Step-by-step explanation:
A health inspector must visit 3 of 13 restaurants on Monday.
In how many way can she pick 3 restaurants = 13 C 4 !
nCr ! = [tex]\frac{n!}{r!(n-r)!}[/tex]
13 C 4! = [tex]\frac{13!}{3!(10)!}[/tex]
= [tex]\frac{11.12.13}{2.3}[/tex]
= 286
Health inspector can pick 3 restaurants of 13 restaurants on Monday in 286 ways
Final answer:
There are 286 different ways for a health inspector to pick 3 out of 13 restaurants to visit, calculated using the combination formula C(n, k) = n! / (k!(n - k)!).
Explanation:
The student asked how many different ways a health inspector could pick 3 out of 13 restaurants to visit on Monday. This is a problem of combinatorics, specifically concerning combinations without repetition since the order of choosing restaurants does not matter.
To calculate this, we use the combination formula, which is defined as:
C(n, k) = n! / (k!(n - k)!)
Where:
n is the total number of items to choose from (in this case, 13 restaurants)k is the number of items to choose (in this case, 3 restaurants)Applying the formula:
C(13, 3) = 13! / (3!(13 - 3)!) = 13! / (3! * 10!) = (13*12*11) / (3*2*1) = 286
So, the health inspector has 286 different ways to pick 3 restaurants from a list of 13.
what can 8 and 6 both go into equally
Findthe
y -intercept
oftheparabola
y = x2 − 2x .
Answer:
Step-by-step explanation:
kupa
645665465
Answer:
y=x(x-2)
Step-by-step explanation:
Suppose it is known that 10% of all people in Texas have a specific blood type. Suppose we take a random sample of 500 Texas residents. We want to find chance that fewer than 40 Texas residents in this sample have that blood type. In the next 4 questions, find the box model, the average and standard deviation of the box and use these values to find the expected value and standard error. Then calculate the associated chance of having fewer than 40 Texas residents in the sample with that specific blood type. Suppose you calculated EV and SE correctly in the previous two problems. The chance that fewer than 40 Texas residents in this sample have that blood type is the area under the normal curve to the:
Answer:
a) 50
b) 6.71
c) 0.0681
Step-by-step explanation:
check the attached file below
In a class of 7 students, there are 5 students who forget their lunch. If the teacher chooses 2 students, what will the probability that neither of them forget their lunch?
Answer:
4711
Step-by-step explanation:
Answer by rothauserc(4711) (Show Source):
You can put this solution on YOUR website!
the probability that the first student picked has a lunch is 6/9 or 2/3
the probability that the second student picked has a lunch is 5/8
QUICK!!! Use the information in the diagram to answer the questions.
100 percent is the 30 dollars wholesale price, 30 percent is the markup, and the retail price is unknown.
The original cost is .
The percent of the markup is .
The markup amount is .
The new price is .
Answer:
the original cost is $30 , the percent of the markup is 30% , the markup amount is $9 , the new price is $39.
Step-by-step explanation:
Answer:
$30,30%,9,39
Step-by-step explanation:
ik u hate edgunity good thing this is ur last day
National data indicates that 35% of households own a desktop computer. In a random sample of 570 households, 40% owned a desktop computer. Does this provide enough evidence to show a difference in the proportion of households that own a desktop? Identify the appropriate null and alternative hypotheses.
Answer:
Yes, this provide enough evidence to show a difference in the proportion of households that own a desktop.
Step-by-step explanation:
We are given that National data indicates that 35% of households own a desktop computer.
In a random sample of 570 households, 40% owned a desktop computer.
Let p = population proportion of households who own a desktop computer
SO, Null Hypothesis, [tex]H_0[/tex] : p = 25% {means that 35% of households own a desktop computer}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 25% {means that % of households who own a desktop computer is different from 35%}
The test statistics that will be used here is One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of 570 households who owned a desktop computer = 40%
n = sample of households = 570
So, test statistics = [tex]\frac{0.40-0.35}{{\sqrt{\frac{0.40(1-0.40)}{570} } } } }[/tex]
= 2.437
Since, in the question we are not given with the level of significance at which to test out hypothesis so we assume it to be 5%. Now at 5% significance level, the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics doesn't lies within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that % of households who own a desktop computer is different from 35%.
