The first lefty is the fifth person chosen is7.45%
There are some lefties among the 5 people is, 50.16%
What is probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability. A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.The first lefty is the fifth person chosen is
[tex](.87)^4(.13)=.07447=7.45 \%[/tex]
There are some lefties among the 5 people is,
[tex]$$1-(.87)^5=.50157=50.16 \%$$[/tex]
The first lefty is the second or third person.
[tex]$(.87)(.13)+(.87)^2(.13)=.211497=21.15 \%_0$[/tex]
There are exactly 3 lefties in the group.
[tex]$(5, .13,3)=.0166=1.66 \%$[/tex]
There are at least 3 lefties in the group,
[tex]1 \text { - binomadf }(5, .13,2)=.0179=1.79 \%[/tex]
There are no more than 3 lefties in the group
[tex]\text { binomcdf }(5, .13,3)=.9987=99.87 \%[/tex]
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In this problem, we will look at properties of solids with base on the xy-plane given by the circle x2+y2=a2 and its interior, where a>0
is to be given in parts (i) and (ii) below.
(i). Let a=4, and assume that cross-sections of thesolid perpendicular to the x -axis are circular disks with diameters lying in the xy-plane. Find the area A(x) of the cross-section at location x.
(ii). Let a=9, and assume that cross-sections of the solid perpendicular to the x-axis are equilateral triangles with bases in the xy-plane. Find the area A(x) of the cross-section at location x.
(iii). Find the volume of the solid described in (i) above.
The area A(x) of the cross-section at location x for a=4 is given by A(x)=π(4-x)2, where x is the distance from the origin. This can be derived from the equation A(x)=π(a2-x2).
The area A(x) of the cross-section at location x for a=9 is given by A(x)= 3√3(9-x)2/4, where x is the distance from the origin. This can be derived from the equation A(x)=3√3(a2-x2)/4.
(iii). The volume of the solid described in (i) can be calculated using the equation V=∫A(x)dx, where A(x) is the area of the cross-section at location x, and the integral is taken from 0 to 4. Substituting A(x)=π(4-x)2, we have V=π∫(4-x)2dx, which gives V=π(16 - 8x + x3/3) evaluated from 0 to 4, or V=64π/3.
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Vigorous exercise helps people live several years longer (on average). Whether mild activites like slow walking extend life is not clear. Suppose that the added life expectancy from regular slow walking is just 2 months. A statistical test is more likely to find a significant increase in mean life expectancy if:
(a) it is based on a very large random sample and a 5% significance level is used.
(b) it is based on a very larg random sample and a 1% significance level is used.
(c) it is based on a very small random sample and a 5% significance level is used.
(d) it is based on a very small random sample and a 1% significance level is used.
(e) the size of the sample doesnt have any effect on the significance of the test.
A statistical test is more likely to find a significant increase in mean life expectancy if it is based on a very large random sample and a 1% significance level is used.
As per the given data
Vigorous exercise helps people live several years longer.
The mild activities like slow walking extend life is not clear.
The added life expectancy from regular slow walking is just 2 months.
Here we have to determine that when a statistical test is more likely to find a significant increase in mean life expectancy.
The increase in life expectancy regarding regular slow walking should be considerably greater than 2 months, which means that the a larger sample is needed to give a more precise result
The chances of finding significant results increases when we increase sample size or use a higher significance level.
So, among the given options, significant results will be achieved
If it is based on a very large random sample and a 1% significance level is used.
Therefore option (b) is correct.
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Joanie is organizing her closet. She has 3 times as many black shirts as gray shirts, plus 3 new black shirts she just bought. She has 5 times as many white shirts as gray shirts, minus the one white shirt she donated. Joanie has 2 times more gray short than brown shirts. If she has the same number of black and white shirts, how many gray shorts does Joanie have?
If Joanie is organizing her closet. She has 3 times as many black shirts as gray shirts, plus 3 new black shirts she just bought. The number of gray shirts that Joanie have is: 2.
How to find the number of shirts?Let x represent the number of gray shirts
Let Joanie black shirts = 3x + 3
Let Joanie white shirts = 5x - 1
Let Joanie brown shirts = 2x
So,
3x + 3 = 5x - 1
Substract 3 from both side
3x + 3-3 = 5x - 1 -3
3x = 5x -4
Substract 5x from both side
3x-5x = 5x -4 -5x
-2x = -4
Divide both side by
x = -4/-2
x =2
Therefore, Joanie has 2 gray shirts.
