Answer:
a) [tex]\mu = 24,\sigma = 3.46[/tex]
b) Significantly low:
[tex]x < 17.08[/tex]
Significantly high:
[tex]x > 30.92[/tex]
c) 42 girls are significantly high.
Step-by-step explanation:
We are given the following in the question:
[tex]p = 0.5[/tex]
a) mean and the standard deviation for the numbers of girls in groups of 48 births
[tex]\mu = np = 48(0.5) = 24\\\sigma = \sqrt{np(1-p)} = \sqrt{48(0.5)(1-0.5)} = 3.46[/tex]
b) Range rule of thumb
Significantly low: According to this rule the observations lying below two standard deviation of mean is considered significantly low.
[tex]x = \mu - 2\sigma\\x = 24 - 2(3.46) = 17.08[/tex]
Significantly high: According to this rule the observations lying above two standard deviation of mean is considered significantly high.
[tex]x = \mu + 2\sigma\\x = 24 + 2(3.46) = 30.92[/tex]
c) Significance of 42 girls
[tex]42 > \mu + 2\sigma[/tex]
Since 42 is greater than 30.92, 42 girls are significantly high. Thus, the method is not significant.
Trenton and Maria record how much dry food their pets eat on average each day.• Trenton's pet: 4/5 cup of dry food• Maria's pet: 1.25 cups of dry food. Based on these averages, how many more cups of dry food will Maria's pet have eaten than Trenton's pet will have eaten over 2 seven-day weeks? *
6.3 many more cups of dry food will Maria's pet have eaten than Trenton's pet will have eaten over 2 seven-day weeks
Step-by-step explanation:
We have , Trenton and Maria record how much dry food their pets eat on average each day.• Trenton's pet: 4/5 cup of dry food• Maria's pet: 1.25 cups of dry food. Based on these averages . We need to find how many more cups of dry food will Maria's pet have eaten than Trenton's pet will have eaten over 2 seven-day weeks . We need to find how much they eat for 14 days as:
Trenton's pet: 4/5 cup of dry food•
With 4/5 per day , for 14 days :
⇒ [tex]14(\frac{4}{5} )[/tex]
⇒ [tex]14(0.8 )[/tex]
⇒ [tex]11.2[/tex]
Maria's pet: 1.25 cups of dry food.
With 1.25 per day , for 14 days :
⇒ [tex]14(1.25 )[/tex]
⇒ [tex]17.5[/tex]
Subtracting Maria's - Trenton's :
⇒ [tex]17.5-11.2=6.3[/tex]
That means , 6.3 many more cups of dry food will Maria's pet have eaten than Trenton's pet will have eaten over 2 seven-day weeks
Final answer:
Over the course of two seven-day weeks, Maria's pet will have eaten 6.3 more cups of dry food than Trenton's pet.
Explanation:
To determine how much more food Maria's pet eats compared to Trenton's, we first need to calculate the daily difference in food consumption, before multiplying that by the number of days in two weeks (14 days).
Maria's pet eats 1.25 cups of dry food each day, while Trenton's pet eats 4/5 cups (which is equivalent to 1 cup). To find out how much more food Maria's pet eats per day, we subtract Trenton's pet's portion from Maria's:
1.25 cups - 0.8 cups = 0.45 cups
Now we multiply this daily difference by 14 to find the total difference over two weeks:
0.45 cups/day x 14 days = 6.3 cups
So, Maria's pet will have eaten 6.3 more cups of dry food than Trenton's pet over the course of two seven-day weeks.
George has $2.00 to spend at a store. He buys 3 cans of soda. Each can of soda costs 65 cents. What calculation should George use to determine how much change he should receive?
Answer:
5 cents.
Step-by-step explanation:
We have been George has $2.00 to spend at a store. He buys 3 cans of soda. Each can of soda costs 65 cents.
First of all George should calculate the total cost of 3 cans of soda by multiplying 3 by $0.65.
