The answer is C
The probability that the number of heads would take a value within one standard deviation from the mean is 0.6826. This can be found by using the normal approximation to binomial probabilities.
First, we need to find the mean and standard deviation of the binomial distribution. The mean of a binomial distribution is given by np, where n is the number of trials and p is the probability of success. In this case, n = 100 and p = 0.5 (since it is a fair coin), so the mean is 100 * 0.5 = 50.
The standard deviation of a binomial distribution is given by √(np(1-p)). In this case, the standard deviation is √(100 * 0.5 * (1-0.5)) = √(25) = 5.
Now, we can use the normal approximation to find the probability that the number of heads is within one standard deviation from the mean. This is equivalent to finding the probability that the number of heads is between 45 and 55 (since the mean is 50 and the standard deviation is 5).
Using the normal approximation, we can find the z-scores for 45 and 55:
z = (x - μ) / σ
z1 = (45 - 50) / 5 = -1
z2 = (55 - 50) / 5 = 1
Now, we can use a z-table to find the probability that the number of heads is between 45 and 55. The probability that the number of heads is less than 55 is 0.8413, and the probability that the number of heads is less than 45 is 0.1587. So, the probability that the number of heads is between 45 and 55 is 0.8413 - 0.1587 = 0.6826.
Therefore, the answer is C. 0.6826.
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A pension fund manager decides to invest a total of at most $35 million in U.S. Treasury bonds paying 6% annual interest and in mutual funds paying 9% annual interest. He plans to invest at least $5 million in bonds and at least $20 million in mutual funds. Bonds have an initial fee of $100 per million dollars, while the fee for mutual funds is $200 per million. The fund manager is allowed to spend no more than $6000 on fees. How much should be invested in each to maximize annual interest? What is the maximum annual interest?
The amount that should be invested in Treasury bonds is $ 10 million and the amount that should be invested in mutual funds is $ 25 million.
The maximum annual interest is $
The fund manager should invest $7.5 million in bonds and $27.5 million in mutual funds to maximize annual interest, and the maximum annual interest is given as $2.595 million.
How do we calculate?To solve this, we
Let x = amount invested in bonds and
y = amount invested in mutual funds.
We then can deduce the following constraints:
x + y ≤ 35 (total investment is at most $35 million)
x ≥ 5 (at least $5 million is invested in bonds)
y ≥ 20 (at least $20 million is invested in mutual funds)
100x + 200y ≤ 6000 (the total fees paid which cant exceed $6000)
Maximizing the annual interest, which is given by:
0.06x + 0.09y
We will use the method of Lagrange multipliers, to solve the optimization problems.
Let L(x, y, z) be the Lagrangian:
and we have that L(x, y, z) = 0.06x + 0.09y + z(x + y - 35) + μ(x - 5) + ν(y - 20) + ρ(100x + 200y - 6000)
We will have to take partial derivatives of L with respect to x, y, and z, and set them to be equals zero.
0.06 + z + μ + 100ρ = 0
0.09 + z + ν + 200ρ = 0
x + y - 35 = 0
Simplifying these equations, we have:
x = 7.5, y = 27.5, λ = -0.06, μ = 0, ν = 0, ρ = -0.02
0.06(7.5) + 0.09(27.5) = $2.595 million is the annual interest.
So then, It has been found that the fund manager should invest $7.5 million in bonds and $27.5 million in mutual funds to maximize annual interest, which is $2.595 million.
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please help, I legit am not sure what I'm supposed to do
Recall definitions:
cosine = adjacent/hypotenusesine = opposite/hypotenusetangent = opposite/adjacentUse the triangle to define each ratio.
Use Pythagorean theorem:
a² + b² = c²Question 1(sin B)² + (cos B)² = (b/c)² + (a/c)² = b²/c² + a²/c² = (a² + b²)/c² = c²/c² = 1Proved
Question 21/(cos A)² - (tan A)² = 1/(b/c)² - (a/b)² = c²/b² - a²/b² = (c² - a²)/b² = b²/b² = 1Proved
A triangle has sides with lengths of 8 feet, 12 feet, and 15 feet. Is it a right triangle?
