Answer:
one property of log is that if the log expressions have the same base (in this case, 2), then you can multiply the added logs.
The answer would then be D
A small manufacturing company recently instituted Six Sigma training for its employees. Two methods of training were offered: online and traditional classroom. Management was interested in whether the division in which employees worked affected their choice of method. Below is a table summarizing the data.
Sales Quality Operations Total
Traditional 16 10 8 34
Online 35 23 44 102
Total 51 33 52 136
Required:
a. What is the probability that an employee chose online training?
b. What is the probability that an employee is in the Quality division and chose online training?
c. What is the probability that an employee chose online training given that he/she is in the Sales division?
Answer:
(a) [tex]P(Online\ Training) = 0.750[/tex]
(b) [tex]Pr = 0.169[/tex] --- Quality Division and Online Training
(c) [tex]P(A\ |\ B) = 0.686[/tex] --- Online Training given Sales Division
Step-by-step explanation:
Given
The two-way table
Solving (a): P(Online Training)
The total employee is:
[tex]Total = 136[/tex]
The employees for online training is:
[tex]Online\ Training = 102[/tex]
So, the probability is:
[tex]P(Online\ Training) = \frac{102}{136}[/tex]
[tex]P(Online\ Training) = 0.750[/tex]
Solving (b): P(Quality Division and Online Training)
The number of employees that choose quality Division and online training is 23
So, the probability is:
[tex]Pr = \frac{23}{136}[/tex]
[tex]Pr = 0.169[/tex]
Solving (c): P(Online Training | Sales Division)
This is calculated as:
Let:
[tex]A \to[/tex] Online training
[tex]B \to[/tex] Sales division
So, we have:
[tex]P(A\ |\ B) = \frac{n(A\ n\ B)}{n(B)}[/tex]
From the table:
[tex]n(A\ n\ B) =35[/tex]
[tex]n(B) = 16 + 35 = 51[/tex]
So, the probability is:
[tex]P(A\ |\ B) = \frac{35}{51}[/tex]
[tex]P(A\ |\ B) = 0.686[/tex]
A ladder is leaning against a building so that the distance from the ground to the top of the latter is 1 foot less than the length of the latter find the length of the latter is the distance from the bottom of the ladder to the building is 7 feet
Answer:
[tex]25\text{ feet}[/tex]
Step-by-step explanation:
The ladder, ground, and building form a right triangle where the vertical distance between the top of the ladder and the bottom of the ground is one leg, the horizontal distance between the bottom of the ladder and the building is another leg, and the length of the ladder is the hypotenuse.
For any right triangle, the Pythagorean Theorem states that the sum of the squares of both legs is equal to the hypotenuse squared ([tex]a^2+b^2=c^2[/tex]), where [tex]c[/tex] is the hypotenuse.
Let the length of the ladder be [tex]\ell[/tex] (hypotenuse of right triangle). The distance between the top of the ladder and the ground (vertical distance) can be represented as [tex]\ell -1[/tex].
From the Pythagorean Theorem, we then have:
[tex]7^2+(\ell-1)^2=\ell^2[/tex]
Expand using [tex](a-b)^2=a^2-2ab+b^2[/tex]:
[tex]49+\ell^2-2\ell+1=\ell^2[/tex]
Subtract [tex]\ell[/tex] from both sides and add [tex]2\ell[/tex] to both sides:
[tex]49+1=2\ell[/tex]
Combine like terms:
[tex]50=2\ell, \\2\ell =50[/tex]
Divide both sides by 2:
[tex]\ell=\frac{50}{2}=\boxed{25\text{ feet}}[/tex]
Therefore, the length of the ladder is 25 feet.
A golf ball is hit from ground level. Its path is modelled by the relation h(t) = -4.9 t2 + 27.2t , where h is the ball’s height above the ground, in meters, and t is the time, in seconds. Determine the time the ball is in the air.
I am need help and an explanation on how to read these graphs.
Answer:
i think its b
Step-by-step explanation:
The store employee works 35 hours per week. Which inequality can be used to find the dollar value, x, of weekly sales that the employee must make to earn more than $400 per week?
a baceball team won 11 on its first 18 games at this rate how many games will the team win in a 162 game season
Answer:
Step-by-step explanation:
Set up the following proportion. x is the number of games you should win.
11/18 = x / 162
11*162 / 18 = x
x = 99 You likely would be out of the playoffs with a number like this.
In sunlight, a vertical yardstick casts a 1 ft shadow at the same time that a nearby tree casts a 15 ft shadow. How tall is the tree? (Make a sketch to help solve the problem. Hint: 3ft equals one yard.)
