The probability that both will experience allergies to pollen is 0.0484, and the probability that at least one will is 0.9516.
The following information is provided in the question:
A large country has a pollen allergy rate of about 22%.
As a result, the probability of people has a chance of having an allergy is 0.22.
P(allergic) = 0.22
P(Not allergic) = 1 - 0.22 = 0.78
If A and B are independent even, then,
P(A∩B) = P(A) × P(B)
Two people are randomly selected.
a) P( both will be allergic to pollen)
Since these are independent events,
P(both will be allergic to pollen)= P(allergic)*P(allergic)
= 0.22*0.22 = 0.0484
b) P(at least one person is allergic to pollen)
= 1 - P(both are not allergic to pollen)
= 1 - P(P(not allergic)*P(not allergic))
= 1 - (0.22*0.22)
= 0.9516
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Find equations of the tangents to the curve x = 9t2 + 3, y = 6t3 + 3 that pass through the point (12, 9). (enter your answers as a comma-separated list. ).
y - 9 = 1(x - 15) is the required equation for the tangent.
What are equations?Equations come in two varieties: identities and conditional equations.
All possible values of the variables result in an identity.
Only certain combinations of the variables' values make a conditional equation true.
Two expressions joined by the equals symbol ("=") form an equation.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance.
When this equation is solved, we discover that the value of the variable x is 7.
So, the equation of the tangent is:
First, with respect to t, differentiate the function as follows:
dx/dt = d(9t² + 6)/dt
dx/dt = 18t
Like this, we have:
dy/dt = d(6t³ + 3)/dt
dy/dt = 18t²
Now, we will obtain:
dy/dx = 18t²/18t
dy/dx = t
We know that (15, 9) occurs on the curve, so we got:
d(9t² + 6)/dt and d(6t³ + 3)/dt ⇒ t = ±1 and t = 1 ⇒ t = 1
So, (15, 9) is the slope.
y - 9 = 1(x - 15) is the equation of the tangent.
Therefore, y - 9 = 1(x - 15) is the required equation for the tangent.
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Correct question:
Find the equations of the tangents to the curve x = 9t2 + 6, y = 6t3 + 3 that passes through the point (15, 9).
the times to complete an obstacle course is normally distributed with mean (μ) 73 seconds and standard deviation (σ) 9 seconds. what is the probability using the empirical rule that a randomly selected finishing time is less than 100 seconds? provide the final answer as a percent rounded to two decimal places.
68.18% is the right answer
please answer the question (ratios)
The following are the amount each person receive:
a. 6 : 4 = $300 : $200b. 1 : 4 : 5 = $50 : $200 : $250c. 1 : 8 : 1 = $50 : $400 : $50d. 8 : 9 : 8 = $160 : $180 : 160e. 10 : 5 : 4 : 1 = $250 : $125 : $100 : $25How to find the amount each person receive?Amount of money = $500a. 6 : 4
Total ratio = 6 + 4
= 10
6/10 × 500
= $300
4/10 × 500
= $200
b. 1 : 4 : 5
Total ratio = 1 + 4 + 5
= 10
1/10 × 500
= $50
4/10 × 500
= $200
5/10 × 500
= $250
c. 1 : 8 : 1
Total ratio = 1 + 8 + 1
= 10
1/10 × 500
= $50
8/10 × 500
= $400
1/10 × 500
= $50
d. 8 : 9 : 8
Total ratio = 8 + 9 + 8
= 25
8/25 × 500
= $160
9/25 × 500
= $180
8/25 × 500
= $160
e. 10 : 5 : 4 : 1
Total ratio = 10 + 5 + 4 + 1
= 20
10/20 × 500
= $250
5/20 × 500
= $125
4/20 × 500
= $100
1/20 × 500
= $25
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2. Tyler has written an incorrect proof to show that quadrilateral ABCD is a
parallelogram. He knows segments AB and DC are congruent. He also knows
angles ABC and ADC are congruent. Find the mistake in his proof.
