The answer is: A) r=0.04; R=0.96 B) 8% C) 92.16%.
The Hardy-Weinberg equilibrium is a method for determining the frequency of certain genetic traits in a population. The following are the frequencies of the red hair (r) and non-red hair (R) alleles in the Norwegian population, according to the question: A) The total frequency of alleles is 1. If red hair (r) is found in approximately 4% of the people in Norway, then the frequency of the R allele must be 0.96 or 96%. R = 0.96 r = 0.04 B) The frequency of hetero zygotes in a population can be determined by multiplying the frequency of the R allele by the frequency of the r allele and then multiplying that number by 2.
Heterogeneous genotype = 2pq Here, p represents the frequency of the R allele, and q represents the frequency of the r allele. p = R = 0.96 q = r = 0.04 Therefore, 2pq = 2(0.96 x 0.04) = 0.077, or approximately 8%. C) In order for a child to have red hair, both parents must carry the r allele. If both parents are homozygous for the R allele, there is no chance that their child will have red hair. This means that the proportion of matings that cannot result in a child with red hair is (0.96 x 0.96) = 0.9216 or 92.16%.
Therefore, the answer is: A) r=0.04; R=0.96 B) 8% C) 92.16%.
Learn more about Heterogeneous
brainly.com/question/30583932
#SPJ11
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
X
The surface area of the triangular prism is 2016 [tex]feet ^2[/tex], we get to the answer by adding area of all faces in this prism.
What is surface area ?
Surface area is the sum of the areas of all the faces or surfaces of a 3D object, measured in square units.
To find the surface area of the triangular prism, we need to calculate the area of each of its faces and then add them up.
First, let's find the area of the triangular base.
Area of triangle = (1/2) x base x height
Area of triangle = (1/2) x 18 x 24
Area of triangle = 216 [tex]feet ^2[/tex]
Next, let's find the area of each rectangular face.
Area of rectangle = length x width
Area of rectangle 1 = 24 x 22 = 528 [tex]feet ^2[/tex]
Area of rectangle 2 = 18 x 22 = 396 [tex]feet ^2[/tex]
Area of rectangle 3 = 22 x 30 = 660 [tex]feet ^2[/tex]
Now, we can add up the areas of all three faces to get the total surface area of the prism:
Surface area = area of rectangle (1+2+3) + 2 x area of triangle
Surface area = 528 + 396 + 660 + 2(216)
Surface area = 2016 [tex]feet ^2[/tex]
Therefore, the surface area of the triangular prism is 2016 [tex]feet ^2[/tex].
To learn more about triangular prism from the given link :
https://brainly.com/question/22023329
#SPJ1
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.
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.
To learn about triangle RST visit:
https://brainly.com/question/28738706?referrer=searchResults
#SPJ4
Which of the following equations is equivalent to 2 x + 6 = 30 - x - 3 2 x + 6 = 10 - x - 3 2 x + 6 = 30 - x + 3
The equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.
What is equation?
In mathematics, an equation is a statement that two expressions are equal, usually written with an equal sign (=) between them. Equations can contain variables, which are symbols that represent unknown or unspecified values.
We can simplify and solve the equation 2x + 6 = 30 - x - 3 as follows:
2x + 6 = 30 - x - 3
Adding x and adding 3 to both sides, we get:
3x + 9 = 30
Subtracting 9 from both sides, we get:
3x = 21
Dividing both sides by 3, we get:
x = 7
So the given equation simplifies to x = 7.
We can now substitute this value of x into each of the answer choices to see which one is equivalent to the given equation:
a) 2x + 6 = 30 - x - 3
Substituting x = 7, we get:
2(7) + 6 = 30 - 7 - 3
14 + 6 = 20
20 = 20
b) 2x + 6 = 10 - x - 3
Substituting x = 7, we get:
2(7) + 6 = 10 - 7 - 3
14 + 6 = 0
20 ≠ 0
Therefore, this equation is not equivalent to the given equation.
c) 2x + 6 = 30 - x + 3
Substituting x = 7, we get:
2(7) + 6 = 30 - 7 + 3
14 + 6 = 26
20 ≠ 26
Therefore, this equation is not equivalent to the given equation.
Therefore, the equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.
To learn more about equation visit:
https://brainly.com/question/2972832
#SPJ1
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.
Learn more about Distance:
https://brainly.com/question/15172156
#SPJ4
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.
