Answer:
595 Trout
Step-by-step explanation:
90 - 45 = 45
450 + 45 = 495
The estimated number of trout in the lake is 495 trouts.
How to the total number of trouts in the lake?The total number of trouts in the lakes that were initially tagged is added with the number of untagged trout that are caught afterward to find the total number of trout in the lake.
We can find the total number of trout in the lake as follows:It is given that 450 trout were initially caught and tagged by a conservationist and were later released into the lake.
Therefore the total number of tagged trout = 450
Later, when the trout are caught again, we notice that 90 are caught and of those 90 trout, 45 have been tagged. This means that there are 45 untagged trout.
Therefore, total number of untagged trout = 90 - 45
= 45
Therefore, the total number of trout in the lake = 450 + 45
= 495
Thus, we have found that the estimated number of trout in the lake is 495 trouts.
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A tower that is 106 feet tall casts a shadow 141 feet long. Find the angle of elevation of the sun to the nearest degree.
Final answer:
To determine the angle of elevation of the sun, calculate the inverse tangent (arctan) of the height of the tower (106 feet) divided by the length of its shadow (141 feet). The angle of elevation is approximately 37 degrees to the nearest degree.
Explanation:
To find the angle of elevation of the sun given that a 106 feet tall tower casts a shadow of 141 feet long, we can use trigonometry. Specifically, the tangent of the angle, which is the ratio of the opposite side (the height of the tower) to the adjacent side (the length of the shadow).
We use the formula:
tangent of angle = opposite / adjacent
Tan(angle) = 106 / 141
Now we need to calculate the inverse tangent (arctan) of this ratio to find the angle in degrees:
Angle = arctan(106/141)
After performing this calculation with a calculator or using a trigonometric table, we find that the angle to the nearest degree is approximately 37 degrees.
The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green?A. 21/55
B. 28/55
C. 34/55
D. 5/8
E. 139/220
Answer: B. [tex]\dfrac{28}{55}[/tex] .
Step-by-step explanation:
Given : Number of blue disks =4
Number of green disks = 8
Total disks = 12
Total number of combinations of drawing any 3 disks from 12 = [tex]^{12}C_3[/tex]
Number of combinations of drawing 1 blue and 2 green disks = [tex]^{4}C_1\times^{8}C_2[/tex]
Now , the probability that 1 of the disks selected is blue, and 2 of the disks selected are green will be :
[tex]\dfrac{^{4}C_1\times^{8}C_2}{^{12}C_3}\\\\=\dfrac{4\times\dfrac{8!}{2!6!}}{\dfrac{12!}{3!9!}}\\\\=\dfrac{4\times28}{220}\\\\=\dfrac{28}{55}[/tex]
Hence, the correct answer is B. [tex]\dfrac{28}{55}[/tex] .
Write some code that uses a loop to read such a sequence of non-negative integers, terminated by a negative number. When the code exits the loop it should print the number of consecutive duplicates encountered. In the above case, that value would be 3.
To solve the programming task, you would create a loop to read integers, use a counter to track consecutive duplicates and print the count after a negative number is entered to end the input.
The student's question involves writing a piece of code that reads a sequence of non-negative integers, ends the input with a negative integer, and reports the number of consecutive duplicate values entered before the negative integer is encountered. This is a programming task that typically involves a loop and a counter.
To address this question, you would write a loop that continues to accept input until a negative number is entered. Inside the loop, you would use a counter to keep track of the number of consecutive duplicates. Here is a pseudocode example:
Initialize the previous Value to None (or some value that won't occur in the sequence).
Initialize the count Of Duplicates to 0.
Start a loop that reads integers until a negative number is encountered.
Inside the loop, compare the current number to the previous Value.
If they are the same, increment the count Of Duplicates by 1.
Set the previous Value to the current number before the next iteration.
Outside the loop, print count Of Duplicates.
The counter pattern is a fundamental concept in programming that is used to tally occurrences within iteration structures like loops.
Does the graph represent a function? Why or Why Not
Answer:
not a function - it does not pass the vertical line test.
Step-by-step explanation:
A furniture salesperson earns 4.5% commission on every piece of furniture sold. The salesperson sells a sofa for $1000 and a chair for $200. What commission does the salesperson earn?
Answer: the salesperson earns $54 as commission.
Step-by-step explanation:
A furniture salesperson earns 4.5% commission on every piece of furniture sold. The salesperson sells a sofa for $1000. This means that the commission that he earned from the sale of the sofa is
4.5/100 × 1000 = 0.045 × 1000 = $45
The salesperson also sold a chair for $200. This means that the commission that he earned from the sale of the chair is
4.5/100 × 200 = 0.045 × 200 = $9
The total commission that the salesperson earns is
45 + 9 = $54
At a college, the cost of tuition increased by 10%. Let b represent the former cost of tuition. Use the expression b+0.10b for the new cost of tuition.
