Answers
The resulting matrix after row 1 is multiplied by 2 is given as follows:
[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
The first row is given as follows:
7, -4 and 8.
Multiplying the first row by two, we have that:
7 x 2 = 14.-4 x 8 = -8.8 x 2 = 16.(when we multiply a matrix by a constant, each element of the matrix is multiplied by the constant).
Hence the resulting matrix is given as follows:
[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]
(the second row was kept constant, while the first row was multiplied by 2).
Missing InformationThe matrix is:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
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Related Questions
Virginia earns $69,500 per year at her job as a speech pathologist, and she is paid every two weeks. Her most recent paycheck included the following deductions: FICA $200.20 Federal income tax $180.65 State income tax $72.00 Health insurance $110.00 Retirement savings $250.00 Considering her deductions, what percentage of her gross pay did Virginia take home? 71.65% 62.34% 69.59% 68.55%
Answers
Answer
Construction Model Stats
User
Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?
ChatGPT
To find the mean, we add up all the values and divide by the number of values:
Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10
Mean = 36.7 / 10
Mean = 3.67
To find the median, we need to put the values in order:
2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4
The middle number is the median, which is 3.35 in this case.
To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.
To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:
2.5, 2.6, 2.8, 3.1, 3.2
The median of this lower half is 2.8, so Q1 = 2.8.
To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:
3.7, 3.8, 4.1, 9.4
The median of this upper half is 3.95, so Q3 = 3.95.
To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1
IQR = 3.95 - 2.8
IQR = 1.15
1.5 times the IQR is 1.5 * 1.15 = 1.725.
The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.
User
The angle of elevation to the top of a building is found to be 18 degrees from the ground at a distance of 510 feet from the base of the building. Using this information, find the height of the building to the nearest whole number.
ChatGPT
We can use trigonometry to solve this problem. Let h be the height of the building, and let d be the distance from the base of the building to the point where the angle of elevation is measured. Then we have:
tan(18 degrees) = h / d
Solving for h, we get:
h = d * tan(18 degrees)
Substituting d = 510 feet and using a calculator to evaluate the tangent of 18 degrees, we get:
h = 510 feet * tan(18 degrees)
h ≈ 157.3 feet
Rounding this to the nearest whole number, we get that the height of the building is approximately 157 feet.
User
The following regular polygon has 15 sides. This distance from its center to any given vertex is 12 inches.
Which of the following is the best approximation for its perimeter?
(1) 68 inches
(3) 84 inches
(2) 75 inches
(4) 180 inches
ChatGPT
To find the perimeter of a regular polygon with n sides, we can use the formula:
Perimeter = n * s
where s is the length of each side. To find s, we can use trigonometry to find the length of one of the sides and then multiply by the number of sides.
In a regular polygon with n sides, the interior angle at each vertex is given by:
Interior angle = (n - 2) * 180 degrees / n
In a 15-sided polygon, the interior angle at each vertex is:
(15 - 2) * 180 degrees / 15 = 156 degrees
If we draw a line from the center of the polygon to a vertex, we form a right triangle with the side of the polygon as the hypotenuse, the distance from the center to the vertex as one leg, and half of the side length as the other leg. Using trigonometry, we can find the length of half of the side:
sin(78 degrees) = 12 / (1/2 * s)
s = 2 * 12 / sin(78 degrees)
s ≈ 2.17 inches
Finally, we can find the perimeter of the polygon:
Perimeter = 15 * s
Perimeter ≈ 32.55 inches
Rounding this to the nearest whole number, we get that the best approximation for the perimeter is 33 inches. Therefore, the closest option is (1) 68 inches.
Answer:
To find the percentage of Virginia's gross pay that she took home after deductions, we need to first calculate her gross pay and then subtract the total amount of deductions to find her net pay. Then, we can divide her net pay by her gross pay and multiply by 100 to find the percentage.
Virginia earns $69,500 per year, so her gross pay per paycheck (assuming she is paid every two weeks) is:
$69,500 / 26 = $2,673.08
Her total deductions from her most recent paycheck were:
$200.20 + $180.65 + $72.00 + $110.00 + $250.00 = $812.85
So her net pay was:
$2,673.08 - $812.85 = $1,860.23
To find the percentage of her gross pay that she took home, we can divide her net pay by her gross pay and multiply by 100:
($1,860.23 / $2,673.08) x 100 ≈ 69.59%
Therefore, the closest option is (3) 69.59%.
