Given:
Number of appetizers offered = 8
Number of appetizers customer is to select = 6
Number of main courses offered = 9
Number of main courses customer is to select = 6
Number of desserts offered = 3
Number of desserts the customer is to select = 2
Let's determine how many ways this can be done.
This is a combination problem.
To determine the number of ways this can be selected, apply the combination formula below:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Thus, we have:
[tex]_nC_r=_8C_6\ast_9C_6\ast_3C_2[/tex]Solving further, let's apply the formula and combine:
[tex]\begin{gathered} _8C_6\ast_9C_6\ast_3C_2=\frac{8!}{6!(8-6)!}\ast\frac{9!}{6!(9-6)!}\ast\frac{3!}{2!(3-2)!} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{8!}{6!(2)!}\ast\frac{9!}{6!(3)!}\ast\frac{3!}{2!(1)!} \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} _8C_6\ast_9C_6\ast_3C_2=\frac{8\ast7\ast6!}{6!(2\ast1)}\ast\frac{9\ast8\ast7\ast6!}{6!(3\ast2\ast1)}\ast\frac{3\ast2!}{2!(1)} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{8\ast7}{2\ast1}\ast\frac{9\ast8\ast7}{3\ast2\ast1}\ast\frac{3}{1} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{56}{2}\ast\frac{504}{6}\ast\frac{3}{1} \\ \\ _8C_6\ast_9C_6\ast_3C_2=28\ast84\ast3 \\ \\ _8C_6\ast_9C_6\ast_3C_2=7056 \end{gathered}[/tex]herefore, there are
Suppose you earn 2% on $1000 for 2 years if this interest rate is doubled then the interest rate will be
When earn 2% on $1000 for 2 years if this interest rate is doubled then the interest rate will be 4% and the interest is $80.
How to illustrate the information?From the information, the person earns 2% on $1000 for 2 years and this interest rate is doubled, the interest rate will be: = 2% × 2 = 4%
It should be noted that simple interest is calculated as:
Interest = Principal × Rate × Time / 100
Interest = 1000 × 4 × 2 /100
Interest = 8000 / 100
Interest = $80
Learn more about interest on:
brainly.com/question/25793394
#SPJ1
Can someone please help meeeee, I have 2 hours remaining
The number of mosquitoes will be increased by 5 inches of rain.
Maximum mosquito population = 25000
solution :We are given the following in the question:
M(x) = 10x - x²
where M(x) denotes the number of mosquitos in millions and x denotes the amount of rainfall in inches.
To begin, we differentiate M(x) with respect to x, yielding
d(M(x)) /dx = d(10x - x²) /dx = 10 -2x
When we set the first derivative to zero, we get
d(M(x)) /dx = 0
10 - 2x = 0
x = 5
We get the same result when we differentiate M(x) with respect to x:
d²(M(x)) / dx² = -2
d²(M(x)) / dx² < 0
As a result of the double differentiation test, the maxima for M(x) occur at x = 5.
when the rainfall is 5 inches, the most mosquitoes are present.
Maximum mosquito population:
M(5) = 10(5) - (5)² = 25
As a result, the maximum number of mosquitos is 25000.
To learn more about derivatives refer to :
https://brainly.com/question/12047216
#SPJ13
Which statement is the most appropriate comparison of the spreads?A. The standard deviation for town A, 20", is greater than thestandard deviation for town B, 10°.B. The interquartile ranges (IQRs) for towns A and B are both 20°.C. The interquartile range (IQR) for town A, 30°, is less than the IQRfor town B, 46".D. The interquartile range (IQR) for town A, 20", is greater than theIQR for town B, 10".
We are given two box plots of a variable, for two different towns. Recall that the structure of a box plot is
where Q1 is the 25th percentile (or quartile 1), Q2 is the median and Q3 is the 75th percentile (or Quartile 3). This type of graphs tells us how the data is distributed, and more specially it can tell us how the data is spread across the different values the variable could take. So the way to analyze the spread from the graph is by considering the inter quartile range (IQR). This amount can be calculated by simply finding the difference between Q3 and Q1. If this range is really small, this would mean that the data is less spread and if this range is big, then this would mean that the data is more spread.
Using the given box plots, we can determine the following:
Town A: Q3 = 40, Q1 = 20, IQR = 40-20=20
Town B: Q3 = 45, Q1=35, IQR = 45-35 = 10
So, this would lead to option D.