Question is Incomplete,Complete question is given below;
At a college, the cost of tuition increased by 10%. Let b be the former cost of tuition. Use the expression b + 0.10b for the new cost of tuition.
a) Write an equivalent expression by combining like terms.
b) What does your equivalent expression tell you about how to find the new cost of tuition?
Answer:
a. The equivalent expression is [tex]1.1b[/tex].
b. The new cost of tuition is 1.1 times the former cost of tuition.
Step-by-step explanation:
Given:
Former cost of tuition = [tex]b[/tex]
the cost of tuition increased by 10%.
New cost of tuition = [tex]b+0.10b[/tex]
Solving for part a.
we need to find the equivalent expression by combining the like terms we get;
Now Combining the like terms we get;
new cost of tuition = [tex]b(1+0.1) = 1.1b[/tex]
Hence The equivalent expression is [tex]1.1b[/tex].
Solving for part b.
we need to to say about equivalent expression about how to find the new cost of tuition.
Solution:
new cost of tuition = [tex]1.1b[/tex]
So we can say that.
The new cost of tuition is 1.1 times the former cost of tuition.
Consider the reaction 2x2y2+z2⇌2x2y2z which has a rate law of rate= k[x2y2][z2] select a possible mechanism for the reaction.
The question is about identifying a reaction mechanism based on the provided rate law, which is derived from the reactant concentrations. A likely mechanism is a single-step process where the reactants come together to form the product, mirroring the rate law's implication that reactant concentration directly influences the reaction rate.
Explanation:The student is asking about the mechanism of a reaction and its rate law. In chemistry, the rate law expresses the relationship among the reaction rate, the reaction mechanism, and the concentrations of the reactants.
The provided rate law is rate = k[x2y2][z2], which suggests that the reaction is first order with respect to both x2y2 and z2. A plausible mechanism for this reaction would involve a single step where one molecule of each reactant comes together to form the product, 2x2y2z.
In a single-step mechanism, the rate law is derived directly from the stoichiometry of the reactants in the balanced chemical equation. Since the rate law matches the stoichiometry of the reactants, it is likely that this could represent an elementary reaction, given that the stoichiometry and the rate law coincide.
The direct relationship implied by the rate law between the concentration of the reactants and the reaction rate can be explained by the likelihood of reactant particles colliding and reacting being greater with increased concentrations, a concept fundamental in kinetics.
Determine whether the data described below are qualitative or quantitative and explain why. The regions of residence of participants in a clinical trial of a new cancer treatment.Choose the correct answer below.A. The data are qualitative because they consist of counts or measurements. B. The data are qualitative because they don't measure or count anything.C. The data are quantitative because they consist of counts or measurements.D. The data are quantitative because they don't measure or count anything.
Answer:
option B
Step-by-step explanation:
The described data is qualitative because regions of a residence has categories and it don't measure or count anything. The regions of residence can be divided into different categories and numerical quantities can be assigned to them but still they will be qualitative variables because numerical quantities will be working as identifiers and they don't measure or count anything.
The polynomial negative 8.5 x squared plus 103 x plus 2026−8.5x2+103x+2026 models the yearly number of visitors (in thousands) x years after 20062006 to a park. Use this polynomial to estimate the number of visitors to the park in 20182018.
Answer:
2038000 visitors
Step-by-step explanation:
Now in question expression has been repeated, so original expression is
[tex]-8.5x^2+103x+2026[/tex]
Now according to given information "x" represent the number of years after 2006. So, for 2018, it will be
2018-2006 = 12 years
So, x = 12
putting value of x in expression
(-8.5)x(12)^2 + (103)x(12) + 2026
-1224 + 1236 + 2026
2038
Now the model shows the number of visitors in thousand, so you have to multiply your answer in thousand
2038 x 1000
= 2038000 visitors
Julia earns $6 an hour babysitting and earns $5 an hour walking dogs. She earned $43 after working a total of 8 hours at her two jobs. Complete the system of equations below to represent the situation. Let b= the number of hours that Julia babysits and d= the number of hours she walks dogs. _+_=8 _+_=43
Answer: the equations are
b + d = 8
6x + 5y = 43
Step-by-step explanation:
Let b represent the number of hours that Julia babysits.
Let d represent the number of hours she walks dogs.