The data table shows the
numbers of eggs laid by
individual chickens in a year
What is the median number of
eggs laid in a year?
A. 231
B 229
C. 230
D. 234.6
Answers
The median number of eggs laid in a year is 231 from the given data, option A is correct.
The data table shows the numbers of eggs laid by individual chickens in a year.
Now, We can arrange it into ascending order as;
⇒ 222, 229, 229, 231, 234, 235, 262
Since, There are 7 terms
Hence, Median = (7 + 1)/2
= 4th term
= 231
Hence, the median number of eggs laid in a year is 231, option A is correct.
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Solve for x. Round to the nearest tenth, if necessary.
Answers
8.69 is the length of the right angle.
Let's call the length you are trying to find x.
Using trigonometry, we know that:
cos(75) = x/9
Solving for x:
x = 9sin(75)
The sine function (sin) is a mathematical function commonly used in trigonometry. It relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse.
Using a calculator to find the cosine of 75 degrees:
x ≈ 8.69
Therefore, the length you are trying to find is approximately 8.69.
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A sphere is pictured below. Select the type of cross section formed when the figure is cut by a horizontal plane.
A) circle
B) triangle
C) hexagon
D) rectangle
Answers
Answer:
A) circle.
When a sphere is cut by a horizontal plane, the resulting cross section is a circle. This is because a sphere is a three-dimensional object that is perfectly symmetrical in all directions, so any plane that intersects it will create a circular cross section.
Answer:
the answer is A) circle.i need help as soon as possible!
Answers
Answer:
2600This is a probability conversion problem.
A recipe uses 1 1/4 cups of milk to make 10 servings. If the same amount of milk is used for each serving, how many servings can be made using 1 gallon of milk?
Answers
Answer:
128 servings
Step-by-step explanation:
It takes 1 1/4 cups to make 10 servings
1 1/4 as a mixed fraction = 5/4
So 5/4 cups makes 10 servings
1 cup makes 10 ÷ 5/4
Use the fraction rule for division
a/b ÷ c/d = a/b x c/d
10 ÷ 5/4 = 10 x 4/5 = 8 servings from 1 cup
1 gallon = 16 cups
At 8 servings per cup, total number of servings for 16 cups
= 8 x 16 = 128 servings ANSWER
Express the following probability as a simplified fraction and as a decimal.
If one person is selected from the population described in the table, find the probability that the person is or .
Answers
Note that the following probability as a simplified fraction and as a decimal is: 0.88617886178 and 109/123
How is this so?Note that the key phrase here is “given that this person is a man.”
This means that all we are interested in is the row labeled Male.
Married Never Div Widowed Total
Male 69 40 11 3 123
We are asked to find the probability that the person was either Married or Never. So the fraction you want is (69 + 40) / 123.
⇒ (69 + 40) / 123.
⇒ 109/123
or 0.886179
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Express the following probability as a simplified fraction and a decimal.
if one person is selected from the population described in the table, find the probability that the person has never been married or is married, given that this person is a man.
Married Never Married Divorced Widowed Total
Male 69 40 11 3 123
Female 67 33 20 5 125
Total 136 73 31 8 248
Question 1.Express the probability as a simplified fraction
when the sun is 35° above the horizon. how long is the shadow cast by a building 15 metres high?
Answers
Therefore , the solution of the given problem of trigonometry comes out to be approximately 21.424 metres long when the sun is 35 degrees above the horizon.
What is trigonometry?Some people assert that the growth of astrophysics was influenced by the merging of various fields. Many metric problems can be solved or the result of a calculation can be ascertained with the use of exact mathematical techniques. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They go by many other names and acronyms, including sine, variance, direction, and others. (csc).
Here,
When the sun is at a 35° elevation angle and the structure is 15 metres tall, we want to determine the length of the shadow (on the next side).
Let x represent the desired shadow's length. Next, we have
=> tan 35° = 15/x
When we multiply both sides by x, we obtain:
=> x tan 35° = 15
By dividing both sides by 35° of tan, we obtain:
=> x = 15 / tan 35°
We may calculate the value of the tangent of 35 degrees using a calculator:
=> tan 35° ≈ 0.7002
Next, we have
=> 15x/0.702x=21.424 metres
Consequently, a building 15 metres high will create a shadow that is approximately 21.424 metres long when the sun is 35 degrees above the horizon.