A) 45 ft
B) 50 ft
C) 44 ft
D) 48 ft
Answer: A) 45 ft
Step-by-step
The yardstick is 3ft tall since 1 yard = 3ft. It is 3 times as tall as its shadow. The tree has a 15ft long shadow. The tree should also be 3 times as tall as its shadow. The tree is 15*3ft tall, so it is 45ft tall. I attached an image of the diagram I made.
Given C(4, 3) and D(-4, -3) are two points on a circle, centered at the origin. Given
that CD is a diameter of the circle?
a) Find the radius of the circle.
b) State the equation of the circle
If there is a song that is 2 minutes and 58 seconds long and it plays 40 times how long does it play convert answer into seconds.
Answer: I got 7120 seconds
Step-by-step explanation:
There's 178 seconds in the song (for more context, I just converted the 2 minutes into seconds and added it with 58) then I multiplied it by the total amount of times it played (in this case, 40)
Hope this helps
A ship sailed 30 kilometers in 1 1/2 hours. What is was its rate in kilometers per hour?
1) 20
2)30
3)45
4)90
5)Not enough information is given.
Answer:
20km/hr
Step-by-step explanation:
Given that a ship sailed 30km in one and a half hours. We need to find out the rate of ship in kilometres/hour . The rate is also called Speed.
Speed:- Distance travelled per unit time is called Speed .
Here , according to Question,
Distance = 30 km
Time = 1½ hrs .
We know that ,
[tex]\rm\implies Distance = Speed \times Time [/tex]
Subsequently ,
[tex]\rm\implies Time = \dfrac{Distance}{Time} [/tex]
Substitute the respective values ,
[tex]\rm\implies Rate =\dfrac{ 30km}{ 1.5 hrs } [/tex]
We can write 1.5 as 3/2 , therefore ,
[tex]\rm\implies Rate = \dfrac{ 2\times 30}{3} km/hr[/tex]
Simplify the RHS ,
[tex]\rm\implies\boxed{\blue{\rm Rate = 20\ km/hr}} [/tex]
Hence the Rate/Speed of the ship is 20km/hr .
in the given figure poq is a line. if x=30 then find qor and ros
Answer:
[tex]2y + 3y + x = 180 \\ 5y + 30 = 180 \\ 5y = 180 - 30 \\ 5y = 150 \\ y = 30[/tex]
QOR =3Y
=3×30
=90°
ROS = 2Y
=2×30
=60°
help I was never taught how to do this im confused
Answer:
36
Step-by-step explanation:
Area of a triangle = (bh)/2
Where b = base length and h = height
Given base length: 18ft
Given height: 4ft
This being known let's define the variables
b = 18
h = 4
Now to find the area we simply plug in these values into the formula
Area = (18)(4)/2
Simplify multiplication 18 * 4 = 72
Area = 72/2
Simplify division
Area = 36
¿COMO PUTAS SE HACE i¹⁰⁰²?
Answer:
nose
Step-by-step explanation:
The ________ and variance are derived from a subset of the population data and are used to make inferences about the population.
a. population standard deviation.
b. population variance.
c. population mean.
d. sample mean.
Answer:
the answer is option A population standard deviation
The temperature on a cold winter day starts out at 10 degrees, but it drops rapidly 24 degrees due to a strong cold front moving in. What is the current temperature?
Plz help me find zero x on the triangle and show work thanks
Answer:
x= 30 degrees
Step-by-step explanation:
This is an isosceles triangle as indicates by the lines on the sides.
Since the sides lengths are equal, the base angles are equal
x= 30 degrees
Which set of angles listed are supplementary
Answer:
A. <BED and <DEA, <AEC and <BEC
Step-by-step explanation:
Supplementary angles add up to give 180°.
m<BED = 90°
m<DEA = 90°
m<BED + m<DEA = 180°
Therefore, <BED and <DEA are supplementary.
m<AEC = 90°
m<BEC = 90°
m<AEC + m<BEC = 180°
Therefore, <AEC and <BEC are supplementary.
An integer is 18 more than 4 times another. If the product of the two integers is -18, then find the integers.
Answer:
Step-by-step explanation:
x = 4y+18
xy = -18
x = -18/y
-18/y = 4y+18
4y² + 18y + 18 = 0
2y² + 9y + 9 = 0
y = [-9 ±√(9²-4(2)(9))]/[2(2)] = [-9 ± 3]/4 = -1.5, -3
-1.5 is an extraneous solution, so y = -3
x = 6
Sixty out of every 100 pieces of candy is red. Which Indicates the
proportion of red candies? 60
60/100
60/40
40/100
Answer:
60/100
Step-by-step explanation:
Hope it helps you in your learning process
A woodworker makes wooden checkerboards. her profit is a function of the price she charges. this graph shows her total profits, y, based on the sales price, x, of each checkerboard.
identify any zeros of the function, and interpret what the zeros mean in terms of the situation.
