Answer:
a. The ball enters the green at Q (-13.46, -32.31)
b. 3.189s
c. 5.824s
d. Closest point = (10.77, -16.15), it occurs 6.102s after the ball starts its journey
Step-by-step explanation:
he rightmost edge is taken as the right end of the horizontal diameter
Coordinates of the hole at H:(0,0)
Coordinates of the ball B:(-40,-50)
Coordinates of the point the ball exits green P:(35,0)
So, the line joining B and P is given by
Looking for the gradient of the line B P we have
(x2-x1)/(y1-y2) =(35 –(-40))/(0-(-50))
= 75/50=3/2
The line equation therefore = (y-(-50))/(x-(-50)) = 2/3
(y + 50)/(x+40) =2/3
y+50 = 2/3 (x+40)
The equation of a circle is given by
x^2+y^2 = 35^2
solving the two equations we have
x = ((3y+150)/2)-40 = 1.5y-35
Substituting the value of x into the above equations we have (1.5y-35)2 + y2 = 352
3.25×y2+105×y = 0
From where we have y×(3.25×y + 105) = 0
From where y = 0 or y = -105/3.25 = -32.31m
Also x = 35 or x = -13.46
The line intersects the circle at
Q:(-13.46,-32.31) and P:(35,0)
a. The ball enters the green at Q (-13.46, -32.31)
b. The ball enters the green after (length BQ)/Velocity
Where length BQ is given as
√((-13.46-(-40))2+(-32.31-(-50))2) = √(26.532+17.692) = 31.89ft
The ball enters after 31.89ft/10ft/s or 3.189s
c. To find out how long the ball spends inside the green we have
Q:(-13.46,-32.31) and P:(35,0)
Length QP2 = (-13.46-(35))2 + (-32.31- 0)2 = 3392.31 = 58.24m
Time spent in the green = 58.24/10 = 5.824s
d. The ball is closest to the cup at the point when the perpendicular from the cup intersects the line PQ
and this is at the center of the line PQ hence the locus of the point is
((-13.46 + (35-(-13.46))/2), (-32.31+(0-(-32.31))/2) = (10.77, -16.15)
This occurs at (√( (10.77-(-40))2 + (-16.15(-50))2))/10 = 61.02ft/10ft/s = 6.102s after the ball starts its journey
As the cup of the 9th hole in the golf course is located as the dead in the center of the milled green circular shape that is 70 feet. A ball follows the straight-line path and exists at the fright most edge.
The rightmost edge is taken as per the right end of horizontal diameter. The coordinates of the hole at H: (0,0) B:(-40,-50) ball exits green P:(35,0) The line joining B and P is given by (x2-x1)/(y1-y2) =(35 –(-40))/(0-(-50)) = 75/50=3/2. Similarly, The ball enters the green at Q (-13.46, -32.31) , b. 3.189s , c. 5.824s, d. Closest point = (10.77, -16.15), it occurs 6.102s after the ball starts its journey.Learn more about the hole of a golf course is located dead center in the middle.
brainly.com/question/2553954.
Plot the points in the coordinate plane. Then find the perimeter and area of the polygon.
A(-3,5), B(1,6), C(3,-2), D(-1,-3)
Perimeter___________
Area__________________
Answer:
The answer to your question is below
Step-by-step explanation:
See the graph below
Process
1.- Find the distance from A to B, B to C, C to D, A to D
Formula
d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
d AB = [tex]\sqrt{(1 + 3)^{2} + (6 - 5)^{2}} = \sqrt{17}[/tex]
dBC = [tex]\sqrt{(-2 -6)^{2} + (3 - 1)^{2}} = \sqrt{68}[/tex]
dCD = [tex]\sqrt{(-1 - 3)^{2} + (-3 +2)^{2}} = \sqrt{17}[/tex]
dAD = [tex]\sqrt{(-1 + 3)^{2} + (-3 - 5)^{2}} = \sqrt{68}[/tex]
2.- Find the perimeter
Perimeter = 2[tex]\sqrt{17} + 2\sqrt{68}[/tex] = [tex]6\sqrt{17}[/tex] u
3.- Find the area
Area = [tex]\sqrt{17} x \sqrt{68}[/tex]
Area = [tex]\sqrt{17x68} = \sqrt{1156} = 34 u^{2}[/tex]
When you graph a square root does it curve
Answer:
yes
Step-by-step explanation:
because it is not a whole number so you cant tell
What is the slope of the line through (-9,6)(−9,6)(, minus, 9, comma, 6, )and (-3,9)(−3,9)(, minus, 3, comma, 9, )?
