a survey of 500 high school students was taken to determine their favorite chocolate candy. of the 500 students surveyed, 139 like snickers, 184 like twix, 181 like reese's peanut butter cups, 129 like snickers and twix, 109 like twix and reese's peanut butter cups, 71 like snickers and reese's peanut butter cups, and 70 like all three kinds of chocolate candy. how many students like at most 2 kinds of these chocolate candies?

Answer:

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = - 120\)

Step-by-step explanation:

By the rule of Integer multiplications,

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = [ (-1) \times (-2) ] \times [(-3) \times (-4)] \times (-5)\)

                                                      \(= [2] \times [12] \times (-5)\)

                                                      \(= -120\)

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Answer:

The required number of buses=340/52=85/13buses

Step-by-step explanation:

The probability that Walmart's quality standard will be satisfied by average weight of a random sample of 10 bags of the Frito-Lay Fiery Mix Variety Pack is calculated using the properties of normal distribution.

The average weight of a random sample of 10 bags from the Frito-Lay Fiery Mix Variety Pack follows a normal distribution with the same mean as the individual bags (556.8g) but with a standard deviation equal to the original standard deviation divided by the square root of the sample size \(\(\frac{{1.2g}}{{\sqrt{10}}}\)\). To find the probability that the average weight falls within Walmart's demanded range (556g to 558g), we need to calculate the area under the normal curve between these two values.

To do this, we can standardize the values by subtracting the mean from each limit and dividing by the standard deviation of the sample mean. This will give us the z-scores for each limit. Using a standard normal distribution table or a statistical calculator, we can find the corresponding probabilities for each z-score. The probability between these two limits represents the chance that Walmart's quality standard will be satisfied.

Please note that the specific decimal value for the probability may vary depending on the z-table or calculator used, but it will typically be a small probability since the demanded range is relatively narrow.

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The normal approximation to the sampling distribution of a proportion can be used when both np and n(1-p) are greater than or equal to 10.

In this problem, we are selecting an SRS of size n=100 from a large population with a proportion p of successes. We need to find the value of p that would make it safe.

To use the normal approximation to the sampling distribution of p.

For each given value of p, we can calculate np and n(1-p), and then determine whether both of these values are greater than or equal to 10.

a) p = 0.85

np = 85, n(1-p) = 15

Both np and n(1-p) are greater than or equal to 10, so the normal approximation is safe.

b) p = 0.975

np = 97.5, n(1-p) = 2.5

Only np is greater than or equal to 10, so the normal approximation is safe.

c) p = 0.999

np = 99.9, n(1-p) = 0.1

Only np is greater than or equal to 10, so the normal approximation is safe.

d) p = 0.01

np = 1, n(1-p) = 99

Only n(1-p) is greater than or equal to 10, so the normal approximation is safe.

e) p = 0.09

np = 9, n(1-p) = 91

Only n(1-p) is greater than or equal to 10, so the normal approximation is safe.

Therefore, for all given values of p, it is safe to use the normal approximation to the sampling distribution of p.

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Answer:

4.9

Step-by-step explanation:

An equation highlighting the discount: y = (65 - 7)x

A simpler equation: y = 58x

Answer:

Minus sign & it represents that the money is a debt

Step-by-step explanation:

Quiana took a loan of $15,234.68. This is also the same amount of money that Quiana wil return to the lender.

A minus sign (-) was inserted before the amount of money that Quiana borrowed. It represents that the money is a debt that Quiana owes and she will have to return (pay back) to the lender.

The difference between consecutive first and second integers is increased by 1 thus the next number 19 - x = 5 → x = 14.

A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint.

For example 2,4,6,8 in this, the difference between any two-term is only 2 and this will be its specific pattern.

As per the given pattern,29, 28, 26, 23, 19

29 - 28 = 1

28 - 26 = 2

26 - 23 = 3

23 - 19 = 4

Since the difference is increasing by 1

So the difference of 19 and the next number (x) will be 4 + 1 = 5.

19 - x = 5

x = 14

Hence "The difference between consecutive first and second integers is increased by 1 thus the next number 19 - x = 5 → x = 14".

