The probability that 3 waiters, 4 waitresses, and 2 cooks will be selected is 0.085.
The probability that an outcome will be recorded is calculated by dividing the whole possibilities of the desired outcome by the total number of possible outcomes.
Probability = Favourable outcomes / Possible outcomes
The total number of staff in the restaurant is 25.
There are 8 waiters, 12 waitresses, and 5 cooks.
Now, on Mother's Day, a total of 9 people need to be selected.
The combination can be used to find the number number of ways people can be selected.
Therefore,
The number of ways to select 3 waiters, 4 waitresses, and 2 cooks will be:
= ₈C₃ × ₁₂C₄ × ₅C₂
= [ 8! / 3! 5! ] × [ 12! / 4! 8! ] × [ 5! / 2! 3! ]
= [ 8 × 7 × 6 / 3 × 2 ] × [ 12 × 11 × 10 × 9 / 4 × 3 × 2 ] × [ 5 × 4 / 2 ]
= 56 × 495 × 10
= 277200 ways
If there are no restrictions and these 9 people are chosen at random from the 25 available staff, then the number of ways is
₂₅C₁₀ = [ 25! / 10! 15! ]
₂₅C₁₀ = [ 25 × 24 × 23 × 22 × 21 × 20 × 19 × 18 × 17 × 16 / 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 ]
₂₅C₁₀ = 3268760
Therefore, the probability that 3 waiters, 4 waitresses, and 2 cooks will be selected is :
= 277200 / 3268760
= 0.08480279983 = 0.085
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The length, x (in inches), and weight, y (in ounces), for
a type of bass were measured for a random sample of
10 bass from a lake. These measurements were then
analyzed and the value for 2 was determined to be
96%.
Which of the following is the best interpretation of this
value?
4% of the variation in the bass's length is
determined by the variation in the bass's weight.
O 96% of the variation in the bass's weight is
determined by the variation in the bass's length.
96% of the variation in the bass's length is
determined by the variation in the bass's weight.
98% of the variation in the bass's weight is
determined by the variation in the bass's length.
Best interpretation of the value of 96% is that there is a strong positive linear relationship between the length and weight of the bass in the sample
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b
The value of 96% refers to a correlation coefficient, which measures the strength of the linear relationship between two variables. In this case, the two variables are length (x) and weight (y) of a type of bass. A correlation coefficient of 96% indicates a very strong positive correlation between the two variables, meaning that as the length of the bass increases, its weight tends to increase as well.
However, the value does not provide information about causality or which variable is influencing the other.
Therefore, none of the given interpretations are accurate. Instead, the best interpretation of the value of 96% is that there is a strong positive linear relationship between the length and weight of the bass in the sample, and further analysis may be needed to determine the direction and strength of causality between the two variables.
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Find the missing side of the triangle.A. √11 miB. 2√2 miC. 1 miD. √19 mi
Since we have a right-angled triangle, we can use the Pythagoras Theorem:
[tex]a^2+b^2=c^2[/tex]where a and b are the shorter sides of the triangle and c is the hypotenuse.
a = x; b = 3 mi; c = sqrt(10).
We substitute our values and then we solve for x:
[tex]\begin{gathered} x^2+3^2=(\sqrt[]{10})^2 \\ x^2=10-3^2 \\ x^2=1 \\ x=1 \end{gathered}[/tex]Therefore, the missing side of the triangle is 1 mi.
The United States is the worlds leading exporter of wheat with approximately 27.8 billion metric tons per year . Suppose turkey exports 10% of the U.S total . About how many metric tons are exported by turkey ?
Answer: 3 billion
Step-by-step explanation:
27.8 x 10% = 2.78 billion which rounds to 3
At 7 pm, the temperature outside was -5°C what does | - 5 | represent in this situation
means it's 5 degrees below zero
Solve and graph 3x+1<10
The given inequality is
3x + 1 < 10
Subtracting 1 from both sides of the inequality, we have
3x + 1 - 1 < 10 - 1
3x < 9
Dividing both sides of the equation by 3, we have
3x/3 < 9/3
x < 3
The number line is shown below
The values to the left of 3 are all less than 3. The circle is not shaded because 3 is not included in the values of x.
which expression represents the sum of 173and32,times by 5
EXPLANATION
The expression that represents the sum of 173 and 32 times by 5 is
(172+32)x5 [OPTION C]
1. How does someone find the equation of a boundary line?2. How does someone determine if the points on the boundary line are solutions to the inequality?
