Answer:
Step-by-step explanation:
You need to find the volume if one shoe box by doing:
Length x Width x Height
Of the shoe box
Then multiply by 30 to get the volume for all the shoe boxes
pls mark me brainliest
Please help, this is due in 10 minutes, im giving 35 points for it.
The scientific and standard notation and clue obtained from the clue sheet are;
1. Name starts with; J
2. Difference = 145 million miles = Weight = 145 lbs
3. Height: 5 ft, 6 in
4. I. 2.54 × 10⁸ miles corresponding to letter I
II. 0.0005825 corresponds to letter G
III. 5.0432 × 10⁶ corresponds to letter N
IV. 1.547 × 10³ corresponds to letter R
V. 4.977 × 10⁻² corresponds to letter W
VI. 1.3 × 10¹⁰ light years away; corresponds to letter D
VII. 5.04 × 10⁻⁵ corresponds to letter A
The suspects hubby is DRAWING
What is the scientific notation of presenting numbers?Scientific notation is a format used to express very large or very small numbers such that they are much easier to work with. The scientific notation format is; a × 10ⁿ, where; a is the coefficient, which is a number between 1 and 10 (10 excluded), and n is an integer.
1. G = (6.07 × 10⁷)/(7.035 × 10³) ≈ 8628.29
J = (6.03 × 10⁻³)/(5.05 × 10⁻⁷) ≈ 11940.59
Therefore; J > G
The suspects name starts with J
2. The distance the telescope in the laboratory allows the viewer to see = 1.5 × 10⁹ miles away
The distance the other telescope a few hours away allows the viewer to see = 1.355 × 10⁹ miles away
The difference between the distances = (1.5 - 1.355) × 10⁹ miles = 1.45 × 10⁸ miles
The difference in the distance is 1.45 × 10⁸ miles = 145 million miles
The suspect weight is 145 lbs
3. The numbers are;
Feet; 532.063 × 10³ = 5.32063 × 10⁵
Inches; 5,030,045 = 5.030045 × 10⁶
The height of the suspect is 5 feet 6 inches (5'6'') = 5.5 feet
Height; = 5 ft, 6 in
4. I. The difference in distances between Earth and Saturn can be found as follows;
The difference in the distances = (1000 - 746) million miles = 254 million miles apart
Scientific notation is the expression of numbers in the form consisting of a number between 1 and 10, multiplied by 10 raised to a power
254 million miles = 2.54 × 10⁸ miles
The corresponding letter from the code cracker is; I
II Standard notation is the expression of numbers in the standard form without the use of exponents or special symbols
The number 5.825 × 10⁻⁴ in standard notation is; 0.0005825
The corresponding letter from the code cracker is; G
III. The number 504.32 × 10⁴ in scientific notation can be obtained by moving the decimal point two places to the left followed by increasing the index of 10 by 2 as follows;
504.32 × 10⁴ = 5.0432 × 10⁶
The corresponding letter from the code cracker is; N
IV. The sum of the numbers 1.202 × 10³ and 3.45 × 10² can be obtained by expressing both numbers to the same power of 10 as follows;
1.202 × 10³ + 3.45 × 10² = 12.02 × 10² + 3.45 × 10² = 15.47 × 10²
15.47 × 10² = 1.547 × 10³
Therefore; 1.202 × 10³ + 3.45 × 10² = 1.547 × 10³
The corresponding letter from the code cracker is; R
V. The difference of the numbers can be obtained as follows;
5.023 × 10⁻² - 4.6 × 10⁻⁴ = 502.3 × 10⁻⁴ - 4.6 × 10⁻⁴ = 497.7 × 10⁻⁴
497.7 × 10⁻⁴ = 4.977 × 10⁻²
Therefore; 5.023 × 10⁻² - 4.6 × 10⁻⁴ = 4.977 × 10⁻²
The corresponding letter from the code cracker is; W
VI. 13 billion light years = 13 × 10⁹ light years = 1.3 × 10¹⁰ light years
The distance a standard telescope can allow to be seen is 1.3 × 10¹⁰ light years away
The corresponding letter from the code cracker is; D
VII. 0.0000504 in scientific notation is; 5.04 × 10⁻⁵
The corresponding letter from the code cracker is; A
IGNRWDA
The suspects favorite hubby is DRAWING
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the classification of student class designation (freshman, sophomore, junior, senior) is an example of a) a categorical random variable. b) a discrete random variable. c) a continuous random variable. d) a parameter.
