190 pairs of scissors came in each box.
This is an example of a word problem. As a model, a word problem depicts circumstances from the actual world that may be converted into phrases.
Weight of each pair of scissors = 0.34 kg
Weight of a box of scissors = 64.6 kg
Therefore, pairs of scissors in each box = Weight of a box of scissors ÷
Weight of each pair
= 64.6 ÷ 0.34
= 190 pairs.
Hence, 190 pairs of scissors came in each box.
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The ratio of distance runners to sprinters on a track is 5:3 how many distance runners and sprinters could be on the track team
Runners and sprinters could be on the track team is 25 distance.
Distance:
Distance is a qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria (such as "more than two counties"). The term Distance is also often used metaphorically to refer to a measure of the amount of difference between two similar objects.
According too the Question:
Based on the based Information:
15× 5÷3
canceling all the common factor, we get:
5 × 5 = 25
Now, the Product or Quotient is 25.
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A machine produces 225,000 insulating washers for electrical devices per day. The production manager claims that no more than 4,000 insulating washers are defective per day. In a random sample of 200 washers, there were 4 defectives. Determine whether the production manager's claim is likely to be true. Explain.
The claim of the production manager is not true because more than 4000 insulating washers are defective per day.
How to determine if the claim was true or not?The total amount of insulating washer for the electrical devices produced per day = 225,000.
The amount chosen at random for sampling = 200 washers.
The amount shown to be defective in the chosen sample = 4
If every 200 = 4 defective
225,000 = X
Make c the subject of formula;
X = 225000×4/200
X = 900000/200
X = 4,500.
This shows that the claim is wrong because more than 4000 insulating washers are defective per day.
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Write the product in standard form.
(x - 7)²
Answer:
x² - 49
Step-by-step explanation:
(x - 7)² =
(x - 7) * (x - 7) =
x * x - 7 * 7 =
x² - 49
Use the graph of f(x)=−8x-2x^2 to answer the question.
Is f(x) increasing, decreasing, or constant for -2
At x = -2, which is the vertex of the quadratic function, the function f(x) is constant.
How to classify a function as increasing, decreasing or constant?To classify the graph of a function as increasing, decreasing, or constant, you need to examine the direction in which the graph is moving.
A function is considered increasing if its graph moves up and to the right as you follow it from left to right. In other words, if the y-values of the function increase as the x-values increase, then the function is increasing.A function is considered decreasing if its graph moves down and to the right as you follow it from left to right. In other words, if the y-values of the function decrease as the x-values increase, then the function is decreasing.A function is considered constant if its graph remains at the same level and does not move up or down as you follow it from left to right. In other words, if the y-values of the function do not change as the x-values increase, then the function is constant.x = -2 is the vertex of the quadratic function, which is the turning point of the function, where it changes from increasing to decreasing, hence the function is considered to be constant at x = -2, as it has a derivative of zero at x = -2.
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A grocer has two kinds of candies, one selling for 90 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
? pounds of 40 − cent candies, ? pounds of candies that cost $1.40 per pound
Using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
So, we have:
x + y = 100 .........A
40 × x + 140 y = 85 × 100
40 x + 140 y = 8500 ........B
Solving (A) and (B) as follows:
(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100
(40 x - 40 x) + (140 y - 40 y) = 8500 - 4000
0 + 100 y = 4500
y = 4500/100
Hence, the price per unit of grocery is $1.40 = y = 45 pounds.
Now, put the value of y in equation (A) as follows:
x + y = 100
x = 100 - y
x = 100 - 45
x = 55 pounds
The number of groceries at the 40-cent price is x = 55 pounds.
Therefore, using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
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Correct question:
A grocer has two kinds of candies, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
Use Lagrange multiplier techniques to find shortest and longest distances from the origin to the curve x2 + xy + y2 = 3. shortest distance longest distance
The shortest distance from the origin to the curve x2 + xy + y2 = 3 is √(6-2√7) and the longest distance is √(6+2√7).
