Chef needs to prepare 32 Servings of cooked beans, each portion 3 oz. How 29. any 12 oz. cans should Chef order, if the Yield factor per can is 0.8 a. 8 cans b. 10 cans c. 6.4 cans d. 120 cans e. NONE of the above answers are corredt

Answer:

The term algorithm derives from the title of the Persian and Muslim mathematician of the 9th century Abu Abdullah Muhammad ibn Musa Al-Khwarizmi.

Step-by-step explanation:

The term algorithm derives from the title of the Persian and Muslim mathematician of the 9th century Abu Abdullah Muhammad ibn Musa Al-Khwarizmi. He was a mathematician, astronomer, and geographer during  Abbasid Caliphate and he was a researcher at the House of Wisdom in Baghdad.

His systematic method of analyzing linear and quadratic problems resulted in algebra. It is a title derived from all his  collection of 830 book title on the topic, "The Compendious Book on Completion and Balancing Calculation."

Answer:

Sum = 10,232

Step-by-step explanation:

The given sequence is Arithmetic Progression.

Arithmetic Progression is a sequence in which every two neighbor digits have equal distances.

For finding the sum of given series firstly we find the number of terms in given series.

For finding the nth term, we use formula

aₙ = a + (n - 1) d

where, aₙ = value of nth term

a = First term

n = number of term

d = difference

Now, In given sequence: 3+11+19+27+.....+395+403

a = 3, d = 8, aₙ = 403

∴ 403 = 3 + (n - 1) × 8

⇒ n = 51

Now, the sum of series is determined by formula,

Sₙ = n ÷ 2 [ a + l]

where l = last term

⇒ Sₙ = 51 ÷ 2 [ 3 + 403]

⇒ Sₙ = 51 × 203

⇒ Sₙ = 10,232

Final answer:

The series 3+11+19+27+.....+395+403 is an arithmetic sequence with a common difference of 8. It has 51 terms, and the sum can be found using the formula Sn = n(a1 + an) / 2, which gives us a sum of 10353.

Explanation:

To add the numbers in the series 3+11+19+27+.....+395+403, we need to recognize that this series is an arithmetic sequence, where each term increases by a common difference. In this case, the common difference is 8 (since 11 - 3 = 8, 19 - 11 = 8, and so on).

First, we need to find the number of terms in the series. We know that an arithmetic series can be expressed as ann = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the number of terms. Plugging in the values we have:

403 = 3 + (n - 1)8
400 = (n - 1)8
n - 1 = 50
n = 51

So there are 51 terms in the series. The sum of an arithmetic series is given by Sn = n(a1 + an) / 2. Plugging in the values we found:

S51 = 51(3 + 403) / 2
S51 = 51(406) / 2
S51 = 10353

Therefore, the sum of the series is 10353.

Answer:

132 games played.

Step-by-step explanation:

Let x be the

We have been given that in a baseball league consisting of 12 teams, each team plays each of the other teams twice.

Since there are 12 teams, so each team will play with [tex](12-1)[/tex] teams except itself.

The total number of games played would be 12 times [tex](12-1)[/tex]:

[tex]\text{The total number of games played}=12(12-1)[/tex]

[tex]\text{The total number of games played}=12(11)[/tex]

[tex]\text{The total number of games played}=132[/tex]

Therefore, there will be 132 games played.

The total number of games that will be played in the baseball league with 12 teams is 66.

To find the number of games that will be played in the baseball league, we need to consider that each team plays each of the other teams twice. Since there are 12 teams, each team will play 11 other teams. However, this counts each game twice (once for each team).

So, to find the total number of games, we can use the formula: Total number of games = (Number of teams * Number of teams - Number of teams) / 2.

Substituting the values, we get: Total number of games = (12 * 12 - 12) / 2 = 66.

Answer:

The correct option is b.

Step-by-step explanation:

The given function is

[tex]f(x)=-5x+1[/tex]

We need to find the value of f(-2). It means we have to find the value of given function at x=-2.

Substitute x=-2 in the given function to find the value of f(-2).

[tex]f(-2)=-5(-2)+1[/tex]

On simplification we get

[tex]f(-2)=10+1[/tex]

[tex]f(-2)=11[/tex]

The value of f(-2) is 11. Therefore the correct option is b.

Answer:

3,500,000,000

Step-by-step explanation:

The total number of human genomic characters is 3.5 billion.

