The stone fell from a height of 1.75 m above the top of the window.
We can use the kinematic equation for the vertical motion of an object in free fall to solve this problem:
y = vi*t + (1/2)at^2
where y is the initial height above the top of the window, vi is the initial velocity (which is zero since the stone is dropped), t is the time it takes for the stone to fall past the window (0.31 s), a is the acceleration due to gravity (-9.8 m/s^2).
Since the stone falls past a window that is 2.2 m tall, the final height of the stone is 2.2 m. Substituting these values into the equation, we get:
2.2 m = 0 + (1/2)(-9.8 m/s^2)(0.31 s)^2 + y
Simplifying and solving for y, we get:
y = 2.2 m - (1/2)(-9.8 m/s^2)(0.31 s)^2
y = 2.2 m - 0.45 m
y = 1.75 m
Therefore, the height from stone fell is 1.75 m.
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Find the dimensions of a rectangle with area 1,000 m^2 whose perimeter is as small as possible. (If both values are the same number, enter it into both blanks.)What is m (smaller value)What is m (Larger value)
10√10 is the dimensions of a rectangle with area 1,000 m² whose perimeter is as small as possible.
a. The smaller value is 10√10 m.
b. The larger value is 10√10 m.
We have to determine the dimensions of a rectangle with area 1,000 m² whose perimeter is as small as possible.
P = 2w + 2L
1000 = Lw
P = 2w + 2(1000/w)
P = 2w + 2000/w
P-prime = 2 -2000/w²
0 = 2 - 2000/w²
Add 2000/w² on both side, we get
2000/w² = 2
Multiply by w² on both side, we get
2000 = 2w²
Divide by 2 on both side
w² = 2000/2
w² = 1000
Taking square root on both side, we get
w = 10√10
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two cards are drawn at random from an ordinary deck of 52 cards what is the probability that thee are no sixes
there is an 85% chance that the two cards drawn at random from an ordinary deck of 52 cards will not be sixes.
The probability of drawing a card from an ordinary deck without replacement can be determined using the concept of conditional probability. Conditional probability is the probability of an event occurring, assuming that another event has already occurred.
In order to calculate the probability that the two cards drawn are not sixes, we can use the formula:
P(A and B) = P(A) x P(B|A)
Where A and B represent two independent events, P(A) is the probability of event A occurring, and P(B|A) is the conditional probability of event B occurring given that event A has already occurred.
The probability of drawing the first card that is not a six is:
P(A) = 48/52 = 0.9231
The probability of drawing the second card that is not a six, given that the first card drawn was not a six, is:
P(B|A) = 47/51 = 0.9216
Therefore, the probability of drawing two cards at random from an ordinary deck of 52 cards and having neither of them be a six is:
P(A and B) = P(A) x P(B|A) = 0.9231 x 0.9216 = 0.8503 or approximately 85%.
This means that there is an 85% chance that the two cards drawn at random from an ordinary deck of 52 cards will not be sixes.
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A store purchased a stylus for $22.00 and sold it to a customer for 20% more than the purchase price. The customer was charged a 6% tax when the stylus was sold. What was the customer’s total cost for the stylus?
Answer: $27.98
Step-by-step explanation:
22.00 × .2= 4.40
22 + 4.40 = 26.40
26.40 × .06 = 1.584
26.40 + 1.584 = 27.984
Round to the nearest hundred so the total paid by the customer would be 27.98
1. If the angle between the vectors a and b is π/4 and | a × b | = 1, then a. b is equal to
Answer:
We can use the formula |a × b| = |a| |b| sin θ to solve for the magnitude of the cross product |a × b|, where θ is the angle between vectors a and b. In this case, we have |a × b| = 1 and θ = π/4, so we can write:
1 = |a| |b| sin(π/4)
Simplifying, we have:
|a| |b| = √2
Now, we need to find the dot product a · b. We know that:
a · b = |a| |b| cos θ
where θ is the angle between vectors a and b. Since we're given the angle between a and b, we can substitute θ = π/4 and use the value we found for |a| |b|:
a · b = (√2) cos(π/4) = (√2)/2
Therefore, a · b is equal to (√2)/2.
Step-by-step explanation:
A fair coin is tossed five times. What is the theoretical probability that the coin lands on the same side every time?
A) 0.1
B) 0.5
C) 0.03125
D) 0.0625
Answer:
d
Step-by-step explanation:
the theoretical probability that the coin lands on the same side every time is 0.0625.