Answer:
D: Find the boundary line equation by replacing the inequality sign with =
Explanation:
Part 1
Given any inequality, say:
[tex]yTo find the equation of the boundary line, replace the inequality sign with the equality(=) sign. This gives the equation of the boundary line to the inequality above as:[tex]y=x+5[/tex]The correct choice is D.
Part 2
When drawing the boundary line:
• Use a solid line for the inequalities: ≤ or ≥
,• Use a broken line for the inequalities: < or >
If the boundary line is solid, the points on the boundary line are solutions to the inequality, otherwise, they are not.
Find the solution to the system of equations. You can use the interactive graph below to find the solution.-2x+2y=-43x+3y=-18x=___y=___
Answer:
• x=-2
,• y=-4
Explanation:
Given the system of equations:
[tex]\begin{gathered} -2x+2y=-4 \\ 3x+3y=-18 \end{gathered}[/tex]Solve for x and y using the graphical method.
The first step is to plot each of the lines using the x and y-intercepts.
First Equation (-2x+2y=-4)
When x=0
[tex]\begin{gathered} 2y=-4 \\ y=-2 \\ \implies(0,-2) \end{gathered}[/tex]When y=0
[tex]\begin{gathered} -2x=-4 \\ x=-\frac{4}{-2} \\ x=2 \\ \implies(2,0) \end{gathered}[/tex]Join the points (0,-2) and (2,0) as shown below:
Second Equation (3x+3y=-18)
When x=0
[tex]\begin{gathered} 3y=-18 \\ y=-6 \\ \implies(0,-6) \end{gathered}[/tex]When y=0
[tex]\begin{gathered} 3x=-18 \\ x=-\frac{18}{3} \\ x=-6 \\ \implies(-6,0) \end{gathered}[/tex]Join the points (0,-6) and (-6,0) on the same graph as shown below:
The solution to the system is the point where the two lines intersect.
The point is (-2,-4).
Therefore:
• x=-2
,• y=-4
,•
h(n) = -2n + 3g(n) = 4nFind (h•g)(-2)
Given:
h(n)=-2n+3
g(n)=4n
The objective is to find
[tex](h\cdot g)(-2)[/tex]Let's rewrite the required function as
[tex]\begin{gathered} (h\cdot g)=h\lbrack g(n)\rbrack \\ h\lbrack g(n)\rbrack=-2(4n)+3 \\ h\lbrack g(n)\rbrack=-8n+3 \\ (h\cdot g)(-2)=-8(-2)+3 \\ (h\cdot g)(-2)=16+3 \\ (h\cdot g)(-2)=19 \end{gathered}[/tex]Hence the value of (hog)(-2)=19
Prove the segments joining the midpoint if consecutive sides of an isosceles trapezoid form a rhombus.
DEFG is a rhombus by definition of rhombus (option B)
Explanation:
To prove that DEFG is a rhombus, we will find the distance between all the 4 sides of the quadrilateral. A rhombus has all 4 sides equal.