Julia worked for a total of 8 hours babysitting and walking the dogs.. This means that
b + d = 8
Julia earns $6 an hour babysitting and earns $5 an hour walking dogs. She earned a total of $43 after working a total of 8 hours at her two jobs. This means that
6x + 5y = 43
Sixty-seven biscuits are to be fed to 10 pets; each pet is either a cat or a dog. Each dog is to get seven biscuits, and each cat is to get six. How many dogs are there?
Answer:
There are 7 dogs.
Step-by-step explanation:
7 (dogs) x 7 (biscuits) = 49
3 (cats) x 6 (biscuits) = 18
49 + 18 = 67
Each chef at "Sushi Emperor" prepares 151515 regular rolls and 202020 vegetarian rolls daily. On Tuesday, each customer ate 222 regular rolls and 333 vegetarian rolls. By the end of the day, 444 regular rolls and 111 vegetarian roll remained uneaten.
Each chef at "sushi emperor" prepares 15 regular rolls and 20 vegetarian rolls daily. On tuesday, each customer ate 2 regular rolls & 3 vegetarian rolls. by the end of the day, 4 regular rolls & 1 vegetarian roll remained uneating. how many chefs were on tuesday ? and how many customers were they ?
Answer:There were 2 chefs and 13 customers on tuesday
Solution:Let x be the number of chefs at Sushi Emperor and y be the number of customers on Tuesday.
From given,
Each chef prepares 15 regular rolls and 20 vegetarian rolls daily
If each chef prepares 15 regular rolls, then x chefs prepare 15x regular rolls
If each customer ate 2 regular rolls, then y customers ate 2y regular rolls
By the end of the day, 4 regular roll remained un eating
Therefore,
15x - 2y = 4 --------- eqn 1
If each chef prepares 20 vegetarian rolls, then x chefs prepare 20x vegetarian rolls
If each customer ate 3 vegetarian rolls, then y customers ate 3y vegetarian rolls
By the end of the day, 1 vegetarian roll remained uneating
Therefore,
20x - 3y = 1 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 1 by 3
45x - 6y = 12 ------- eqn 3
Multiply eqn 2 by 2
40x - 6y = 2 ------- eqn 4
Subtract eqn 4 from eqn 3
45x - 6y = 12
40x - 6y = 2
( - ) --------------
5x = 10
x = 2
Substitute x = 2 in eqn 1
20(2) - 3y = 1
40 - 3y = 1
3y = 39
y = 13
Thus there were 2 chefs and 13 customers
Two different suppliers, A and B, provide a manufacturer with the same part. All supplies of this part are kept in a large bin. in the past, 5% of the parts supplied by A and 9% of the parts supplied by B have been defective. A supplies four times as many parts as B. Suppose you reach into the bin and select a part, and find it is nondetective. What is the probability that it was supplied by A
Answer:
The probability of selecting a non-defective part provided by supplier A is 0.807.
Step-by-step explanation:
Let A = a part is supplied by supplier A, B = a part is supplied by supplier B and D = a part is defective.
Given:
P (D|A) = 0.05, P(D|B) = 0.09
A supplies four times as many parts as B, i.e. n (A) = 4 and n (B) = 1.
Then the probability of event A and B is:
[tex]P(A)=\frac{n(A)}{n(A)+N(B)}= \frac{4}{4+1}=0.80\\P(B)\frac{n(B)}{n(A)+N(B)}= \frac{1}{4+1}=0.20[/tex]
Compute the probability of selecting a defective product:
[tex]P(D)=P(D|A)P(A)+P(D|B)P(B)\\=(0.05\times0.80)+(0.09\times0.20)\\=0.058[/tex]
The probability of selecting a non-defective part provided by supplier A is:
[tex]P(A|D')=\frac{P(D'|A)P(A)}{P(D')} = \frac{(1-P(D|A))P(A)}{1-P(D)}\\=\frac{(1-0.05)\times0.80}{(1-0.058)}\\ =0.80679\\\approx0.807[/tex]
Thus, the probability of selecting a non-defective part provided by supplier A is 0.807.
The required probability of selecting a non-defective part provided by supplier A is 0.807.
Let,
A part is supplied by supplier A,
B part is supplied by supplier B,
And D = a part is defective.
Given:
P ([tex]\frac{D}{A}[/tex]) =5% = 0.05,
P([tex]\frac{D}{B}[/tex]) = 9% = 0.09
A supplies four times as many parts as B, .
Then, n (A) = 4 and n (B) = 1.
