Answer:
a. The sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time for several reasons. Firstly, in 1936, only a small fraction of the US population had magazine subscriptions or owned cars, telephones or club memberships. Hence, the sample was biased towards the more affluent and educated sections of society, and did not include a representative cross-section of the population. Secondly, the sample was limited to people who could read and write, which excluded many poor and illiterate people who may have had different political views.
b. The low response rate of 2,300,000 out of the 10,000,000 postcards sent out indicates a response rate of only 23%. This means that the sample was not a random sample, and that the respondents were not representative of the larger population. Low response rates tend to increase sampling error and decrease the reliability of the sample.
c. These problems are examples of nonsampling error, which occur due to factors other than the sample selection process. The bias in the sample resulted from the sampling frame, which was not representative of the population, and the low response rate.
d. Quota sampling is an example of non-probability sampling, where researchers select a specific number of participants from different subgroups of the population based on predetermined quotas. In this method, the goal is to obtain a sample that is representative of the population in terms of certain characteristics, such as age, gender, or ethnicity. Quota sampling was used by George Gallup in 1936, and is still used today in various forms, such as stratified sampling.
(please could you kindly mark my answer as brainliest)
which statements correctly describe how the graph of the geometric sequence below should appear? 640, 160, 40, 10, ... select two options. the graph will show exponential growth. the graph will appear linear. the domain will be the set of natural numbers. the range will be the set of natural numbers. the graph will show exponential decay.
The following statements correctly describe how the graph of the geometric sequence: 640, 160, 40, 10, ... should appear:
the graph will show exponential decay. the domain will be the set of natural numbers.About geometric sequenceThe given sequence is 640, 160, 40, 10, ... which is a geometric sequence.
Here, the first term is 640 and the common ratio is ¼
The terms of a geometric sequence can be written as an = a₁(r)⁽ⁿ⁻¹⁾
Here, a₁ = 640, and r = ¼.
Hence, the nth term of the given sequence is given by the formula:
an = 640(1/4)⁽ⁿ⁻¹⁾
The graph of the given sequence will appear as shown below:
The given sequence is a decreasing sequence, which means the terms of the sequence keep decreasing as the value of n increases.
Therefore, the graph will show exponential decay.
The domain of the sequence will be the set of natural numbers, which is {1, 2, 3, ...}, since we cannot find any term before the first term.
Therefore, the first term is the initial term and we can count the other terms of the sequence in natural numbers.
Hence, the domain will be the set of natural numbers.
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Answer:
the graph will show exponential decay.
the domain will be the set of natural numbers.
Step-by-step explanation:
The answer above is correct.
Hanna has a bag of 20 sweets and eats 7 of them what fraction of the sweets does she eat?
The fraction of sweets that does she eat is 7/20
In this case, we will be using fractions to describe the portion of sweets that Hanna eats from her bag of 20.
Hanna has a bag of 20 sweets, and she eats 7 of them. To find out what fraction of the sweets she eats, we need to determine the ratio of the number of sweets she eats to the total number of sweets in the bag.
So in this case, Hanna eats 7 sweets, and there are 20 sweets in the bag. Therefore, the fraction of sweets she eats can be written as:
=> 7/20
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Question 4(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Order √50,-7.1.3-7 from least to greatest.
0 -7.1.-7. √50,23
O
0-71.-7.7.23,√50
O
0 -7.1.-723√50
0-7-7.1,√50,23
Answer:
D
Step-by-step explanation:
The square root of 50 is approximately equal to 7.07
-7.1111… can be rounded to -7.11
23/3 is equal to approximately 7.67
-7 1/5 is equal to -7.2
URGENT PLEASE HELP!!
Given that f(x)=x^2+3x-7, g(x)=3x+5 and h(x)=2x^2-4, find each of the following. Solve each of the problems showing work.
f(g(x))
h(g(x))
(h-f) (x)
(f+g) (x)
Explain what method you used when had a squared term that had to be multiplied out.
For the given functions, f(x)=x²+3x-7, g(x)=3x+5 and h(x)=2x²-4, f(g(x))= 9x² + 30x + 33, h(g(x))= 18x² + 60x + 46, (h-f)(x)= x² - 3x + 3, (f+g)(x)= x² + 6x - 2.