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The linear equation that gives the rule for this table is y = -5x + 15

The table of values is given as:

x y

1 10

2 5

3 0

4 –5

On the above table, we can see that:

As x increases by 1, the value of y decreases by 5

This means that the slope is

Slope = -5

Also, the above table can be modified as follows (using the slope of -5)

x y

0 15

1 10

2 5

3 0

4 –5

This means that the y-intercept is

y-intercept = 15

A linear equation is represented as

y = slope * x + y-intercept

So, we have

y = -5x + 15

So, the equarion is y = -5x + 15

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Step-by-step explanation:

3a-26

3(5)-26

15-26

=-11

Answer:

\(3a - 26 \\ 3 \times 5 - 26 \\ 15 - 26 \\ = - 11\)

Answer:

(3x+7)(x+5)

Step-by-step explanation:

i think lol

Answer:

x = 19, ARC MP = 104º

Step-by-step explanation:

9x-43 = 5x+33

4x = 76

x = 19

Arc MP = 360 - (9x-43 + 5x+33)

Arc MP = 360 - (9(19)-43 + 5(19)+33)

= 360 - 256

MP = 104º

The scalar product of the given vectors is -2.

Given that a = 3i - k and

b = i + j + 5k

We are to find a⋅b.

To calculate a⋅b, we need to calculate the dot product of the two vectors.

Here's how we can calculate the dot product of a and b:

a⋅b = (3i - k)⋅(i + j + 5k)

= 3i⋅i + 3i⋅j + 3i⋅5k - k⋅i - k⋅j - k⋅5k

Taking the dot product of i⋅i = 1,

j⋅k = 0, and

k⋅k = 1, and substituting the values we get:

3i⋅i

= 3i²

= 3k⋅i

= -k⋅i

= -11 ⋅ 0

= 0

Thus, a⋅b = 3i⋅i + 3i⋅j + 3i⋅5k - k⋅i - k⋅j - k⋅5

k= 3i² + 3i⋅j - 5k

= 3(1) + 3(0) - 5(1)

= -2

Therefore, a⋅b = -2.

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The result of the expression [(282.3×105)−(1.300×103)]×2.8978, expressed with the appropriate number of significant digits, is approximately 8.16×10^7.

The given expression [(282.3×105)−(1.300×103)]×2.8978 involves multiplication and subtraction operations. To express the answer with the appropriate number of significant digits, we need to consider the significant figures in the original numbers and apply the rules of significant digits during the calculations.

The result of the expression, considering significant digits, is approximately 8.16×10^7. This value is rounded to three significant digits to maintain consistency with the significant figures in the original numbers and the multiplication factor.

When performing calculations with significant digits, it is important to carry forward the precision of the least precise number involved in the calculation to avoid introducing additional inaccuracies.

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Answer:

i think d or a

Step-by-step explanation:

Answer:

52 hours and 25 min

Step-by-step explanation:

2 1/2+45+4.75= 52.25

Answer:

Step-by-step explanation:

Your difference of perfect cubes formula is given as

\((a-b)(a^2+ab+b^2)\) and you have already correctly identified a as \(5q^2\)  and b as \(r^2s\). So we fill in the formula as follows:

\((5q^2-r^2s)((5q^2)^2+(5q^2)(r^2s)+(r^2s)^2)\) and we simplify.  Remember that

\((5q^2)^2=(5)^2*(q^2)^2=25q^4\). It's important that you remember the rules.

Simplifying then gives us

\((5q^2-r^2s)(25q^4+5q^2r^2s+r^4s^2)\)

That's it, so fill it in however you need to on your end. Learn the patterns for the sum and difference of cubes and it will save you a ton of headaches...promise!!