Distance formula is given as:
[tex]$$dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}$$[/tex][tex]\begin{gathered} distance\text{ DE: D}(-a-b,\text{ c})\text{ and E}(0,\text{ 2c}) \\ x_1=-a-b,y_1=c,x_2=0,y_2\text{ = 2c} \\ distance\text{ DE = }\sqrt{(0\text{ - }(-a-b))^2\text{ + }(2c\text{ - c})^2} \\ distance\text{ DE = }\sqrt{(0\text{ +}a+b)^2\text{ + c}^2}\text{ } \\ distance\text{ DE = }\sqrt{(\text{a + b})^2+c^2} \end{gathered}[/tex][tex]\begin{gathered} distance\text{ EF: E}(0,\text{ 2c})\text{ and F}(a\text{ + b, c}) \\ x_1=0,y_1=2c,x_2=a+b,y_2\text{ = c} \\ distance\text{ EF = }\sqrt{(c\text{ - 2c})^2+\text{ }(a\text{ + b - 0})^2} \\ distance\text{ EF = }\sqrt{(-c)^2+(a+b)^2}\text{ } \\ \text{distance EF = }\sqrt{c^2\text{ + }(a+b)^2} \end{gathered}[/tex][tex]\begin{gathered} distance\text{ GF: G}(0,\text{ 0})\text{ and F }(a+b,\text{ c}) \\ x_1=0,y_1=0,x_2=a+b,y_2\text{ = c} \\ distance\text{ GF = }\sqrt{(c\text{ - 0})^2+\left(a+b-0\right)^2} \\ distance\text{ GF = }\sqrt{c^2+(a+b)^2} \end{gathered}[/tex][tex]\begin{gathered} distance\text{ DG: D}(-a-b,\text{ c})\text{ and G }(0,\text{ 0}) \\ x_1=-a-b,y_1=c,x_2=0,y_2\text{ = 0} \\ distance\text{ GD = }\sqrt{(0-c)^2+(0-(-a-b))^2} \\ distance\text{ GD = }\sqrt{(-c)^2+\left(0+a+b\right)^2} \\ distance\text{ GD = }\sqrt{c^2\text{ + }(a+b)^2} \end{gathered}[/tex]From our calculation, Distance DE = Distance EF = Distance GF = Distance GD
All 4 sides are equal (congruent)
DEFG is a parallelogram with congruent sides. So DEFG is a rhombus by definition of rhombus (option B)
Which inequality symbol should be placed in the blank to make the statement true? - 12_ -8
Answer:
<
Step-by-step explanation:
Negative 12 is less than negative 8.
What are the coordinates of the focus of the parabola?y=18x2+2x
The equation of the given parabola is
[tex]y=\frac{1}{8}x^2_{}+2x[/tex]Rewrite the equation in the vertex form
[tex]y=a(x-h)^2+k[/tex]The equation becomes
[tex]\begin{gathered} y=\frac{1}{8}x^2+2x \\ y=\frac{1}{8}(x^2+16x) \\ 8y=x^2+16x \\ 8y=x^2+6x+64-64 \\ 8y=(x+8)^2-64 \end{gathered}[/tex]Divide through the equation by 8
This gives
[tex]y=\frac{1}{8}(x+8)^2-8[/tex]Comparing the equation with the vertex form
It follows
[tex]a=\frac{1}{8},h=-8,k=-8[/tex]The focus of a parabola in vertex form is given as
[tex]F=(h,k+\frac{1}{4a})[/tex]Substitute h = -8, k = -8 and a = 1/8 into the formula for focus
This gives
[tex]F=(-8,-8+\frac{1}{4(\frac{1}{8})})[/tex]Simplify the expression
[tex]\begin{gathered} F=(-8,-8+\frac{1}{\frac{1}{2}}) \\ F=(-8,-8+2) \\ F=(-8,-6) \end{gathered}[/tex]Therefore, the focus of the parabola is at (-8, -6)
r2/r12 A. r10B. 1/r6C.1/r10D. r8E. r6
this is
[tex]\frac{r^2}{r^{12}}=r^{2-12}=r^{-10}=\frac{1}{r^{10}}[/tex]answer: C
rewrite the sum in the form a(b+c) such that integers b and c have no common factor
The given format of the sum is
[tex]a(b+c)[/tex]The sum is,
24+16
The greatest common factor of 24 and 16 is 8, since,
[tex]\begin{gathered} 24=12\times2=3\times2\times2\times2 \\ 16=8\times2=4\times2\times2=2\times2\times2\times2 \end{gathered}[/tex]Therefore we can write, 24+16 as,
[tex]24+16\rightarrow8\times3+8\times2=8(3+2)[/tex]Describe how CPCTC would help you here. (8x-6) D T Students DE VOLTRON
CPCTP = Corresponding parts of congruent triangles are congruent:
That means that since both angles are congruent (equal) the sides are also congruent:
8x+6 = 3x+9
Solve for x
8x-3x = 9-6
5x= 3
x= 3/5
this is a practice assessment! Therefore it isn’t for a grade . I just need help solving this
We are given a quadrilateral inscribed in a circle, therefore, the sum of opposite angles is equal to 180 degrees, therefore:
[tex]\angle O+\angle M=180[/tex]Replacing the values we get:
[tex]100+x=180[/tex]Solving for "x":
[tex]\begin{gathered} x=180-100 \\ x=80 \end{gathered}[/tex]Therefore, the value of "x" is 80 degrees.