3⁴-21÷7 use pemdas. to solve this
3⁴-21÷7
According to PEMDAS ( order of operations):
First, Do exponents before multiplying or dividing: 3^4
81-21÷7
Then, divide before subtracting (27÷7 )
81- 3
Finally, subtract
78
PLEASE HELP DUE SOON WILL GIVE 20 POINTS!!
Answer:
$5.19
Step-by-step explanation:
10.33 × $2.51 = $25.93
$25.93÷5=$5.19
10. Using the two formulae, A=B/6.5 + 2.5, C= B/9A, obtain an expression for C in terms of A alone:
Answer:
43a + c = 13.25
Step-by-step explanation:
A = 9
C = 81
5/6x-5/12x-1/3+1/4x+1/12
(8x-3)/12
Step-by-step explanation:
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select
and test 54 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3
batteries do not meet specifications. A shipment contains 4000 batteries, and 3% of them do not meet specifications.
What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will
many be rejected?
The probability that this whole shipment will be accepted is
(Round to four decimal places as needed.)
The company will accept % of the shipments and will reject% of the shipments, so
(Round to two decimal places as needed.)
This probability of shipment being accepted is 84%.
And most similar deliveries will be allowed since the likelihood of receiving a sample with much more than three damaged batteries is extremely low.
If at least three batteries fail to satisfy standards, the delivery would be approved.
This may be described as a binomial distribution, with n = 54 samples as well as a p = 0.03 probability of not satisfying the parameters of any battery.
If n ≤ 3 the package will be accepted.
The probability of this event is:
P(D ≤ 3) = P(D = 0) + P(D = 1) + P(D = 2) + P(D = 3)
P(D = k) = (n! ÷ (k!(n-k)!)) × [tex]p^{k}[/tex] × [tex](1 - p)^{n - k}[/tex]
P(D = 0) = (54! ÷ (0!(54)!)) × [tex]0.03^{0}[/tex] × [tex](0.97)^{54}[/tex]
P(D = 0) = 1 × 1 × 0.110
P(D = 0) = 0.110
P(D = 1) = (54! ÷ (1!(53)!)) × [tex]0.03^{1}[/tex] × [tex](0.97)^{53}[/tex]
P(D = 1) = 54 × 0.03 × 0.205
P(D = 1) = 0.3321
P(D = 2) = (54! ÷ (2!(52)!)) × [tex]0.03^{2}[/tex] × [tex](0.97)^{52}[/tex]
P(D = 2) = 1431 × 0.0009 × 0.205
P(D = 2) = 0.264
P(D = 3) = (54! ÷ (3!(51)!)) × [tex]0.03^{3}[/tex] × [tex](0.97)^{51}[/tex]
P(D = 3) = 24804 × 0.000027 × 0.211
P(D = 3) = 0.141
Then,
P(D ≤ 3) = P(D = 0) + P(D = 1) + P(D = 2) + P(D = 3)
P(D ≤ 3) = 0.110 + 0.3321 + 0.264 + 0.141
P(D ≤ 3) = 0.8471
Learn more about the binomial distribution at
https://brainly.com/question/13044555?referrer=searchResults
#SPJ9
Number 12 I don’t get it y’all know ?
please hurry due today I will give you brainlest
Which numbers are solutions of 4p+6 < 3p? Choose exactly two answers that are correct.
6 and -6
please give brainliest
math problem uploaded
From the graph provided, it can be seen that:
There is a maximum at (6,1)
Therefore, the answer is the following:
The function has a relative maximum of 1 at x = 6
2 X (6+ 2 + 8) -4 show your work pls
Answer:
Step-by-step explanation:
32
Francis heard that a car stereo system was on sale for 30% off. If the sale price was 57.75, what was the original price of the stereo?
Answer:
$82.50
Step-by-step explanation:
82.5 times 0.7 = 57.75
doing 57.75 + 30% wouldn't work, so you have to increase the number (original price) being discounted until you get 57.75
also, the '0.7' is 70% which also means '30% off' because you took 30% away from the original price that was 100%
math calculator saves the day? dont use paper or it would take a long time (unless it was a test or teacher said no)
please can an expert help me
The Range of the given function graph is gotten as; Option D: (-4, -1, 0, 1, 2)
How to find the range of a function graph?
The range of a function is defined as a set of all possible output values for which a function is said to hold.