What is Probability?
The area of mathematics known as probability is concerned with how random events turn out. The definition of probability is chance or potential for a result. It clarifies the likelihood of a specific occurrence. We regularly use words like - 'It will probably rain today, 'he will probably pass the test', 'there is very less possibility of receiving a storm tonight', and 'most certainly the price of onion will go high again. In essence, probability is the forecasting of an outcome that is either based on the analysis of past data or the variety and quantity of alternative outcomes.
The theoretical probability of getting the same side every time in five coin tosses is:
Since the coin has two sides, there are 2^5 = 32 possible outcomes in total. Out of these outcomes, there are only two ways to get the same side every time (either all heads or all tails). Therefore, the probability of getting the same side every time is:
P(E) = favorable outcomes / total outcomes
= 2/32
= 1/16 = 0.0625 or 6.25%
So, the theoretical probability of getting the same side every time in five coin tosses is 0.0625 or 6.25%.
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Does 9:45 am and 9:45 pm considered total of 12 hours
Answer:
Yes. If you are asking if the duration between those two times is a total of 12 hours, the answer is yes.
Step-by-step explanation:
9:45am is 12 hours away from 9:45pm. This applies to all times and their am/pm counterparts such as 12am/12pm.
What is tangent and how do you calculate it from the unit circle?
Answer:
The unit circle has many different angles that each have a corresponding point on the circle. The coordinates of each point give us a way to find the tangent of each angle. The tangent of an angle is equal to the y-coordinate divided by the x-coordinate.
What is the equation of the line that is parallel to the
given line and passes through the point (-3, 2)?
V(o, 3)
O 3x - 4y = -17
(-3,2
O 3x - 4y = -20
4x + 3y = -2
4x + 3y = -6
The equation of the line that is parallel to the given line and passes through the point (-3, 2) is 3x - 4y = -17.
What is the formula for a parallel line equation?If the line's equation is axe + by + c = 0 and the coordinates are (x1, y1).
To find the equation of a line parallel to a given line, we must first understand that parallel lines have the same slope. As a result, we must first determine the slope of the given line.
3x - 4y = -17 is the given line. To determine its slope, solve for y and write the equation in slope-intercept form:
-3x - 4y = -3x - 17 y = (3/4)x + (17/4)
This line has a 3/4 slope.
Now we want to find the equation of a parallel line that passes through the point (-3, 2). Because the new line is parallel to the given line, it has a slope of 3/4.
We can write the equation of the new line using the point-slope form of the equation of a line as:
y - y1 = m(x - x1)
where m represents the slope and (x1, y1) represents the given point (-3, 2).
When m = 3/4, x1 = -3, and y1 = 2, we get:
y - 2 = (3/4)(x - (-3))
y - 2 = (3/4)(x + 3)
Divide both sides by 4 to get rid of the fraction.
4y - 8 = 3x + 9
3x - 4y = -17
As a result, the equation of the parallel line that passes through the point (-3, 2) is 3x - 4y = -17.
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Can Anyone Help?
A poster is to have a total area of 245cm2. There is a margin round the edges of 6cm at the top and 4cm at the sides and bottom where nothing is printed.What width should the poster be in order to have the largest printed area?
The poster should have width ____ cm
Answer: The poster should have width 17.50 CM
Step-by-step explanation:
Given that boasted I have a total area 245 cm square area of a poster is 200 and 45 20 m square. And it is in the rectangle format. So we know that the poster is always in the rectangle format and the area of rectangular area is equal to L N T W. So 245 will be equal to Ln tW. From this. We need to find L. So L is equal to 245 divided by W. Now consider the diplomatic representation of the poster. So it has mentioned that there is a margin around the edges of six cm at the top. This is 6cm and four cm at the sites. All the four sides 3 sides are four cm. So from this we need to find land and the doctor posted area that is printed area. The first wine printed with www. Z. Quilter. Now let this be total birth will be W. And this will be four and this will be four. Therefore posted with will be we need to find this part alone. So W -4 -4 will give the this part with. So W -4 -4. So post printed with PW will be equal to W -8. Similarly printed lunch will be equal to The total length is already we have found 245 by W. And we need to find this part length. So we have to subtract six and four from the total length so that that will give them this part length, So -6 -4. So printed length will be equal there 245 Divided by W -10. And we know that formula for area of a rectangle. Urz D is equal to L W. Now substitute the printed with and printed length in the area formula. We have to find the printed area. So Printed area Zeke Walter W -8 into 245 Divided by W -10. To simplify this, we get 325 minus 10. W -100 and 30,960 W. to the power of -1. Now fine D A by D. T. Not D D. This is D. W. So this is equal to differentiation of constant alma zero, this is minus 10 plus 900 and 60 W. to the power of -2 and equate this to be equal to zero. We out to find the maximum width so D A by D W is equal to zero, therefore minus 10 1960 W. To the power of -2 will be equal to zero. To simplify this, we get them maximum with value the W is equal term I wrote off 196. Therefore the value of W. Z quilter plus or minus 14. We will neglect the negative values since we cannot be negative. So one we assume the positive values. So what will be equal to 14 and length will be equal to 245 divided by 14, So which will be equal to 17.50 centimeters. And they have concluded that At W is equal to 14 cm and lunch will be equal to 17.50 cm needed to print the largest area. I hope you found the answer to school. Thank you.
