7 women and 8 men are on the faculty in the mathematics department at a school. how many ways are there to select a committee of five members of the department if at least one woman and at least one man must be on the committee?

Answer:

2n+4y+14

Step-by-step explanation:

Answer:

So we are going to Simplify 2n+6+4y+8

First thing we add the numbers:

2n+6+4y+8=

2n+14+4y=

Which equals

2n+4y+14

Answer :

2n+4y+14

Answer:

Collinear because the points are all connected to each other

Noncollinear would be like Point G, I, and B (Because they're separated)

Step-by-step explanation:

Answer:

a = 3

b = 1

c = 5

d = 2

Step-by-step explanation:

To find the prime factorization of 600, we can use trial division by dividing by the smallest prime numbers until we reach a prime factor:

600 ÷ 2 = 300

300 ÷ 2 = 150

150 ÷ 2 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

Therefore, the prime factorization of 600 is:

600 = 2^3 × 3^1 × 5^2

So, a = 3, b = 1, c = 5, and d = 2.

The null hypothesis states that the proportion of users suffering side effects is less than or equal to 3%, while the alternative hypothesis suggests that the proportion is greater than 3%. A one-sided alternative is used because the concern is about an increase in side effects

a) The hypotheses for this claim can be stated as follows:

Null hypothesis (H0): The proportion of users suffering side effects (p) is less than or equal to 3% (p ≤ 0.03).

Alternative hypothesis (Ha): The proportion of users suffering side effects (p) is greater than 3% (p > 0.03).

A one-sided alternative is used because the concern is specifically about an increase in side effects.

b) To perform the hypothesis test, the test statistic is calculated using the provided data. In this case, the sample proportion of subjects suffering side effects is 23/440 = 0.0523. The test statistic is then determined based on the assumed conditions being met (e.g., large sample size). Using the binomial distribution, the test statistic can be approximated using a normal distribution. With α = 0.05, the critical value is obtained from the standard normal distribution. The test statistic is compared to the critical value to make a decision. If the test statistic exceeds the critical value, the null hypothesis is rejected in favor of the alternative hypothesis.

c) If the conclusion was found to be incorrect, it would imply making an error in the hypothesis test. Specifically, it would either be a Type I error or a Type II error.

d) In this situation, a Type I error would be more serious. A Type I error occurs when the null hypothesis is incorrectly rejected, suggesting that stronger warning labels are needed when, in fact, the proportion of users suffering side effects is not significantly higher than 3%. This would result in unnecessary warnings, potentially causing undue concern or unnecessary restrictions on ibuprofen use.

e) A 95% confidence interval for the proportion of subjects who will suffer side effects can be calculated using the sample proportion and the standard error. The confidence interval provides a range of values within which the true population proportion is likely to fall. The formula for the confidence interval is: sample proportion ± (critical value * standard error). The critical value can be obtained from the standard normal distribution based on the desired confidence level. The standard error is calculated as the square root of (p(1-p)/n), where p is the sample proportion and n is the sample size.

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Answer:

are equal to 180 degrees

Step-by-step explanation:

If you want to invest $1000, there are at least two terms (variables) you would consider regarding your investment. These terms are the interest rate and the length of time you will invest your money.

The first term, the interest rate, will affect how much you will earn because it determines the amount of money you will receive in return for your investment. A higher interest rate will result in a higher return on your investment, while a lower interest rate will result in a lower return.

The second term, the length of time you will invest your money, will also affect how much you will earn. The longer you invest your money, the more interest you will accumulate and the more money you will earn.

In conclusion, if you want to invest $1000, you should consider the interest rate and the length of time you will invest your money as these two terms (variables) will affect how much you will earn.

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Answer:

1, 2, and 4 are true statements.

Step-by-step explanation:

1. The positive symbols will become negative once you removed the parenthese. For instance, 2-(3+2)=2-3-2. It’s the same in this problem. 4-2(3+7)=4-(2•3+2•7)=4-2•3-2•7

2. Distributive property. 4-2(3+7)=4+[-2(3+7)]=4+(-2•3+-2•7)

3 is false because the positive symbol is not changed into negative symbol after the parentheses were removed.