The probability of event A and B is:
Probability of event P(A) = [tex]\frac{n (A)}{n (A) + n(B)}[/tex] = [tex]\frac{4}{4+1}[/tex]
P(A) = [tex]\frac{4}{5}[/tex]
And Probability of Event P(B) = [tex]\frac{n (B )}{n (A) + n(B)} = \frac{1}{4+1}[/tex]
P(B) = [tex]\frac{1}{5}[/tex]
Then , the probability of selecting a defective product:
P(D) = [tex]P(\frac{D}{A}) P(A) + P(\frac{D}{B}) P(B)[/tex]
P(D) = 0.50×0.80 + 0.09×0.20
P(D) = 0.058
The probability of selecting a non-defective part provided by supplier A is
[tex]P(\frac{A}{D'} )= \frac{P(D'(A)) . P(A)}{P(D')} \\\\[/tex]
= [tex]\frac{1- P(D(A)). P(A)}{1-P(A)} \\\\\frac{(1-0.05) . 0.80}{1- 0.05} \\\\[/tex]
= 0.807
Hence, the probability of selecting a non-defective part provided by supplier A is 0.807.
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Jacob bought 13 packs of gum to add to the 5 pieces he already had. He then shared all of his pieces of gum with six friends. If Jacob and his six friends each revived 27 pieces of gum, how many were in each pack
Answer:
14 gums.
Step-by-step explanation:
Given: Jacob bought 13 pack of gum
He already had 5 piece of gum.
He shared gum with six of his friends.
Each one of them received 27 pieces of gum.
Lets assume the number of gums in each pack be "x".
Total number of gum= [tex]number\ of\ gum\ in\ each\ pack\times number\ of\ pack + 5[/tex]
Also gum has been shared among jacob and his 6 friends, which is 7 person.
∴ Share of each person= [tex]\frac{Total\ number\ of\ gums}{number\ of\ person}[/tex]
Now, forming equation to find number of gums in each pack.
⇒ [tex]\frac{13\times x+5}{7} = 27[/tex]
Multiplying both side by 7
⇒ [tex]13x+5= 189[/tex]
Subtracting both side by 5
⇒ [tex]13x= 189-5[/tex]
⇒[tex]13x= 184[/tex]
Dividing both side by 13
⇒ [tex]x= \frac{184}{13}[/tex]
∴[tex]x= 14.15 \approx 14\ gum[/tex]
Hence, each pack have 14 gums.
please help with a, b, and c. thank you!:)
Answer:
The answer to your question is below
Step-by-step explanation:
a) The intervals in which the graph is decreasing are the right section of the first parabola, the left section of the second parabola and also the right section of the third parabola.
(9, 11) U (14.5, 17) U (21, 27)
b) There are only two intervals in which the graph is increasing
(1, 9) U (17, 21)
c) During the time the graph is increasing, Andre is getting away from his origin.
My sister was fooling around wi her money the other night and left the coins in a pattern of four rows with four coins in each row. Each row had exactly one penny, one nickel,one dime , and one quater
Answer:
one penny = S
one nickel = T
one dime = U
one quater = V
∴ Probability one obtaining at least one of S, T, U or V = 4/24 = 1/6
Step-by-step explanation: They can be arranged as follows
1) STUV
2)TSUV
3) TSVU
4) UVST
5) VUST
6) VUTS
7) TVUS
8) TVSU
9) TUVS
10) SVUT
11) VSTU
12) VSUT
13) SVTU
14) UTSV
15) UTVS
16) USTV
17) USVT
18) VTUS
19) VTSU
20) SUTV
21) SUVT
22) STVU
23) TUSV
24) UVTS
Which two-dimensional cross sections are squares?
Select all that apply.
a cross-section that is perpendicular to the base of a cube
a cross-section that is parallel to the base of a triangular pyramid
a cross-section that is parallel to the base of a cylinder
a cross section through the center of a sphere
a cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same
Answer:
A cross-section that is perpendicular to the base of a cube.
A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.
Step-by-step explanation:
We have to select from options that the two-dimensional cross section are squares.
The correct options are :
A cross-section that is perpendicular to the base of a cube.
A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.
In both the cases the length and the width of the section are equal. (Answer)
Among the given options, only the cross-section that is perpendicular to the base of a cube is guaranteed to be a square. The other options will generally result in different shapes, such as triangles or circles.
Explanation:The question asks which two-dimensional cross sections are squares. To find the answer, we must consider the shape of the object and the orientation of the cross section.