Answer:
0.5
Step-by-step explanation:
The slope m of a linear equation y = mx + b that goes through point (-9,6) and point (-3, 9) would have the following formula
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 6}{-3 - (-9)} = \frac{3}{6}= \frac{1}{2}[/tex] or 0.5
Where [tex](x_1,y_1), (x_2, y_2)[/tex] are the coordinates of the 2 points that this line goes through
Carrie had a bag of jelly beans she ate 5 and then gave the bag to her brother to share with the eight other boys on his basketball yteam carrie's brother ate 4 jelly beansd the first teammate ate 6, then the next one ate 8 and so on aftyer the last teammate took his jelly beans there were 3 jelly beansd left in the bag how many jelly beans lewere in the bag to start with
Answer:
There were 116 jelly beans in the bag to start with
Explanation:
a. Let's start with Carries brother and his friends.
We are given that Carrie's brother ate 4 jelly beans, the first teammate ate 6, the second teammate ate 8 and so on.
Noticing the pattern, we can see that each teammate ate 2 jelly beans more that the one preceding him.
We are also given that Carrie's brother has 8 teammates.
This means that:
Carrie's brother ate 4 jelly beans
First teammate ate 4 + 2 = 6 jelly beans
Second teammate ate 6 + 2 = 8 jelly beans
Third teammate ate 8 + 2 = 10 jelly beans
Fourth teammate ate 10 + 2 = 12 jelly beans
Fifth teammate ate 12 + 2 = 14 jelly beans
Sixth teammate ate 14 + 2 = 16 jelly beans
Seventh teammate ate 16 + 2 = 18 jelly beans
Eighth teammate ate 18 + 2 = 20 jelly beans
Now, we calculate the total number of jelly beans eaten by Carrie's brother and his teammates
Total jelly beans = 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 108 jelly beans
b. Next, we move to Carrie:
We are given that Carrie ate 5 jelly beans
Adding that to the total number of jelly beans from part a, we get the total number of eaten jelly beans
Therefore:
Total number of eaten jelly beans = 108 + 5 = 113 jelly beans
c. Getting the number of jelly beans that were in the bag to start with:
We are given that the remaining number of jelly beans in the bag after all has eaten was 3 jelly beans
This means that, if we added the number of eaten jelly beans to the number of remaining jelly beans, we will get the total number of jelly beans that were in the bag to start with
Therefore:
Total number of jelly beans in the bag to start with = 113 + 3 = 116 jelly beans
Hope this helps :)
Final answer:
By calculating the total number of jelly beans eaten and adding the three left in the bag, we find that there were originally 119 jelly beans in Carrie's bag.
Explanation:
To figure out how many jelly beans were in the bag initially, we need to work backwards from the information given. Carrie ate 5 beans and then her brother ate 4. Combining that with the 3 beans left at the end, we have a subtotal of 12 beans (5+4+3). We're told that each of Carrie's brother's teammates ate an increasing number of beans, starting with 6 and increasing by 2 each time.
Let's find the total number of beans eaten by the teammates. Since there are 8 teammates and the number of jelly beans increases by 2 for each subsequent teammate, starting at 6, we have an arithmetic sequence.
The first teammate ate 6 beans.The second ate 6+2 = 8 beans.This pattern continues until the eighth teammate.To find the total beans eaten by teammates, we sum the arithmetic sequence: T = (n/2) * (first term + last term). Here, n=8, the first term is 6, and the last term is 6 + 2*(8-1) = 20 (since the increase is by 2 for each of the 7 teammates after the first).