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ces
Which sequence below would best model the
following description?
A newly planted tree releases 250 pounds of
oxygen over the period of its first year. The amount
of oxygen released by the tree grows at a rate of
12% per year, but the tree cannot generate more
than 6000 pounds of oxygen per year.
Answers
The correct sequence to model the given scenario is (b) f(n) = 1.12f(n-1)(1- f(n-1/6000)), and we can use this formula to calculate the oxygen released by the tree in each year, option (b) is correct.
The amount of oxygen released by the tree increases at a rate of 12% per year, which is represented by the factor 1.12f(n-1).
However, the tree cannot generate more than 6000 pounds of oxygen per year, which is represented by the limiting factor:
(1- f(n-1/6000)).
To understand this better, let's calculate the oxygen released by the tree in the second year using the formula
f(n) = 1.12f(n-1)(1- f(n-1/6000)).
f(2) = 1.12f(1)(1- f(1)/6000)
= 1.12(250)(1- 250/6000)
= 295.67 pounds of oxygen
Hence, option (b) is correct.
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The correct question is:
Which sequence below would best model the following description? A newly planted tree releases 250 pounds of oxygen over the period of its first year. The amount of oxygen released by the tree grows at a rate of 12% per year, but the tree cannot generate more than 6000 pounds of oxygen per year.
a. f(n) = 1.12f(n-1)(1+ f(n-1/6000)
b. f(n) = 1.12f(n-1)(1- f(n-1/6000)
c. f(n) = 1.12f(n-1) {6000/f(n-1)}
d. f(n) = 1.12f(n-1)(f(n-1) -6000)
A vehicle purchased for $29800 depreciates at a constant rate of 7% per year. Determine the approximate
value of the vehicle 11 years after purchase.
Round to the nearest whole number.
Answers
The exponential value decay equation is solved and the value of the vehicle after 11 years is A = $ 13,413
Given data ,
Let the initial cost of the vehicle be = $ 29,800
Now , the rate of depreciation be r = 7 %
Let the number of years be n = 11 years
And , the exponential decay is given by the equation ,
x ( t ) = x₀ × ( 1 + r )ⁿ
On simplifying , we get
x ( 11 ) = 29800 ( 1 - 0.07 )¹¹
x ( 11 ) = 29800 ( 0.93 )¹¹
x ( 11 ) = 13,413.085
Hence , the cost of the vehicle after 11 years is A = $ 13,413
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Malachi asks students in his class, "How long does it take you to get to school?" The histogram
shows the data.
Which statement best describes the distribution?
Answers
Answer:
The distribution is symmetric
Step-by-step explanation:
Because in both sides it has the same structure, so that means that the value is the same in both sides
collect data on the OBSERVATION table in ANNEXURE A to record 30 days of the minimum and maximum temperature in your community
Answers
Here, We provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.
To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:
25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22
The sum of the values is:
25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813
Dividing by the number of values (30), we get:
Mean = 813/30 = 27.1
To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.
To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:
20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34
There are 30 values, so the median is the 15th value, which is 28.
To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:
Range = 34 - 20 = 14
To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:
20-24, 25-29, 30-34
The frequency table would look like this:
Interval | Frequency
20-24 | 4
25-29 | 18
30-34 | 8
To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:
Proportion = Frequency/Total frequency = 18/30 = 0.6
Angle = Proportion x 360° = 0.6 x 360° = 216°
We can repeat this calculation for each interval to obtain the angles for the pie chart.
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HELP
Solve for c.
34 degrees
27 degrees
11
c?
Answers
The value of side length c is 13.55 units.
What is the length of side C?The length of side c is calculated by applying sine rule as shown below;
The formula for sine rule is given as;
a/sinC = b/sinA
For the given question, we will have the following equation,
c/sin (34) = 11 / sin (27)
The value of c in the triangle is calculated as follows;
c = (sin 34 / sin 27 ) x 11
c = 13.55 units
Thus, the value of side length c is determined by applying sine rules.
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Pls help i rlly need help
Answers
Answer:
C. Luisa is incorrect, it's not 0. It's only zero when you get "x=0" as an answer but the variable x got canceled here. And as 3=3, it is a true statement so it includes all real numbers. If you had gotten 3=8 for example, it would be a fake statement, so then no solution.
