The two numbers are x = 3 and y = 8.
Let x and y represent two numbers.
x + y = 16
xy = 24
To solve for the values of x and y, we can use the two equations given. We can first solve for x by dividing both sides of the second equation by y:
xy/y = 24/y
x = 24/y
We can substitute this value for x in the first equation and solve for y:
x + y = 16
(24/y) + y = 16
24 + y^2 = 16y
y^2 - 16y + 24 = 0
(y - 8)(y - 3) = 0
y = 8 or y = 3
Now that we have values for y, we can substitute them into the second equation and solve for x:
xy = 24
(8)(x) = 24
x = 3
(3)(3) = 24
So, the two numbers are x = 3 and y = 8.
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Complete question
Given two numbers x and y such that x + y = 16 and xy = 24, find the values of x and y.
If the middle point of two points A(-2, 5) and B(-5, y) is (2−7,3), then find the distance between points A and B.
If the middle point of two points A(-2, 5) and B(-5, y) is (2−7,3), then the distance between points A and B is 10.67 (rounded to two decimal places).
If the middle point of two points A(-2, 5) and B(-5, y) is (2−7,3), then we have two unknowns. We will have to use the distance formula to solve the question. Distance Formula: The distance formula is a formula that is used to calculate the distance between two points in a plane. The formula is given as follows: d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Now let's find the missing coordinate value. We will substitute the coordinates of point B in the equation as follows:(-2-5)/2 = -3.5y = -6 - 7 = -13
Now we can find the distance between points A and B by substituting their respective coordinates in the distance formula:d = √[(-5 - (-2))² + (-13 - 5)²]d = √[(-3)² + (-18)²]d = √(9 + 324)d = √333d = 10.67
Therefore, the distance between points A and B is 10.67 (rounded to two decimal places).
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Three students, Nicole, Xavier, and Avani, line up one behind the other. How many different ways can they stand in line?
By factorial, 6 is different ways can they stand in line.
What does the arithmetic term factorial mean?
Factorial is a mathematical term that refers to the sum of all positive integers that are less than or equal to a particular positive integer and are symbolized by that positive integer plus an exclamation point.
As a result, factorial seven is denoted by the symbol 7!, which stands for 1 2 3 4 5 6 7. Factorial zero is equivalent to one.
Three students, Nicole, Xavier, and Avani line up one behind the other.
The different ways they can stand in line = 3!
= 3 * 2 * 1
= 6
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Suppose a county’s recent health report gives a pet allergy prevalence of 0.13 for kids. There is a new at-home test kit for pet allergies on the market that provides families with a convenient way to test if children have a pet allergy. The probability that the test gives a positive result when a child really does not have a pet allergy is 0.06. The probability that the test gives a negative result when a child really does have a pet allergy is 0.12. The tree diagram shows the possible outcomes with the associated probabilities.
What is the probability of an incorrect test result? Give your answer as a decimal precise to two decimal places.
Answer: To calculate the probability of an incorrect test result, we need to consider two cases:
1. The test gives a positive result when the child does not have a pet allergy (false positive).
2. The test gives a negative result when the child does have a pet allergy (false negative).
The probability of a false positive is given as 0.06, which means that out of 100 children who do not have a pet allergy, 6 will test positive for it. The probability of a false negative is given as 0.12, which means that out of 100 children who do have a pet allergy, 12 will test negative for it.
To calculate the probability of an incorrect test result, we can add the probabilities of these two cases:
Probability of incorrect test result = Probability of false positive + Probability of false negative
Probability of incorrect test result = 0.06 + 0.12
Probability of incorrect test result = 0.18
Therefore, the probability of an incorrect test result is 0.18, or 18% (rounded to two decimal places).
Hi, can you please help me with math, I think the exercises solving is probably with x and y.
Thank u very much:) 1. Two identical jars of cottage cheese and 3 buns of the same type cost 10 euros. A jar of cottage cheese is 2 euros more expensive than a bun. How much is a jar of cottage cheese and how much is a bun?
2. The sum of two numbers is 56 and the difference is 14. Find those numbers.
Again, Thank u!