[tex]\text{Cost of 3 cans of soda}=\$0.65\times 3[/tex]
[tex]\text{Cost of 3 cans of soda}=\$1.95[/tex]
Now, George should subtract $1.95 from $2.00 to find the amount of change as:
[tex]\text{Amount of change that George will receive}=\$2.00-\$1.95[/tex]
[tex]\text{Amount of change that George will receive}=\$0.05[/tex]
Therefore, George will receive 5 cents in change.
Answer:
0.05 cents
Step-by-step explanation:
Given that George has $2.00 to spend at a store. He buys 3 cans of soda. Each can of soda costs 65 cents.
George has to use both multiplication and subtraction to find out the change
Spending at a store ... 2.00$
Cost of each can ... 0.65$
cost of 3 cans ... 3*0.65 = 1.95$
Change he receives ... 2-1.95 =0.05 cents
The formula Upper V equals LWH is used to find the volume of a box. If the length of a box is increased 4 times, the width is increased 4 times, and the height is tripled, how does this affect the volume?
Answer:
the volume of the box increases 48 times compared to the 1st one.
Step-by-step explanation:
Volume of the box (1) = LWH
length of a box is increased 4 time = 4L width is increased 4 times = 4Wthe height is tripled = 3H=> The new volume of the box = 4L * 4W * 3H = 48LWH
So the volume of the box increases 48 times compared to the 1st one.
Nestor cuts a cake with a 12-inch dameter One of the pleces he cuts has a central angle of 24° What is the area of the sice of cake? What fraction of the entire cake is this? Explain pleces he cuts has a central angle of 24 s
Answer:
7.54 sq. inches
Step-by-step explanation:
The cake with the cut portion has been shown in the figure below.
For calculating the area of cut part we first need to calculate the area of whole cake.
Diameter of the cake is given in the question as 12 inches.
So the area of the cake = [tex]\pi \frac{Diameter^2}{4}[/tex] = [tex]3.14 \times \frac{12\times12}{4} = 113.04[/tex] [tex]inches^2[/tex]
Since when the central angle is 360°, the area is 113.04 square inches
So when the central angle is 24°, the area of the section will be
[tex]\frac{113.04\times 24}{360} =7.54[/tex]
Thus area of the slice cut by Nestor is 7.54 sq. inches.
Fraction = [tex]\frac{7.54}{113.04} = 0.07[/tex]
Geometry 25 points. PLEASE help and show work ya boy be struggling
Answer:
6) x = 17 ft
7) 42 in
Step-by-step explanation:
6) length of the tangents are equal.
2x - 7 = 27
2x = 34
x = 17
7) if you draw a line from T passing through the centre of the circle, it will divide the triangle into two congruent triangles
Perimeter = 2(5+7+9) = 42 in
At a local community college, five statistics classes are randomly selected out of 20 and all of the students from each class are interviewed. Identify the type of sampling used in this example.
Answer:
cluster sampling
Step-by-step explanation:
In cluster sampling, the population is divided into groups or clusters (in this case, students divided in the 20 classes), the researcher then randomly selects a subset of clusters and samples the individuals within those clusters. In this example, since students from 5 out of 20 classes are sampled, the sampling process can be characterized as cluster sampling.
A person has 8 friends, of whom 5 will be invited to a party. (a) How many choices are there if 2 of the friends are feuding and will not attend together? (b) How many choices if 2 of the friends will only attend together?
Answer:
THE ANSWER ISSS B
Step-by-step explanation:
A wedding planner uses 72 ivy stems for 18 centerpieces. When she arrives at the venue,she realizes she will only need 16 centerpieces.How many ivy stems should she use so that the ratio of ivy stems to centerpieces stays the same?
Answer:
64
Step-by-step explanation:
18/72 = 16/x
16 x 72= 1152
1152/18= 64
The ratio of stems to center pieces is 2/8 so it cchecks out.