And for the second part,
1. No solution
5x+24=5x+25
24=25
It's false
2. One solution
12p-7=-3p+8
15p=15
P=1
3. One solution.
3x+20=5x
20 = 2x
X = 10
Of the 22 students in a classroom, 10 are transfer students, 7 are nursing students, 4 are AAS students and 1 student is undecided. If 5 students are chosen randomly, with replacement, find the probability that at least one student is a transfer student.
Answers
The probability that a randomly chosen student is not a transfer student is 12/22, since there are 12 students who are not transfer students out of a total of 22 students. Therefore, the probability that none of the 5 students chosen are transfer students is:
(12/22)^5 = 0.068
To find the probability that at least one student is a transfer student, we can subtract this from 1:
1 - 0.068 = 0.932
Therefore, the probability that at least one student is a transfer student is 0.932.
find surface area of rectangular prism 2.5 2 14 1.5
Answers
The surface area of the rectangular prism is 24.62 square units
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
2.5 by 2.14 by 1.5
The surface area of the rectangular prism is calculated as
Area = 2 * (Length * Width + Length * Height + Height * Width )
substitute the known values in the above equation, so, we have the following representation
Area = 2 * (2.5 * 2.14 + 2.5 * 1.5 + 2.14 * 1.5)
Evaluate
Area = 24.62
Hence, the surface area is 24.62 square units
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the perimeter of a triangle is 53 inches. the length of the one side is 15 inches the other two sides are congruent find the lengths
Answers
Billy Bob wants to paint the outside wall of his circular pool. The circular
wall is 4 feet tall and has a radius of 15 feet. If paint cost $28 per gallon and
covers 225 square feet, how much will it cost to paint the wall. The paint is
only avaliable in gallon containers.
Answers
The first step is to calculate the surface area of the circular wall of the pool, which can be calculated using the formula:
A = 2πrh
where A is the surface area, π is the mathematical constant pi (approximately equal to 3.14159), r is the radius of the circular wall, and h is the height of the wall.
In this case, the radius is 15 feet and the height is 4 feet, so:
A = 2π(15)(4)
A = 376.99 square feet
The next step is to calculate how many gallons of paint will be needed. Since one gallon of paint covers 225 square feet, we can divide the surface area by the coverage per gallon:
Gallons = A / Coverage per gallon
Gallons = 376.99 / 225
Gallons = 1.68
Since the paint is only available in gallon containers, Billy Bob will need to purchase 2 gallons of paint to ensure that he has enough to cover the entire surface.
Finally, we can calculate the total cost of the paint by multiplying the number of gallons by the cost per gallon:
Total cost = Number of gallons x Cost per gallon
Total cost = 2 x $28
Total cost = $56
Therefore, it will cost Billy Bob $56 to paint the circular wall of his pool.
The amount it would cost to paint the wall, given the cost of paint and the area covered is $ 56 .
How to find the cost to paint ?The surface area of the circular wall would be :
A = 2 x π x r x h
The area is therefore:
= 2 x π x r x h
= 2 x 3. 14 x 15 x 4
= 376. 8 square feet
The number of gallons needed is therefore:
= 376. 8 / 225
= 1. 674
= 2 gallons
The cost of two gallons is:
= 2 x 28
= $ 56
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In the given Venn-diagram, if n(AUB) = 50, find n (A).
n°(A) = 2a
n°(B)=a
n(A[intersection]B)=20
Answers
n(A U B) = n(A) + n(B) - n(A [intersection] B)
Substituting the given values, we get:
50 = 2a + a - 20
Simplifying and solving for a, we get:
a = 35
Therefore, n(A) = 2a = 2(35) = 70.
So, the value of n(A) is 70.
Answer:
n(A U B) = n(A) + n(B) – n(A ∩ B)
putting values we get
50 = 2a + a - 20
solving eqn.
70 = 3a
a = 70 / 3
now n(a) = 2a
= 2 x 70/3
= 140/3
hence, n(a) = 140/3
How do I find the parabola of the following. I tried to start. I do not know if I am on the right track, and if I am on the right track, what are the next steps to find and plot the parabola?
Thank you,
(x+4)(x+2)=0
((x+2)+4(x+2)
x^2 +2x+4x+8
X^2+6x+8
Answers
You are on the right track! To find the equation of the parabola given by the equation x^2 + 6x + 8 = 0, you can use the standard form of a quadratic equation, which is:
y = a(x - h)^2 + kwhere (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the parabola.