A cross-section that is perpendicular to the base of a cube. If we cut a cube with a plane perpendicular to one of its faces, the cross section is the same shape as the face, which is a square.A cross-section that is parallel to the base of a triangular pyramid would not be a square because the base itself is a triangle.A cross-section that is parallel to the base of a cylinder would be a circle, as it would be cut along the cylinder's circular base.A cross section through the center of a sphere would also result in a circle, assuming the cut goes through the sphere's diameter.A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same, also known as a right circular cylinder, would only result in a square if the cylinder is cut along a plane that is at 45 degrees to the base, which is not the typical perpendicular cut, so typically it would not be a square.At first glance, only the cross-section perpendicular to the base of a cube is a square. However, depending on specific conditions not typically met by the listed shapes, other cross-sections can appear square-shaped. Therefore, generally, the answer is a cross-section that is perpendicular to the base of a cube will be square.
Assume that the weight of two year old babies have distribution that is approximately normal with a mean of 29 pounds and a standard deviation of 3 pounds. what weight of two year old baby corresponds to 10th percentile?
Answer:
25.15 ponds is the weight of two year old baby corresponds to 10th percentile.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 29 pounds
Standard Deviation, σ = 3 pounds
We are given that the distribution of weight of two year old babies is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.10
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 29}{3})=0.10[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z < -1.282) = 0.10[/tex]
[tex]\displaystyle\dfrac{x - 29}{3} = -1.282\\x = 25.154 \approx 25.15[/tex]
Thus, 25.15 ponds is the weight of two year old baby corresponds to 10th percentile.
Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment, and they have an average credit score. How much is the principal balance after applying their first month’s payment of $925.67?
Answer:
$88812.33
Step-by-step explanation:
Principal = $89,000
But there's a sales tax of 4.2%
Tax = (4.2 / 100) * 89000 = $3738
Total cost of the mobile house = $89000 + $3738 = $92,738
However, they made a down payment of $3000
Balance after down payment = $92,738 - $3000 = $89,738
They've also paid the first monthly payment of $925.67
Balance after first monthly payment =
$89,738 - $925.67 = $88,812.33
The principal balance after applying there first monthly payment is $88,812.33
The principal balance, after applying the first month's payment of $925.67 to an initial loan of $89,738 for a mobile home, is $88,812.33.
Explanation:To calculate the principal balance after the first month’s payment, start by adding the initial price of the mobile home and the sales tax. The sales tax is 4.2% (or 0.042) of $89,000, which comes out to $3,738. Then, subtract the down payment from the sum to get the initial loan amount. So, $89,000 + $3,738 - $3,000 equals $89,738. After applying the first month’s payment of $925.67, subtract that amount from the initial loan, leaving a principal balance of $88,812.33.
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Statistics can be referred to as numerical facts. In a broader sense, statistics is the field of study dealing with the collection, analysis, presentation and interpretation of data. a. True b. False
Answer:
True
Step-by-step explanation:
Statistics is indeed a procedure consists of collection, presentation, analysis and presentation of the data. Statistics is widely used in every field of life. For example we want to assess the performance of students. For this purpose we choose a sample of students and ask about their grading. This is the procedure of collection of data. Then this data can be presented in tabular form or graphical form and this stage is known as presentation of the data. Then we evaluate their average and this procedure is known as analysis of data. Then according to average we make statement about performance of students and this stage is interpretation of the data.
What is the ratio cosC?
Answer: 61.9°
Approximately: 62°
Step-by-step explanation:
Using Pythagoras
(AC)^2 = 17^2 - 15^2
= 289 - 225
√AC = √64
AC = 8
Cos C = Adj/ Hyp
Cos C = 8/17
Cos C = 0.4706
Inverse of Cos C
C = 61.93°
Approximately: 62°
On another map the distance between saugerties and kingston is 2 inches. Whar would tge distance from saugerties to catskill be on this map
The question is incomplete. The map is attached as a photo and here is the complete question:
a. What is the actual distance between Saugerties and
Kingston? ___________________________
b. Catskill is 15 miles from Saugerties. What would the
distance on the map be? ___________________________
c. On another map, the distance between Saugerties and
Kingston is 2 inches. What would the distance from Saugerties to
Catskill be on this map? __________________
Since you have asked the answer for part (c) only, here is the answer:
Answer:
The distance from Saugerties to Catskill would be 3 inches on this map.
Step-by-step explanation:
On the given map, the distance between Saugerties and Kingston is 4 inches and the scale is 1 inch = 2.5 miles.
To calculate the actual distance in miles between Saugerties and Kingston, consider the given scale:
1 inch ---------- 2.5 miles
4 inches ------ x miles
Cross multiplying:
1x = 2.5 x 4
x = 10 miles
The actual distance between Saugerties and Kingston is 10 miles.
On another map, the distance between Saugerties and Kingston is 2 inches. Which means the scale is 2 inches = 10 miles. So 1 inch = 10/2 = 5 miles
The scale on the other map is 1 inch = 5 miles.
