14) Out of the following options, pick the one that
can be expressed as a rational number.
a) 1.16321632...
b) 0.00120345...
c) 5.672101234 ...
d) 2.75757575...
i have no idea what this means

Answer:

f(x)=(6x+6)(x+10)

Explanation:

Given the quadratic expression:

First, we can rewrite it in the form below:

Next, factor the terms:

Thus, the quadratics as a product of two binomials is:

Find the normal approximation to the chance that the face with six spots appears between 9, 10, or 11 times.

The exact chance that the face with six spots appears 9, 10, or 11 times?

my solution; in one roll of the die P(6 spots)=16 In 60 rolls of the die the expected number of times the face with 6 spots appears is given by E(X)=Mean=606=10 times.

SE(6spots)=SD=SQR(606⋅56)=2.8868

Applying the normal approximation to the chance that the face with six spots appears 10 times, I obtain the following: mean = 10

Standard deviation=2.8868

Using the continuity correction of 0.5 the following z-scores are found: z1=(9.5−10)/2.8868=−0.1732 and z2=(10.5−10)/2.8868=0.1732 Subtracting the cumulative probabilities for the two z-scores gives 0.5688−0.4312=0.1376 which is the approximate chance that the face with six spots appears 10 times. find the six spots appears between 9,10, or 11?

The exact chance that the face with six spots appears 10 times is found from

60C10(16)10×(56)50=0.137 find six spots appears 9, 10 or 11 times

The sum of five terms is 208/375 or the value of S(4) is 208/375 option third is correct.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

\(\rm \sum_{n=1}^\infty\dfrac{2}{3}(\dfrac{-1}{5})^{n-1}\)

Plug n = 1

We will get the first term:

a = 2/3

The sum of the terms of a geometric sequence is given by the formula:

\(\rm S_n = \dfrac{a(1-r^n)}{1-r}\)

r = -1/5

\(\rm S_4 = \dfrac{a(1-(-1/5)^4)}{1-(-1/5)}\)

After solving:

S(4) = 208/375

Thus, the sum of five terms is 208/375 or the value of S(4) is 208/375 option third is correct.

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Answer:

B. 44.93

Step-by-step explanation:

The law of sines states
\(\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}\)

where a, b and c are the 3 sides of the triangle and A is the angle opposite side a, B the angle opposite side b and C the angle opposite side c

In this particular problem we have

side a = 44, angle A = 46.7
side c = ? , angle C = 48

So 44/sin(46.7) = c/sin(48) or by multiplying both sides by sin(48)

c = sin(48) * 44/sin(46.7)  = 44.92937 which is 44.93 rounded to 2 decimal places

Answer:

I think 1,600

Step-by-step explanation:

Answer:

ABC

Step-by-step explanation:

Answer:40ft/second

Step-by-step explanation:

Divide 160ft by 4sec to find the unit rate.

Answer:

40

Step-by-step explanation:

You would divide 160 by 4 to get the number of feet dropped in one second. 160 divided by 4 is 40

Hope this helps! Good luck :)

Answer:

-11.2

Step-by-step explanation:

Answer:

\(2(3m + 6n) + 3(5m - 2n) + 5( - 6m + n) \\ \)

open the brackets:

\( = (6m + 12n) + (15m - 6n) + ( - 30m + 5n) \\ \)

group the coefficients of m and n in their brackets:

\( = (6 + 15 - 30)m + (12 - 6 + 5)n \\ \)

then operate the brackets:

\( = - 9m + 11n\)

Answer:

Original price is 11.25

Step-by-step explanation:

Answer: 60

The percent of sale price is 100% - 25% = 75%

the original price is (45/75).100 = 60$

Step-by-step explanation:

The given argument is invalid. It says that if one person has more gray hair in their beard than another person, then they have a higher percentage of gray hair in their beard.

The argument is invalid because it is possible for one person to have a higher percentage of gray hair in their beard but a lower number of gray hairs in total.One possible counterexample by model is:Suppose Plato has 200 hairs in his beard and 50 of them are gray. So, 1/4 of his hairs are gray. Now, let's suppose Aristotle has 400 hairs in his beard, and 300 of them are gray. So, 3/4 of his hairs are gray. Even though Plato has fewer gray hairs than Aristotle, his percentage of gray hairs is more significant (1/4) than Aristotle's (3/4).

Therefore, the given argument is invalid since Aristotle's beard contains more gray hairs in quantity, but Plato has a higher percentage of gray hair in his beard.

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The product of three numbers is 12,295.

We are given that the sum of three numbers x, y, and z is 165, so we can write:

x + y + z = 165

We are also told that when the smallest number x is multiplied by 7, the result is n. So we can write:

x * 7 = n

It is also given that the value n is obtained by subtracting 9 from the largest number y, so we can write:

y - 9 = n

And that this number n also results by adding 9 to the third number z, so we can write:

z + 9 = n

We have 3 equations with 3 unknowns, we can use these equations to solve the problem.