What is the missing angel in the triangle 69,34,
Answer:
77
Step-by-step explanation:
69+34=103
180-103=77
all triangles add up to 180
I hope this helps!
Answer:
The answer is 77
Step-by-step explanation: We know the angles add up to 180 in a triangle. so we simply do 69+34=103 then we do 180-103= 77
The area of a cross section at station 4+50 is 10.31 sq. in., and at station 5+00 is 14.18 sq. in. The horizontal scale of the cross section is 1" = 40’ and the vertical scale is 1" = 10’. What is the volume of earthwork between these two stations, in cubic yards, using the average end area method? Group of answer choices
A) 45
B) 18141
C) 9070
D) 907
Answer:
12233445555?????????
A group of five friends ate lunch at a restaurant the bill came to $42 And the friends agreed to spilt it equally. which expression represents the number of dollars each person paid?
Answer:
8.40
Step-by-step explanation:
42 divided by 5 equals 8.40 so each person would have to pay $8.40
Final answer:
The expression to represent the split cost of a $42 bill by five friends is 42 / 5, or $8.40 per person.
Explanation:
The expression representing the number of dollars each person paid when five friends split a $42 lunch bill equally would be $42 divided by 5. This can also be written as 42 / 5, which equals $8.40 per person.
For additional practice, let's look at a similar scenario: Mr. and Mrs. Green and their four children went out to dinner, and the meal cost was $72 with a restaurant-added tip of 18%. To find the total cost of the dinner, first calculate the tip amount by multiplying 18% (or 0.18) by the cost of the meal ($72). The tip would be $12.96. Adding this to the original cost, the total comes to $84.96.
What are the solutions of the quadratic equation 49x2 = 9? x = StartFraction 1 Over 9 EndFraction and x = StartFraction negative 1 Over 9 EndFraction x = StartFraction 3 Over 7 EndFraction and x = Start Fraction negative 3 Over 7 EndFraction x = StartFraction 3 Over 4 EndFraction and x = StartFraction negative 3 Over 4 EndFraction x = StartFraction Over 49 EndFraction and x = StartFraction negative 9 Over 49 EndFraction
The solution of the quadratic equation is x = ±3/7
How to solve quadratic equationsQuadratic equations are equations that have a leading degree of 2
Given the quadratic function
49x^2 = 9
Divide both sides by 49
49x^2/49 = 9/49
x^2 = 9/49
x = √9/49
x = ±3/7
Hence the solution of the quadratic equation is x = ±3/7
Learn more on quadratic equation here: https://brainly.com/question/1214333
Need help with this question
Answer:
[tex] \overline{AB} \cong \overline{DB} \:\: and \:\: \overline{AC} \cong \overline{DC}[/tex]
Step-by-step explanation:
[tex] \red{ \boxed{ \bold{\overline{AB} \cong \overline{DB} \:\: and \:\: \overline{AC} \cong \overline{DC}}} }\\ \overline{BC} \cong \overline{BC}... (common\: side) \\ [/tex]
What’s the answer to a^2b^2-100
Answer:
(ab - 10)(ab + 10)
Step-by-step explanation:
[tex] {a}^{2} {b}^{2} - 100 \\ = (ab) ^{2} - (10)^{2} \\ = (ab - 10)(ab + 10) \\ [/tex]
There is a red, a green, and a yellow bulletin board hanging in the hallway. All of the bulletin boards are rectangular with a height of 4 feet. Their lengths are 6 feet, 5 feet, and 3 feet. The red bulletin board has the largest area and the yellow one has the smallest area. What is the area of the green bulletin board
Answer:
it would be 5 feet
Step-by-step explanation:
Verify that the given two-parameter family of functions is the general solution of the nonhomogeneous differential equation on the indicated interval.