Now, when it comes to a function graph, we can easily say that the range of the function of the graph will be the set of possible values along the y-axis. That is all possible y-values.
Now, in the given graph, we are given 5 coordinates and the y values at each of these coordinates would represent the range of the graph. Thus;
Range = (-4, -1, 0, 1, 2)
Read more about Range of function graph at; https://brainly.com/question/12200177
#SPJ1
Which recursive sequence would produce the sequence 2, -11, 54, ...
Answer:
[tex]n_{i+1} = -5n_i - 1[/tex]
Step-by-step explanation:
-5*2 - 1 = -11
-5*-11 - 1 = 54
Multiply 4(Q+2) what's the answer
Given the expression:
[tex]4(Q+2)[/tex]Let's multiply the expression.
To multiply apply the distributive property of multiplication.
Distribute 4 to the values in the parentheses:
[tex]\begin{gathered} 4(Q)+4(2) \\ \\ =4Q+8 \end{gathered}[/tex]ANSWER:
[tex]4Q+8[/tex]The first four terms of a sequence are given below.
11, 9, 7, 5, ...
What is the seventh term of the sequence?
A. 5
B. -3
C. 1
D. -1
Answer: D:-1
Step-by-step explanation: 11,9,7,5,3,-1,-3,... => dãy số trên có quy luật là số lẻ
monroe's teacher wants each students to draw a sketch of the longest specimen which specimen is the longest
The most appropriate choice for tabular data will be given by-
Specimen B is the longest and its size is 0.011 cm. So Monroe's teacher wants each student to draw the sketch of Specimen B
What is tabular data?
Data given in the form of rows and columns is known as tabular data.
Here,
Size of specimen A = 0.008 cm
Size of specimen B = 0.011 cm
Size of specimen C = 0.0025 cm
Size of specimen D = 0.004 cm
Size of the longest specimen = 0.011 cm
Specimen B is the longest and its size is 0.011 cm. So Monroe's teacher wants each student to draw the sketch of Specimen B
To learn more about tabular data, refer to the link-
https://brainly.com/question/3632175
#SPJ9
Complete Question
The table has been attached
Specimen Actual length(cm) Size seen under microscope (cm)
A 0.008
B 0.011
C 0 .0025
D 0.0040
Current Attempt in Progress
In a list of 15 households, 9 own homes and 6 do not own homes. Four households are randomly selected from these 15 households.
Find the probability that the number of households in these 4 who own homes is exactly 4.
Round your answer to four decimal places.
The most appropriate choice for probability will be given by:
Probability that the number of households in these 4 who own homes is exactly 4 = [tex]\frac{42}{455}[/tex]
What is Probability?
Probability of an event is the chance of occurance of that event.
Probability can be obtained by Number of favourable outcomes divided by the total number of outcomes
Probability varies from 0 to 1.
Here,
Total number of households = 15
No of households to be selected = 4
4 households can be selected from 15 households in [tex]15 \choose 4[/tex] ways
= [tex]\frac{15!}{(15-4)! \times 4!}\\[/tex]
= [tex]\frac{15!}{11! \times 4!}[/tex]
[tex]=\frac{15 \times 14 \times 13 \times 12}{1 \times 2 \times 3 \times 4}[/tex]
= [tex]1365[/tex] ways
Now,
Number of households who own homes = 9
4 households can be chosen from 9 households in [tex]9 \choose 4[/tex] ways
[tex]\frac{9!}{(9-4)! \times 4!}\\[/tex]
= [tex]\frac{9!}{5! \times 4!}[/tex]
[tex]=\frac{9 \times 8 \times 7 \times 6}{1 \times 2 \times 3 \times 4}[/tex]
= [tex]126[/tex]
Probability that the number of households in these 4 who own homes is exactly 4 = [tex]\frac{126}{1365}[/tex]
= [tex]\frac{42}{455}[/tex]
To learn more about probability, refer to the link:
brainly.com/question/251701
#SPJ9
Find all solutions of the equation x^2+2x+6=0 and give your answer as a list of complex numbers, such as 3-4i, 5+i.
