In a restaurant there are 7 starter dishes, 14 main dishes and 9 desserts. phil is going to choose one of the combinations for his meal. a starter dish and a main dish, a main dish and dessert, a starter dish, main dish and dessert dish. how many different ways are there for him to choose the meal.
Answers
There are 1106 different ways for him to choose the meal.
For given question,
In a restaurant there are 7 starter dishes, 14 main dishes and 9 desserts.
The possibilities of selecting a starter = 7
The possibilities of selecting a main dish = 14
The possibilities of selecting a dessert = 9
The meal combinations are: a starter dish and a main dish; a main dish and dessert; a starter dish, main dish and dessert dish.
The possibility of selecting each meal combinations would be,
1) a starter dish and a main dish = 7 × 14
= 98
2) a main dish and dessert = 14 × 9
= 126
3) a starter dish, main dish and dessert dish
= 7 × 9 × 14
= 882
We need to find the total number of different ways to choose the meal.
= 98 + 126 + 882
= 1106
Therefore, there are 1106 different ways for him to choose the meal.
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Related Questions
what is the rank of a 4 x 5 matrix whose null space is three-dimensional?
Answers
The rank of the 4 x 5 matrix is 2 whose null space is three-dimensional
Matrix is defined as a rectangular array of rows and columns.
Rank of a matrix is defined as the maximum number of linearly independent columns (or rows ) that the matrix has.
Rank–nullity theorem is defined as a theorem described in linear algebra, which says that the dimension of the domain of a map is the sum of its rank and its nullity.
The rank-nullity theorem states that for a matrix A,
rank(A)+nullity(A)= number of pivot columns of A
That implies (the number of pivot columns) - (the null space dimension) = rank
The rank-nullity theorem states that for any matrix A, the rank of A plus the dimension of the null space of A equals the number of columns of A. In other words:
rank(A) + dim(null(A)) = number of columns of A
In this case, we have a 4 x 5 matrix A with null space of dimension 3. Therefore, we can solve for the rank of A as follows:
rank(A) + dim(null(A)) = number of columns of A
rank(A) + 3 = 5
rank(A) = 2
So the rank of the 4 x 5 matrix is 2.
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What is the m_ACB?
O 10°
B.
0 50°
(4x)
O 90°
O 180°
(7x-20)
С
Answers
Answer:
180
Step-by-step explanation:
90 + 4x + 7x - 20 equals to 180
Answer:
B. 50
Step-by-step explanation:
James takes out a loan of 9000 euros which keeps on charging simple interest at a rate of 3% of the original amount per annum until it is cleared. James pays of 770 euros each year to reduce the loan. After how many years will James have fully cleared the loan?
Answers
James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.
To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.
The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.
In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.
In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.
This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.
Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.
Combining like terms, we have 9000 + 270 = 1.04x.
Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.
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Please help ? Help !!!
Answers
The area of the rectangle is 8- square units
Area of the triangle is 10 square units
The total area is 90 square units
How to determine the valueThe formula for the area of a rectangle is expressed mathematically as;
A = lw
Given that the parameters are;
A is the area of the rectangle.l is the length of the rectangle.w is the width of the rectangle.Now, substitute the values, we have
Area = 8(10)
Multiply the values
Area = 80 square units
The formula for area of a triangle is;
Area = 1/2 base × height
Substitute the values
Area = 1/2 × 10 × 2
Multiply the values
Area = 10 square units
Total area = 10 + 80 = 90 square units
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what do ducks short necks help them to do? pls help :/
Answers
Answer:
In some circumstances these displays may allow the female to observe the performance of males and to evaluate them as potential mates. To elicit displays from a group of males, a female Mallard may swim with her neck outstretched and her head just above the water
Step-by-step explanation:
hope this helps
What is y=4x-1 in standard form?
Answers
Answer:
Algebra Examples
Algebra ExamplesThe standard form of a linear equation is Ax+By=C A x + B y = C . Move all terms containing variables to the left side of the equation. Add 4x 4 x to both sides of the equation.
A manager drew this box-and-whisker plot to represent the weights, in pounds, of the 440 crates the company is shipping. Box-and-whisker plot ranging from 80 to 180 with ticks at increments of 2. 5. Plot defined by points at 84, 99. 5, 113, 143, 170. How many crates weigh more than 99. 5 pounds?
Answers
0(zero) crates weigh more than 99. 5 pounds.
