
Answer:
2 ounces per person
Step-by-step explanation:
Letter answer only answer only!
Answer: B
Step-by-step explanation:
what is 46x squared times 24x squard
Answer:
the answer to ur question is: 1218816
Sal stands a candle up inside a paper bag, opened at the top. The candle and bag are both in the shape of right rectangular prisms. The dimensions, in inches, are given.
Length Width Height
Bag 2 4 8
Candle 1 2 3
Sal wants to put sand inside the bag surrounding the base of the candle. He wants the sand to be between 12 and 34 inches deep. How much sand, in cubic inches, should Sal put inside the bag? Select your answers from the drop-down lists
Sal should put the sand which is in between the amount of 3 cubic inches and 4.5 cubic inches inside the bag surrounding the base of the candle.
Base area of the bag = 4 × 2 = 8 in²
Base area of the candle = 2 × 1 = 2 in²
therefore, we know that base area to be filled with sand:
= 8 - 2 = 6 in²
now, height of sand is known to be between 1/2 and 3/4 inches,
therefore, we can make out that the volume of land is between 6 × 1/2 in³ and 6 × 3/4 in³
3 in³ and 4.5 in ³
therefore, amount of sand is between 3 cubic inches and 4.5 cubic inches, with this we know that Sal should put the sand which is in between the amount of 3 cubic inches and 4.5 cubic inches inside the bag surrounding the base of the candle.
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Do the three lines 5x - y = 7, x + 3y = 11, and 2x + 3y = 13 have a common point of intersection? If so, find it. if not, explain why not .
Answer:
429
Step-by-step explanation:
PLEASE SHOW WORK!!!!!!!!!
Answer:
The answer is G
Use substitution to solve the system of equations. Show your work.
Check your answer to show proof that the solution works in each equation.
[tex]4x+y=14\\y=8+2x[/tex]
Answer:
x = 1 , y = 10
Step-by-step explanation:
Given : y = 8 + 2x
by substitution,
4x + 8 + 2x = 14
6x + 8 = 14
6x = 14 - 8
6x = 6
x = 6/6 = 1
y = 8 + 2x
y = 8 + 2(1)
y= 10
Proof :
if x = 1,
4 (1) + 8 +2 (1) = 14
4 + 8 + 2 = 14
14 = 14
if y = 10 and x = 1
4 ( 1) + 10 = 14
4 + 10 = 14
14 = 14
For both equations, LHS = RHS
Therefore Proved.
hope it helps!
The cost price of an article when 22% profit is made after selling it for 's'
The cost price of the article when a profit of 22% is made after selling it for a certain price 's' can be calculated using the formula c = 0.78 * s.
Let's assume the cost price of the article is 'c'. Then, the profit made on selling the article is:
Profit = Selling price - Cost price
Since a profit of 22% was made on the selling price 's', we can express the selling price as:
Selling price = Cost price + Profit
= Cost price + 0.22 * Selling price
Rearranging this equation, we get:
0.78 * Selling price = Cost price
Substituting the given selling price 's' into this equation, we get:
0.78 * s = c
Therefore, the cost price of the article is 0.78 times the selling price. If we know the selling price 's', we can calculate the cost price 'c' using this formula. For example, if the selling price of the article is $100, then the cost price would be:
c = 0.78 * s
= 0.78 * $100
= $78
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Relative to the origin O, the position vectors of two points A and B are a and b respectively. b is a unit vector and the magnitude of a is twice that of b. The angle between a and b is 60°. Show that [a×[ob + (1-o)a] =√k, where k is a constant to be determined.
Using cross product, the vector can be proven as [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.
What is the proof that [a * [ob + (1 - o)a] = √kThe vector OB can be expressed as OB = b since b is a unit vector and O is the origin.
The vector OA can be expressed as OA = 2b since the magnitude of a is twice that of b.