The classification of student class designation (freshman, sophomore, junior, senior) is an example of a categorical random variable. The correct option is A.
What is a random variable?A random variable is a numerical or categorical quantity whose value is unknown but whose behavior can be forecast based on data that has been measured or observed. Random variables are typically used to represent quantities that fluctuate over time or are subject to chance occurrences.
The types of random variables are as follows:
i) Categorical random variable: This type of variable contains categorical data or data that are descriptive in nature. It is used to classify items or events into categories, which can be named or identified. For example, a set of data that includes categories like gender, eye color, or country of origin.
ii) Discrete random variable: This type of variable takes on discrete values, which means it can only take on whole numbers. For example, the number of cars sold at a dealership on any given day is a discrete random variable because it can only take on integer values.
iii) Continuous random variable: This type of variable takes on continuous values, which means it can take on any value within a given range. For example, the temperature in a room can take on any value between a certain minimum and maximum value.
Therefore, the correct option is A.
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Solve each equation for the other variable. (Hint: This will involve rewriting each equation in exponential form at some step in the process.)
a. y = log6(X)
b. X = log2(y/21)
The solution for the other variable, according to the stated statement, is[tex]X = 6^y[/tex] and [tex]y = 21 * 2^X[/tex]
What is an exponential number?Exponential numbers are represented by an, where an is multiplied by itself n times. An easy example is 8=2³=222. In exponential notation, an is known as the base, whereas n is known as the power, exponent, or index. Scientific notation is an example of an exponential number, with 10 usually typically serving as the base number.
Why is the term exponential used?Exponential functions are often employed in the biological sciences to describe the amount of a certain quantity over time, such as population size. Experiment data graphs are often created with time on the x-axis and amount on the y-axis.
a. y = log6(X)
[tex]6^y = X[/tex]
[tex]X = 6^y[/tex]
b. [tex]X = log2(y/21)[/tex]
[tex]2^X = y/21[/tex]
[tex]21 * 2^X = y[/tex]
[tex]y = 21 * 2^X[/tex]
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Smoothie Activity
6. Using the relative frequency table, create a segmented bar graph by employee type using technology or by hand. If using Excel technology the columns may need to be switched after inserting the chart. Click on the chart and the "Chart Design" ribbon will pop up. Then select "Switch Row/Column." (10 points)
By answering the presented question, we may conclude that I used the following procedures to produce this graph.
What is graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph contains vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.
I used the following procedures to produce this graph:
I classified the personnel as full-time, part-time, and temporary.
I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."
I used the following procedures to produce this graph:
I classified the personnel as full-time, part-time, and temporary.
I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."
I made the segmented bar graph using these percentages.
The graph was made using Excel technology. You may make a similar graph with Excel or any other software that supports segmented bar graphs.
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Find the total amount and total interest after six months if the interest is compounded every quarter. Principal =₹10 000 Rate of interest =20% per annum.
Answer:I=(PxRxT)/100
I=(10000x20x1)/100x2
I=200000/200
I=1000
Step-by-step explanation:
1)A factory makes propeller drive shafts for ships. A quality assurance engineer at the factory needs to estimate the true mean length of the shafts. She randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. The lengths are known to follow a normal distribution whose standard deviation is 2 mm. Calculate a 95% confidence interval for the true mean length of the shafts. Input your answers for the margin of error, lower bound, and upper bound.
a)Determine Margin of Error for this 95% confidence interval.
b)Input the lower bound. (Round to three decimal places)
c)Input the upper bound. (Round to three decimal places)
2)To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n times and the mean of the weighings is computed. Suppose the scale readings are normally distributed with unknown mean μ and standard deviation σ = 0.01 g. How large should n be so that a 95% confidence interval for μ has a margin of error of ± 0.0001?
3)A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis for the standard treatment is two years. So the null hypothesis is that average survival time after diagnosis is the same for the new treatment and the standard treatment.
In an early trial, she tries the new treatment on three subjects, who have an average survival time after diagnosis of 4.5 years. Even though the sample is small, the results are statistically significant at the 0.05 significance level. Consequently, she rejects the null hypothesis.