Answer:
64
Step-by-step explanation:
creating a chart would be useful when doing this type of problem
Find the arc length of AB. Round your answer to the nearest hundredth.
!no absurd answers, please! : (
The arc length of AB = 8.37 meters.
Solution:
Given data:
Degree of AB (θ) = 60°
Radius of the circle = 8 m
The value of π = 3.14
Arc length formula:
[tex]$\text{Arc length}=2 \pi r\left(\frac{\theta}{360^\circ}\right)[/tex]
[tex]$=2 \times 3.14 \times 8 \left(\frac{60^\circ}{360^\circ}\right)[/tex]
[tex]$=2 \times 3.14 \times 8 \left(\frac{1}{6}\right)[/tex]
Arc length = 8.37 m
The arc length of AB = 8.37 meters.
The polynomial of degree 5, P ( x ) has leading coefficient a=1, has roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 Find a possible formula for P ( x ) .
Answer:
[tex]p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}[/tex], for [tex]r_{1} = 0[/tex]
Step-by-step explanation:
The general form of quintic-order polynomial is:
[tex]p_{5}(t) = a\cdot x^{5} + b\cdot x^{4} + c\cdot x^{3} + d\cdot x^{2} + e \cdot x + f[/tex]
According to the statement of the problem, the polynomial has the following roots:
[tex]p_{5} (t) = (x - r_{1})\cdot (x-3)^{2}\cdot x^{2} \cdot (x+1)[/tex]
Then, some algebraic handling is done to expand the polynomial:
[tex]p_{5} (t) = (x - r_{1}) \cdot (x^{3}-6\cdot x^{2}+9\cdot x) \cdot (x+1)\\p_{5} (t) = (x - r_{1}) \cdot (x^{4}-5\cdot x^{3} + 3 \cdot x^{2} + 9 \cdot x)[/tex]
[tex]p_{5} (t) = x^{5} - (5+r_{1})\cdot x^{4} + (3 + 5\cdot r_{1})\cdot x^{3} +(9-3\cdot r_{1})\cdot x^{2} - 9 \cdot r_{1}\cdot x[/tex]
If [tex]r_{1} = 0[/tex], then:
[tex]p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}[/tex]
The polynomial P(x) given has a degree of 5, leading coefficient of 1, roots at 3, 0 (both with multiplicity 2), and -1 (with multiplicity 1). It can be written as P(x) = (x - 3)^2 * x^2 * (x + 1), according to the Fundamental Theorem of Algebra.
Explanation:A polynomial P(x) of degree 5 with a leading coefficient of 1 and roots at x = 3, x = 0 with multiplicity 2, and x = -1 with multiplicity 1 can be expressed as:
P ( x ) = (x - 3)^2 * x^2 * (x + 1)
This polynomial function is derived based on the fundamental theorem of algebra that states each polynomial equation of degree 'n' has 'n' roots or zeros, considering multiplicity. Here, the factors (x-3)^2, x^2 and (x+1) correspond to the roots 3, 0 and -1 with their respective multiplicities. Multiplicity refers to the number of times a number occurs as a root in the polynomial function.
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find the length of ladder
Answer:
33 feet
Step-by-step explanation:
Use SOHCAHTOA to determine which trigonometric function to use:
sin(65)=30/x
sin(65)x=30
x=30/sin(65)
x=33.1
So the length of the ladder rounded to the nearest foot is 33 feet
On Kathleen's credit card statement get last balance was $89.70. She made a payment of $20, had new charges totaling $32.11, and pays a periodic rate of 1.23%. What was kathleens finance charge?
1.25
1.23
1.10
0.86
Answer:
Well, the first $100 gets charged $1.50
The next 146.07 gets charged 1% so that is 1.46
1.50 + 1.46 = 2.96
2.3 89.70 - 20 + 32.11 = 101.81. 1.23 percent of that is 1.25
The answer would be the third choice.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
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Step-by-step explanation:
Answer:
110
Step-by-step explanation:
took the test
The formula V =s3 where s repesents the lengthe of an edge can be use to find the value of a cud . What is the volume of a cud that has edges of 12 inch .