T = (8/2) * (6 + 20) = 4 * 26 = 104 beans eaten by all teammates combined.
Adding Carrie's and her brother's consumption to the teammates' total gives us: 12 beans (Carrie and her brother) + 104 beans (teammates) = 116 beans. Therefore, there were 116 + 3 (left in the bag) = 119 jelly beans in the bag to start with.
9. Calculate the median 5, 10, 12, 4, 6, 11, 13, 5
Answer:
8.
Step-by-step explanation:
5, 10, 12, 4, 6, 11, 13, 5
Arrange in ascending order:
4, 5, 5, 6, 10, 11, 12, 13.
The median is the mean of the 2 middle numbers:
= (6 + 10) / 2
= 8.
Find the piece wise function for the graph
Answer:
See below.
Step-by-step explanation:
x < 2 f(x) = |x|.
x ≥ 2 f(x) = 3.
Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities 0.81, 0.09, 0.08, and 0.02, respectively. A particular company offers a $500 deductible policy. If the company wishes its expected profit to be $100, what premium amount should it charge?
Answer:
$600
Step-by-step explanation:
Let the random variable [tex]X[/tex] denote the damage in $ incurred in a certain type of accident during a given year. The probability distribution of [tex]X[/tex] is given by
[tex]X : \begin{pmatrix}0 & 1000 & 5000 & 10\; 000\\0.81 & 0.09 & 0.08 & 0.02\end{pmatrix}[/tex]
A company offers a $500 deductible policy and it wishes its expected profit to be $100. The premium function is given by
[tex]F(x) = \left \{ {{X+100, \quad \quad \quad \quad \quad \text{for} \; X = 0 } \atop {X-500+100} , \quad \text{for} \; X = 500,4500,9500} \right.[/tex]
For [tex]X = 0[/tex], we have
[tex]F(X) = 0+100 = 100[/tex]
For [tex]X = 500[/tex],
[tex]F(X) = 500-500+100 = 100[/tex]
For [tex]X = 4500[/tex],
[tex]F(X) = 4500-500+100 = 4100[/tex]
For [tex]X = 9500[/tex],
[tex]F(X) = 9500-500+100 = 9100[/tex]
Therefore, the probability distribution of [tex]F[/tex] is given by
[tex]F : \begin{pmatrix} 100 & 100 & 41000 & 91000\\0.81 & 0.09 & 0.08 & 0.02\end{pmatrix}[/tex]
To determine the premium amount that the company should charge, we need to calculate the expected value of [tex]F.[/tex]
[tex]E(F(X)) = \sum \limits_{i=1}^{4} f(x_i) \cdot p_i = 100 \cdot 0.81 + 100 \cdot 0.09 + 4100 \cdot 0.08 + 9100 \cdot 0.02[/tex]
Therefore,
[tex]E(F) = 81+9+328+182 = 600[/tex]
which means the $600 is the amount the should be charged.
Many mechanics advised people not to drive their cars more than 5,000 miles between oil changes kaci has driven her car 3450 miles since the last oil change write and solve an inequality to find out how many more miles she might drive before having her oil changed again
Answer:
See explanation!
Step-by-step explanation:
We know that the maximum miles allowed before oil change is 5,000miles (thus Kaci can drive less or up to 5,000 miles but not more).
Kaci has already driven 3,450miles since last oil change.
Inequalities are typically employed to show a relating or comparative relationship between expressions and can be identified by the sybolism of less, more or/and equal to (i.e. [tex]<[/tex] , [tex]>[/tex] , [tex]\leq[/tex], [tex]\geq[/tex] ).
Let us denote the miles Kaci can drive before oil changing again by [tex]x[/tex], then we can write the following inequality:
[tex]3450+x\leq 5000[/tex]
solving for the remaining miles [tex]x[/tex] allowed
[tex]3450+x\leq 5000\\x\leq 5000-3450\\x\leq 1550[/tex]
Thus Kaci can drive up to and including 1550 miles before chaging car oil again.