Describe Function?In mathematics, a function is a mathematical object that takes an input (or several inputs) and produces a unique output. It is a relationship between a set of inputs, called the domain, and a set of outputs, called the range.
Formally, a function f is defined by a set of ordered pairs (x, y) where x is an element of the domain, and y is an element of the range, and each element x in the domain is paired with a unique element y in the range. We write this as f(x) = y.
Functions can be represented in various ways, such as algebraic expressions, tables, graphs, or verbal descriptions. They can be linear or nonlinear, continuous or discontinuous, and may have various properties such as symmetry, periodicity, and asymptotic behavior.
To solve these problems, we substitute the function g(x) for x in f(x) and h(x) and simplify the resulting expressions.
f(g(x)):
f(g(x)) = f(3x+5) = (3x+5)² + 3(3x+5) - 7 (using the definition of f(x))
= 9x² + 30x + 33
h(g(x)):
h(g(x)) = h(3x+5) = 2(3x+5)² - 4 (using the definition of h(x))
= 18x² + 60x + 46
(h-f)(x):
(h-f)(x) = h(x) - f(x) = (2x² - 4) - (x² + 3x - 7) (using the definitions of h(x) and f(x))
= x² - 3x + 3
(f+g)(x):
(f+g)(x) = f(x) + g(x) = x² + 3x - 7 + 3x + 5 (using the definitions of f(x) and g(x))
= x² + 6x - 2
When multiplying out a squared term, such as (3x+5)², we can use the FOIL method, which stands for First, Outer, Inner, Last. We multiply the first terms, then the outer terms, then the inner terms, and finally the last terms, and then add up the results. For example:
(3x+5)² = (3x)(3x) + (3x)(5) + (5)(3x) + (5)(5)
= 9x² + 15x + 15x + 25
= 9x² + 30x + 25
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Assume that head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. Suppose a recruit was found with a head size of 23 inches Find the approximate Z-score for this recruit. a. 0 -0.18 b. 0.18 c. 0.96 d. 476.73
The approximate Z-score for this recruit is b. 0.18.
The mean of the head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. The head size of a recruit was found to be 23 inches.
The approximate Z-score for this recruit. The formula for Z-score is given by:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
where X is the head size of the recruit, μ is the mean head size of recruits, and σ is the standard deviation of head sizes of recruits. Substituting the given values in the above formula, we get,
Z=(23-22.8)(1.1)
Z=0.2/1.1
Z [tex]\approx[/tex] 0.18
Thus, the approximate Z-score for this recruit is b. 0.18.
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Given the price R64,00 (excluding VAT), find the total cost to the buyer (including VAT at 15%).
Therefore, the total cost to the buyer, including VAT at 15%, is R73,60.
What is vat?The term "VAT" usually refers to "Value Added Tax," which is a type of consumption tax that is levied on the value added to goods and services at each stage of production and distribution. It is commonly used by governments around the world as a way to generate revenue and to shift the tax burden from income and sales taxes onto consumption.
by the question.
To calculate the total cost to the buyer including VAT at 15%, you need to add the VAT amount to the original price. Here's how to do it:
Calculate the VAT amount:
VAT = 15% of R64,00
VAT = 0.15 x R64,00
VAT = R9,60
Add the VAT amount to the original price to get the total cost to the buyer:
Total cost = R64,00 + R9,60
Total cost = R73,60
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Can someone please help me out with these two problems. I’ll award brainliest!! Thank you very very much
Answer:
QUESTION 24
To estimate the intercepts, we set f(x) to zero and solve for x:
f(x) = x^3 + 2x^2 - 5x - 6 = 0
Using synthetic division, we can find that x = -2 is a zero of the function. This means that (x + 2) is a factor of f(x), and we can write:
f(x) = (x + 2)(x^2 + x - 3)
Setting each factor to zero, we find that the intercepts are:
x + 2 = 0 -> x = -2
x^2 + x - 3 = 0 -> x = (-1 ± √13)/2
To estimate the turning points, we can use the fact that the derivative of a function is zero at a turning point. The derivative of f(x) is:
f'(x) = 3x^2 + 4x - 5
Setting f'(x) to zero, we find:
3x^2 + 4x - 5 = 0 -> x = (-2 ± √19)/3
We can now use these values to sketch the graph:
The intercepts are (-2,0) and approximately (-2.3,0.0) and (0.8,-7.5).