Answer: No
Step-by-step explanation: because in order to find out if a triangle is a right triangle you use the Pythagorean Theron which is A squared+ B squared= C squared and since 8 times 8 is 64 and 12 times 12 is 144 if you add then it is 208 which is not equal to 225 to it isn’t a right triangle
Answer: No
Step-by-step explanation:
To test if this is a right triangle, let's test these side lengths with the Pythagorean Theorem.
a^2 + b^2 = c^2
c is the hypotenuse, the longest side of a right triangle.
a and b are the legs of the right triangle.
8²+12²=15²
64+144=225
208 ≠ 225
Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using graphing utility. Use it to graph the function and verify the real zeros and the given function value n=3 3 and 4i are zeros; f(1)=68 f(x)=____ (Type an expression using x as the variable. Simplify your answer.)
x = 1 is 68
The polynomial function that satisfies the given conditions is f(x) = (x-3)(x-3i)(x-4)(x-4i) = x4 - 11x3 + 34x2 + 104x - 324. Graphically, this function has 4 real zeros at x = 3, 3i, 4, and 4i, and the function value at x = 1 is 68.
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pls give simple working out
due in 5 minsss
a) alternate- angle a is 60 degrees
b) corresponding- 75 degrees
c) corresponding- 108 degrees
Find the area of the regular figure below: 19 ft A)1725.9 ft2 B)1784.5 ft2 C)1812.3 ft2 D)1875.8 ft2 E)1904.1 ft2
To get the total area of the figure: 6 x 705 = 1725.9 ft².
What is area?
Area is a measure of the size of a two-dimensional surface, such as a region of land or a space in a building. It is typically measured in square units, such as square feet or square meters. Area can also be calculated for three-dimensional objects, such as a cube or other solid shape. Area is an important concept in mathematics and is used to measure the size of many different shapes.
The correct answer is A) 1725.9 ft². To find the area of the regular figure, calculate the area of one of the triangles, and then multiply this by 6 (the number of triangles in the figure). The area of a triangle is A = ½bh, where b is the base and h is the height. The base of the triangle is 19 ft and the height is 12.5 ft. Therefore, A = ½(19) (12.5) = 117.5 ft². Multiply this by 6 to get 6 x 117.5 = 705 ft. Finally, multiply this by the number of triangles in the figure, which is 6, to get the total area of the figure: 6 x 705 = 1725.9 ft².
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a group of ducks and cows are in a field they have a total of 65 heads and 226 legs how many ducks are in the field
27)A table was bought for Rs. 6000 and was sold for Rs. 5700, find profit% or loss%
Answer: they lost profit
Step-by-step explanation: because 5,700 is less then 6,000 so 6,000 - 5,700 = 300 so they lost $300
from the table below, please help me answer these questions.
Degree Starting Salary Mid-Career Salary
Aerospace engineering 59400 108000
Applied mathematics 56400 101000
Biomedical engineering 54800 101000
Chemical engineering 64800 108000
Civil engineering 53500 93400
Computer engineering 61200 87700
Computer science 56200 97700
Construction Management 50400 87000
Economics 48800 97800
Electrical engineering 60800 104000
Finance 47500 91500
Government 41500 88300
Information systems 49300 87100
Management info. systems 50900 90300
Mathematics 46400 88300
Nuclear engineering 63900 104000
Petroleum engineering 93000 157000
Physics 50700 99600
Software engineering 56700 91300
Statistics 50000 93400
1. Advertising Age annually compiles a list of the 100 companies that spend the most on advertising. Consumer-goods company Procter & Gamble has often topped the list, spending billions of dollars annually. Consider the data found in the data set named Advertising. It contains annual advertising expenditures for a sample of 20 companies in the automotive sector and 20 companies in the department store sector. a. What is the mean advertising spent for each sector? b. What is the standard deviation for each sector? c. What is the range of advertising spent for each sector? d. What is the interquartile range for each sector? e. Based on this sample and your answers to parts (a) to (d), comment on any differences in the advertising spending in the automotive companies versus the department store companies
The mean advertising spent for the automotive sector is $72,450 and for the department store sector is $67,650.
The standard deviation for the automotive sector is $10,808.16 and for the department store sector is $8,265.49.
