In a mixture of 240 gallons, the ratio of ethanol and gasoline is 3:1. If the ratio is to be 1:3, then find the quantity of gasoline that is to be added.

Answer:

2.-P = 0.38

3.-P [ Lb | Wt ]  =  0.788

Step-by-step explanation:

1.-Probability of choosing any box is, 1/3. So the probability of choosing the lucky box is 1/3

Let´s say the lucky box is the number 2 box  ( that consideration does not in any way change the problem generality)

Then we have

p₁ probability of choosing box  1 is 1/3   p₁´ Probability of win ticket is  0.12

p₂ probability of choosing box 2 is 1/3  p₂´Probability of win ticket is  0.90

p₃ probability of choosing box 3 is 1/3  p₃´ Probability of win ticket is  0.12

Then

P (of choosing a winning ticket is) = p₁*p₁´ + p₂*p₂´ +  p₃*p₃´

P  =  1/3*0.12 + 1/3*0.9 + 1/3*0.12

P  =  0.04 + 0.3 + 0.04

P = 0.38

3.- if I draw a winning ticket what is the probability it came from Lucky box

According to Bayes theorem

P [ Lb | Wt ]  =   P(Lb) * P[ Wt|Lb]/ P(Wt)

P(Lb) = 1/3  =  0.33333

P[Wt|Lb]  = 0.9

P(Wt) = 0.38

Then By substitution

P [ Lb | Wt ]  =  0.333 *  0.9 / 0.38

P [ Lb | Wt ]  =  0.788

Answer:

xlog(64)−xlog(2)−2

Step-by-step explanation:

Simplify 6log(2) by moving 6 inside the logarithm.

log(2^6)x − log(2)x − 2

Raise 2 to the power of 6.

log(64)x − log(2)x − 2

Reorder factors in log(64)x − log(2)x −2.

Answer:

BC = 28

Step-by-step explanation:

The midsegment DF is half the measure of the third side BC , then

BC = 2 × DF = 2 × 14 = 28

9514 1404 393

Answer:

  3/4

Step-by-step explanation:

It might be easier to start by expressing the ratios with AD as the denominator.

  AD/AC = 2/1   ⇒   AC/AD = 1/2

  AD/AB = 3/1   ⇒   AB/AD = 1/3

From the latter, we have ...

  (AD -AB)/AD = 1 -1/3 = 2/3 = BD/AD

Then the desired ratio is ...

  AC/BD = (AC/AD)/(BD/AD) = (1/2)/(2/3) = (3/6)/(4/6)

  AC/BD = 3/4

Answer:

The correct answer would be - 9.75 laps (if runs 12 laps in 8 days) or 78 laps (if 12 laps each day for 8 days)

Step-by-step explanation:

Given:

a) Laps covered in 8 days = 12

interval = 1 and half day

total laps = ?

Solution:

To know the total laps with intervals we need to calculate the laps run each day :

= 12/8 laps per day

= 3/2 laps per day

Now multiply the daily run with days

= (3/2)*6.5              (due to 8 - 1.5 = 6,5 days)

= 9.75 laps

B) Given:

Laps covered in 8 days = 12*8 =96

interval = 1 and half day

total laps = ?

Solution:

To know the total laps with intervals we need to calculate the laps run each day :

= 96/8 laps per day

= 12laps per day

Now multiply the daily run with days

= 12*6.5              (due to 8 - 1.5 = 6,5 days)

= 78 laps

Answer:

B

Step-by-step explanation:

Let the base of the triangle be b and the height be h.

The sum of the base and height is 14. Thus:

[tex]b+h=14[/tex]

Recall that the area of a triangle is given by:

[tex]\displaystyle A=\frac{1}{2}bh[/tex]

From the first equation, solve for either variable:

[tex]h=14-b[/tex]

Substitute:

[tex]\displaystyle A=\frac{1}{2}b(14-b)[/tex]

Distribute:

[tex]\displaystyle A=\frac{1}{2}(14b-b^2)[/tex]

Distribute:

[tex]\displaystyle A=-0.5b^2+7b[/tex]

Let b = x. Hence:

[tex]A=-0.5x^2+7x[/tex]

Therefore, our answer is B.

Answer:

5

Step-by-step explanation:

3-(-2) will become positive 5. so number line will go towards positive 5.