The distance between the median and the third quartile on the plot is equal to the interquartile range,
IQR.IQR = Q3 − Q1
Using the values given in the plot:
Q1 = 99.5Q3
= 143IQR
= 143 − 99.5
= 43.5
The upper bound of the plot can be determined by adding 1.5 times the interquartile range to the third quartile.
UPPER = Q3 + 1.5(IQR)
UPPER = 143 + 1.5(43.5)
UPPER = 209.25
Since the upper bound of the plot is 209.25, any crate weighing more than 209.25 pounds is an outlier, which means that all crates on the plot are within the reasonable range.
To determine the number of crates weighing more than 99.5 pounds, we need to look at the box-and-whisker plot again.
We can see that the crate's weight starts at 84 and ends at 170.
So, we need to determine how many crates weigh more than 99.5 pounds, which is the third value on the plot.
From the plot, we can see that 170 is the largest weight and the next-largest weight is 143, which is less than 170.
Thus, there are no crates weighing more than 170 pounds.
Therefore, the number of crates weighing more than 99.5 pounds is the same as the number of crates weighing more than 143 pounds.
This means that no crate weighs more than 99.5 pounds. So the answer is 0.
There are zero crates weighing more than 99.5 pounds, and this can be written as 0 in numerals. This answer can be verified by looking at the plot.
| | | | |
180| | | | |
| | | | |
| | | | |
| |_____________________| | |
| | | | |
| |_____________________| | |
| | | | |
| | | | |
| | | | |
| | | | |
| | |____________________| |
| | | | |
| | | | |
140| | | | |
| | | | |
120| | | | |
| | | | |
|______________|_____________________|____________________|______________|
80 100 120 140 160
Therefore, the number of crates is 0.
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I need help with this It’s from my trigonometry prep guide *it asks to round the answer to the nearest tenth of a degree
Answers
Answer: 50.8
We can answer this question by using the Trigonometric Functions sine and cosine.
To find an angle using the sine function, we know that:
\(\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \theta=\sin ^{-1}\frac{opposite}{hypotenuse} \end{gathered}\)This will give us:
\(\theta=\sin ^{-1}\frac{2\sqrt[]{6}}{2\sqrt[]{15}}=39.2\degree\)Then, to find the other angle, we can either:
- Add 39.2 and 90, then subtract from 180, or
- Use the trigonometric function cosine.
Let us first try using the function cosine:
\(\begin{gathered} \cos \theta=\frac{adjacent}{hypotenuse} \\ \theta=\cos ^{-1}\frac{adjacent}{hypotenuse} \end{gathered}\)This will give us:
\(\theta=\cos ^{-1}\frac{2\sqrt[]{6}}{2\sqrt[]{15}}=50.8\degree\)Then let us try adding 90 and 39.2 then subtract it from 180
\(180\degree-(90\degree+39.2\degree)=50.8\degree\)Now, we have the value of two acute angles which are 39.2 and 50.8. Since we are asked for the larger acute angle, the answer would be 50.8.
a number is equal to . what is the smallest positive integer such that the product is a perfect cube?
Answers
The smallest positive integer y such that the product xy is a perfect cube is 3.
To find the value of y, we need to factorize x, which is 7 * 24 * 48.
We can then find the prime factorization of xy, which will help us determine the smallest integer y that will make the product a perfect cube.
Since 7, 24, and 48 are already factored, we can express x as:
x = 2⁴ * 3 * 7²
To make xy a perfect cube, we need to ensure that the exponents of all the prime factors are multiples of 3.
Therefore, we need to add a factor of 3 to the exponent of 2 in x to make it a multiple of 3. This gives us:
xy = 2⁷ * 3² * 7²
The smallest integer y that can make this product a perfect cube is 3, because we need to add a factor of 1 to the exponent of 2 in xy to make it a multiple of 3, and the smallest integer that can achieve this is 3.
Thus, the smallest positive integer y such that the product xy is a perfect cube is 3.
The question is: A number x is equal to \($7\cdot24\cdot48$\). What is the smallest positive integer y such that the product xy is a perfect cube
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each system of equations to its graph.
Answers
The groups of equation are as follows;
The y-intercept of equation = 1
The x-intercept of equation = -1/2
And The slope of equation = 2
Then,
At x = 0, y = 1
And at y = 0, x = -1/2
And at x = 2, y = 3
The first and second equation Corresponding with the third graph.
The y-intercept of equation = 0
The x-intercept of equation = 0
The slope of equation = 3
So at x = 0, y = 0 and at x = 2, y = 6
The equation Corresponds with the first graph
The y-intercept of equation = -2
The x-intercept of equation = 2
The slope of equation = 2
So at x = 0, y = -2 and at x = 2, y = 0
The equation Corresponds with the first graph.