More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
a cyclist rides her bike at a speed of 21 kilometers per hour. what is this speed in kilometers per minute? how many kilometers will the cyclist travel in 2 minutes? (do not round the answer)
Answer:
see the answer and explanation in the attached figure below
Step-by-step explanation:
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
Learn more about average here
brainly.com/question/1416374
#SPJ4
given the results of the two hypothesis tests, would you reject or fail to reject your null hypotheses (assuming a 0.05 significance level)? what does your decision mean in the context of this problem? would you proceed with changing the design of the shopping cart icon, or would you stay with the original design?
Assuming a 0.05 significance level, both hypothesis tests would reject the null hypothesis. This means that there is enough evidence to suggest that the shopping cart icon's design affects the users' behavior. Therefore, the design should be changed to improve the user's experience.
Step by step explanation:
The problem is not stated, so we need to make some assumptions. We will assume that the hypothesis tests were done to determine whether a change in the shopping cart icon design would affect the users' behavior.
The null hypothesis (H0) is that the design of the shopping cart icon does not affect the users' behavior, while the alternative hypothesis (Ha) is that the design of the shopping cart icon affects the users' behavior.
The significance level is 0.05, which means that we are willing to accept a 5% chance of making a type I error (rejecting the null hypothesis when it is actually true).
If both hypothesis tests reject the null hypothesis, it means that the p-values were less than 0.05, and there is enough evidence to suggest that the design of the shopping cart icon affects the users' behavior.
Therefore, it is recommended to proceed with changing the design of the shopping cart icon to improve the user's experience.
See more about null hypothesis at: https://brainly.com/question/4436370
#SPJ11
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.
To know more about polygons visit:
https://brainly.com/question/24464711
#SPJ1
suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. if the population grows to 500 after one year, what will the population be after another three years?
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, the population will be 852.78 after another three years.
What is the logistic model?A logistic model, also known as the Verhulst-Pearl model, is a type of function used to describe population growth that is limited. It’s a form of exponential growth that takes into account the carrying capacity of an environment.
Population growth that is limited and slows down as the population approaches its carrying capacity is modeled using the logistic model. It is given by this equation:
[tex]P(t) = K / (1 + Ae^{-rt})[/tex]
where P(t) is the population at time t, K is the carrying capacity, A is the constant of proportionality, and r is the growth rate.
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, substitute this information into the logistic model: [tex]P(1) = 500[/tex], [tex]K = 2000[/tex], and [tex]P(0) = 200[/tex].
[tex]500 = 2000 / (1 + Ae^{-r(1)})[/tex]
Now, solve for A by dividing both sides by 2000 / (1 + A):
[tex]1 + A = 4A = 3[/tex]
Substitute the value of A back into the logistic model equation:
[tex]P(t) = 2000 / (1 + 3e^{-rt})[/tex]
Solve for r by using the data provided in the problem for the first year (t = 1) and second year (t = 4):
[tex]P(1) = 500 = 2000 / (1 + 3e^{-r(1)})[/tex]
[tex]P(4) = ? = 2000 / (1 + 3e^{-r(4)})[/tex]
Solve the first equation for r:
[tex]500 = 2000 / (1 + 3e^{-r})\\1 + 3e^{-r} = 4e^{-r}\\1 + 3e^r = 4e[/tex]
Solve for e using the quadratic formula to get:
e = 0.4274 and e = 1.1713
Let e = 0.4274:
[tex]1 + 3e^{-r} = 4e^{-r}\\1 + 3(0.4274)^{-r} = 4(0.4274)^{r}\\1 + 0.5746^r = 1.7166^r[/tex]
Take the natural logarithm of both sides:
[tex]ln(1 + 0.5746^r) = ln(1.7166^r) - lnr\\ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]
Use a graphing calculator to solve for r:
[tex]ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]; -0.1568 < r < 0.7534
Solve for r using the second year’s data:
[tex]2000 / (1 + 3e^{-r(4)}) = P(4)\\2000 / (1 + 3(0.4274)^{-r(4)}) = P(4)\\P(4) = 852.78[/tex]
Thus, the population will be 852.78 after another three years.
Learn more about logistic model here:
https://brainly.com/question/30995760
#SPJ11
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.
To learn more about "Binomial random variable": brainly.com/question/30657837
#SPJ11
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.
Know more about equations here:
https://brainly.com/question/2972832
#SPJ1
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?
Solve the following: 2x + y = 15 y = 4x + 3
John Paszel took out a loan for 51 months but paid it in full after 25 months. Find the refund fraction he should use to
calculate the amount of his refund.
Answer: calculate the amount of his refund.