Expressing this quantity numerically without using a decimal we can write it as ;

3,500,000,000

Answer:

1. ∀ y ∈ Z such that ∃ x ∈ Z, ¬R (x + y)

2. ∃ x ∈ Z, ∀ y ∈ Z such that ¬R(x + y)

Step-by-step explanation:

If we negate a quantified statement, first we negate all the quantifiers in the statement from left to right, ( keeping the same order ) then we negative the statement,

Here, the given statement,

1. ∃y ∈Z such that ∀x ∈Z, R (x + y)

By the above definition,

Negation of this statement is ∀ y ∈ Z such that ∃ x ∈ Z, ¬R (x + y),

2. Similarly,

The negation of statement ∀x ∈Z, ∃y∈Z such that R(x + y),

∃ x ∈ Z, ∀ y ∈ Z such that ¬R(x + y)

Final answer:

The negation of a mathematical statement involving existential and universal quantifiers involves switching the quantifiers and negating the inner statement. An example of a statement and its negation is 'All swans are white' and its negation 'Not all swans are white.' The law of noncontradiction implies the law of the excluded middle by rejecting the possibility of a middle ground.

Explanation:

When negating mathematical statements involving existential and universal quantifiers, the negation of an existential quantifier ∃ (there exists) becomes a universal quantifier ∀ (for all), and vice versa. Additionally, the statement inside the quantifiers gets negated. Here is the negation of each statement:

1. The original statement is ∃y ∈Z such that ∀x ∈Z, R(x + y). The negation becomes ∀y ∈Z, ∃x ∈Z such that ¬R(x + y).

2. The original statement is ∀x ∈Z, ∃y∈Z such that R(x + y). The negation becomes ∃x ∈Z, ∀y∈Z such that ¬R(x + y).

For an example of a statement and its negation: "All swans are white" is a universal affirmative statement, which can be negated to "Not all swans are white," or equivalently "There exists at least one swan that is not white."

The law of noncontradiction states that a statement and its negation cannot both be true simultaneously. The law of the excluded middle asserts that for any proposition, either the proposition is true, or its negation is true. The law of noncontradiction logically implies the law of the excluded middle, as if a statement and its negation can't both be true, then one of them must be true, rejecting the possibility of a middle ground.

Answer:

The correct answers are marked.

Step-by-step explanation:

Line k is indicated as perpendicular to RX by the little square at their point of intersection.

Congruence of different line segments will be indicated by marks on them, or by the nature of the geometry containing them (a parallelogram, for instance). There is nothing in this diagram indicating RZ is congruent to GR.

The named points, X, B, V, N, are all shown as being in plane F, so are coplanar.

A plane contains an infinite number of points. In the diagram, there are 5 named points in plane F.

The endpoint of ray RH is point R, which is on line K. However, that is the extent of their intersection. Ray RH heads off in a different direction than line k, so is not part of it.

Segment VN is in plane F; ray RH is not in the plane, but is skew to segment VN. They are not headed in the same direction.

Points R and G are both on line k, so line RG is the same as line k.

In the given figure, line K is perpendicular to RX, points X, B, V, and N are coplanar in plane F, and line RG is the same as line K.

1. Line K is perpendicular to RX:

  - This statement is true because there is a right-angle symbol (∟) at the intersection point of lines K and RX, indicating that line K is perpendicular to line RX.

2. RZ is congruent to GR:

  - There is no information or markings in the given description that suggest RZ is congruent to GR. Congruence typically requires specific markings or information about the lengths or angles of the line segments, which are not provided in this description.

3. Points X, B, V, and N are coplanar:

  - This statement is true. Coplanar points are points that lie in the same plane. In the description, it's mentioned that all these points are in plane F, so they are indeed coplanar.

4. Plane F contains six points:

  - This statement is not true. Plane F contains only five named points (R, X, B, V, N) as indicated in the description.

5. Ray RH is part of line K:

  - This statement is not true. While the endpoint of ray RH is point R, which is on line K, ray RH heads off in a different direction than line K and does not extend along line K, so it's not considered part of line K.

6. VN is headed the same direction as RH:

  - This statement is not true. Segment VN and ray RH are not headed in the same direction. VN is a line segment in plane F, while RH is a ray that extends from point R but does not align with VN.

7. Line RG is the same as line K:

  - This statement is true. Both line RG and line K coincide and are represented by the same line in the figure, indicating that they are the same line.

So, statements 1, 3, and 7 are the accurate descriptions of the figure based on the information provided.

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Answer:

Non representative

Step-by-step explanation:

A representative sample would be a subset of a population that accurately describes some characteristic from a larger group of people.

A sample of 40 patients from a local hospital is not a big enough sample to estimate the mean cholesterol level of U.S citizens (citizens from an entire country).

Therefore, this sample would be non representative.