The y-intercept of equation = 3
The x-intercept of equation = -2
The slope of equation = 2
So at x = 0, y = 3 and at x = -5, y = 0
The equation Corresponds with the fourth graph.
The y-intercept of equation = 2
The x-intercept of equation = -1/2
The slope of equation = 4
So at x = 0 y = 2 and at y = 0 x = -1/2 and at x = 0.5 y = 4
The equation Corresponding with the second graph.
I need help fast plss
Answers
The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°
Finding the measures of the anglesFrom the question, we have the following parameters that can be used in our computation:
The transversal lines and the other lines
So, we have
∠1 = 180 - 53
Evaluate
∠1 = 127°
Also, we have
∠5 = 53°
By vertical angles, we have
∠2 = 53°
∠3 = 127°
Next, we have
∠4 = 127 - 90°
∠4 = 37°
Solving further, we have
∠6 = 90°
By corresponding angles, we have
∠7 = 37°
∠9 = 180 - 90 - 53°
∠9 = 37°
∠10 = 90 + 53°
∠10 = 143°
∠8 = 143°
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Algebra II 5.02: Solve Radical Equations
Answers
Radical Equations
Step 1
To demonstrate how to solve a radical equation, let's use the following equation as an example:
The goodness-of-fit measure that quantifies the proportion of the variation in the response variable that is explained by the sample regression equation is the coefficient of
Answers
Determination, also known as R-squared. The coefficient of determination, denoted by \(R^{2}\), is a statistical measure that ranges from 0 to 1 and indicates how well the regression equation fits the data.
An \(R^{2}\) value of 0 indicates that the regression equation does not explain any of the variation in the response variable, while an \(R^{2}\) value of 1 indicates that the regression equation perfectly explains all of the variation in the response variable. In general, a higher \(R^{2}\) value indicates a better fit of the regression equation to the data.
The formula for calculating \(R^{2}\) is:
\(R^{2} = \frac{SSR}{SSTO}\)
where SSR is the sum of squares due to regression (also known as explained sum of squares), and SSTO is the total sum of squares (also known as the total variation).
The coefficient of determination is an important tool in regression analysis because it helps to determine the strength and direction of the relationship between the independent and dependent variables.
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HURRY AND ANSWER NEED IT BY TOMORROW!! WILL MARK YOU BRAINIEST :
1.) If a boulder is pushed off a cliff, at what point of its motion will the potential energy of the
boulder be at its maximum and minimum values? Explain your answer.
Answers
When a boulder is pushed off a cliff, the potential energy of the boulder will be at its maximum just before it starts to fall and at its minimum just as it hits the ground.The potential energy of the boulder is at its maximum just before it starts to fall because it is at its highest point and has not yet begun to move.
The potential energy of an object is determined by its location relative to other objects and the conditions that surround it. When a boulder is pushed off a cliff, the energy stored in it is converted from potential energy to kinetic energy.
Therefore, when a boulder is pushed off a cliff, the potential energy of the boulder will be at its maximum just before it starts to fall and at its minimum just as it hits the ground.The potential energy of the boulder is at its maximum just before it starts to fall because it is at its highest point and has not yet begun to move.
At this point, the boulder has stored the maximum amount of energy that can be converted into kinetic energy when it starts to fall. At this point, the potential energy is equal to the gravitational potential energy (GPE) of the boulder, which is given by the equation GPE = mgh, where m is the mass of the boulder, g is the acceleration due to gravity, and h is the height of the cliff.The potential energy of the boulder is at its minimum just as it hits the ground because it has no more height to lose.
At this point, all of the potential energy that the boulder had at the top of the cliff has been converted into kinetic energy as it fell, and this kinetic energy has been transferred to other objects as the boulder collided with them. Therefore, the potential energy of the boulder is zero at this point.
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PLEASE HELP NO ONES ANSWERING SEE IMAGE BELOW
Answers
Answer:
Step-by-step explanation:
A)16
B)25
C)121
Answer:
(1.) 12
(2.) 20
(3.) 110
Step-by-step explanation: The first answer I'm going to use as an example. Because there is 4 people, one person who is shaking everybody's hands does not count. So we wouldn't count that person making the equation 4x3=12.
If we did add that person we would be basically saying that everyone is shaking their own hands as well as everybody else.
Because there is 4 people and even if you wrote this out on paper and put it out... like
1,2,3,4 showing the number of people and underneath it putting 3 and then adding it all up you would still get 12.