4. 4-2(3+7)=4-[2(3+7)]=4-(2•3+2•7)

Answer:

the common difference is 1/3.

it is a arithmetic progression.

If the inflation rate is 180%, the average prices will double in less than one year.

This is because inflation measures the increase in the prices of goods and services over a period of time. Therefore, the formula for calculating how many years it will take for average prices to double at a given inflation rate is:Years to double = 70/inflation rate

In this case, the inflation rate is 180%.

Therefore:Years to double = 70/180%

Years to double = 0.389 years

This means that average prices will double in approximately 4.67 months (0.389 years multiplied by 12 months per year).

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Answer:

have a good day

Step-by-step explanation:

rump 2020

The probability that car A, car B, car C, and car D are used is 0.2. This is calculated by dividing the number of favorable outcomes (1) by the total number of possible combinations (5).

To find the probability that car A, car B, car C, and car D are used, we need to determine the total number of possible combinations and the number of favorable outcomes.

1. The total number of possible combinations can be found using the formula for combinations:

nCr = n! / r!(n-r)!
2. In this case, we have 5 cars available and need to select 4 cars, so the total number of combinations is 5C4 = 5! / 4!(5-4)! = 5.
3. The number of favorable outcomes is 1, as we want car A, car B, car C, and car D to be used together.
4. The probability is given by the number of favorable outcomes divided by the total number of possible combinations:

1/5 = 0.2.
The probability that car A, car B, car C, and car D are used is 0.2. This is calculated by dividing the number of favorable outcomes (1) by the total number of possible combinations (5).

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Equilibrium is the term refers to coordination, balance, and balance in three dimensional space.

The equilibrium condition of an object exists when Newton's first law is valid. An object is in equilibrium in a reference coordinate system when all external forces (including moments) acting on it are balanced. This means that the net result of all the external forces and moments acting on this object is zero.

There are three types of equilibrium: stable, unstable, and neutral.

Examples of equilibrium in everyday life:

A book kept on a table at rest. A car moving with a constant velocity. A chemical reaction where the rates of forward reaction and backward reaction are the same.

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To compute the values of (r) and (x) for the different states of the harmonic oscillator, we need to consider the wavefunction solutions for each state.

The wavefunctions for the harmonic oscillator are given by Hermite polynomials multiplied by a Gaussian factor. The energy eigenvalues for the harmonic oscillator are given by (n + 1/2) * h * ω, where n is the quantum number and ω is the angular frequency of the oscillator. (a) Ground State: The ground state of the harmonic oscillator corresponds to n = 0. The wavefunction for the ground state is: ψ₀(x) = (mω/πħ)^(1/4) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₀) is equal to 1/2 * h * ω. Therefore, for the ground state: (r) = 0 (since n = 0). (x) = √(ħ/(2mω)). (b) First Excited State:The first excited state corresponds to n = 1. The wavefunction for the first excited state is: ψ₁(x) = (mω/πħ)^(1/4) * √2 * (mωx/ħ) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₁) is equal to 3/2 * h * ω. Therefore, for the first excited state: . (r) = 1. (x) = √(ħ/(mω)). (c) Second Excited State:The second excited state corresponds to n = 2. The wavefunction for the second excited state is: ψ₂(x) = (mω/πħ)^(1/4) * (2(mωx/ħ)^2 - 1) * exp(-mωx²/2ħ)  where m is the mass of the oscillator. In this state, the energy (E₂) is equal to 5/2 * h * ω.

Therefore, for the second excited state: (r) = 2. (x) = √(ħ/(2mω)). In summary: (a) Ground State: (r) = 0, (x) = √(ħ/(2mω)). (b) First Excited State: (r) = 1, (x) = √(ħ/(mω)). (c) Second Excited State: (r) = 2, (x) = √(ħ/(2mω)).

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There are 715 ways to select 9 players for the starting lineup.

Permutation is used whenever there is arrangement or where order is important . denoted by \(P(n,r)=\frac{n!}{(n-r)!}\)

n= no of item  , r = no of items to be arranged.