Final answer:
Kaci can drive up to 1550 more miles before needing an oil change, based on the advice not to exceed 5000 miles between oil changes and the fact she has already driven 3450 miles.
Explanation:
The question asks us to write and solve an inequality that will help determine how many more miles Kaci can drive before needing an oil change. It is given that her car has already been driven 3450 miles since the last oil change, and she has been advised not to exceed 5000 miles between oil changes.
To solve this, let x represent the number of miles Kaci can still drive before reaching the 5000-mile limit. The inequality that represents this situation would be:
3450 + x ≤ 5000
To find the value of x, we subtract 3450 from both sides of the inequality:
x ≤ 5000 - 3450
x ≤ 1550
Therefore, Kaci can drive up to 1550 more miles before needing her oil changed again.
(Answer asap) Name all of the radii of the circle
Answer:
OT, OU, OR
Step-by-step explanation:
Point O is the center of the circle, so will be one end of any radius. Segments are shown from point O to points T, U, and R on the circle. Each of those segments is a radius:
OT, OU, OR . . . . are radii
_____
OS would also be a radius, but no segment is shown there, and it doesn't show in any answer choice.
For #1-4, graph the polygon with the given vertices and its image after the transformation. Label all vertices in both the Pre-image and image using the correct notation.
See the attached picture:
Edited graph 4. I missed the negative sign in front of the one. The new graph is attached.
Ms Thomas drove at a constant rate for 45. She drove 39 miles during that time. If distance is determined by the equation d=rt where r is the constant rate in miles per hours what was ms Thomas constant rate?
Answer:
Ms. Thomas was driving at constant rate of 52 miles/hour.
Step-by-step explanation:
Given:
Total time to travel (t) = 45 minutes
Distance drove (d) = 39 miles
we need to find the constant rate in miles per hour at which she was driving.
Solution:
Now we know that;
We need to find constant rate at miles per hour;
But time is given in minutes.
So we will convert minutes into hour by dividing by 60 we get;
time [tex]t =\frac{45}{60}= 0.75\ hrs[/tex]
Now we know that;
Distance is equal to rate times time.
framing in equation form we get;
distance [tex]d =rt[/tex]
Or
rate [tex]r= \frac{d}{t} = \frac{39}{0.75}= 52 \ mi/hr[/tex]
Hence Ms. Thomas was driving at constant rate of 52 miles/hour.
Tiwa spent 1 1/2 hours setting up her computer. It took her 3 times as long to install the software. How long did it take Tiwa to set up the computer and install the software
Answer:
Total time spent by Tiwa to set up the computer and install software = 6 hours
Step-by-step explanation:
Given:
Time spent by Tiwa to set up her computer = [tex]1\frac{1}{2}\ hours[/tex]
Time spent to install the software is 3 times the time she took to set up the computer.
To find the total time Tiwa took to set up her computer and install the software.
Solution:
Time spent by Tiwa to install the software can be given as:
⇒ [tex]3\times 1\frac{1}{2} \ hours[/tex]
In order to multiply mixed numbers we first change them to fractions.
We multiply the denominator to the whole number and add the numerator to it. Then we write the number as numerator of a fraction with the same denominator.
So, [tex]1\frac{1}{2}=\frac{3}{2}[/tex]
So, we have:
⇒ [tex]3\times \frac{3}{2}\ hours[/tex]
⇒ [tex]\frac{9}{2}\ hours[/tex]
Total time spent by Tiwa to set up the computer and install software can be given as:
⇒ [tex]\frac{3}{2}\ hours+\frac{9}{2}\ hours[/tex]
Since denominators are same, so we simply add the numerators.
⇒ [tex]\frac{3+9}{2}\ hours[/tex]
⇒ [tex]\frac{12}{2}\ hours[/tex]
⇒ [tex]6\ hours[/tex]
At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. In how many ways a voter can vote?
Answer:
Voters can select their members in 10possible ways
Step-by-step explanation:
According to the question, the voters are to elect 3members out of 5 candidates, this means they are to select any 3 candidates of their choice from a pool of 5 candidates. Since "combination" has to do with selection, we use the combination formula.
