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Luisa is planning a bridal shower for her best friend. At the party, she wants to serve 3 beverages, 3 appetizers, and 3 desserts, but she does not have time to cook. She can choose from 15 bottled drinks, 10 frozen appetizers, and 13 prepared desserts at the supermarket. How many different ways can Luisa pick the food and drinks to serve at the bridal shower
Answer:
Luisa can pick the food and drinks to serve at the bridal shower in 15,615,600 different ways.
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
Also
The order in which the food and drinks are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Beverages:
3 from a set of 15. So
[tex]B = C_{15,3} = \frac{15!}{3!12!} = 455[/tex]
Appetizers:
3 from a set of 10. So
[tex]A = C_{10,3} = \frac{10!}{3!7!} = 120[/tex]
Desserts:
3 from a set of 13. So
[tex]D = C_{13,3} = \frac{13!}{3!10!} = 286[/tex]
How many different ways can Luisa pick the food and drinks to serve at the bridal shower?
By the fundamental counting principle, as beverages, appetizers and desserts are independent:
[tex]T = B*A*D = 455*120*286 = 15,615,600[/tex]
Luisa can pick the food and drinks to serve at the bridal shower in 15,615,600 different ways.
Find the probability of choosing a letter other than the letter E from a bag that contains the fifteen letters of the name DANIEL BERNOULLI. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer:
The probability of getting a letter which is not E is 13/15.
Step-by-step explanation:
DANIEL BERNOULLI
The total number of elements in sample space = 15
The probability of getting letter E is
= 2/15
The probability of getting a letter which is not E is
[tex]1 - \frac{2}{15}\\\\\frac{13}{15}[/tex]
Match each pair of equations with the property that justifies why they are equivalent.
Not all properties will be used.
9514 1404 393
Answer:
subtractionmultiplicationcombine like termsStep-by-step explanation:
The properties of equality say the value of the variable does not change if the same function is performed on both sides of the equal sign.
a) 4x +7 = 19 ⇒ 4x = 12
The value -7 was added to both sides. Equivalently, 7 was subtracted from both sides. The Subtraction Property of Equality was used.
__
b) 2x/3 = 8 ⇒ 2x = 24
Both sides were multiplied by 3. The Multiplication Property of Equality was used.
__
c) 5x -6 +2x = 22 ⇒ 7x -6 = 22
Terms 5x and 2x were combined and written as 7x. We call this Combine Like Terms.
Which of these would be the opposite of a progressive tax?
Answer:
b
Step-by-step explanation:
Which of the following is not a property of zero?
Answer:
D is not correct
Step-by-step explanation:
"If you add zero to a number, the answer will be that same number" is incorrect
Answer: Option
2 (or B)
Step-by-step explanation:
You can't divide by 0.
Noah is carrying a bag that weighs 2.5 pounds. What is the weight of the bag equal to?
A. 30 oz.
B. 40 oz.
C. 50 oz.
D. 60 oz.
Answer:
B. 40 oz.
Step-by-step explanation:
Pleaseee helpppp!!! 20 points
Answer:
The correct option is (A).
Step-by-step explanation:
The given expression is :
[tex]\dfrac{14x^4y^6}{7x^8y^2}[/tex]
The numerator contains 14x⁴y⁶ and the denominator is 7x⁸y².
We can write it as :
[tex]\dfrac{14x^4y^6}{7x^8y^2}=\dfrac{7\times 2\times x^4\times y^2\times y^4}{7x^4\times x^4\times y^2}[/tex]
Canceling the common terms,
[tex]=\dfrac{2y^4}{x^4}[/tex]
So, the correct option is (A).
