Solve each proportion​

The probability that there will be 2 or fewer arrivals 0.42319 if the distribution of arrivals is Poisson.

Given that,

An active check-out counter sees an average of three customers per minute.

We have to find the probability that in any given minute there will be two or fewer arrivals if the distribution of arrivals is Poisson.

We know that,

Average rate of 3 per minute.

X- Poisson λ = 3

Now, we use the method

The probability distribution of Poisson distribution is

P(X = x) = \(\frac{e^{-\lambda}(\lambda)^x}{x!}\)

The probability that there will be 2 or fewer arrivals in a minute is

P(X ≤ 2) =P(X = 0) +P(X = 1) +P(X = 2)

P(X ≤ 2) = \(\frac{e^{-3}(3)^0}{0!}\) + \(\frac{e^{-3}(3)^1}{1!}\) + \(\frac{e^{-3}(3)^2}{2!}\)

P(X ≤ 2) = e⁻³ + e⁻³(3) + \(\frac{e^{-3}(9)}{2}\)

P(X ≤ 2) = 0.4979 + 0.14936 + 0.22404

P(X ≤ 2) = 0.42319

Therefore, The probability that there will be 2 or fewer arrivals 0.42319.

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The margin of error is approximately 0.014 grams, rounded to three decimal places.

To construct a 98% confidence interval for the mean of repeated measurements of the weight, we can use the following formula:

CI = x ± z × (σ/√n)

Where:
x = mean result = 10.230 grams
σ = standard deviation of scale readings = 0.020 gram
n = number of repeated measurements = 40
z = z-score for 98% confidence interval = 2.326

Plugging in the values, we get:

CI = 10.230 ± 2.326×(0.020/√40)
CI = 10.230 ± 0.014
CI = (10.216, 10.244)

Therefore, the 98% confidence interval for the mean of repeated measurements of the weight is (10.216, 10.244) grams.

The margin of error is the difference between the upper and lower bounds of the confidence interval divided by 2, so:

Margin of error = (10.244 - 10.216)/2
Margin of error = 0.014

Thus, the margin of error is 0.014 grams.

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Answer:

45°

Step-by-step explanation:

well all the side are equal. Since each angle of this square is 90, and if I'm not mistaken, the two angle are equal to each other.

So both angle x and y are 45°

The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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Answer:

C choice.

Step-by-step explanation:

Since line a is given a slope as -4.

Another line which is line b is given that it's perpendicular to line a or we can say that line a is perpendicular to line b.

Perpendicular is defined as:

\( \displaystyle \large{m_1m_2 = - 1}\)

Both slopes multiply and yield -1.

We know that m1 is -4; we want to find m2 which is slope of line b.

\( \displaystyle \large{ - 4m_2 = - 1}\)

Divide both sides by -4.

\( \displaystyle \large{ \frac{ - 4m_2}{ - 4} = \frac{ - 1}{ - 4} } \\ \displaystyle \large{ m _2 = \frac{1}{4} }\)

Therefore, the slope for line b is 1/4.

Thus, the C choice is correct.

The residual of a regression is the difference between the actual value and the predicted value

The values of (a) and (b) are -0.4 and 0, respectively.

The entries are given as:

x  Given  Predicted    Residual

1    -0.7         -0.6             -1

2   2.3         1.95            0.35

3   4.1           4.5              a

4   7.2          7.2              b

The residual of a line of best fit is calculated using:

\(Residual = Actual - Predicted\)

Using the entry headings, the formula would be:

\(Residual = Given - Predicted\)

To calculate the value of (a), we make use of entry (3).

So, we have:

\(a = 4.1- 4.5\)

\(a = -0.4\)

To calculate the value of (b), we make use of entry (4).

So, we have:

\(b = 7.2- 7.2\)

\(b = 0\)

Hence, the values of (a) and (b) are -0.4 and 0, respectively.

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I think I need to know what the cat weighs first...

Answer:

y=-1/2x+3

Step-by-step explanation:

2y=6-x

y=-x/2+3

y=-1/2x+3

Answer:

y=-1/2(x)+3

Step-by-step explanation:

2y=-x+6

y = -1/2(x)+3

Answer:

164 cm.

Step-by-step explanation:

First, I solved for the bottom and top. 10 times 3 is 30. Then I doubled it because it's the same answer for the bottom and top. I got 60.

Next I solved for the sides. 4 times 3 is 12. Then I doubled it because it's the same answer for both sides. I got 24.

Lastly I solved for the front and back. 10 times 4 is 40. Then I doubled it because it's the same answer for both the front and back. I got 80.

After all this, I added everything together. 60 + 24 + 80 = 164.

Sorry, I'm not the best at explaining things.

A) An equation to represent Janice’s account balance after t years is A = 1200\((1 + 0.035/52)^{(52t)\)

B) It will take approximately 6 years for the account to reach $1500.