Step-by-step explanation:

I'll just give you 2 examples if you need a better understanding tell me

1) 2 * 2/4

a. First make 2 --> 2/1 so it's a fraction

b. Multiply 2 by 2 giving you 4

c. Multiply 1 by 4 giving you 4

d. You'll get 4/4

e. Simplify to 1 by dividing by the numerator and denominator 4

Answer : 1

2) 3 * 4/6

a. First make 3 --> 3/1 so it's a fraction

b. Multiply 3 by 4 giving you 12

c. Multiple 1 by 6 giving you 6

d. You'll get 12/6

e. Simiply to 2 by dividing the numerator and denominator by 6

Answer : 2

Mauricio takes 24 hours, and Alyson takes 24/5 hours if the Mauricio does a job in 6 hrs less time than Alyson.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

Let x and y be the time to take the job for Mauricio and Alyson respectively

1/x = 1/y - 1/6 ..(1)

1/x + 1/y = 1/4 ..(2)

After solving the equations:

\(\rm \dfrac{1}{\dfrac{6y}{6-y}}+\dfrac{1}{y}=\dfrac{1}{4}\)

y = 24/5 hours

x = 24 hours

Thus, Mauricio takes 24 hours, and Alyson takes 24/5 hours if Mauricio does a job in 6 hrs less time than Alyson.

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Answer:

2x-3y-6=0

Step-by-step explanation:

move the constant to the left hand side and change its sign (-2x+3y+6=0)

change the signs on both sides of the equation (2x-3y-6=0)

hope this helps, have great day! :)

The statement "System analysts define an object's attributes during the systems design process" is true because  defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.

In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.

For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.

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The equation can you use to find the distance of the flowerbed from the hive  is  mathematically given as

(a)Equation is \frac{d}{10}+\frac{d}{6}=240 (\(\frac{d}{10}+\frac{d}{6}=240\))

(b)900ft

Generally, the equation for is  mathematically given as

The distance between the flower bed and the hive should be d.

11 seconds have passed during the bee's visit to the flower bed.

15 seconds is the amount of time the bee is away from the colony.

The time it took for the bees to travel from the hive to the flower bed and then back again;

t=4*60

t=240 seconds

The formula for calculating time is distance multiplied by speed.

The duration of my terror was 240 seconds.

Create an expression for the amount of time spent flying;

The amount of time needed to fly from the hive to the flowerbed is equal to d/10ft/s.

\(=\frac{d}{10}+\frac{d}{6}=240\)

\(\begin{aligned}&=\frac{3 a+5 a}{30}=240 \\&=\frac{8 d}{30}=240\end{aligned}\)

8 d=240 * 30

8 d=7200

\(d=\frac{7200}{8}=900 \mathrm{ft}\)

(a) Equation is

\(\frac{d}{10}+\frac{d}{6}=240\)

In conclusion,

(b) The distance between the flower bed and the hive is 900 feet.

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a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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Using the limit definition of partial differentiation,

lim (x,y) → (0,0) 5x²y/(x² + y²) = 0 is correct.

Given f(x, y) = 5x²y/(x² + y²), f(x, y) = 0 at (x, y) = (0, 0).

Let's find the partial derivatives of f at (0, 0):

fx (0, 0) = lim(h→0) [f(h, 0) - f(0, 0)]/h

fx (0, 0) = lim(h→0) [5h²*0]/h = 0

Similarly, fy (0, 0) = lim(h→0) [f(0, h) - f(0, 0)]/h

fy (0, 0) = lim(h→0) [50h²]/h = 0

Hence, both fx and fy exist.

Let's check the continuity of f at (0, 0):

Along the line y = x,

f(x, x) = 5x⁴/(2x²) = 5x²/2

f(x, x) → 0 as x → 0

Along the curve y = x²,

f(x, x²) = 5x⁴/(x² + x⁴) = 6x⁴

f(x, x²) → 0 as x → 0

Therefore, f is continuous at (0,0).

Therefore, lim f(x, y) = 0. (x,y) →(0,0)

Therefore, using the limit definition of partial differentiation,

lim (x,y) → (0,0) 5x²y/(x² + y²) = 0 is correct.

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Using the limit definition of partial differentiation,

lim (x,y) → (0,0) 5x²y/(x² + y²) = 0 is correct.