Catskill is 15 miles from Saugerties (given in the previous part). So on the map:
1 inch -------- 5 miles
y inch ------- 15 miles
Cross multiplying:
15 = 5y
y = 15/5
y = 3 inches.
The distance from Saugerties to Catskill would be 3 inches on this map.
A lacrosse player throws a ball into the air from a height of 6 feet with an initial vertical velocity of 64 feet per second. What is the maximum height of the ball? When will the ball hit the ground? Round the answers to two decimal places if necessary.
Answer:
Step-by-step explanation:
I'm going to use calculus to solve this, because it's the simplest way.
The acceleration due to gravity in feet is the second derivative of the position function. We will start with the acceleration and work backwards with antiderivatives to get to the position function.
a(t) = -32. Going backwards and using the fact that the initial vertical velocity is 64 ft/sec, our velocity function is
v(t) = -32t + 64. Going backwards and using the fact that the initial height of the ball is 6 feet, our position function is
[tex]s(t)=-16t^2+64t+6[/tex]
The first part of this question asks us the maximum height of the ball. From Physics, we learn that the maximum height of a projectile is reached when the velocity is 0, which happens to be right where the projectile stops for a nanosecond in the air to turn around and come back down. We set the velocity function equal to 0 and solve for t.
0 = -32t + 64 and
0 = -32(t - 2). By the Zero Product Property, either -32 = 0 or t - 2 = 0. It's obvious that -32 does not equal 0, so t - 2 must equal 0. Solving this for t:
t - 2 = 0 so
t = 2 seconds. Since the maximum height is reached at a time of 2 seconds, we plug 2 seconds into the position function to get its position at 2 seconds (which is also the max height of the ball).
[tex]s(2)=-16(2)^2+64(2)+6[/tex] and
s(2) = -64 + 128 + 6 so
s(2) = 70 feet
Now we want to know when the ball will hit the ground. "When" is a time value, and we know that the height of the ball on the ground is 0, so we sub in a 0 for s(t) and factor the quadratic.
Using the quadratic formula:
[tex]t=\frac{-64+/-\sqrt{4096-4(-16)(6)} }{-32}[/tex] and
[tex]t=\frac{-64+/-\sqrt{4480} }{-32}[/tex] which gives us the 2 solutions
[tex]t=\frac{-64+\sqrt{4480} }{-32}[/tex] and
[tex]t=\frac{-64-\sqrt{4480} }{-32}[/tex]
Plugging into your calculator, the first t = -.0916500 and the second t = 4.091
We all know that time cannot ever be negative, so our t value is 4.09.
Again, from Physics, we know that a projectile reaches it max height at halfway through its travels, so it just goes to follow logically that if it halfway through its travels at 2 seconds, then it will hit the ground at 4 seconds. And it does!! How awesome is that?!
The maximum height of the ball is 32 feet. The ball will hit the ground after 4 seconds.
Explanation:To find the maximum height of the ball, we can use the equation for motion under constant acceleration.
The equation is h = (v0^2)/(2g),
where h is the maximum height, v0 is the initial vertical velocity, and g is the acceleration due to gravity.
Plugging in the given values, we have h = (64^2)/(2*32), which gives us a maximum height of 32 feet.
Next, to find when the ball will hit the ground, we can use the equation for time of flight.
The equation is t = (2v0)/g, where t is the time of flight.
Plugging in the given values, we have t = (2*64)/32, which gives us a time of flight of 4 seconds.
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Help!
Which is the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3?
A) 2
B) 3
C) 4
D) 6
The average rate of change for the function over the interval 1 ≤ x ≤ 3 is 2.
Explanation:The average rate of change for a function can be calculated by finding the difference in the function values over the given interval and dividing it by the difference in the x-values over the same interval.
For the given function graphed, the average rate of change over the interval 1 ≤ x ≤ 3 is calculated as follows:
Average rate of change = (f(3) - f(1)) / (3 - 1)
By evaluating the function at x = 1 and x = 3 and applying the formula, we find:
Average rate of change = (6 - 2) / 2 = 4 / 2 = 2
Therefore, the BEST estimate of the average rate of change for the function over the interval 1 ≤ x ≤ 3 is 2 (option A).
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4 Erin and Devon are playing a game. Erin has 42 points. If Devon had 14 more points, he'd have double the points Erin has. How many points does Devon have?
Final answer:
The question is a mathematical problem where we find that Devon has 70 points after setting up and solving an algebraic equation based on the conditions given.