Stretch or compress each linear function. Let g(x) be a vertical stretch of f(x)=2x-2 by a factor of 5. Write the rule for g(x).
If g(x) = cf(x), then g(x) is a vertical stretch of f(x) by a factor of c. It means that the rule for g(x) is:
g(x) = 5*f(x)
Replacing f(x) by 2x - 2, we get:
g(x) = 5*(2x - 2)
g(x) = 5*2x - 5*2
g(x) = 10x - 10
Answer: g(x) = 10x - 10
Write the augmented matrix for the following system of equations.
9y-5+9z = 0
7x=-3y+7+z
5x + 7y = 5
The augmented matrix of the given equations is shown (Refer to the matrix attached below.)
What is an augmented matrix?An augmented matrix in linear algebra is a matrix created by joining the columns of two given matrices, typically so that the same basic row operations can be applied to each of the given matrices individually. An augmented matrix for a system of equations is a matrix of numbers where each column represents all the coefficients for a single variable and each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign).So, the augmented matrix will be:
Equations are,
9y-5x+9z = 07x=-3y+7+z5x + 7y = 5Rewrite them systematically as:
-5x + 9y + 9z = 07x + 3y - z = 75x + 7y + 0 = 5Now, augmented matrix:
(Refer to the matrix attached below)Therefore, the augmented matrix of the given equations is shown (Refer to the matrix attached below.)
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19 students reported seeing the latest blockbuster film over the summer, 76 total students were surveyed. Which fraction represents the ratio of students who saw the movie to total students surveyed?A. 1/4B. 4/15C. 2/7D. 3/7
In this case the answer is very simple. .
We must find the proportion and compare it with the options.
Step 01:
ratio of students who saw the movie
[tex]\frac{\text{students saw the movie}}{\text{total students surveyed}}\text{ = }\frac{19}{76}\text{ = }\frac{1}{4}[/tex]The answer is:
Option A.
given the following list of axioms drawing model on a separate sheet of paper to properly represent the information describing drawing in your own words there exists by points each line contains only these Five Points there exist two lines each line contains at least two points
Five random points, 3 of them collinear:
To go through all the points with only two lines, one of the five points has to be colinear with other 2 points.
If the fifth point wasn't colinear, we would need another line to draw.
If four of the five points were colinear between them, we could have had a line that goes through this 4 points, and the other line going through the remaining point.
If the five points were colinear, we would have need only one line to go through them.
Divide the fraction. Express your answer to the nearest tenth. A calculator may be used.0.70.09Enter a number as an exact integer or decimal.eBookSubmit Answer
The given fraction is
[tex]\frac{0.7}{0.09}[/tex]Using a calculator, we have
[tex]\frac{0.7}{0.09}=7.77777777777\ldots[/tex]However, rounded to the nearest tenth would be
[tex]7.7777777777\ldots=7.8[/tex]Therefore, the answer is 7.8.A triangle on a coordinate plane is translated according to the rule T-8, 4(x, y). Which is another way to write this rule?
(x, y)
(x + 4, y-8)
(x-4, y-8)
O(x, y)
O (x,y) - (x-8, y + 4)
O(x, y) (x+8, y-4)
A triangle coordinate translate T-8, 4(x, y). Then we can rewrite the translation rule as :
( x, y ) → ( x - 8, y + 4).
Solution:A translation is a type of transformation in which every point in a figure moves the same distance in the same direction. Slides are another term for translations. A translation can be described using words like "moved up 3 and over 5 to the left" or with notation.The function translation / transformation rules are as follows: f (x) + b raises the function by b units. The function f (x) b is shifted downward by b units. f (x + b) moves the function to the left by b units.Here we know that according to the translation rule Ta,b( x , y) the translation of a point (x,y) by (a,b) is given by:
(x , y) → ( x + a , y + b)
The following statement is true: A triangle on a coordinate plane is translated according to the rule.
T₋₈ , ₄(x , y).
Then, another way to write this rule is:
( x , y) → (x + (-8) , y + (4))
( x, y ) → ( x - 8, y + 4).
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Estimate the total cost of the following items for your dorm room round the individual cost to the nearest $10 round your answer to the nearest dollar (cents)
We will determine the approximate cost as follows:
[tex]149.67+59.58+29.56+19.79=258.60[/tex]So, the total cost would be $258.60.