We have to find the shortest and longest distances from the origin to the curve x^2 + xy + y^2 = 3. This can be done using the Lagrange multiplier technique.
Given, x^2 + xy + y^2 = 3.
We have to minimize and maximize the distance of the origin from the given curve. The distance of the origin from the point (x, y) is given by √(x²+y²).
Therefore, we have to minimize and maximize the function f(x, y) = √(x²+y²) subject to the constraint x^2 + xy + y^2 = 3.
Now, we have to form the Lagrange function.
L(x, y, λ) = f(x, y) + λ(g(x, y))
where, g(x, y) = x2 + xy + y2 - 3L(x, y, λ) = √(x²+y²) + λ(x2 + xy + y2 - 3)
Now, we have to find the partial derivatives of L with respect to x, y, and λ.
∂L/∂x = x/√(x²+y²) + 2λx+y = 0 ............. (1)
∂L/∂y = y/√(x²+y²) + λx+2λy = 0 ............. (2)
∂L/∂λ = x² + xy + y² - 3 = 0 ............. (3)
Solving equations (1) and (2), we get x/√(x²+y²) = 2y/x.
Since x and y cannot be equal to 0 simultaneously, we can say that x/y = ±2.
Substituting x = ±2y in equation (3), we get y²(5±2√7) = 9.
Now, we can solve for x and y to get the values of (x, y) at which the minimum and maximum value of the distance of the origin occurs.
Using x = 2y, we get y²(5+2√7) = 9 ⇒ y = ±3/√(5+2√7)
Using x = -2y, we get y²(5-2√7) = 9 ⇒ y = ±3/√(5-2√7)
Therefore, the four points at which the distance is minimum and maximum are {(2/√(5+2√7), 1/√(5+2√7)), (-2/√(5+2√7), -1/√(5+2√7)), (2/√(5-2√7), -1/√(5-2√7)), (-2/√(5-2√7), 1/√(5-2√7))}.
To find the minimum and maximum distances, we can substitute these points in f(x, y) = √(x²+y²).
After substituting, we get the minimum distance as √(6-2√7) and the maximum distance as √(6+2√7).
Therefore, the shortest distance from the origin to the curve x^2 + xy + y^2 = 3 is √(6-2√7) and the longest distance is √(6+2√7).
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At the bookstore, best-sellers are normally $19.95 each. During the store-wide 20% off sale, how much would it cost you, before tax, to buy two best-sellers?
F. $3.99
G. $7.98
H. $15 96
J. $31.92
K. $39.90
Step-by-step explanation:
20% off means you pay 80 % of the original price for two books
80% * ( 2 x 19.95 ) = .8 ( 39.90) = $ 31.92
a researcher wishes to study railroad accidents. he wishes to select 3 railroads from 10 class i railroads, 2 railroads from 6 class ii railroads, and 1 railroad from 5 class iii railroads. how many different possibilities are there for his study?
There are, 6300 different possibilities for the researcher’s study.
How do we calculate the different possibilities?Total number of class I railroads = 10Number of class I railroads selected = 3Total number of class II railroads = 6Number of class II railroads selected = 2Total number of class III railroads = 5Number of class III railroads selected = 1Number of different possibilities for selecting 3 class I railroads from 10 class I railroads = 10C3 = (10 x 9 x 8)/(3 x 2 x 1) = 120
Number of different possibilities for selecting 2 class II railroads from 6 class II railroads = 6C2 = (6 x 5)/(2 x 1) = 15Number of different possibilities for selecting 1 class III railroad from 5 class III railroads = 5C1 = 5Total number of different possibilities for selecting 3 class I railroads from 10 class I railroads, 2 class II railroads from 6 class II railroads, and 1 class III railroad from 5 class III railroads = 10C3 x 6C2 x 5C1= 120 x 15 x 5= 6300Therefore, there are 6300 different possibilities for the researcher’s study.
