Answer:
Explained below.
Step-by-step explanation:
The complete question is:
A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet (he only drinks red wine), all from different wineries. a. If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? b. If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this? c. If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? d. If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? e. If 6 bottles are randomly selected, what is the probability that all of them are the same variety?
Solution:
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
Permutation is the number of ways to select k items from n distinct items in a specific order.
The formula to compute the permutation or arrangement of k items is:
[tex]^{n}P_{k}=\frac{n!}{(n-k)!}[/tex]
(a)
The number of ways to serve 3 bottles of zinfandel, with a specific order is:
[tex]^{8}P_{3}=\frac{8!}{(8-3)!}=\frac{8\times7\times6\times5!}{5!}=336[/tex]
(b)
The number of ways to select 6 bottles from the 30 is:
[tex]{30\choose 6}=\frac{30!}{6!(30-6)!}=\frac{30!}{6!\times 24!}=593775[/tex]
(c)
The number of ways to select two bottles of each variety is:
[tex]{8\choose 2}\times {10\choose 2}\times {12\choose 2}=\frac{8!}{2!\times6!}\times \frac{10!}{2!\times8!}\times \frac{12!}{2!\times10!}[/tex]
[tex]=\frac{12!}{(2!)^{3}\times 6!}\\\\=83160[/tex]
(d)
Compute the probability of selecting two bottles of each variety if 6 bottles are selected:
[tex]P(\text{2 bottles of each})=\frac{83160}{593775}=0.14[/tex]
(e)
Compute the probability of selecting the same variety of bottles, if 6 bottles are selected:
[tex]P(\text{Same Variety})=\frac{{8\choose 6}+{10\choose 6}+{12\choose 6}}{{30\choose 6}}[/tex]
[tex]=\frac{28+210+924}{593775}\\\\=0.0019570\\\\\approx 0.002[/tex]
Given the equation y=1/3x+2 what is the rate of change?
Answer:
1/3
Step-by-step explanation:
thats the slope so im assuming :/
What is the value of x?
20
35
60
70
Answer:
20°
Step-by-step explanation:
Step 1:
x + 40° = 3x Vertical ∠'s
Step 2:
40° = 2x Subtract x on both sides
Step 3:
x = 40° ÷ 2 Divide
Answer:
x = 20°
Hope This Helps :)
what is a thesis statement?
Answer:
es discurso que da un una persona sobre un hecho o circunstancia concreta, en éste, se especifican todos los detalles sobre estos, por lo que la mayor parte del tiempo está planificado. El uso de esta palabra está dirigido, principalmente, al campo jurídico.
PLEASE HELPPPPPPP
multiply
Answer:
-156.9*0.01= -1.569
-62(-0.4)= 20.8
Answer:
1. -156.9 x 0.01 = -1.569
2. -62(-0.4) = 24.8
Step-by-step explanation:
Write the word sentence as an inequality. Then solve the inequality. 3/4 is greater than or equal to a number k divided by -8
Answer:
[tex]\frac{3}{4} \geq \frac{k}{-8}[/tex] k ≥ -6Step-by-step explanation:
Re-arrange: [tex]\frac{3}{4} \geq \frac{k}{-8}[/tex] Multiply each side by -8 to cancel out the -8 under k. It should now look like this: k ≥ -6I hope this helps!
Find the slope will mark brainliest
Step-by-step explanation:
Hey there!
The given equation is;
[tex]y = \frac{1}{2} x - \frac{1}{3} [/tex]
Comparing the equation with y = mx+c, we get;
Slope(m)= 1/2.
Hope it helps...
1) y = 2(x + 2) + 1
AM
6
Answer:
Y=2x+5
Step-by-step explanation:
Hope this helps
Find the slope of the line
Answer: -4/5 or -0.8
Step-by-step explanation:
m= change in y / change in x
-4/ 5
Noah bought two boxes of fruit bars to share with his football team they are 12 bars in each box and 16 people on the team if the bars are shared equally how many fruit bars will each person get
Answer:
1.5
Step-by-step explanation:
this is because 24 divided by 16 equals 1.5
Answer:
7 bars
Step-by-step explanation:
and a bake sale there were 72 raising cookies sold if the ratio of raging cookies sold to oatmeal cookie show was 9 to 1 what is the combined amount of raisin in oatmeal cookie sold
80
9 to 1 is equivalent to 72 to 8 and 72+8=80
Sketch the region enclosed by the given curves.
y = tan(9x), y = 2 sin(9x), −π/27 ≤ x ≤ π/27
Find its area.