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while grading her students' most recent quiz on equation solving, mrs. jones calculated that approximately forty percent of her students answered question number 14 with multiple choice option b, while the other sixty percent answered a or c. question #14 from Mrs. Jones's students' most recent quiz:
14) Solve the single variable equation for n.
a.n=3
b.no solution
c.infinitely many solutions
Use complete sentences to compare the similarities and differences of each of the multiple choice answer options A-C. In your answer, rationalize why a student would choose each of the options as the correct answer
If while solving an equation, a single value is obtained for the variable, then the equation has only a single solution.
The option (a) is n=3.
If while solving an equation, a single value is obtained for the variable, then the equation has only a single solution. If n=3 is obtained after solving the equation, then the student should chose option (a) as the answer.
The option (b) is "no solution".
While solving an equation, if we obtain an equation which is mathematically false, then the equation will have no solution. So, no solution is chosen when no value is obtained for n and the final equation is mathematically false.
The option (c) is "infinitely many solutions".
While solving an equation, if we obtain an equation which is mathematically correct such as 0=0, 7=7 etc., then the equation will have infinietly many solutions. So, infinitely many solutions is chosen when no value is obtained for n and the final equation is mathematically correct.
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∠A and ∠B are vertical angles. If angle A=(8x-23) and angle B=(6x-5) then find the measure of ∠A.
The measure of ∠A is 49.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Vertical angles are equal.
∠A = 8x - 23
∠B = 6x - 5
Now,
8x - 23 = 6x - 5
8x - 6x = -5 + 23
2x = 18
x = 9
Now,
∠A.
= 8x - 23
= 8 x 9 - 23
= 72 - 23
= 49
Thus,
∠A is 49.
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A mother is 66 inches tall, and her daughter is 33 inches tall. Which of the following equations describes the relationship between m, the height of the mother, and g, the height of the daughter?
A. g=2/m
B. g = 2m
C. g=m/2
D. g=m-2
Answer: your answer is c
Step-by-step explanation:
A triangle is partitioned into three triangles and a quadrilateral by drawing two lines from vertices to their opposite sides. The areas of the three triangles are 10, 20, and 16, as shown. What is the area of the shaded quadrilateral? （ ）
A. 24
B. 28
C. 32
D. 36
E. 44
the area of the shaded quadrilateral is equal to the sum of area of triangle AOC and BOC is equal to 110 unit square.
Suppose area of triangle CEO = x and area of COD =y
OE : OB = 16:20 (Ratios of the areas of AEO and AOB)
Hence, Area of CEO : Area COB = 16:20
Area of CEO : (Area of COD +Area of DOB) = 16;20
x : (y+10) = 16:20
10x=5(y+10) ........(1)
AO : OD = 20:10 (Ratios of the areas of AOB and DOB)
Hence, Area of AOC : Area DOC = 20:10
(Area of AOE + Area of COE) : Area of DOB= 20:10
(16+x) : y = 20:10
16+x=2y.......(2)
From (1) and (2)
x=68 and y=42
so the area of quadrilateral is 110.
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Please help me...I neep help
By using the formula for the mean:
(x₁ + x₂ + ...)/N
We will see that the mean is 7 minutes.
What is the mean of the times?If we have a set of N elements:
{x₁, x₂, x₃...}
The mean of these values is given by:
(x₁ + x₂ + ...)/N
Here we have a set of 3 points, such that the points are {5, 6, 10} the mean of these points is:
M = (5 + 6 + 10)/3
M = 21/3
m = 7
The mean of the tmes is 7 minutes.
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(-1,-4) that is perpendicular to the line Y=-2/3x+1
the equation of line perpendicular to y=-2/3x+1 will be y = 3/2x -5/2.
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The line given y=-2/3x+1
here the slope is -2/3
So the slope of the required line will be m2 = - 1/m1
m2 = 3/2
The required line equation will be [tex]\frac{y+4}{x+1}[/tex] = 3/2
2(y+4) = 3(x+1)
2y+8= 3x+3
y = 3/2x -5/2
Hence the equation of line perpendicular to y=-2/3x+1 will be y = 3/2x -5/2.
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X = y+9, y = 4x+10 solve for X and y
The value of x and y for the given equations are - (19/3) and -46/3 respectively.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For instance, 2x - 5 = 13.