Given f(x, y) = 5x²y/(x² + y²), f(x, y) = 0 at (x, y) = (0, 0).

Let's find the partial derivatives of f at (0, 0):

\(f_x (0, 0)\) = lim(h→0) [f(h, 0) - f(0, 0)]/h

\(f_x (0, 0)\) = lim(h→0) [5h²*0]/h = 0

Similarly, \(f_y (0, 0)\) = lim(h→0) [f(0, h) - f(0, 0)]/h

\(f_y (0, 0)\) = lim(h→0) [50h²]/h = 0

Hence, both \(f_y\) and \(f_y\) exist.

Let's check the continuity of f at (0, 0):

Along the line y = x,

f(x, x) = 5x⁴/(2x²) = 5x²/2

f(x, x) → 0 as x → 0

Along the curve y = x²,

f(x, x²) = 5x⁴/(x² + x⁴) = 6x⁴

f(x, x²) → 0 as x → 0

Therefore, f is continuous at (0,0).

Therefore, lim f(x, y) = 0. (x,y) →(0,0)

Therefore, using the limit definition of partial differentiation,

lim (x,y) → (0,0) 5x²y/(x² + y²) = 0 is correct.

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The 8.4 inches length of g and the 79° and 25° measures of the angles ∠G and ∠E, using the law of sines, indicates that the length of the side  EG = f is about 8,3 inches.

The law of sines states that the ratio of the sine of an interior angle of a triangle to the length of the opposite side to the angle is the same for the three sides and angles in a triangle.

Mathematically, the law of sines can be presented as follows;

\(\dfrac{a}{sin(A)} = \dfrac{b}{sin(B)} =\dfrac{c}{sin(C)}\)

Where;

a, b, and c are the length of each of the sides of the triangle, and ∠A, ∠B, and ∠C are the measure of each of the interior angles of the triangle.

The details of the triangle ΔEFG, specifying the side g as the side opposite the angle ∠G, and the side f as the side opposite the ∠F we get;

The length of EF = g = 8.4 inches

Length of EG = f

The angle sum property of a triangle indicates that we get;

∠E + ∠F + ∠G = 180°

∠F = 180° - (∠E  + ∠G)

∠F = 180° - (25°  + 79°) = 76°

According to the law of sines, we get;

8.4/(sin(79°) = f/(sin(76°))

f = (sin(76°)) × 8.4/(sin(79°) ≈ 8.3

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The probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.

To find the probability that a random student will be taking both Algebra 2 and Chemistry, we need to use the concept of conditional probability.

Let's denote the event of taking Algebra 2 as A and the event of taking Chemistry as C. We are given that P(A) = 0.08 (8% probability of taking Algebra 2) and P(C|A) = 0.17 (17% probability of taking Chemistry given that the student is taking Algebra 2).

The probability of taking both Algebra 2 and Chemistry can be calculated using the formula for conditional probability:

P(A and C) = P(C|A) * P(A)

Substituting the given values:

P(A and C) = 0.17 * 0.08

P(A and C) = 0.0136

Therefore, the probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.

It is important to note that the probability of taking both Algebra 2 and Chemistry is determined by the intersection of the two events, which means students who are taking both courses. In this case, the probability is relatively low, as it depends on the individual probabilities of each course and the conditional probability given that a student is taking Algebra 2.

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For spinning the spinner one time A could be {1, 2, 3} or, A = {1, 2, 3, 4} is possible.

The set is mathematical model for a collectionof different things;a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables or even other sets.

The given spinner is divided into 8 equal sized sections, so the possible set can be written as-

S = {1, 2, 3, 4, 5, 6, 7, 8}

Now the possible subsets can be-

Even numbers = {1,3,5,7}

Odd numbers = {2,4,6,8}

Any number or group from 1 to 8, inclusive

Hence for spinner the spinner for one time, suppose A be the possible set. Then,

    A could be {1, 2, 3}.

or, A = {1, 2, 3, 4}.

where A is the subset of S.

Hence, For spinning the spinner one time A could be {1, 2, 3} or, A = {1, 2, 3, 4} is possible.

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