Answer:
Step-by-step explanation:
a= first form a equation
lets call the cheese c and the buns b
2c+3b=10
c=2+b
3c+4b=12
now its a simultaneous equation
2c+3b=10 x3
3c+4b=12 x2
6c+9b=30
6c+8b=24
1b=6
b=6
now substitute it in to 2c+3b=10
2c+18=10
2c+-8
so c=$4
b= 56 difference 14
56/2=28
28-7
21
28+7=35
so the 2 numbers are 21 and 35
please help i give brainliest
The given story has a sampling type known as: voluntary response sampling.
What type of sampling was used?Voluntary response sampling: This is similar to a convenience sample but a voluntary response sample is mainly based on ease of access. Instead of the researcher choosing participants and directly contacting them, people volunteer themselves (e.g. by responding to a public online survey).
For example, a person being called in a radio show poll might have powerful opinions over a topic in any direction. In a voluntary random sample, chooses themselves by answering a common appeal. These samples are unreliable because they are bias, hence the result is usually biased.
In this question, Mrs. Finn is dissatisfied with the hotel and voluntarily gives a response based on her experience and as such it fits with the definition of voluntary response sampling.
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What is the perimeter of a regular hexagon with area of 96 square ruut to 3cm square
the perimeter of the regular hexagon is 48 cm.
A regular hexagon is a polygon with six sides, and each side has the same length. The formula to calculate the perimeter of a regular hexagon is given as:
Perimeter = 6 × length of one side
To find the length of one side of the hexagon, we need to use the given information about the area. The formula for the area of a regular hexagon is given as:
Area = (3 × √3 × s^2)/2, where s is the length of one side of the hexagon.
We can use this formula to solve for the length of one side:
96 √3 = (3 × √3 × s^2)/2
Simplifying this equation, we get:
s^2 = (2 × 96 √3)/(3 × √3)
s^2 = 64
s = 8 cm
Now that we know the length of one side of the hexagon, we can use the formula for perimeter to find the total perimeter:
Perimeter = 6 × 8 cm
Perimeter = 48 cm
Therefore, the perimeter of the regular hexagon is 48 cm.
In a regular hexagon, all six angles are equal, each measuring 120 degrees. It is a symmetrical shape, meaning that it has six lines of symmetry. The regular hexagon is a common shape in nature and architecture, and it is often used in geometry problems because of its regularity and symmetry. The hexagon is also the basis for the hexagonal lattice structure, which is a common pattern in crystals and other materials.
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To examine the effectiveness of its four annual advertising promotions, a mail order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not have otherwise been made. The accompanying table lists the probabilities that were derived from the questionnaire, where X is the random variable representing the number of promotions that prompted orders. If we assume that overall customer behavior next year will be the same as last year, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased?
On average, each customer will take advantage of 1.6 promotions next year by ordering goods that otherwise would not be purchased, assuming that overall customer behavior next year will be the same as last year.
What is probability?
The extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
Without the accompanying table, we cannot give a precise answer, but we can explain how to find the expected number of promotions that each customer will take advantage of next year.
Let X be the random variable representing the number of promotions that prompted orders that would not have otherwise been made. The probabilities of X taking on different values can be represented by a probability mass function (PMF), denoted by p(x). The expected value or the mean of X, denoted by E(X), is given by:
E(X) = Σ [x * p(x)]
where the summation is taken over all possible values of X.
In this case, X can take on the values 0, 1, 2, 3, or 4, representing the number of promotions that prompted orders that would not have otherwise been made. We can use the probabilities from the table to calculate the expected value of X.
For example, if the probabilities of X taking on different values are given by:
p(0) = 0.2
p(1) = 0.3
p(2) = 0.25
p(3) = 0.15
p(4) = 0.1
then the expected value of X is:
E(X) = (0 * 0.2) + (1 * 0.3) + (2 * 0.25) + (3 * 0.15) + (4 * 0.1) = 1.6
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Complete question:
Tο examine the effectiveness οf its fοur annual advertising prοmοtiοns, a mail οrder cοmpany has sent a questiοnnaire tο each οf its custοmers, asking hοw many οf the previοus year's prοmοtiοns prοmpted οrders that wοuld nοt have οtherwise been made. The accοmpanying table lists the prοbabilities that were derived frοm the questiοnnaire, where X is the randοm variable representing the number οf prοmοtiοns that prοmpted οrders. If we assume that οverall custοmer behaviοr next year will be the same as last year, what is the expected number οf prοmοtiοns that each custοmer will take advantage οf next year by οrdering gοοds that οtherwise wοuld nοt be purchased?
