A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many sets of seven marbles include at least one yellow one but no green ones

Complete Question

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Answer:

The 95% confidence interval is  [tex]49.85 < \mu < 54.15[/tex]

This means that there is 95% chance that the true population mean is within this interval

Step-by-step explanation:

From the question we are told that

    The  sample size is n = 30  

    The sample mean is  [tex]\= x = 52[/tex]

    The population standard deviation is  [tex]\sigma = 6[/tex]

Given that the confidence level is 95% then the level of confidence is evaluate as

             [tex]\alpha = 100 - 95[/tex]

            [tex]\alpha = 5\%[/tex]

            [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is

                 [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

           [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

            [tex]E = 1.96 * \frac{ 6 }{\sqrt{30} }[/tex]

           [tex]E = 2.147[/tex]

The  95% confidence interval is mathematically represented as

          [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

         [tex]52 - 2.147 < \mu < 52 + 2.147[/tex]

         [tex]49.85 < \mu < 54.15[/tex]

Answer:

Step-by-step explanation:

-6x²+26x+20

=-2(3x²-13x-10)

=-2(3x²-15x+2x-10)

=-2[3x(x-5)+2(x-5)]

=-2(x-5)(3x+2)

Answer:

False

Step-by-step explanation:

Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.

Answer:

please mark my answer brainliest

Step-by-step explanation:

question is unclear to give u correct answer

Answer:

The Variable has a coefficient.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

it's simply 13 - 6

7 it the answer, that was easy

Answer:

5

----------

( n+1)(n+2)

Step-by-step explanation:

5

----------

n ( n+1)

Replace n with n+1

5

----------

(n+1) ( n+1+1)

5

----------

( n+1)(n+2)

We replace every 'n' with n+1 and simplify

[tex]\frac{5}{(n+1)(n+1+1)} = \frac{5}{(n+1)(n+2)}[/tex]

Answer: -1.33 .

Step-by-step explanation:

Formula to find the Z-score :

[tex]Z=\dfrac{\text{Expected value - Mean}}{\text{Standard deviation}}[/tex]

Given: Mean = 191  and Standard deviation = 21

Then , the z-score corresponding to the expected value of 163 will be :

[tex]Z=\dfrac{163-191}{21}\\\\=\dfrac{-28}{21}\approx-1.33[/tex]

Hence, the z score corresponding to selling 163 inhalers is -1.33 .

Answer:

Step-by-step explanation:

The graph tells you the zeros of the function are x=-3/4 and x=4.

The y-intercept is the constant in the function: 12.

The maximum is 22.5625 at x = 1.625.

Answer:

1 box of 20 and 1 box of 14

They will cost $410

Step-by-step explanation:

1. Find how many boxes of 20 DVD movies can be bought

415 - 240 = 175

1 box of 20 DVD movies can be sold

2. Find how many boxes of 14 DVD movies can be bought from $175

175 - 170 = 5

1 box of 14 DVD movies can be bought

3. Find the cost

240 + 170 = 410

Answer:

D: 450 miles

Step-by-step explanation:

So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):

[tex]0.4D=180[/tex]

This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:

[tex]0.4D=180\\D=450[/tex]

So the answer is D or 450 miles.

Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.

Answer:

James town is 5 meters higher than Takoradi​ .

Step-by-step explanation:

Given:

Height of James town = 2 meters below sea level

Height of Takoradi town = 7 meters below sea level

To find:

How much higher is James town that Takoradi = ?

Solution:

As we can see the standard of height is how much the town is below the sea level.

So, the height of town having lesser value will be at a higher level.

Value of Height of James town is lesser than that of Takoradi town.

Therefore, James town is at a higher level.

Difference of height = 7 meters - 2 meters = 5 meters

So, the answer is:

James town is 5 meters higher than Takoradi.

Answer:

Step-by-step explanation:

This problem can be solved using the compound interest formula

[tex]A= P(1+r)^t[/tex]

Given data

A, final amount =?

P, principal = $586

rate, r= 6.6% = 0.066

Time, t= 13 years

Substituting our values into the expression we have

[tex]A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87[/tex]

To the nearest cent the in 13 years the CD will be worth $1344.9

Answer:

The respiratory system extends from the nose and upper airway to the alveolar surface of the lungs, where gas exchange occurs. Inhaled tobacco smoke moves from the mouth through the upper airway, ultimately reaching the alveoli. As the smoke moves more deeply into the respiratory tract, more soluble gases are adsorbed and particles are deposited in the airways and alveoli. The substantial doses of carcinogens and toxins delivered to these sites place smokers at risk for malignant and nonmalignant diseases involving all components of the respiratory tract including the mouth.

