Question 4 < > A jar contains 6 red marbles numbered 1 to 6 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability of the given event, please show your answ

Answer:

10/21=30/63

4/9=28/63

Step-by-step explanation:

Find the lcm (least common multiple) of 21 an 9, which is 63. Then divide 21 and 9 separately by 63. The multiply that number by the numerator.

Answer:

25%

Step-by-step explanation:

25 out of 100 is 25%

Answer:

27,736.5

Step-by-step explanation:

18,491 / (2/3)

When dividing by a fraction

flip it over and multiply

18,491 * 3/2

55,473/2

27,736.5

Answer:

22736.5   2/3 of a foot in 18491 ft

Step-by-step explanation:

Take the number of feet and divide by 2/3

18491 ÷ 2/3

Copy dot flip

18491 * 3/2

55473/2

22736.5   2/3 of a foot in 18491 ft

The probability that less than 4 U.S. adults who have very little confidence in newspapers is 0.04945.

The number of U.S. adults sampled (n) is 10.

The probability of U.S. adults having very little confidence in newspapers (p) is 0.60.

The probabiltiy of not having very little confidence ("failure") is,

q=1-p

= 1-0.6

= 0.4

Let X be the random variable that models the number of U.S. adults that have very little confidence in newspapers. So, the random variable X follows the binomial distribution.

a) The probability that exactly 5 U.S. adults who have very little confidence in newspapers is given by,

P(X=5) = ¹⁰C₅(0.6)⁵(0.4)¹⁰⁻⁵

= 10!/5!(10-5)! (0.6)⁵(0.4)⁵

= 10×9×8×7×6×5!/5!×5! ×0.000796

= (10×9×8×7×6)/(5×4×3×2×1) ×0.000796

= 2×3×2×7×3×0.000796

= 0.200592

Therefore, the probability that exactly 5 U.S. adults who have very little confidence in newspapers is 0.200592.

The probability that less than 4 U.S. adults who have very little confidence in newspapers is given by,

P(X<4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)

= ¹⁰C₀(0.6)⁰(0.4)¹⁰⁻⁰+¹⁰C₁(0.6)¹(0.4)¹⁰⁻¹+¹⁰C₂(0.6)²(0.4)¹⁰⁻²+¹⁰C₃(0.6)³(0.4)¹⁰⁻³

= ¹⁰C₀(0.6)⁰(0.4)¹⁰+¹⁰C₁(0.6)¹(0.4)⁹+¹⁰C₂(0.6)²(0.4)⁸+¹⁰C₃(0.6)³(0.4)⁷

= 10!/0!(10-0)! ×(0.6)⁰(0.4)¹⁰+10!/1!(10-1)! ×(0.6)¹(0.4)⁹+ 10!/2!(10-2)! ×(0.6)²(0.4)⁸ + 10!/3!(10-3)! ×(0.6)³(0.4)⁷

= 1×(0.6)⁰(0.4)¹⁰+10×(0.6)¹(0.4)⁹+5×9×(0.6)²(0.4)⁸+5×3×7×(0.6)³(0.4)⁷

= 0.0001048576+0.001572864+0.010616832+0.037158912

= 0.04945

Therefore, the probability that less than 4 U.S. adults who have very little confidence in newspapers is 0.04945.

To learn more about the confidence interval visit:

https://brainly.com/question/14041846.

#SPJ4

The maximal value of the sample covariance is \(sx*sy\), which represents the highest correlation possible between X and Y.

The formula for the sample covariance between X and Y is given by \(cov(X,Y) = (1/(n-1)) Σ (xi - xmean)(yi - ymean)\). The maximal value for the sample covariance is equal to the product of the standard deviations of X and Y, which can be calculated using the formula \(sx*sy = (1/(n-1)) Σ (xi - xmean)^2 * (1/(n-1)) Σ (yi - ymean)^2\). Using the Cauchy-Schwarz Inequality, we can know that \(cov(X,Y) < = sx*sy\). Therefore, the maximal value of the sample covariance is sx*sy, which represents the highest correlation possible between X and Y.