Segment AC is congruent to itself, so triangle ABC is congruent to triangle ADC by
Side-Angle-Side Triangle Congruence Theorem. Since the triangles are congruent, so
are the corresponding parts, and so angle DAC is congruent to ACB. In
quadrilateral ABCD, AB is congruent to CD and AD is parallel to CB. Since AD is
parallel to CB, alternate interior angles DAC and BCA are congruent. Since
alternate interior angles are congruent, AB must be parallel to CD. Quadrilateral
ABCD must be a parallelogram since both pairs of opposite sides are parallel.
Answer: specific analyze is as it follows
Step-by-step explanation:
52=2(x+19)
Please help me
aclub is hosting an ice cream sundae party with four different flavors of ice cream and six different toppings available. how many sundaes are possible using one flavor of ice cream and three different toppings?
There are 80 sundaes possible using one flavor of ice cream and three different toppings.
Here, we are given that a club is hosting an ice cream sundae party with four different flavors of ice cream and six different toppings.
For choosing 1 flavor of ice cream from 4, we have 4 ways.
Now, we need to choose 3 different toppings from the given 6.
This can be done in 6C3 ways
6C3 = 6! / (3! × 3!)
= (6 × 5 × 4) / (3 × 2)
= 120/ 6
= 20
Thus, we have 20 ways of choosing 3 different toppings.
Now, the number of ways of making the sundaes would be-
4 × 20
= 80
Thus, there are 80 sundaes possible using one flavor of ice cream and three different toppings.
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the top 5% of applicants on a test will receive a scholarship. if the test scores are normally distributed with a mean of 76 and a standard distribution of 12, what is the lowest test score that still qualifies for a scholarship?
As per the standard distribution, the lowest test score is 27.76%
Standard distribution:
In statistics, standard distribution means a normal distribution with a mean of zero and standard deviation of 1.
Given,
The top 5% of applicants on a test will receive a scholarship. if the test scores are normally distributed with a mean of 76 and a standard distribution of 12.
Here we need to find the lowest test score that still qualifies for a scholarship.
As per the given question, we have identified the value of
=> μ = 76 (mean)
=> σ = 12 (standard deviation)
Then we need to take the value of x as,
x < 5% (find the probability)
Now, converting the problem in standard form
=> Z = (5 − 76) / 12
=> Z = -5.91
Then as per the z table the value is 0.2786
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The graph of y=√x is translated 4 units left and 1 unit up to create the function h(x). The graph of h(x) is shown on the coordinate grid.What is the range of h(x)?
{y|y ≥-4}
{y|y ≥ -1}
{y|y ≥ 1}
{y|y ≥ 4}
Answer:
(c) {y|y ≥ 1}
Step-by-step explanation:
You want the range of the square root function after it has been translated left 4 units and up 1 unit.
RangeThe range of the function is the vertical extent of its graph. The original square root function has a range of y ≥ 0. Translating it up 1 unit gives it a range of ...
y ≥ 1
Ray has $1600 in his bank account. How much interest will the money earn in one year at 2%. What will his balance be?
Answer: 32 every month or day. if its every month the answer is 384, if its every day it would be 11680
Step-by-step explanation:
Given:
Initial amount = $1600,Interest rate = 2%,Time = 1 year.Find the amount of interest:
$1600*2/100 = $32Find the balance after one year:
$1600 + $32 = $1632a company has three corporate offices and wishes to determine if there is a difference in the average age of the corporate executives at the three locations. the ages were recorded for the five top executives at each location. the appropriate test statistic is the test and the degrees of freedom for this problem are
The appropriate statistic test should be ANOVA and The degree of freedom is 12.
What are Statistical tests?
An instrument for making quantitative judgments about a process or processes is a statistical test. The goal is to decide whether there is sufficient data to "reject" a theory or hypothesis on the process.
In the given problem the average age of the corporate executives at the three locations is being calculated, it means more than two groups are being compared. hence, The appropriate statistic test would be ANOVA.