a plumber can do a job in 5 hours, and his apprentice can do the same job in 8 hours. What part of the job is left if they start the job and work together for 2 hours.
question 1 write an inequality and a word sentence that represent the graph. let x represent the unknown number.
The inequality is X > 0 and a word sentence represent the graph is X the graph of a number line with an open circle on zero and an arrow pointing to the right.
The inequality X > 0 represents the graph of a number line with an open circle on zero to left and an arrow pointing to the right. This means that any value of X that is greater than zero is a valid solution for the inequality.
In other words, X can be any positive number, such as 1, 2, 3, and so on. However, X cannot be zero or any negative number, as those values do not satisfy the inequality. Therefore, the word sentence that represents this inequality is "X is greater than zero."
This means that X must be a positive number, and it can be any value that is greater than zero.
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At Snobby Girls School, 65% of the girls are Clothes Ponies (C), 50% are Makeup Missies (M) and 30% are both. A girl from SCS is
chosen at random.
a) What is the probability she is a C?
b) What is the probability she is an M?
c) What is the probability she is both a C and an M?
d) If the chosen girl is an M, what is the probability she is also a C?
e) Are the two events C and M independent? Why or why not?
In response to the stated question, we may respond that Given that she is an M, the probability that the chosen female is both a M and a C is 0.6.
What is probability?Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.
a) The girl has a 0.65 chance of being a Clothes Pony (C).
b) The girl has a 50% chance of being a Makeup Missie (M).
c) The girl has a 0.30 chance of being both a Clothing Pony and a Makeup Missie.
d) Using the conditional probability formula, we can calculate the likelihood that the chosen female is both a M and a C provided that she is a M:
P(C|M) = P(C and M) divided by P (M)
Part (c) tells us that P(C and M) = 0.30, while Part (b) tells us that P(M) = 0.50. Therefore:
P(C|M) = 0.30 / 0.50 = 0.6
Given that she is an M, the likelihood that the chosen female is both a M and a C is 0.6.
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Solve the following equations. Show your complete solutions.
A.
1)x+7=18
2)x-13 15
3) 8x=64
4)5x-13-12
I need a complex solution
And pls can u not simplyfy it
Answer:
1. x = 11
Step-by-step explanation:
1. x + 7 = 18
move 7 to right then change the sign
x = 18 - 7
x = 11
2. x - 13 = 15
move -13 to right then change the sign
x = 15 + 13
x = 28
3. 8x = 64
8 8
divided by 8 both side
x = 8
4. 5x-13-12=0 it this the correct given?
add same variable
5x = 13 + 12
5x = 25
5 5
divided by 5 both side
x = 5
The rectangle can be made to have rotation symmetry of order 2 by colouring one of the squares blue. Put a cross in the middle of the square which would have to be made blue.
To make a rectangle with a rotation symmetry of order 2, first draw the rectangle on a piece of paper. Then draw a cross in the middle of one of the squares in the rectangle. This is the square that needs to be coloured blue in order to create the rotation symmetry. Finally, colour the square with the cross blue to create the rotation symmetry.
determine the factor of the shape, needed in a fraction or whole number please help
Therefore, the scale factor of the dilation of the shape is 2.