In a future study, it is determined that the new treatment does not increase the mean survival time in the population of all patients with this particular type of cancer. The researcher has
Committed a type I error.
Incorrectly used a 0.05 significance test when she should have computed the P-value.
Incorrectly used a 0.05 significance level when she should have used a 0.01 significance level.
Committed a type II error.
4)If the level of significance, α{"version":"1.1","math":"\alpha"}, is made very small, thereby making the probability of committing a Type 1 error very small, what happens to the probability of committing a Type 2 error?
By reducing the probability of committing a Type 1 error, we increase the probability of committing a Type 2 error.
There is no specific relationship between the two probabilities.
By reducing the probability of committing a Type 1 error, we also reduce the probability of committing a Type 2 error.
The relationship between the two probabilities depends on how the study is set up.
Therefore, with a 95% confidence interval, we can estimate the true mean length of the drive shafts to be between 992.16 mm and 1007.84 mm.
The true mean length of the drive shafts can be estimated using a 95% confidence interval. The margin of error is calculated as 2*1.96*2 = 7.84 mm. The lower bound of the confidence interval is 1000 - 7.84 = 992.16 mm and the upper bound is 1000 + 7.84 = 1007.84 mm.
This confidence interval states that there is a 95% probability that the true mean length of the drive shafts falls within the range of 992.16 mm to 1007.84 mm. The relationship between the two probabilities is that the probability of the true mean length falling within the confidence interval is 95%. If the sample size was increased, the margin of error would decrease, resulting in a tighter range and higher probability that the true mean would fall within the confidence interval.
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F= (y + 2x, 2x + 5z, 7y + 8x), C is the circle with radius 5, cen- ter at (2,0,0), in the plane x = 2, and oriented counterclockwise as viewed from the origin (0,0,0).
The set of points that represent the intersection of the curve of vector function F and circle C is
{(4+10cos(t), 4+10cos(t), 16+40cos(t)) | t ranges from 0 to 2π}.
We have,
Vector function F = (y + 2x, 2x + 5z, 7y + 8x)
C is the circle with radius 5, center at (2,0,0), in the plane x = 2
C is oriented counterclockwise as viewed from the origin (0,0,0)
The vector function F represents a three-dimensional curve in space.
The circle C is a two-dimensional object in space, lying in the plane x = 2 and centered at (2,0,0) with a radius of 5. It is also oriented counterclockwise as viewed from the origin (0,0,0).
To find the intersection of vector function curve F and circle C, we can substitute the equation of the circle into the equation of the curve and solve for the parameter(s) that satisfy the equation. However, since the equation of the circle is given in terms of x only, we can simplify the equation of the curve by substituting y = 0 and z = 0:
F = (2x, 2x, 8x)
Now, we can substitute x = 2 + 5cos(t) and y = 5sin(t) (the parameterization of the circle C in the plane x = 2) into the equation of the curve F:
F = (2(2+5cos(t)), 2(2+5cos(t)), 8(2+5cos(t)))
= (4+10cos(t), 4+10cos(t), 16+40cos(t))
Thus, the intersection of vector function curve F and circle C is given by the set of points:
{(4+10cos(t), 4+10cos(t), 16+40cos(t)) | t in [0, 2π)}
Note- that the parameter t represents the angle of rotation around circle C, and ranges from 0 to 2π to cover the entire circle.
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a school pays 1,852 for 150 shirts . this includes the 25$ flat-rate shipping costs. c. what are the initial value and rate of change of the function? what does each on represent
Therefore, the initial value of the function is $1,852 and the rate of change is $12.18 per shirt. The initial value represents the cost of the shirts before any were purchased,
What is function?In mathematics, a function is a rule that assigns to each element in a set called the domain, a unique element in another set called the range. In other words, a function is a mathematical object that takes an input and produces a specific output, according to a specific set of rules or operations.
by the question.
et the initial value be represented by a and the rate of change by r.
The given information can be represented by the following equation:
a + 150r = 1,852
Since the flat-rate shipping cost is $25, the cost of the 150 shirts alone would be:
a + 150r - 25 = 1,827
The initial value, a, represents the cost of the shirts before any shirts were purchased. In this case, it would be the cost of the shirts if no shirts were purchased plus the flat-rate shipping cost of $25.