To select 'r' objects from 'n' pool of objects, we have;
nCr = n!/(n-r)!r!
5C3 = 5!/(5-3)!3!
5C3 = 5!/2!3!
5C3 = 5×4×3×2×1/2×3×2
= 120/12
5C3 = 10
Candidates can therefore vote in 10 possible ways
Solve the system of linear equations and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express x, y, and z in terms of the parameter
a) x + 2y − 7z = −8
b) 2x + y + z = 23
c) 3x + 9 y − 36 z = −63
Answer:No Solution
Step-by-step explanation: the explanation can be found in the attached picture
The given system of linear equations does not have a unique solution, as one equation is a multiple of another. Therefore, this is a dependent system and the solution can be expressed in terms of a parameter satisfying all equations.
Explanation:In order to solve a system of linear equations, one can use a variety of methods such as substitution, elimination, or matrix method. Let's use the elimination method here. The given system of equations is:
a) x + 2y - 7z = -8, b) 2x + y + z = 23 and c) 3x + 9y - 36z = -63. It is seen that equation c) is simply 3 times equation a), hence these equations are dependent and will not provide any unique solution. The system of equations is therefore dependent and does not have a unique solution. It can be expressed in terms of a parameter which will satisfy all given equations. The solution cannot be expressed in terms of x, y and z.
Learn more about System of Linear Equations here:
https://brainly.com/question/20379472
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If the three angles of a triangle have equal measures, find that measure. The measure of each angle is degrees.
Step-by-step explanation:
the sum of angles in a triangle is 180°. so if a triangle is equivalent, each degree will be 180/3 = 60°
Malcom coasted 32 miles from Moonridge to to Mentine and then pedaled back hard. If the round trip took 4 hours, what was Malcombs average speed in mph
Answer:
16 mph
Step-by-step explanation:
The relationship between distance, speed, and time is ...
speed = distance/time . . . . . "miles per hour"
Malcom's distance was 32 miles each way, for a total of 64 miles. Then his average speed was ...
speed = (64 mi)/(4 h) = 16 mi/h
Suppose that a chemist is mixing two acid solutions, one of 20% concentration and the other of 30% concentration. Which of the following concentrations could not be obtained?
1. 22%,
2. 24%,
3. 28%,
4. 34%
Final answer:
A chemist cannot achieve a 34% concentration by mixing 20% and 30% acid solutions, as it is outside the possible range of concentrations achievable by combining these two solutions, option no 4.
Explanation:
When a chemist is mixing two acid solutions, one with a 20% concentration and the other with a 30% concentration, they can obtain a range of concentrations between the two provided percentages by varying the proportions of each solution mixed. The concentrations that could not be obtained would be any value outside of the 20% to 30% range because the resulting mixture cannot exceed the concentration of the higher concentrated solution or be lower than the concentration of the less concentrated solution. Therefore, a 34% concentration could not be obtained by mixing a 20% solution with a 30% concentration.
Maria made one dozen cookies.She gave six cookies to her teacher and three to her friend.Which fraction is equivalent to the amount of cookies Mari gave away
Answer:
3/4
Step-by-step explanation:
1 question 60 points need help now
Solve the equation and show all your work
[tex]\frac{x}{x-2} + \frac{x-1}{x+1} =-1[/tex]
Answer:
The answer to your question is x = 0 and x = 1
Step-by-step explanation:
Equation
[tex]\frac{x}{x - 2} + \frac{x - 1}{x + 1} = -1[/tex]
1)
[tex]\frac{x(x + 1) + (x - 2)(x - 1)}{(x - 2)(x + 1)} = - 1[/tex]
Expand
2) x² + x + x² - x - 2x + 2 = -1(x - 2)(x + 1)
Simplify
3) 2x² -2x + 2 = -1(x² + x - 2x - 2)
4) 2x² - 2x + 2 = -x² + x + 2
Equal to zero
5) 2x² - 2x + 2 + x² - x - 2 = 0
6) 3x² - 3x = 0
Factor
7) 3x(x - 1) = 0
8) 3x₁ = 0 x₂ - 1 = 0
9) x₁ = 0/3 x₂ = 1
10) x₁ = 0 x₂ = 1
A typical marathon has 26.2 miles. allan makes an average of 12 kilometers per hour when running marathons. Determine how long it would take allan to complete a marathon at the nearest tenth of an hour.