In order to calculate the degree of freedom, we must know the no. of observations.
here, no. of observations are 15 ( 3 × 5 ) and the no. of groups are 3.
∴ Degree of freedom = no. of observations - no. of groups
= 15 - 3 = 12.
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what is the quotient of 7.81\times 10^67.81×10 6 and 7.1 \times 10^37.1×10 3 expressed in scientific notation?
The quotient of 7.81 × 10⁶ and 7.1 × 10³ expressed in scientific notation is approximately 1.10 × 10³.
To find the quotient of 7.81 × 10⁶ and 7.1 × 10³ expressed in scientific notation, we can perform the division first and then convert the result into scientific notation.
Step 1: Perform the division: (7.81 × 10⁶) ÷ (7.1 × 10³)
Step 2: Divide the numerical values: 7.81 ÷ 7.1 = 1.09859155 (approximately)
Step 3: Divide the exponents of the powers of 10: 10⁶ ÷ 10³ = 10³ (since 6 - 3 = 3)
Step 4: 1.09859155 × 10³
Step 5: Adjust the result to be in scientific notation format: 1.09859155 × 10³ ≈ 1.10 × 10³
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The complete question:
What is the quotient of 7.81 × 10⁶ and 7.1 × 10³ expressed in scientific notation?
a survey of a group of 116 tourists was taken in st. louis. the survey showed the following: 66 of the tourists plan to visit gateway arch; 50 plan to visit the zoo; 10 plan to visit the art museum and the zoo, but not the gateway arch; 14 plan to visit the art museum and the gateway arch, but not the zoo; 18 plan to visit the gateway arch and the zoo, but not the art museum; 9 plan to visit the art museum, the zoo, and the gateway arch; 14 plan to visit none of the three places. how many plan to visit the art museum only?
12 People plan to visit the art museum only.
What is Set Theory?
We study sets and their characteristics in the area of mathematical logic known as set theory. A set is a collection of things or a group of things. These things are frequently referred to as elements or members of a set. A set is, for instance, a group of cricket players. A set is a clearly defined collection of things or people, as we already learnt in the introduction. Numerous examples from everyday life, such as the number of rivers in India and the colors in a rainbow, can be used to relate sets.
Given,
Total no of people =116
No of people visiting any of the three places = total - people visiting none of the places
= 116 -14 = 102
No of people visiting only Gateway arch = total people visiting gateway arch - (people visiting all the three + people visiting Gateway ans museum butnot zoo +people visiting gateway and zoo butnot museum)
= 66 - (18+9+14) = 25
Similarly, people visiting only zoo = 14
Total no of people plan to visit Art Museum only = 102 - (25+14+9+18+10+14) = 112
12 People plan to visit the art museum only.
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what is the answer to the picture the two answers on there
In the expression given as -5 - (-7) = -5 + x, the value of x is 7.
What is the value of the expression?In Mathematics, expression simply means the mathematical statements which have at least two terms which are then related by an operator. It should be noted that they illustrate the relationship between the data given.
In this situation, it should be noted that the expression is given as:
-5 - (-7) = -5 + x
Collect like terms
-5 + 7 = -5 + x
x = -5 + 5 + 7
x = 7
The value of x is 7.
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Graph:
3/4 times 2^x
Answer:
According to graph calculators online, there is no solution to this equation.
Step-by-step explanation:
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a biologist collected 326 fern and moss samples. there were 66 fewer ferns than moss samples. how many fern samples did the biologist collect?
There are 130 fern samples did the biologist collect.
What is fern and moss samples?
In contrast to ferns, which are vascular plants, mosses are nonvascular primitive plants that produce spores. Furthermore, unlike ferns, which have a plant body that is divided into real stems, leaves, and roots, mosses have none of these features. Ferns also have circinate vernation, which is not true of mosses.
Given:
A biologist collected 326 fern and moss samples. there were 66 fewer ferns than moss samples.