So, a = 1,827 + 25 = 1,852.
The rate of change, r, represents the increase in cost for each additional shirt purchased. In this case, it would be the cost of one shirt.
So, r = (1,852 - 25)/150 = 12.18.
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Una pintura incluyendo su marco tiene 25 cm de largo y 10 cm de ancho cuánto es el area del marco, si este tiene 4cm de ancho?
216 cm2 is the size of the rectangle border.
the translation of the question is
A painting including its frame is 25 cm long and 10 cm wide, what is the area of the frame if it is 4 cm wide?
What is a rectangle's area?
When the dimensions of a rectangle with length and width are multiplied, the area of the rectangle is determined as follows:
A = lw.
The total area is therefore given by:
A = 25 x 10 = 250 cm².
The white region's size is shown by:
A = (25 - 2 x 4) x (10 - 2 x 4) is equal to 17x 2 and 34 cm2.
Hence, the border's area is as follows:
216 cm2 = 250 cm2 - 34 cm2.
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Write an expression that can be a rule for the number sequence below.
5, 9, 13, 17, 21, …
The possible expression that can be a rule for the number sequence is:[tex]$a_n = 4n + 1$[/tex],
What is expression?As an illustration, the expression x + y is one where x and y are words with an addition operator in between. There are two types of expressions in mathematics: numerical expressions, which only comprise numbers, and algebraic expressions, which also include variables.
According to question:
One possible expression that can be a rule for the number sequence is:
[tex]$a_n = 4n + 1$[/tex], where n is the position of the term in the sequence.
Using this expression, we can find the values of the first few terms as follows:
[tex]$a_1 = 4(1) + 1 = 5$[/tex]
[tex]$a_2 = 4(2) + 1 = 9$[/tex]
[tex]$a_3 = 4(3) + 1 = 13$[/tex]
[tex]$a_4 = 4(4) + 1 = 17$[/tex]
[tex]$a_5 = 4(5) + 1 = 21$[/tex]
Thus, possible expression that can be a rule for the number sequence is:[tex]$a_n = 4n + 1$[/tex],
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Answer:
5n, where n is equal to 0, 1, 2, 3, 4
Step-by-step explanation:
5, 9, 13, 17, 21,
What is the probability of
drawing a face card, then
drawing a heart with
replacement
Answer:
n(s) =52. n(f) = 12 n(h) = 13
p (f)= 13/52. p(f)= 12/52
an inner city revitalization zone is a rectangle that is twice as long as it is wide. the width of the region is growing at a rate of 32 m per year at a time when the region is 220 m wide. how fast is the area changing at that point in time?
The area is changing at a rate of 28,160 m²/year at that point in time.
The area of the rectangular region is given by:
A = lw
Where l is the length of the rectangular region and w is the width of the rectangular region.
The width of the rectangular region is given to be 220 m. Therefore, we have the width w = 220 m. The length l of the rectangular region can be found knowing that it is twice as long as it is wide. Therefore, the length of the rectangular region is given by:
l = 2w
l = 2 x 220
l = 440
Therefore, the length l of the rectangular region is 440 m.
At the given point in time, the width of the rectangular region is growing at a rate of 32 m per year. Therefore, we have the rate of change of the width dw/dt to be 32 m per year. We need to find how fast the area of the rectangular region is changing at that point in time. Therefore, we need to find the rate of change of the area of the rectangular region dA/dt.
A = lw
dA/dt = w dl/dt + l dw/dt
dA/dt = 220 d/dt(2w) + 440 dw/dt
dA/dt = 220 x 2 dw/dt + 440 dw/dt
dA/dt = 880 dw/dt
Substitute the value of dw/dt to get:
dA/dt = 880 x 32
dA/dt = 28,160 m²/year
Therefore, the area of the rectangular region has a rate of change of 28,160 m² per year at that point in time.
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If Julie drives from York to corby via Derby. How many miles will she drive
Julie will have driven a total distance of 289 miles if she travels from York to Corby via Derby.
Starting from York, Julie needs to travel to Derby. The distance between York and Derby is given as 89 miles. So, we know that Julie will have driven 89 miles once she reaches Derby.