Answer:
3hr 31mins
Step-by-step explanation:
First we convert miles to kilometers
1 miles to km = 1.60934 km
26.2 miles = 26.2 x 1.60934 = 42.164708
A typical marathon approx = 42.165km
If our runner covers 12 km = 1 hr
then he'll cover 42.165km = 42.165/12 = 3.5137 hrs
= 3 hrs + (0.514 * 60 mins) = 3hrs + (30.84mins)
Allan going at that speed would complete the marathon in appox = 3hrs : 31mins.
Answer:
2.34m2
Step-by-step explanation:
boom
Jeff wants to know how many miles it is from his house to school. On a map, the scale is 0.5 inches=2 miles. If his house island school are 3 inches apart on the map, how many miles is it to the school?
It is 12 miles from house to school
Solution:
Given that, Jeff wants to know how many miles it is from his house to school
On a map, the scale is 0.5 inches = 2 miles
His house island school are 3 inches apart on the map
So, from the given scale,
0.5 inches = 2 miles
Distance between school and house in map = 3 inches
Therefore,
0.5 inches = 2 miles
Muliply both sides by 6
[tex]0.5 \times 6\ inches = 6 \times 2\ miles\\\\3\ inches = 12\ miles[/tex]
Thus, it is 12 miles from house to school
Malcolm has been watching a roulette-style game at a local charity bazaar. The game has only ten numbers on the wheel, and every number except 8 has come up as a winner during the last 15 minutes. Malcolm decides to bet $10 on number 8, because it eventually has to come up. In this case, Malcolm is showing evidence of…
Answer:
Malcolm is showing evidence of gambler's fallacy.
This is the tendency to think previous results can affect future performance of an event that is fundamentally random.
Step-by-step explanation:
Since each round of the roulette-style game is independent of each other. The probability that 8 will come up at any time remains the same, equal to the probability of each number from 1 to 10 coming up. That it has not come up in the last 15 minutes does not increase or decrease the probability that it would come up afterwards.
Out of 290 racers who started the marathon, 259 completed the race, 27 gave up, and 4 were disqualified. What percentage did not complete the marathon? Round your answer to the nearest tenth of a percent.
Answer:11.38
Step-by-step explanation:
290-257=33 /290=.11379 x 100=11.37 =11.38
Final answer:
To find the percentage of racers who did not complete the marathon, we add those who gave up and those who were disqualified, a total of 31 racers. The percentage is then calculated using the formula for percentage, resulting in 10.7% of racers not completing the marathon.
Explanation:
To find the percentage of racers who did not complete the marathon, we first need to determine the total number of racers who did not finish. This includes those who gave up and those who were disqualified. In this case, 27 racers gave up, and 4 were disqualified, giving us a total of 31 racers who did not complete the marathon.
To calculate the percentage, we use the formula:
Percentage = (Number of racers who did not complete / Total number of racers) × 100%
Plugging the numbers into the formula gives us:
Percentage = (31 / 290) × 100% = 0.1069 × 100% = 10.69%
Rounding to the nearest tenth of a percent, 10.7% of racers did not complete the marathon.
A scatter plot shows a set of data points that are clustered close to a line that slopes down to the right. Which of the following values would be closest to the correlation for these data? a. -0.40 b. 0.40 c. 0.80 d. -0.80
Answer:
Option D. -0.80
Step-by-step explanation:
A scatter plot that shows a set of data points having two properties
1). If the points are clustered close to the line that reveals the high correlation.
2). Data points are clustered close to the line having slope down to the right or negative slope.
Therefore, Option D. has the highest correlation with negative slope.