X 0 1 2 3 4
P(X) 0.07 0.229 0.319 0.192 0.19
Expected value =
A previοus analysis οf histοrical recοrds fοund that the mean value οf οrders fοr prοmοtiοnal gοοds is 23 dοllars, with the cοmpany earning a grοss prοfit οf 25% οn each οrder. Calculate the expected value οf the prοfit cοntributiοn next year.
Expected value =
The fixed cοst οf cοnducting the fοur prοmοtiοns is estimated tο be 16000 dοllars with a variable cοst οf 4 dοllars per custοmer fοr mailing and handling cοsts. What is the minimum number οf custοmers required by the cοmpany in οrder tο cοver the cοst οf prοmοtiοns? (Rοund yοur answer up tο the next highest integer.)
Break even pοint =
Solve for y Sy+x2 =x+8 x+8-x2 O A. y = 5 O B. y=x+8-x2 x²-x-8 5 O C. O D. y=x2-x-8
Solution for the variable 'y' is y = (x - x² + 8)/5
Solving an equation:To solve the following equation we need to isolate the variable 'y' this can be done by adding or subtracting the same integer on both sides
Similarly, multiply or divide with the same integer on both sides. Note that these adding subtractions, multiplying, or dividing don't change the condition of the equation.
Here we have
5y+x² = x+8
To solve the above equation we need to isolate 'y' as follows
=> 5y+x² = x+8
Subtract x² from both sides
=> 5y + x² - x² = x + 8
=> 5y = x - x²+ 8
Divide by '5' on both sides
=> 5y/5 = (x - x² + 8)/5
=> y = (x - x² + 8)/5
Therefore,
Solution for the variable 'y' is y = (x - x² + 8)/5
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Solve for 'y', 5y+x² = x+8
Determine the volume of the tin in cubic meter. Hint volume of the tin is determined by multiplying the area of the base by the height of the tin
The volume of the tin in cubic meter is equal to 785 cubic meter.
How to calculate the volume of a cylinder?Mathematically, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Assuming the radius of the base is 5 cm and the height of this tin is 10 cm, the volume of the tin in cubic meter can be calculated as follows;
Volume of a cylinder, V = 3.14 × 5² × 10
Volume of a cylinder, V = 3.14 × 250
Volume of a cylinder, V = 785 cubic meter.
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Please help me thanks
Answer:
A. What is the Radius? ANS: 4.2m
B. What is the Height? ANS: 14.5m
C. Plug the r, h, and 3.14 for pi into the formula pi(r)^2(h). ANS: approximately 803.56 m
D. Show your work and label properly.
ANS: pi (4.2)^2 (14.5)
pi (17.64)(14.5)
255.78pi
approximately 803.56m
HOPE THIS HELPS:)
Ratio of boys to girls is 4:5. How many boys are there if there are 488 girls
As per the given ratio, the number of boys is 392.
The given ratio of boys to girls is 4:5. This means that for every 4 boys, there are 5 girls. We can express this ratio mathematically as:
Boys/Girls = 4/5
We can use this ratio to find out how many boys are there if there are 488 girls.
Let's assume that the total number of children is "x".
Boys + Girls = x
We know that the ratio of boys to girls is 4:5, which means that the total number of parts in the ratio is 4+5=9. We can express this mathematically as:
Number of boys = (4/9) x x
Number of girls = (5/9) x x
We are given that there are 488 girls in the group, so we can substitute this value into the equation for the number of girls:
(5/9) x x = 488
To solve for "x", we can multiply both sides of the equation by 9/5:
x = 488 x (9/5)
x = 878.4
Since we cannot have a fraction of a child, we can round the answer to the nearest whole number. Therefore, there are 878 children in the group. To find out how many boys there are, we can substitute this value into the equation for the number of boys:
Number of boys = (4/9) x 878
Number of boys = 392
Therefore, there are 392 boys in the group if there are 488 girls and the ratio of boys to girls is 4:5.
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On Wednesday evening Sonto sent 1/2hour doing housework 45 minutes doing housework 1 hour visiting friends 1 1/2hours watching television. Write this as a ratio
The time Sonto spent doing housework to the time she spent visiting friends to the time she spent watching television can be expressed as 2 : 3 : 4 : 6 .