Next, Julie needs to travel from Derby to Corby, but the given information is a bit tricky here. The distance from Derby to Corby is not given directly. Instead, we are given two distances - Derby to Dory and Dory to Corby.
To find the distance from Derby to Corby, we need to add the distances between Derby and Dory, and Dory and Corby. From the question, we know that the distance between Derby and Dory is 127 miles and the distance between Dory and Corby is 73 miles. Adding these two distances gives us the total distance from Derby to Corby, which is 200 miles.
Finally, we can add up the distances traveled between each location to find the total distance traveled by Julie. Adding the distances of each leg of the journey, we get:
89 miles (York to Derby) + 200 miles (Derby to Corby via Dory) = 289 miles
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Complete Question:
If Julie drives from York to Corby via Dory how many miles will she have driven?
York 89
Derby 127 73
Corby
difference between repeating & terminating decimal
Answer: If you end up with a remainder of 0, then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.
Step-by-step explanation:
I hope that this helped! :)
5 x _ = -35
Topic: Multiplying and Dividing Integers
Given:
5× ______ = - 35
• -35/5
• -7
Answer:5 x -7 = -35
Answer:
The answer is 7
Step-by-step explanation:
Divide each term in 5x=-35 by 5 and simplify.x=−7
James have 18 litres of water. He poured unequally into 3 tank
I. Poured three quarter of water from tank one into tank 2
II. Poured half of the water that is now in tank 2 into tank 3
III. Poured one third of water that is now in tank 3 into tank 1
Answer:
Tank 1: 6 litres
Tank 2: 6.75 litres
Tank 3: 4.5 litres
Step-by-step explanation:
Initially, James had 18 litres of water, and he poured three-quarters of it from tank 1 into tank 2. This means that the volume of water left in tank 1 is:
18 - (3/4) * 18 = 4.5 litres
The volume of water in tank 2 is:
(3/4) * 18 = 13.5 litres
Next, he poured half of the water in tank 2 (which is now 13.5 litres) into tank 3. The volume of water left in tank 2 is:
(1/2) * 13.5 = 6.75 litres
The volume of water in tank 3 is:
13.5 * (1/2) = 6.75 litres
Finally, he poured one-third of the water in tank 3 (which is now 6.75 litres) into tank 1. The volume of water in tank 1 after this is:
4.5 + (1/3) * 6.75 = 6 litres
The volume of water in tank 3 after this is:
6.75 * (2/3) = 4.5 litres
So the final volume of water in each tank is:
Tank 1: 6 litres
Tank 2: 6.75 litres
Tank 3: 4.5 litres
Y= 1/3x-9
Write the equation of a line PERPENDICULAR to
point (-6, 10).
that passes through the
The equation of the line perpendicular to y = 1/3x - 9 that passes through the point (-6, 10) is y = -3x - 8.
The given equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
So, we can see that the slope of the given line is 1/3.
A line perpendicular to this line will have a slope that is the negative reciprocal of the slope of the given line.
The negative reciprocal of 1/3 is -3.
Now, we have the slope of the perpendicular line and a point that it passes through. We can use point-slope form to find the equation of the line.
Point-slope form, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values we have
y - 10 = -3(x - (-6))
y - 10 = -3(x + 6)
y - 10 = -3x - 18
y = -3x - 8
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The given question is incomplete, the complete question is:
Write the equation of a line perpendicular to y = 1/3x - 9 that passes through the point (-6, 10)
If P(A)=0. 3, P(B)=0. 2, and P(A∩B)=0. 1, find the probability
a. P(
)
b. P(A∪B)
c. P(
∩B)
d. P(A∩
)
e. P(
∪B)
P(∅) = 0, P(A∪B) = 0.4 , P(A∩B) = 0.1 ,Since the sample space is not defined in the question, we cannot calculate P(B'). Therefore, we cannot calculate P(A∩B').and P(A∪B) = 0.4. are the required solutions ofgiven probability check .
a. The probability of an empty set is always zero. Therefore, P(∅) = 0.
b. The probability of the union of two events, A and B, is given by the formula P(A∪B) = P(A) + P(B) - P(A∩B). Substituting the values given in the question, we get:
P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.3 + 0.2 - 0.1
= 0.4
Therefore, P(A∪B) = 0.4.