Learn more about sample covariance here:

https://brainly.com/question/14661221

#SPJ4

Answer:

51.3

Step-by-step explanation:

The amount of milk the 3 students drink is 4 11/12 cups of milk

From the question, we have the following parameters that can be used in our computation:

Dasia = 2 3/4

Taniya = 1 1/6

Calixte = 8/8

The amount of milk the 3 students drink is calculated as

Total = 2 3/4 + 1 1/6 + 8/8

Evaluate the sum

Total = 4 11/12

Hence, the total is 4 11/12 cups of milk

Read more about fractions at

https://brainly.com/question/1330447

#SPJ1

Answer:

10^5

Step-by-step explanation:

10 is multiplied by itself 5 times so you use 5 as the exponent

10 is the number you're multiplying so it the bottom number

10^5

Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

Answer:

(x+2)(x+6)

Step-by-step explanation:

that is the answer because math

=>x^2+8x+12

=>x^2+6x+2x+12

=>x(x+6)+2(x+6)

=>(x+6)(x+2)

Hope it helps you

The solution to the linear system Ax=b is x=[-2 4].

To solve the linear system Ax=b using LU factorization, we first need to decompose matrix A into the product of a lower triangular matrix L and an upper triangular matrix U. Then we can solve the system using forward and backward substitution.

The LU factorization of matrix A=[1 -3; 4 -2] yields L=[1 0; 4 1] and U=[1 -3; 0 10]. Now, we can rewrite the system as LUx=b.

Next, we solve Lc=b using forward substitution, where c is a new vector. Applying forward substitution, we find c=[7 36].

Finally, we solve Ux=c using backward substitution. By performing the backward substitution, we obtain x=[-2 4].

Learn more about factorization here : brainly.com/question/14452738

#SPJ11

Answer:

\((-3,-12)\)

\(x=-3, y=-12\)

Step-by-step explanation:

So we have the system:

\(3x+y=-21\\y=4x\)

To solve this, we can do some substitution. Substitute the y in the first equation for the 4x in the second:

\(3x+y=-21\\3x+(4x)=-21\)

Combine like terms:

\(7x=-21\)

Divide both sides by 7. The left side cancels:

\((7x)/7=(-21)/7\\x=-3\)

So we determined that x is -3. Now, plug this number back into the second equation:

\(y=4x\\y=4(-3)=-12\)

So the solution is:

\((-3,-12)\)

Answer:

\(\Large \boxed{x=-3 \ } \\ \\ \Large \boxed{y=-12}\)

Step-by-step explanation:

3x + y = -21

y = 4x

Substitue y = 4x in the first equation.

3x + 4x = -21

Combine like terms.

7x = -21

Divide both sides by 7.

x = -3

Let x = -3 for the second equation.

y = 4(-3)

Multiply.

y = -12

The solution for the system of equations is x = -3 and y = -12.

The surface area of the square pyramid is 384 cm squared.

The surface area of the square base pyramid can be found as follows:

surface area of the square base pyramid = base area + 2al

where

Therefore,

base area = 12 × 12

base area = 144 cm²

Hence,

surface area of the square base pyramid = 144 + 2 × 12 × 10

surface area of the square base pyramid = 144 + 240

surface area of the square base pyramid = 384 cm²

learn more on pyramid here: https://brainly.com/question/12847837

#SPJ1

Answer:

b=1519.87? (If not correct please clarify what sides the 1600 and 500 ft are on. In my answer the 1600 ft was the hypotenuse since it was the longest of the two and it said to find the base of the triangle. This means the 500 ft is the side adjacent to 90 degrees and 1600 ft is the hypotenuse. Sorry if it's not clear!)