The actual volumes of soda in quart-sized bottles can be described by a Normal model with a mean of 32.3 fluid ounces and a standard deviation of 1.2 fluid ounces. What percentage of bottles can we expect to have a volume of less than 32 fluid ounces?
Answer:The percentage of bottles expected to have a volume less than 32 or is 40.13%
Step-by-step explanation: The volumes of soda in quart soda bottles can be represented by a Nomal model with a= 32.3 oz
b=1.2 oz
Let S be the volume of randomly selected soda bottles
Y-score: S-a/b
For S=32 oz
Substitute the values of S,a and b into the equation
Y=32-32.3/1.2
Y=-0.25
Probability of bottles that have a volume less than 32 oz is
P(S<32)=P(Y<-025)= 0.40129
Percentage of bottles that have volume less than 32 oz will be
0.40127×100%=40.13%
Mrs. Hall went to work for the shirt factory on May 23, 1885. She earned nineteen cents per hour. If she worked thirteen hours per day, how much money would she earn in a week (six days)
Answer:
She would earn in a week (six days) 1482 cents.
Step-by-step explanation:
Given:
Mrs. Hall went to work for the shirt factory.
She earned nineteen cents per hour.
She worked thirteen hours per day.
Now, to find the money she earn in a week (six days).
Money she earned per hour = 19 cents.
As she she worked 13 hours per day.
So, money she earned per day = [tex]19\times 13=247.[/tex]
Now, to get the total money she earned in a week (six days) we multiply 6 by money earned in per day:
[tex]6\times 247[/tex]
[tex]=1482\ cents.[/tex]
Therefore, she would earn in a week (six days) 1482 cents.
. The weights of the fish in a certain lake are normally distributed with a mean of 19 lb and a standard deviation of 6. If 4 fish are randomly selected, what is the probability that the mean weight will be between 16.6 and 22.6 lb?
Answer:
[tex]P(16.6 < \bar X < 22.6) = P(\frac{16.6-19}{3} <Z< \frac{22.6-19}{3})= P(-0.8 < Z < 1.2)[/tex]
[tex]P(16.6 < \bar X < 22.6) =P(-0.8<Z<1.2) = P(Z<1.2)-P(Z<-0.8) = 0.88493- 0.211855= 0.673[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(19,6)[/tex]
Where [tex]\mu=19[/tex] and [tex]\sigma=6[/tex]
And we select n =4 fish. For this case we want to find this probability:
[tex] P(16.6 < \bar x < 22.6) [/tex]
And since the distribution for X is normal then the distribution for the sample mean is also normal and given by:
[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}}=3)[/tex]
And the z score is given by:
[tex]z = \frac{\bar x -\mu}{\sigma_{\bar x}}[/tex]
And if we apply this formula we got:
[tex]P(16.6 < \bar X < 22.6) = P(\frac{16.6-19}{3} <Z< \frac{22.6-19}{3})= P(-0.8 < Z < 1.2)[/tex]
And we can find this probability with this operation using the normal standard table or excel:
[tex] =P(-0.8<Z<1.2) = P(Z<1.2)-P(Z<-0.8) = 0.88493- 0.211855= 0.673[/tex]
To find the probability that the mean weight of four randomly selected fish will be between 16.6 and 22.6 pounds, we can use the Central Limit Theorem. The probability is 0.7556.
Explanation:To find the probability that the mean weight of four randomly selected fish will be between 16.6 and 22.6 pounds, we can use the Central Limit Theorem. The Central Limit Theorem states that if we take multiple samples from a population with any distribution, the distribution of the sample means will approach a normal distribution. In this case, we have a normally distributed population with a mean of 19 pounds and a standard deviation of 6 pounds.
To calculate the probability, we need to standardize the range of weights using the formula for the standard error of the mean:
Standard error of the mean (SE) = Standard deviation / sqrt(sample size)
We will use the formula:
Z = (X - mean) / SE
Where X is the upper and lower bounds of the range, mean is the population mean, and SE is the standard error of the mean.