What is scale factor?A scale factor is a ratio that describes the proportional relationship between two similar figures. It represents how much larger or smaller one figure is compared to the other, and it is calculated by dividing a corresponding measurement (such as side length, perimeter, or area) of the larger figure by the corresponding measurement of the smaller figure. Scale factor is used in mathematics, particularly in geometry and measurement, to describe the transformation of one figure into another through dilation or resizing. It is represented by a number or a ratio, such as 2:1 or 1/2, which indicates how many times larger or smaller the new figure is compared to the original.
Here,
In the given picture, it appears that the distance from the center of dilation (the origin) to the pre-image (the original figure) is 4 units, and the distance from the center of dilation to the image (the transformed figure) is 8 units. The scale factor of the dilation is equal to the ratio of the distance from the center of dilation to the image and the distance from the center of dilation to the pre-image.
So, the scale factor of the dilation is:
8 units ÷ 4 units = 2
Therefore, the scale factor of the dilation is 2.
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1. Find an equation for the line with the given properties.
Perpendicular to the line x = 5; containing the point (5,6)
y =
2. Find an equation for the line with the given properties. Use lowercase letter x for the variable.
Parallel to the line 7x - y = -7; containing the point (0,0)
y =
3. Find an equation for the line with the given properties.
Slope undefined; containing the point (8,2)
For the first question, the equation for the line is y = -x + 11. This comes from the fact that the slope for a line perpendicular to the line x = 5 is -1. From there, we can use the point (5,6) to calculate the y-intercept, which is 11.
For the second question, the equation for the line is y = 7x. This comes from the fact that the slope for a line parallel to the line 7x - y = -7 is 7. Since the point (0,0) is already on the line, the equation is already solved.
For the third question, the equation for the line is x = 8. This comes from the fact that the slope for a line with an undefined slope is 0. Since the point (8,2) is already on the line, the equation is already solved.
Calculate the standard deviation of ABC stock returns given the following historical series of returns. Year Rate of Return 1 −12% 2 10% 3 5% 4 −7% 5 3%
The value of standard deviation of the stock returns is 10.246%.
What is standard deviation?The variance or dispersion of a group of data points is measured by standard deviation. Finding the square root of the variance, which is the sum of the squared deviations between each data point and the mean, is how it is determined. In statistics, the term "standard deviation" is used to characterise the distribution of a data collection and to estimate the probability of certain outcomes or events.
The standard deviation is determined using the formula:
√(V).
The mean of the given data is:
(−12 + 10 + 5 − 7 + 3) / 5 = −0.2%
Now, the variance is:
Variance = [ (−12 − (−0.2))² + (10 − (−0.2))² + (5 − (−0.2))² + (−7 − (−0.2))² + (3 − (−0.2))² ] / 5
Variance = 104.96
Now, for standard deviation:
Standard deviation = √(104.96) = 10.246%
Hence, the value of standard deviation of the stock returns is 10.246%.
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One month Maya rented 5 movies and 3 video games for a total of $34. The next month she rented 2 movies and 12 video games for a total of $73. Find the rental cost for each movie and each video game. Rental cost for each movie: s Rental cost for each video game: s 3 Es
The rental cost for each movie and each video game is $3.5 and $5.5 respectively.
What is the the rental cost for each movie and each video game?Let
cost of each movie = x
Cost of each video game = y
5x + 3y = 34
2x + 12y = 73
Multiply (1) by 4
20x + 12y = 136
2x + 12y = 73
subtract the equations to eliminate y
18x = 63
divide both sides by 18
x = 63/18
x = 3.5
Substitute x = 3.5 into (1)
5x + 3y = 34
5(3.5) + 3y = 34
17.5 + 3y = 34
3y = 34 - 17.5
3y = 16.5
y = 16.5/3
y = 5.5
Therefore, $3.5 and $5.5 is the rental cost of each movie and video game respectively.
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What is the equation of the circle in the standard (x, y) coordinate plane that has a radius of 4 units and the same center as the circle determined by x^2 + y^2 - 6y + 4=0?
A. x² + y^2 = -4
B. (x+3)^2 + y^2 = 16
C. (x-3)^2 + y^2 = 16
D. x^2 + (y+3)^2 = 16
E. x^2 + (y-3)^2 = 16
Answer:
E. x² + (y - 3)² = 16
Step-by-step explanation:
The equation of a circle in the standard (x, y) coordinate plane with center (h, k) and radius r is given by:
[tex]\boxed{(x - h)^2 + (y - k)^2 = r^2}[/tex]
To find the equation of the circle with a radius of 4 units and the same center as the circle determined by x² + y² - 6y + 4 = 0, we need to first write the equation of the second circle in the standard form.