To get the equation of your parabola, you first need to complete the square on the x terms of the given equation:
x^2 + 6x + 8 = 0x^2 + 6x = -8(x + 3)^2 - 9 = -8(x + 3)^2 = 1From this equation, you can see that the vertex of the parabola is at (-3, -1) and the value of a is positive. This means that the parabola opens upwards.
To find the value of a, you can compare the equation with the standard form of the quadratic equation:
y = a(x - h)^2 + kwhere h = -3, k = -1, and a is the coefficient you need to find. Substituting these values into the equation gives:
-1 = a(-3 - (-3))^2 - 1-1 = a(0)^2 - 1a = 1So the equation of the parabola is:
y = (x + 3)^2 - 1To plot the parabola, you can use the vertex (-3, -1) as a starting point and then use the coefficient a to determine the shape of the parabola. Since a is positive, the parabola opens upwards.
HELP ASAP WILL GIVE BRAINLIEST
Use the graph to answer the question.
2
O
21/1/201
O
D'
IN
A
2
Determine the scale factor used to create the image.
C'
2.5
B'
D
A
11
C
2
В
B
Answers
Answer:
1/4
Step-by-step explanation:
The scaled image is 1/4 of the size of the original, we can see this as one side of the original shape is 4 units, and the scaled side is 1 unit.
Daniel incorrectly solved the equations shown. Explain what he did wrong in each solution and then solve both equations correctly.
25x^2-16=9
√(25x^2 )-√16=√9
5x-4=±3
5x=±7
x=±7/5
z^3-2=6
z^3=8
∛(z^3 )=∛8
z=±2
PLease help
Answers
1. 25x^2 - 16 = 9
Daniel's mistake: He took the square root of each term separately, which is not correct.
Explanation: When we take the square root of an equation, we must take the square root of both sides of the equation, not just each term separately.
Correct solution:
25x^2 - 16 = 9
25x^2 = 25
x^2 = 1
x = ±1
Therefore, the correct solutions are x = 1 and x = -1.
2. z^3 - 2 = 6
Daniel's mistake: He correctly found the cube root of 8, but forgot to consider the negative cube root as well.
Explanation: When we take the cube root of an equation, we must consider both the positive and negative cube roots, since a cube can have both a positive and negative cube root.
Correct solution:
z^3 - 2 = 6
z^3 = 8
z = ∛8
z = 2 or -2
Therefore, the correct solutions are z = 2 and z = -2.
Can someone help me with this? I can't figure it out
Answers
In linear equation, 9 is the constant of variation k.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.
given x varies inversely with y then
xy = k ← k is the constant of variation
to find k use the condition x = - 4 when y = - 9, hence
k = -4 × -9 = 36
x = 36/y
when x = 4 , then y = 36/4
x = 9
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A sidewall of a building is shown below. Apply a formula to find the area of the wall.
Answers
Answer:1020 ft (squared)
Step-by-step explanation:
Base width 1 (28 ft) x Base width 2 (40 ft) x height (6 ft) = 1020 ft (squared)
AM
CM
AM = CM
Which step is missing in the proof?
A. AMDA
B.
AMDA
OC. AMDA
D.
AMDA
CPCTC
definition of congruence
=
~
~
AMCB by ASA
AMBC by ASA
AMBC by SAS
ABMC by SAS
Answers
The missing step of the congruent triangles is ΔMDA ≅ ΔMBC by ASA theorem
Given data ,
Let the two triangles be represented as ΔMDA and ΔMBC
Now , the measure of side MD ≅ MB ( given )
And , the measure of angle ∠DMA ≅ ∠BMC ( vertical angles theorem )
Now , the measure of ∠MDA ≅ measure of ∠MBC ( alternate interior angles)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
So , ΔMDA ≅ ΔMBC by ASA theorem
Hence , the congruent triangles are solved
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4. Which of the following has the best price per unit?
Brand A $5.00 for 2
Brand C $7.00 for 7
Brand B $6.00 for 3
Brand C $8.00 for 3
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a cylinder candle has a diameter of 9 cm and a height of 12 CM. It is placed in a cylindrical box. there's a space of 0.5 CM between the candle and the box to allow for packaging material. what is the height of the cylindrical box?
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If a candle having diameter as 9 cm, height as 12 cm is placed in a cylindrical box, then the height of the cylindrical box will be 13cm.