First, let's calculate the standard error of the mean:
SE = 6 / sqrt(4) = 3
Then, we can calculate the z-scores for the upper and lower bounds:
Z_upper = (22.6 - 19) / 3 = 1.2
Z_lower = (16.6 - 19) / 3 = -1.1333
Since the z-scores are in standard deviation units, we can look up the corresponding probabilities in the standard normal distribution table:
P(16.6 < X < 22.6) = P(-1.1333 < Z < 1.2)
Using the table, we can find the probabilities:
P(Z < -1.1333) = 0.1293
P(Z < 1.2) = 0.8849
Finally, we can calculate the probability between the two bounds:
P(16.6 < X < 22.6) = P(Z < 1.2) - P(Z < -1.1333) = 0.8849 - 0.1293 = 0.7556
Learn more about Probability here:https://brainly.com/question/32117953
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Identify the transformation from ABCD to A'B'C'D'. a. Reflection across the X-axis b. Translation c. Reflection across the y-axis d. 90° counter clockwise rotation
The transformation type may be identified by understanding each option: reflection would flip the figure across an axis, translation would slide it, and a 90° counter-clockwise rotation would pivot it around the origin. The right choice depends on the specific positioning of ABCD and A'B'C'D'.
Explanation:The student's question revolves around identifying the type of transformation that maps quadrilateral ABCD to A'B'C'D'. Without the specific coordinates or a visual representation it's difficult to provide the exact transformation.
However, the choices given are reflections across the X-axis or the Y-axis, translation, or a 90° counter-clockwise rotation.
Reflecting across the X-axis would mean to move every point of ABCD to the opposite side vertically, while the Y-axis reflection would be a horizontal flip. A translation involves sliding the figure in any direction without altering its orientation or shape.
But, the 90° counter-clockwise rotation is a pivot of every point at a 90-degree angle around the origin in the counter-clockwise direction, which appears to be the action described in the subsequent figures and discussion of the merry-go-round example.
The three types of descriptions involving the positive x direction, vertically upward, and horizontally to the right side can be related to the translation movement in the coordinate system.
PLEASE
it will mean a lot and it would help me extremely!!!!
Answer:
The answer to your question is below
Step-by-step explanation:
Data
∠1 = 105°
Process
a)
∠2 = 180 - 105 = 75° supplementary angles
∠3 = ∠2 = 75° supplementary angles
∠4 = 105° vertical angles
∠5 = 105° corresponding angles
∠6 = 180 - 105 = 75° alternate interior angles
∠7 = ∠6 = 75° supplementary angles
∠8 = 105° alternate interior angles
b)
∠3 = 80°
∠1 = 180 - 80 = 100° supplementary angles
∠2 = 80° vertical angles
∠4 = 100° supplementary angles
∠5 = 100° supplementary angles
∠6 = 80° alternate interior angles
∠7 = 80° corresponding angles
∠8 = 100° supplementary angles
Pablo wishes to grow his baseball card collection to at least 3000 cards. He currently has 1200 and his favorite type of cards have 15 cards per package which inequality and solution represent the number of packages of cards that pablo wishes to buy , select all that apply
Answer:
x ≥ 120
Step-by-step explanation:
i) Let x be the number of packages of cards
ii) we know that Pablo currently has 1200 cards.
iii) Therefore the equation required is
15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards
iv) Solving the equation we get
15x + 1200 ≥ 3000
⇒ 15x ≥ (3000 - 1200)
⇒ 15x ≥ 1800
⇒ x ≥ (1800 ÷ 15)
∴ x ≥ 120
answer
x ≥ 120
Step-by-step explanation:
Step-by-step explanation:
i) Let x be the number of packages of cards
ii) we know that Pablo currently has 1200 cards.
iii) Therefore the equation required is
15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards
iv) Solving the equation we get
15x + 1200 ≥ 3000
⇒ 15x ≥ (3000 - 1200)
⇒ 15x ≥ 1800
⇒ x ≥ (1800 ÷ 15)
∴ x ≥ 120