We can complete the square for y to rewrite this equation in standard form. To do this move the constant to the right side of the equation:
[tex]\implies x^2 + y^2 - 6y + 4 = 0[/tex]
[tex]\implies x^2 + y^2 - 6y = -4[/tex]
Add the square of half the coefficient of the term in y to both sides of the equation:
[tex]\implies x^2 + y^2 - 6y +\left(\dfrac{-6}{2}\right)^2= -4+\left(\dfrac{-6}{2}\right)^2[/tex]
[tex]\implies x^2 + y^2 - 6y +9= -4+9[/tex]
[tex]\implies x^2 + y^2 - 6y +9=5[/tex]
Factor the perfect square trinomial in y:
[tex]\implies x^2+(y-3)^2=5[/tex]
[tex]\implies (x-0)^2 + (y-3)^2=5[/tex]
So the center of this circle is (0, 3) and its radius is √5 units.
Since the new circle has the same center, its center is also (0, 3).
We know its radius is 4 units, so we can write the equation of the new circle as:
[tex]\implies (x - 0)^2 + (y - 3)^2 = 4^2[/tex]
[tex]\implies x^2 + (y - 3)^2 = 16[/tex]
Therefore, the equation of the circle in the standard (x, y) coordinate plane with a radius of 4 units and the same center as the circle determined by x² + y² - 6y + 4 = 0 is x² + (y - 3)² = 16.
To find:-
The equation of circle which has a radius of 4units and same centre as determined by x² + y² - 6y + 4 = 0.Answer:-
The given equation of the circle is ,
[tex]\implies x^2+y^2-6y + 4 = 0 \\[/tex]
Firstly complete the square for y in LHS of the equation as ,
[tex]\implies x^2 + y^2 -2(3)y + 4 = 0 \\[/tex]
Add and subtract 3² ,
[tex]\implies x^2 +\{ y^2 - 2(3)(y) + 3^2 \} -3^2 + 4 = 0 \\[/tex]
The term inside the curly brackets is in the form of a²-2ab+b² , which is the whole square of "a-b" . So we may rewrite it as ,
[tex]\implies x^2 + (y-3)^2 -9 + 4 = 0 \\[/tex]
[tex]\implies x^2 + (y-3)^2 - 5 = 0 \\[/tex]
[tex]\implies x^2 + (y-3)^2 = 5\\[/tex]
can be further rewritten as,
[tex]\implies (x-0)^2 + (y-3)^2 = \sqrt5^2\\[/tex]
now recall the standard equation of circle which is ,
[tex]\implies (x-h)^2 + (y-k)^2 = r^2 \\[/tex]
where,
(h,k) is the centre.r is the radius.So on comparing to the standard form, we have;
[tex]\implies \rm{Centre} = (0,3)\\[/tex]
Now we are given that the radius of second circle is 4units . On substituting the respective values, again in the standard equation of circle, we get;
[tex]\implies (x-h)^2 + (y-k)^2 = r^2 \\[/tex]
[tex]\implies (x-0)^2 + (y-3)^2 = 4^2 \\[/tex]
[tex]\implies \underline{\underline{\red{ x^2 + (y-3)^2 = 16}}}\\[/tex]
and we are done!
QUICK ANSWER THIS PLEASE What is the constant of proportionality between the corresponding areas of the two pieces of wood?
3
6
9
12
Answer:
Step-by-step explanation:
D
The function rule for this graph is Y equals___ X + ___
The answer is below in case someone needs it.
The function rule for this graph is y = -1/2(x) + 2.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]
Where:
m represent the slope.x and y represent the points.At data point (0, 2), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 2 = \frac{(0- 2)}{(4 -0)}(x -0)[/tex]
y - 2 = -1/2(x)
y = -1/2(x) + 2.
In this context, we can reasonably infer and logically deduce that an equation of the line that represents this graph in slope-intercept form is y = -1/2(x) + 2.
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A blue whale is currently diving down beneath the ocean. After 4 minutes, the blue whale is 33.7 meters below sea level, and after 13mins, the blue whale is 99.4 meters below sea level. If the blue whale is diving at a constant rate, how long will it take to reach a depth of 190.65 meters below sea level? To answer this, construct a linear function.
please hurry i dont want to fail
The problem asks for the time, we know that the blue whale will reach a depth of 190.65 meters below sea level after 26.7 minutes.