A) To find the account balance after t years, we can use the formula for compound interest:

A = P\((1 + r/n)^{(nt)\)

Where:

A = the account balance after t years

P = the principal (initial investment) = $1200

r = the annual interest rate in decimal form = 0.035

n = the number of times the interest is compounded per year (weekly in this case) = 52

t = the number of years

Substituting the given values, we get:

A = 1200\((1 + 0.035/52)^{(52t)\)

B) To determine how many years it will take for the account to reach $1500, we can set A equal to 1500 and solve for t:

1500 = 1200\((1 + 0.035/52)^{(52t)\)

1.25 = \((1.000673)^{52t\)

ln(1.25) = 52t ln(1.000673)

t = ln(1.25)/(52 ln(1.000673))

Using a calculator, we find that it will take approximately 6 years for the account to reach $1500. Note that we rounded to the nearest year as instructed.

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Answer:

x=-2

Step-by-step explanation:

R=1

Y=1

So the equation is

4x+9=1

4x=1-9

4x=-8

x=-8/4

x=-2

Answer:

x=-2

Step-by-step explanation:

R=1

Y=1

So the equation is

4x+9=1

4x=1-9

4x=-8

x=-8/4

x=-2

Answer: The rate of change in the y coordinate is 75. 78 - 3= 75.

Answer:

Part a: Answer is 1/2

78 - 3/150 - 0 = 75/150

= 1/2

Part b: Answer is -1/2

3 - 78/300 - 150

= -75/150

= -1/2

Part c: No, the two rates aren’t the same, because one is positive and the other is negative.

Part d: The rate of change of the function determined by using the two pairs of coordinates is not the same. So, the function modeling the movement of the ball is a nonlinear function

Step-by-step explanation:

The sum of the series ∑n=1[infinity]6n(n + 2) is ∞.

To find the sum of the series ∑n=1[infinity]6n(n + 2), we can use the formula for the sum of a series of the form ∑n=1[infinity]an = ∞∑n=1(an − an−1), where a0 = 0.

First, we need to find an expression for the nth term of the series, an. Using the formula for the product of two consecutives integers, we can write:

an = 6n(n + 2) = 6n^2 + 12n

Next, we can compute the difference between consecutive terms:

an - an-1 = [6n^2 + 12n] - [6(n-1)^2 + 12(n-1)]

= 6n^2 + 12n - 6(n^2 - 2n + 1) - 12(n - 1)

= 6n^2 + 12n - 6n^2 + 12n - 6 - 12n + 12

= 6

Therefore, we have:

∑n=1[infinity]6n(n + 2) = ∞∑n=1(6) = ∞

The series diverges to infinity.

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Answer:

Correct option is (a)

Step-by-step explanation:

According to question in the triangle ΔJKL

JK = 9 and KL =4

according to the condition of triangle sum of two sides must be greater than the third side

Here sum of its two sides is 9 + 4 = 13

⇒ third side must be greater than 13 say 13.2 = JL

therefore, perimeter of triangle ΔJKL is

JK + KL + JL = 9 + 4 + 13.2 = 26.2

Therefore correct option is (a)

Answer:

3. increasing

4. decreasing

Step-by-step explanation:

well for graph 3 the values are increasing

and for graph 4 the values are decreasing

Answer:

21 is your answer

Step-by-step explanation:

The combination formula is used to calculate the number of ways to choose r items from a set of n items without regard to order. The formula is:

C(n,r) = n! / (r! * (n-r)!)

where n is the total number of items and r is the number of items to be chosen.

Using this formula, we can solve the problem when n = 7 and r = 5 as follows:

C(7,5) = 7! / (5! * (7-5)!)

= (7 x 6 x 5 x 4 x 3 x 2 x 1) / [(5 x 4 x 3 x 2 x 1) x (2 x 1)]

= (7 x 6) / (2 x 1)

= 21

Therefore, there are 21 ways to choose 5 items from a set of 7 items without regard to order.

The approximate length of the radius, r is 4.51 cm. SO the option 1 is correct.

In the given question we have to find the approximate length of the radius, r.

As given, circle O has a circumference of approximately 28.3 cm.

The calculation of the circle's boundary is referred as the perimeter or circumference of the circle. Although the circumference of the circle determines the space it occupies.

The circumference of a circle is its length when it's actually opened and represented as a single direction. Units like cm or unit m are typically used to measure it.

As we know that the formula of circumference of circle = 2πr

As circumference of circle = 28.3 cm

So 2πr = 28.3 cm

Divide by 2π on both side, we get

r = 14.15/π

π = 3.14

So r = 14.15/3.14

r = 4.51 cm

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The complete question is:

Circle O has a circumference of approximately 28.3 cm.