Given equation [tex]x^{2} +2x+6=0[/tex]
we use in Quadratic formula
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }[/tex]
So a=1, b=2, c=6
[tex]{\displaystyle x={\frac {-2\pm {\sqrt {2^{2}-4*1*6}}}{2*1}}\ \ }[/tex]
[tex]{\displaystyle x={\frac {-2\pm {\sqrt {4-24}}}{2}}\ \ }[/tex]
[tex]{\displaystyle x={\frac {-2\pm {\sqrt {20}}}{2}}\ \ }[/tex]
[tex]{\displaystyle x={\frac {-2\pm 2i{\sqrt {5}}}{2}}\ \ }[/tex]
[tex]{\displaystyle x= {-1\pm i{\sqrt {5}}}[/tex]
What is the Quadratic formula?
A second-degree equation is a quadratic equation. It implies that at least one term in which the variable is squared will be present. This equation's conventional form is:
ax²+ bx + c = 0
where a, b, and c are variables or coefficients.
X is also an unknowable variable.
The fact that the coefficient "a" cannot be 0 is one unbreakable law.
Two potential choices for its variable X will fulfill the equation because of the degree of 2. Quadratic equations may reflect a wide range of real-world scenarios, as is clear to observe. We'll now look at several solutions.
Quadratic is derived from the term "quad," which means square. Here, we'll create the formula for quadratic equations so that they may be solved.
The factorization approach fails to reduce a large number of equations. Such equations are solved using a more potent approach. Every quadratic problem may be solved using this technique. This is the formula for a quadratic equation in general.
This is how it is explained:
If ax2 + bx + c = 0, then
is a quadratic equation, then the following formula provides the value of x.
Simply enter the numbers for a, b, and c, and the computations will be performed.
The values of a, b, and c are extracted from the equation and entered into the quadratic equation formula.
A, B, and C in this case only numbers. These are the quadratic equation's numerical coefficients, which you must solve.
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }[/tex]
Learn more about the Quadratic formula visit:
https://brainly.com/question/9300679
#SPJ1
HELP!! The table compares the average daily temperature and ice cream sales each day.
Temperature (°F) Ice Cream Sales
58.2 $112
64.2 $135
64.3 $138
66.8 $146
68.4 $166
71.6 $180
72.7 $188
76.2 $199
77.8. $220
82.8 $280
What is the slope of the line of best fit, where x represents the average daily temperature and y represents the total ice cream sales? (Round your answer to one decimal place.)
4.2
6.5
8.1
9.1
The slope of line of best fit is 6.47887 which is approximately 6.5.
Line of Best FitA line of best fit is a straight line that minimizes the distance between it and some data. The line of best fit is used to express a relationship in a scatter plot of different data points. It is an output of regression analysis and can be used as a prediction tool for indicators and price movements.
To calculate the slope of the equation, we need to solve for some parameters.
The sum of x = 703The sum of y = 1764Mean of X = 70.3Mean of Y = 176.4The sum of squares (SSx) = 490.24Sum of product (SP) = 3176.2The equation of regression is given as
[tex]y = bX + a[/tex]
let's solve for the unknown parameters b and a.
[tex]b = \frac{SP}{SS_x}=\frac{3176.2}{490.24} = 6.47887 = 6.5[/tex]
The slope of the line of best fit is given as 6.5.
Learn more on line of best fit here;
https://brainly.com/question/1441182
#SPJ1
Answer: 6.5
Step-by-step explanation: i took the test
Absolute value |-6.809 > |-6.812 which is greater
Answer: 6.809 < 6.812. 6.812 is greater.
Step-by-step explanation:
If you mean if...
|-6.809| > |-6.812|
then, -6.812 will be bigger because when you absolute value an answer the number inside the | | will become positive. So the simplified equation will look like this:
6.809 > 6.812
So, the sign is wrong and should be flipped.
6.809 < 6.812
4. Write a comparison statement for 9 x 3 = 27
Given the following expression:
[tex]\text{ 9 x 3 = 27}[/tex]Making a comparison statement out of this will be: 27 is 3 times more than 9.
PLEASEEE HELP ( ALOT OF POINTS)
For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Greg bought a regular-sized box of his favorite cereal. A regular-sized box contains 12 servings.
Part A: If Greg eats 1 1/2 servings for breakfast every day, how many breakfasts can Greg eat from 1 box? Show all work.
Part B: The regular-sized box of cereal costs $4.29. How much does 1 breakfast from a regular-sized box of cereal cost Greg? Round to the nearest hundredth. Show all work.
Part C: If Greg purchased the family-sized box of cereal that contains 18 servings, how many more breakfasts could Greg eat from 1 box? Show all work.
The number of breakfast Greg can eat from a box of cereal if he eats 1 1/2 servings for breakfast everyday is 8 breakfast.