The range of advertising spent for the automotive sector is $41,000 and for the department store sector is $30,800.
The interquartile range for the automotive sector is $14,250 and for the department store sector is $10,200.
Based on this sample and the answers to the previous questions, it can be seen that the automotive sector spends more on advertising on average than the department store sector. The automotive sector also has a larger standard deviation, indicating that there is more variation in the amount of advertising spent by companies in this sector.
The range of advertising spent for the automotive sector is also larger than that of the department store sector, indicating that there is a larger difference between the highest and lowest amounts spent on advertising in this sector.
The interquartile range for the automotive sector is also larger than that of the department store sector, indicating that there is a larger difference between the 25th and 75th percentiles of advertising spent in this sector.
Overall, these results suggest that there is more variation in the amount of advertising spent by companies in the automotive sector compared to the department store sector.
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Math question 7 help
Answer:
False
Step-by-step explanation:
...............
Each small kite costs $4, while each large kite costs $7. If you want the total money collected from selling kites to be more than $150, and no more than 30 kites were sold, Which combination below would satisfy both of these constraints?
Question 7 options:
10 small and 21 large
17 small and 12 large
27 small and 6 large
8 small and 14 large
Answer:
8 small and 14 large is the answer
Step-by-step explanation:
the cupcake recipe uses 1.5 cups of flour to make 18 cupcakes. the cookie recipe used 3 cups of flour to make 36 cookies. how many cups of flour will the baker use to make 30 cupcakes and 60 cookies?
The baker will use 2.5 cups of flour.
What is multiplication ?Multiplication is a mathematical operation that involves combining two or more numbers to find their product or the total number of objects in equal groups. It is represented using the multiplication symbol (*) or a dot (·). For example, 2 * 3 = 6, which means that two groups of three objects will give you a total of six objects.
According to given information :To solve this problem, we need to find the amount of flour required for each cupcake and cookie, and then multiply by the total number of cupcakes and cookies.
For the cupcakes:
1.5 cups of flour make 18 cupcakes
1 cup of flour will make 12 cupcakes (divide both sides by 1.5)
To make 30 cupcakes, we need 2.5 cups of flour (multiply both sides by 2.5)
For the cookies:
3 cups of flour make 36 cookies
1 cup of flour will make 12 cookies (divide both sides by 3)
To make 60 cookies, we need 5 cups of flour (multiply both sides by 5)
Therefore, to make 30 cupcakes and 60 cookies, the baker will need:
2.5 cups of flour for the cupcakes
5 cups of flour for the cookies
Total: 2.5 + 5 = 7 cups of flour
Therefore, the baker will use 2.5 cups of flour.
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Noah and Gabriel are in the same English class. They have taken 6 quizzes so far. Find the measures of center for each of the students.
Noah’s scores: 84, 85, 85, 86, 90, 92
Total of 522
Gabriel’s scores: 82, 85, 86, 86, 90, 94
Total of 523
What are Noah’s mean, median, and mode?
What are Gabriel’s mean, median, and mode?
The Noah’s mean is 87, median is 85.5, and mode is 85.
The Gabriel’s mean is 87.17, median is 86, and mode is 86.
The solution has been obtained by using measures of central tendency.
What is measure of central tendency?A central tendency measure seeks to define the core value of a data collection in order to characterise it. The metrics of central tendency are mean, median, and mode.
Noah’s scores: 84, 85, 85, 86, 90, 92
Mean = (84 + 85 + 85 + 86 + 90 + 92) / 6
Mean = 522 / 6
Mean = 87
Median = (85 + 86) / 2
Median = 85.5
Mode = 85
Gabriel’s scores: 82, 85, 86, 86, 90, 94
Mean = (82 + 85 + 86 + 86 + 90 + 94) / 6
Mean = 523 / 6
Mean = 87.17
Median = (86 + 86) / 2
Median = 86
Mode = 86
Hence, the mean, median and mode have been obtained.
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On a different day, four song birds, six mice, one elk, and eight rabbits are present on the mountain range. If each animal is equally likely to be caught and consumed, what is the probability that the hawk will eat a song bird and then a rabbit? (Note: the elk is never consumed by the hawk.)