A rectangular prism has a volume of 840 cubic inches. The height of the prism is 6 inches and the width
iS 10 inches. Find the length of the prism and explain how you found it.?
Answers
Answer:50400cm2
Step-by-step explanation:lxWxH
Answer:
The length of the prism can be found by using the formula for volume of a rectangular prism, which is: V = lwh. Rearranging the formula to solve for l, the length, we get l = V / (wh). In this case, V is 840, w is 10, and h is 6. Plugging these values into the equation, we get l = 840 / (10 * 6) = 14 inches. Therefore, the length of the rectangular prism is 14 inches.
Step-by-step explanation:
The length of the prism can be found by using the formula for volume of a rectangular prism, which is: V = lwh. Rearranging the formula to solve for l, the length, we get l = V / (wh). In this case, V is 840, w is 10, and h is 6. Plugging these values into the equation, we get l = 840 / (10 * 6) = 14 inches. Therefore, the length of the rectangular prism is 14 inches.
The number of fish on a fish farm increases by approximately 10% each month. If there were originally 350 fish, calculate to the nearest 100 how many fish there would be after 12 months.
Answers
Answer:
There would be 600 fish after 12 months.
Step-by-step explanation:
The number of fish on the farm increases by 10% each month, so the formula to calculate the number of fish after n months is:
F = 350 * (1 + 0.1)^n
where,
F is the number of fish after n months
We want to find the number of fish after 12 months, so:
F = 350 * (1 + 0.1)^12
F = 350 * 1.719178
F = 603.56 to the nearest 100, which is 600.
M(-5,9) and N(-2,7)
P(-3,-7) and Q(3,-5
Answers
Answer:
M=(4,112)=(4,5.5) A
Step-by-step explanation:
The midpoint for two points P=(px,py) and Q=(qx,qy) is M=(px+qx2,py+qy2).
We have that px=3, py=2, qx=5, qy=9.
Thus, M=(3+52,2+92)=(4,112).
George makes $20 doing lawn work for 4 hours each
week. He wants to buy a $2,500 used car from his
grandmother. He has been saving this money for
30 weeks. How much has he saved?
Answers
Answer:
$600
Step-by-step explanation:
1 week = $20
30 weeks = 20 x 30 = $ 600
The saving of 30 weeks would be an amount of 600 dollars.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
George makes $20 doing lawn work for 4 hours each week.
He has been saving this money for 30 weeks
The saving of one week = $20
The saving of 30 weeks = $20 × 30
Apply the multiplication operation to get
The saving of 30 weeks = $600
Alternative method :
According to the given situation, we can write a ratio as
one week : 20 dollars = 30 weeks : x dollars
⇒ 1 / 20 = 30 / x
Apply the cross-multiplication operation,
⇒ 1 × x = 30 × 20
Apply the multiplication operation to get
⇒ x = 600
Hence, the saving of 30 weeks would be an amount of 600 dollars.
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PLS HELP FAST I WILL MARK THE FIRST BRAINLIEST
In science class, Alex estimates the volume of a sample to be 42 mL. The actual volume of the sample is 38 mL. Find the percent error of Alex’s estimate. Round your answer to the nearest tenth.
Group of answer choices
1.9%
2.1%
9.5%
10.5%
SHOW YOUR WORK PLS
Answers
Answer:
\(10.5\%\)
Step-by-step explanation:
\(\% \: error = \frac{absolute \: error}{actual \: value} \times 100\)
actual value = 38ml, measurement error = 42ml
absolute error = actual value - measurement error (where actual value > measurement error) OR measurement error - actual value (where actual value < measurement error)
(Note: absolute error is different from measurement error. Absolute error is the distance between the actual value and the measurement error, while measurement error is the error made in measurement).
Therefore, absolute error = 42 - 38 = 4
\(\% \: error = \frac{4}{38} \times 100\)
\(\% \: error = 10.52\)
Therefore: % error = 10.5 (to the nearest tenth)
I hope this helps...In 10 minutes a heart can beat 700 times.At this rate in how many minutes will a heart beat 140 times? AT what rate can a heart beat
Answers
Answer:
2 minutes
Step-by-step explanation:
700/10 = 70
1 minute = 70 times
140/70 = 2 minutes
Answer:
2 minutes
Step-by-step explanation:
The heart beats 70 times per minute so 70+70=140.
a. If the two premises fit the pattern of Law of Detachment, Law of Contrapositive, or Law of Syllogism, determine the conclusion that logically follows and which law.