Let, f denotes the number of ferns collected and
m denotes the number of mosses collected
From the given information,
m + f = 326 ..(1)
m - 66 = f ..(2)
Plug equation (2) in equation (1),
m + m - 66 = 326
2m = 326 + 66
2m = 392
m = 196
Plug m = 196 in equation (2),
f = 196 - 66
f = 130
Hence, there are 130 fern samples did the biologist collect.
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Drag statements and reasons to each row to show why the slope of the line between D D and E E is the same as the slope between E E and F F , given that triangles A A and B B are similar.
By definition of slope , we have seen that Slope = 4/3 and 4/3 = 16/12
How to find the slope of a Line?The slope of a line is basically a measure of its steepness. Mathematically, the slope is calculated as rise over run.
To find the slope, we divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points. This is change in y divided by change in x.
From definition of slope, we know that;
Slope between line D and E is; Slope = 4/3
Similarly, by definition of slope, we know that;
Slope between line D and E is; Slope = 16/12
Now, 16/12 can be reduced to 4/3 and as such;
4/3 = 16/12
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x + 4y = 10
2x + 8y = 20
Answer:
x = 2, y = 2
Step-by-step explanation:
Looking at the equations,
x + 4y = 10
2x + 8y = 20
If x = 2, and y = 0 then it would look something like this:
2 + (4×2) = 10
Let's apply that to the next equation:
(2×2) + (8×2) = 20
In conclusion, x = 2, y = 2
Select all the equations that are equivalent to
8k = 20.
Answer: The first and the last answer choice
Step-by-step explanation:
They are equal to 8k=20 because they are the same equation but reduced or increased by the same multiple.
Answer:
it's the first option, 3rd option, and fifth option because the rest of the equation cancels out on them (ex. for the first option, divide each side by 3 that would remove the •3 from each side and leave you with 8k=20)
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The solutions are given below.
What is angle?An angle is the formed when two straight lines meet at one point, it is denoted by θ.
Given that,
lines u and v are parallel,
And ∠ 9 = 80° and ∠ 5 = 68°
(a)
Angle 12 is supplementary angle of angle 9,
Therefore, ∠12 = 180 - 80 = 100
(b)
Angle 1 and angle 9 are corresponding angle and are equal.
∠ 1 = ∠ 9 = 80
(c)
Angle 1 is supplementary angle of angle 4,
Therefore, ∠ 4 = 180 - 80 = 100
(d)
Angle 3 and angle 1 are vertically opposite angles,
Therefore, ∠ 3 = ∠ 1 = 80°
(e)
Angle7 and angle 5 are vertically opposite angles,
Therefore, ∠ 7 = ∠ 5 = 68°
(f)
Angle 16 and 7 are supplementary angles,
Therefore, ∠16 = 180 - 68 = 112
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the volume of a sample of nitrogen is 6.00 liters at 35oc and 0.974 atm. what volume will it occupy at stp?
5.152 L volume will it occupy at STP.
What is ideal gas law?
The equation of state for an ideal gas, in theory, is known as the ideal gas law. Even though it has a number of shortcomings, it provides a good approximation of the behavior of several gases under various circumstances. Theoretical point particles that move randomly and only collide in elastic ways make up an ideal gas.
Using the ideal gas equation PV=nRT, where n is the number of moles, it is possible to determine the volume that will be present at STP as follows.
n= PV/RT
p=0.974 atm
V=6.0 L
R = 0.0821 L.atm/k.mol
T= 35 +273= 308k
n= (0.974 atm x 6.0 L)/( 0.0821 L.atm/k.mol x 308 k)= 0.178 moles
STP 1 mole= 22.4 L what obout 0.23 moles
=22.4 x0.178moles/ 1moles =5.152 L
Hence, 5.152 L volume will it occupy at STP
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Harper runs 2200 meters in 10 minutes. How many meters can Harper run in one minute?