How can you tell if a function is linear?If a function is linear or not, its graph can be examined to determine. A straight line results from the graphing of a linear function. A nonlinear function has some sort of curve in contrast to a linear function.
The slope and y-intercept must first be determined in order to build a linear function. The slope can be determined using the two provided locations (4, -33.7) and (13, -99.4):
slope is the product of (y-change) and (change in x)
slope = (-99.4 - (-33.7)) / (13 - 4)
slope = -65.7 / 9
slope = -7.3
We can now use the point-slope form of a linear equation to obtain the equation of the line since we know its slope:
y - y1 = m(x - x1)
y - (-33.7) = -7.3(x - 4)
y + 33.7 = -7.3x + 29.2
y = -7.3x - 4.5
The following is the linear function that plots the blue whale's depth below sea level against time (x):
y = -7.3x - 4.5
We can plug in this number for y and solve for x to get how long it will take the blue whale to descend 190.65 metres below sea level:
190.65 = -7.3x - 4.5
195.15 = -7.3x \sx = -26.7
We know that the blue whale will descend to a depth of 190.65 metres below sea level in 26.7 minutes because the problem specifically asks for the time.
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A screen has a zoom of 140%, which means that images on the screen are 140% as long and 140% as wide as when they are printed on a sheet of paper. An image of a house is 17 cm tall when printed on a sheet of paper. How tall would the image of the house be on the screen? Give your answer in centimetres (cm).
Answer:
23.8 cm
Step-by-step explanation:
17 * 140% = 17 * 1.4 = 23.8 cm
The image of the house would be 23.8 cm tall on the screen.
To calculate the height of the image of the house on the screen, we can use the given zoom factor of 140%.
The zoom factor of 140% means that the images on the screen are 140% as long and 140% as wide compared to when they are printed on a sheet of paper.
To calculate the height of the image on the screen, we need to multiply the printed height by the zoom factor (140% or 1.4).
Height on the screen = Printed height * Zoom factor
Height on the screen = 17 cm * 1.4
Height on the screen = 23.8 cm
Therefore, the image of the house would be 23.8 cm tall on the screen.
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Find the area of the parallelogram. Round to the nearest hundredth if necessary.
Answer:
Step-by-step explanation:
5m(4m) = 20m^2
Daniel opens a new savings account and makes an initial deposit of $1,200.
If the account earns 2.5%
annual interest, which equation shows how much money is in the account in 9
months?
Responses
A x=1,200+1,200(0.25)(0.75)
x is equal to 1 comma 200 plus 1 comma 200 0 point 2 5 0 point 7 5
B x=1,200+1,200(0.025)(0.75)
x is equal to 1 comma 200 plus 1 comma 200 0 point 0 2 5 0 point 7 5
C x=1,200+1,200(0.25)(9)
x is equal to 1 comma 200 plus 1 comma 200 0 point 2 5 9
D x=1,200+1,200(0.025)(9)
Answer:
D) x = 1,200 + 1,200(0.025)(9)
In this equation, 1,200 is the initial deposit, 0.025 is the decimal representation of the annual interest rate, and 9 represents the time period in months. The multiplication of 0.025 and 9 gives the proportion of interest earned in 9 months, which is then multiplied by the initial deposit and added to it to give the total amount in the account after 9 months.
Simplifying the equation:
x = 1,200 + (1,200)(0.025)(9)
x = 1,200 + 270
x = 1,470
Therefore, there would be $1,470 in the account after 9 months
HELP what is the answer to this using systems of equations
y=1/8x−1
−5x+4y=−13
Answer:
x = 2
y = -3/4
Step-by-step explanation:
1. Substitute y=1/8x -1 in −5x+4y=−13
-5x+4(1/8x -1) = -13
2. Solve for x
-5x + 4/8x - 4 = -13
-9/2x - 4 = -13
-9/2x = -9
x = 2
3. Now that you know x = 2, plug it into y=1/8x - 1 to find what y is.
y= 1/8(2) - 1
y= 2/8 - 1
y= -3/4
Answer this imagine please
Answer:
B) Group 2
Step-by-step explanation:
Group 1 wrote it correctly because there are 3 groups of 4x and 3 groups of 3
Group 2 wrote it incorrectly because that would mean 9 groups of 4x, which is not the case here
Group 3 wrote it correctly because 3(4x) + 3(3) = 3(4x+3) due to the Distributive Property
Group 4 wrote it correctly because it is an expansion of Group 3's expression
11/12 x 8/25 x 15/16 x 9/44
The base of a triangle is 3 inches shorter than its height. Its area is 275 square inches. Set up a quadratic equation and solve to find its base and height.