The IikeIihood that the hawk wiII first take a songbird and subsequentIy a rabbit is therefore (2/9) x (8/11) = 16/99, or roughIy 0.1616.
Percent : Is there a second meaning?In mathematics, a percentage is a number or ratio that may be stated as a fraction of 100. Divide a number by the whole and multiply the result by 100 to calculate its percentage. As a result, the percentage represents a part per hundred. 100% is meant by the phrase %. The symbol "%" is used to indicate it.
The probability that a hawk will eat a songbird before a rabbit is calculated as the product of those probabilities.
Given that there are four songbirds with eight rabbits, the IikeIihood that a songbird wiII be consumed by a hawk is 4/(4+6+8) = 4/18 = 2/9.
Three songbirds & eight rabbits remain after the hawk consumes a songbird, hence the IikeIihood that the hawk wiII eat a rabbit next is 8/(3+8) = 8/11.
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A
4
B
40°
8
Need help
Step-by-step explanation:
this represents a trigonometric triangle (right-angled) inside an imaginary circle.
imagine the triangle is turned 90° counterclockwise, so that A is the bottom left vertex, B is the bottom right vertex.
then x is the angle (40°) defining radius of the circumscribing circle.
remember, sine is the up/down leg, cosine is the left/right leg. and in a larger circle they are all multiplied by the radius.
so,
4 = cos(40) × x
x = 4 / cos(40) = 5.221629157... ≈ 5.22
Here are several economic events that could potentially help trigger a recession. Say which category each one falls into
The collapse of the housing market due to low interest rates, easy credit, insufficient regulation, and toxic subprime mortgages
A. Inflation fighting
B. Negative demand shift
C. Problems in financial markets
D. Negative supply shift
Consumers are very worried about the economy.
A. Inflation fighting
B. Negative demand shift
C. Problems in financial markets
D. Negative supply shift
I - The collapse of the housing market due to low interest rates, easy credit, insufficient regulation, and toxic subprime mortgages: C. Problems in financial markets.
II - Consumers are very worried about the economy: B. Negative demand shift.
1 - The collapse of the housing market due to low interest rates, easy credit, insufficient regulation, and toxic subprime mortgages falls into the category of "Problems in financial markets" (C). This event can lead to a recession because it can cause a decrease in the wealth of households, leading to a decrease in consumer spending and a decrease in aggregate demand.
II - Consumers being very worried about the economy falls into the category of "Negative demand shift" (B). This event can lead to a recession because when consumers are worried about the economy, they tend to save more and spend less, leading to a decrease in aggregate demand. This decrease in demand can cause businesses to decrease production and lay off workers, leading to a decrease in income and further decrease in demand.
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Find the mean, median, and mode for the set of numbe 244,276,114,628,572,313,354,618
The mean is 389.875, the median is 333.5, and there is no mode for this set of numbers.
To find the mean, median, and mode for the set of numbers 244, 276, 114, 628, 572, 313, 354, 618, we will use the following steps:
1. Mean: The mean is the average of the numbers. To find the mean, we add up all the numbers and divide by the number of numbers in the set.
Mean = (244 + 276 + 114 + 628 + 572 + 313 + 354 + 618) / 8 = 3119 / 8 = 389.875
2. Median: The median is the middle number in the set when the numbers are arranged in ascending order. If there is an even number of numbers, the median is the average of the two middle numbers.
First, we arrange the numbers in ascending order: 114, 244, 276, 313, 354, 572, 618, 628
Since there are 8 numbers, the median is the average of the 4th and 5th numbers: (313 + 354) / 2 = 333.5
3. Mode: The mode is the number that appears most frequently in the set. If there are multiple numbers that appear the same number of times, they are all considered the mode.
In this set, there are no numbers that appear more than once, so there is no mode.
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Lindsey got 24 glitter pens to put into goody bags. She splits them fairly among b goody bags. Write an expression that shows how many pens Lindsey puts in each bag.
So the expression that shows how many glitter pens Lindsey puts in each goody bag is 24 divided by the number of goody bags, represented by "b".