Answer:

The improper integral converges and [tex]\int_0^{-\infty} e^{7x}dx = -\frac{1}{7}[/tex].

Step-by-step explanation:

First, I assume that the integral in question is

[tex]\int_0^{-\infty} e^{7x}dx[/tex].

Now, the integral is improper because, at least, one of the limits is [tex]\pm\infty[/tex]. We need to recall that an improper integral

[tex]\int_0^{-\infty} f(x)dx[/tex]

converges, by definition, if the following limit exist:

[tex]\lim_{A\rightarrow -\infty} \int_0^A f(x)dx = \int_0^{-\infty} f(x)dx[/tex].

In this particular case we need to study the limit

[tex]\lim_{A\rightarrow -\infty} \int_0^A e^{7x}dx[/tex].

In order to complete this task we calculate the integral [tex]\int_0^A e^{7x}dx[/tex]. Then,

[tex]\int_0^A e^{7x}dx = \frac{e^{7x}}{7}\Big|_0^A = \frac{e^{7A}}{7} - \frac{1}{7}[/tex].

Substituting the above expression into the limit we have

[tex]\lim_{A\rightarrow -\infty} \frac{e^{7A}}{7} - \frac{1}{7} = - \frac{1}{7}[/tex]

because

[tex]\lim_{A\rightarrow -\infty} \frac{e^{7A}}{7}=0[/tex].

Answer:

True

Step-by-step explanation:

Yes, In Descriptive Statistics we are most often interested in the summary of data in words. It is done by describing the features of the data. Mostly we explain the five-number summary of the data, central tendency of data, dispersion, skewness, etc. Overall we summarize the quantitative data in words.

Answer:

(a) 1:2

(b) 6 cups

(c) [tex]\dfrac{2}{3}[/tex]

Step-by-step explanation:

(a) Given,

amount of rice mixture contains= 1 cup

amount of water mixture contains= 2 cups

[tex]\textrm{So, the ratio of rice to water}\ =\ \dfrac{\textrm{amount of rice in mixturte}}{\textrm{amount of water in mixture}}[/tex]

                                                              [tex]=\ \dfrac{1}{2}[/tex]

So, the ratio of rice to water is 1:2.

(b) Amount of rice in mixture = 3 cups

[tex]\textrm{So, the ratio of rice to water}\ =\ \dfrac{\textrm{amount of rice in mixturte}}{\textrm{amount of water in mixture}}[/tex]

                      [tex]=>\ \dfrac{1}{2}\ =\ \dfrac{3}{\textrm{amount of water in mixture}}[/tex]

                       => amount of water in mixture = 3 x 2

                                                                          = 6 cups

(c) [tex]\textrm{amount of rice in mixture}\ =\dfrac{1}{3}[/tex]

 [tex]\textrm{So, the ratio of rice to water}\ =\ \dfrac{\textrm{amount of rice in mixturte}}{\textrm{amount of water in mixture}}[/tex]

   [tex]=>\ \dfrac{1}{2}\ =\ \dfrac{\dfrac{1}{3}}{\textrm{amount of water in mixture}}[/tex]

  [tex]=>\textrm{amount of water in mixture}\ =\ \dfrac{2}{3}[/tex]

So, the amount of water in the mixture will be [tex]\dfrac{2}{3}[/tex] cup.

Answer:

The general solution of the differential equation y' + 3x^2 y = 0 is:

[tex]y=e^{-x^3+C}[/tex]

Step-by-step explanation:

This equation its a Separable First Order Differential Equation, this means that you can express the equation in the following way:

[tex]\frac{dy}{dx} = f_1(x)*f_2(x)[/tex], notice that the notation for y' is changed to [tex]\frac{dy}{dx}[/tex]

Then you can separate the equation and put the x part of the equation on one side and the y part on the other, like this:

[tex]\frac{1}{f_2(x)}dy=f_1(x)dx[/tex]

The Next step is to integrate both sides of the equation separately and then simplify the equation.