Combination is used when there is selection . denoted by\(C(n,r)=\frac{n!}{r!(n-r)!}\)

n=no of item  , r= no of item to be selected.

Part (a)

In the given question

we have to select 9 players out of 13 player , combination will be used

\(C(13,9)=\frac{13!}{9!*(13-9)!}=\frac{13*12*11*10*9!}{9!*4!} =\frac{13*12*11*10}{4*3*2}\)=715 ways.

Part(b)

In this part we have to find how many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters.

Since the batting order is important , permutation will be used.

\(P(13,9)=\frac{13!}{4!} =\frac{13*12*11*10*9*8*7*6*5*4!}{4!} =13*12*11*10*9*8*7*6*5\)

=259459200 ways.

Part(c)

In this part we have to do selection of  3 left-handed outfielders and have all other 6 positions occupied by right-handed players.

Since order is not important Combination  will be used.

To select 3 left handers from total 6 left handers = C(6,3)

& to select 6 positions of left handers from remaining 7 right handers=C(7,6)

No of ways of selection = C(6,3)*C(7,6)

\(=\frac{6!}{3!*(6-3)!} *\frac{7!}{6!*(7-6)!} \\ \\= \frac{6!}{3!*3!} *\frac{7!}{6!*1!} \\ \\\)

On solving further we get

\(= \frac{7!}{3!*3!} =\frac{7*6*5*4*3!}{3!*3*2*1} =7*5*4=140ways\)

Therefore ,(a)There are 715 ways to select 9 players for the starting lineup.

(b) there are 259459200 ways to to select 9 players for the starting lineup and a batting order for the 9 starters and 140 ways .

(c)there are 140 ways to select 3 left-handed outfielders and have all other 6 positions occupied by right-handed players.

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Speed is given by Distance/ Time taken

The Velocity is 7.27m/s in the direction of the runner

Answer:

Step-by-step explanation:

all values are true

Answer:

5

120

20

Step-by-step explanation:

Answer:

Step-by-step explanation:

As per the given simple interest, the principal amount is $165.35.

The term simple interest in math is defined as  the interest charge on borrowing that's calculated using an original principal amount only and an interest rate that never changes.

Here we have given that If the simple interest on a sum of a money invested at 3. 5% per annum for 44 years is birr 420.

Therefore, through the given question we have identified the value of

interest rate = 3.5%

time period = 44

sum amount = 420.

Then the principal amount is calculated by using the formula of simple interest as,

P = A / (1 + rt)

Here first we have to convert R percent to r a decimal, then we get

r = R/100 = 3.5%/100 = 0.035 per year.

Now, we have to apply the values on the equation and then we have to solve our equation, then we get

P = 420 / ( 1 + (0.035 × 44)) = 165.35433070866

P = $165.35

Therefore, the principal investment required to get a total amount, principal plus interest, of $420.00 from simple interest at a rate of 3.5% per year for 44 years is $165.35.

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Point C

Hope This helps!! : }

The point D represents the product of the three integers.

Number line is defined as the straight line drawn horizontally where the integers are placed at an equally spaced way.

Integers includes natural numbers, 0 and negative of the natural numbers.

Given is the three numbers 5, -2 and -1.

We have to find the product of these three numbers.

When multiplying integers, negative multiplied to negative and positive multiplied to positive gives positive. If one of the number is negative and other is positive, then the result is negative.

(5) (-2) (-1) = (5 × -2) (-1)

                = (-10) (-1)

                = 10

Hence the product of the three integers 5, -2 and -1 is 10 which is marked as point D on the number line.

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Answer:

7.50x + 12.50y = 300

Step-by-step explanation:

Answer:

y - 7 = (-2/3)(x + 3)

Step-by-step explanation:

Two points on the line are given:  (-3, 7) and (3, 3).  The change in x as we go from the first point to the second is 6 and that in y is -4.  Thus the slope of this line is

          rise

m = ------------ = -4/6 = -2/3

          run

Now we know the slope of this line and can choose either point as a point on the line.  Using the point-slope formula y - k = m(x - h), we get:

y - 7 = (-2/3)(x - [-3], or

y - 7 = (-2/3)(x + 3)

To determine the area of the trapezoid we need to use the following expression:

Applying the dimmensions given in the problem we can calculate the area as shown below:

The area of the trapezoid is 18 square inches.

zw in polar form is zw = 24√2(cos(75°) + i*sin(75°)).

z/w in polar form is z/w = (4√2/3)(cos(-15°) + i*sin(-15°)).