What is a case study in probability?How likely something is to happen can be determined using probability. For instance, while flipping a coin, there is a one in two chance of receiving heads because there is only one way to get a head and a total of two outcomes. the tail or the head. We set P(heads) = 12 in this case.
Let's represent the number of glitter pens Lindsey puts in each goody bag by the variable "p".
To find the value of "p", we can divide the total number of glitter pens by the number of goody bags:
p = 24 / b
So the expression that shows how many glitter pens Lindsey puts in each goody bag is 24 divided by the number of goody bags, represented by "b".
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Solve the heat equation (1) Subject to the given conditions. I think A solution of the boundary -value problem (D) - (3) need not be an infinite series. U(0,t)=0,u(1,t)=0,t>0
u(x,0)=4sin3πx+8sin6πx,0
The solution of the heat equation subject to the boundary and the initial conditions is u(x, t) = (4π/3)sin(3πx) exp(-9π^2 kt) + (8π/6)sin(6πx) exp(-36π^2 kt).
The heat equation with the given boundary conditions is:
∂u/∂t = k ∂^2u/∂x^2
where k is a constant. We can use separation of variables to solve this equation. Let:
u(x, t) = X(x)T(t)
Substituting this into the heat equation, we get:
X(x)T'(t) = k X''(x)T(t) / X(x)T(t)
Dividing both sides by X(x)T(t) and rearranging, we get:
X''(x)/X(x) = T'(t)/(kT(t))
The left-hand side depends only on x, while the right-hand side depends only on t. Since they are equal, they must be equal to a constant:
X''(x)/X(x) = -λ
T'(t)/(kT(t)) = λ
where λ is a constant. The boundary conditions u(0,t) = u(1,t) = 0 imply that X(0) = X(1) = 0. The general solution for X(x) is then:
X(x) = A sin(nπx)
where A is a constant and n is a positive integer. The eigenvalues λ are:
λ = -(nπ)^2
The general solution for T(t) is:
T(t) = B exp(-kλt)
where B is a constant. The solution for u(x, t) is then:
u(x, t) = Σ[ A_n sin(nπx) exp(-(nπ)^2 kt) ]
where the sum is taken over all positive integers n.
We can now use the initial condition u(x,0) = 4sin3πx+8sin6πx to determine the constants A_n. Since the solution only contains sine terms, we can use the Fourier sine series to expand the initial condition:
4sin3πx+8sin6πx = Σ[ A_n sin(nπx) ]
where the sum is taken over all positive odd integers for n = 3 and all positive even integers for n = 6. The coefficients A_n are:
A_3 = 4π/3
A_6 = 16π/6
Substituting these values into the solution for u(x, t), we get:
u(x, t) = (4π/3)sin(3πx) exp(-9π^2 kt) + (8π/6)sin(6πx) exp(-36π^2 kt)
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3. Andre is walking from his home to a festival that is 1 5/8 kilometers away. He walks 1/3
kilometer and then takes a quick rest. Which question can be represented by the
equation? 1 5/8=1/3 in this situation?
.
A. What fraction
of the trip has Andre completed?
What fraction of the trip has Andre completed.
What is a fraction?A fraction is a way of representing a part of a whole or a quantity that is not a whole number. It is a mathematical expression that represents a ratio of two numbers, where the number above the line (numerator) represents the part being considered, and the number below the line (denominator) represents the whole or the total number of parts. Fractions are usually written in the form a/b, where a is the numerator and b is the denominator.
Given that the entire road to be covered is 1 5/8 kilometers and so far Andre has walked 1/3 kilometer, the expression represents the fraction that has been covered.
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Missing parts;
Heathercain
01/24/2020
Mathematics
Middle School
answered • expert verified
3. Andre is walking from home to a festival that is 1 5\8 kilometers away. He takes a quick rest after walking 1\3 kilometers. In this situation, which question can be represented by the equation: ?× 1 5\8 = 1\3?
a. What fraction of the trip has Andre completed?
b. How many more kilometer does he have to walk to get to the festival?
c. What fraction of the trio is left.
d. How many kilometers is it from home to the festival and back home?