2x2y'' + 5xy' + y = x2 − x;
y = c1x−1/2 + c2x−1 + 1/15(x^2)-1/6(x), (0,infinity)
The functions (x^-1/2) and (x^-1) satisfy the differential equation and are linearly independent since W(x^-1/2, x^-1)= ____?____ for 0
The question is :
2x²y'' + 5xy' + y = x² - x;
y = c1x^(1/2) + c2x^(-1) + 1/15(x^2) - 1/6(x), (0,infinity)
The functions (x^-1/2) and (x^-1) satisfy the differential equation and are linearly independent since W(x^-1/2, x^-1)= ____?____ for 0
Answer:
The functions x^(-1/2) and x^(-1) are linearly independent since their wronskian is (-1/2)x^(-5/2) ≠ 0.
Step-by-step explanation:
Suppose the functions x^(-1/2) and x^(-1) satisfy the differential equation 2x²y'' + 5xy' + y = x² - x;
and are linearly independent, then their wronskian is not zero.
Wronskian of y1 and y2 is given as
W(y1, y2) = y1y2' - y1'y2
Let y1 = x^(-1/2)
y1' = (-1/2)x^(-3/2)
Let y2 = x^(-1)
y2' = -x^(-2)
W(y1, y2) =
x^(-1/2)(-x^(-2)) - (-1/2)x^(-3/2)x^(-1)
= -x^(-5/2) + (1/2)(x^(-5/2)
= (-1/2)x^(-5/2)
So, W(y1, y2) = (-1/2)x^(-5/2) ≠ 0
Which means the functions are linearly independent.
The functions [tex]\rm (x^\frac{-1}{2})[/tex] and [tex]\rm (x^{-1})[/tex] satisfy the differential equation and are linearly independent since [tex]W(x^{-1/2}, x^{-1})[/tex] = [tex](-x^{5/2} )+ \dfrac{1}{2}.(x^{5/2})[/tex] .
Given that,
The given two-parameter family of functions is the general solution of the non-homogeneous differential equation on the indicated interval.
[tex]\rm 2x^2y^n+5xy'+y = x^2-x[/tex]
[tex]\rm y = c_1x^{\frac{-1}{2} }+c_2{-x} \dfrac{1}{15}x^2=\dfrac{1}{5}x ,[/tex]
We have to determine,
The functions [tex]\rm (x^\frac{-1}{2})[/tex] and [tex]\rm (x^{-1})[/tex] satisfy the differential equation and are linearly independent since [tex]W(x^{-1/2}, x^{-1})[/tex] for 0?
According to the question,
The functions [tex]\rm (x^\frac{-1}{2})[/tex] and [tex]\rm (x^{-1})[/tex] satisfy the differential equation,
[tex]\rm 2x^2y^n+5xy'+y = x^2-x[/tex]
And are linearly independent, then their differentiation is not zero.
The differential equation is given by,
[tex]\rm Y(y_1, y_2) = y_1.y_2'- y_2.y_1'[/tex]
The value [tex]\rm y_1'[/tex] is,
[tex]\rm y_1 = x^{(-1/2})\\\\ y_1' = \dfrac{-1}{2} x^{(-3/2)}[/tex]
And value of [tex]\rm y_2'[/tex]
[tex]\rm y_2 = x^{(-1)}\\\\y_2' = -x^{(-2)}[/tex]
Therefore,
[tex]\rm Y(y_1, y_2) = (x^{-1/2}.(-x)^{-2}-(-\dfrac{1}{2}.x^{-3/2}).(x^{-1})\\\\\rm Y(y_1, y_2) = (-x^{5/2} )+ \dfrac{1}{2}.(x^{5/2})\neq 0\\\\[/tex]
Hence, The value of the function is not equal to zero then the function is linearly independent.