Answer:
1728 cubic inches
Step-by-step explanation:
Given that the formula
[tex]V=s^3[/tex],
where s represents the length of an edge that can be used to find the value of a cud.
Given that a cud has edge as 12 inches
Using the above formula we can find volume by substituting for s.
Here we substitute s =12 inches so that we get volume in cubic inches
Volume of the cud = [tex]12^3\\=12*12*12\\\\=1728[/tex]
1728 cubic inches
Problems with the join and separate structures, with the start or initial amount unknown, tend to be the hardest for young students to understand and accurately solve. Identify the reason for they are more challenging for young children to use __________.A) Children can model the physical action.
B) Children can act out the situation.
C) Children cannot use counters for the initial amount.
D) Children cannot grasp a quantity represents two things at once.
Answer:C) Children cannot use counters for the initial amount.
Step-by-step explanation:Problem solving allows students to use mathematical concepts, skills and the relationships among them to solve problem situations with different levels of difficulties. Problem solving framework allows students to solve mathematical situations by assisting them to handle or approach problem solving systemically.
There are basically four structures they are
(1) Join
(2) Separate
(3) Part-Part-Whole
(4) Compare.
JOIN AND SEPARATE STRUCTURES INCLUDE ACTIONS THAT INCREASE OR DECREASE A QUANTITY.
The part-part whole does not involve an action but it has a relationship between a particular whole and its two separate parts.
The compare structure also does not involve an action,but it compares two unconnected and distinct sets.
[[ ANSWER PLS ]]
A parking space is in the shape of a parallelogram. The figure below is a model of the parking space. The measure of Angle B is 75°. What are the measures of the other 3 angles?
Answer:
Option 4
Step-by-step explanation:
B = D = 75
A = C = 180 - 75 = 105
In a parallelogram, opposite angles are equal and consecutive angles are supplementary. Given that Angle B is 75°, the other angles are 105° (Angle A), 75° (Angle D), and 105° (Angle C).
Explanation:The parking space is in the shape of a parallelogram. The properties of a parallelogram tell us that opposite angles are equal, and consecutive angles are supplementary (add up to 180 degrees). Given that the measure of Angle B is 75°, the angle opposite to it (Angle D) will also be 75° as they are opposite angles. This leaves us with Angles A and C. Since angles A and B are consecutive, Angle A is 180° - 75° = 105°. Similarly, since angles C and D are consecutive, Angle C is also 180° - 75° = 105°. Thus, the measures of the four angles in the parallelogram are 75°, 105°, 75°, and 105° respectively.
A plastic rod 1.5 m long is rubbed all over with wool, and acquires a charge of -9e-08 coulombs. We choose the center of the rod to be the origin of our coordinate system, with the x-axis extending to the right, the y-axis extending up, and the z-axis out of the page. In order to calculate the electric field at location A = < 0.7, 0, 0 > m, we divide the rod into 8 pieces, and approximate each piece as a point charge located at the center of the piece. 1. What is the length of one of these pieces? 2. What is the location of the center of piece number 2? 3. How much charge is on piece number 2?
Answer:
a) I = 0.1875 m
b) r_2 = 0.46875 m
c) q = -1.125*10^-8 C
Step-by-step explanation:
Given:
- The total Length of rod L = 1.5 m
- The total charge of the rod Q = -9 * 10^8 C
- Total section of a rod n = 8
Find:
1. What is the length of one of these pieces?
2. What is the location of the center of piece number 2?
3. How much charge is on piece number 2?
Solution:
- The entire rod is divided into 8 pieces, so the length of each piece would be:
l = L / n
l = 1.5 / 8
I = 0.1875 m
- The distance from center of entire rod and center of section 2 is 2.5 times the section length
r_2 = 2.5*l
r_2 = 2.5*(0.1875)
r_2 = 0.46875 m
- Assuming the charge on the rod is uniformly distributed. The the charge for each section of rod is given by q:
q = Q / n
q = -9 * 10^8 / 8
q = -1.125*10^-8 C
Jacob jogged 3 miles in 30 minutes on Wednesday and 5 miles in 50 minutes on Thursday. Otto jogged 4 miles in 32 minutes on Wednesday and 6 miles in 50 minutes on Thursday. Whose data shows the proportional relationship between the number of miles jogged and the time spent jogging?
Answer:
Jacob
Step-by-step explanation:
Because you can tell from the top of your head that it took Jacob 10 minutes for each mile for both days. While Otto his Wednesday time and Thursday time are not the same. Otto jogged an extra 2 minutes for his 6 miles on Thursday. So I would go with Jacob
Answer:
yggt7g7\
Step-by-step explanation:
Given that Sine theta = StartFraction 21 Over 29 EndFraction, what is the value of cosine theta, for 0 degrees less-than theta less-than 90 degrees?
Answer:
Step-by-step explanation:
We can use the identity:
[tex]sin^{2}A + cos^{2}A= 1[/tex]
[tex]sinA = \frac{21}{29}[/tex]
Solving we get,
cosA = 20/29
Answer:
C. 20/29
e2020
Which function is shown in the graph below?
A) y=(1/2)^x+3 -1
B) y=(1/2)^x-3 +1
C) y=(1/2)^x-1 +3
D) y=(1/2)^x+1 -3
Answer:
b just answered on edge
Step-by-step explanation:
y=(1/2)^x+3. -1
The function of the graph is [tex]y = (\frac12)^{x +3} -1[/tex]
The root expression of the graph is:
[tex]y = (\frac12)^x[/tex]
The graph is first shifted to the right by 3 units.
So, we have:
[tex]y = (\frac12)^{x +3}[/tex]
Next, the graph is shifted down by 1 unit.
So, we have:
[tex]y = (\frac12)^{x +3} -1[/tex]
Hence, the function of the graph is [tex]y = (\frac12)^{x +3} -1[/tex]
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Consider the set of all propositions. If T(x) means that x is a tautology and C(x) means that x is a contradiction, express the following statement using logical operators, predicates, and quantifiers. A. The conjunction of two tautologies is a tautology. B) Some propositions are tautologies. C) The negation of a contradiction is a tautology. D) The disjunction of two contingencies can be a tautology.
The four statements can be expressed in mathematical symbols using logical operators, predicates, and quantifiers. Conjunction of tautologies, existence of tautologies, negation of contradiction, and disjunction of contingencies have been expressed as mathematical propositions.
Explanation:In the realm of propositional logic, each statement can be expressed using logical operators, predicates, and quantifiers:
A) ∀x∀y(T(x) ∧ T(y) → T(x ∧ y)) - This states that for any two propositions, if both are tautologies, the conjunction (AND operation) of the two is also a tautology.
B) ∃xT(x) - This implies that there exists at least one proposition that is a tautology.
C) ∀x(C(x) → T(¬x)) - This implies that for all propositions, if a proposition is a contradiction, the negation of that proposition is a tautology.
D) ∃x∃y(¬T(x) ∧ ¬C(x) ∧ ¬T(y) ∧ ¬C(y) ∧ T(x ∨ y)) - This states that there exist two propositions where neither is a tautology or a contradiction (i.e., both are contingencies), such that their disjunction (OR operation) can be a tautology.
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The logical expressions use quantifiers, predicates, and logical operators to express concepts about tautologies and contradictions, emphasizing that propositions have intrinsic logical properties based on their structure.
Logical expressions employ quantifiers, predicates, and logical operators to articulate concepts about tautologies and contradictions, highlighting the intrinsic logical properties of propositions.