The turning points are approximately (-1.8,-11.1) and (0.5,-6.8).
The graph starts in the third quadrant, goes through the origin in the second quadrant, has a local maximum in the first quadrant, goes through the x-axis in the fourth quadrant, has a local minimum in the third quadrant, and goes to infinity in the second and fourth quadrants.
QUESTION 26
Here is a sketch of the graph of the polynomial function y = f(x) based on the given information:
| /
| /
| /
| /
| /
| /
| /
| /
-----------+---------------
| /
| /
|/
The graph has two x-intercepts, one around x = -3 and one around x = 2. There is also a turning point or local maximum around x = -1 and a turning point or local minimum around x = 1. The end behavior of the graph is that it approaches negative infinity as x approaches negative infinity and approaches positive infinity as x approaches positive infinity.
Answer:
To estimate the intercepts and turning points of the function f(x) = x^3 + 2x^2 - 5x - 6, we can use a table of values.
When x = 0, f(x) = -6. So the y-intercept is (0, -6).
Factoring the polynomial, we find that the zeros are x = -3, x = -1, and x = 2. Therefore, the x-intercepts are (-3, 0), (-1, 0), and (2, 0).
To find the turning points, we can look for where the slope changes sign. We can estimate that there is a local minimum at (-2.5, -13.6) and a local maximum at (1.1, -7.3).
Using this information, we can sketch the graph of f(x).
To sketch the graph of y = f(x) with the given information, we can plot the x-intercepts (-3, 0), (-1, 0), and (2, 0). We know that the function is positive on the intervals (-∞, -3), (-2, 0), and (2, 3), so we can sketch the function above the x-axis in these regions. Similarly, we know that the function is negative on the intervals (-3,-2), (0, 2), and (3,∞), so we can sketch the function below the x-axis in these regions.
We also know that the function is increasing on the intervals (-2.67, -1) and (1, 2.5), and decreasing on the intervals (-∞, -2.67), (1, 1) and (2.5,∞). Using this information, we can sketch the function as increasing in the intervals (-2.67, -1) and (1, 2.5), and decreasing in the intervals (-∞, -2.67), (1, 1), and (2.5, ∞).
Finally, we can connect the intercepts and turning points with smooth curves to obtain a sketch of the function y = f(x).
Loving the LED's btw!
P(A) = 1/2 P(B) = 3/4 and P(A U B) = 3/8 Find P(A n B)
Answer:
P(A n B) = 1/4
Step-by-step explanation:
We know that:
P(A U B) = P(A) + P(B) - P(A n B)
Substituting the given values, we get:
3/8 = 1/2 + 3/4 - P(A n B)
Simplifying, we get:
P(A n B) = 1/4
Answer: P ( A n B ) = 7/8
Step-by-step explanation: P ( A U B ) = P(A) + P(B) - P( A n B )
3/8 = 1/2 + 3/4 - P( A n B )
3/8 = 5/4 - P ( A n B )
P ( A n B ) = 5/4 - 3/8
P ( A n B ) = 7/8
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP
Answer:
The perimeter of the shape is 53km.
Answer : 53km
Step-by-step explanation: To find the perimeter you need to add all the sides so 8+18+18+9=53 and dont forget the unit km! Have a great day! And good luck!
25.71 rounded to 2 Decimal Place
Answer:
25.71 (2 d.p)
Step-by-step explanation:
[tex].[/tex]
A forest ranger sights a fire directly to the south. A second ranger, 9 miles east of the first ranger, also sights the fire
The bearing from the second ranger to the fire is S 28° W. How far is the first ranger from the fire?
4Interpreting z-scores: Complete the following statements using your knowledge about z-scores.
a. If the data is weight, the z-score for someone who is overweight would be
zero
positive
negative
b. If the data is IQ test scores, an individual with a negative z-score would have a
average IQ
high IQ
low IQ
c. If the data is time spent watching TV, an individual with a z-score of zero would
watch the average amount of TV
watch very little TV
watch a lot of TV
d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be
positive
negative
zero
a. If the data is weight, the z-score for someone who is overweight would be positive.
b. If the data is IQ test scores, an individual with a negative z-score would have a low IQ.
c. If the data is time spent watching TV, an individual with a z-score of zero would watch the average amount of TV.
d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be negative.