For more details refer to the link given below.
https://brainly.com/question/18510715
Four cups are placed upturned on the counter. each cup has the same number of sweets and a declaration about the number of sweets in it. The declaration are: Five or six, seven or eight, six or seven, seven or five. Only one of the declaration is correct. How many sweets are there under each cup?
Answer:
6? i hope this helps some! :)
Step-by-step explanation:
each has 6 in between the number
5 or 6 p there is a possibility of there being 6
7 or 8 there is at least 6 in this cup
6 or 7 there is at least 6 in this cup
7 or 5 there is a possibility of there being 6
Final answer:
There are either 7 or 5 sweets under each cup. The declaration 'Seven or five' is correct.
Explanation:
Each cup has a declaration about the number of sweets in it: 'Five or six', 'Seven or eight', 'Six or seven', and 'Seven or five'. Only one of the declarations is correct. To find the number of sweets under each cup, we need to analyze the given information.
If the declaration 'Five or six' is correct, then there can be 5 or 6 sweets under the cup. But since there are no other cups with 5 or 6 as a declaration, this declaration cannot be correct.
If the declaration 'Seven or eight' is correct, then there can be 7 or 8 sweets under the cup. But since there are no other cups with 7 or 8 as a declaration, this declaration cannot be correct.
If the declaration 'Six or seven' is correct, then there can be 6 or 7 sweets under the cup. But since there is another cup with the declaration 'Seven or five', and both declarations share the number 7, this declaration cannot be correct.
Therefore, the only remaining declaration 'Seven or five' must be correct. So, there are either 7 or 5 sweets under the cup with this declaration.
In conclusion, there are either 7 or 5 sweets under each cup, and the declaration 'Seven or five' is correct.
The time between consecutive eruptions of Mont Etna in Sicily is exponentially distributed denoted by random variable X, with the mean of ????[X] = 1/???? years. The exponential pdf fX(x) = ????e−????x for x ≥ 0, and zero elsewhere. Find the probability of the next eruption occurs before next 2 years, P(x < 2) =?
Answer:
0.9975
Step-by-step explanation:
check the attached files below
If d ran 12 meters in 6 second and c ran 15 meters in 5 seconds who ran faster or was it the same
Answer:
12/6 = 2 miles per second for d
15/5 = 3 miles per second for c
c runs faster because runs 3 miles every second while d only runs 2 miles per second
Step-by-step explanation:
Dalgliesh the detective fancies himself a shrewd judge of human nature. In careful tests, it has been discovered that he is right 80 percent of the time about whether a suspect is lying or telling the truth. Dalgliesh says that Jones is lying. The polygraph expert, who is right 100 percent of the time, says that 40 percent of the subjects interviewed by Dagliesh are telling the truth. What is the probability that Jones is lying?
Answer:
The probability that Jones is lying is 6/7
Step-by-step explanation:
First we will list out 2 different cases when the outcome is a lie
1.probability that Jones tells lies is = 0.6 and probability that dalgiliesh analyses it correctly is 0.8
So the probability that dagliesh correctly analyses that he is telling lies is 0.8*0.6=0.48
2.Probability that Jones tells truth is 0.4 and if dagliesh analyses it incorrectly (which has a probability of 0.2) the outcome(as analysed by dagiliesh) is a lie
So probability that dagliesh analyses Jones truth as a lie is 0.2*.0.4=0.08
Total probability of outcome being a lie is 0.48+0.08=0.56
But we need the probability of Jones actually saying a lie which is nothing but 0.48/0.56= 6/7
The probability of that Jones is lying is [tex]\frac{6}{7}[/tex] .
Probability is defined as, divide favourable outcomes by total outcomes.