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]q(t) = 4t^3-1\\\\(qop)(t)=q(p(t))=4\left( p(t) \right) ^3-1=4t-21\\\\p(t)^3=\dfrac{4t-21+1}{4}=\dfrac{4(t-5)}{4}=t-5\\\\p(t)=\sqrt[3]{t-5}[/tex]

Cheers.

Taking into account the definition of composite function, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].

The composite function is one that is obtained through an operation called composition of functions, which consists of evaluating the same value of the independent variable (x) in two or more functions successively.

In other words, a composite function is generally a function that is written inside another function. The composition of a function is done by substituting a function into another function.

Solving a composite function means finding the composition of two functions.

The expression of the composite function (q∘p)(t) is read "p composite with q". This means that you should do the following compound function: q[p(t)].

The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). And q(t)=4t³ – 1. Then:

s(t)= q[p(t)]

4t -21= 4[p(t)]³ – 1

Solving:

4t -21 +1= 4[p(t)]³

4t -20 = 4[p(t)]³

(4t -20)÷ 4 = [p(t)]³

4t÷4 -20÷ 4 = [p(t)]³

t -5 = [p(t)]³

[tex]\sqrt[3]{t-5}=p(t)[/tex]

Finally, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].

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Answer:

Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.

Step-by-step explanation:

First of all let's define the hypothesis;

Null hypothesis;H0; μ = $48,722

Alternative hypothesis;Ha; μ > $48,722

Now, let's find the test statistic for the z-score. Formula is;

z = (x' - μ)/(σ/√n)

We are given;

x' = 48,722

μ = 49,870

σ = 3900

n = 50

Thus;

z = (49870- 48722)/(3900/√50)

z = 2.08

So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526

This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722

Answer:

5x+4f-1(x)=3 this is short answer

Answer:

  A.  1,162.5

Step-by-step explanation:

Write the next two terms and add them up:

  S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A

================================================

Explanation:

{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5

Sn = a*(1-r^n)/(1-r)

S5 = 600*(1-0.5^5)/(1-0.5)

S5 = 1,162.5

-----------

Check:

first five terms = {600, 300, 150, 75, 37.5}

S5 = sum of the first five terms

S5 = 600+300+150+75+37.5

S5 = 1,162.5

Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.

Answer:

Lori will pay $12 more if she makes monthly payments

Step-by-step explanation:

to find how much she will pay for 6 months, we have to multiply 12 by 6 to get $72

subtracting the amount she would pay as a down payment

$72 - $60 is $12

Lori will pay $12 more if she makes monthly payments

Answer:

C

Step-by-step explanation:

An arithmetic sequence has a common difference d between consecutive terms.

Sequence a

30 - 10 = 20

90 - 30 = 60

270 - 90 = 180

This sequence is not arithmetic

Sequence b

200 - 100 = 100

300 - 200 = 100

400 - 300 = 100

This sequence is arithmetic but is finite, that is last term is 400

Sequence c

300 - 150 = 150

450 - 300 = 150

600 - 450 = 150

This sequence is arithmetic and infinite, indicated by ........ within set

Sequence d

2 - 1 = 1

4 - 2 = 2

8 - 4 = 4

This sequence is not arithmetic

Thus the infinite arithmetic sequence is sequence c

Answer:

see details in graph and below

Step-by-step explanation:

There are many ways to generate the function.

We'll generate a function whose first derivative f'(x) satisfies the required conditions, say, a quadratic.

1. f(x) has a local minimum at x = -3, and

2. a local maximum at x = 3

Therefore f'(x) has to cross the x-axis at x = -3 and x=+3.

Furthermore, f'(x) must be increasing at x=-3 and decreasing at x=+3.

f'(x) = -x^2+9

will satisfy the above conditions.

Finally f(x) must be decreasing at x= -5, which implies that f'(-5) must be negative.

Check: f'(-5) = -(-5)^2+9 = -25+9 = -16 < 0  so ok.

f(x) can then be obtained by integrating f'(x) :

f(x) = integral of -x^2+9 = -x^3/3 + 9x = 9x - x^3/3

A graph of f(x) is attached, and is found to satisfy all three conditions.