can someone PLEASE help me solve this equation ? due soon
[tex]\sf{Given : 3tanx + 7 = \dfrac{2}{(1 - sinx)(1 + sinx)}}[/tex]
We know that : (a - b)(a + b) = a² - b²
[tex]\implies \sf{3tanx + 7 = \dfrac{2}{1 - sin^2x}}[/tex]
We know that : 1 - sin²x = cos²x
[tex]\implies \sf{3tanx + 7 = \dfrac{2}{cos^2x}}[/tex]
[tex]\sf{\bigstar \ \ We \ know \ that : \boxed{\sf{\dfrac{1}{cos^2x} = sec^2x}}}[/tex]
[tex]\implies \sf{3tanx + 7 = 2sec^2x}[/tex]
We know that : sec²x = 1 + tan²x
[tex]\implies \sf{3tanx + 7 =2(1 + tan^2x)}[/tex]
[tex]\implies \sf{2 + 2tan^2x - 3 tanx - 7 = 0}[/tex]
[tex]\implies \sf{2tan^2x - 3 tanx - 5 = 0}[/tex]
[tex]\implies \sf{2tan^2x - 5tanx + 2tanx - 5 = 0}[/tex]
[tex]\implies \sf{2tanx(tanx + 1) - 5(tanx + 1) = 0}[/tex]
[tex]\implies \sf{(tanx + 1)(2tanx - 5) = 0}[/tex]
[tex]\implies \sf{tanx = -1 \ (or) \ tanx = \dfrac{5}{2} }[/tex]
which of the following is a proportion 4/6 =9/12, 6/9= 8/12, 8/10=6/8 , 3/4=12/15
please help me please!!!!
Answer:
A) angle ACD
B) angle CBA
C) angle ACB
D) angle EBD and angle DBA
E) MDB and CDA
F)DBA
Step-by-step explanation:
Insta: lankey.t
Exponents are really not my thing but i am force to do it.
Answer:
1. False
2. True
3. False
Step-by-step explanation:
describe an experiment to determine convection currents in water
Answer:
When you boil water heat transfer takes place and the heat gets transferred to the water from the stove ( could be considered conduction or radiation), and when the heat is transferred to the water the cold water sinks whereas the hot water rises this rapid movement of convection is called convection currents.
Hope I helped :)
Determine whether ABC and DEF are similar. If so, write the similarity ratio and a similarity statement.
Answer:
Step-by-step explanation:
DEF is similar to CBA
because angle
angle C = angle D
angle B = angle E
angle A = angle F
The ratio is
10.8/5.4 = 9/4.5 = 6.4/3.2 = 2
Solve for x.
4
15
6
X
x = [?]
Enter the number in decimal form
Answer:
66
Step-by-step explanation:
x / 6 + 4 = 15
To find x ;
Subtrac4 from both sides
x / 6 + 4 - 4 = 15 - 4
x / 6 = 11
Multiply both sides by 6
x / 6 * 6 = 11 * 6
x = 66
Value of x = 66
the volume of a cone with a radius of 6 and slant height of 10
Answer:
21.161
Step-by-step explanation:
use Pythagoras theorem ti find your slant height
then you use your formula which
[tex]1 \3\pi {r }^{2} h[/tex]
Which relationship has a zero slope?
A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2.
A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3.
A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5)
A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).
Answer:
B. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3.
PLEASE HELP ME!!!!
Find the expected value of the winnings
from a game that has the following
payout probability distribution:
6 8
10
Payout ($) 0 4
Probability 0.5 0.2 0.15 0.1 0.05
Expected Value = [?]
Round to the nearest hundredth.
Answer:
3.00
Step-by-step explanation:
Given that :
Payout(X) : ___ 0 ___ 4 ___ 6 ____ 8 _____ 10
Probability (p(x) 0.5 _ 0.2 __0.15 __0.1 ___ 0.05
Expected value :E(X) = ΣX* p(x)
E(X) = (0*0.5) + (4*0.2) + (6*0.15) + (8*0.1) + (10*0.05)
E(X) = 3
Expected value = 3.00
Which of the following is an example of a conditional statement?
Answer:
The correct answer is A, If I practice football, then I will improve.
Use the zero product property to find the solutions to the equation x2 – x – 6 = 0.