First case:
Probability that Jones tells lies is = 0.6
Probability that Dalgliesh analyses it correctly is, = 0.8
Therefore, the probability that Dalgliesh correctly analyses that Jones is telling lies is,
[tex]P=0.8*0.6=0.48[/tex]
Second case :
Probability that Jones tells truth is, = 0.4
Probability of Dalgliesh analyses it incorrectly that Jones tells truth is,
= 0.2
So, Probability that Dalgliesh analyses Jones truth as a lie is,
[tex]0.2*.0.4=0.08[/tex]
Total probability of outcome being a lie is,
[tex]0.48+0.08=0.56[/tex]
Thus, Probability of Jones telling lie is, [tex]=\frac{0.48}{0.56} =\frac{6}{7}[/tex]
Learn more:
https://brainly.com/question/12594357
uppose a small cannonball weighing 16 pounds is shot vertically upward, with an initial velocity v0 = 290 ft/s. The answer to the question "How high does the cannonball go?" depends on whether we take air resistance into account. If air resistance is ignored and the positive direction is upward, then a model for the state of the cannonball is given by d2s/dt2 = −g (equation (12) of Section 1.3). Since ds/dt = v(t) the last differential equation is the same as dv/dt = −g, where we take g = 32 ft/s2. If air resistance is incorporated into the model, it stands to reason that the maximum height attained by the cannonball must be less than if air resistance is ignored. (a) Assume air resistance is proportional to instantaneous velocity. If the positive direction is upward, a model for the state of the cannonball is given by m dv dt = −mg − kv, where m is the mass of the cannonball and k > 0 is a constant of proportionality. Suppose k = 0.0025 and find the velocity v(t) of the cannonball at time t.
Solving for the velocity v(t) of a cannonball considering air resistance involves integrating the differential equation m dv/dt = -mg - kv, where k is a constant of proportionality. Given initial conditions, this allows one to calculate the cannonball's velocity at any time.
Explanation:A student has asked how to find the velocity v(t) of a cannonball, considering air resistance, modeled by m dv/dt = -mg - kv, where m is the mass of the cannonball, g is the acceleration due to gravity (32 ft/s2), and k is a constant of proportionality (0.0025). Given the initial velocity v0 = 290 ft/s, the solution involves solving this differential equation with the given initial condition.
However, solving this specific differential equation requires integration techniques that account for the linear dependence of the air resistance on the velocity, which will yield an expression for v(t) as a function of time t. This formula can then be used to calculate the velocity of the cannonball at any given time, illustrating how air resistance affects its ascent and eventual descent.
Dr. Potter provides vaccinations against polio and measles. Each polio vaccination consists of 4 doses and each measles vaccination consists of 2 doses. Last year Dr. potter gave a total of 60 vaccinations that consisted of a total of 184 doses. How many polio vaccinations did dr. potter give last year
Answer:
Dr. Potter gave 32 polio vaccinations and 28 measles vaccinations
Step-by-step explanation:
Total of 184 doses
Polio vaccination= 4 doses
Measles vaccination=2 doses
184=4p+2m
92=2p+m
Lets plug in 32+28
92=(2*32)+28
92=64+28
p=32, m=28
Suppose you have 18 objects (10 of type A, 5 of type B, and 3 of type C). Objects of type A are indistinguishable from each other; objects of type B are indistinguishable from each other; and objects of type C are indistinguishable from each other. In how many ways can you Pick 5 of the 18 objects (order does not matter)
Answer:
[tex] \binom{18}{5}= 8568[/tex]
Step-by-step explanation:
Note that we have in total 18 items. Even though we are given information regarding the amounts of items per type, the general question asks the total number of ways in which you can pick 5 out of the 18 objects, without any restriction on the type of chosen items. Therefore, the information regarding the type is unnecessary to solve the problem.
Recall that given n elements, the different ways of choosing k elements out of n is given by the binomial coefficient [tex]\binom{n}{k})[/tex].
Therefore, in this case the total number of ways is just [tex]\binom{18}{5}=8568[/tex]
Answer:
Given:
Number of objects: n = 18
Type A objects: 10
Type B objects: 5
Type C objects: 3
To find:
In how many ways can you Pick 5 of the 18 objects (order does not matter)
Step-by-step explanation:
When the order does not matter we use Combination.