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polygon ABCD is similar to polygon ZYXW list the relationships between angles and sides
The corresponding sides and angles of two polygons ABCD and ZYXW must be proportionate if they are identical.
What does a polygon shape mean?With straight sides around its perimeter, a polygon is really a circular, two-dimensional, flat of planar structure. Its sides are straight with no bends. Another term for a polygon's sides is its edges. The points at which two sides of a polygon converge are known as its vertices (or corners). These are numerous examples of polygonal geometry.
Has a polygon always had four sides?A closed polygon is a form with more than three sides. A quadrilateral is a 4-sided polygonal shape. A quadrilateral is any closed 4-sided form, however there are six particular quadrilaterals with distinctive characteristics that give them their own names.
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Your friend Frans tells you that the system of linear equations you are solving cannot have a unique solution because the reduced matrix has a row of zeros. Comment on his claim. The claim is right. The claim is wrong. Need Help?
Answer: Incorrect
Step-by-step explanation:
Your friend Frans' claim is incorrect. A row of zeros in the reduced matrix means that the corresponding equation in the system is redundant and does not provide any additional information. This does not necessarily mean that the system does not have a unique solution. In fact, a row of zeros in the reduced matrix is common when solving systems of linear equations using Gaussian elimination, and it can still lead to a unique solution or even an infinite number of solutions. Therefore, Frans' claim is wrong.
Question
The average of three numbers is 16. If one of the numbers is 18, what is the sum of the other two
numbers?
12
14
20
30
If the average of three numbers is 16 and one of the numbers is 18, then the sum of the other two numbers is option (d) 30
Let's use algebra to solve this problem. Let x and y be the other two numbers we are looking for. We know that the average of the three numbers is 16, so we can write:
(18 + x + y) / 3 = 16
Multiplying both sides by 3, we get,
[(18 + x + y) / 3] × 3 = 16 ×3
18 + x + y = 48
Subtracting 18 from both sides, we get,
18 + x + y - 18 = 48
x + y = 30
Therefore, the correct option is (d) 30
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Solve the following: 2x + y = 15 y = 4x + 3
Suppose you roll a special 37-sided die. What is the probability that one of the following numbers is rolled? 35 | 25 | 33 | 9 | 19 Probability = (Round to 4 decimal places) License Points possible: 1 This is attempt 1 of 2.
The probability of rolling one of these five numbers is 5/37.
Suppose you roll a special 37-sided die. The probability that one of the following numbers is rolled is as follows:
35 | 25 | 33 | 9 | 19.
The total number of sides of a die is 37. As a result, there are 37 numbers in the die.
Rolling one of the 5 given numbers implies that you can select either 35 or 25 or 33 or 9 or 19.
Therefore, the probability of rolling any of these numbers is:
1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 = 5 / 37
So, the probability of rolling one of these five numbers is 5/37.
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find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7.
The number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is 4680.
Step by step explanation:
The number of positive integers with exactly four decimal digits between 1000 and 9999 inclusive can be obtained as follows:
Total number of four decimal digits = 9999 − 1000 + 1 = 9000
Numbers that are multiples of 5 are obtained by starting with 1000 and adding 5, 10, 15, 20, ..., 1995, that is, 5k, where k = 1, 2, 3, ..., 399.
Therefore, the number of positive integers with exactly four decimal digits that are multiples of 5 is 399.
Numbers that are multiples of 7 are obtained by starting with 1001 and adding 7, 14, 21, 28, ..., 1428, that is, 7m, where m = 1, 2, 3, ..., 204.
Therefore, the number of positive integers with exactly four decimal digits that are multiples of 7 is 204.
Note that some numbers in the interval [1000, 9999] are divisible by both 5 and 7. Since 5 and 7 are relatively prime, the product of any number of the form 5k by a number of the form 7m is a multiple of 5 × 7 = 35.