The "cylindrical-candle" diameter is given as = 9 cm;
The "cylindrical-candle" height is given as = 12 cm;
The candle is placed in a box which has a space of 0.5 cm between the candle and the box for packaging material;
which means that, there will an additional 0.5 cm in the top and bottom of the candle,
So, the height of the "cylindrical-box" is written as : 0.5 + 12 + 0.5;
Therefore, the "cylindrical-box" has a height of 13 cm.
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A bank charges a monthly fee of 0.5% for a checking account. Lily’s account has $325 in it. Which function models the balance B of Lily’s account in dollars, as a function of time in months?
A. B(t) = 325(1 − 0.005)t
B. B(t) = 325(1 + 0.0005)t
C. B(t) = 0.05(1 − 3.25)t
D. B(t) = 325 + 12(1 + 0.0005)t
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The correct function that models the balance B of Lily’s account as a function of time in months is option A, which is B(t) = 325(1 − 0.005)ᵗ.
To see why, we can start with the initial balance of $325 and note that each month, the bank charges a monthly fee of 0.5%, which is equivalent to a monthly interest rate of 0.005. This means that after one month, the balance will be reduced by 0.5% or 0.005 times the original balance, giving:
B(1) = 325 - 0.005(325)
Similarly, after two months, the balance will be reduced by another 0.5% of the new balance, giving:
B(2) = (325 - 0.005(325)) - 0.005(325 - 0.005(325))
We can simplify this expression by factoring out the common factor of 325(1 - 0.005) after each term, giving:
B(2) = 325(1 - 0.005)²
Generalizing this pattern, we can see that after t months, the balance will be:
B(t) = 325(1 - 0.005)ᵗ
Therefore, option A is the correct function that models the balance of Lily’s account.
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I complete lost on this problem can you help me solve it
The line described by y = 3/4x+5 is tangent to a circle at the point (0, 5). The line described by 3x + 4y = 38 is tangent to the same circle at the point (6, 5). Find the equation of the circle.
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Answer:
(x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25
Step-by-step explanation:
The equation of a circle can be written in the form (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is its radius. Since the lines are tangent to the circle at points (0,5) and (6,5), we can use these points to find the center and radius of the circle.
First, let’s find the slope of each line. The slope of the line y = 3/4x+5 is 3/4. The slope of the line 3x + 4y = 38 can be found by rearranging it into slope-intercept form: y = (-3/4)x + 19/2. So the slope of this line is -3/4.
Since the lines are tangent to the circle, they are perpendicular to the radius at their point of tangency. This means that the center of the circle lies on the line that passes through (0,5) and has a slope of -4/3, and also on the line that passes through (6,5) and has a slope of 4/3.
Let’s find the equation of these two lines. The line passing through (0,5) with a slope of -4/3 has an equation y - 5 = (-4/3)(x - 0), or y = (-4/3)x + 5. The line passing through (6,5) with a slope of 4/3 has an equation y - 5 = (4/3)(x - 6), or y = (4/3)x - 3.
The center of the circle is at the intersection of these two lines. To find it, we can set their right-hand sides equal to each other and solve for x: (-4/3)x + 5 = (4/3)x - 3. Solving this equation gives us x = 24/5. Substituting this value into either equation for y gives us y = (4/3)(24/5) - 3 = 21/5.
So the center of the circle is at (24/5, 21/5). To find its radius, we can use either point of tangency. Let’s use (0,5). The distance between this point and the center is given by sqrt((0-24/5)^2 + (5-21/5)^2), which simplifies to sqrt(481)/5.
Therefore, the equation of the circle is (x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25.
For the function f(x)=|x-3 | select all the true statements. A. The function is increasing on the interval [3, 5) B. The function is increasing of the Interval (0, 3) C. The vertex is (0, 3) D. The vertex is (3, 0). E. The y-intercept is (0, 3). F. The y-intercept is (3, 0).
Answers
Answer:
D and E----------------------
See attached graph to help with answer choices.
Given function:
f(x) = | x - 3 |Answer choices:
A. The function is increasing on the interval [3, 5) - False, correct interval is [3, + ∞)B. The function is increasing on the Interval (0, 3) - False, as shown aboveC. The vertex is (0, 3) - False, the vertex is (3, 0)D. The vertex is (3, 0) - TRUEE. The y-intercept is (0, 3) - TRUEF. The y-intercept is (3, 0) - False, the correct one is given above