Formula to calculate combination:
C(n,r) = n! / r! ( n - r )!
n = 18
r = 5
Putting the values:
C(n,r)
= C(18,5)
= 18! / 5! ( 18 - 5 )!
= 18! / 5! ( 13 )!
= ( 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 ) / ( 5 * 4 * 3 * 2 * 1 ) * (13 * 12 * 11 * 10 *9* 8 * 7 *6 * 5 * 4 * 3 * 2 *1 )
Cancel 13!
= (18 * 17 * 16 * 15 * 14 ) / ( 5 * 4 * 3 * 2 * 1 )
= 1028160 / 120
= 8568
So you can pick 5 of the 18 objects in 8568 ways.
Carrie has 3 gallon of paint. Bryan has 10 quarts of paint. How many more pints of paint does carrie have than Bryan
Answer:
4 pints
Step-by-step explanation:
There are 8 pints in one gallon, and 2 pints in one quart.
Carrie has 3 gallons of paint. 8*3 = 24 pints of paint.
Bryan has 10 quarts of paint. 10*2 = 20 pints of paint.
24 - 20 = 4. Carrie has 4 more pints of paint.
Answer:
Step-by-step explanation:
Use a special right triangle to express the cosine of 45 degree as a fraction and as a decimal to the nearest hundredth
The special triangle you need is a right isosceles triangle, with legs 1 and hypotenuse [tex]\sqrt{2}[/tex].
As for every right triangle, you can find of the cosine of an angle using the "adjacent/hypotenuse" ratio.
In this case, the two base angles are equal, and so are the two legs. So, it doesn't matter which angle or leg you'll choose, the ratio will be
[tex]\cos(45)=\dfrac{1}{\sqrt{2}}[/tex]
which indeed is both the sine and cosine of 45°
Its approximated value is 0.707...
The cosine of 45 degree as a fraction and as a decimal to the nearest hundredth are [tex]\( \frac{\sqrt{2}}{2} \)[/tex] and 0.71 respectively.
In a 45-45-90 triangle, which is a special right triangle, the sides are in the ratio [tex]\( 1:1:\sqrt{2} \).[/tex] This means if the legs (both shorter sides) are [tex]\( a \)[/tex], then the hypotenuse is [tex]\( \sqrt{2} \cdot a \).[/tex]
To find the cosine of [tex]\( 45^\circ \):[/tex]
The cosine of an angle in a right triangle is given by the ratio of the adjacent side to the hypotenuse. In a 45-45-90 triangle, each leg is adjacent to the 45° angle, and the hypotenuse is opposite the 90° angle.
Therefore, [tex]\( \cos(45^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{a}{\sqrt{2} \cdot a} \).[/tex]
Simplifying this gives:
[tex]\[ \cos(45^\circ) = \frac{a}{a\sqrt{2}} = \frac{1}{\sqrt{2}} \][/tex]
Rationalizing the denominator:
[tex]\[ \cos(45^\circ) = \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2} \][/tex]
Therefore, the cosine of [tex]\( 45^\circ \)[/tex] as a fraction is [tex]\( \frac{\sqrt{2}}{2} \).[/tex]
To find the decimal value of [tex]\( \frac{\sqrt{2}}{2} \):[/tex]
First, approximate [tex]\( \sqrt{2} \):[/tex]
[tex]\[ \sqrt{2} \approx 1.414 \][/tex]
Now, calculate [tex]\( \frac{1.414}{2} \):[/tex]
[tex]\[ \frac{1.414}{2} \approx 0.707 \][/tex]
Rounded to the nearest hundredth, the decimal form of [tex]\( \cos(45^\circ) \)[/tex] is 0.71.
The diagram of question is:
At a middle school, 30% of students buy lunch in the cafeteria and the remaining students bring lunch from home. A spinner with 10 equal-sized sections numbered 0-9 will be used to simulate the lunch trend. How can you design a simulation to guess whether the next 20 students buy lunch or bring lunch from home?
Allocating 3 portions to x and 7 portions to y.