Answer:
Area (A) [tex]\simeq[/tex] 0.0682
Step-by-step explanation:
The sketch for the region enclosed by the given curves can be found in the image attached below.
From the image below;
The two curves intersect in the area of tan 9x = 2 sin 9x
Recall that:
[tex]\dfrac{sin \ 9x }{cos \ 9x } = 2 \ sin \ 9x[/tex]
[tex]cos \ 9 x= \dfrac{1}{2}[/tex]
making x the subject; then:
[tex]x = \dfrac{1}{9} cos ^{-1}(\dfrac{1}{2})[/tex]
[tex]x = \dfrac{1}{9}(\dfrac{\pi}{3})[/tex]
[tex]x = \dfrac{\pi}{27}[/tex]
The subdivision of the domain is in two intervals [tex][-\dfrac{\pi}{27}, 0], [0, \dfrac{\pi}{27}][/tex]
where;
[tex]x \ \ \varepsilon \ \ [ -\dfrac{\pi}{27},0]; tan \ 9x > 2 sin \ 9x[/tex]
[tex]x \ \ \varepsilon \ \ [ 0,\dfrac{\pi}{27}]; tan \ 9x < 2 \ sin \ 9x[/tex]
Area (A) = [tex]\int ^0_{-\pi/27}}} ( tan \ 9x - 2 \ sin \ 9x ) \ dx + \int ^{\pi/27}_{0}(2 \ sin \ 9x - tan \ 9x \ ) \ dx[/tex]
[tex]= \begin {bmatrix} \dfrac{1}{9} In \ sec 9x + \dfrac{2}{9} \ cos \ 9x \end {bmatrix}^0_{-\pi/27} + \begin {bmatrix} -\dfrac{2}{7} cos 9x - \dfrac{1}{9} \ In \ sec \ 9x \end {bmatrix}^{-\pi/27} _0[/tex]
[tex]= \dfrac{1}{9}(1-In 2) + \dfrac{1}{9}(1-In 2)\\[/tex]
[tex]= \dfrac{2}{9}(1 - In 2)[/tex]
Area (A) = 0.06818
Area (A) [tex]\simeq[/tex] 0.0682
There are 400 boys at Oak Middle school and 12% play football. What is a reasonable number of boys that play football?
Answer:
About 48 students play football
Step-by-step explanation:
400 times 12% is 48
alexis rolled a six sided die and recored the results of each roll as shown below. what is the probability of rolling a six
Answer:
1/6
Step-by-step explanation:
there is six sides so theres only a 1/6 chance it will land on 6
Resuelve los problemas de una bodega que exporta tomates al extranjero
Answer:
1. 34.42 Toneladas
2. 28.640 toneladas
3. 38 toneladas
4.[tex]\frac{15}{10}[/tex] o [tex]1\frac{5}{10}[/tex]
5.[tex]\frac{16}{6}[/tex] o [tex]2\frac{4}{6}[/tex]
6.[tex]\frac{8}{4}[/tex] o [tex]2[/tex]
1.1 Solucioné el problema convirtiendo el .25 en fracción.
2.1 Conviertes el denominador en el mismo buscando el minimo comun multiplo
3.1 0.099
[tex]\frac{1}{4}[/tex]
[tex]\frac{1}{3}[/tex]
[tex]\frac{2}{3}[/tex]
0.7
0.75
1.1
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Acuerdate que para solucionar las fracciones mixtas solo tienes que dividir el denominador al nominador, por ejemplo en si tienes [tex]\frac{10}{3}[/tex] entonces el 3 cabe 3 veces en el 10, y sobra 1, entonces quedamos que en mixta la fracción sería [tex]3\frac{1}{3}[/tex]
Entonces una vez que recordamos eso, podemos resolver los problemas de fracciones sin ningún problema vamos a resolver la número 4:
[tex]\frac{8}{10} +\frac{7}{10}[/tex]
Como el denominador es igual, sólo sumamos el nominador:
[tex]\frac{8+7}{10}[/tex]
[tex]\frac{15}{10}[/tex]
Cómo el 10 cabe 1 vez en el 15, tenemos un entero y sobran 5:
[tex]1\frac{5}{10}[/tex]
Amanda correctly answered 48 out of 60 questions on a math exam. what percent of questions did she answer correctly?
giving out brainlist ❤️
Answer:77% are corect
Step-by-step explanation:
because
big brain
Find the slope of the line
graphed below.
Answer:
[tex]\frac{3}{5}[/tex] or 0.6
Step-by-step explanation:
This problem requires the slop formula which is [tex]\frac{y2-y1}{x2-x1}[/tex]
You start with the first point which is (-1,1). This will be x1 and y1.