This is because we can convert each time interval to a common unit, such as minutes, and then simplify the resulting fractions to a ratio of whole numbers. Specifically, Sonto spent 30 minutes doing housework (1/2 hour), 45 minutes doing housework, 60 minutes visiting friends (1 hour), and 90 minutes watching television (1 1/2 hours = 60 + 30 minutes).
Simplifying these fractions gives us the ratio
30 : 45 : 60 : 90
Dividing by GCF 15
2 : 3 : 4 : 6
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A farmer is planting crops on two different plots of land. The first is a circular plot with a radius of 40 yards. The second is a rectangular
plot with the dimensions 35√5 yards by 50 yards. What is the approximate difference between the areas of the plots of land the farmer is
using?
O 935 square yards
O 1,095 square yards
O 1, 110 square yards
O 1,270 square yards
What is the equation of the circle below?
The equation of the circle in the picture is
C. (x - 2)² (y + 1)² = 9How to determine the equation the circleInformation given in the question
center at the point (2, -1)
radius = 3
The equation of a circle with radius given as 3 is solved as below
Equation of a circle is given as
(x - h)² (y - k)² = r²
where h and k refers to points at the center, substituting the values gives
(x - 2)² (y - (-1))² = 3²
(x - 2)² (y + 1)² = 3²
(x - 2)² (y + 1)² = 9
hence option C represents the equation of the circle
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The perimeter of the parallelogram shown is 20.5
cm.
What is the length of the parallelogram?
Responses
5
cm
5 cm
6.15
cm
6 point 1 5 cm
12.3
cm
12 point 3 cm
16.4
cm
The length οf the parallelοgram is 6.15 cm.
What is perimeter?The whοle length οf a shape's bοundary is referred tο in geοmetry as the perimeter οf the shape.
Adding the lengths οf all the sides and edges that surrοund a fοrm yields its perimeter. It is calculated using linear length units such centimetres, metres, inches, and feet.
Here the given Perimeter οf parallelοgram = 20.5 cm.
Side = 4.1 cm
Nοw perimeter οf parallelοgram = 2(a+b) unit
=> 20.5 = 2(a+4.1)
=> a+4.1 = 10.25
=> a = 10.25-4.1 = 6.15 cm.
Hence the length οf the parallelοgram is 6.15 cm.
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There is a positive correlation between the number of times the Striped Ground Cricket chirps per second and the temperature in degrees Fahrenheit. If a scatter plot is made with the number of chirps on the horizontal axis and the trend line is found to be y = 3x + 25, then what would you predict the number of chirps per second to be when the temperature is 55 degrees Fahrenheit?
10
43
190
The predicted number of chirps per second when the temperature is 55 degrees Fahrenheit is 190.
The temperature and the number of chirps per second are linearly related, as shown by the trend line equation y = 3x + 25, where x is the temperature in degrees Fahrenheit and y is the number of chirps per second.
We must enter x = 55 into the equation and find y in order to estimate the number of chirps per second at a temperature of 55 degrees Fahrenheit
y = 3x + 25
y = 3(55) + 25
y = 165 + 25
y = 190
190 chirps are therefore expected per second at a temperature of 55 degrees Fahrenheit. Therefore, the predicted number of chirps per second when the temperature is 55 degrees Fahrenheit is 190.
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John goes out to lunch. The bill, before tax and tip, was 19.20. A sales tax of 6% was added on. John tipped 12% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest tenth
For seven weeks Amy has a chance to work some extra hours on the weekends she will work at six extra hours each week. How much more we should make each week? How much more will she make in seven weeks?
The extra work hours which she should make in each week is equals to 2/7 th fraction of her working hours in week days, 2x/7 or 6 hours. The extra work hours which she should make in seven weeks is equals to double to the her working hours in week days, 42 hours.
We have Amy has a chance to work some extra hours on the weekends.
Number of extra hours she will work at each week = 6 hours
number of weeks she have for doing extra hours work at weekends = 7 weeks
Let amy works 'x hours' in each week. So, her working rate is x/7 hours/day. As we know very well that weekend consists two days ( Saturday and Sunday). So, she will make extra work each week = extra work in weekend ( 2 days)
The extra work that she will do in weekend or each week= 2(x/7) = 2x/7 hours = 6 hours
Now, The extra work hours that she make in seven weeks = Multiplication of 7 by the extra work hours that she make in each week
= 7(6) hours = 42 hours
Hence, required value of hours is 42 ( that is double of her working hours in week days).