Answer:
Option B.
Step-by-step explanation:
Remember that the profit is defined as the difference between the revenue and the cost.
So, having a profit y = 0 means that the woodworker did not win nor lose anything.
Then the zeros of the function, the values of x such that the graph intersects the x-axis, are the prices such that she does not win nor loss anything.
In the graph we can see that the zeros are at:
x = 15 (the first one)
x = 70 (the second one)
so the zeros are at x = 15 and x = 70, and these are the prices such that the profit is zero, so at these prices she does not make nor lose money.
The correct option is B.
Answer:
x = 15 and x = 70, and these are the prices such that the profit is zero, so at these prices she does not make nor lose money.
Step-by-step explanation:
what’s 9-3 2/5? because i can’t find it
Answer:
Step-by-step explanation:
(9-3)(2/5) = 6(2/5) = 12/5 = 2 2/5
9-32/5 = 2.6
Determine whether the three points are colinear (0,-4),(-3,-18),(2,6) are the three points colinear?
9514 1404 393
Answer:
they are not collinear
Step-by-step explanation:
A graph shows that a line through points A and C misses point B, so the points are not collinear.
__
If the points are collinear, then the slope of the segment between the first pair would be the same as the slope of the segment between the second pair.
m = (y2 -y1)/(x2 -x1)
m = (-18 -(-4))/(-3 -0) = -14/-3 = 14/3 . . . . slope of AB
__
m = (6 -(-18))/(2 -(-3)) = 24/5 . . . . slope of BC ≠ slope of AB
The points are not collinear.
_____
Additional comment
With about the same amount of computational effort, you can find the area of the triangle bounded by the three points. If it is zero, then the points are collinear. Here, it is 1 square unit, so the points are not collinear.
Write a linear equation in point slope form that passes through the points (-2,18) and (1,9)
Answer:
y-18=-3(x+2)
Step-by-step explanation:
The Slope-intercept form is -3x+12
A high school baseball player has a 0.305 batting average. In one game, he gets 9 at bats. What is the probability he will get at least 7 hits in the game
The probability that the player will get at least 7 hits in the game is approximately 0.192, or 19.2%.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
To solve this problem, we need to use the binomial distribution formula. The binomial distribution is used when we have a fixed number of independent trials (in this case, 9 at bats), where each trial has only two possible outcomes (hit or no hit), and the probability of success (getting a hit) is constant across all trials (0.305 in this case).
Let X be the number of hits the player gets in the game. Then X follows a binomial distribution with parameters n=9 (number of trials) and p=0.305 (probability of success).
The probability of getting at least 7 hits is equal to the sum of the probabilities of getting exactly 7, 8, or 9 hits:
P(X ≥ 7) = P(X=7) + P(X=8) + P(X=9)
Using the binomial probability formula:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
where C(n,k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.
For k=7:
P(X=7) = C(9,7) * 0.305^7 * (1-0.305)^(9-7) = 0.154
For k=8:
P(X=8) = C(9,8) * 0.305^8 * (1-0.305)^(9-8) = 0.036
For k=9:
P(X=9) = C(9,9) * 0.305^9 * (1-0.305)^(9-9) = 0.002
Therefore:
P(X ≥ 7) = 0.154 + 0.036 + 0.002 = 0.192
Therefore, the probability that the player will get at least 7 hits in the game is approximately 0.192, or 19.2%.
To learn more about Probability from given link.
https://brainly.com/question/30034780
#SPJ1
How can the distributive property be use to solve this expression?
53x24
9514 1404 393
Answer:
= 53(20 +4) or =24(50 +3) or =(20 +4)(50 +3)
Step-by-step explanation:
Either number can be rewritten as a sum. Typically, the sum will be based on place value: 53 = 50 + 3, for example, as opposed to something like 53 = 26 +27.
The usual method of multiplication taught in grade school makes use of this sort of rewriting.
53 × 24 = 53 × (4 +20) = 53×4 +53×20 = 212 +1060 = 1272
__
Additional comment
We find this easier to multiply as 53(20 +4) than as 24(50 +3) because doubling (multiplying by 2) and doubling again (multiplying by 4) is generally easier than multiplying by 3 or 5.
In grade school, we did this digit by digit, so ...
53×24 = (3 +50)(4 +20) = 3(4 +20) +50(4 +20) = 3×4 +3×20 +50×4 +50×20
= 12 +60 +200 +1000 = 1272
Which is equivalent to 104
༡/16**?
o (10)4x
4(10)3
o (10)**
O (10)
Answer:
I think it is the last one.