The numbers of the form 35n in the interval [1000, 9999] are
1035, 1070, 1105, 1140, ..., 9945, 9980.
We can check that there are 285 numbers of this form.
To find the number of positive integers with exactly four decimal digits that are not divisible by either 5 or 7, we will subtract the number of multiples of 5 and 7 and add the number of multiples of 35.
Therefore, the number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is
9000 - 399 - 204 + 285 = 4680.
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a normal distribution of exam scores has a standard deviation of 8. a score that is 12 points above the mean would have a z-score of: a score that is 20 points below the mean would have a z-score of:
The standard deviation of a normal distribution of exam scores is 8. A score that is 12 points above the mean would have a z-score of 1.5, and a score that is 20 points below the mean would have a z-score of -2.5.
What is the z-score?The z-score can be calculated by dividing the difference between a data value and the mean of the data set by the standard deviation of the data set.
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8.
z = (x−μ)/σ = (x−μ)/σ = (12−0)/8 = 1.5
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8 is 1.5.
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8.
z = {x-μ}/{σ} = {-20-0}/{8} = −2.5
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8 is -2.5.
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Jenny works at Sammy's Restaurant and is paid according to the rates in the following
table.
Jenny's weekly wage agreement
Basic wage $600.00
PLUS
$0.90 for each customer served.
In a week when Jenny serves n customers, her weekly wage, W, in dollars, is given by
the formula
W = 600+ 0.90n.
(i) Determine Jenny's weekly wage if she served 230 customers.
(ii) In a good week, Jenny's wage is $1 000.00 or more. What is the LEAST number
of customers that Jenny must serve in order to have a good week?
(iii) At the same restaurant, Shawna is paid a weekly wage of $270.00 plus $1.50 for
each customer she serves.
If W, is Shawna's weekly wage, in dollars, write a formula for calculating Shawna's
weekly wage when she serves m customers.
(iv) In a certain week, Jenny and Shawna received the same wage for serving the same
number of customers.
How many customers did they EACH serve?
Jenny works at Sammy's Restaurant and is paid according to the rates in the following
table.
Jenny's weekly wage agreement
Basic wage $600.00
PLUS
$0.90 for each customer served.
In a week when Jenny serves n customers, her weekly wage, W, in dollars, is given by
the formula
W = 600+ 0.90n.
(i) Determine Jenny's weekly wage if she served 230 customers.
(ii) In a good week, Jenny's wage is $1 000.00 or more. What is the LEAST number
of customers that Jenny must serve in order to have a good week?
(iii) At the same restaurant, Shawna is paid a weekly wage of $270.00 plus $1.50 for
each customer she serves.
If W, is Shawna's weekly wage, in dollars, write a formula for calculating Shawna's
weekly wage when she serves m customers.
(iv) In a certain week, Jenny and Shawna received the same wage for serving the same
number of customers.
How many customers did they EACH serve?
3 / 3
(i) If Jenny serves 230 customers, her weekly wage is
W = 600 + 0.90n = 600 + 0.90(230) = $807.00
Therefore, Jenny's weekly wage if she serves 230 customers is $807.00.
(ii) We want to find the least number of customers, n, that Jenny must serve in order to earn $1,000 or more. That is,
600 + 0.90n ≥ 1,000
0.90n ≥ 400
n ≥ 444.44
Since n must be a whole number, Jenny must serve at least 445 customers in order to earn $1,000 or more in a week.
(iii) Shawna's weekly wage, W, in dollars, when she serves m customers is given by the formula:
W = 270 + 1.50m
Therefore, Shawna's weekly wage when she serves m customers is $270.00 plus $1.50 for each customer she serves.