The z-score represents how far a data point is from the mean in terms of standard deviations. If someone is overweight, their weight would be above the mean weight, so their z-score would be positive.
Again, the z-score represents how far a data point is from the mean in terms of standard deviations. If someone has a negative z-score for IQ test scores, it means their score is below the mean score, so their IQ would be low.
A z-score of zero means the data point is exactly at the mean, so someone with a z-score of zero for time spent watching TV would watch the average amount of TV.
Again, the z-score represents how far a data point is from the mean in terms of standard deviations. If someone is making minimum wage, their salary would be below the mean salary, so their z-score would be negative.
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A dairy made 98.38 ounces of yogurt. Then a local market bought 86.2 ounces of the yogurt.
How much yogurt does the dairy have left?
The amount of yoghurt left is 12. 18 ounces
How to determine the numberThe algebraic expressions are defined as those expressions that are made up of variables, terms, constants, factors and coefficients.
The expressions are also composed of some arithmetic or mathematical operations, such as;
BracketParenthesesDivisionAdditionSubtractionMultiplicationFrom the information given,
Let the total number of ounces of yoghurt be x
Let the number of ounces of yoghurt sold be y
We have that;
The number left= x - y
= 98.38 - 86.2
= 12. 18 ounces of yoghurt
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Can someone assist me?The cheerleading squad at Morristown High School had 20 members with the old coach. Now, with the new coach, there are 45% more members on the squad. How many members are on the squad now?
Answer:
29
Step-by-step explanation:
First, let's find out how many members are added to the squad with the new coach:
45% of 20 = 0.45 x 20 = 9
So, with the new coach, there are 9 more members added to the squad.
Now, to find the total number of members on the squad with the new coach, we just need to add the old number of members (20) to the number of new members added (9):
20 + 9 = 29
Therefore, there are now 29 members on the cheerleading squad at Morristown High School with the new coach.
a biased dice was rolled and the probability distribution of the outcomes are as follows. what will be the possible probability of getting 3 and of getting 5 when rolling this dice?
The possible probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice is 0.2.
What is the probability?Probability is a branch of math that studies the chance or likelihood of an event occurring.
A biased dice was rolled and the probability distribution of the outcomes are as follows then the outcomes are [tex] 1, 2, 3, 4, 5, 6[/tex]
Probability: [tex]0.2, 0.1, 0.3, 0.1, 0.2, 0.1[/tex]
To find the probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice.
Probability of getting [tex]3[/tex]:
Outcome = [tex]3[/tex]
Probability of getting = [tex]^3P(3) = 0.3[/tex]
So, the possible probability of getting [tex]3[/tex] is [tex]0.3[/tex].
Probability of getting [tex]5[/tex]
So, the outcome of [tex]5[/tex]
Probability of getting [tex]^5P(5) = 0.2[/tex]
So, the possible probability of getting 5 is 0.2.
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Q-15) Ahmadi, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 64 of the automobiles. The sample showed an average of 51.5 miles per gallon with a standard deviation of 4 miles per gallon.
a.Formulate the hypotheses to determine whether or not the manufacturer's advertising campaign is legitimate.
b.Compute the test statistic.
c.What is the p-value associated with the sample results and what is your conclusion? Let a = .05.
It has been established that the manufacturer is legal.
The test statistic is 13
The p-value is 0.
a. Formulate the hypotheses:
The hypotheses for this test are:
H 0: μ ≤ 50
H a: μ > 50.
b. test statistic:
The test statistic will be a t-test because we do not know the population standard deviation.
Since this is a one-sided test, we will use a one-sample t-test.
The test statistic can be calculated using the formula below:
Substituting these values into the formula gives:
t = (51.5 - 50) / (4 / √64)
t = 6.5 / 0.5
t = 13
The test statistic is 13.
c. When the p-value associated with the sample results, using a t-distribution table with 63 degrees of freedom (64 - 1), we find that the p-value associated with a t-statistic of 13 is 0.