A. The conjunction of two tautologies is a tautology: (∀x)(∀y)(T(x) ^ T(y) ➡ T(x ^ y))
B. Some propositions are tautologies: (∃x) T(x)
C. The negation of a contradiction is a tautology: (∀x)(C(x) ➡ T(~x))
D. The disjunction of two contingencies can be a tautology: (∃x)(∃y)(C(x) ^ C(y) ➡ T(x ∨ y))
These expressions elucidate fundamental principles governing the logical structure and interplay of propositions, enriching our understanding of logical reasoning and inference.
You are renting a limousine that charges certain rates to visit each of the following cities. You need to visit each city once and you need to start in Athens and end in Athens. Use the "Brute Force" Algorithm to find the cheapest route to visit each city and return home again to Athens.
A. B. C. D.
Answer:
the answer is Athens-Buford-Cu-Dacul-Athens
Step-by-step explanation:
just took the quiz
Answer:
Way 3 and 4
Step-by-step explanation:
The Algorithm of Brute Force
Let A is Athens,
Let B is Buford,
Let C is Cuming,
Let D is Dacula
Use the "Brute Force" Algorithm to find the cheapest route to visit each city and return home again to Athens, we can see that there are 6 ways to visit each city and return home again to Athens.
Way 1: A→C→D→B→A = 50 + 30 + 70 + 70 = $220
Way 2: A→D→B→C→A = 60 + 70 + 25 + 50 = $205
Way 3: A→D→C→B→A = 60 + 30 + 25 + 70 = $185
Way 4: A→B→C→D→A = 70 + 25 + 30 + 60 = $185
Way 5: A→B→D→C→A = 70 + 70 + 30 + 50 = $220
Way 6: A→C→B→D→A = 50 + 25 + 70 + 60 = $205
Way 3 and 4 are the cheapest so we choose them.
Hey diameter of a bowling ball is about 22 cm in diameter of a tennis ball is about 7 cm what is the approximate difference in volume between bowling ball and tennis ball
Answer:
Step-by-step explanation:
The bowling ball and the tennis ball are spherical in shape.
The formula for determining the volume of a sphere is expressed as
Volume = 4/3 × πr³
Where
r represents the radius of the sphere.
π is a constant whose value is 3.14
Considering the bowling ball,
Diameter = 22 cm
Radius = diameter/2 = 22/2 = 11 cm
Volume = 4/3 × 3.14 × 11³ = 5572.5cm³
Considering the Tennis ball,
Diameter = 7 cm
Radius = diameter/2 = 7/2 = 3.5 cm
Volume = 4/3 × 3.14 × 3.5³ = 179.5 cm³
the approximate difference in volume between bowling ball and tennis ball is
5572.5 - 179.5 = 5393 cm³
Question 6 options:
Consider the line which is perpendicular to y=−2x+3 and passes through the point (4, -3). If the equation of this line is written in the form Ax + By + C = 0, then the exact value of A + B + C is ______
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
c represents the y intercept
m represents the slope of the line.
The equation of the given line is
y = - 2x + 3
Comparing with the slope intercept form, slope = - 2
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.
Therefore, the slope of the line passing through (4, - 3) is 1/2
To determine the y intercept, we would substitute m = 1/2, x = 4 and y = -3 into y = mx + c. It becomes
- 3 = 1/2 × 4 + c
- 3 = 2 + c
c = - 3 - 2
c = - 5
The equation becomes
y = x/2 - 5
Multiplying through by 2, it becomes
2y = x - 5
x - 2y - 5 = 0
Therefore
A = 1
B = - 2
C = - 5
The body loses approximately _____ pints of water a day through sweat
Answer: 5-6 pints.
PLZ GIVE BRAINLEST :)
Answer:
Range from 6 to 21 pints
Step-by-step explanation:
Sweat rate is proportional to metabolic rate, and can thus amount to 3 to 4 liters per hour (6.34013-8.45351 pints) or as much as 10 liters (21.1338 pints) per day.