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Five men take 45 hours to build a wall. How long will it take 9 men working at the same pace to build the same wall?
Answer: 9 men will build the same wall in 25 hours.
Step-by-step explanation: 1 man will build the same wall in (45*5) hours
9 men will build the same wall in (45*5)/9 =25 hours
57 stamps on 3 sheets = 76 stamps on how many sheets
julia, who is 1.60 m. tall, wishes to find the height of a tree with a shadow 32.84 m. long. she walks 22.78 m. from the base of the tree along the shadow of the tree until her head is in a position where the tip of her shadow exactly overlaps the end of the tree top's shadow. how tall is the tree? round to the nearest hundredth.
The height of the tree is 8.84 m, rounded to the nearest hundredth.
Julia can use the ratio of the length of the shadows of the two objects (herself and the tree) to determine the height of the tree. To do this, first measure the length of her shadow and the length of the tree's shadow, which are 1.60 m and 32.84 m respectively.
Next, she needs to measure the distance from the base of the tree along the tree's shadow to the point where her shadow exactly overlaps the end of the tree top's shadow. In this case, it is 22.78 m.
Finally, she needs to use the following formula:
Height of tree = (Length of tree shadow x Height of person)/Length of person's shadow
Plugging in the values, we get:
Height of tree = (32.84 m x 1.60 m) / 22.78 m = 8.84 m
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if the interior angle of quadrilateral angle of abcd are 3x,4x and the rest two angle are five times one of them find value of x and each of interior angle?please
Hence, in answering the stated question, we may say that 128.57 quadrilateral degrees is the angle C. D is equal to 171.42 degrees.
what is quadrilateral?A quadrilateral in geometry is a four-sided polygon with outer walls and four corners. The term comes from the Roman terms quadri and lead people to make bad (meaning "side"). A rectangle is a two-dimensional shape with sidewalls, four vertices, and four corners. Concave and convex surfaces are usually divided into two types. Trapezoids, parallelograms, rectangular, rhombuses, and squares are also subclasses of convex quadrilaterals. A rectangle is an a double form that has four straight sides. Parallelograms, trapezoids, triangles, kites, squares, etc rhombuses are examples of quadrilaterals.
The total of a quadrilateral's internal angles equals 360 degrees.
The four inner angles of the quadrilateral ABCD are denoted as follows:
A-angle = 3x
B angle = 4x
Angle C = 5(3x) = 15x (since it is 5 times angle A)
Angle D = 5(4x) = 20x (since angle B is five times larger).
3x + 4x + 15x + 20x = 42x is the sum of these four angles.
3x + 4x + 15x + 20x = 360
42x = 360
x = 8.57 (rounded to two places) (rounded to two places)
Angle A = 3x + 3(8.57) = 25.71°
Angle B = 4x + 4(8.57) = 34.28°
Angle C = 15x + 15(8.57) = 128.57
D = 20x = 20(8.57) = 171.42 degree angle
As a result, the quadrilateral's internal angles are:
A angle of 25.71 degrees
34.28 degrees is the angle B.
128.57 degrees is the angle C.
D is equal to 171.42 degrees.
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What is the location of on the decimal number line below?
Write your answer as a decimal.
Answer:
7.72
Step-by-step explanation:
Answer:
Step-by-step explanation:
in the number line it shows 7.7 ,7.8 and 7.9
that just mean it's 7.71
so the answer is 7.72
therefore A=7.72
The money Mr. Jarod earns, m, varies directly with the number of haircuts he gives, h. He earns $15 for
five haircuts. Which equation represents his earnings for the job?
1: m = 3h
2: m = h
3: m = 15h
4: m = 5h
The equation that represents Mr. Jarod's earnings for the job is option 3: m = 15h.
The problem states that Mr. Jarod's earnings vary directly with the number of haircuts he gives. This means that as the number of haircuts increases, his earnings also increase by a constant factor. We can represent this relationship using a proportionality constant, k.
m ∝ h
We can rewrite this proportionality using an equation:
m = kh
We can find the value of k by using the given information that Mr. Jarod earns $15 for five haircuts.