Therefore, we can reject the null hypothesis and conclude that the manufacturer's advertising is permitted.
The sample provides sufficient evidence to show that the new small cars average more than 50 miles per gallon of gasoline.
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How can I use the compound angle formula to write sin 165degrees as surds?
We may approximate the sin 165 angles using trigonometric formulas as: tan 165°/(1 + tan2(165°)) (1-cos2(165°))...
Trigonometric identities enable the expression of sin 165° as,
Sin (15°) = sin(180° - 165°)
(-sin 180 + -sin 165) = -sin 345
cos(-75°) = cos(-90° - 165°)
(90 + 165)/255 = -cos 255
Explanation: We know that cos(165) is negative and sin(165) is positive because 165 is in QII. We will use 330 with in half angle formulae because 165=3302.
165 degrees are somewhere between 90 and 180 degrees. Hence, it has an acute angle.
Hence, the 165° angle's addition is 15°. Q. Below are a few angles' measurements.
525 is a positive number of interactions angle, while 195 is a negative coterminal angle.
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If a certain apple tree grew 2 feet and then tripled its height, it would become 4 feet
shorter than the pine tree that grows on the other end of the street. Which
of the formulas below describes the relation between the height of the apple tree a
and the height of the pine tree p?
A) P-4=3a+2
B) P=2(a+3)+4
C) P=3(a+2)-4
D) P=3a+10
Answer:
Step-by-step explanation:
C.) P = 3(a+2)-4
The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given that;
Growth of apple tree= 2feet
Now,
Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:
3(h+2) - 4 = p
Simplifying, we get:
3h + 2 = p
Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.
Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:
P = 3a + 6
This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:
P = 2a + 10
This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:
P = 3a + 2
Therefore, by equation the answer will be P=3(a+2)-4.
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Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree.
Answer:
Were sorry! Answer is not available right now check in later.
Step-by-step explanation:
[ 8 11 2 8 ] [ 1 -2 0 5]
[ 0 -7 2 -1] [ 0 7 1 5]
A = [ -3 -7 2 1], B = [ 0 4 4 0]
[ 1 1 2 4] [ 0 0 0 2]
a. use matlab to compute the determinants of the matrices a+b, a-b, ab, a^-1, and b^t. (recall that in matlab, bt is written as b'.)
b. which of the above matrices are not invertible? explain your reasoning.
c. suppose that you didn't know the entries of a and b, but you did know their determinants. which of the above determinants would you still be able to compute from this information, even without having a or b at hand? explain your reasoning.
if the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square. the area of this square will be 40cm^2 greater than the area of the rectangle. Find the area of the rectangle.
Answer: 30 cm^2.
Step-by-step explanation:
Let the original length of the rectangle be l and its width be w. Then, according to the problem:
(l - 4) = (w + 5) (equation 1)
Also, the area of the square is 40 cm^2 more than the area of the rectangle. Mathematically, we can represent this as:
(l - 4 + 5)^2 = lw + 40
Simplifying the left-hand side and substituting equation 1, we get:
l^2 - 2lw + w^2 = lw + 40
l^2 - 3lw + w^2 - 40 = 0
(l - 8)(l - 5) = 0
Therefore, l = 8 or l = 5. If we substitute l = 8 into equation 1, we get:
w = (l - 4) - 5 = -1
This is not a valid solution since the width cannot be negative. Therefore, the only valid solution is l = 5, which gives:
w = (l - 4) + 5 = 6
So the area of the rectangle is:
A = lw = 5 x 6 = 30 cm^2.
Answer:
steps explanations: x - 4 = y + 5 (sides of a square)
(x - 4)(y + 5) = 40
Which gives;
(y + 5) (y + 5) = 40
y² + 10y + 25 = 40
y² + 10y + 25 - 40 = 0
y² + 10y - 15 = 0
a=1 b=10 and c=-15
If n(Ax B) = 72 and n(A) = 24, find n(B).
Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.
What is Cartesian product?The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.
In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.
For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.
By the question.
We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.