For the differential equation in question y' + 3x^2 y = 0 the process is:

Step 1: Separate the x part and the y part

[tex]\frac{1}{y}dy=3x^2}dx[/tex]

Step 2: Integrate both sides

[tex]\int\frac{1}{y}dy=\int 3x^2}dx[/tex]

Step 3: Solve the integrals

[tex]Ln(y)+C=-x^3+C[/tex]

Simplify the equation:

[tex]Ln(y)=-x^3+C[/tex]

To solve the Logarithmic expression you have to use the exponential e

[tex]e^{Ln(y)}=e^{-x^3+C}[/tex]

Then the solution is:

[tex]y= e^{-x^3+C}[/tex]

Answer:

You can use the given hint as follows:

Step-by-step explanation:

Let [tex]A[/tex] be a square matrix that is a skew-symmetric matrix. Since the matrix [tex]R={\bf x}^{T}A{\bf x}[/tex] is matrix of size [tex]1\times 1[/tex] then it can be identified with an scalar. It is clear that [tex]R=R^{T}[/tex]. Then applying the properties of transposition we have

[tex]({\bf x}^{T}A{\bf x})^{T}=({\bf x}^{T})A^{T}({\bf x}^{T})^{T}={\bf x}^{T}(-A){\bf x}=-{\bf x}^{T}A{\bf x}[/tex]

Then,

[tex]{\bf x}^{T}A{\bf x}+{\bf x}^{T}A{\bf x}=0[/tex]

[tex]2{\bf x}^{T}A{\bf x}=0[/tex]

Then,

[tex]{\bf x}^{T}A{\bf x}=0[/tex]

For all column vector [tex]{\bf x}[/tex] of size [tex]n\times 1[/tex] .

Answer with Step-by-step explanation:

Part 1)

we know that

[tex]e^{i\theta }=cos(\theta )+isin(\theta )[/tex]

thus [tex]-i=e^{\frac{-i\times (4n-1)\pi }{2}}[/tex]

thus [tex](-i)^i=(e^{\frac{-i\times (4n-1)\pi }{2}})^i\\\\(-i)^i=e^{\frac{-i^2\times (4n-1)\pi }{2}}=e^{\frac{(4n-1)\pi }{2}}\\\\\therefore (-i)^i=e^{\frac{(4n-1)\pi }{2}}[/tex] where 'n' is any integer

Part 2)

We have [tex]-1=e^{(2n+1)\pi }\\\\\therefore (-1)^{i}=(e^{i(2n+1)\pi })^{i}\\\\(-1)^i=(e^{i^2(2n+1)\pi })\\\\(-1)^i=e^{-(2n+1)\pi }[/tex] where 'n' is any integer

Answer: There are 9 T.V. and 29 radio ads.

Step-by-step explanation:

Since we have given that

Total amount spend on TV and radio = $41,500

Total number of voters using the allocated funds = 148,000

Let the number of TV be 'x'.

Let the number of radio ads be 'y'.

Cost of each TV = $3000

Cost of each radio ads = $500

Number of voters see T.V. = 10,000

Number of voters use radio = 2000

So, According to question, it becomes,

[tex]3000x+500y=\$41500\implies\ 30x+5y=415\\\\10000x+2000y=148000\implies 10x+2y=148[/tex]

Using the graphing method, we get that

These two lines are intersect at (9,29).

Hence, there are 9 T.V. and 29 radio ads.

Answer:  9 TV ads and 29 radio ads will contact 148,000 voters using the allocated funds .

Step-by-step explanation:

Let x denotes the number of users of TV ads and y denotes the number of radio ads.

Then by considering the given information, we have the foolowing system of equation:-

[tex]\text{Number of voters}\ :10000x+2000y=148000----(1)\\\\\text{Total costs}\ :3000x+500y=41500------(2)[/tex]

Multiply 4 on both sides of equation (2) , we get

[tex]12000x+2000y=166000---------(3)[/tex]

Subtract (1) from (3) , we get

[tex]2000x=18000\\\\\Rightarrow\ x=\dfrac{18000}{2000}=9[/tex]

Put x= 9 , in (2), we get;

[tex]3000(9)+500y=41500\\\\\Rightarrow\ 27000+500y=41500\\\\\Rightarrow\ 500=14500\\\\\Rightarrow\ y=\dfrac{14500}{500}=29[/tex]

Hence, the number of TV ads will be 9 and the number of radio ads will will be 29.

Answer: 1000 hot dogs and and 1600 sodas were sold.

Step-by-step explanation:

Let x be the number of hot dogs and y be the number of sodas.

Given : The concession stand at an ice hockey rink had receipts of $6200 from selling a total of 2600 sodas and hot dogs.

Each soda sold for $2 and each hot dog sold for $3 .

Then, we have the following system of two linear equations:-

[tex]x+y=2600-----------(1)\\\\3x+2y=6200-----------(2)[/tex]

Multiplying 2 on both sides of (1), we get

[tex]2x+2y=5200------------(3)[/tex]

Now, Eliminate equation (3) from equation (2), we get

[tex]x=1000[/tex]

Put x=1000 in (1), we get

[tex]1000+y=2600\\\\\Rightarrow\ y=2600-1000=1600[/tex]

Hence, 1000 hot dogs and and 1600 sodas were sold.