(iv) Let's assume that Jenny and Shawna received the same wage, W, for serving the same number of customers, x. Then we have:
Jenny's wage = 600 + 0.90x
Shawna's wage = 270 + 1.50x
Setting these two expressions equal to each other, we get:
600 + 0.90x = 270 + 1.50x
330 = 0.60x
x = 550
Therefore, Jenny and Shawna each served 550 customers.
Find a basis for the vector space of polynomialsp(t)of degree at most two which satisfy the constraintp(2)=0. How to enter your basis: if your basis is1+2t+3t2,4+5t+6t2then enter[[1,2,3],[4,5,6]]
In the following question, among the conditions given, {q1, q2} is a basis for the vector space of polynomials p(t) of degree at most two that satisfy the constraint p(2) = 0. In this particular case, we must enter our basis as [[1,0,-4],[0,1,-2]], since q1(t) = t^2 - 4 and q2(t) = t - 2.
To find a basis for the vector space of polynomials p(t) of degree at most two which satisfy the constraint p(2)=0, we can take the following steps:
1. Rewrite the polynomials as linear combinations of the form a + bt + ct^2
2. Use the constraint p(2) = 0 to eliminate one of the coefficients a, b, or c
3. Normalize the polynomials so that they are unit vectors
For example, if your basis is 1 + 2t + 3t^2, 4 + 5t + 6t2 then you can enter it as [[1,2,3],[4,5,6]].
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For each problem, select the best response (a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is A. a large positive number. OB. exactly 1.96 c. a large negative number. D. close to o E. close to 1. (b) A study was performed to examine the personal goals of children in elementary school. A random sample of students was selected and the sample was given a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Each student's sex (boy or girl) was also recorded. If a contingency table for the data is evaluated with a chi-squared test, what are the hypotheses being tested? A. The null hypothesis that boys are more likely than girls to desire good grades vs. the alternative that girls are more likely than boys to desire good grades. OB. The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. C. The null hypothesis that there is no relationship between personal goals and sex vs. the alternative hypothesis that there is a positive, linear relationship. OD. The null hypothesis that the mean personal goal is the same for boys and girls vs. the alternative hypothesis is that the means differ. O E. None of the above. (C) The variables considered in a chi-squared test used to evaluate a contingency table A. are normally distributed. B. are categorical. C. can be averaged. OD. have small standard deviations. E. have rounding errors.
a) Option A, A x2 statistic provides strong evidence in favor alternative hypothesis if its value is a large positive number.
b) Option B, The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.
c) Option B, The variables considered in a chi-squared test used to evaluate a contingency table B. are categorical.
(a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number. The x2 statistic is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. A large positive value indicates that the observed frequencies are significantly different from the expected frequencies, which supports the alternative hypothesis.
(b) The hypotheses being tested in a chi-squared test on a contingency table are the null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. This test determines whether there is a significant association between two categorical variables.
(c) The variables considered in a chi-squared test used to evaluate a contingency table are categorical. These variables cannot be averaged or assumed to be normally distributed. The chi-squared test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.
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4-77 Is the relationship shown in the 28+
graph at right below proportional? If
241
so, find the unit rate. If not, explain
why not.
The graph is/is not proportional
because
Unit rate:
Cost ($)
20
16-
12+
8
2 3 4 5
Number of Books
Purchased
Answer:
Step-by-step explanation:
A graph is proportional if the relationship between the two variables represented on the axes is constant, meaning that if one variable increases, the other variable also increases by the same factor. In other words, the graph forms a straight line that passes through the origin.
To find the unit rate, you need to look for the constant of proportionality, which is the ratio between the two variables represented on the graph. In this case, the variables are the number of books purchased and the cost in dollars.
If the graph is proportional, then the unit rate is the constant of proportionality, which is the cost per book. You can find the unit rate by dividing the total cost by the number of books purchased. For example, if the total cost for 4 books is $16, then the unit rate would be $4 per book.
If the graph is not proportional, then there is no constant of proportionality, and the unit rate cannot be calculated. The relationship between the two variables may be nonlinear, meaning that the rate of change between the variables is not constant.