1/z in polar form is 1/z = (1/8)(cos(-30°) + i*sin(-30°)).

Now that we have z and w in polar form, we can find the polar forms for the products and reciprocal of these complex numbers.

Product (zw): To multiply two complex numbers in polar form, we multiply their magnitudes and add their arguments. Applying this to z and w, we have: zw = 8(cos(30°) + isin(30°)) * 3√2(cos(45°) + isin(45°))

Multiplying the magnitudes: |zw| = 8 * 3√2 = 24√2

Adding the arguments: θzw = 30° + 45° = 75 degrees

Therefore, zw in polar form is zw = 24√2(cos(75°) + i*sin(75°)).

Division (z/w): To divide two complex numbers in polar form, we divide their magnitudes and subtract their arguments. Applying this to z and w, we have: z/w = 8(cos(30°) + isin(30°)) / 3√2(cos(45°) + isin(45°))

Dividing the magnitudes: |z/w| = 8 / (3√2) = 8 / 3√2 = 8 / (3 * √(2)) = (8 / 3) * (1 / √(2)) = (8 / 3) * (√(2) / 2) = (4√2) / 3

Subtracting the arguments: θz/w = 30° - 45° = -15 degrees

Thus, z/w in polar form is z/w = (4√2/3)(cos(-15°) + i*sin(-15°)).

Reciprocal (1/z): To find the reciprocal of a complex number in polar form, we take the reciprocal of its magnitude and negate its argument. Applying this to z, we have: 1/z = 1 / [8(cos(30°) + i*sin(30°))]

Taking the reciprocal of the magnitude: |1/z| = 1 / 8 = 1/8

Negating the argument: θ1/z = -30°

Hence the 1/z in polar form is 1/z = (1/8)(cos(-30°) + i*sin(-30°)).

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Answer:

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 3 3

Step-by-step explanation:

9514 1404 393

Answer:

  a. 123.2 cm²

  b. 136 m²

Step-by-step explanation:

Use the formulas.

a) The formula is ...

  SA = 2πr(r+h) . . . . where r is half the diameter, and h is the height.

  SA = 2π(2 cm)(2 cm +7.8 cm) = 2·2·9.8π cm² = 123.2 cm²

__

b) The formula is ...

  SA = 2(LW +H(L+W))

  SA = 2((8 m)(3 m) +(4 m)(8 m +3 m)) = 2(24 m² +44 m²) = 136 m²

_____

For the cylinder, we used the "pi button" and rounded to tenths. If you use 3.14 for π, you get 123.1 cm² when rounded to tenths.

Answer:

\(\text{a. }123.2\:\mathrm{cm^2},\\\text{b. }136\:\mathrm{m^2}\)

Step-by-step explanation:

Part A:

The total surface area of the cylinder consists of two circular bases and a side area. The area of a circle is given by \(A=r^2\pi\), where \(r\) is the radius of the circle. Since the diameter is given as 4 cm, the radius must be 2 cm.

Area of two circular bases: \(2\cdot 2^2\pi=8\pi=25.1327412287\)

Area of side: \(7.8\cdot 2\cdot 2\cdot \pi=31.2\pi=98.017690792\)

Therefore, the cylinder's total surface area is \(25.1327412287+98.017690792=123.150432021\approx \boxed{123.2\:\mathrm{cm^2}}\)

Part A:

The total surface area of a rectangular prism with width \(w\), length \(l\), and height \(h\) is given by \(2(hl+hw+lw)\).

Thus, the total surface area of the rectangular prism is \(2(4\cdot 8+4\cdot 3+8\cdot 3)=2(32+12+24)=2(68)=\boxed{136\:\mathrm{m^2}}\)