Explanation:
The student's question revolves around a Mathematical problem concerning the points scored by two players, Erin and Devon, in a game. Erin has 42 points, and the question provides a condition that if Devon had 14 more points, he would have double the points Erin has. This scenario can be translated into an algebraic equation to solve for the number of points Devon currently has.
Let's denote the current number of points Devon has as D. According to the problem, if Devon had 14 more points, his total would be D + 14. We are also told that this hypothetical total would be double the points Erin has, which is 42. Therefore, we can write the equation as:
D + 14 = 2 × 42
By solving this equation, we can find out how many points Devon has:
D + 14 = 84 (since 2 × 42 equals 84)D = 84 - 14D = 70Devon currently has 70 points.
Erin has 42 points. Devon has 70 points. If he had 14 more, he'd have double Erin's points.
let's break it down step by step:
Given:
- Erin has 42 points.
- If Devon had 14 more points, he'd have double the points Erin has.
Let's denote Devon's points as [tex]\( D \).[/tex]
According to the given information, if Devon had 14 more points, he'd have double the points Erin has. So, mathematically, we can represent Devon's points as [tex]\( 2 \times 42 \)[/tex] when we add those 14 points.
So, we can write the equation:
[tex]\[ D + 14 = 2 \times 42 \][/tex]
Now, let's solve for [tex]\( D \):[/tex]
[tex]\[ D + 14 = 84 \][/tex]
Subtract 14 from both sides of the equation:
[tex]\[ D = 84 - 14 \]\[ D = 70 \][/tex]
So, Devon currently has 70 points.
Significance tests A test of H0: p = 0.65 against Ha: p < 0.65 has test statistic z = −1.78. (a) What conclusion would you draw at the 5% significance level? At the 1% level? (b) If the alternative hypothesis were Ha: p ≠ 0.65, what conclusion would you draw at the 5% significance level? At the 1% level?
Answer:
(a) At 5% significance level, reject H0
At 1% significance level, reject H0
(b) At 5% significance level, fail to reject H0
At 1% significance level, fail to reject H0
Step-by-step explanation:
(a) The test is a one tailed test
At 5% significance level, the critical value is 1.645
Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 1.645
At 1% significance level, the critical value is 2.326
Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 2.326
(b) The test is a two tailed test
At 5% significance level, the critical value is 1.96. The region of no rejection of H0 lies between -1.96 and 1.96
Conclusion: Fail to reject H0 because the test statistic -1.78 falls within -1.96 and 1.96
At 1% significance level, the critical value is 2.576. The region of no rejection of H0 lies between -2.576 and 2.576
Conclusion: Fail to reject H0 because the test statistic falls within -2.576 and 2.576
The conclusion that can be made from an hypothesis test depends on
the significance level and p-value.
Response:
(a) The conclusion at 5% is there is statistical evidence to suggest that p < 0.65
At 1% level; fail to reject H₀: p = 0.65, there is statistical evidence to suggest that p = 0.65
(b) With Hₐ ≠ 0.65, the conclusion at the 5% significance level is that there is sufficient statistical evidence that p = 0.65
At the 1% level, fail to reject H₀: p = 0.65,
Which is the method to draw conclusion from an hypothesis test?The null hypothesis, H₀: p = 0.65
The alternative hypothesis, Hₐ: p < 0.65
The z-score is z = -1.78, which gives;
The p-value = 0.0375
(a) The significance level is 5%
Which gives, α = 0.05
Given that the p-value is less than the significant level, we have that
there is sufficient evidence against the null hypothesis, given that the
probability that the null hypothesis is correct is less than the significant
level of 5%.
Therefore, reject H₀, p = 0.65
There is sufficient statistical evidence to suggest that the the p is less than 0.65, (p < 0.65)However, at 1% significant level, α = 0.01, and the p-value, p = 0.0375 is
larger than the significance level.
Therefore, we fail to reject the null hypothesis and there is sufficient statistical evidence to suggest that p = 0.65(b) Hₐ: p ≠ 0.65
We have;
[tex]\alpha = \dfrac{5 \%}{2} = 2.5 \% = \mathbf{0.025}[/tex]
Which gives;
The p-value (0.0375) is larger than the significant level, therefore, we
fail to reject the null hypothesis.
There is sufficient statistical evidence to suggest that p = 0.65At the 1% level of significance, we have;
[tex]\alpha = \dfrac{1 \%}{2} = 0.5 \% = 0.005[/tex]
Which gives;
The p-value at z = -1.78 (p = 0.0375) is larger than the significant level
Therefore;
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A Ferris wheel is 50 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. How many minutes of the ride are spent higher than 40 meters above the ground?