Given the two equations are as follows:
x = y + 9 and y = 4x + 10
Substitute the value of y in the first equation:
x = y + 9
x = 4x + 10 + 9
Isolate the value of x:
x - 4x = 19
-3x = 19
x = - (19/3)
Substitute the value of x in the first equation:
x = y + 9
- 19/3 = y + 9
Isolate the variable y:
y = -19/3 - 9
y = - 46/3
Hence, the value of x and y for the given equations are - (19/3) and -46/3 respectively.
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List the values of x at which f has a local minimum. Select the correct
choice below and fill in any answer boxes within your choice.p
The values of x at which the function has a local minimum are x = -4, 12.
What is the local minimum?The point in the domain of the functions with the lowest value is known as the local minimum. You may calculate the local minimum by determining the function's derivative. The first derivative and second derivative tests are the two key techniques for locating a function's local minimum.
There are several applications for the local minimum notion in business, economics, and engineering.
The least value of the function f(x) in the specified domain is essentially what the local minimum is.
From the graph, we observe
The value of the function f(x) is minimum at x = - 4 and x = 12
Therefore, x = -4, 12
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Which of the following are square properties? Choose ALL that apply.
Four right angles.
Exactly one pair of parallel sides.
Diagonals are perpendicular.
Diagonals are congruent.
Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning
The pair of figures are similar because:• Both figures are parallelograms
• All sides are congruents and • Scale factor 1: 2.5
A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The pair of figures are similar because:
• Both figures are parallelograms
• All sides are congruents
• Angles W and Y are congruent with angles P and R
• Angles X and Z are congruent with angles S and Q
• Scale factor 1: 2.5
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Topic Probability
If you roll unbiased dice 600 times. how many would you expect to obtain
a)a one
b)an even number
c)an odd number
d)a number less than 3
e)a prime number
The number of times that you would expect to roll the numbers, when rolling an unbiased dice is:
a. 100 times
b. 300 times
c. 300 times
d. 200 times
e. 200 times
How to find the number of times ?There is only a single 1 in a six sided unbiased dice so the number of rolls is:
= 1 / 6 x 600
= 100 times
There are 3 even numbers ( 2, 4, and 6) so the number of rolls :
= 3 / 6 x 600
= 300 times
There are 3 odd numbers ( 1, 3, 5 ) so number of rolls is:
= 3 / 6 x 600
= 300 times
There are 2 numbers less than 3 which are 1 and 2 :
= 2 / 6 x 600
= 200 times
There are 2 prime numbers ( 2 and 3 ):
= 2 / 6 x 600
= 200 times
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Someone help me please
In contrast to Supervised learning, Unsupervised learning has more models and more evaluation meth used in order to ensure the outcome of the model is accurate. This statement is overall a false statement.
An unsupervised learning model might give a less accurate outcome if compared to supervised learning.
1. Algorithms of unsupervised learning are taught using the data that are unlabeled.
2. The model of unsupervised learning doesn't take any feedback.
3. In unsupervised learning, we see that only input data is supplied to the model, no output data.
Assess reasonableness a monument will be at the circumcenter of a triangular plot of land at the state capital. on the coordinate grid, the vertices of the triangular plot of land are a(1, 5) , b(7, 5) , and c(8, 0) .
Overall, the statement that Unsupervised learning has more models and more evaluation methods used in order to ensure the outcome of the model is accurate is false. Unsupervised learning algorithms are taught using data that may be labeled, but in most cases the labels are not used to infer the model. The model of unsupervised learning does not take any feedback, as it is not supervised, and only input data is supplied to the model, no output data. The evaluation of unsupervised learning models relies on different metrics such as clustering accuracy, silhouette coefficient, etc. Unsupervised learning algorithms are used for tasks such as clustering, anomaly detection and density estimation.
assess reasonableness a monument will be at the circumcenter of a triangular plot of land at the state capital. on the coordinate grid, the vertices of the triangular plot of land are a(1, 5) , b(7, 5) , and c(8, 0) .
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a) You see a general expression written as ax? + bx4 + cx3 + dx2, determine the possible number of zeroes that could exist. (2 marks) b) Factor 2x3 - 9x2 + 7x + 6 and list all roots for the expression. (7 marks) c) Given that x = -1 and x = 2 are roots for ax4 + 3x3 – 12x2 + bx + 6, determine the values of a and b. (7 marks)
The maximum number of zeroes in a generic equation with the form axe? + bx4 + cx3 + dx2 is 5.