In right triangle RST, with m∠S = 90°, what is sin T?
The ratio of the length of the side directly opposite the angle to the length of the hypotenuse is known as the sine of an acute angle in a right triangle.
Hence, the sine of angle T in the right triangle RST with a right angle at S is given by:
opposite side / hypotenuse = sin T
We must know the triangle's side lengths in order to calculate the value of sin T. We can use trigonometric ratios to calculate the lengths of the remaining sides.
if we know the length of the hypotenuse and the measurement of one acute angle.
thus, we cannot define the value of triangle RST.
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[amc10b.2011.7] the sum of two angles of a triangle is $\frac{6}{5}$ of a right angle, and one of these two angles is $30^{\circ}$ larger than the other. what is the degree measure of the largest angle in the triangle?
The degree measure of the largest angle is 72° in the triangle.
We have, The sum of two angles of a triangle is 6/5 of a right angle.
One of these two angles is 30° larger than the other.
Let A and B be the two angles of the triangle such that A = B + 30°.
We know that the sum of three angles in a triangle is 180°.
⇒ A + B + C = 180°
⇒ B + 30° + B + C = 180°
⇒ 2B + C = 150°
We also know that the sum of two angles of a triangle is 6/5 of a right angle.
⇒ A + B = 6/5 × 90°
⇒ B + 30° + B = 108°
⇒ 2B = 78°
⇒ B = 39°
C = 150° - 2B ⇒ 72°
A = B + 30° ⇒ 39° + 30° ⇒ 69°
Therefore, the degree measure of the largest angle in the triangle is 72°.
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What is the slope of the line described by the equation below?
y = -6x +3
O A. -6
() в. -з
O C. 6
OD. 3
SUBMIT
twenty percent of americans ages 25 to 74 have high blood pressure. if 16 randomly selected americans ages 25 to 74 are selected, find each probability. a. none will have high blood pressure. b. one-half will have high blood pressure. c. exactly 4 will have high blood pressure.
Then we will get the following odds
a. None will have high blood pressure. Let the probability of having high blood pressure be denoted by P(A) and the probability of not having high blood pressure be denoted by P(A'). Since none will have high blood pressure, it means all the sixteen Americans selected are healthy, and therefore P(A') = 1. Therefore
P(A) = 1 - P(A')= 1 - 1= 0
b. One-half will have high blood pressure. The probability that one-half of the sixteen Americans will have high blood pressure can be found using the binomial distribution formula that is given by the expression
[tex]P(X = r) = (nCr) * p^r * q^{(n-r)}[/tex]
Where
r = 8n = 16 p = 0.2 q = 1 - p = 0.8Therefore
[tex]P(X = 8) = (16C8) * 0.2^8 * 0.8^8= 0.202[/tex]
c. Exactly 4 will have high blood pressure Similarly, the probability that exactly four of the sixteen Americans will have high blood pressure can be found using the binomial distribution formula as follows:
[tex]P(X = r) = (nCr) * p^r * q^{(n-r})[/tex]
Where
r = 4n = 16p = 0.2q = 1 - p = 0.8Therefore
[tex]P(X = 4) = (16C4) * 0.2^4 * 0.8^{12}= 0.236[/tex]
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PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited and depends on a single gene that codes for a taste receptor on the tongue. Interestingly, although the PTC molecule is not found in nature, the ability to taste it correlates strongly with the ability to taste other naturally occurring bitter substances, many of which are toxins. About 75 % of Italians can taste PTC. You want to estimate the proportion of Americans with at least one Italian grandparent who can taste PTC. (a) Starting with the 75 % estimate for Italians, how large a sample must you collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence? (Enter your answer as a whole number.) n = (b) Estimate the sample size required if you made no assumptions about the value of the proportion who could taste PTC. (Enter your answer as a whole number.) n =
(a) Starting with the 75% estimate for Italians, the sample you must collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence is n = 51.