c. The probability of the intersection of A and B is given by the formula P(A∩B). Substituting the values given in the question, we get:
P(A∩B) = 0.1
Therefore, P(A∩B) = 0.1.
d. The probability of the intersection of A and the complement of B is given by the formula P(A∩B'). The complement of B is the set of all outcomes that are not in B. Since the sample space is not defined in the question, we cannot calculate P(B'). Therefore, we cannot calculate P(A∩B').
e. The probability of the union of A and B is given by the formula P(A∪B). Substituting the values given in the question, we get:
P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.3 + 0.2 - 0.1
= 0.4
Therefore, P(A∪B) = 0.4.
In probability theory, the union of two events A and B is the set of outcomes that belong to either A or B or both. The intersection of two events A and B is the set of outcomes that belong to both A and B. The complement of an event A is the set of outcomes that do not belong to A. These concepts are fundamental in probability theory and are used extensively in solving various problems.
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Write in the standard form of a conic if possible, and identify the conic section represented by r = 6/(cos x + 3sin x)
The standard form of a conic section represented by r = 6/(cos x + 3sin x) is r^2 = 6(x + 3y) and the represented equation is a line.
The equation r = 6/(cos x + 3sin x) is in polar form, where r represents the distance from the origin to a point (x, y) in the plane, and x is the angle that the line connecting the origin to (x, y) makes with the positive x-axis. To determine the standard form of the conic represented by this equation, we need to convert it to Cartesian coordinates.
Using the trigonometric identity cos x = x/r and sin x = y/r, we can rewrite the equation as:
r = 6/(x/r + 3y/r)
Multiplying both sides by r, we get:
r^2 = 6(x + 3y)
This is the standard form of a conic section in Cartesian coordinates, namely an equation of a line. Therefore, the conic represented by the equation r = 6/(cos x + 3sin x) is a line in the Cartesian coordinate system.
In summary, to determine the standard form of a conic represented by an equation given in polar form, we can use trigonometric identities to rewrite it in Cartesian coordinates.
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Erica's bedroom is shaped like the letter L. One of the rectangles that makes up her room measures 10 feet by 8 feet. The other rectangle measures 12 feet by 8 feet. What is the area of her entire bedroom?
the area of her entire bedroom is 176 feet².
What is rectangle?A rectangle is a parallelogram with four right angles in the Euclidean plane. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equivalent. A square is a rectangle with four equal edges.
What is area?The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
Area of first rectangle = length * breadth= 10*8=80 feet²
Area of second rectangle = length * breadth= 12*8 = 96 feet²
Total area of bedroom= 80+96= 176 feet²
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If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, where will B' be?
Reflection over the y-axis, rotation 90° clockwise, and translation (x + 2, y - 1)
B'( , )
If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, B' would be located at B' (3, 2).
What is a reflection over the y-axis?In Geometry, a reflection over or across the y-axis is represented and modeled by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate (y-axis) while the sign of the x-coordinate (x-axis) would change from positive to negative or negative to positive.
By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:
Coordinate B = (-3, 1) → Coordinate B' = (-(-3), 1) = (-3, 1).
Next, we would apply a rotation of 90° clockwise as follows;
(x, y) → (y, -x)
Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)
Lastly, we would apply a translation (x + 2, y - 1) as follows:
Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).
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How do you do this I need help please
Answer:
30,000 grams
Step-by-step explanation:
multiply the 30KG by 1,000 (that is the conversion) and you get 30,000g
Answer:
hi I'm really sorry I can't help
i do not understand how to answer this question
a. Hence proved that the sum of fractions [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]
b. The value will be 7 for the expression
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
What is square root?Square rοοt οf a number is a value, which οn multiplicatiοn by itself, gives the οriginal number. The square rοοt is an inverse methοd οf squaring a number. Hence, squares and square rοοts are related cοncepts.
Suppοse x is the square rοοt οf y, then it is represented as x=√y, οr we can express the same equatiοn as x² = y. Here, ‘√’ is the radical symbοl used tο represent the rοοt οf numbers. The pοsitive number, when multiplied by itself, represents the square οf the number. The square rοοt οf the square οf a pοsitive number gives the οriginal number.