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Value of the expression in which each variable was swapped out with a number from its corresponding domain sinh⁡ (l5)

sinh (5)

=sinh(1.6094) =2.39990 rad

=sinh⁡(1.6094) =2.3

By doing the following, you may determine the numerical value of an algebraic expression: Replace each variable with the specified number. Then, enter your score in your team's table.

Value of the expression in which each variable was swapped out with a number from its corresponding domain. In the case of a number with only one digit, referring to the numerical value associated with a digit by its "value" is a convenient shorthand.

To learn more about Value of the expression refer to:

https://brainly.com/question/13961297

#SPJ2

Answer:

To divide a decimal by another decimal:

Move the decimal point in the divisor to the right until it is a whole number.

Move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number.

Then divide the new dividend by the new divisor

Step-by-step explanation:

see in the example

Answer:

Step-by-step explanation:

46.327=46 ( neaarest whole number)

-4.801=-5 (nearest whole number)

46-(-5)=46+5=51

Answer:

0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose a large shipment of televisions contained 9% defectives

This means that [tex]p = 0.09[/tex]

Sample of size 393

This means that [tex]n = 393[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]

What is the probability that the sample proportion will differ from the population proportion by less than 3%?

Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.

X = 0.12

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]

[tex]Z = 2.08[/tex]

[tex]Z = 2.08[/tex] has a p-value of 0.9812

X = 0.06

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]

[tex]Z = -2.08[/tex]

[tex]Z = -2.08[/tex] has a p-value of 0.0188

0.9812 - 0.0188 = 0.9624

0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%

9514 1404 393

Answer:

  5/8

Step-by-step explanation:

The area of the smaller circles is proportional to the square of the ratio of their diameters. The two smallest circles have diameters equal to 1/4 the diameter of the largest circle. Hence their areas are (1/4)^2 = 1/16 of that of the largest circle.

Similarly, the medium circle has a diameter half that of the largest circle, so its area is (1/2)^2 = 1/4 of the are of the largest circle.

The smaller circles subtract 2×1/16 +1/4 = 3/8 of the area of the largest circle. Then the shading is 1-3/8 = 5/8 of the area of the largest circle.

Answer:

1.5/2

Step-by-step explanation:

slope formula = y2-y1/ x2 - x1

point one (2,0)

point 2 (0, 1.5)

you dont really need to subtract anything because the intercepts, so the slope is 1.5/2

(slope or m = 1.5 - 0 / 2 - 0 )

x intercept = value of x when y is 0

y intercept = value of y when x is 0

Answer:

The price elasticity of demand is -10

Step-by-step explanation:

Given

[tex]p_1,p_2 = 50,40[/tex]

[tex]q_1,q_2 = 400,500[/tex]

Solving (a): The coefficient of price elasticity of demand (k)

This is calculated as:

[tex]k = \frac{\triangle q}{\triangle p}[/tex]

So, we have:

[tex]k = \frac{500 - 400}{40 - 50}[/tex]

[tex]k = \frac{100}{-10}[/tex]

[tex]k = -10[/tex]

Because |k| > 0, then we can conclude that the company made a wise decision.

Step-by-step explanation:

here is the answer to your question

Answer:

21.4 m

Step-by-step explanation:

Let x represent the sum of the tall metal, medium metal and short metal heights. Since the tall metal has a length of 1.44 m, and the ratio is in 9:8:7, hence:

(9/24) * x = 1.44

x = 3.84 m

For the medium metal pieces:

(8/24) * 3.84 = medium metal height

medium metal height = 1.28 m

For the short metal pieces:

(7/24) * 3.84 = short metal height

short metal height = 1.12 m

Total horizontal metal piece length  = 3 * 1.8 m = 5.4 m

Total tall metal piece length  = 2 * 1.44 m = 2.88 m

Total medium metal piece length  = 5 * 1.28 m = 6.4 m

Total short metal piece length  = 6 * 1.12 m = 6.72 m

Total length of metal = 5.4 + 2.88 + 6.4 + 6.72 = 21.4 m

Answer:

310/[tex]3^{3}[/tex] = 310/27 =11.48

Step-by-step explanation:

Answer:

310/ = 310/27 =11.48

Step-by-step explanation:

Answer:

33.51 cm

Step-by-step explanation:

240/360 = 2/3 (Arc length is 2/3 of the total circumference)

C = 2[tex]\pi[/tex]r             ( Calculate the total circumference)    

C = 2(8)[tex]\pi[/tex]

C = 50.265

2/3(50.265)      (Take 2/3 of the circumference. times 2 divide by 3)

33.51

Use a calculator and leave the answer to C and then multiply and divide. You get a more precise answer.

The exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.

The arc length in approximate form is 33.49 radians.

[tex]s = r\times \theta[/tex]

where r is the radius of the circle and [tex]\theta[/tex] is the central angle in radians.

Radians = Degrees ×[tex]\frac{\pi}{180^{\circ}}[/tex]

For given question,

We have been given a circle with a 8-cm radius associated with a central angle of 240 degrees.

[tex]r=8~cm,~\theta=240^{\circ}[/tex]

First we convert angle in radians.

[tex]\theta=240^{\circ}\\\\\theta=240^{\circ} \times \frac{\pi}{180^{\circ}}\\\\ \theta=\frac{4\pi}{3}[/tex]

Using the formula of the arc length,

[tex]s=8\times \frac{4\pi}{3} \\\\s=\frac{32\pi}{3}[/tex]

The exact answer of the arc length is [tex]s=\frac{32\pi}{3}[/tex]

Substitute the value of [tex]\pi = 3.14[/tex]

So, the arc length would be,

[tex]\Rightarrow s=\frac{32\times \pi}{3}\\\\\Rightarrow s=\frac{32\times 3.14}{3}\\\\\Rightarrow s=33.49[/tex]radians

Therefore, the exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.

the arc length in approximate form is 33.49 radians.

Learn more about the arc length here:

https://brainly.com/question/16403495

#SPJ2

Answer:

Step-by-step explanation:

21,753

at unit place=3 not an even number,not equal to 5 and not equal to 0

so 21,753 is not divisible by 2,5 and 10

again

2+1+7+5+3=18 divisible by 3 and 9.

so 21,753 is divisible by 3 and 9.

Answer:

45 km por galón

60 galones en 2700 Km

Step-by-step explanation:

180 / 4

45 km por galón

900 / 45

20 galones

2700 / 45

60 galones en 2700 Km

Answer: 0.108

Step-by-step explanation:

Since the probability of the uninsured is 21.6% of the population, then the probability of insured will be:

= 1 - 21.6%

= 78.4%

The probability of high cost patients is 5%. Therefore, the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured will be:

= 5% × 21.6%

= 0.05 × 0.216

= 0.108

Answer:

there is no file attached

Step-by-step explanation:

Answer:

C.No, the two triangles can only be proven congruent through SSS.

Answer:

C

Step-by-step explanation:

p=20+1

Answer:

19.80

Step-by-step explanation:

Given the equation :

y = a (e)^kt

If a = 100, y = 50, and k = -0.035, find t.

50 = 100(e)^(-0.035t)

50/100 = e^(-0.035t)

0.5 = e^-0.035t

Take the In

In(0.5) = - 0.035t

-0.693147 = - 0.035t

-0.693147 / - 0.035 = t

19.8042 = t

Hence, t = 19.80

Answer:

b= 5i square root of 3

b = -5i square root of 3

Step-by-step explanation:

4b^2+300=0

4b^2 = -300

b^2 = -75

b = square root of -75

b = -75^1/2

^1/2 means square root

b = 25^1/2 * 3^1/2 * i

b= 5i square root of 3

b = -5i square root of 3

Answer:

I have not been able to answer it sorry

9514 1404 393

Answer:

Step-by-step explanation:

Each image point has its signs reversed from the pre-image point.

  (x, y) ⇒ (-x, -y) . . . . describes the rotation

Rotation from the third quadrant (A) to the first quadrant (A') is a rotation of 180°.

Answer:

3rd and 2nd option

Step-by-step explanation:

Step-by-step explanation:

sin ∅ = -(√3)/2

Note that

cos²∅ + sin²∅ = 1

cos²∅ = 1 - sin²∅

= 1 - (-√3 / 2)²

= 1 - (-√3)²/ 2²

= 1 - 3/4

= 1/4

cos²∅ = 1/4

Taking square root of both sides

cos∅ = 1/2

Note that tan∅ = sin∅/cos∅

therefore, tan∅ = -(√3)/2 ÷ 1/2

= -(√3)/2 × 2/1

= -√3

tan∅ = -√3

Since sin∅ = -√3 /2

Then ∅ = -60⁰

The value of ∅ for the given range (third quadrant) is 240⁰.

NB: sin∅ = sin(180-∅)

Also, since 180⁰ is π radians, then ∅ = 4π/3