Answer:

Maximum safe height can be reached by ladder = 15.03. ft

Step-by-step explanation:

Given,

Let's assume the maximum safe height of wall = h

angle formed between ladder and ground = 70°

length of ladder = 16 ft

From the given data, it can be seen that ladder will form a right angle triangle structure with the wall

So,from the concept of trigonometry,

[tex]Sin70^o\ =\ \dfrac{\textrm{maximum safe height of wall}}{\textrm{length of ladder}}[/tex]

[tex]=>Sin70^o\ =\ \dfrac{h}{16\ ft}[/tex]

[tex]=>\ h\ =\ 16\times Sin70^o[/tex]

=> h = 16 x 0.9396

=> h = 15.03 ft

So, the maximum safe height that can be reached by the ladder will be 15.03 ft.

Answer:

462 000mg

Step-by-step explanation:

1gram = 1000milligrams

Hence...462 grams...,

; 462 × 1000 = 462 000mg

462 grams is equal to 462,000 milligrams .

To convert grams ( g ) to milligrams ( mg ), you need to use the following conversion factor:

1 gram ( g ) = 1000 milligrams ( mg )

milligram (mg) is equal to 1/1000 grams (g).

1 mg = (1/1000) g = 0.001 g

The mass m in grams (g) is equal to the mass m in milligrams (mg) divided by 1000:

m(g) = m(mg) / 1000

This means that there are 1000 milligrams in 1 gram. Now, let's use this conversion factor to calculate 462 grams in milligrams:

462 grams * ( 1000 mg / 1 g ) = 462,000 milligrams

So, 462 grams is equal to 462,000 milligrams.

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Answer:

There is a 44.12% probability that the defective product came from C.

Step-by-step explanation:

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

-In your problem, we have:

P(A) is the probability of the customer receiving a defective product. For this probability, we have:

[tex]P(A) = P_{1} + P_{2} + P_{3}[/tex]

In which [tex]P_{1}[/tex] is the probability that the defective product was chosen from plant A(we have to consider the probability of plant A being chosen). So:

[tex]P_{1} = 0.35*0.25 = 0.0875[/tex]

[tex]P_{2}[/tex] is the probability that the defective product was chosen from plant B(we have to consider the probability of plant B being chosen). So:

[tex]P_{2} = 0.15*0.05 = 0.0075[/tex]

[tex]P_{3}[/tex] is the probability that the defective product was chosen from plant B(we have to consider the probability of plant B being chosen). So:

[tex]P_{3} = 0.50*0.15 = 0.075[/tex]

So

[tex]P(A) = 0.0875 + 0.0075 + 0.075 = 0.17[/tex]

P(B) is the probability the product chosen being C, that is 50% = 0.5.

P(A/B) is the probability of the product being defective, knowing that the plant chosen was C. So P(A/B) = 0.15.

So, the probability that the defective piece came from C is:

[tex]P = \frac{0.5*0.15}{0.17} = 0.4412[/tex]

There is a 44.12% probability that the defective product came from C.

Answer:

11.78 hours.

Step-by-step explanation:

We are asked to find the time that an "H" cylinder will last having 1350 PSI of gas in it at a flow of 6 LPM.

[tex]\text{Duration of tank (in minutes)}=\frac{\text{Tank pressure (in PSI)}\times\text{Conversion factor}}{\text{Flow (LPM)}}[/tex]

[tex]\text{Duration of H tank (in minutes)}=\frac{1350\times 3.14}{6}[/tex]

[tex]\text{Duration of H tank (in minutes)}=\frac{4239}{6}[/tex]

[tex]\text{Duration of H tank (in minutes)}=706.5[/tex]

To convert the time in hours, we will divide 706.5 by 60 as i hour equals 60 minutes.

[tex]\text{Duration of H tank (in hours)}=\frac{706.5}{60}[/tex]

[tex]\text{Duration of H tank (in hours)}=11.775[/tex]

Therefore, it will take 11.78 hours to last the given cylinder.

As per the question,

Note:

''A positive integer is any integer that is greater than zero (0)''.  Also, a positive integer is any integer that is a member of the set of natural numbers, i.e., counting numbers; therefore, the positive integers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 34, 25, 26, 27, 28, 29, 30, 31, 32, 33, ...

“Relatively Prime” (also called “co-prime”) numbers are numbers whose HCF is 1.  Any consecutive positive integers are co-prime (e.g.: 42 and 43)

Now,

First case: If n = 15

Positive integers (less than n = 15) are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 and 14.

