1. The diner sells 4 different sandwiches, 6 different drinks, and 3
different deserts. How many different orders could you place if you
decided to buy a sandwich and a desert?

2. The Downtown Theater has 1 ticket window. In how many ways can 2 people line up to buy tickets?

3. The Downtown Theater has 1 ticket window. In how many ways can 3 people line up to buy tickets?

4. The Downtown Theater has 1 ticket window. In how many ways can 4 people line up to buy tickets?

5. The Downtown Theater has 1 ticket window. In how many ways can 6 people line up to buy tickets?

Answer: 10 feet

Step-by-step explanation:

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

calculated using the binomial coefficient:

6 choose 3 = 6! / (3! * (6-3)!) = 20 ways

The binomial coefficient can be used to compute the following:

7 select 2 is equal to 7 / (2! * (7-2)!) = 21 ways.

1. We simply need to take three steps down and three steps to the right in order to move from (-3,2) to (-1,-1) by doing so. It doesn't matter in whatever sequence we do these stages.

As a result, the number of ways to select 3 steps out of a total of 6 steps is the number of ways to travel from (-3,2) to (-1,-1). The binomial coefficient can be used to compute the following:

6 select 3 is equal to 6!/(3!*(6-3)!) = 20 ways.

2. We need to take 5 steps to the right and 2 steps up in order to move from (-1,-2) to (4,0) by simply moving up and to the right. It doesn't matter in whatever sequence we do these stages.

Hence, the variety of routes to and from The range of options for selecting 2 stages out of a total of 7 steps is from (-1,-2) to (4,0). The binomial coefficient can be used to compute the following:

7 select 2 is equal to 7 / (2! * (7-2)!) = 21 ways.

The number of possibilities to choose k things randomly from a set of n items is represented mathematically by the binomial coefficient. The formula: It is represented by the symbol "n pick k" or "C(n,k)" and can be calculated.

C(n,k) = n!/(k!*(n-k))!

where the factorial function is shown by "!" A non-negative integer's factorial is the sum of all positive integers that are less than or equal to that number. 5!, for instance, equals 5 x 4 x 3 x 2 x 1 = 120.

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Answer: C

Step-by-step explanation: I've had this question before. Hope it helps :)

Economics is the science that studies strategies of allocating financial resources in the most varied field of applications, involving people, business, land, an so on.

It is important because it helps allocating the financial resources in the most effective way possible.

Economics is the study of how people, businesses, and societies make decisions about the allocation and use of resources, such as land, labor, and capital. It is a social science that deals with the production, distribution, and consumption of goods and services.

Economics is important because it helps us understand how the world works and make informed decisions about how to allocate resources in the most efficient and effective way. Additionally, it provides insights into social and political issues, such as unemployment, inflation, and trade policy.

Understanding economics can help individuals make better personal financial decisions, such as how to save and invest money, and it can also help policymakers design policies and programs that promote economic growth and stability.

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\( \bf \underline{Given-} \\ \)

\( \rm{x = \frac{ \sqrt{3} }{2} } \\ \)

\( \bf \underline{To \: find-} \\ \)

\(\mathsf{ \frac{1 + x}{1 + \sqrt{1 + x} } + \frac{1 - x}{1 - \sqrt{1 - x} } = ?} \\ \)

\( \bf \underline{Solution-} \\ \)

\( \rm{ \sqrt{1 + x} } \\ \)

\(= \sqrt{1 + \frac{ \sqrt{3} }{2} } \:\:\:\: \: \: \: \sf{ [∵\: \:x = √3/2\:(Given)]}\\\)

\( = \sqrt{ \frac{ 2 + \sqrt{3} }{2} } \\ \)

\( = \sqrt{ \frac{4 + 2 \sqrt{3} }{4} } \\ \)

\( = \sqrt{ \frac{3 + 1 + 2 \times \sqrt{3} \times 1}{4} } \\ \)

\( = \sqrt{ \frac{( \sqrt{3} + 1 {)}^{2} }{4} } \\ \)

\( = \frac{ \sqrt{3} + 1 }{2} \\ \)

\(\textsf{Similarly,} \\ \)

\(\rm{ \sqrt{1 - x} } \\ \)

\(\rm{ = \frac{ \sqrt{3} - 1}{2} } \\ \)

\( \rm{\therefore \: \frac{1 + x}{1 + \sqrt{1 + x} } + \frac{1 - x}{1 - \sqrt{1 - x} } } \\ \)

\( \rm{= \frac{1 + \frac{ \sqrt{3} }{2} }{1 + \frac{ \sqrt{3} + 1 }{2} } + \frac{ 1 - \frac{ \sqrt{3} }{2} }{1 - \bigg( \frac{ \sqrt{3} - 1 }{2} \bigg) } } \\ \)

\(\rm{= \frac{2 + \sqrt{3} }{2 + \sqrt{3} + 1 } + \frac{2 - \sqrt{3} }{2 - ( \sqrt{3} - 1)} } \\ \)