Using the formula for the size of the Cartesian product, we have:
n (Ax B) = n(A) x n(B)
Substituting the given values, we get: 72 = 24 x n(B)
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calculate the value of expression 2x squared - 3x + 1 if x equals to -2
The value of expression is 15.
Define the term quadratic expression?A quadratic equation is a mathematical expression of the second degree, in which the highest power of the variable is 2. An expression is a mathematical phrase that combines numbers, variables, and mathematical operations to represent a value or a set of values.
It takes the form of ax² + bx + c = 0, where a, b, and c are coefficients, and x is the variable.
Given equation is;
⇒ 2x² - 3x + 1
If x = -2, then the solution of equation will be,
⇒ 2×(-2)² - 3×(-2) + 1
⇒ (2×4) + 6 + 1
⇒ 8 + 6 + 1
⇒ 15
Therefore, the value of expression 2x² - 3x + 1 if x = -2 is 15.
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*NEED HELP PLEASE*
Solve each radical equation for x
and check your solution. (Isolate,
solve, check)
Step-by-step explanation:
1. sqrt(x + 6)/5 = 2
sqrt(x + 6) = 10
x + 6 = 100
x = 94
sqrt(94 + 6)/5 = 2
sqrt(100)/5 = 2
10/5 = 2
2 = 2
confirmed.
2.
sqrt(9x + 2) = sqrt(11x - 12)
9x + 2 = 11x - 12
14 = 2x
x = 7
sqrt(9×7 + 2) = sqrt(11×7 - 12)
sqrt(63 + 2) = sqrt(77 - 12)
sqrt(65) = sqrt(65)
confirmed.
3.
cubic root(6x + 3) + 10 = 13
cubic root(6x + 3) = 3
6x + 3 = 27
6x = 24
x = 4
cubic root(6×4 + 3) + 10 = 13
cubic root(24 + 3) + 10 = 13
cubic root(27) + 10 = 13
3 + 10 = 13
13 = 13
confirmed.
4.
2×sqrt(5x - 4) - 24 = -6
sqrt(5x - 4) - 12 = -3
sqrt(5x - 4) = 9
5x - 4 = 81
5x = 85
x = 17
2×sqrt(5×17 - 4) - 24 = -6
2×sqrt(85 - 4) - 24 = -6
2×sqrt(81) - 24 = -6
2×9 - 24 = -6
18 - 24 = -6
-6 = -6
confirmed.
If the ratio a: b is 1 : 4 and the ratio b: c= 3:2, find the ratio (a + c) : c.
The required ratio of is (a + c) : c 11:8.
How to find ratio ?Given that a:b=1:4 and b:c=3:2.
We can simplify the ratio b:c by multiplying both sides by 4 to get b:c=12:8=3:2.
To find the ratio (a+c):c, we need to express a and c in terms of b. From the first ratio, we have [tex]a=\frac14 b$[/tex]. From the second ratio, we have [tex]c=\frac{2}{3}b$[/tex]. Substituting these values into the expression (a+c):c, we get:
[tex]$$(a+c):c = \left(\frac{1}{4}b + \frac{2}{3}b\right):\frac{2}{3}b$$[/tex]
Simplifying the expression inside the parentheses, we get:
[tex]$\frac{1}{4}b + \frac{2}{3}b = \frac{3b}{12} + \frac{8b}{12} = \frac{11b}{12}$$[/tex]
Therefore, the ratio [tex]$(a+c):c$[/tex] is:
[tex]$(a+c):c = \frac{11b}{12}:\frac{2}{3}b = 11:8$$[/tex]
Hence, the required ratio is 11:8$.
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1/sinx+cosx + 1/sinx-cosx = 2sinx/sin^4x-cos^4x
The simplified expression is 2cos²(x) + sinx - 1 = 0
The expression we will be simplifying is
=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.
To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:
(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)
Simplifying this expression using the distributive property, we get:
(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)
Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:
1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1
Similarly, for the second fraction, we can use the same identity to obtain:
1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1
Substituting these values back into the original expression, we get:
1 + 1 = 2sinx/(sin⁴x - cos⁴x)
Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:
sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ
Substituting this back into the expression, we get:
2 = 2sinx/(sin²ˣ - cos²ˣ)
Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):
2 = -2sinx/cos(2x)
Multiplying both sides by -cos(2x), we get:
-2cos(2x) = 2sinx
Dividing both sides by 2, we get:
-cos(2x) = sinx
Using the double-angle formula for cosine, we get:
-2cos²(x) + 1 = sinx
Simplifying this expression, we get:
2cos²(x) + sinx - 1 = 0
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Water flows into a lake at a constant rate.