The next point is (4,4). This will be x2 and y2.
You plug these values into your equation which gives you [tex]\frac{4-1}{4-(-1)}[/tex]
To solve, you evaluate, [tex]\frac{4-1}{4-(-1)}[/tex] = [tex]\frac{3}{5}[/tex] or 0.6
Which equation expresses d in terms of t and a?
Answer:
Option D
Step-by-step explanation:
I got it right
The expression 3x^2 + x +1 is the height of the building. The expression 2x - 2 is the distance from the floor of the cafeteria to the top of the building. What is the expression for the height from the ground to the floor of the cafeteria?
Answer:
3x²-x+3
Step-by-step explanation:
Given
Height of the building = 3x^2 + x +1
distance from the floor of the cafeteria to the top of the building = 2x -2
To get the expression for the height from the ground to the floor of the cafeteria, we will use the formula:
Height of the building = (distance from the floor of the cafeteria to the top of the building ) + (he height from the ground to the floor of the cafeteria)
substitute the given parameter into the formula:
3x^2 + x +1 = 2x -2 + P
P = 3x^2 + x +1 - (2X-2)
P = 3x^2 + x +1 - 2x+2
collect like terms:
P = 3x^2 + x-2x+2+1
P = 3x²-x+3
Hence the expression for the height from the ground to the floor of the cafeteria is 3x²-x+3
In the expression 3x²y + 4x – 5x’y, are the terms 3x’y
and –5x+y like terms? Explain by providing support for
your answer.
Answer:
Yes. 3x²y and -5x²y are like terms because the variables x and y have the same exponents.
cos^2A( 1+ tan^2A) =1
I
Answer:
Simplest form of 1+tan^2A/ 1 + cot^2A is 2
Step-by-step explanation:
Company Bloses $1.575 for every employee who quits before 90 days. What is the
total amount the company will lose if 2 employees quit before 30 days, 1 employee
quits on Day 41, and 1 employee quits on Day 100?
Answer:
43
Step-by-step explanation:
5 1
1)
4 3
What is the anwser
What is the coefficient of determination for this data set?
Answer:
0.91
explanation:
please help me and respond with legitimate answers!
Answer:
They are all obtuse scalene triangles I think
The population of a country in 2015 was estimated to be 321.3 million people. This was an increase of 21% from the population in 1990. What was the population of the country in 1990?
Answer:
249.5 (Note: I am not really sure of my answer so sorry)
Step-by-step explanation:
Let 'x' be the population in 1990.
The population in 2015 is 321.9 million.
The increase in x by 29% = 321.910^6
129% of x = 321.910^6
1.29x = 321.910^6
x = 321.910^6/1.29
x = 249.510^6
x = 249.5 million.
249.5 is the answer
i used siri
Brainliest will be given to the correct answer!
The formula for the area of a trapezoid is A = 1/2h (b1 + b2), where h is the height of the trapezoid, and b1 and b2 are the lengths of the bases.
Part A: Solve the formula for h. What is the height of a trapezoid that has an area of 91 cm2 and bases of 12 cm and 16 cm?
Part B: What method would you use to solve the formula for b1? What is the formula when solved for b1?
Part C: What is the length of the other base if one base of a trapezoid is 30 cm, the height of the trapezoid is 8.6 cm, and the area is 215 cm2?
Part D: If both bases of a trapezoid have the same length, can you find their lengths given the area and height of the trapezoid? Explain.
Answer:
A) The height of the trapezoid is 6.5 centimeters.
B) We used an algebraic approach to to solve the formula for [tex]b_{1}[/tex]. [tex]b_{1} = \frac{2\cdot A}{h}-b_{2}[/tex]
C) The length of the other base of the trapezoid is 20 centimeters.
D) We can find their lengths as both have the same length and number of variable is reduced to one, from [tex]b_{1}[/tex] and [tex]b_{2}[/tex] to [tex]b[/tex]. [tex]b = \frac{A}{h}[/tex]
Step-by-step explanation:
A) The formula for the area of a trapezoid is:
[tex]A = \frac{1}{2}\cdot h \cdot (b_{1}+b_{2})[/tex] (Eq. 1)
Where:
[tex]h[/tex] - Height of the trapezoid, measured in centimeters.
[tex]b_{1}[/tex], [tex]b_{2}[/tex] - Lengths fo the bases, measured in centimeters.
[tex]A[/tex] - Area of the trapezoid, measured in square centimeters.
We proceed to clear the height of the trapezoid:
1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.