When I ski, I fall down.
I didn’t fall down.
I didn't go skiing.
I went skiing.
If I go skiing I will fall down.
No valid conclusion.
Question 2
b. What Law of Logic led you to your conclusion in part a?
Law of Syllogism
Law of Contrapositive
No law, it's not a valid conclusion
Law of Detachment
Answers
Answer:
law of detachment
Step-by-step explanation:
What is the value of q in the equation 0.5q = 6.25?
Write the answer as a decimal to the nearest tenth.
Answers
Answer:
q=12.5
Step-by-step explanation:
Divide each term by 0.5 and simplify
Answer:
12.5
Step-by-step explanation:
0.5q = 6.25
/0.5 /0.5
q = 12.5
What is the surface area of a cylinder that has the following measurements
Area of each base 50.24
Area of lateral surface 75.36ft^2
Height of cylinder 3 ft
A. 150.72
B.175.84
C. 125.6
D. 128.6
Answers
What is the value of a in the equation?
a + 6 = 22 - 7
A.11
B.9
C.14
D.8
Answers
Answer:
B.
Step-by-step explanation:
a + 6 = 22 - 7
a + 6 = 15
a + 6 - 6 = 15 - 6
a = 9
Let P,Q ve proporitional variables. Definie a junctor P∣Q e.g. by giving a truth table or a sutable formula Q, so that you can find proporitionally equivalert formulas for IP and P∧Q that ouly use the conrective I use. Iustify this as well, e.g. by spec ifying switable truth tables.
Answers
The junctor P∣Q can be defined as "if P is true, then Q is true; otherwise, P can be false."
How can we show that P∣Q is propositionally equivalent to IP and P∧Q?To show that P∣Q is propositionally equivalent to IP (implication) and P∧Q (conjunction), we can construct truth tables for all three expressions. Let's denote "T" for true and "F" for false.
1. Truth table for P∣Q:
| P | Q | P∣Q |
|---|---|----|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
2. Truth table for IP (Implication):
| P | Q | IP |
|---|---|----|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
3. Truth table for P∧Q (Conjunction):
| P | Q | P∧Q |
|---|---|-----|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
By comparing the truth tables, we can see that P∣Q and IP have identical truth values for all combinations of P and Q. Similarly, P∣Q and P∧Q have identical truth values for all combinations of P and Q as well. Therefore, P∣Q is propositionally equivalent to both IP and P∧Q.
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I need to find common multiples
Answers
Answer:
3,6,9,12,15,18,21,24
Step-by-step explanation:
suppose that an agency collecting clothing for the poor finds itself with a container of 20 unique pairs of gloves (40 total) randomly thrown in the container. if a person reaches into the container, what is the probability they walk away with two of the same hand?
Answers
The probability that a person walks away with two gloves of the same hand is approximately 0.0256 or 2.56%.
To calculate the probability that a person walks away with two gloves of the same hand, we can consider the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
When a person reaches into the container and randomly selects two gloves, the total number of possible outcomes can be calculated using the combination formula. Since there are 40 gloves in total, the number of ways to choose 2 gloves out of 40 is given by:
Total possible outcomes = C(40, 2) = 40! / (2! * (40 - 2)!) = 780
Number of favorable outcomes:
To have two gloves of the same hand, we can choose both gloves from either the left or right hand. Since there are 20 unique pairs of gloves, the number of favorable outcomes is:
Favorable outcomes = 20
Probability:
The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
Probability = Favorable outcomes / Total possible outcomes = 20 / 780 ≈ 0.0256
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amy usually swims 20 laps in 30 minutes what is her rate per minutes
Answers
Answer:
1.5
Step-by-step explanation:
Because if you divide 30 by 20 you get 1.5 to check if it’s correct you multiple 1.5 by 20
1. Consider the expression 2 1/2 - (3/4 + 5/8).
a. Which operation is done first, subtraction or addition?
_____________________________________________
b. Write the computation in words.
_____________________________________________
2. Consider the expression 4.5 + 6 x 0.1.
a. Which operation is done first, addition or multiplication?
_____________________________________________
b. Write the computation in words.
_____________________________________________
Answers
1. Addition is first. Bracket comes first
BODMAS
1 ADDITION
2½ - (¾ - ⅝)
Subract the sum of 3/4 and 5/8 from 2½
2. BODMAS
Multiplication first
4.5 + 0.6 = 5.1
Five and one tenth
Add 4.5 to the product of 6 and 0.1