Convert 50 grains to milligrams (to the nearest tenth).



mg

Answer:

0.0512

Step-by-step explanation:

Probability of making a correct guess ; p = 1 / 5 = 0.2

q = 1 - p = 1 - 0.2 = 0.8

Number of questions, n = 5

Using the binomial probability relation :

P(x = x) = nCx * p^x * q^(n-x)

P(x = 3) = 5C3 * 0.2^3 * 0.8^2

P(x = 3) = 0.0512

Heuristics refers to rules of thumb that simplify the decision-making process. Heuristics are mental shortcuts that help individuals make decisions quickly, often relying on previous experience or intuition rather than a more systematic approach.

While heuristics can be useful, they can also lead to biases and errors in judgment if they are applied too broadly or without careful consideration. It is important to be aware of these heuristics and how they can affect decision-making processes, especially in complex or high-stakes situations where careful consideration is necessary.

The answer is C.

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Answer:

-6.8125

Step-by-step explanation:

Convert 13/16 to a decimal.

Write -6 down

You get -6.8125.

Hope this helps! If it does, please mark me brainliest, and press thank you to help me. Thank you! ;)

Good luck on whatever you are doing.

Explanation:

This equation represents a line, so there are many points that are solutions to the equation. To fill in this boxes we just have to pick a x-value that's in the domain, replace it into the equation and solve for y. The domain of this function is all real numbers, so any number will work.

Using x = 1:

Answers:

A solution is (-24) = 8( 1 ) - 32

Answer:

4 pounds

Step-by-step explanation:

The ratio of pounds of dog bones to dollars is 1:1/4. Multiplying this by 4 to get to 1 dollar leaves you with 4 pounds of dog bones. Hope this helps!

Answer:

yes ✔‍♀️

Step-by-step explanation:

just flip it over and dividend by 1.2

Answer:

Volume = 4.2m³

Total surface area = 31.84m²

Lateral surface area = 24.84m²

Step-by-step explanation:

1m = 100cm

Cuboid's;

Length (l) = 10m

Width (w) = 35cm = 0.35m

height(h) = 1.2m

Volume:

Volume (v) of a cuboid is given by: Length × Width × Height = l × w × h

v = 10m × 0.35m × 1.2m = 4.2m³

Total Surface Area:

Total surface area (\(A_{T}\)) is given by adding the areas of all rectangles that make the cuboid.

\(A_{T}\) = 2(10m × 1.2m) + 2(0.35m × 1.2m) + 2(10m × 0.35m)  = 24m² + 0.84m² + 7m² = 31.84m²

\(A_{T}\) = 31.84m²

Lateral Surface Area:

Lateral surface area (\(A_{L}\)) is found by subtracting base and top area from the total surface area.

Base and top area = 2(10m × 0.35m) = 7m²

∴ \(A_{L}\) = 31.84m² = 7m² = 24.84m²

The predicted values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350, therefore, the correct option is IC.

Given,

Mean of X = 600

Standard deviation of X = 10

Mean of Y = $5000

Standard deviation of Y = 1000

Correlation r= 0.9

Future value of X = 595

Z score of X = (X- Mean of X) / Standard deviation of X= (595-600) / 10 = -0.5

Using the formula, Predicted y = average of y+ r* (Z score of X)* standard deviation of y

Predicted y = $5000 + 0.9 * (-0.5) * 1000 = $4750

The predicted value of Y for X = 595 is $4750.

Now, to find the values of A, B, C, and D; we need to calculate the Z score of X = 615 and find the corresponding predicted value of Y.

Z score of X = (X- Mean of X) / Standard deviation of X= (615-600) / 10 = 1.5

Predicted y = average of y+ r* (Z score of X)* standard deviation of y

Predicted y = $5000 + 0.9 * (1.5) * 1000 = $6350

The predicted value of Y for X = 615 is $6350.

Hence, the values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350

Therefore, the correct option is IC.

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Answer:

#5 is X=63.5

#6 is X=32.9

Step-by-step explanation:

i hope it helps

have a nice day ^_^

The smallest number a such that A + BB is regular for all B > a can be determined by finding the eigenvalues of the matrix A. The value of a will be greater than or equal to the largest eigenvalue of A.

A matrix A is regular if it is non-singular, meaning it has a non-zero determinant. We can consider the expression A + BB as a sum of two matrices. To ensure A + BB is regular for all B > a, we need to find the smallest value of a such that A + BB remains non-singular. One way to check for singularity is by examining the eigenvalues of the matrix A. If the eigenvalues of A are all positive, it means that A is positive definite and A + BB will remain non-singular for all B. In this case, the smallest number a can be taken as zero. However, if A has negative eigenvalues, we need to choose a value of a greater than or equal to the absolute value of the largest eigenvalue of A. This ensures that A + BB remains non-singular for all B > a.

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Answer:

22

Step-by-step explanation:

blue = 1

red = 10

green= 2

Answer:

43

Step-by-step explanation:

red:10

green 1:4

green 2:8

blue 1:3

blue 2:6

blue 1 + red 1 * green 1

PEMDAS: (10*4)=40

3+40=43

The probability of no significant rainfall on a day, if there was no significant rainfall on the prior day, is dependent on various factors such as the location, climate, and season.