Apply radical rule
= (10^1/2)3/4x
Apply exponent rule: (a^b)^c = a^bc
= 10^1/2 . 3/4x
Simplify: 1/2 . 3/4x: 3x/8
= 10^3x/8
A professor has learned that nine students in her class of 35 will cheat on the exam. She decides to focus her attention on ten randomly chosen students during the exam. a. What is the probability that she finds at least one of the students cheating
Answer:
[tex]\frac{73,331}{75,516}\approx 97.11\%[/tex]
Step-by-step explanation:
The probability that she will find at least one student cheating is equal to the probability that she finds no students cheating subtracted from 1.
Each time she randomly chooses a student the probability she will catch a cheater is equal to the number of cheaters divided by the number of students.
Therefore, for the first student she chooses, there is a [tex]\frac{9}{35}[/tex] chance that the student chosen is a cheater and therefore a [tex]\frac{26}{35}[/tex] chance she does not catch a cheater. For the second student, there are only 34 students to choose from. If we stipulate that the first student chosen was not a cheater, then there is a [tex]\frac{9}{34}[/tex] chance she will catch a cheater and a [tex]\frac{25}{34}[/tex] chance she does not catch the cheater.
Therefore, the probability she does not catch a single cheater after randomly choosing ten students is equal to:
[tex]\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26}[/tex]
Subtract this from one to get the probability she finds at least one of the students cheating after randomly selecting nine students. Let event A occur when the professor finds at least one student cheating after randomly selecting ten students from a group of 35 students.
[tex]P(A)=1-\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26},\\\\P(A)=1-\frac{2,185}{75,516},\\\\P(A)=\boxed{\frac{73,331}{75,516}}\approx 0.97106573441\approx \boxed{97.11\%}[/tex]
If f(2) = 13 and f '(x) ≥ 2 for 2 ≤ x ≤ 7, how small can f(7) possibly be?
Answer:
23
Step-by-step explanation:
We are given that
f(2)=13
[tex]f'(x)\geq 2[/tex]
[tex]2\leq x\leq 7[/tex]
We have to find the possible small value of f(7).
We know that
[tex]f'(x)=\frac{f(b)-f(a)}{b-a}[/tex]
Using the formula
[tex]f'(x)=\frac{f(7)-f(2)}{7-2}[/tex]
[tex]f'(x)=\frac{f(7)-13}{5}[/tex]
We have
[tex]f'(x)\geq 2[/tex]
[tex]\frac{f(7)-13}{5}\geq 2[/tex]
[tex]f(7)-13\geq 2\times 5[/tex]
[tex]f(7)-13\geq 10[/tex]
[tex]f(7)\geq 10+13[/tex]
[tex]f(7)\geq 23[/tex]
The small value of f(7) can be 23.
g Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. In poker, a flush (5 in same suit) in any suit
Answer:
The answer is "[tex]1.54 \times 10^{-6}[/tex]".
Step-by-step explanation:
Calculating the probability of the cards that hand from a 52-card deck.
The aces are high or low in poker.
There are 13 cards in the bridge hand.
A royal flush (5 suit top cards) in poker.
There are 5 various poker hands with [tex]\binom{52}{5}[/tex].
There are four royal flushes, one in each suit.
[tex]P (royal\ flush) =\frac{4}{\binom{52}{5}}\\\\[/tex]
[tex]=\frac{4}{2598960}\approx 1.54 \times 10^{-6}[/tex]
Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23, 19, 26, 17, 21, 24, 22. a. Compute the mean and median number of apples in a bag. (Round your answers to 2 decimal places.)
Answer:
The mean and median number of apples in a bag are 21.71 and 22 respectively.
Step-by-step explanation:
The mean is the arithmetic mean of a set of numbers. In other words, the mean is the average value of all my data.
The mean is calculated by adding all the values and dividing the sum by the total number of values. In this case:
[tex]Mean=\frac{23+19+26+17+21+24+22}{7}[/tex]
[tex]Mean=\frac{152}{7}[/tex]
Mean= 21.71
The median of a set of numbers is the average number in the set, that is, it is the value that occupies the central place of all the values.
The median can be calculated by putting the numbers in ascending order and then:
if the quantity is numbers it is odd: the median is the number in the center of that distribution. if the number of numbers is even: the median is the mean of the two middle numbers.In this case:
Putting the numbers in ascending order: 17, 19, 21, 22, 23, 24, 26
Since the quantity is odd numbers, the median is the number in the center of that distribution. So Median= 22
The mean and median number of apples in a bag are 21.71 and 22 respectively.