What is the approximate length of the radius, r?

a. 4.5 cm

b. 9.0 cm

c. 14.2 cm

d. 28.3 cm

The approximate length of the radius, r, is 4.5 cm.

The formula for calculating the radius, r, of a circle is r = C/2π, where C is the circumference of the circle. In order to calculate the approximate length of the radius, we must first calculate the circumference.

Let's assume that the circumference of the circle is 28.3 cm. To calculate the circumference, we can use the formula C = 2πr. We know the circumference and want to solve for the radius, so we can rearrange the formula to solve for r: r = C/2π.

Plugging in our values, we can calculate the approximate length of the radius: r = 28.3 cm/2π = 4.5 cm. Therefore, the approximate length of the radius, r, is 4.5 cm.

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Question:

the equation of a polynomial to match the dotted graph

Points given (-3,0), (-2,0), (0,0), (3,0)​

Solution:

Notice that if P is a polynomial and c is a real number, then the following are equivalent:

1. c is a zero of P.

2. x = c is a solution of the equation P(x) = 0.

3. x- c is a factor of P(x).

4. c is an x-intercept of the graph of P.

Then, due to the above, we can conclude that as -3, -2, 0, and 3 are zeroes of P, the P(x) can be written as:

this is equivalent to:

In expanded form, this is equivalent to:

then, the correct answer is:

The graph of the relationship between the amount of fuel remaining in the trucks tank (in liters) and distance driven (in kilometers) is a linear equation given by, y = 400 - 0.8x

Given that Karl filled up the tank with 400 liters of fuel initially.

As time passes and more distance is covered, the amount of fuel will decrease. Thus the amount remaining is inversely proportional to the distance driven.

Let 'x' be the distance driven (in kilometers) by the truck and 'y' be the remaining fuel (in liters) in the tank.

It says that the truck consumes 0.8 liters of fuel for each kilometer driven.

Then the linear equation modelling this will be :

y = 400 - 0.8x

The graph can be drawn with values of 'x' on the x-axis and the values 'y' on the y-axis.

  x        y

 1        399.2

 2       398.4

 3       397.6

 4        396.8  and so on.

The question is incomplete. Find the complete question below:

Karl filled up the tank of his truck with 400 liters of fuel and set out to deliver a shipment of bananas to Alaska. The truck consumed 0.8 liters for each kilometer driven.

Graph the relationship between the amount of fuel remaining in the trucks tank (in liters) and distance driven (in kilometers).

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Answer:

480

Step-by-step explanation:

12 x 40 = 480

Answer:

close countess

Step-by-step explanation:

remember that the sign has to be postive so just change all the signs ,  then,   you'll have a leading coefficient of  +1,  in front of the \(x^{2}\),  the 5 is in front of the 2nd term,  they were just trying to trick you with that.   the last answer is good     :)

Answer:

if there is 40 passengers and 4 passengers per car there are 10 cars

Answer:

A deck of cards

Answer:

Step-by-step explanation:

To simplify this, I can think in terms of what those exponents mean. "To the third" means "multiplying three copies" and "to the fourth" means "multiplying four copies". Using this fact, I can "expand" the two factors, and then work backwards to the simplified form. First, I expand:

(x3)(x4) = (x‍x‍x)(x‍x‍x‍x)

Now I can remove the parentheses and put all the factors together:

(x‍x‍x)(x‍x‍x‍x) = x‍x‍x‍x‍x‍x‍x

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This is seven copies of the variable. "Multiplying seven copies" means "to the seventh power", so this can be restated as:

x‍x‍x‍x‍x‍x‍x = x7

1. The given polynomial is:

Start by applying the distributive property:

Now, rearrange the terms so that they're written in descending order of exponent:

The degree of a polynomial is given by the largest exponent, then its degree is 3 and the number of terms is 3.

2. Polynomial:

Start by combining like terms:

And rearrange the terms in descending order of exponent:

The degree is 5 and the number of terms is 4.

3. Polynomial:

It is the factored form of the difference of two squares:

By replacing the known values we have:

Then the degree is 4 and the number of terms is 2.

Answer:

but it is correct

Step-by-step explanation:

please mark me as brainliest

Answer:

Cab B charged more

It charged $(30-x) more

Step-by-step explanation:

Here, we want to know which of two cabs charged more for a ride from the airport to the mall.

To know the cab that charged more, we shall be substituting any same value of x in both of the fees

Let’s say x is 10

Thus 5x + 20 becomes 5(10) + 20 = 50 + 20 = 70

while 4x + 50 becomes 4(10) + 50 = 40 + 50 = 90

Clearly we can see that 4x + 50 is greater then 5x + 20, so we can conclude that 4x + 50 is a greater fee

Now since we know the one that’s higher, we can now know the value by which it is higher

That would be (4x + 50)-(5x + 20)

= 4x + 50 -5x -20

= 4x-5x + 50-20

= -x + 30 or simply 30-x