However, assuming a stable weather pattern, the probability of no significant rainfall on a day following a day with no significant rainfall would be higher than if there was significant rainfall on the prior day. This is because weather patterns tend to persist for several days, meaning that if there was no significant rainfall on the prior day, it is more likely that there will be no significant rainfall on the following day as well. Additionally, if the region is experiencing a dry season, the probability of no significant rainfall on a day would be higher regardless of the prior day's weather. The probability of no significant rainfall on a day, given that there was no significant rainfall on the prior day, depends on the weather patterns and climate in your specific location.

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a)There are \(2^m^n\) possible relation

b)Similarly \(n^m\)

c)\(\frac{n^m}{2^m^n}\)

a)Set A has m elements and set B has n elements

Firstly determine the number of elements A*B by using the multiplication rule

Number of elements\(=A*B=m*n=mn\)

For each element, \(A*B\) we have two option

First element 2 ways

Second element 2 ways

mn element 2 ways

By using the multiplication rule

\(2*2*2......=2^m^n }\)

Then there are \(2^m^n\) possible relation

b)Similarly \(n^m\)

c)\(\frac{n^m}{2^m^n}\)

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The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

Step-by-step explanation:

To analyze the equation -12 + x + 10x² + 3x³ = 0, we can determine the number of complex roots, the possible number of real roots, and the possible rational roots.

Number of Complex Roots:

The equation is a polynomial of degree 3 (highest power of x is 3), so it can have up to 3 complex roots. However, we need to evaluate the discriminant to determine the nature of the roots more precisely.

Possible Number of Real Roots:

The possible number of real roots can be determined by analyzing the signs of the coefficients. Counting the sign changes in the coefficients when arranged in descending order, we can identify the potential number of positive and negative real roots.

In this case, we have the coefficients: 3, 10, 1, -12.

- The number of sign changes is 2, indicating there are 2 or 0 positive real roots.

- We can also check the number of sign changes when considering f(-x) (replacing x with -x) to find the number of negative real roots. In this case, there is 1 sign change, indicating there is 1 negative real root or an odd number of negative real roots.

Possible Rational Roots:

According to the Rational Root Theorem, any rational root of the equation must be of the form p/q, where p is a factor of the constant term (-12) and q is a factor of the leading coefficient (3).

The factors of -12 are ±1, ±2, ±3, ±4, ±6, and ±12.

The factors of 3 are ±1 and ±3.

Therefore, the possible rational roots can be expressed as:

±1/1, ±1/3, ±2/1, ±2/3, ±3/1, ±3/3, ±4/1, ±4/3, ±6/1, ±6/3, ±12/1, ±12/3.

Simplifying these fractions, we have:

±1, ±1/3, ±2, ±2/3, ±3, ±1, ±4, ±4/3, ±6, ±2, ±12, ±4.

These are the possible rational roots of the equation -12 + x + 10x² + 3x³ = 0.

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Answer:

bust stop #2 6.5 minutes

Step-by-step explanation:

Answer:

bust stop #2 6.5 minutes

Step-by-step explanation:

Answer:

f(x)=-12

Step-by-step explanation:

Since x=-4 substitute -4 into the equation

f(x)=3*-4

f(x)=-12

Hope this helped!

The optimal number of carts and pretzel price will depend on the size of the population and the competitive landscape. The park should conduct market research to determine the ideal price point and number of carts for their specific market.

To determine how many carts the amusement park should put out and what they should set their pretzel price to in order to maximize their profit for an arbitrary population p, several factors need to be considered.

Firstly, the demand for pretzels will depend on the size of the population p. If p is large, the park should put out more carts to meet the demand. However, if p is small, fewer carts would be sufficient.

Secondly, the price of the pretzels will also affect demand. If the price is too high, people may choose to buy other snacks or not purchase anything at all. On the other hand, if the price is too low, the park may not be able to cover their costs and make a profit. Therefore, the park should set the pretzel price to a level that is competitive with other snacks but still allows for a reasonable profit margin.

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Answer:

the smallest r is the 4r and the biggest r is the r^2

VERTEX (-2,-64)

Step-by-step explanation:

Answer:

smaller r = -10

larger r = 6

The ordered pair for the vertex of the parabola is \((-2,-64)\)

Step-by-step explanation:

We have the function \(f(r)=r^2+4x-60\)

In order to factor this quadratic equation, we need to look for two numbers that will

Add together to get 4

Multiply together to get -60

Lets look for the numbers that multiply to give us -60.

-1 and 60

1 and -60

2 and -30

-2 and 30

3 and -20

-3 and 20

4 and -15

-4 and 15

5 and -12

-5 and 12

6 and -10

-6 and 10

Now, we just need to determine which of these numbers will add together to get us 4.

Those two numbers would be -6 and 10.

This means that our factored form of this equation will be

\(f(r)=(r-6)(r+10)\)

From this, we can find our roots, which are the solutions to the equation when it is equal to 0.