Step-by-step explanation:
Design a cylindrical can (with a lid) to contain 1 liter (= 1000 cm3) of water, using the minimum amount of metal.
To design a cylindrical can (with a lid) to contain 1 liter (= 1000 cm3) of water, using the minimum amount of metal, we need to consider the following parameters:Height and Diameter of the canThickness of the metalMaterial used for making the canLet's assume we use Aluminium as a material. Now, let's start designing the can:Height of the can:
Volume of water = 1000 cm3Volume of cylinder = πr²hVolume of cylinder = π (d/2)² hVolume of cylinder = π (d²/4) hVolume of cylinder = 1000 cm³π (d²/4) h = 1000 cm³d²h = 4000 cm³h = (4000 cm³) / (π d²) h = (4000 cm³) / (3.14 * d²) h = (1273.24) / d²Diameter of the can:
Volume of cylinder = πr²hVolume of cylinder = π (d/2)² hVolume of cylinder = π (d²/4) hVolume of cylinder = 1000 cm³π (d²/4) h = 1000 cm³d²h = 4000 cm³d² = (4000 cm³) / h d² = (4000 cm³) / (1273.24/d²) d² = 3.1425d = 17.8 cmThickness of the metal:We can assume the thickness to be 0.5 mm.Material used for making the can:AluminiumTotal Surface Area of the can:Total Surface Area of cylinder = 2πrhTotal Surface Area of cylinder = 2π(d/2)(1273.24/d²)Total Surface Area of cylinder = 1273.24/d Total Surface Area of lid = πr²Total Surface Area of lid = π (d/2)²Total Surface Area of lid = π (17.8/2)²Total Surface Area of lid = 248.5Total Surface Area of the Can = 1273.24/d + 248.5Now, we can calculate the minimum amount of Aluminium required to make the can by minimizing the Total Surface Area of the can.Total Surface Area of the can = 1273.24/d + 248.5d (in cm)Total Surface Area of the can = 1273.24/7.09 + 248.5(7.09)Total Surface Area of the can = 584.24Therefore, the minimum amount of Aluminium required to make the can is 584.24 cm².
for such more questions on Total Surface Area
https://brainly.com/question/31186196
#SPJ11
[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°.
To know more about the "sum of two angles" of a triangle: https://brainly.in/question/19076450
#SPJ11
-17.R Using Percents, Homework
Sarted: Mar 10 at 8:30pm
Question 1 of 9
The Quick Slide Skate Shop sells the Ultra 2002 skateboard for a price of $60.20. However, the Quick Slide
Skate Shop is offering a one-day discount rate of 45% on all merchandise. About how much will the Ultra 2002
skateboard cost after the discount?
$33.00
$87.00
$46.20
$27.00
The price after discount is $33 and option 1 is the correct answer.
What is a discount?A discount is a drop in a product's or service's price. Discounts can be provided for a variety of purposes, such as to entice consumers to make larger purchases, to get rid of excess inventory, or to draw in new clients. Discounts can be represented as a set monetary amount or as a %, as in the example above. For instance, a shop may give customers $10 off any purchase of more than $50.
Given that, one-day discount rate of 45% is applied.
Thus,
Discount = 60.20 * 0.45 = 27.09
Price after discount = 60.20 - 27.09 = 33.11
Hence, the price after discount is $33 and option 1 is the correct answer.
Learn more about discount here:
https://brainly.com/question/16999193
#SPJ1
. A circular fence is being used to surround a dog house. How much fencing is needed to build the fence?
45.53 ,fencing is needed to build the fence.
What is area?A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition polyhedra of arc length for one-dimensional curves and the definition of surface area for (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double much simpler mathematical concepts than the definition of surface area integration and is based on techniques used in infinitesimal calculus.sought a general definition of surface area.
Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.
2*3.14*14.5/2
45.53ft
learn more about area click here:
brainly.com/question/16519513
#SPJ1
three traffic lights on a street span 120 yards. if the second traffic light is 85 yards away from the first, how far in yards is the third traffic light from the seccond
The distance between the third traffic light from the second traffic light is 35 yards.
What is the distance?Three traffic lights on a street span 120 yards.
If the second traffic light is 85 yards away from the first.
Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.
This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.
Thus, the distance between the third traffic light from the second traffic light is 35 yards.
Learn more about Traffic light here:
https://brainly.com/question/29033668
#SPJ11
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.