Here,
a. [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]
Using (a + b)(a - b) = a² - b²
⇒ [tex]${\frac{1 \cdot \sqrt{1}-\sqrt{2}}{\sqrt{1}+\sqrt{2}\cdot \sqrt{1 }-\sqrt{2}}+{\frac{1 \cdot \sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}\cdot \sqrt{1}-\sqrt{2}}}+{\frac{1 \cdot \sqrt{3}-\sqrt{4}}{\sqrt{3}+\sqrt{4}\cdot \sqrt{3}-\sqrt{4}}}$[/tex]
⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{1-2}+{\frac{ \sqrt{2}-\sqrt{3}}{2-3}+{\frac{\sqrt{3}-\sqrt{4}}{3-4}}$[/tex]
⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-\sqrt{4}}{-1}}$[/tex]
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]
⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}}-{\sqrt{3}+2}$[/tex]
⇒ [tex]$ -1+2}$[/tex]
⇒ 1
a. Hence proved that the sum of fractions [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]
B. This will be done with the same process,
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}} \cdot \cdot \cdot -{\sqrt{63}+8}$[/tex]
There, will be same roots of every number until - 8
So,
⇒ [tex]$ -1+8}$[/tex]
= 7
b. The value will be 7 for the expression
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
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help me i have a test tmmr
Answer:
Step-by-step explanation:
[tex]\frac{2}{x} -3=\frac{1}{2}[/tex]
[tex]\frac{2}{x}=\frac{1}{2}+3[/tex] (-3 both sides)
[tex]\frac{2}{x}=\frac{7}{2}[/tex] (added fraction)
[tex]2=\frac{7x}{2}[/tex] (×[tex]x[/tex] both sides)
[tex]4=7x[/tex] (×2 both sides)
[tex]x=\frac{4}{7}[/tex] (÷7 both sides)
show that v is an eigenvector of A and find the corresponding eigenvalue, λ.A= [\begin{ccc}-1&1\\6&0\end{array}\right], v = [\begin{ccc}1\\3\end{array}\right]λ=_____
The matrix A does not eigenvector v corresponding to the given eigen value.
λ.A = [ -11 60 ]
v = [ 1 3λ ]
v is an eigenvector of A calculate corresponding eigenvalue,
A × v = λ × v
where A is the given matrix.
v is the given vector.
λ is the corresponding eigenvalue.
× denotes matrix multiplication.
Let's first calculate A × v we have,
A × v
= [-11 60] × [ 1 3λ]
= [-11-33λ 60+ 180λ]
Check A× v is equal to λ × v ,
λ × v =
λ × [ 1 3λ]
= [λ 3λ^2]
Set these two vectors equal to each other and get the following system of equations ,
-11-33λ = λ __(1)
60+ 180λ = 3λ^2 ___(2)
From equation (1) we get,
⇒34λ = -11
⇒ λ = -11/34
Substituting this value of λ into the second equation, we have,
60+ 180λ = 3λ^2
⇒ 60 + 180(-11/34) = 3(-11/34)^2
⇒ (2040 -1980)/ 34 = 3(-11/34)^2
⇒ 60/34 = 3( 11/34)^2
⇒ 60 × 34 = 3 × 11 × 11
⇒20× 34 = 11 × 11
Which is not true.
so the value of λ does not satisfies both equations.
Therefore, v is not an eigenvector of A with corresponding eigenvalue λ.
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The above question is incomplete, the complete question is:
Check whether v is an eigen vector of A if yes find the corresponding eigen value.
λ.A = [ -11 60 ]
v = [ 1 3λ ]
I NEED HELP ON THIS ASAP!!
a) Graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380
b) The maximum profit of $5200 achieved.
Define the term selling profit?Selling profit is the profit that a business makes on the sale of its products or services. It is the difference between the selling price and the cost of product.
a) Let x be the number of boards of mahogany sold and y be the number of boards of black walnut sold. Then, the constraints of the problem can be represented by the following system of inequalities:
x ≥ 0 (non-negative constraint)
y ≥ 0 (non-negative constraint)
x ≤ 260 (maximum number of mahogany boards available)
y ≤ 320 (maximum number of black walnut boards available)
x + y ≤ 380 (maximum number of boards that can be sold)
To graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380 on a coordinate plane and shade the feasible region that satisfies all of the constraints. The feasible region is the area that is bounded by these lines and includes the origin (0, 0).
b) The profit function P(x, y) can be defined as follows:
P(x, y) = 20x + 6y
To maximize the profit, we need to find the values of x and y that satisfy all of the constraints and maximize the profit function P(x, y).