A function is differentiable at [tex]x = a[/tex], if the function is continuous at [tex]x = a[/tex]. The function that satisfy the given properties is [tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]

Given that:

The function decreases at [tex]x = -5[/tex] means that: [tex]f(-5) < 0[/tex]

The local minimum at [tex]x = -3[/tex] and local maximum at [tex]x = 3[/tex] means that:

[tex]x = -3[/tex] or [tex]x = 3[/tex]

Equate both equations to 0

[tex]x + 3 = 0[/tex] or [tex]3 - x = 0[/tex]

Multiply both equations to give y'

[tex]y' = (3 - x) \times (x + 3)[/tex]

Open bracket

[tex]y' = 3x + 9 - x^2 - 3x[/tex]

Collect like terms

[tex]y' = 3x - 3x+ 9 - x^2[/tex]

[tex]y' = 9 - x^2[/tex]

Integrate y'

[tex]y = \frac{9x^{0+1}}{0+1} - \frac{x^{2+1}}{2+1} + c[/tex]

[tex]y = \frac{9x^1}{1} - \frac{x^3}{3} + c[/tex]

[tex]y = 9x - \frac{x^3}{3} + c[/tex]

Express as a function

[tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]

[tex]f(-5) < 0[/tex] implies that:

[tex]9\times -5 - \frac{(-5)^3}{3} + c < 0[/tex]

[tex]-45 - \frac{-125}{3} + c < 0[/tex]

[tex]-45 + \frac{125}{3} + c < 0[/tex]

Take LCM

[tex]\frac{-135 + 125}{3} + c < 0[/tex]

[tex]-\frac{10}{3} + c < 0[/tex]

Collect like terms

[tex]c < \frac{10}{3}[/tex]

[tex]c <3.33[/tex]

We can then assume the value of c to be

[tex]c=3[/tex] or any other value less than 3.33

Substitute [tex]c=3[/tex] in [tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]

[tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]

See attachment for the function of f(x)

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Answer:

d. 27 cubic feet

Step-by-step explanation:

volume of cube = s^3 = B * s

volume of pyramid = (1/3) * B * h

The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.

volume of pyramid = 9 cu ft

volume of cube = 3 * 9 cu ft = 27 cu ft

Answer: d. 27 cubic feet

Answer:

27 ft^3 (Answer d)

Step-by-step explanation:

Here the volume of the pyramid is (1/3) the volume of the cube:

Letting s represent the length of one side of the base,

(1/3)(s)^2(s) = 9 ft^3, equivalent to  s^3 = 27.

Solving for s, we get s = 3 ft.

Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)

Answer:

Find a common denominator on the right side of the equation

Step-by-step explanation:

The equation before the problem is

X² + b/a(x) + (b/2a)²= -c/a + b²/4a²

The next step in solving the above equation is to fibd tge common denominator on the right side of the equation.

X² + b/a(x) + (b/2a)²= -c/a + b²/4a²

X² + b/a(x) + (b/2a)²= -4ac/4a² + b²/4a²

X² + b/a(x) + (b/2a)²=( b²-4ac)/4a²

The right side of the equation now has a common denominator

The next step is to factorize the left side of the equation.

(X+b/2a)²= ( b²-4ac)/4a²

Squaring both sides

X+b/2a= √(b²-4ac)/√4a²

Final equation

X=( -b+√(b²-4ac))/2a

Or

X=( -b-√(b²-4ac))/2a

Answer:

2·5·5·5·5

Step-by-step explanation:

2(5)^4 is equivalent to 2·5·5·5·5; 2 is used as a multiplicand just once, but 5 is used four times.

Answer:

number of nickel = 60

number of dimes  = 20

Step-by-step explanation:

1 nickel = 5 cents

1 dimes = 10 cents

$1 = 100 cents

we will use these value to solve the questions

_______________________________

Total no of coins = 80

let the number of nickels be x

let the number of dimes be y

thus,

x+y = 80

y = 80-x   equation 2

value of x nickels = 5x

value of y dimes = 10y

Total value of x nickels and y dimes = 5x+10y

The total value of the coins is $5.00

total value of the coins in cents = 5*100 = 500

thus

5x+10y = 500

using y = 80-x   from equation 2

5x + 10(80 - x) = 500

5x + 800 - 10x = 500

-5x = 500 - 800 = -300

x = -300/-5 = 60

Thus,

number of nickel = 60

number of dimes = 80-60 = 20

Answer:

sine and tangent

will be positive.

Answer:

x= 5.5

Step-by-step explanation:

(segment piece) x (segment piece) =    (segment piece) x (segment piece)

x*4 = 11*2

4x = 22

Divide each side by 4

4x/4 = 22/4

x =5.5