(b) The sample size required if you made no assumptions about the value of the proportion who could taste PTC is n = 68.
(a) To estimate the sample size needed to find the proportion of PTC tasters within ± 0.1 with 90% confidence, we will use the formula for sample size estimation in proportion problems:
n = (Z² * p * (1-p)) / E²
Where n is the sample size, Z is the Z-score corresponding to the desired confidence level (1.645 for 90% confidence), p is the proportion of PTC tasters (0.75), and E is the margin of error (0.1).
n = (1.645² * 0.75 * (1-0.75)) / 0.1²
n = (2.706 * 0.75 * 0.25) / 0.01
n ≈ 50.74
Since we need a whole number, we round up to the nearest whole number:
n = 51
(b) If no assumptions were made about the proportion of PTC tasters, we would use the worst-case scenario, which is p = 0.5 (maximum variance):
n = (1.645² * 0.5 * (1-0.5)) / 0.1²
n = (2.706 * 0.5 * 0.5) / 0.01
n ≈ 67.65
Again, rounding up to the nearest whole number:
n = 68
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1. Find the given derivative by finding the first few derivatives and observing the pattern that occurs. (d115/dx115(sin(x)). 2. For what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable. Enter your answers as a comma- separated list.) f(x) = x + 2 sin(x).
The values of x such that the graph of f has a horizontal tangent are;x = 2π/3 + 2πn, 4π/3 + 2πn, where n is an integer.
1. The given derivative can be found by finding the first few derivatives and observing the pattern that occurs as shown below;Differentiating sin x with respect to x gives the derivative cos x. Continuing this process, the pattern that emerges is that sin x changes sign for every odd derivative, and stays the same for every even derivative. Therefore the 115th derivative of sin x can be expressed as follows;(d115/dx115)(sin x) = sin x, for n = 58 (where n is an even number)2. To find the values of x such that the graph of f has a horizontal tangent, we differentiate f with respect to x, and then solve for x such that the derivative equals zero. We have;f(x) = x + 2sin xDifferentiating f(x) with respect to x gives;f'(x) = 1 + 2cos xFor a horizontal tangent, f'(x) = 0, thus;1 + 2cos x = 02cos x = -1cos x = -1/2The solutions of the equation cos x = -1/2 are;x = 2π/3 + 2πn or x = 4π/3 + 2πnwhere n is an integer. Therefore the values of x such that the graph of f has a horizontal tangent are;x = 2π/3 + 2πn, 4π/3 + 2πn, where n is an integer.
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On January 1,1999 , the average price of gasoline was $1.19 per gallon. If the price of gasoline increased by 0.3% per month, which equation models the future cost of gasoline? y=1.19(1.003)^(x) y=1.19(x)^(1.03) y=1.19(1.03)^(x)
Answer:
first one
Step-by-step explanation:
The equation that models the future cost of gasoline is y=1.19(1.003)^(x), where "y" represents the future cost of gasoline per gallon and "x" represents the number of months since January 1, 1999.
In this equation, the initial cost of gasoline is $1.19 per gallon, and the cost increases by 0.3% per month, which is represented by the factor of (1.003)^(x).
Using this equation, you can calculate the future cost of gasoline for any number of months after January 1, 1999. For example, if you want to calculate the cost of gasoline 24 months after January 1, 1999, you can plug in x=24 and calculate y as follows:
y = 1.19(1.003)^(24)
y = 1.19(1.08357)
y = 1.288 per gallon
Therefore, the predicted cost of gasoline 24 months after January 1, 1999 is $1.288 per gallon.
how many square tiles are shaded and not shaded for the 8th figure?
Let Y be a binomial random variable with n trials and probability of success given by p. Use the method of moment-generating functions to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p.
U is a binomial random variable with n trials and probability of success given by 1 - p.