From the equation x * 7 = n, we can substitute n = y-9, and we get:

x * 7 = y - 9

From the equation z + 9 = n, we can substitute n = y-9, and we get:

z + 9 = y - 9

Now we have 2 equations with 3 unknowns x,y,z.

To solve for the third unknown, we can use the equation x + y + z = 165 and substitute the values that we know from the previous equations:

x + (y - 9) + (z + 9) = 165

Solving for x we get:

x = (165 - (y-9) - (z+9)) = (165 - y + 9 - z - 9) = (165 - y - z + 18) = (183 - (y+z))

Now we can substitute this value into one of the previous equations:

(183 - (y+z)) * 7 = y - 9

Solving for y and z we get:

y = 95 and z = 71

And the product of the three numbers is:

x * y * z = (183 - (y+z)) * y * z = (183 - (95 +71)) * 95 * 71 = (183 - 166) * 95 * 71 = 17 * 95 * 71 = 12,295

So the product of three numbers is 12,295.

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Answer:

Step-by-step explanation:

The first thing we need to do is set up the problem.

5\(\frac{1}{10}\) - 2\(\frac{8}{10}\)

After we do this, we have to combine the whole numbers into the fraction to make an improper fraction.

5\(\frac{1}{10}\) becomes \(\frac{51}{10}\) because we get 5 times 10 + 1.

2\(\frac{8}{10}\) becomes\(\frac{28}{10}\) because we get 2 times 10 + 8.

After doing this we can subtract and get the answer.

51 - 28 = 23

So the answer is \(\frac{23}{10}\).

Answer:

x=5+√136or x=5−√136

Step-by-step explanation:

To solve this equation we have to factorize 3x2−5x+1. Since we can not use any

Answer:

Basically what you wanna do is find all points on the x axis since it is at 0 y

So the answer is -2 1 or 3 only

9514 1404 393

Answer:

  $2.563

Step-by-step explanation:

To find dollars per gallon, divide dollars by gallons.

  $34.60/(13.5 gal) ≈ $2.563 /gal

Michelle paid about $2.563 per gallon.

__

Additional comment

We have reported the price to the nearest 1/10th cent, as that is the way gas prices are usually posted.

Answer:

monthly cost with 20 slices:

5 + (1.75 x 20)

5+35

40

monthly cost with x slices:

1.75x + 5

Hope this helps!

Answer:

$175

Step-by-step explanation:

you need to specify if harriet got the 7 portion or the 5 portion. I'll answer as if she got the 7 portion.

They split it into 12 portions because the ratio is 7:5 and 7+5=12. So do $300/12=25

Assuming Maya got the 5 portion, do $25 x 5 = $125, so Maya got $125.

Assuming Harriet got the 7 portion, do $25 x 7 = $175, so Harriet got $175.

Answer: 145

Step-by-step explanation:

I hope the answer is correct  

I am not so sure of it though

The number of students that would be expected to choose cheese pizza is 217.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

Cheese and pepperoni pizzas are served by the school cafeteria.

To find the preference for pizzas:

A random survey was given to 175 students.

The pepperoni pizza was preferred by 80 students.

That means the ratio of preference for cheese pizza = (175 - 80)/175

= 0.54

The population of the school is 400 students.

The number of students that would be expected to choose cheese pizza is,

= 400 x 0.54

= 217.1

≈ 217 students.

Therefore, the required number of students is 217 students.

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Answer:

slope = - \(\frac{11}{4}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 18, 7 ) and (x₂, y₂ ) = (- 10, - 15 )

m = \(\frac{-15-7}{-10-(-18)}\) = \(\frac{-22}{-10+18}\) = \(\frac{-22}{8}\) = - \(\frac{11}{4}\)

Reena's original speed as compared to her new speed concludes that Reena arrived at her destination in her planned amount of time which is 20 hours.

What is speed?

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Reena's original plan was to drive for 20 hours at an average speed of 50 mph, which means that she would have covered a distance of -

Distance = Speed x Time

Distance = 50 mph x 20 hours

Distance = 1000 miles

Now calculate the distance that Reena actually traveled.

She drove at an average speed of 60 mph for the first 5 hours, covering a distance of -

Distance1 = Speed1 x Time1

Distance1 = 60 mph x 5 hours

Distance1 = 300 miles

For the remaining 15 hours of the journey, she drove at an average speed of 50 mph, covering a distance of -

Distance2 = Speed2 x Time2

Distance2 = 50 mph x 15 hours

Distance2 = 750 miles

The total distance that Reena traveled is the sum of the two distances -

Total Distance = Distance1 + Distance2

Total Distance = 300 miles + 750 miles

Total Distance = 1050 miles

Reena actually traveled 1050 miles to reach Chicago, which is 50 miles more than her planned distance of 1000 miles.