Step-by-step explanation:

\(500^{2} +b^2=1600^2\\250000+b^2=2560000\\b^2=2560000-250000\\b^2=2310000\\\sqrt{b^2}=\sqrt{2310000}\\ b=1519.87\)

Answer:

side 2 (\(b^{2}\)) = 1519.87

OR

hypotenuse (\(c^{2}\))= 1676.31

Explanation:

If 1600 ft = hypotenuse and 500 ft = side

\(1600^{2}\) = \(500^{2}\) + \(b^{2}\)

2560000 = 250000 + \(b^{2}\)

2560000 - 250000 = \(b^{2}\)

2310000 = \(b^{2}\)

\(\sqrt{2310000}\) = \(\sqrt{b^{2} }\)

\(b\) = 1519.87

side 2 = 1519.87

OR

If 1600 ft = side 1 and 500 ft = side 2

\(1600^{2}\) + \(500^{2}\) = \(c^{2}\)

2560000 + 250000 = \(c^{2}\)

2810000 = \(c^{2}\)

\(\sqrt{2810000}\) = \(\sqrt{c^{2} }\)

\(c\) = 1676.31

hypotenuse = 1676.31

Volume is a three-dimensional scalar quantity. The depth of the YMCA lap pool is 2 meters.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given that the following details about the YMCA lap pool:

Since the pool is in the space of a right rectangular prism, therefore, the volume of the prism will be the product of length, width and depth. Therefore, the volume of the pool can be written as,

The volume of the pool = Length × width × depth

1472m³ = 36.8m × 20 m × depth of the pool

Depth of the pool = (1472m³ ) / (36.8m × 20m)

                              = 2 meter

Hence, the depth of the YMCA lap pool is 2 meters.

Learn more about Volume here:

https://brainly.com/question/13338592

#SPJ1

Answer:

x = 6

Step-by-step explanation:

Assuming the equation is

\(\frac{2x+3}{3}\) - \(\frac{3x}{2}\) = - 4

Multiply through by 6 ( the LCM of 3 and 2 ) to clear the fractions

2(2x + 3) - 9x = - 24

4x + 6 - 9x = - 24

- 5x + 6 = - 24 ( subtract 6 from both sides )

- 5x = - 30 ( divide both sides by - 5 )

x = 6

Answer:

1. (1, -3.5)

2. (-9, 25) *note, there is a typo in the question, please ask your teacher about this

Step-by-step explanation:

Use the midpoint formula to calculate the midpoint.

Use the formula to find the end point, and double the distance between your endpoint and midpoint to find the other endpoint.

Since the distance between the x coordinate is 8 (from -1 to 7), then the other endpoint is 8 away from -1, or -9.  

please give thanks :)

Answer:

a ≥ -4

Step-by-step explanation:

a/2 +1 ≥ -1

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.

When the distribution is normal, we use the z-score formula.

In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:

Z = (X – µ) / σ

The Z-score shows how many standard deviations the measure is from the mean. After finding the Z-score, need to look at the z-score table and discover the p-value associated with the z-score. This p-value is the probability that the value of the measure is smaller than X, means, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

So, in this case, given that:

µ = 249, σ = 20

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:

100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.

Now, put all the values into the formula:

Z = (X – µ) / σ

–0.253 = (X – 249) / 20

X – 249 = –0.253 * 20

X = 244

Hence, the candle burns for 244 minutes.

Learn more about z-score at: https://brainly.com/question/15016913

#SPJ4

Answer:

x should equal three

Step-by-step explanation:

5(x + 1) - 8 = 5x(2 - 4)

5x+1-8=5x-4

5x-7=5x-4

+7 +7

5x= 5x +3

÷ 5 ÷5

×=3

There are total 35 students in the class.

Given that,

Vikas ranks 9th in the class,

Assume that there are 'n' number of students in the class  

Therefore,

There are 8 students who have scored better than him.

So, The total number of students with a rank better or equal to Vikas,

= 8 + 1 (Vikas himself)

= 9.

Now, his friend got the 35th rank which is the last rank

This means that there are a total of 35 students in the class.

Also, also given that,

Vikas's rank from the last is 27th,

This means that there are 26 students who have scored lower than Vikas.

So, the total number of students with a rank worse or equal to Vikas,

= 26 + 1 (Vikas himself)

 = 27.

Therefore, The total number of students in the class = 35.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ12

Answer:

see explanation

Step-by-step explanation:

Given

\(\frac{2}{5\sqrt{3} }\)

To rationalise the denominator, multiply the numerator/ denominator by \(\sqrt{3}\)

= \(\frac{2\sqrt{3} }{5\sqrt{3}(\sqrt{3}) }\)

= \(\frac{2\sqrt{3} }{15}\)

-----------------------------------------------------------------------

Given

\(\frac{\sqrt{5}+2 }{\sqrt{5}-2 }\)

Multiply the numerator/ denominator by the conjugate of the denominator.

The conjugate of \(\sqrt{5}\) - 2 is \(\sqrt{5}\) + 2 , then

= \(\frac{(\sqrt{5}+2)(\sqrt{5}+2) }{(\sqrt{5}-2)(\sqrt{5}+2) }\) ← expand numerator/denominator using FOIL

= \(\frac{5+4\sqrt{5}+4 }{5-4}\)

= \(\frac{9+4\sqrt{5} }{1}\)

= 9 + 4\(\sqrt{5}\)

Answer:

angle 4= 80°

Step-by-step explanation:

Angles 2, 3, 6 and 7 are equal 100°

Angles 4, 8 and 5 are equal 80°

I hope this help you

Answer:

15 and 12

Step-by-step explanation:

Answer:

three thirds is one whole

Step-by-step explanation:

The answer is 18 because three thirds is one whole which in this case is 18! Have a nice day!

The perimeter of the triangle is given by an expression 18m³ + 2m² - m

Consider the following diagram.

In this question we have been given a triangle.

The sides of the triangles are represented by a mathematical expressions

(5m³ + 3m² - 2m), (8m³ - 4m² + 3m) and (5m³ + 3m² - 2m)

From given expression we can observe that, there are two sides with expression 5m³ + 3m² - 2m.

This means, the triangle must be an isosceles triangle.

We know that the formula for the perimeter of isosceles triangle.

P = 2a + b

where, a = side and b = base of isosceles triangle

Using above formula the perimeter of given triangle would be,

P = 2(5m³ + 3m² - 2m) + (8m³ - 4m² + 3m)

P = (10m³ + 6m² - 4m) + (8m³ - 4m² + 3m)

P = (10 + 8)m³ + (6 - 4)m² + (-4 + 3)m            .....(combine like terms)

P = 18m³ + 2m² - m

Learn more about an expression here:

https://brainly.com/question/30091997

#SPJ4

the vector equation for the line segment from (3, -4, 4) to (7, 2, 3) is:

r = <3, -4, 4> + t<4, 6, -1>

We can find a vector equation for the line segment by first finding the direction vector of the line segment, and then using it to write the equation in vector form.

The direction vector of the line segment is the difference between the two endpoints:

d = <7, 2, 3> - <3, -4, 4> = <4, 6, -1>

To write the vector equation in terms of the parameter t, we can use the parametric form of the equation of a line:

r = r_0 + td

where r is the position vector of a point on the line, r_0 is the position vector of a known point on the line (in this case, (3, -4, 4)), t is a scalar parameter, and d is the direction vector we just found.

Substituting the values we know, we get:

r = <3, -4, 4> + t<4, 6, -1>

To know more about vector visit:

brainly.com/question/24256726

#SPJ11

the distance between the tree and the flagpole is approximately 23.29 feet.

To find the distance between the tree and flagpole, we can use the Pythagorean theorem, which states that the square of the distance between the two points (the hypotenuse of the right triangle) is equal to the sum of the squares of the other two sides.

In this case, the distance between the tree and flagpole (the hypotenuse of the triangle) is equal to the square root of (20^2 + 12^2) = square root of (400 + 144) = square root of 544.

So the distance between the tree and the flagpole is approximately 23.29 feet.

Learn more about Pythagorean Theorem here: brainly.com/question/28361847

#SPJ4