Relatively prime are : (1 and 15), (2 and 15), (4 and 15), (7 and 15), (8 and 15),  (11 and 15), (13 and 15) and (14 and 15).

Second case: If n = 18

Positive integers (less than n = 18) are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 and 17.

Relatively prime are : (1 and 18), (5 and 18), (7 and 18), (11 and 18), (13 and 18) and (17 and 18).

Third case: If n = 22

Positive integers (less than n = 22) are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 and 21.

Relatively prime are : (1 and 22), (3 and 22), (5 and 22), (7 and 22), (9 and 22),  (13 and 22), (15 and 22),  (17 and 22),  (19 and 22) and (21 and 22).

Fourth case: If n = 30

Positive integers (less than n = 30) are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28 and 29.

Relatively prime are : (1 and 30), (7 and 30), (11 and 30), (13 and 30),

(17 and 30), (19 and 30), (23 and 30) and (29 and 30).

Fifth case: If n = 35

Positive integers (less than n = 35) are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33 and 34.

Relatively prime are : (1 and 35), (2 and 35), (3 and 35), (4 and 35), (6 and 35), (8 and 35), (9 and 35), (11 and 35), (12 and 35), (13 and 35), (16 and 35), (17 and 35), (18 and 35), (19 and 35), (22 and 35), (23 and 35), (24 and 35), (26 and 35), (27 and 35), (29 and 35), (31 and 35), (32 and 35), (33 and 35) and (34 and 35).

Answer:

0.024

Step-by-step explanation:

Given,

Red marbles = 4,

Green marbles = 7,

Total marbles = 4 +7 = 11,

Ways of choosing 3 marbles =[tex]^{11}C_3[/tex]

Ways of choosing 3 red marble = [tex]^4C_3[/tex]

Hence, the probability of 3 red marble = [tex]\frac{^4C_3}{^{11}C_3}[/tex]

[tex]=\frac{\frac{4!}{3!1!}}{\frac{11!}{3!8!}}[/tex]

[tex]=\frac{4}{165}[/tex]

≈ 0.024

Answer:

There are 4,148,350,734,528 ways

Step-by-step explanation:

We have

(a) How many ways are there to select a committee of 10 senate members with the same number of Demonstrators and Repudiators?

We want to choose 5 Demonstrators and 5 Repudiators. The number of ways to do this is [tex]{44} \choose {5}[/tex] and [tex]56 \choose 5[/tex] respectively. Therefore, the number of ways to select the committee is given by:

[tex]{{44}\choose {5}} \times {{56}\choose{5}}=\frac{44!}{39!5!}\times\frac{56!}{51!5!}=\frac{44!56!}{51!39!5!5!}=\frac{44\times43\times42\times41\times40\times56\times55\times54\times53\times52}{5!5!}=\\\\=\frac{44\times43\times42\times41\times8\times56\times11\times54\times53\times52}{4!4!}= \frac{11\times43\times42\times41\times2\times56\times11\times54\times53\times52}{3!3!}=\\\\\frac{11\times43\times14\times41\times2\times56\times11\times18\times53\times52}{2!2!}=[/tex]

[tex]11\times43\times14\times41\times28\times11\times18\times53\times52=4,148,350,734,528[/tex]

(b) Suppose that each party must select a speaker and a vice speaker. How many ways are there for the two speakers and two vice speakers to be selected?

[tex]44\times43\times56\times55=5,827,360.[/tex]

This is because there are (in the case of Demonstrators) 44 possibilities to choose an speaker and after choosing one, there would be 43 possibilities to choose a vice speaker. The same situation happens in the case of Repudiators.

[tex]5\times4\times5\times4=400[/tex].

Final answer:

To select a committee with an equal number of members from both parties, we use the combination formula to calculate the number of ways to choose 5 out of 44 Demonstrators and 5 out of 56 Repudiators, and then multiply these numbers together. For selecting speakers and vice speakers, we multiply the number of possible choices for each position within each party. The committee selection results in 4,149,395,102,528 ways, and selecting speakers and vice speakers yields 5,825,760 ways.

Explanation:

For part (a), if the committee requires an equal number of members from both parties, and we have 44 Demonstrators and 56 Repudiators, we need to select 5 members from each party to have a committee of 10 with an equal number of senators from both parties.

The number of ways to select 5 Demonstrators from 44 is given by the combination formula C(44, 5), which represents the number of ways to choose 5 members out of 44 without regard to order. Similarly, the number of ways to select 5 Repudiators from 56 is C(56, 5).

To find the total number of ways to form the committee, we multiply the two results:

The total number of ways is 1,086,008 * 3,819,416 = 4,149,395,102,528 ways.