Grace recorded that 400 litres of water flowed into the lake in 1 minute.
She recorded the number of litres to the nearest 20 litres.
She recorded the time to the nearest
10 seconds.
Calculate the upper bound for the rate at which the water could have flowed into the lake.
Give your answer in litres per second to 2 d.p.
The upper bound for the rate at which the water could have flowed into lake is 8.2 liters per second.
What is an upper bound?An upper limit is a value that is larger than or equal to all the values in a set. In mathematics, it is used to specify a cap or a maximum value for a collection of data. For instance, an upper bound is frequently employed in optimization issues to place a cap on the highest value that a function or variable may take. Upper limits are used in statistics to specify a data set's maximum range which may be used to spot outliers or other abnormalities in the data. In calculus, upper bounds are used to specify a sequence's or series' limit, or the highest number that it may possibly approach.
Given that, 400 liters of water flowed into the lake in 1 minute.
The upper bound of water flow will be the maximum amount of water.
For the nearest measures taken by Grace the amount of water needs to ne more than 400, while the time must be less than 10 seconds from the recorded 1 min.
That is time must be 60 - 10 = 50 seconds.
Approximating the values we have:
410/50 = 8.2 liters per second.
Hence, the upper bound for the rate at which the water could have flowed into lake is 8.2 liters per second.
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VAT is added at 15% for good and services in South Africa. What will be the selling price of a laptop that costs R4200 before VAT
The selling price of laptop after VAT (15 percent) is Rs 4830.
To determine the quantity or percentage of something in terms of 100, use the percentage formula. Percent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed.
A number that is expressed as a fraction of hundred is what it is.
it is mostly used to compare and determine ratios and is represented by the symbol %.
We are given that:-
the selling price of laptop before VAT = Rs 4200VAT= 15%so the amount after VAT = 4200+4200*15%
= 4200+4200+0.15
= 4200+630= 4830.
therefore, the selling price of laptop after VAT is Rs 4830.
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The annual salaries (in $) within a certain profession are modelled by a random variable with the cumulative distribution function F(x)= {1−kx^−3 for x>44000 {0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. a)Find the constant k here and provide its natural logarithm to three decimal places. b)Calculate the mean salary given by the model.
a) The constant k is 5.427 x 10^−12 and its natural logarithm is -26.68.
b) The mean salary of the given model by using the probability density function is approximately $270.86.
a) The cumulative distribution function of the given random variable is provided as follows:
F(x) = {1−kx^−3 if x>44000, and 0 otherwise
The cumulative distribution function is given as
F(x) = 1−kx^−3 if x>44000 and F(x) = 0, if x≤44000i)
We need to check the value of the cumulative distribution function at 44000
We have, F(44000) = 0
0 = 1−k(44000)^−3
⇒ 1 = k(44000)^−3
⇒ k = 1/(44000)^−3
⇒ 5.427 x 10^−12
Taking the natural logarithm of k, we have ln(k) = −28.68 (approx.)
Hence, the constant k is 5.427 x 10^−12 and its natural logarithm to three decimal places is -28.68
b) The probability density function is given as,
f(x) = F'(x) = 3kx^−4, for x>44000 and f(x) = 0, otherwise
The mean or expected value of the random variable is given as
E(X) = ∫[−∞,∞]xf(x)dx
= ∫[44000,∞]x(3kx^−4)dx
= 3k∫[44000,∞]x^−3dx
= 3k[(−1/2)x^−2] [∞,44000]
= (3k/2)(44000)^−2
= 270.86 (approx.)
Therefore, the mean salary given by the model is $270.86 (approx.)
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Classify each as Polynomial or Not a Polynomial.
1.) 9x-^3 - 2y
2.) 2x^2 - 4√x
3.) 2x 2/3 - 4y
4.) 20x^2
5.) w/2 + 7
6.) 4y/2x
7.) -20x^2 + y