\(\rm{= \frac{2 + \sqrt{3} }{3 + \sqrt{3} } + \frac{2 - \sqrt{3} }{3 - \sqrt{3} } } \\ \)

\(\rm{= \frac{2 + \sqrt{3} }{3 + \sqrt{3} } \times \frac{3 - \sqrt{3} }{3 - \sqrt{3} } + \frac{2 - \sqrt{3} }{3 - \sqrt{3} } \times \frac{3 + \sqrt{3} }{3 + \sqrt{3} } } \\ \)

\( \rm{= \frac{(2 + \sqrt{3} )(3 - \sqrt{3} ) + (2 - \sqrt{3})(3 + \sqrt{3} )}{(3 {)}^{2} - ( \sqrt{3} {)}^{2} } } \\ \)

\(\rm{= \frac{6 - 2 \sqrt{3} + 3 \sqrt{3} - 3 + 6 + 2 \sqrt{3} - 3 \sqrt{3} - 3}{9 - 3} } \\ \)

\(\rm{= \frac{12 - 6}{6} } \\ \)

\(\rm{= \frac{6}{6} } \\ \)

\(\rm{= 1} \\ \)

\( \bf \underline{Answer-} \\ \)

\(\mathsf{\underline{Hence, the \: value \: of \: \frac{1 + x}{1 + \sqrt{1 + x} } + \frac{1 - x}{1 - \sqrt{1 - x} } \: is \: 1}} \\ \)

Answer:

h=sqrt2*5i, h=-sqrt 2*5i

Step-by-step explanation:

Answer:

DNE

No real solutions

Step-by-step explanation:

This Quadratic Equation: 2h² + 100 = 0

Answer:

Graph A

Step-by-step explanation:

you can write the equation into desmos (search it up on google) and it will produce a graph for you and just match it to the ones you have shown

Answer: true

Step-by-step explanation:

Answer:

The speed of the plane in the still air is 420 miles/hour

The speed of the wind 60 miles/hour

Step-by-step explanation:

Let the speed of the plane with the wind be v

Let the speed of the plane against the wind be u

Now, speed = distance/time

With the wind,

v = (1440 miles)/(3 hours) = 480 miles/hour

v = 480 miles/hour

Against the wind,

u = (1440 miles)/(4 hours) = 360 miles/hour

u = 360 miles/hour

Now, let the speed of plane be p, and speed of wind be w,

Now, with the wind, the speed is 480 mph,

so,

speed of plane + speed of wind = 480 mph

p + w = 480  (i)

and against the wind, the speed is 360 mph,

so,

speed of plane - speed of wind = 360mph

p-w = 360 (ii)

adding equations (i) and (ii), we get,

p+w + p-w = 480 + 360

2p = 840

p = 840/2

p = 420 miles/hour

Then, the speed of the wind will be,

p + w = 480,

420 + w = 480

w = 480 - 420

w = 60 miles/hour

The speed of the plane in still air is calculated to be 420 mph, and the speed of the wind is calculated to be 60 mph by solving the two simultaneous equations obtained from the time, rate, and distance relationship.

This problem is about the rate, time, and distance relationships. The rate at which the airplane travels in still air is r (unaffected by wind), and the speed of the wind is w. When the plane flies with the wind, it is 'assisted' and therefore travels faster - at a speed of (r + w); against the wind, it travels slower - at a speed of (r - w).

From the problem, we know that:

By solving these two equations, we get the following:

Adding these two gives 2r = 840 => r = 420 mph (the speed of the plane in still air), and subtracting gives 2w = 120 => w = 60 mph (the speed of the wind).

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The measure of angle ABC is 23.5°

An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the center.

Some of the theorem if arc angle relationships are;

The central angle of an arc is the central angle subtended by the arc.

The measure of an arc is the measure of its central angle.

The angle at the centre is twice the angle at the circumference.

Therefore;

angle ABC = 1/2 × arc ADC

= 1/2 × 47

= 23.5°

therefore angle ABC = 23.5°

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Answer:

x = -2, y = -3

x = -1, y = -1

x = 0, y = 1

x = 1, y = 3

x = 2, y = 5

Step-by-step explanation:

Locate each value of x on the x-axis.

Then go up or down until you reach the red line.

Then read the y-value off the y-axis.

x = -2, y = -3

x = -1, y = -1

x = 0, y = 1

x = 1, y = 3

x = 2, y = 5

The single fraction is 7x/20

A fraction can be defined as the part of a whole variable, number or element.

The different types of fractions are;

Algebraic expressions are mathematical expressions consisting of terms, coefficients, variables, factors and constants.

They are made of operations such as multiplication, addition, subtraction, division, etc

Given the expression;

3/4x - 2/5x

Find the LCM

15x - 8x/20

7x/20

Thus, the value is 7x/20

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Answer:

câu này là 500 nhen

Answer:

a) 0.4219 = 42.19% probability that one out of the next four cars needs oil.

b) 0.3115 = 31.15% probability that two out of the next eight cars needs oil.

c) 0.2581 = 25.81% probability that three out of the next 12 cars need oil.