Answer: hope its help
Let's start by assigning variables to the unknown quantities in the problem. Let h be the height of the triangle in inches, and let b be the base of the triangle in inches.
According to the problem, the base of the triangle is 3 inches shorter than its height. This can be expressed as:
b = h - 3
The formula for the area of a triangle is:
A = (1/2)bh
We are given that the area of the triangle is 275 square inches, so we can substitute these values into the formula to get:
275 = (1/2)(h)(h-3)
Simplifying the right-hand side, we get:
275 = (1/2)(h^2 - 3h)
Multiplying both sides by 2 to eliminate the fraction, we get:
550 = h^2 - 3h
Rearranging this equation to standard quadratic form, we get:
h^2 - 3h - 550 = 0
Now we can solve for h using the quadratic formula:
h = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -3, and c = -550, so we can substitute these values into the formula to get:
h = (-(-3) ± sqrt((-3)^2 - 4(1)(-550))) / (2(1))
Simplifying the expression inside the square root, we get:
h = (3 ± sqrt(2209)) / 2
We can ignore the negative solution since height must be positive, so we get:
h = (3 + sqrt(2209)) / 2 ≈ 29.04
Now that we know the height of the triangle is approximately 29.04 inches, we can use the equation b = h - 3 to find the length of the base:
b = 29.04 - 3 = 26.04
Therefore, the base of the triangle is approximately 26.04 inches, and the height is approximately 29.04 inches.
Step-by-step explanation:
In each of Problems 6 through 9, determine the longest interval in which the given initial value problem is certain to have a unique twice- differentiable solution. Do not attempt to find the solution. 6. ty" + 3y = 1, y(1) = 1, y'(1) = 2 7. t(t – 4)y" + 3ty' + 4y = 2, y(3) = 0, y'(3) = -1 8. y" + (cost)y' + 3( In \t]) y = 0, y(2) = 3, y'(2) = 1 9. (x - 2)y"+y' +(x - 2)(tan x) y = 0, y(3) = 1, y'(3) = 2 = ) y( = = = - =
(a) The interval (-∞, ∞).
(b) The interval (-∞, ∞).
(c) The interval (-∞, ∞).
(d) The interval (-π/2, π/2) \ {0}.
(a) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient function, 3t, is continuous and bounded. Since 3t is a continuous and bounded function for all t in the interval (-∞, ∞), the given initial value problem is certain to have a unique twice-differentiable solution for all t in (-∞, ∞).
(b) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient functions, t(t - 4), 3t, and 4, are continuous and bounded. Since t(t - 4), 3t, and 4 are continuous and bounded functions for all t in the interval (-∞, ∞), the given initial value problem is certain to have a unique twice-differentiable solution for all t in (-∞, ∞).
(c) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient functions, cost and In|t|, are continuous and bounded. Since cost and In|t| are continuous and bounded functions for all t in the interval (-∞, ∞), the given initial value problem is certain to have a unique twice-differentiable solution for all t in (-∞, ∞).
(d) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient functions, x - 2, 1, and (x - 2)tanx, are continuous and bounded. Since x - 2, 1, and (x - 2)tanx are continuous and bounded functions for all x in the interval (-π/2, π/2) \ {0} , the given initial value problem is certain to have a unique twice-differentiable solution for all x in (-π/2, π/2) \ {0}.
Learn more about twice-differentiable solution here
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The given question is incomplete, the complete question is:
determine the longest interval in which the given initial value problem is certain to have a unique twice- differentiable solution. Do not attempt to find the solution. (a) ty" + 3y = 1, y(1) = 1, y'(1) = 2 (b) t(t – 4)y" + 3ty' + 4y = 2, y(3) = 0, y'(3) = -1 (c) y" + (cost)y' + 3( In |t|) y = 0, y(2) = 3, y'(2) = 1 (d) (x - 2)y"+y' +(x - 2)(tan x) y = 0, y(3) = 1, y'(3) = 2