\((r-6)(r+10)=0\\\\r=-10, r=6\)

These are our r values.

The vertex of a parabola will always be directly between the two roots.

The number that is between -10 and 6 is \(r=-2\)

To find the y-value of the coordinate pair, we just need to plug -2 into our function.

\(f(-2)=(-2)^2+4(-2)-60\\\\f(-2)=4-8-60\\\\f(-2)=-64\)

This means that the ordered pair for the vertex of the parabola is \((-2,-64)\)

The sequence whose nth term is (2n+1)/(3n-1) converges to the number 2/3.

To use L'Hopital's rule, we need to take the limit of the ratio of the nth term and (n-1)th term as n approaches infinity.

Let a_n be the nth term of the sequence. lim (n->∞) a_n / a_(n-1) = lim (n->∞) (2n+1)/(3n-1) / (2n-1)/(3n-4) = lim (n->∞) [(2n+1)/(3n-1)] * [(3n-4)/(2n-1)] = lim (n->∞) [6n^2 - 5n - 4]/[6n^2 - 7n + 4]

By applying L'Hopital's rule, we can find that the limit of this ratio as n approaches infinity is 1. Thus, the sequence converges to the same limit as the ratio of consecutive terms, which is 2/3.

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we have the expression

11.5x(x+3)+350

this is the same that

11.5(A)+350

where A is the area of rectangular room

11.5 is the rate per square feet

350 is the fee for materials

therefore

the answer is

11.5 represent -----> option E

x(x+3) ------> option F

350 -----> option B

x -----> option C

x+3 ----> option D

Answer:

\( \huge \boxed{3 {x}^{2} + 5x - 4}\)

In this equation the constant is -4.

Answer:

First term = a = 125

Step-by-step explanation:

Question: find the number of shoppers on the first day

This is a geometric progression question

The sum of the terms = 671

Sum of a geometric sequence,Sn = (ar^n - 1) / (r - 1)

Where,

n = number of term in the sequence.

a = first term in the sequence.

r = common ratio

r = 1 + 20%

= 1 + 20/100

= 1 + 0.2

= 1.2

n = 4 (first 4 days)

Sn = (ar^n - 1) / (r - 1)

Sn = 671 where n = 4

671 = {a × 1.2^(4) - 1} / 1.2 - 1

671 = {a × 2.0736 - 1} / 0.2

671 = (2.0736a - a) / 0.2

671 = 1.0736a / 0.2

671 = 5.368a

Divide both sides by 5.368

a = 671 / 5.368

a = 125

It would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

Dennis' reasoning is incorrect.

To determine the rate of picking apples per minute, Dennis correctly divided the total number of apples (24) by the time it took (6 minutes), resulting in 4 apples per minute. However, his approach to calculating the number of apples that could be picked in 8 minutes is flawed.

Dennis multiplied the rate of picking apples per minute (4 apples) by the given time (8 minutes), assuming that the rate remains constant. This approach would be valid if the rate of picking apples per minute were constant, but in this scenario, it is not necessarily the case.

The rate of picking apples could vary depending on factors such as fatigue, efficiency, or other variables. Therefore, it is not accurate to assume that the rate of picking apples per minute remains the same over a longer duration of time.

To determine the number of apples that could be picked in 8 minutes, it would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

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Answer:

150.183

Step-by-step explanation:

0.9 x (8.2 x 20.35) =

0.9 x (166.87) =

150.183

The probability that 8 < Y < 13 is 0.4181 or 41.81% found using the concept of  normal distribution.

Given that the random variable X has normal distribution with parameters µ = 5 and σ² = 4, we are to find the probability that 8 < Y < 13, where Y = 2X + 1.

Here, Y = 2X + 1.

Using the formula for a linear transformation of a normal random variable, we have;

μy = E(Y) = E(2X + 1) = 2

E(X) + 1μy = 2μx + 1

= 2(5) + 1

= 11

σy² = Var(Y) = Var(2X + 1) = 4

Var(X)σy² = 4

σ² = 4(4) = 16

Therefore, the transformed variable Y has normal distribution with parameters μy = 11 and σy² = 16.

We need to find P(8 < Y < 13).

Converting this to the standard normal distribution, we have;P(8 < Y < 13) = P((8 - 11)/4 < (Y - 11)/4 < (13 - 11)/4)

P(8 < Y < 13) = P(-0.75 < Z < 0.5)

We look up the standard normal distribution table and obtain:

P(-0.75 < Z < 0.5) = P(Z < 0.5) - P(Z < -0.75)

P(-0.75 < Z < 0.5) = 0.6915 - 0.2734

P(-0.75 < Z < 0.5) = 0.4181

Therefore, the probability that 8 < Y < 13 is 0.4181 or 41.81%.

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Answer:

(x, y) → (x+8, y-3)

Step-by-step explanation:

You are moving the x coordinates 8 steps to the right, which is in the positive direction. This makes the change +8. This is where the x+8 comes from.

For the y coordinates, you are moving 3 down, which is in the negative direction which means it is y-3.

(You can pick one point, D, and track its movements. We can see that point D had to move 8 units to the right and 3 units down to become D'.)