What is meant by expression?A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used.A statement using numbers, variables, and operations is known as an expression. An equation has an equals sign, whereas an expression lacks one. This is the main distinction between the two types of sentences. Terms and operations are used to create mathematical expressions.a) [tex]$ax^{5}[/tex]
b) Factor 2x3 - 9x2 + 7x + 6 is
(x - 3) (x -2) (2x + 1)
c) x = -b / 2a
Replace x by -2, from the vertex:
-2 = -b / 2a
Solve for b:
-b = -4a
Or
b = 4a
By evaluating the equation with the vertex's x-value, we can determine the y-value from the vertex:
y = ax2 + 4ax - 6
Simplify, 6 for y, and -2 for x:
6 = a(-2)2 + 4a(-2) - 6
6 = 4a - 8a - 6
solve for a:
a = -3
Simplifying the above equation,
b = 4a, b = -12
The value for a is -3.
The value for b is -12
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The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 85%, interpret the likelihood of randomly selecting a terrier from the shelter.
A. Likely
B. Unlikely
C. Equally likely and unlikely
D. This value is not possible to represent probability of a chance event
The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. P(terriers) = 85% is likely Option B
What is probability?Generally, Probability is the area of mathematics that deals with providing numerical descriptions of the likelihood that an event will take place or the likelihood that a statement will be correct.
A number between 0 and 1 may be thought of as representing the chance of an event happening, with 0 indicating that the occurrence is impossible and 1 indicating that it will definitely happen.
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Need Help ASAP
I still don't understand this
Read carefully and do as it says
By using divisibility rule, the possible factors of number are-
495 : 3, 5 and 9924 : 3 and 4210 : 2, 5 and 10Explain the term divisibility rule?A simple technique to determine if a given number may be divided by such a fixed divisor before carrying out the division operation is to run a divisibility test. When a number is fully divided by yet another number, the remainder should equal zero and the quotient ought to be a whole number. A factor is really a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, or else the numbers we are adding are factors of both the product since the product is divisible by them.For the stated number:
495 : 3, 5 and 9 as 495 is completely divisible by 3, 5 and 9.924 : 3 and 4, as 924 is completely divisible by them.210 : 2, 5 and 10 as 210 is completely divisible by 2 and 5.To know more about the divisibility rule, here
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Find each angle measure to the nearest degree
sin x = 0.7547
The each angle measure of the trigonometric ratios are obtained.
Define the term trigonometric ratios?A mathematical discipline called trigonometry examines connections between triangles' sides and angles. Due to the fact that every straight-sided form can be decomposed into a group of triangles, trigonometry may be found across all of geometry.The given values is:
sin x = 0.7547,
Using trigonometric properties,
cos x = √(1 - sin²x)
= √(1 - 0.7547²)
cos x = 0.6560
Cosec x = 1 / sin x
= 1 / 0.7547
Cosec x = 1.3250
Now,
1 + cot²x = cosec²x
cot x = √(cosec²x - 1)
= √(1.3250² - 1)
cot x = 0.8692
tan x = 1 / cot x
= 1 / 0.8692
tan x = 1.1544
Thus, the each angle measure of the trigonometric ratios are obtained.
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she created ordered pairs, (height , weight), from the data and found they defined a function. which of the following actions would cause alex's set of ordered pairs to no longer define a function?
Option(B) is the correct answer. The answer is - Adding data from a student who is 154 cm tall and weighs 69kg.
A function is a set of ordered pairs in which no two different ordered pairs have an identical x -coordinate. An equation that makes such a set of ordered pairs defines a function.The domain of the function is the set of all inputs and the range of the function is the set of all outputs. To check to see if a set of ordered pairs or a list presented by a table is a function or not, check to make sure that each input value is paired with only one output value.Read more about function:
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Which facts could be applied to simplify this expression? Check all that apply. 5 x + 3 y + (negative x) + 6 z Group of answer choices The simplified expression is 5 x + 3 y + 6 z. To add like terms, add the coefficients, not the variables. First add 5x + x. Only combine terms which contain the same variable. The simplified expression is 4 x + 3 y + 6 z.
Answer:
I dont understand what this is can you add a picture of the question?
Step-by-step explanation:
How long is the line of sight? Round your answer to the nearest hundredth.
Answer:
77.78 feet-----------------------
The line of sight is the hypotenuse of the 45° right triangle.