To calculate the time spent above 40 meters on a Ferris wheel, we analyze the wheel's structure and use trigonometry to find the proportional time of the ride corresponding to the arc above the 40-meter mark.
Explanation:Calculating Time Spent Above 40 meters on a Ferris Wheel
To determine how many minutes of the ride on the Ferris wheel are spent higher than 40 meters above the ground, we need first to understand the wheel's structure and motion. Given that the Ferris wheel has a diameter of 50 meters and is boarded from a platform 4 meters above the ground, we can calculate the highest and lowest points riders will reach during the ride. The highest point of the wheel will be 50 meters (the radius) plus 4 meters (the platform height), totaling 54 meters. The lowest point will be 4 meters (platform height) above the ground since the diameter is equal to twice the radius and the wheel's lowest point touches the platform level.
Because riders want to be above 40 meters, we're interested in the segment of the ride where they are between 40 meters and the maximum of 54 meters above the ground. This range covers a portion of the wheel's circumference. If the wheel's highest point is at 12 o'clock and the loading platform is at 6 o'clock, then the 40-meter height will be somewhere between 6 o'clock and 12 o'clock.
Using the fact that the Ferris wheel completes one revolution in 4 minutes, we can find the time spent over 40 meters by calculating the angle θ that corresponds to the arc between 40 meters and 54 meters above the ground. The 40-meter height will fall at the point where the vertical distance from the top of the wheel equals the wheel's radius minus 40 meters. Using this, we can use trigonometry to find θ, and then convert this angle to a proportion of the full revolution time to determine the time spent on this segment of the ride.
If circumstances are less than desirable or if something seems suspicious or amiss, approach the vehicle form the right-hand or passenger side, especially when:________
Answer:
Only one person is in the stopped vehicle
Step-by-step explanation:
Suppose that 20% of all personal computers of a certain brand break down in the first year of operations. In an office with 10 such computers, find the probability that: a) none break down; b) exactly five break down; c) at least one breaks down; d) at most two breaks down; e) all break down.
Answer:
d
Step-by-step explanation:
The probability of computers are 20%. Therefore to determine the amount that would break out of 10 we simply just multiply by 0.2.
[tex]=10\cdot{0.2}=2[/tex]
Therefore at most two breaks down. The answer is d
PLEASE HELP PLEASE PLEASE DUE TONIGHT AAA
Answer:
Measurement of all angle= [tex]76.79\º+102.66\º+15.35\º+265.16\º= 360\º[/tex]
Step-by-step explanation:
Given angles are [tex]x\º, (\frac{5x}{9} +60)\º, (\frac{x}{5} )\º, (4x-142)\º[/tex]
The given is a quardilateral.
We know the sum of all angles of quardilaterals is 360º
∴ [tex]x\º+ (\frac{5x}{9} +60)\º+ (\frac{x}{5} )\º+(4x-142)\º= 360\º[/tex]
Now, solving the equation to find value of x.
⇒ [tex]x\º+ (\frac{5x}{9} +60)\º+ (\frac{x}{5} )\º+(4x-142)\º= 360\º[/tex]
Opening parenthesis.
⇒ [tex]x\º+ \frac{5x}{9} +60\º+ \frac{x}{5} \º+4x-142\º= 360\º[/tex]
⇒ [tex]5x\º+ \frac{5x}{9} + \frac{x}{5} \º-82\º= 360\º[/tex]
Adding both side by 82
⇒ [tex]5x+ \frac{5x}{9} + \frac{x}{5} = 442[/tex]
Taking LCD 45
⇒ [tex]\frac{45\times 5x+ 5\times 5x+9x}{45} = 442[/tex]
Multiplying both side by 45
⇒ [tex]225x+25x+9x= 19890[/tex]
⇒[tex]259x= 19890[/tex]
Dividing both side by 259
⇒[tex]x= \frac{19890}{259}[/tex]
∴[tex]x= 76.79\º[/tex]
Next subtituting the value of x to find measurement of other interior angle.
[tex]x\º, (\frac{5x}{9} +60)\º, (\frac{x}{5} )\º, (4x-142)\º[/tex]
2. [tex](\frac{5x}{9} +60)\º[/tex]
= [tex]\frac{5\times 76.79}{9} +60= 42.66+ 60[/tex]
= [tex]102.66\º[/tex]
3. [tex](\frac{x}{5} )\º[/tex]
= [tex](\frac{76.79}{5} )\º= 15.35\º[/tex]
4. [tex](4x-142)\º[/tex]
= [tex]4\times 76.79- 42= 307.16-42[/tex]
= [tex]265.16\º[/tex]