If a random sample of 300 children is selected, let X be the number of these children who have been diagnosed with ASD. What distribution does X follow? What is the expected value and standard deviation of X?
Answer:
The random variable X follows a Binomial distribution.
[tex]E(X)=X\\SD(X)=\sqrt{\frac{X(300-X)}{300}}[/tex]
Step-by-step explanation:
The random variable X defined as the number of children who have been diagnosed with ASD.
The random sample of children selected is of size n = 300.
The probability of children diagnosed with ASD is, [tex]P(X)=p=\frac{X}{300}[/tex].
A children diagnosed with ASD is independent of all the others.
The random variable X follows a Binomial distribution.
[tex]X\sim Bin(n=300, p=\frac{X}{300})[/tex]
The expected value of X is:
[tex]E(X)=np=300\times \frac{X}{300}=X[/tex]
The standard deviation of X is:
[tex]SD(X)=\sqrt{np(1-p)}=\sqrt{300\times \frac{X}{300}[1-\frac{X}{300}]}=\sqrt{\frac{X(300-X)}{300}}[/tex]
In a large corporate computer network, user log-ons to the system can be modeled as a Poisson RV with a mean of 25 log-ons per hour. (20pts) (a) What is the probability that there are no logons in an interval of 6 minutes? (b) What is the probability that the distance between two log-ons be more than one hour?
Answer:
F(t<0.1 ) = 0.91791
Step-by-step explanation:
Solution:
- Let X be an exponential RV denoting time t in hours from start of interval to until first log-on that arises from Poisson process with the rate λ = 25 log-ons/hr. Its cumulative density function is given by:
F(t) = 1 - e ^ ( - 25*t ) t > 0
A) In this case we are interested in the probability that it takes t = 6/60 = 0.1 hrs until the first log-on. F ( t < 0.1 hr ), we have:
F(t<0.1 ) = 1 - e ^ ( - 25*0.1 )
F(t<0.1 ) = 0.91791
The probabilities of events in a Poisson process can be calculated using the Poisson distribution for a given number of events in a specific time frame and the exponential distribution for the time between events.
Explanation:The probability of events occurring in a fixed interval of time in a Poisson process can be calculated using the Poisson distribution formula:
P(X = k) = (e-\(\lambda\)\(\lambda\)k)/k!, where \(\lambda\) is the average number of events per interval, and k is the number of events for which we want to find the probability.
For part a), we need to find the probability of no log-ons in an interval of 6 minutes. With a mean of 25 log-ons per hour, 6 minutes corresponds to \(\lambda\) = (25/60)*6. We calculate the probability for k = 0 using the Poisson Distribution.
For part b), the time between two log-ons follows an exponential distribution, which is continuous and has the probability density function f(x) = \(\lambda\)e-\(\lambda\)x. The probability that the time between two log-ons is more than one hour can be found using the complement of the cumulative distribution function for the exponential distribution.
In summary, by calculating the probabilities for part a) and b), we can use the characteristics of the Poisson and exponential distributions to find the desired probabilities.
a group of 8 people went to the movies. tickets are $6 each for adults and $3 each for kids. together they pay $33 for the tickets. there are _______ adults in that group and _______ kids. can someone explain how to solve this in words for an essay.
Number of kids is 5 and number of adults is 3.
Step-by-step explanation:
Step 1: Let the number of adults be x. Then the number of kids is (8-x). Cost of tickets for adults = 6xCost of tickets for kids = 3(8-x) = 24 - 3x
Total cost = 33 = 6x + 24 - 3x = 3x + 24
⇒ 3x = 9
∴ x = 3
⇒ 8 - x = 8 - 3 = 5
∴ Number of kids is 5 and number of adults is 3.
Final answer:
To solve this problem, you can use a system of equations. The group consists of 3 adults and 5 kids.