For the selection of speakers and vice speakers, for each party, we can choose 1 speaker and 1 vice speaker. There are 44 Demonstrators, so there are 44 choices for the speaker and 43 choices for the vice speaker since the same person cannot hold both positions. Similarly, there are 56 Repudiators, so there are 56 choices for the speaker and 55 for the vice speaker.

The total number of ways to select the speakers and vice speakers for both parties is:

Final calculation: (44 * 43) * (56 * 55) = 1,892 * 3,080 = 5,825,760 ways.

Final answer:

To find the quadratic function whose graph contains the points (0, -2), (-5, -17), and (3, -17), we can substitute the x and y values of each point into the standard quadratic function equation y = ax² + bx + c...Therefore, the quadratic function whose graph contains the points (0, -2), (-5, -17), and (3, -17) is y = -x² - 2x - 2.

Explanation:

To find the quadratic function whose graph contains the points (0, -2), (-5, -17), and (3, -17), we can substitute the x and y values of each point into the standard quadratic function equation y = ax^2 + bx + c. This will give us a system of three equations with three variables (a, b, c) that we can solve to find the values of a, b, and c.

Substituting the coordinates (0, -2), we get -2 = a(0)²+ b(0) + c, which simplifies to -2 = c.

Substituting the coordinates (-5, -17), we get -17 = a(-5)² + b(-5) + c, which simplifies to -17 = 25a - 5b + c.

Substituting the coordinates (3, -17), we get -17 = a(3)² + b(3) + c, which simplifies to -17 = 9a + 3b + c.

Since we know that c = -2, we can substitute this value into the other two equations to get -17 = 25a - 5b - 2 and -17 = 9a + 3b - 2.

Simplifying these equations, we get:

25a - 5b = -15 (equation 1)

9a + 3b = -15 (equation 2)

Now we can solve this system of equations using any method such as substitution or elimination to find the values of a and b.

Multiplying equation 1 by 3 and equation 2 by 5, we get:

75a - 15b = -45 (equation 3)

45a + 15b = -75 (equation 4)

Adding equation 3 and equation 4 together, we eliminate the variable b and get:

120a = -120

Dividing both sides by 120, we get a = -1.

Substituting this value of a back into equation 1, we get:

25(-1) - 5b = -15

-25 - 5b = -15

Adding 25 to both sides, we get -5b = 10.

Dividing both sides by -5, we get b = -2.

Therefore, the quadratic function whose graph contains the points (0, -2), (-5, -17), and (3, -17) is y = -x² - 2x - 2.

Answer:

tatho you get the aswer

Step-by-step explanation:

all you have to do is add

Answer:

noice

Step-by-step explanation:

Answer:

Square of a rational number is a rational number.

Step-by-step explanation:

Let m be a rational number. Thus, m can be written in the form of  fraction [tex]\frac{x}{y}[/tex], where x and y are integers and [tex]y \neq 0[/tex].

The square of m = [tex]m\times m = m^2[/tex]

[tex]m^2 = \frac{x}{y} \times\frac{x}{y} = \frac{x^2}{y^2}[/tex]

It is clearly seen, that [tex]m^2[/tex], can be easily written in the form of fraction and the denominator is not equal to zero.

Hence, [tex]m^2[/tex] is a rational number.

This can also be understood with the help of the fact that rational numbers are closed under multiplication that is product of a rational number is also a rational number.

Answer:

Step-by-step explanation:

a) We want to prove that [tex]f^{-1}(A\cap B)\subset f^{-1}(A)\cap f^{-1}(B)[/tex]. Then, we can do that proving that every element of  [tex]f^{-1}(A\cap B)[/tex] is an element of [tex]f^{-1}(A)\cap f^{-1}(B)[/tex] too.

Then, suppose that [tex]x\in f^{-1}(A\cap B)[/tex]. From the definition of inverse image we know that [tex]f(x)\in A\cap B[/tex], which is equivalent to [tex]f(x)\in A[/tex] and [tex]f(x)\in B[/tex]. But, as [tex] f(x) \in A [/tex] we can affirm that [tex]x\in f^{-1}(A)[/tex] and, because  [tex]f(x)\in B[/tex] we have [tex]x\in f^{-1}(B)[/tex].

Therefore, [tex]x\inf^{-1}(A)\cap f^{-1}(B)[/tex].

b) We want to prove that [tex]f(A\cap B) \subset f(A)\cap f(B)[/tex]. Here we will follow the same strategy of the above exercise.