Step-by-step explanation:
Given that,
The percentage of students buy lunch at cafeteria: 30% = x = 0.3
Hence, the students bringing the lunch from home would be = y = 1 - 0.3 = 0.7
Now, the spinner has that equal-sized sections. Also, the probability of x and y are 0.3 and 0.7.
After multiplying both the probability by 10, we get
x = 3
y = 7
It shows that for every three students who buy lunch from cafeteria, seven students bring food from home. Hence, we can allocate the side of spinner for simulation in such as way:
Section 0 = y
Section 1 = y
Section 2 = x
Section 3 = y
Section 4 = y
Section 5 = x
Section 6 = y
Section 7 = y
Section 8 = x
Section 9 = y
Keely is planning a bridal shower for her best friend. At the party, she wants to serve 4 beverages, 3 appetizers, and 4 desserts, but she does not have time to cook. She can choose from 11 bottled drinks, 10 frozen appetizers, and 8 prepared desserts at the supermarket. How many different ways can Keely pick the food and drinks to serve at the bridal shower?
Answer:
The different ways in which Keely can pick the food and drinks to serve at the bridal shower is 2,772,000.
Step-by-step explanation:
Combinations is a mathematical procedure to determine the number of ways to select k items from n different items, without replacement and irrespective of the order of selection.
The formula to compute the combination of k items from n items is:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
The menu for the bridal shower consists of:
Beverages: 4
Appetizers: 3
Dessert: 4
It is provided that Keely does not have time to cook. SO she goes to the supermarket and there she has the following options:
Beverages: 11
Appetizers: 10
Dessert: 8
Compute the number of ways Keely can select 4 beverages from 11 bottled drinks as follows:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
[tex]{11\choose 4}=\frac{11!}{4!(11-4)!}[/tex]
[tex]=\frac{11!}{4!\times 7!}[/tex]
[tex]=\frac{11\times 10\times 9\times 8\times 7!}{4!\times 7!}[/tex]
[tex]=330[/tex]
Keely can select 4 beverages in 330 ways.
Compute the number of ways Keely can select 3 appetizers from 10 frozen appetizers as follows:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
[tex]{10\choose 3}=\frac{10!}{3!(10-3)!}[/tex]
[tex]=\frac{10!}{3!\times 7!}[/tex]
[tex]=\frac{10\times 9\times 8\times 7!}{3!\times 7!}[/tex]
[tex]=120[/tex]
Keely can select 3 appetizers in 120 ways.
Compute the number of ways Keely can select 4 desserts from 8 prepared desserts as follows:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
[tex]{8\choose 4}=\frac{8!}{4!(8-4)!}[/tex]
[tex]=\frac{8!}{4!\times 4!}[/tex]
[tex]=\frac{8\times 7\times 6\times 5\times 4!}{4!\times 4!}[/tex]
[tex]=70[/tex]
Keely can select 4 desserts in 70 ways.
Compute the total number of ways in which Keely can select 4 beverages, 3 appetizers, and 4 desserts for the party as follows:
Total number of ways = n (4 beverages) × n (appetizers) × n (dessert)
[tex]={11\choose 4}\times {10\choose 3}\times {8\choose 4}[/tex]
[tex]=330\times 120\times 70\\=2772000[/tex]
Thus, the different ways in which Keely can pick the food and drinks to serve at the bridal shower is 2,772,000.
Suppose you are the CEO of a company that produces sheets of metal that are 1 centimeter thick. This metal is evaluated on the basis of its hardness which is determined by measuring the depth of penetration of a hardened point. Suppose that this depth of penetration is normally distributed with a mean of 1 millimeter and a standard deviation of .02 millimeters.
You are on trial for distributing faulty metal. If the metal is deemed faulty when the depth of penetration is more than 1.3 millimeters, what is the probability you are guilty?
Answer:
0% probability you are guilty
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 1, \sigma = 0.02[/tex]
If the metal is deemed faulty when the depth of penetration is more than 1.3 millimeters, what is the probability you are guilty?