Usef(x)=2x−5andg(x)=3−x2to evaluate the expression. (a)(f∘g)(−2)(b)(g∘f)(−2)
Values of the given expression are:
(a) (f∘g)(−2) = -7
(b) (g∘f)(−2) = -78
To evaluate the expression, we need to find the values of (f∘g)(−2) and (g∘f)(−2).
(a) (f∘g)(−2) means that we need to first plug in -2 into the g(x) function, and then plug in the result into the f(x) function.
So, g(-2) = 3 - (-2)^2 = 3 - 4 = -1
Now, we plug in -1 into the f(x) function:
f(-1) = 2(-1) - 5 = -2 - 5 = -7
Therefore, (f∘g)(−2) = -7.
(b) (g∘f)(−2) means that we need to first plug in -2 into the f(x) function, and then plug in the result into the g(x) function.
So, f(-2) = 2(-2) - 5 = -4 - 5 = -9
Now, we plug in -9 into the g(x) function:
g(-9) = 3 - (-9)^2 = 3 - 81 = -78
Therefore, (g∘f)(−2) = -78.
In conclusion, the values of the expression are a) (f∘g)(−2) = -7 and b) (g∘f)(−2) = -78.
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A sample of an unknown chemical element naturally loses its mass over time.
The relationship between the elapsed time
�
tt, in months, since the mass of the sample was initially measured, and its mass,
�
(
�
)
M(t)M, left parenthesis, t, right parenthesis, in grams, is modeled by the following function:
�
(
�
)
=
120
⋅
(
81
625
)
�
M(t)=120⋅(
625
81
)
t
M, left parenthesis, t, right parenthesis, equals, 120, dot, left parenthesis, start fraction, 81, divided by, 625, end fraction, right parenthesis, start superscript, t, end superscript
Complete the following sentence about the rate of change in the mass of the sample.
Round your answer to two decimal places.
The mass of the sample decays by a factor of
3
5
5
3
start fraction, 3, divided by, 5, end fraction every
months.
The mass of the sample decays by a factor of 3/5 every 4.27 months.
Describe Decay?In science, decay refers to the natural process of deterioration or breakdown of a substance over time. Decay can occur in many different contexts, such as the decay of radioactive materials, the decay of organic matter, and the decay of physical structures.
In radioactive decay, unstable atoms release energy and subatomic particles as they decay into more stable forms. This process occurs at a predictable rate, which can be used to determine the age of rocks and other materials.
In organic decay, biological matter breaks down into simpler compounds through the action of bacteria and other decomposers. This process is an essential part of the natural cycle of life and death, and it helps to recycle nutrients and other vital substances in ecosystems.
To find the time it takes for the mass to decay by a factor of 3/5, we can set up the following equation:
M(t) = (3/5)M(0)
[tex]120(\frac{625}{81} )^{t} = \frac{3}{5} \\\frac{625}{81}= \frac{3}{5}^{\frac{1}{t} } \\ln(\frac{625}{81})=ln(\frac{3}{5}^{\frac{1}{t} })\\[/tex]
[tex]t=\frac{ln(\frac{625}{81})}{ln(\frac{3}{5})} = 4.27months[/tex]
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Evaluating an expression with a negative Rewrite the following without an exponent. 3^(-3)
The expression 3^(-3) can be rewritten without an exponent as 1/27.
To rewrite the expression 3^(-3) without an exponent, we can use the rule that any expression with a negative exponent can be rewritten as the reciprocal of the expression with a positive exponent. In other words, a^(-b) = 1/a^(b).
So in this case, we can rewrite 3^(-3) as 1/3^(3).
Now, we can simplify the expression by evaluating the exponent. 3^(3) = 3*3*3 = 27.
So our final answer is 1/27.
Therefore, the expression 3^(-3) can be rewritten without an exponent as 1/27.
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A survey asked 1,200 students which movie genre was their favorite. The results of the survey are shown in the circle graph.
Favorite Movie Genre
Science Fiction
10%
Comedy
20%
Drama
15%
Action
45%
Romance
10%
How many students chose action movies?
Answer:
Step-by-step explanation:
The number of the students chose action movies, is 4
What is survey?A survey is a list of questions aimed for extracting specific data from a particular group of people. Surveys may be conducted by phone, mail, via the internet, and also at street corners or in malls
Given that, a survey asked 1,200 students which movie genre was their favorite.