Step-by-step explanation:

For each car, there are only two possible outcomes. Either they need oil, or they do not need it. The probability of a car needing oil is independent of any other car, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

One out of four cars needs to have oil added.

This means that \(p = \frac{1}{4} = 0.25\)

a. One out of the next four cars needs oil.

This is P(X = 1) when n = 4. So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 1) = C_{4,1}.(0.25)^{1}.(0.75)^{3} = 0.4219\)

0.4219 = 42.19% probability that one out of the next four cars needs oil.

b. Two out of the next eight cars needs oil.

This is P(X = 2) when n = 8. So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{8,2}.(0.25)^{2}.(0.75)^{6} = 0.3115\)

0.3115 = 31.15% probability that two out of the next eight cars needs oil.

c.Three out of the next 12 cars need oil.

This is P(X = 3) when n = 12. So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 3) = C_{12,3}.(0.25)^{3}.(0.75)^{9} = 0.2581\)

0.2581 = 25.81% probability that three out of the next 12 cars need oil.

Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

Answer:

what is this ?

Step-by-step explanation:

By comparing the result obtained in Part B (6N) with the result obtained in Part A, we can see that the conjecture holds true. The result of the process is indeed related to the original number (N) by multiplying it by 6.

Part A:

Based on the given process, the conjecture that relates the result of the process to the original number (represented as N) is as follows:

Start with the original number N.

Multiply N by 4.

Add 12 to the product.

Divide the sum by 2.

Subtract 6 from the quotient.

The result of this process is the final number obtained.

Part B:

To prove the conjecture using deductive reasoning, we will follow the steps given in Part A:

Start with the original number N.

Multiply N by 12.

Add 4 to the product.

Divide the sum by 2.

Subtract 2 from the quotient.

We will simplify the steps using algebraic notation:

Step 1: N

Step 2: 12N

Step 3: 12N + 4

Step 4: (12N + 4) / 2

Step 5: [(12N + 4) / 2] - 2

Now, let's simplify Step 5:

Step 5: (12N + 4) / 2 - 2

      = (12N + 4 - 2*2) / 2

      = (12N + 4 - 4) / 2

      = 12N / 2

      = 6N

Therefore, the result of this process is 6N.

We may verify that the supposition is correct by comparing the result from Part B (6N) with the result from Part A. By multiplying the outcome by 6, the process does in fact relate to the original number (N).

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The complete question is:

Multiply the number by 4. Add 12 to the product. Divide this sum by 2. Subtract 6 from the quotient. 1st number is 3 and the results 2nd number is 6 and the results 3rd number is 8 and the results 4th number is 12 and the results part A. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as N. What is the result part b Represent the original number as N, use deductive reasoning to prove the conjecture in part (a) multiply the number by 12 and the results add 4 to the product and the results divide the sum by 2 subtract 2 from the quotient

Answer:

6/1 is what i got, is that a right answer?

Step-by-step explanation:

3/7 by 1/14

2*3/1*1 over 14 =6/1 over 14 simplified 3/7.

Answer:

\(y=-4x+5\)

Step-by-step explanation:

The equation of a line with slope \(m\) and \(y\)-intercept \((0,b)\) is \(y=mx+b\).

Answer:

PN: 15

QP: 15

Step-by-step explanation:

if QN is 30 and P is in the middle of N and Q then the distance from P must be 15

Answer:

I think it's 3.09

Step-by-step explanation:

The number of photos from Julia dance class = 5/7 or 40/56 photos.

We shall use mathematical operations to calculate the photos that are of Julia dance class

Five sevenths of the images are photos from dance class, meaning that 5/7 x 56 = 40 photos from dance class.

We express the answer as a fraction with a denominator of 56 like this:

Number of photos / Total number of photos = 40/56

Number of photos from dance class / Total number of photos = 5/7

Therefore, the fraction of photos that are of Julia dance class (as a fraction with a denominator of 56) = 5/7 or 40/56.

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Answer: 308.8

Step-by-step explanation: 38.6* 8 = 308.8

Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.

In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.

To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).

It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.

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Answer: 50

Step-by-step explanation:

5 = Fifty

6 = Six

. = decimal

1 = One tenths

3 = Three hundredth

The equation of the axis of symmetry of the parabola is x = 7.

We have,

The axis of symmetry of a parabola is a vertical line that passes through the vertex.

Now,

The equation of the axis of symmetry is the vertical line passing through the x-coordinate of the vertex.

And,

The x-coordinate of the vertex is 7.

Now,

So the equation of the axis of symmetry is x = 7.

Thus,

The equation of the axis of symmetry of the parabola is x = 7.

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Answer: False

Step-by-step explanation: If you multiply a fraction between 0 and 1 by another fraction between 0 and 1, the result would be smaller than 1.

For example,  \(\frac{3}{5} * \frac{1}{2} = \frac{3}{10}\)