This is 1 subtracted by the pvalue of Z when X = 1.3. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.3 - 1}{0.02}[/tex]
[tex]Z = 15[/tex]
[tex]Z = 15[/tex] has a pvalue of 1
1 - 1 = 0
0% probability you are guilty
We can use the z-score formula to calculate the probability of being guilty of distributing faulty metal based on the depth of penetration. The probability is practically zero.
Explanation:To find the probability that you are guilty of distributing faulty metal, we need to calculate the probability that the depth of penetration is more than 1.3 millimeters. Since the depth of penetration is normally distributed with a mean of 1 millimeter and a standard deviation of 0.02 millimeters, we can use the z-score formula to standardize the value. The z-score is calculated as (x - μ) / σ, where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
Substituting the values into the formula, we have z = (1.3 - 1) / 0.02 = 15. Therefore, we need to find the probability that the z-score is greater than 15. Using a standard normal distribution table or calculator, we find that this probability is practically zero. Hence, the probability that you are guilty is practically zero.
Learn more about Calculating probability based on z-scores here:https://brainly.com/question/40005132
#SPJ3
Dave rented a jet ski for $6 per hours plus $20 for insurance. How many hours did he use the jet ski if he spent a total of $68? solving equation applications equations and solution
Answer:
8 hours
Step-by-step explanation:
6x+20=68
subtract 20 from both sides
6x=48
divide 6 both sides
x=8
Answer:
Step-by-step explanation:
A list of five positive integers has a median of 3 and a mean of 11. What is the maximum possible value of the list's largest element? please
Answer:
47
Step-by-step explanation:
Since the 5 numbers have a mean of 11, the sum of the numbers is 5 X 11 = 55. To make the largest number as large as possible, we make the other numbers must be as small as possible. However, in order for the median to be 3, the middle number must be 3. Since this is the middle number, there must be two other numbers that are at least 3. So, we let three of the other four numbers be 1, 1, and 3 to make them as small as possible. Finally, this means the remaining number is 55 - 1 - 1 - 3 - 3= 47. Hope that helps!
Answer:
47
Step-by-step explanation:
In circle K with mLJKL = 112 and
JK = 7 units find area of sector JKL.
Round to the nearest hundredth.
Area of the sector JKL is 47.89 unit²
How the area of the sector is calculated
From the figure
Given that
JKL is a sector that subtends ∠JKL at the center of the circle JL.
The radius of the circle is KL or JK
Area of a sector = θ/360 * πr²
where
r is the radius
θ is angle subtended at the center
m∠JKL = 112⁰ = θ
JK = 7 units = radius
Therefore,
Area = 112/360*π(7)²
A = 112/360 * 3.142 * 49
= 17243.296/360
= 47.89 unit²
Therefore, area of the sector JKL is 47.89 unit²
A certain circle can be represented by the following equation. x2 + y2 + 10x + 12y + 25 = 0. What is the center of this circle? What is the radius of this circle? Please help!
Let's try to complete the squares.
The x-part starts with [tex]x^2+10x[/tex], which is the beginning of [tex]x^2+10x+25=(x+5)^2[/tex]. So, we'll think of [tex]x^2+10x[/tex] as [tex](x+5)^2-25[/tex]
Similarly, we have that
[tex]y^2+12y = (y+6)^2-36[/tex]
So, the equation becomes
[tex]x^2 + y^2 + 10x + 12y + 25 = 0 \iff (x+5)^2-25 + (y+6)^2-36+25=0 \iff (x+5)^2+ (y+6)^2-36=0 \iff (x+5)^2+ (y+6)^2=36[/tex]
Now we have writte the equation of the circle in the form
[tex](x-k)^2+(y-h)^2=r^2[/tex]
When the equation is in this form, everything is more simple: the center is [tex](k,h)[/tex] and the radius is [tex]r[/tex].
Answer:
Center// (-5,-6)
Radius// 6