Fractions and Mixed Numbershogy Commercing eng yourStephan owns a landscaping compary. Today, he is mowing three lawns: one is 1/4 of an acre, one is of 1/2 an acre, and one is 1 1/3 acres. How many acres of lawn is Stephan going to nowtoday. Simplify your answer and write it as a mixed fraction if necessary25 acresSvendoseSotPassHold
We would add each of the given fraction. Thus, the number of acres that he is going to mow
Your Aunt is having a baby. You have created a party game for a baby shower. It is called pick the gender. You put pink and blue tiles into a bag. You ask two guests to pick one tile each out of the bag without looking. You tell your guests that if they are the same color, player A wins and if they are two different colors, then player B wins.How many tiles of which colors did you put into the bag to make sure that both players have an equal chance of winning?
There have to be an equal number of pink and blue tiles in the bag make sure that both players A and B have an equal chance of winning as they events of probability.
What is probability of an event?If an event say A can occur in a-ways and fail to occur in b-ways and as well (a + b)-ways are equally likely, then the probability of A is given as P(A) = a/(a + b).
Let the probability of having a winner at the party be P(W) = 1, which is a certain event.
then addition of the probability of player A = P(A) winning and the probability of player B = P(B) winning must be equal to 1.
Hence,
P(A) + P(B) = (1/2) + (1/2)
P(A) + P(B) = 1
This implies there must be equal number of the pink and blue tiles.
Thus, there have to be equal number of pink and blue tiles so that any of the event occurring must result in the two players having equal chance of winning.
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Find the percent of change from 80 kmph to 60 kmph
33.3% increase
25% increase
25% decrease
33.3% decrease
The most appropriate choice for Percentage will be given by
There is a 25 % decrease in speed
3rd option is correct
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. Then that number is called percentage.
For example, 2% means [tex]\frac{2}{100}[/tex]
Original speed = 80 kmph
New speed = 60 kmph
Decrease in speed = (80 - 60) kmph
= 20 mph
Percentage decrease = [tex]\frac{20}{80} \times 100\\[/tex]
= 25 %
There is a 25% decrease in speed.
3rd option is correct
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m³ +9n when m = 4
and n = 5
Answer:
109
Step-by-step explanation:
you first cube 4 which means 4x4x4
64
then multiply 9x5 and get 45
then add 45+64 and you get your answer
Bob is spending money at a constant rate. Suppose he initially has $1000, and after 8 months, he has $200.
Which of these expresses the rate at which Bob's amount of money is changing?
The required rate at which Bob's amount of money is changing is $100 per month.
Given that,
Bob is spending money at a constant rate. Suppose he initially has $1000, and after 8 months, he has $200. The expression of the rate at which Bob's amount of money is changing is to be determined.
Here,
Initial money = $1000
Rest money = $200
Time = 8 months,
Rate = [1000 - 200] / 8
Rate = [800] / 8
Rate = $100
Thus, the required rate at which Bob's amount of money is changing is $100 per month.
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(1/5+1/2 to the 2nd power)+3/10x5
The value of this given algebraic addition is 51/100.
The problem is in sentence format, we have to convert this to a mathematical format.
We can find the value of these given mathematical digits by following a few steps.
1/5 + ( 1/2 )^2 + 3/10×5
= 1/5 + 1/4 + 3/50 = 40/ 200 + 50/200 + 12/200
( we have multiplied both denominator and nominators with different numbers to assure that denominator of all numbers is the same )
= 102/200 ( here we have divided both with 2, to minimize the given fraction )
= 51/100.
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Which inequality is true for all real numbers? Check all that apply.
a-b
ac≥ bc
If az b, then a + c≥ b + c
If c> d, then a-c
If a
The inequalities 3 and 4 are the right ones, because they are actually properties of inequalities.
What do math inequalities mean?
inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.Income gap, gender inequality, access to health care, and social class are some of the most prominent instances of social inequality. Some people receive better and more skilled care in the medical field than others.The inequalities 3 and 4 are the right ones, because they are actually properties of inequalities.
The alternate options are incorrect. For instance, the first option, a - b a + b, is false because the expression would be ruined if you don't apply the same adjustment to both sides of the inequality.
Both options 2 and 5 are incorrect.
The proper responses are thus 3 and 4.
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Answer:
3,4
Step-by-step explanation:
