There is a bag filled with 3 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?

Answer:

D

Step-by-step explanation:

We want to find the difference between the two polynomials:

[tex](5x^3+4x^2)-(6x^2-2x-9)[/tex]

Distribute the negative:

[tex]=(5x^3+4x^2)+(-6x^2+2x+9)[/tex]

Rearrange the terms:

[tex]=(5x^3)+(4x^2-6x^2)+(2x)+(9)[/tex]

Combine like terms. Hence:

[tex]=5x^3-2x^2+2x+9[/tex]

Our answer is D.

Answer:

Option D, 55.45 to 70.95

Step-by-step explanation:

Alpha = 1 – confidence interval  

Alpha = 1 – 0.98 = 0.02

Sample size = n = 8

t (alpha/2) ; (n-1) = t (0.02/2) ; (8-1) = t 0.01, 7 = 2.998

Mean = sum of all frequencies /total number of frequency = 505.6/8 = 63.2

s = 7.309

E = t (0.01;7) * s/sqrt n

Substituting the given values, we get –  

E = 2.998 * 7.309 /sqrt  (8)

E = 7.75  

98% confidence interval  

Mean – E  and Mean + E

63.2 – 7.75 and 63.2 + 7.75  

(55.45, 70.95)

Answer: 55.45 to 70.95

Step-by-step explanation:

Answer:

(-1, 5/2)

Step-by-step explanation:

Midpoint = (-4 + 2)/ 2 ,  (6 - 1)/2

= (-2/2), (5/2)

= (-1, 5/2)

Answer:

Step-by-step explanation:

The midpoints of two coordinate is = [tex]\frac{x2 + x1}{2}[/tex] , [tex]\frac{y2 +y1}{2}[/tex].

Let x2 = 2

x1 = -4

y2 = -1

y1 = 6

Solution:

[tex]\frac{2+-4}{2} , \frac{-1+6}{2} \\\\\\= (-1,\frac{5}{2})[/tex]

Answer:

26,812 ft

Step-by-step explanation:

The drawing given is very helpful in this case.  When solving problems like this, it's important to realize what trigonometric ratio we're going to use.  From the given angle (50°), we are given the hypotenuse (35,000 ft) and we're trying to solve for the opposite side ([tex]a[/tex]).  

So since we're trying to find the opposite side side and we have the hypotenuse, we should try to find a trigonmetric ratio between the opposite side and the hypotenuse.  Using SOH-CAH-TOA, hopefully you can see that we should pick SOH (i.e. [tex]\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]).  Therefore, we can set up our equation given the angle [tex]\theta=50^\circ[/tex].  

[tex]\sin(50^\circ)=\frac{a}{35000}[/tex]

Since we're solving for [tex]a[/tex], we can just rearrange to get [tex]a=35000\sin(50^\circ)=26812[/tex]

Therefore, the plane's altitude [tex]a[/tex] is 26,812 ft.

The approximation altitude of the plane at 35,000 feet from an air traffic control tower will be 26812 feet hence option (B) will be correct.

the trigonometric functions are real functions for only an angle of a right-angled triangle to ratios of two side lengths.

The domain input value for the six basic trigonometric operations is the angle of a right triangle, and the result is a range of numbers.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

Given that 35000 feet are the distance between a plane and the air traffic control tower.

Hypotaneous =  35000 feet

The angle of elevation is 50°

By trigonometric function sin

Sinx = perpendicular/hypotaneous

Sin50° = Altitude/35000

Altitute = 35000 × sin50°

Altitude = 26811.55 ≈ 26812 feet will be the correct answer.

For more information about the trigonometric function

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Answer:

6.27

Step-by-step explanation:

We are to obtain the standard deviation of the given values :

{24, 18, 31,25, 34}

The standard deviation = √(Σ(x - mean)²/ n)

The mean = (ΣX) /n

Using calculator to save computation time :

The standard deviation, s = 6.27 (2 decimal places)

Answer:

77

Step-by-step explanation:

Answer:

z (min) = 360      x₁  =  x₃ = 0   x₂ = 3

Step-by-step explanation:

                             Protein      Carbohydrates    Iron      calories

Food 1  (x₁)               10                       1                   4              80

Food 2 (x₂)               15                       2                  8              120

Food 3 (x₃)               20                       1                  11              100

Requirements         40                        6                 12

From the table we get

Objective Function z :

z  =  80*x₁   +  120*x₂   +   100*x₃     to minimize

Subjet to:

Constraint 1.  at least 40 U of protein

10*x₁  +  15*x₂ + 20*x₃  ≥  40

Constraint 2. at least  6 U of carbohydrates

1*x₁  +  2*x₂  + 1*x₃    ≥  6

Constraint 3.  at least  12 U of Iron

4*x₁   +  8*x₂  +  11*x₃  ≥  12

General constraints:

x₁    ≥  0     x₂   ≥  0    x₃   ≥  0    all integers

With the help of an on-line solver after 6 iterations the optimal solution is:

z (min) = 360      x₁  =  x₃ = 0   x₂ = 3

Answer:

-3.5, -3, -1, 3, 4.5

Step-by-step explanation:

Answer:

-3.5, -3, -1, 3, 4.5 because the higher the negative is, the lower the number.

The following statistics which would provide a good comparison between data sets is all of the above and is denoted as option A.

This refers to the branch of science which involves the collection and interpretation of data sets or variables. There are different ways or techniques which are used and they vary according to the features of the data set.

There are statistics which provide a good comparison between data sets include the following below:

This comparison is done so as to to prove that there are no differences between them and other reasons.

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Answer: A) (x + 12) and (x + 9)

Step-by-step explanation:

You need to get x^2 + 21x + 108.

A) (x + 12) (x + 9) = x^2 + 12x + 9x + 108 = x^2 + 21x + 108

B) (x - 12) (x - 9) = x^2 - 9x - 12x + 108 = x^2 -21x + 108

C) (x - 27) (x - 4) = x^2 - 4x - 27x + 108 = x^2 - 31x + 108

D) (x + 27) (x + 4) = x^2 + 27x + 4x + 31 = x^2 + 31x + 31

So, the answer is A).

Answer:

9

Step-by-step explanation:

the only thing we can say for sure is that JL is splitting the triangle and also its baseline IK in half.

so, both sides of the baseline must be equal :

3x = x + 6

2x = 6

x = 3

=> LK = x + 6 = 3 + 6 = 9

Answer:

-x^2+3x-2

Step-by-step explanation:

I think one of the signs are wrong in the equation.

50626 ways with a probability of 0.77

If a coin is tossed once, there are two possible results - a head or a tail. i.e 2¹ = 2

If the coin is tossed twice, there are four possible results - 4 heads no tail, 4 tails no head, 1 head 3tails or 2 heads 2 tails. That is 2² = 4

If the coin is tossed thrice, there are eight possible results. That is 2³ = 8.

Now, if the coin is tossed 16 times, there are 2¹⁶ = 65536 likely results.

From these 16 tosses, let's calculate the number of ways of achieving or selecting 7, 8, 9, 10, 11, 12, 13 or 14 heads. We use the combination formula given as follows;

Cₙ, ₓ = n! ÷ [ (n-x)! (x)! ]

Where;

n = number of tosses

x = number of selection

number of ways of getting 7 heads;

n = 16

x = 7

=> C₁₆, ₇ = 16! ÷ [ (16-7)! (7)! ]

=> C₁₆, ₇ = 16! ÷ [ (9)! (7)! ]

=> C₁₆, ₇ = 11440

number of ways of getting 8 heads;

n = 16

x = 8

=> C₁₆, ₈ = 16! ÷ [ (16-8)! (8)! ]

=> C₁₆, ₈ = 16! ÷ [ (8)! (8)! ]

=> C₁₆, ₈ = 12870

number of ways of getting 9 heads;

n = 16

x = 9

=> C₁₆, ₉ = 16! ÷ [ (16-9)! (9)! ]

=> C₁₆, ₉ = 16! ÷ [ (7)! (9)! ]

=> C₁₆, ₉ = 11440

number of ways of getting 10 heads;

n = 16

x = 10

=> C₁₆, ₁₀ = 16! ÷ [ (16-10)! (10)! ]

=> C₁₆, ₁₀ = 16! ÷ [ (6)! (10)! ]

=> C₁₆, ₁₀ = 8008

number of ways of getting 11 heads;

n = 16

x = 11

=> C₁₆, ₁₁ = 16! ÷ [ (16-11)! (11)! ]

=> C₁₆, ₁₁ = 16! ÷ [ (5)! (11)! ]

=> C₁₆, ₁₁ = 4368

number of ways of getting 12 heads;

n = 16

x = 12

=> C₁₆, ₁₂ = 16! ÷ [ (16-12)! (12)! ]

=> C₁₆, ₁₂ = 16! ÷ [ (4)! (12)! ]

=> C₁₆, ₁₂ = 1820

number of ways of getting 13 heads;

n = 16

x = 13

=> C₁₆, ₁₃ = 16! ÷ [ (16-13)! (13)! ]

=> C₁₆, ₁₃ = 16! ÷ [ (3)! (13)! ]

=> C₁₆, ₁₃ = 560

number of ways of getting 14 heads;

n = 16

x = 14

=> C₁₆, ₁₄ = 16! ÷ [ (16-14)! (14)! ]

=> C₁₆, ₁₄ = 16! ÷ [ (2)! (14)! ]

=> C₁₆, ₁₄ = 120

Therefore, the total number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 heads is the sum of the results above. i.e

11440 + 12870 + 11440 + 8008 + 4368 + 1820 + 560 + 120 = 50626 ways

P(getting number of heads between 7 and 14 inclusive) = [number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 ] ÷ [total number of possible outcomes]

= [tex]\frac{50626}{65536}[/tex]

= 0.77

Answer:

a)CI 95 %  =  ( 6.7063  ;  6.7593)  ( in hundredths of an inch)

b) CI 95 %  =  ( 0.05 <  σ  <  0.089 ) ( in hundredths of an inch)

Step-by-step explanation:

From the problem statement, we have a manufacturing  process and we we assume a normal distribution, from sample data:

x =  6.7328        and  s  =  0.0644

a) CI 95 %  =  (  x ±  t(c) * s/√n )

t(c)    df =  n  -1    df  =  25 - 1     df = 24

CI  =  95 %   α = 5 %     α  = 0.05     α /2  =  0.025

Then  from t-student table   t(c) = 2.060

s/√n  =  0.0644/ √ 25      s/√n = 0.01288

CI 95 %  =  (  x ±  t(c) * s/√n )  =  ( 6.7328  ± 2.060*0.01288)

CI 95 %  = ( 6.7328 ±  0.02653 )

CI 95 %  =  ( 6.7063  ;  6.7593)  ( in hundredths of an inch)

b) CI 95 % of the variance  is:

CI 95 %  =  (  ( n - 1 ) * s² / χ²₁ - α/₂ ≤  σ²  ≤   ( n - 1 )*s² / χ²α/₂ )

( n - 1 ) * s²   = ( 25 - 1 ) * (0.0644)² =  24* 0.00414

( n - 1 ) * s²   = 0.09936

And from  χ²  table we look for values of

χ² α/₂ ,df    df = 24   and  α/2 =  0.025

χ² (0.025,24)  = 12.40      and    χ²₁ - α/₂  =   χ² (0.975, 24)

χ² (0.975, 24) = 39.36

Then

CI 95 %  = ( 0.09936 / 39.36  ≤  σ²  ≤   0.09936 / 12.40)

CI 95 %  = ( 0.0025  ≤   σ²  ≤  0.0080)

Then for the standard deviation,  we take the square root of that interval

CI 95 %  =  ( 0.05 <  σ  <  0.089 )

Answer:

[tex](a)\ G(t) = 100 *e^{0.1823t}[/tex]

[tex](b)\ t = 6[/tex]

[tex](c)\ t = 1.7[/tex]

Step-by-step explanation:

Given

[tex]G_0 = 100[/tex] --- initial

[tex]G(1) = 120[/tex] --- after 1 year

[tex]r \to rate[/tex]

Solving (a): The expression for g

Since the rate is constant, the distribution of G follows:

[tex]G(t) = G_0 * e^{rt}[/tex]

[tex]G(1) = 120[/tex] implies that:

[tex]G(t) = G_0 * e^{rt}[/tex]

[tex]120 = G_0 * e^{r*1}[/tex]

Substitute [tex]G_0 = 100[/tex]

[tex]120 = 100 * e^{r[/tex]

Divide both sides by 100

[tex]1.2 = e^{r[/tex]

Take natural logarithm of both sides

[tex]\ln(1.2) = \ln(e^r)[/tex]

[tex]0.1823 = r[/tex]

[tex]r = 0.1823[/tex]

So, the expression for G is:

[tex]G(t) = G_0 * e^{rt}[/tex]

[tex]G(t) = 100 *e^{0.1823t}[/tex]

Solving (b): t when G(t) = 300

We have:

[tex]G(t) = 100 *e^{0.1823t}[/tex]

[tex]300 = 100 *e^{0.1823t}[/tex]

Divide both sides by 100

[tex]3 = e^{0.1823t}[/tex]

Take natural logarithm

[tex]\ln(3) = \ln(e^{0.1823t})[/tex]

[tex]1.099 = 0.1823t[/tex]

Solve for t

[tex]t = \frac{1.099}{0.1823}[/tex]

[tex]t = 6[/tex] --- approximated

Solving (c): When there will be no grass

Reduction at a rate of 80 tons per year implies that:

[tex]G(t) = 100 *e^{0.1823t}- 80t[/tex]

To solve for t, we set G(t) = 0

[tex]0 = 100 *e^{0.1823t}- 80t\\[/tex]

Rewrite as

[tex]80t = 100 *e^{0.1823t}[/tex]

Divide both sides by 100

[tex]0.8t = e^{0.1823t}[/tex]

Take natural logarithm of both sides

[tex]\ln( 0.8t) = \ln(e^{0.1823t})[/tex]

[tex]\ln( 0.8t) = 0.1823t[/tex]

Plot the graph of: [tex]\ln( 0.8t) = 0.1823t[/tex]

[tex]t = 1.7[/tex]

B làm k cho mình KQ với

Answer:

8x+(-20x)

Step-by-step explanation:

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

Explanation:

When using the SSS congruence rule, we can prove that triangle DCA is congruent to triangle BCA.

Since the triangles are congruent, the corresponding pieces angle DCA and angle BCA are equal in measure (if they weren't, then the triangles wouldn't be congruent).

Recall that any square has four right angles, ie all angles are 90 degrees each. Angle DCB is cut in half to get 90/2 = 45.

The angles DCA and DCB are 45 degrees each.

Answer:  a + ( 2a - 7 ) = 41

Explanation:

Let be "a" the Nicci's age and "s" the Nicci's sister.

You know that the sum of Nicci's age and her sister's age is 41. This can be represented with the following equation:

a + 8 = 41

And knowing that Nicci's sister is 7 years less than twice Nicci's age, you can write another equation to represent this:

8 = 2a - 7

Now, substitute the second equation into the first equation in order to find the equation that represents this relationship.

Then, this is:

a + ( 2a - 7 ) = 41

Hope it helps...

Answer:

t=2 plz mark me as brainliest

Step-by-step explanation:

Answer:

Domain = -6 < x < 3

range = -6 < x < -4

Step-by-step explanation:

The domain is the input values along the x-axis. According to the graph, the x values are within the interval;

Domain= -6 < x < 3

The range is the output values along the y-axis. According to the graph, the y values are within the interval;

range = -6 < x < -4

Answer:

The perimeter is 50 cm.

Step-by-step explanation:

P= 14 + 10 + 6 + 20= 50 cm

Answer:

x = 12

Step-by-step explanation:

g(x) - × + 4 =0

put g(x) = 8

so, 8 - x + 4 = 0

x = 12

Answer:

x = - 4

Step-by-step explanation:

Given g(x) = - x + 4 and g(x) = 8 , the equate the right sides, that is

- x + 4 = 8 ( subtract 4 from both sides )

- x = 4 ( multiply both sides by - 1 )

x = - 4

Answer:

36%

Step-by-step explanation:

Step-by-step explanation:

Loss percentage= loss/cost× 100%

250-180=70

70/180=0.3888

0.3888×100%=39%

Answer:

12.56 feet cubed

Step-by-step explanation:

Diameter of 8= radius of 4

4 x 3.14=12.56

12.56x3=37.68

37.68/3=12.56

Answer:26.4

Step-by-step explanation:1.2 x22

Answer:

A proof for the statement by selecting the given sentences are as follows;

Suppose there is an integer m such that 7·m + 4 is divisible by 7

By definition of divisibility, 7·m + 4 = 7·k for some integer k

Subtracting 7·m from both sides of the equation gives 4 = 7·k - 7·m = 7·(k - m)

Dividing both sides of the equation by 7 results in 4/7 = k - m

But k - m is an integer and 4/7 is not an integer

Therefore, for every integer m, 7·m + 4 is not divisible by 7

Step-by-step explanation:

The given equation can be expressed as follows;

Where 7·m + 4 is divisible by 7, we have;

7·m + 4 = 7·k

Where 'k' is an integer

We have;

7·m + 4 - 7·m = 4 = 7·k - 7·m

∴ k - m = 4/7, where k - m is an integer

∴ k - m cannot be equal to 4/7, from which we have;

7·m + 4 cannot be divisible by 7.