One way to do this is to use the corner-point method. We can evaluate the profit function at each of the corners of the feasible region and find the corner that gives the maximum profit.
The corners of the feasible region are (0, 0), (0, 320), (260, 0), and (120, 260).
P(0, 0) = 0
P(0, 320) = 6(320) = 1920
P(260, 0) = 20(260) = 5200
P(120, 260) = 20(120) + 6(260) = 4720
Therefore, the maximum profit of $5200 can be achieved by selling 260 boards of mahogany and 0 boards of black walnut.
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3
The ratio of desktop computers to laptop computers sold by
a mail-order company last week was 8 to 3. What could be
the numbers of computers sold by the company last week?
A
B
C
D
448 desktops, 168 laptops
448 desktops, 165 laptops
440 desktops, 168 laptops
400 desktops, 165 laptops
using the ratio given, the number of computers could be sold by the company last week is: A. 448 desktops, 168 laptops.
How to Calculate Ratios?To find the actual numbers of desktop and laptop computers sold, we need to choose a common factor for the ratio 8:3.
Let's assume that the total number of computers sold is 33x (where x is a positive integer). Then, the ratio 8:3 corresponds to 8x desktops and 3x laptops. We can check which of the given options satisfies this condition:
A. 8x = 448, 3x = 168 --> This satisfies the condition, as 8:3 = 448:168
B. 8x = 448, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 448:165
C. 8x = 440, 3x = 168 --> This does not satisfy the condition, as 8:3 is not equal to 440:168
D. 8x = 400, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 400:165
Therefore, the answer is option A: 448 desktops and 168 laptops could be the numbers of computers sold by the company last week.
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Lisa uses her railcard to buy a ticket.
She gets off the normal price of the ticket.
The normal price of the ticket is £24.90
Work out how much Lisa pays for the ticket.
The discount percentage is different, the amount that Lisa pays will also be different.
What exactly is the discounted method?The act of estimating the present value of a future payment or series of cash flows that will be received in the future is referred to as discounting. A discount rate (also known as a discount yield) is the rate at which future cash flows are discounted back to their present value.
We need to know what percentage of the regular ticket price Lisa saves with her railcard. We cannot calculate the exact amount Lisa pays for the ticket without this information.
Assuming Lisa receives a 1/3 discount with her railcard, we can calculate the cost of her ticket as follows:
Discounted price = Regular price minus discount amount
Normal price x Discount percentage = Discount amount
Discount rate = 1/3 = 33.33% (rounded to two decimal places)
Discount amount = £24.90 multiplied by 33.33% = £8.30 (rounded to two decimal places)
Price after discount = £24.90 - £8.30 = £16.60 (rounded to two decimal places)
As a result, if Lisa receives a 1/3 discount with her railcard, she will pay£16.60 for the ticket. However, if the discount percentage is different, Lisa's payment will be different as well.
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Lisa uses her railcard to buy a ticket.
She gets off the normal price of the ticket.
The normal price of the ticket is £24.90
Work out how much Lisa pays for the ticket.
In △PQR
how many degrees is m∠Q?
Answer:
105 degrees
Step-by-step explanation:
sum of angles in triangle is 180 degrees
11x-5+6x+5+x = 180
simplify this to get 18x=180
180/18 = 10 = x
plug in 10 for x
11(10) - 5
110-5
105
One of the legs of a right triangle measures 4 cm and its hypotenuse measures 11 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer: 10.2 cm
Step-by-step explanation:
We can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's call the unknown length of the other leg "x". Then we can set up the following equation:
4^2 + x^2 = 11^2
Simplifying this equation, we get:
16 + x^2 = 121
Subtracting 16 from both sides, we get:
x^2 = 105
Taking the square root of both sides, we get:
x = sqrt(105)
x ≈ 10.2 cm (rounded to the nearest tenth)
Therefore, the measure of the other leg is approximately 10.2 cm.