The angle between a and b is 60°, so we have:
|a| |b| cos 60° = a · b
2|b| · 1/2 = a · b
|b| = a · b
We can now express the vector [OB + (1 - O)A] as:
[OB + (1 - O)A] = b + (1 - O)2b
= (2 - O) b
The cross product of a and [OB + (1 - O)A] is:
a × [OB + (1 - O)A] = a × [(2 - O) b]
= (2 - O) (a × b)
The magnitude of the cross product is:
|a × [OB + (1 - O)A]| = |(2 - O) (a × b)|
= |2 - O| |a| |b| sin 60°
= √3 |2 - O| |b| |a| / 2
= √3 |2 - O| |b|^2 |b| / 2
= √3 |2 - O| |b|^3 / 2
Substituting |b| = a · b, we get:
|a × [OB + (1 - O)A]| = √3 |2 - O| (a · b)^3 / 2
Since |a × [OB + (1 - O)A]| is equal to √k for some constant k, we can set:
√k = √3 |2 - O| (a · b)^3 / 2
Squaring both sides, we get:
k = 3 (2 - O)^2 (a · b)^6 / 4
Therefore, [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.
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What is the advantage
of a two-way relative frequency table for
showing relationships between sets of
paired data?
A two-way relative frequency table, in general, is an effective instrument for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and conduct methodical hypothesis testing.
A tool used to display the connection between two sets of paired data is a two-way relative frequency table, which arranges the data in rows and columns. The frequency of each combination is indicated in the chart, which can also be used to determine its relative frequency, which is calculated as the frequency of the combination divided by the total number of observations.
The benefit of using a two-way relative frequency table to illustrate relationships between pairs of paired data is that it gives a more comprehensive image of the data and the interrelationships between the variables. More specifically, it enables us to:
Finding patterns and trends is simple thanks to the table's presentation of the data. We can see which combinations are more or less prevalent than others by examining the relative frequencies of each set of values, and we can spot patterns in the data that might not be obvious otherwise.
Calculate conditional probabilities: Conditional probabilities are the likelihoods of one event given the occurrence of another event, and they can be determined using the chart. We can determine the likelihood that a smoker is male or female and the likelihood that a non-smoker is male or female, for instance, if we have a two-way table illustrating the connection between gender and smoking status.
Testing hypothesis: The table can be used to evaluate theories about how the variables are related to one another. A chi-square test, for instance, can be used to determine whether gender and smoking status are significantly associated.
In general, a two-way relative frequency table is an effective tool for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and test theories in a methodical manner.
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Hello!
Please help me for this geometry problem
I appreciate it!
Answer:
x = 48
Step-by-step explanation:
given a line parallel to a side of a triangle and it intersects the other two sides, it divides those sides proportionally, that is
[tex]\frac{x}{18}[/tex] = [tex]\frac{56}{21}[/tex] ( cross- multiply )
21x = 18 × 56 = 1008 ( divide both sides by 21 )
x = 48
Please help me with this needs to be done by today thanks
Answer:
cubic unit eg m³
Step-by-step explanation:
Raised to power 3
Answer:
Units cubed or unit^3
Explanation:
Volume= (base)(width)(height), therefore, this would be cubed. x^3
Area=(base)(height), therefore, this would be squared. x^2
Points C and D are plotted on a graph.
C has coordinates (1, -5) and D has coordinates (6, 4)
Calculate the length of the line segment CD.
Leave your answer to 2 decimal places.
Answer:
The length of line segment CD is 10.3 units (rounded to 2 decimal places).
Step-by-step explanation:
To find the length of line segment CD, we need to use the distance formula, which is:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Here, (x1, y1) = (1, -5) and (x2, y2) = (6, 4).
So, substituting these values in the distance formula, we get:
Distance = √[(6 - 1)^2 + (4 - (-5))^2]
= √[5^2 + 9^2]
= √(25 + 81)
= √106
≈ 10.3 (rounded to 2 decimal places)
Therefore, the length of line segment CD is 10.3 units (rounded to 2 decimal places).
Hope this helps!
-8x253.96 pls help if you can because i'm stuck on this problem, so please help if you can.