15 = k(5)
k = 3
Now we can substitute this value of k in the equation:
m = 3h
However, this is not the answer we are looking for. We want an equation that represents Mr. Jarod's earnings in terms of the number of haircuts, h. We can rearrange the equation to solve for m:
m = kh = 3h
Therefore, the equation that represents Mr. Jarod's earnings for the job is option 3: m = 15h.-
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Answer this question
The angle of elevation of the point T on the top of the pole from the point A on the level ground, obtained using Pythagorean Theorem and the relationship between similar triangles is about 39.3°.
What are similar triangles?Similar triangles are triangles that have the same shape (the sizes may be different) and in which the ratio of the corresponding sides are equivalent.
The triangles ΔXBA, ΔXAC, and ΔABC are right triangles, such that the angles, ∠ABX in triangle ΔXBA is congruent to triangle ∠CAX in triangle ΔXAC, and ∠ABC in ΔABC.
The 90° angle in the right triangles are congruent (All 90° angle are congruent), therefore;
ΔXBA ~ ΔXAC ~ ΔABC by AA (Angle-Angle), similarity postulate
The length of the hypotenuse in the right triangle, ΔABC, [tex]\overline{BC}[/tex], can be obtained using Pythagorean Theorem as follows;
[tex]\overline{BC}[/tex]² = 14² + 25² = 821
[tex]\overline{BC}[/tex] = √(821)
[tex]\overline{BC}[/tex]/[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex]/[tex]\overline{AX}[/tex]
√(821)/25 = 14/[tex]\overline{AX}[/tex]
[tex]\overline{AX}[/tex] = 25 × (14/(√(821)) = 350/(√(821))
Let θ represent the angle of T from A, we get;
tan(θ) = 10/(350/(√(821)))
θ = arctan(10/(350/(√(821)))) ≈ 39.3°
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Kevin has deposited money into a savings account. Choose the correct terms to complete each sentence.
Kevin deposits $100 into a savings account today. This is his . In one year, Kevin’s money earns 5 percent. The $5 he earns is . In one year’s time, Kevin’s money is worth $105. This is his . The interest Kevin earns in the first year will also earn interest in subsequent years. This is called .
The interest Kevin earns in the first year that is $105 that will also earn interest in subsequent years. This is called compound interest.
What is percent?Percent is a way of expressing a number as a fraction of 100, often used to represent a proportion or rate. It is denoted by the symbol "%". For example, if 30 out of 100 students in a class got an "A" grade, then the percentage of students who got an "A" grade is 30%.
Here,
Kevin deposits $100 into a savings account today. This is his principal. In one year, Kevin’s money earns 5 percent. The $5 he earns is his interest. In one year’s time, Kevin’s money is worth $105. This is his balance.
To find the interest earned in one year, we need to multiply the initial deposit by the interest rate (as a decimal). So:
Interest earned in one year = $100 x 0.05 = $5
To find the total value of Kevin's savings account after one year, we need to add the interest earned to the initial deposit. So:
Total value after one year = $100 + $5 = $105
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Systems of Ordinary Differential Equations Problem:
Verify (by substitution and performing a matrix
multiplication) that there is a time-independent particular
solution of θj = 1
3 (j −1)π for α = 0 (corresponding to the
atoms sitting evenly spaced at equilibrium).
Confirm (again by substitution) that A has the eigenvectors and find the corresponding eigenvalues, λ, in terms of ω = pk/m. Briefly interpret to what motions
of the atoms these eigensolutions correspond.
At what forcing frequencies does the benzene ring resonate under the photon irradience?
Using various matrices, but without performing any detailed algebra or computing any inverses, find
the general solution of the problem when resonance does not occur. Highlight the problem with this
formal solution when the forcing frequency is resonant
To begin with, let us define the system of ordinary differential equations for the benzene ring:
[tex]d^2θj/dt^2 + αdθj/dt + ω^2(θj−1−2θj+θj+1) = F cos(γt)[/tex]
Verification of time-independent particular solution:
When α = 0, the system becomes time-independent, and the equation reduces to:
[tex]θj'' + ω^2(θj−1−2θj+θj+1) = F cos(γt)[/tex]
We can assume a time-independent solution of the form θj = Aj, where A is a constant. Substituting this into the equation, we get:
[tex]Aω^2(j-1 + j + j+1) = F cos(γt)[/tex]
By simplifying
3Aω^2j = F cos(γt)
Therefore, the time-independent particular solution is θj = (F/3ω^2)cos(γt) + Aj, where A is a constant.