To calculate how much earlier Reena arrived in Chicago than she originally planned, we need to compare the time it took her to travel the two distances -

Time1 = Distance1 / Speed1

Time1 = 300 miles / 60 mph

Time1 = 5 hours

Time2 = Distance2 / Speed2

Time2 = 750 miles / 50 mph

Time2 = 15 hours

Total Time = Time1 + Time2

Total Time = 5 hours + 15 hours

Total Time = 20 hours

Reena arrived in Chicago in 20 hours, which was exactly the same as her original plan.

Therefore, she did not arrive earlier than planned.

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According to the Central Limit Theorem, for a sufficiently large sample size, the distribution of sample means will be approximately normal, regardless of the shape of the population distribution.

To calculate the probability, we need to convert the sample mean score to a z-score and then find the corresponding area under the standard normal distribution curve.

Calculate the standard error of the mean (SE):

SE = σ / sqrt(n)

SE = 127 / sqrt(72)

SE ≈ 14.96

Calculate the z-score:

z = (X - μ) / SE

z = (567 - 572) / 14.96

z ≈ -0.334

Find the probability corresponding to the z-score:

We can find the area to the left of the z-score -0.334. Let's denote this probability as P(z < -0.334).

The probability that the sample mean score is less than 567 is approximately equal to P(z < -0.334).

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Answer:

b and c

Step-by-step explanation:

i just know

The probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.

What is a binomial distribution?

The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.

Formula to calculate the binomial distribution

P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ

Here, we know that

Solar-heat installations successfully reduce the utility bill 60% of the time.

We have to calculate the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill.

We have 60% = 0.6 = p and n = 10.

We have a binomial distribution: X : (10, 0.6).

We use the binomial distribution formula to calculate the probability

P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ, we get

P(x ≥ 9) = 1 - P(x < 9)

P(x ≥ 9) = 1 - P(x ≤ 8)

P(x ≥ 9) = 1 - ∑⁸₀ P(x = x)

P(X ≥ 9) = 1 - ∑⁸₀¹⁰Cₓ × (0.6)ˣ × (1-0.6)¹⁰⁻ˣ

P(X ≥ 9) = 1 -( 0.00011 + 0.00157 + 0.01062 + 0.04247 + 0.11148 + 0.20066 + 0.25082 + 0.21499 + 0.12093)

P(X ≥ 9) = 1 -0.95365

P(X ≥ 9) = 0.04635

Hence, the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.

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The correct value of  the MLE of \(\hat{\sigma}^2 = \frac{1}{n} \sum_{i=1}^{n}(Y_i - \mu)^2\)

To find the maximum likelihood estimator (MLE) of σ^2 given the i.i.d. normal random variables Y1, ..., Yn with known mean μ, we need to maximize the likelihood function.The likelihood function for a normal distribution is given by:

\(L(\sigma^2) = \left(\frac{1}{\sqrt{2\pi\sigma^2}}\right)^n \cdot \exp\left(-\frac{1}{2\sigma^2}\sum_{i=1}^{n}(Y_i - \mu)^2\right)\)

To find the MLE of σ^2, we maximize the log-likelihood function (logarithm simplifies calculations):

\(\log(L(\sigma^2)) = -\frac{n}{2}\log(2\pi) - \frac{n}{2}\log(\sigma^2) - \frac{1}{2\sigma^2}\sum_{i=1}^{n}(Y_i - \mu)^2\)

To maximize the log-likelihood, we differentiate it with respect to σ^2 and set the derivative to zero:

\(\frac{d}{d(\sigma^2)} \log(L(\sigma^2)) = -\frac{n}{2\sigma^2} + \frac{1}{2\sigma^4}\sum_{i=1}^{n}(Y_i - \mu)^2 = 0\)

Simplifying, we get:

nσ^2 + ∑(Yi - μ)^2 = 0

Rearranging the equation, we have:

σ^2 = (1/n)∑(Yi - μ)^2

This expression is the MLE of σ^2, which is the sample variance of the differences between each observation Yi and the known mean μ, divided by n.Therefore, the MLE of σ^2 is (1/n)∑(Yi - μ)^2.

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Answer:

Given

4x+1 is a factor of p(x) = 4x³ + 5x² - 23x - 6,

so

4x+1 =0

4x = -1

x = -1/4

Answer -p(x) = 0 when x = -1/4

Answer:

No, because the first equation equals -1.5x + 2.5 when simplified, but when the second equation is simplified it equals 1

Answer:

200 sq cm

Step-by-step explanation:

Lateral surface area is the surface area without the bases, or without the top and bottom. So, you just add up the area of the 4 sides.

The front and back are both 10 x 20, so 200 each = 400

The left and right are 5 x 20, so 100 each = 200

The lateral surface area is 200 sq. cm.