If a regular-sized box of cereal costs $4.29, the cost of 1 breakfast from a regular-sized box of cereal is $0.54The number of more servings of breakfasts Greg could eat from 1 family-sized box is 4 servings.How to find unit rate of Greg's breakfast?A regular-sized box of cereal = 12 servingsIf Greg eats 1 1/2 servings for breakfast every dayNumber of breakfast Greg can eat in a regular-sized box = A regular-sized box of cereal / servings of breakfast eaten everyday
= 12 ÷ 1 1/2
= 12 ÷ 3/2
multiply by the reciprocal of 3/2= 12 × 2/3
= 24/3
= 8 breakfast
Cost of regular-sized box of cereal = $4.29.
Cost of one breakfast from a regular-sized box of cereal = Cost of regular-sized box of cereal ÷ Number of breakfast Greg can eat in a box
= $4.29 / 8
= 0.53625
Approximately,
$0.54 per breakfast
If Greg purchased the family-sized box of cereal that contains 18 servingsNumber of breakfast Greg can eat in a family-sized box = A family-sized box of cereal / servings of breakfast eaten everyday
= 18 servings / 1 1/2
= 18 ÷ 3/2
= 18 × 2/3
= 36/3
= 12 servings
Therefore, the number of more servings of breakfasts Greg could eat from 1 family-sized box
= Number of breakfast Greg can eat in a family-sized box - Number of breakfast Greg can eat in a regular-sized box
= 12 servings - 8 servings
= 4 servings
Read more on unit rate:
https://brainly.com/question/620388
#SPJ1
Answer:
= 4 servings
Step-by-step explanation:
The answer to one and two
Solution
(a) There are 9 students entering the school district science project:
medals for 1st, 2nd and 3rd
k1 = 1O ways to choose first person to be chosen from the group of 10.
99
k2 = 8 ways for the second person to be chosen from the remaining people(9–1).
k3 = 7 ways for the second person to be chosen from the remaining people(8–1).
then all you need to do is multiply these k1 * k2 * k3.
[tex]\begin{gathered} 1st\text{ 2nd 3rd} \\ 1st=9\text{ option} \\ 2nd=8\text{ }options \\ 3rd=7\text{ options} \end{gathered}[/tex][tex]\begin{gathered} 9\times8\times7 \\ =504 \end{gathered}[/tex](b) There are 7 unique names in a bowl. In how many orders can 2 names be chosen:
This is a permutation problem in order
There are 7 names, and the 2 name have to be in same order
[tex]\begin{gathered} 7P_2 \\ \frac{7!}{(7-2)!} \\ =\frac{7!}{5!} \\ =\frac{7\times6\times5!}{5!} \\ =42 \end{gathered}[/tex]An angle measures 108° more than the measure of its supplementary angle. What is the
measure of each angle?
The measure of each angle are 36° and 144°
What is Supplementary angle?
Two angles are said to be supplementary if their sums total 180 degrees. A linear pair's two angles, like angles 1 and 2 in the illustration below, are always supplementary. But two angles don't have to be close to one another to be supplementary. In the following image, 3 and 4 are supplementary since their sums equal 180 degrees.
Let the provided angle be x, the supplementary angle be y.
y = x + 108 since x has 108° greater than y.
The total of the additional angles is 180°.
x + y = 180,
x + x + 108 = 180,
and x = 180 - 108.
2x = 72
x = 72/2
x = 36
Then,
y = x + 108
y = 36 + 108
y = 144
Consequently, the angles are 36° and 144°.
To learn more about Supplementary angle click on the link
https://brainly.com/question/12919120
#SPJ9
pls help i dont get it
Please help I’ll mark you as brainliest if correct!!
Answer:
it would be 29 five
Step-by-step explanation:
I can't do the small number so it's just typed big
Looking to receive help on the following problem, thank you!
olution
or this case we have the following vectors:
u= -3i +2j, w= 4j, v= 6i -4j
And we can do the following:
art a
u*v= -3*6 + 2*-4= -18 -8= -26
Part b
w*v= 0*6 + 4*-4 =-16
Solving systems of inequalities
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
y < 6x + 9 eq. 1
Step 02:
systems of inequalities
y > 6x + 7 eq. 1
<9
Graph
y = 6x + 9 eq. 2
Unlimited/Infinite solutions
The answer is:
(-4 , 32)
(3 , 25)