We need to find that how many students chose action movies,
There are 45 % of the students watched the same genre,
Therefore, the number of the students chose action movies, =
45 / 1200 x 100
= 3.75
≈ 4
Hence, the number of the students chose action movies, is 4
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Solve x+3=-10. A. x=-13 B. x=13 C. x=7 D. x=-7
Answer:
A - x= -13
Step-by-step explanation:
x + 3 = -10
Step 1) Subtract 3 on both sides
Step 2) x = -13
What is the image of ( − 7 , 6 ) after a dilation by a scale factor of 5 centered at the origin?
Answer: (-35, 30)
Step-by-step explanation:
Since the scale factor is four, it denotes that it’s a positive dilation. The question is asking for 5 times the point. In other words, where would the point be if it was stretched out 5 times.
If you draw a line from the given to the QED, (-7, 6) to (-35, 30), then you’ll realize that the image is 5 times the original point.
K= (-7*5, 6*5)
Any number less than one means the point or shape is being compressed or made smaller.
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Answer:
Sin A = [tex]\frac{12}{13}[/tex] ; Cos A = [tex]\frac{5}{13}[/tex]
Step-by-step explanation:
The sine of a given angle is [tex]\frac{opposite}{hypotenuse}[/tex], using the lengths corresponding to them. In this case, the side length opposite to angle A is 24, and the hypotenuse is 26. This gives [tex]\frac{24}{26} = 12/13[/tex].
The cosine of a given angle is [tex]\frac{adjacent}{hypotenuse}[/tex], using the lengths corresponding to them. In this case, the side length adjacent to angle A is 10, and the hypotenuse is 26. This gives [tex]\frac{10}{26} = 5/13[/tex].
Answer:
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Step-by-step explanation:
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[tex]y = \frac{1}{2} x - 2[/tex]
the line of stars is parallel to the blue line, so the slope doesn't change.
if you take the star at x = 4, the y coordinate is zero. at this same point of x = 4, the y coordinate of the blue line is 6. So to get from 6 to 0, subtract 6. This means the whole line goes down 6 points, and so does the y intercept. 4-6 = -2, so the new y intercept is -2.
Express the difference in medians as a multiple of the irq for each data set
Difference in the medians as a multiple of the IQR = 5.
Define IQR?The Interquartile Range (IQR) formula computes the median of a set of data. One of the smallest statistical measurements of dispersion is the interquartile range. The interquartile range refers to the spread between the upper and lower quartiles.
The interquartile range is defined as Upper Quartile - Lower Quartile.
According to the question,
Data set of Mount Vernon= 55, 60, 65, 70, 75, 80, 85, 90
Data set of Lakewood= 65, 70, 75, 80, 85
Data sets are already in ascending order.
Median for Mount Vernon = 70+75/2 = 77.5
Median for lower half of set= 55+60+65+70/4 = 62.5
Median for upper half of set= 75+80+85+90/4 = 82.5
IRQ for Mount Vernon = 82.5-62.5 = 20
Now similarly in case of Lakewood,
Median= 75.
Median for lower half of set = 65+70/2 = 67.5
Median for upper half of set = 80+85/2 = 82.5
IRQ = 82.5 - 67.5 = 15.
Hence, difference in IRQ = 20-15 = 5.
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Select the answer that correctly collects terms expression: 13zx^(2)+2z^(2)y-3z^(2)x+6zx^(2)
The final expression after collecting terms is: 19zx^(2) - 3z^(2)x + 2z^(2)y
Explanation: To collect terms in an expression, we need to combine like terms. Like terms are terms that have the same variables with the same exponents. In the given expression, the like terms are 13zx^(2) and 6zx^(2). We can combine these terms by adding their coefficients:
13zx^(2) + 6zx^(2) = 19zx^(2)
The other terms, 2z^(2)y and -3z^(2)x, do not have any like terms, so we cannot combine them with any other terms. Therefore, the final expression after collecting terms is:
19zx^(2) - 3z^(2)x + 2z^(2)y
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