As per the property of the 45° right triangle, the length l is:
l = b√2 orl = 55×√2 ≈ 77.78 feetAnswer:77.7f
Step-by-step explanation: pythagorean theorem
55*55=3025
3025*2=6050
square root 6050=77.7
Please help me!! It is 5 questions
You prοbably know our football and basketball teams, but we have 21 Divisiοn I varsity programs that all raise the bar whenever they compete.
How many attended the Nοrth Carolina State or the Butler game?There were 465 people whο were surveyed in all.
The attendance at the FSU-Marist game was (M), n(M)=240.
The attendance at the FSU-Butler game was (B), n(B)=200.
The tοtal number οf spectators for the FSU-NC State game was n(NCS)=240.
The cοmbined attendance at the NC State game and the Marist game was n(MNCS)=90.
The cοmbined attendance at the Butler vs. NC State game was n(NCSB)=80.
The cοmbined attendance at the Butler and Marist games was n(BM)=100.
n(MBNCS)=30 peοple attended all three of the games.
When NC State's first football game was οrganised by students in 1892, the school's long histοry of intercollegiate athletics officially started.
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whats 2 2 56799065 times 569050890562 plus 69 x 420 plus 9 10 9 10 21 69 420 21 - 9 x3 y3 z3
The answer for 2 2 56799065 times 569050890562 plus 69 x 420 plus 9 10 9 10 21 69 420 21 - 9 x3 y3 z3 is 32185024125880310
Let x = 2, y = 56799065, z = 569050890562, a = 69, b = 420 and c = 9.
The equation is: 2x + y × z + a × b + (9 + 10 + 9 + 10) × (21 + 69 + 420 + 21) - 9 × 3 × y × 3 × z × 3
We can calculate this equation as follows:
2 × 2 + 56799065 × 569050890562 + 69 × 420 + (9 + 10 + 9 + 10) × (21 + 69 + 420 + 21) - 9 × 3 × 56799065 × 3 × 569050890562 × 3
= 4 + 32185023742042530 + 28380 + 145800 - 1365466177461590
= 32185024125880310
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What is the greatest common factor of {42,10}
Answer:
5
Step-by-step explanation:
If p is a prime number greater than 3, which of the following is not a factor of 6p
When p is a prime number greater than 3, the. option that is not a factor of 6p is A. p^2 (B
What is the factor about?The process of factorization simply has to do with the division of arithmetic algebraic expressions into the sum of their factors. in this case, multiplying the variables will yield the original expression. It means the writing of a number into smaller or simpler numbers that give the original number.
6*p / 6*p = 1
6*p / 3*p = 2
6*p / 2*p = 3
6*p / 3 = 2*p
6*p / p^2 = 6 / p which is not divisible by any prime number greater than 3.
The correct option is A.
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Complete question
If p is a prime number greater than 3, which of the following is NOT a factor of 6p ?
(A) p^2 (B) 6p (C) 3p (D) 2p (E) 3
Evaluate the expression 3s - 4q - m² where m= 4, q= -3, and s = -24.
We can substitute the given values into the expression to find the result:
3s - 4q - m² = 3(-24) - 4(-3) - 4² = 72 + 12 - 16 = 60.
So the expression equals 60 when m= 4, q= -3, and s = -24.
2
10 points
(2p+3)(3p-2)
O5p²-23p-10
O 6p²+5p-6
O 6p²-6
O 5p²-10
Answer:
B. 6p²+5p-6
Step-by-step explanation:
[tex]\bf \left(2p+3\right)\left(3p-2\right)[/tex]
Let's apply the FOIL method:-
[tex]\bf \left(2p+3\right)\left(3p-2\right)=[/tex]
[tex]\bf 2p\times \:3p+2p\left(-2\right)+3\times\:3p+3\left(-2\right)[/tex]
[tex]\bf 6p^2-4p+9p-6[/tex]
[tex]\bf 6p^2+5p-6[/tex]
Therefore, option B. 6p²+5p-6, is your answer!
__________________
Hope this helps!
Have a great day!
1,3,6,10,15,21,28 as a function
It seems that the sequence you provided is the sequence of triangular numbers. The function that generates this sequence could be defined as:
f(n) = n*(n+1)/2
Where n is the position of the number in the sequence.
So, for example:
f(1) = 1*(1+1)/2 = 1
f(2) = 2*(2+1)/2 = 3
f(3) = 3*(3+1)/2 = 6
and so on.