2) [tex]A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})[/tex] Definition of division.
3) [tex]2\cdot A\cdot (b_{1}+b_{2})^{-1} = (2\cdot 2^{-1})\cdot h\cdot [(b_{1}+b_{2})\cdot (b_{1}+b_{2})^{-1}][/tex] Compatibility with multiplication/Commutative and associative properties.
4) [tex]h = \frac{2\cdot A}{b_{1}+b_{2}}[/tex] Existence of multiplicative inverse/Modulative property/Definition of division/Result
If we know that [tex]A = 91\,cm^{2}[/tex], [tex]b_{1} = 16\,cm[/tex] and [tex]b_{2} = 12\,cm[/tex], then height of the trapezoid is:
[tex]h = \frac{2\cdot (91\,cm^{2})}{16\,cm+12\,cm}[/tex]
[tex]h = 6.5\,cm[/tex]
The height of the trapezoid is 6.5 centimeters.
B) We should follow this procedure to solve the formula for [tex]b_{1}[/tex]:
1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.
2) [tex]A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})[/tex] Definition of division.
3) [tex]2\cdot A \cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot (b_{1}+b_{2})[/tex] Compatibility with multiplication/Commutative and associative properties.
4) [tex]2\cdot A \cdot h^{-1} = b_{1}+b_{2}[/tex] Existence of multiplicative inverse/Modulative property
5) [tex]\frac{2\cdot A}{h} +(-b_{2}) = [b_{2}+(-b_{2})] +b_{1}[/tex] Definition of division/Compatibility with addition/Commutative and associative properties
6) [tex]b_{1} = \frac{2\cdot A}{h}-b_{2}[/tex] Existence of additive inverse/Definition of subtraction/Modulative property/Result.
We used an algebraic approach to to solve the formula for [tex]b_{1}[/tex].
C) We can use the result found in B) to determine the length of the remaining base of the trapezoid: ([tex]A= 215\,cm^{2}[/tex], [tex]h = 8.6\,cm[/tex] and [tex]b_{2} = 30\,cm[/tex])
[tex]b_{1} = \frac{2\cdot (215\,cm^{2})}{8.6\,cm} - 30\,cm[/tex]
[tex]b_{1} = 20\,cm[/tex]
The length of the other base of the trapezoid is 20 centimeters.
D) Yes, we can find their lengths as both have the same length and number of variable is reduced to one, from [tex]b_{1}[/tex] and [tex]b_{2}[/tex] to [tex]b[/tex]. Now we present the procedure to clear [tex]b[/tex] below:
1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.
2) [tex]b_{1} = b_{2}[/tex] Given.
3) [tex]A = \frac{1}{2}\cdot h \cdot (2\cdot b)[/tex] 2) in 1)
4) [tex]A = 2^{-1}\cdot h\cdot (2\cdot b)[/tex] Definition of division.
5) [tex]A\cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot b[/tex] Commutative and associative properties/Compatibility with multiplication.
6) [tex]b = A \cdot h^{-1}[/tex] Existence of multiplicative inverse/Modulative property.
7) [tex]b = \frac{A}{h}[/tex] Definition of division/Result.
What is the equation of the line in slope-intercept form that passes through the points (4,2) and is parallel to the graph of y = 2x +2?
Answer:
y = 2x - 6
Step-by-step explanation:
PARALLEL to y = 2x + 2
This means that the equation will have the same slope as the above equation.
Subsitute y and x.
2 = 2(4) + b
Solve for b.
b = -6
10) Mrs. Jimenez bought some jeans to sell at her store. The wholesale
price for the jeans was $65 and she marked up the price by 25%. What
was the retail price of the jeans?
O $65.25
Answer:
The retail price of the jeans was $81.25.
Second Choice: $81.25.
Step-by-step explanation:
Mrs. Jimenez paid $65 for some jeans.
She intended to sell them at her store by marking their price up by 25%.
We have to add 25% to $65:
25 * $65 / 100 = $16.25
$65 + $16.25 = $81.25
The retail price of the jeans was $81.25.
Second Choice: $81.25.
Answer:
B
Step-by-step explanation:
what is 2x + 5x - 11 = -46
Answer: x= -5 hope this helps
Step-by-step explanation:
James has $36.42 if he can only spend 1/6 of his money, how much money can he spend? 6 1
Answer:6.07
Step-by-step explanation:
Answer:
$6.07
Step-by-step explanation:
36 / 6 = 6
.42 / 6 = 7
6.07
bc we skip two decimal spaces to put it before the 0, there for the answer is $6.07!