Explanation:
To solve this problem, we can use a system of equations. Let's represent the number of adults as 'A' and the number of kids as 'K'. We know that there are 8 people in total, so we have the equation A + K = 8. We also know that the cost of tickets for adults is $6 and for kids is $3, and they paid a total of $33. This gives us the equation 6A + 3K = 33.
We can solve this system of equations by substitution or elimination. For simplicity, let's use substitution. From the first equation, we can rewrite K as K = 8 - A. Substituting this into the second equation, we get 6A + 3(8 - A) = 33.
Simplifying the equation, we get 6A + 24 - 3A = 33. Combining like terms, we have 3A + 24 = 33. Subtracting 24 from both sides, we get 3A = 9. Dividing both sides by 3, we find A = 3.
Now that we know there are 3 adults, we can plug this into the first equation to find K. A + K = 8, so 3 + K = 8. Subtracting 3 from both sides, we get K = 5. Therefore, there are 3 adults and 5 kids in the group.
A science experiment involves periodically measuring the number of mold cells present on a piece of bread. At the start of the experiment, There are 50 mold cells. Each time a periodic observation is made, the number of mold cells triples. For example, observation #1, there are 150 mold cells.
Answer:
y = 50·3^x(2, 450), (3, 1350), (4, 4050), (5, 12150)Step-by-step explanation:
The problem statement tells you each observed count is 3 times the last one.
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Expressed as an exponential function with an initial value of 50 and a growth factor of 3, the formula is ...
y = (initial value)×(growth factor)^x
y = 50·3^x
The question asks about a mold growth experiment which demonstrates exponential growth, where the number of mold cells triples with each measurement. Starting with 50 cells, the cell count increases to 150, 450, and so on.
Explanation:The situation described in your question is an example of exponential growth, a mathematical concept often used in biology to describe how populations like your mold cells multiply over time, trebling with each measurement. Considering your initial mold count was 50, each subsequent measurement or observation will be 3 times the previous count:
For observation 1, you have 50 * 3 = 150 cells For observation 2, it's 150 * 3 = 450 cells For observation 3, it'll be 450 * 3 = 1350 cells
And so on. The pattern continues, with each period's mold cell count being three times that of the previous period.
Learn more about Exponential Growth here:https://brainly.com/question/12490064
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what is the midpoint of the line segment with endpoints (-2, -2) and (4, 6)?
A (1,4)
B (2,2)
C (2,4)
D (1,2)
Option D: [tex](1,2)[/tex] is the midpoint of the line segment.
Explanation:
The endpoints of the line segment is [tex](-2,-2)[/tex] and [tex](4,6)[/tex]
We need to determine the midpoint of the line segment.
The midpoint of the line segment can be determined using the formula,
[tex]\text { midpoint }=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
Substituting the coordinates [tex](-2,-2)[/tex] and [tex](4,6)[/tex] in the formula, we have,
[tex]\text { midpoint }=\left(\frac{-2+4}{2}, \frac{-2+6}{2}\right)[/tex]
Adding the numerator, we have,
[tex]\text { midpoint }=\left(\frac{2}{2}, \frac{4}{2}\right)[/tex]
Dividing, we have,
[tex]\text { midpoint }=\left(1, 2)[/tex]
Thus, the midpoint of the line segment is [tex](1,2)[/tex]
Hence, Option D is the correct answer.
The baseball infield at the right has an area of 90^2 square feet .what is the area of the infield?
Step-by-step explanation:
If the given baseball field is in the rectangle shape.
Then area of the field is : Side x Side
Let us assume the side of the field = k feet
So, the area of the filed = k x k
⇒ 90 = k²
⇒ k = 9.486 feet
If the baseball field is in rectangle shape. then the area of the field is
⇒ Area = Length x Breadth
⇒ 90 = L x B
So the blabbering above me is completely wrong and makes no sense whatsoever.
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Your answer would be 8100 square feet. your welcome.
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