See more about calculate possibilities at: https://brainly.com/question/4658834
#SPJ11
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]
See more about probability at: https://brainly.com/question/13604758
#SPJ11
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
Find the slope-intercept form of the line with the slope m= 1/7 which passes through the point (-1, 4).
Answer:
y = 1/7x + 29/7
Step-by-step explanation:
Slope intercept form is y = mx + b
m = the slope
b = y-intercept
m = 1/7
Y-intercept is located at (0, 29/7)
So, the equation is y = 1/7x + 29/7
I NEED HELP ON THIS ASAP!!
From the graph, the feasible region from the system of linear inequalities is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.
What is the system of linear inequalitiesa. Let x be the amount of loam soil (in tons) sold, and y be the amount of peat soil (in tons) sold. The system of inequalities representing the constraints of the problem situation is:
x ≥ 0 (non-negative amount of loam soil)
y ≥ 0 (non-negative amount of peat soil)
x + y ≤ 120 (total amount of soil sold is at most 120 tons)
x ≤ 60 (maximum amount of loam soil available is 60 tons)
y ≤ 90 (maximum amount of peat soil available is 90 tons)
To graph these inequalities, we can plot the feasible region (the region that satisfies all the inequalities) in the x-y plane, as shown below;
The feasible region is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.
b. The profit function P(x, y) for selling x tons of loam soil and y tons of peat soil is:
P(x, y) = 50x + 75y
To maximize profit, we need to find the values of x and y that satisfy the constraints of the problem situation and maximize the profit function P(x, y). One way to do this is to use the method of linear programming, which involves finding the corner points of the feasible region and evaluating the profit function at each corner point.
The corner points of the feasible region are (0, 0), (60, 0), (60, 60), (30, 90), and (0, 90). Evaluating the profit function at each corner point, we get:
P(0, 0) = 0
P(60, 0) = 3000
P(60, 60) = 9000
P(30, 90) = 6750
P(0, 90) = 6750
Therefore, the maximum profit is $9000, which occurs when the company sells 60 tons of loam soil and 60 tons of peat soil.
learn more on system of linear inequalities here;
https://brainly.com/question/5897935
#SPJ1
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 $1.50 for each customer she serves.
(iv) Let's assume that Jenny and Shawna received the same wage, W, for serving the same number of customers, x. Then we have:
Jenny's wage = 600 + 0.90x
Shawna's wage = 270 + 1.50x
Setting these two expressions equal to each other, we get:
600 + 0.90x = 270 + 1.50x
330 = 0.60x
x = 550
Therefore, Jenny and Shawna each served 550 customers.
a normal distribution of exam scores has a standard deviation of 8. a score that is 12 points above the mean would have a z-score of: a score that is 20 points below the mean would have a z-score of:
The standard deviation of a normal distribution of exam scores is 8. A score that is 12 points above the mean would have a z-score of 1.5, and a score that is 20 points below the mean would have a z-score of -2.5.
What is the z-score?The z-score can be calculated by dividing the difference between a data value and the mean of the data set by the standard deviation of the data set.
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8.
z = (x−μ)/σ = (x−μ)/σ = (12−0)/8 = 1.5
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8 is 1.5.
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8.
z = {x-μ}/{σ} = {-20-0}/{8} = −2.5
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8 is -2.5.
Learn more about Z-score here:
https://brainly.com/question/15016913
#SPJ11
4-77 Is the relationship shown in the 28+
graph at right below proportional? If
241
so, find the unit rate. If not, explain
why not.
The graph is/is not proportional
because
Unit rate:
Cost ($)
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.
Solve the following proportion for y. 13 11 8 y Round your answer to the nearest tenth. 1 X Ú
Answer:
Were sorry! Answer is not available right now check in later.
Step-by-step explanation:
anyone know the answer?
The required value of the base of the triangle is [tex]\frac{7\sqrt{3} }{3}[/tex].
What is right angled triangle?Right-angle triangles are formed when the angle formed by two of their edges is exactly 90 degrees. Obtuse angle triangle: An obtuse angle triangle is one in which the angle formed by two sides is larger than 90 degrees.
According to question:In the given triangle, we will use tangent function to find the value of x.
tan(∅) = Perpendicular/ base
tan(60°) = 7/x
x = 7/tan(60°)
x = 7/√3 ∴ (tan(60°) =√3 )
On rationalizing
x = [tex]\frac{7\sqrt{3} }{3}[/tex]
Thus, required value of x is [tex]\frac{7\sqrt{3} }{3}[/tex].
To know more about Triangle visit:
brainly.com/question/2773823
#SPJ1