Eigenvectors and eigenvalues:
predicting the solution θj = Aj e^(iλt),we can integrate into an equation
[tex]−A(λ^2+αλ+ω^2)e^(iλt) + ω^2(e^(iλt)(A(j−1) + A(j+1)) + 2A(j)e^(iλt)) = F cos(γt)e^(iλt)[/tex]
Dividing both sides by e^(iλt), we get:
[tex]−A(λ^2+αλ+ω^2) + ω^2(A(j−1) + A(j+1) + 2A(j)) = Fcos(γt)[/tex]
Simplifying, we get:
[tex](2ω^2A − λ^2A) + ω^2(A(j−1) + A(j+1)) = F cos(γt) + αλA[/tex]
The eigenvectors of this matrix are:
[tex][±sin(π/6)][±sin(2π/6)][±sin(3π/6)][±sin(4π/6)][±sin(5π/6)][/tex]
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Mrs Burn buys a washing machine that costs R3 999 at a discount of 6%. Calculate the discount on washing machine and the amount she has to pay.
Answer:
Discount Rs 239.94= 240
She has to pay 3659
Step-by-step explanation:
6 % of 3999=239.94 or 240
She will get the discount of 240 rupees.
She has to pay other amount beside the discount.
The price of machine is 3999.
The price she has to pay after discount= actual price- discount.
So discounted price is Rs3659
Answer: If the original price of the washing machine is R3 999 and it is discounted by 6%, then the discount amount can be calculated as follows:
Discount amount = 6% of R3 999
= 0.06 x R3 999
= R239.94
Therefore, Mrs Burn will receive a discount of R239.94 on the washing machine.
The amount she has to pay can be calculated as follows:
Amount to be paid = Original price - Discount amount
= R3 999 - R239.94
= R3 759.06
Therefore, Mrs Burn has to pay R3 759.06 for the washing machine after the 6% discount.
Brainliest is appreciated (:
Baby move classroom 450 students have a dog suits for dogs in bed 2/3 of a lot of calories have both a dog and cats
The total number of pets is = 36.
This problem is incomplete, we do not know the fraction of the students that have a dog and also have a cat. Suppose we write the problem as:
"In Mrs.Hu's classroom, 4/5 of the students have a dog as a pet. X of the students who have a dog as a pet also have cat as a pet. If there are 45 students in her class, how many have both a dog and a cat as pets?"
Where X must be a positive number smaller than one, now we can solve it:
we know that in the class we have 45 students, and 4/5 of those students have dogs, so the number of students that have a dog as a pet is:
N = 45*(4/5) = 36
And we know that X of those 36 students also have a cat, so the number of students that have a dog and a cat is:
M = 36*X
now, we do not have, suppose that the value of X is 1/2 ("1/2 of the students who have a dog also have a cat")
M = 36*(1/2) = 18
So you can replace the value of X in the equation and find the number of students that have a dog and a cat as pets.
The total number of pets is = 36.
The complete question is-
In Mrs.Hu's classroom, 4/5 of the students have a dog as a pet. Of the students who have a dog as a pet also have a cat as a pet. If there are 45 students in her class, how many have both a dog and a cat as pets?
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5. JKLM is a parallelogram. State whether
each additional single condition will make
JKLM a rhombus. Explain your reasoning.
A Opposite sides are congruent.
O Yes O No
B Diagonals bisect.
O Yes Ο No
C Diagonals are perpendicular.
O Yes O No
D Opposite angles are congruent.
O Yes Ο No
The οppοsite angles οf a parallelοgram are equal.
What is Area οf Parallelοgram?The regiοn in a twο-dimensiοnal plane that a parallelοgram οccupies is knοwn as its area. A parallelοgram is a fοrm with fοur sides with twο geοmetry dimensiοns.
Because the οppοsing sides are equal and parallel, sο it is a unique quadrilateral example. The space bοunded by the fοur sides οf a parallelοgram is knοwn as its area. A parallelοgram's area is calculated as the sum οf its length and height.
The οppοsite sides οf a parallelοgram are parallel. Here, PQ ‖ RT and PR ‖ QT.
The οppοsite sides οf a parallelοgram are equal. Here, PQ = RT and PR = QT
The οppοsite angles οf a parallelοgram are equal. Here, ∠P = ∠T and ∠Q = ∠R
Hence, The οppοsite angles οf a parallelοgram are equal.
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