Answer: 220 meters in 1 minute
Step-by-step explanation:
if harper can run 2200 meters in 10 min then that means you can run 220 in 1 min
2200/10 = 220
Answer:
220
Step-by-step explanation:
2200/10 is 220
I spent $2000 to get
Brownie Town up and running. We make all sorts of brownies. Some have peanuts, some have chocolate chips, and others have icing.
Every month I earn $200
from Brownie Town sales.
The equation form as per the statement in the question will be y = -200x - 2000.
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the given information in the question,
They spent $2,000 therefore that would be -2,000, and they make $200 per month selling brownies.
So simply add -2,000 each time on the chart under "Income made," and the final amount should be 600.
So, the equation will be,
y = -200x - 2000.
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suppose you want to perform a test to compare the mean gpa of all freshmen with the mean gpa of all sophomores in a college? what type of sampling is required for this test?
The type of sampling required for this test is Independent sampling with quantitative data.
Randomly chosen samples are known as independent samples since their results are independent of other observations' values. The premise that samples are independent underlies many statistical analyses.
In the hypothetical situation, independent sampling is required since the researcher needs two distinct samples: one from freshmen and one from sophomores. These samples are independent since there would be no relationship between them.
The information would be quantitative in nature. Student GPAs are the dependent variable in this study. Since GPA is a qualitative indicator, the kind of data being collected is also quantitative.
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The square on the right is a scaled copy of the square on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
The scale factor of the figure of the two squares is 1.5
How to find the scale factorThe scale factor is determine using division
The formula involve:
let the scale factor be r then we say
area of square A * r = area of square B
8 * 8 * r = 12 * 12
64r = 144
r = 144 / 64
r = 1.5
using the dimensions
8r = 12
r = 12 / 8
r = 1.5
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Which statements are true about the ordered pair (−1, 5) and the system of equations? {x+y=4x−y=−6 Select each correct answer. Responses The ordered pair (−1, 5) is a solution to the first equation because it makes the first equation true. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the first equation because it makes the first equation true. The ordered pair (−1, 5) is a solution to the second equation because it makes the second equation true. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the second equation because it makes the second equation true. The ordered pair (−1, 5) is not a solution to the system because it makes at least one of the equations false. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is not a solution to the system because it makes at least one of the equations false. The ordered pair (−1, 5) is a solution to the system because it makes both equations true. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the system because it makes both equations true.
The statements that are true about the ordered pair (−1, 5) and the system of equations include the following;
A. The ordered pair (−1, 5) is a solution to the first equation because it makes the first equation true.
B. The ordered pair (−1, 5) is a solution to the second equation because it makes the second equation true.
D. The ordered pair (−1, 5) is a solution to the system because it makes both equations true.
How to determine the true statement?In order to determine if this ordered pair is a true solution based on the given system of linear equations, we would have to test the ordered pair (-1, 5) by substituting it into each of the linear equation as follows;
For the first linear equation, we have the following:
x + y = 4
-1 + 5 = 4
4 = 4 (True).
For the first linear equation, we have the following:
x - y = -6
-1 - 5 = -6
-6 = -6 (True).
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you are instructed to subtract four points from each score, square the resulting value, and find the sum of the squared numbers. how would this set of instructions be expressed in summation notation?
The summation is Σ(xᵢ-4)², i=1,2,3...
What is summation ?
When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Functions, vectors, matrices, polynomials, and, generally, any sort of mathematical object on which an operation labelled "+" is defined can all be added together, in addition to numbers.
Series are summations of infinite sequences. They are related to the idea of limit but are not covered in this article.
Let x serve as the definition of a score.
Each score will be xi, i.e. x1, x2, x3, x4... for the first four consecutive scores, and so on.
By deducting 4 from each score, you get xi-4.
Squaring the Resulting Value = (xi-4)²
The sum of the squared numbers is equal to (xi-4)²
where i=1, 2, 3.
Σ(xᵢ-4), The set of instructions written in summation notation is 2.
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Σ(xᵢ-4)² is the set of instruction expressed in summation notation.
What is Summation Notation?