As Y is a binomial random variable with n trials and probability of success given by p. Using the moment-generating functions method, it can be shown that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The binomial distribution is described by two parameters: n, which is the number of trials, and p, which is the probability of success in any given trial. If a binomial random variable is denoted by Y, then:[tex]P(Y = k) = \binom{n}{k}p^{k}(1 - p)^{n-k}[/tex]
The method of generating moments can be used to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The moment-generating function of a binomial random variable is given by: [tex]M_{y}(t) = [1 - p + pe^{t}]^{n}[/tex]
The moment-generating function for U is: [tex]M_{u}(t) = E(e^{tu}) = E(e^{t(n-y)})[/tex]
Using the definition of moment-generating functions, we can write: [tex]M_{u}(t) = E(e^{t(n-y)})$$$$= \sum_{y=0}^{n} e^{t(n-y)} \binom{n}{y} p^{y} (1-p)^{n-y}[/tex]
Taking the summation of the above expression: [tex]= \sum_{y=0}^{n} e^{tn} e^{-ty} \binom{n}{y} p^{y} (1-p)^{n-y}$$$$= e^{tn} \sum_{y=0}^{n} \binom{n}{y} (pe^{-t})^{y} [(1-p)^{n-y}]^{1}$$$$= e^{tn} (pe^{-t} + 1 - p)^{n}[/tex]
Comparing this expression with the moment-generating function for a binomial random variable, we can say that U is a binomial random variable with n trials and probability of success given by 1 - p.
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use a blank number line to solve. which of the following expressions have a value that is less than 0? select all that apply. Sorry is it says i am in high school i am in 7th grade
a)-5+3
b)6+(-8)
c)5+(-3)
d)-2+5
The expressions that have values less than 0 are a) and b)
According to the question
Here's how you can use a number line to solve this problem:
Draw a blank number line with a zero in the middle.For each expression, start at zero and move to the right or left depending on the sign of the first number.Then, add or subtract the second number to get the final position on the number line.If the final position is to the left of zero, the expression has a value that is less than 0.For example in expression a) -5 + 3, start at zero and move 5 units to the left (because of the negative sign on 5), and then move 3 units to the right. The final position is at -2, which is to the left of zero. Therefore, expression a) has a value that is less than zero.
Similarly expression b) has a value that is less than zero.
Also expressions c) and d) can be solved in the same way. If the final position is to the right of zero, the expression does not have a value that is less than zero.
In conclusion, expressions a) and b) have a value that is less than zero, while expressions c) and d) do not.
What is a number line?
A number line is a visual representation of real numbers arranged in a straight line used to compare, add, and subtract numbers.
What is meant by expressions?
An expression is a combination of numbers, variables, and mathematical operations used to represent a quantity or a mathematical statement.
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a 20-volt electromotive force is applied to an lr-series circuit in which the inductance is 0.1 henry and the resistance is 40 ohms. find the current i(t) if i(0) = 0.
i(t) = ___
Determine the current as t → [infinity].
lim t→[infinity] i(t) =_____
The time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
The current of the given LR-series circuit can be determined using the formula I = (E/R) * (1 - e^-Rt/L).The current i(t) if i(0) = 0 in the LR-series circuit is given by i(t) = 0.125A. The current as t → [infinity] is given by lim t→[infinity] i(t) = 0.How to solve this?The formula for the current in the LR-series circuit is given by:Where E is the electromotive force, R is the resistance, L is the inductance, t is time and I is the current.I = (E/R) * (1 - e^-Rt/L)Given E = 20V, R = 40Ω, L = 0.1H, and i(0) = 0Substitute these values in the above formula.I = (20/40) * (1 - e^-40t/0.1)I = 0.5(1 - e^-400t)I = 0.5 - 0.5e^-400tSo the current is i(t) = 0.5 - 0.5e^-400t.Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0. Answer: The current is i(t) = 0.5 - 0.5e^-400t. Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
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