Assume that [tex]y\in f(A\cap B)[/tex]. Then, there exists [tex]x\in A\cap B[/tex] such that [tex]y=f(x)[/tex]. But, as [tex]x\in A\cap B[/tex] we know that [tex]x\in A[/tex] and [tex]x\in B[/tex]. From this, we deduce [tex]f(x)=y\in f(A)[/tex] and [tex]f(x)=y\in f(B)[/tex]. Therefore, [tex]y\in f(A)\cap f(B)[/tex].

c) Consider the constant function [tex]f(x)=1[/tex] for every real number [tex]x[/tex]. Take the sets [tex]A=(0,1)[/tex] and [tex]B=(1,2)[/tex].

Notice that [tex]A\cap B = (0,1)\cap (1,2)[/tex]=Ø, so [tex]f(A\cap B)[/tex]=Ø. But [tex]f(A) = \{1\}[/tex] and [tex]f(B) = \{1\}[/tex], so [tex]f(A)\cap f(B) =\{1\}[/tex].

Answer:[tex]x-2y-2=0[/tex]

Step-by-step explanation:

Given :

[tex]f(x) = x^2 - 4 \\ g(x) = - 3x^2 + 2x + 8[/tex]

Point of intersection :

[tex]f(x)=g(x)\\x^2-4=-3x^2+2x+8\\4x^2-2x-12=0\\2x^2-x-6=0\\2x^2-4x+3x-6=0\\2x(x-2)+3(x-2)=0\\(x-2)(2x+3)=0\\x=2\,,\,\frac{-3}{2}[/tex]

[tex]x=2\,;f(2)=2^2-4=0\\x=\frac{-3}{2}\,; f\left ( \frac{3}{2} \right )=\left ( \frac{3}{2} \right )^2-4=\frac{-7}{4}=-1.75[/tex]

So, we have points [tex]\left ( 2,0 \right )\,,\,\left ( -1.5,-1.75\ \right )[/tex]

Equation of line passing through two points [tex]\left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right )[/tex] is given by [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\left ( x-x_1 \right )[/tex]

Let [tex]\left ( x_1,y_1 \right )=\left ( 2,0 \right )\,,\,\left ( x_2,y_2 \right )=\left ( -1.5,-1.75\ \right )[/tex]

So, equation is as follows :

[tex]y-0=\frac{-1.75-0}{-1.5-2}\left ( x-2 \right )\\y=\frac{-1.75}{-3.5}\left ( x-2 \right )\\y=\frac{1}{2}(x-2)\\2y=x-2\\x-2y-2=0[/tex]

Answer:

The mileage must the new model get so that the manufacturer meets the government requirement is 59 mpg.

Step-by-step explanation:

Consider the provided information.

Here it is given that the average mpg for the four models manufactured is 24 mpg.

The total mpg for the four models = 4 × 24 = 96

The manufacturer will add a model and the government standard is 31 mpg.

This can be written as:

[tex]\frac{96+x}{5}=31[/tex]

[tex]96+x=155[/tex]

[tex]x=155-96[/tex]

[tex]x=59[/tex]

Hence, the mileage must the new model get so that the manufacturer meets the government requirement is 59 mpg.

Final answer:

The new model car must achieve 59 mpg in order for the manufacturer to meet the government requirement of an average of 31 mpg when this model is added to the existing four models that average 24 mpg.

Explanation:

The student has asked what mileage a new model car must get so that the manufacturer meets the government requirement of an average of 31 miles per gallon (mpg). Currently, the average mpg for the manufacturer's four models is 24 mpg.

To calculate the required mpg for the fifth model, we use the formula for the average of a set of numbers, which is the sum of all numbers divided by the number of items. In this case, if x is the mpg the new model needs to achieve, the equation is:

(4 ×24 + x) / 5 = 31

Which simplifies to:

96 + x = 155

Therefore:

x = 155 - 96

x = 59 mpg

The new model will need to have an efficiency of 59 mpg for the manufacturer to meet the Corporate Average Fleet Efficiency (CAFE) standard of 31 mpg.

Answer: a. 1

Step-by-step explanation:

Given : Population mean :[tex]\mu=28\ cm[/tex]

Standard deviation : [tex]\sigma=1.3\ cm[/tex]

Let n be the number of times  a beach ball with a diameter of 26.7 cm differ from the mean.

Then, we have

[tex]28-n(1.3)=26.7\\\\\Rightarrow\ 1.3n=28-26.7\\\\\Rightarrow\ 1.3 n=1.3\\\\\Rightarrow\ n=1[/tex]

Hence, a beach ball with a diameter of 26.7 cm is 1 standard deviation differ from the mean.