The summation symbol, S, tells us to add up the sequence's components. To the right of the summation sign is a typical component of the sequence that is being summed. An index that appears below the summation sign designates the variable of summation.
Let a score be defined by x,
Each score will be xᵢ i.e. x₁, x₂, x₃, x₄... for the first four consecutive scores and so on.
Subtracting 4 from each score = xᵢ-4
Squaring the Resulting Value = (xᵢ-4)²
The sum of the squared numbers = Σ(xᵢ-4)², i=1,2,3...
Σ(xᵢ-4)² is the set of instruction expressed in summation notation.
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Which of the following pairs of correlation coefficients most closely corresponds to the observed correlations between the intelligence scores of adopted children and those of their adoptive or biological parents?
a. child-adoptive: 0.20; child-biological: 0.40
b. child-adoptive: 0.40; child-biological: 0.40
c. child-adoptive: 0.20; child-biological: 0.20
d. child-adoptive: 0.50; child-biological: 0.50
correlation coefficients most closely corresponds to the observed correlations between the intelligence scores of adopted children is a. child-adoptive: 0.20; child-biological: 0.40
Children for adoption
Adoption is the social, emotional, and legal process in which children who will not be raised by their birth parents become full and permanent legal members of another family while maintaining genetic and psychological connections to their birth family.
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A soap maker wants to ship as many bars of soap as she can to a store. Each bar of soap weighs 1/5 pound. The box that she will use to ship the soap can hold a maximum of 18 pounds of soap.
How many bars of soap can the soap maker ship to the store?
The number of bars of soap that the soap maker ship to the store is 90.
How to calculate the number of bars?From the information, the soap maker wants to ship as many bars of soap as she can to a store. Each bar of soap weighs 1/5 pound.
Since the box that she will use to ship the soap can hold a maximum of 18 pounds of soap. The number of soaps will be:
= 18 ÷ 1/5
= 18 × 5
= 90
The number of soaps is 90.
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(x+2)(x+1) expand and simplify
Hello!
To expand:
==> we must multiply each variable with each other
[tex](x+2)(x+1)=x*x+x*1+2*x+2*1=x^2+x+2x+2=x^2+3x+2[/tex]
Thus: when (x+2)(x+1) is expanded and simplified
==> [tex]x^2+3x+2[/tex]
Answer:
Step-by-step explanation: First we will expand so
x times x = x^2
x times 1 = x ( don’t need to put 1 in front)
2 times x is = 2x
2 times 1 = 2
Now we line them all up and look out if there are any like terms.
x^2 + x + 2x + 2 = x^2 +3x + 2
the height of a cylinder is increasing at a constant rate of 2 centimeters per second, and the volume is increasing at a rate of 1152 cubic centimeters per second. at the instant when the height of the cylinder is 33 centimeters and the volume is 403 cubic centimeters, what is the rate of change of the radius? the volume of a cylinder can be found with the equation v
Answer:
about 2.758 cm/s
Step-by-step explanation:
You want the rate of change of a cylinder's radius, when its height is 33 cm increasing at 2 cm/s, and its volume is 403 cm³ increasing at 1152 cm³/s.
Rate of changeThe volume of a cylinder is given by the equation ...
V = πr²h
Solving for the radius gives ...
r = √(V/(πh))
Differentiating, we have ...
[tex]r'=\dfrac{1}{\sqrt{\pi}}\left(\dfrac{1}{2}V^{-\frac{1}{2}}h^{-\frac{1}{2}}V'-\dfrac{1}{2}V^{\frac{1}{2}}h^{-\frac{3}{2}}h'\right)=\dfrac{hV'-Vh'}{2h\sqrt{\pi Vh}}[/tex]
Filling in the values V = 403, V' = 1152, h = 33, h' = 2, we have ...
r' = (33·1152 -403·2)/(2·33·√(π·403·33)) = 37210/(66√(13299π))
r' ≈ 2.758 . . . . . cm/s
The rate of change of the radius is about 2.758 cm/s.