Answer:
x=3 and x=-2 is the root of given eq
Answer:
Use the zero product property to find the solutions to the equation x2 – x – 6 = 0.?
x = –2 or x = 3 is the answer
Step-by-step explanation:
What is 17.445 - 6.76 rounded to the nearest tenth
Answer:
10.7
Step-by-step explanation:
17.445 - 6.76= 10.685
10.685 is 10.7 when rounded to the nearest tenth!
Use the expression below to answer the question.
6n(19−8)÷3=22
In describing the expression, which term would not be used?
a.difference
c.product
b.sum
d.quotient
Answer:
b sum
Step-by-step explanation:
Solve each equation.
a) 2x = 7
b) 4x = 3
c) 6x = 3
d) 7x = 13
HOW DO YOU SOLVE THESE I NEED THE ANSWER FOR THE QUESTION HELPPPP PLEASEEEE!!!!!!
Step-by-step explanation:
hey :) if you need help download algebrator. I use it ALL the time pls download it and try it out. it'll give you explanations
Answer:
a) x = 7/2
b) x = 4/3
c) x = 1/2
d) x = 13/7
Step-by-step explanation:
(this is the same process for every one of them. I did C for you)
Let's solve your equation step-by-step.
6x=3
Step 1: Divide both sides by 6.
6x/6 = 3/6
x=1/2
I can’t figure it out!! Please help!
Need help
Even
Odd
Neither
Answer:
Odd function
Step-by-step explanation:
....
y adjusted for wind chill (in degrees Fahrenheit, give
formula:
y=-26 + 1.3x
Estimate the actual temperature if the temperature
Fahrenheit.
Answer:
The actual temperature is: -6.92
Step-by-step explanation:
Given
[tex]y = -26 + 1.3x[/tex]
Required
Find x when [tex]y = -35[/tex]
Substitute [tex]y = -35[/tex] in [tex]y = -26 + 1.3x[/tex]
[tex]-35 = -26 + 1.3x[/tex]
Collect like terms
[tex]1.3x = 26 - 35[/tex]
[tex]1.3x = -9[/tex]
Solve for x
[tex]x =-9/1.3[/tex]
[tex]x =-6.92[/tex]
In 2003, 520,000 acres of farmland in a region were devoted to growing nuts. By 2012 ,the number of acres used to grow nuts had increased 820,000.Find the average rate of change in the number of acres in a region used to grow nuts from 2003 to 2012.
Answer:
Average rate of change = 33,333.33acre per year
Step-by-step explanation:
Given:
Farm land in 2003 = 520,000 acre
Farm land in 2012 = 820,000 acre
Find:
Average rate of change
Computation;
Number of year = 2012 - 2003
Number of year = 9 year
Average rate of change = [Farm land in 2012 - Farm land in 2003] / Number of year
Average rate of change = [820,000 - 520,000] / 9
Average rate of change = [300,000] / 9
Average rate of change = 33,333.33acre per year
A salesman with an annual base salary of $35,000 gets a 5% commission on the first $600,000
in sales, a 7% commission on the next $300,000, and 8% on sales above $900,000. What would
be his total compensation for the year if he sold $1 million of product?
Answer:
11%
I think im sorry if im wrong
Step-by-step explanation:
Which of the following is the correct graph of a linear equation below Y +3 equals -2/3 times X -4
Answer:
Where are the graphs?
Step-by-step explanation:
When setting the temperature of a refrigerator, is -1 or -5 the coldest!
Answer:
-5 is the answer
Step-by-step explanation:
Answer:
-5 corresponds to the coldest temperature here.
Step-by-step explanation:
-5 is to the left of -1 on a number line and is therefore smaller than -1.
NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at math.
A student divided f(x) = 3x^3 + 8x^2+ 5x - 4 by x+ 2 and found the remainder was r= -6.Based on the remainder theorem, what can be concluded about f(x)?
A: The function f(x) = 3x^3 + 5x- 4 has a zero at -6.
B: The point (-2,-6) lies on the graph of f(x).
C: The y-intercept of the graph of f(x) is -6.
D: The function f(x) = 3x^3 + 8x^2 + 5x - 4 has a zero at -2.
Answer:
b
Step-by-step explanation: