The sum of Bill's and Ben's ages is 91. Bill is now twice as old as Ben was when Bill was as old as Ben is now. How old are Bill and Ben? Use one pronumeral

Answer:

Of (multiplication) 0*-1=0, sum (addition) 0+(-1)=-1

Step-by-step explanation:

Step-by-step explanation:

To find the area of the whole mosaic, we need to multiply the length by the width. In this case, the mosaic is a 7 x 7 array of square tiles, and each tile is 1 ft long.

Area = Length × Width

Area = 7 ft × 7 ft

Area = 49 square feet

So, the area of the whole mosaic is 49 square feet.

The probability that one of the scores in the sample is less than 1484 is 0.2437 .

a)Given that mean u = 1403

standard deviation σ = 200

sample size n = 32

P(x>1484) = P(X-u/σ > 1484-1403/200)

                = P (z > 0.405)

P(x>1484) = 0.2437 .

hence the probability that one score is greater than 1484 is 0.405 .

b) Now we have to find the average of the scores of 48 samples.

P(x>1484)

= P(x-μ/ σ/√n> 1484-1403 /200/√48)

= P(z>2.805.)

Now we will use the normal distribution table to calculate the p value to be 0.002516.

p-value = 0.0025

Normal distributions are very crucial to statistics because not only they are commonly used in the natural and social sciences but also to describe real-valued random variables with uncertain distributions.

They are important in part because of the central limit theorem. This claim states that, in some cases, the average of many samples (observations) of a random process with infinite mean and variance is itself a random variable, whose distribution tends to become normal as the number of samples increases.

To learn more about probability visit:

https://brainly.com/question/29383481

#SPJ4

Answer:

option B is correct(ASA)because the S in the middle of the two A(s) makes it congruent

The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw is 0.39.

The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, can be calculated using conditional probability.

P(A|B) = P(A and B) / P(B)

P(A and B) = P(T or P on second draw and F on first draw) = P(T on second draw and F on first draw) + P(P on second draw and F on first draw)

= (3/9) x (4/10) + (2/9) x (4/10) = 14/90

To find P(B), we know that it is 0.4.

Therefore, the conditional probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is:

P(A|B) = P(A and B) / P(B) = (14/90) / 0.4 ≈ 0.39

So the probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is approximately 0.39.

Learn more about probability, here:

https://brainly.com/question/30034780

#SPJ1

Answer:

C:8 units to the right and 7 units up

Step-by-step explanation:

sana po makatulong Yan

To write an explicit function in the form f(n) = mn + b to represent the number of sit-ups, f(n), Michael does daily in week n, we first need to determine the slope (m) and y-intercept (b).

The slope represents the rate of change of the function, which in this case is the rate at which the number of sit-ups increases each week. Since Michael wants to increase the number of sit-ups he does daily by 2 sit-ups each week, the slope is 2.

The y-intercept represents the starting point of the function, which in this case is the number of sit-ups Michael does daily in the first week. Since he does 15 sit-ups each day in the first week, the y-intercept is 15.

Therefore, the explicit function in the form f(n) = mn + b to represent the number of sit-ups, f(n), Michael does daily in week n is:

f(n) = 2n + 15

This means that in the second week, Michael will do 2n + 15 sit-ups each day, where n is 2, since he is increasing the number of sit-ups by 2 each week. In the third week, he will do 2(3) + 15 = 21 sit-ups each day, and so on.

To learn more about y-intercept click here, brainly.com/question/14180189

#SPJ11

Answer:

S = 3

S = 5

S = 7

S = 9

Step-by-step explanation:

t = 3s + 2

when t = 11

11 = 3s + 2

11 – 2 = 3s

9 = 3s

s = 3

t = 3s + 2

when t = 17

17 = 3s + 2

17 – 2 = 3s

15 = 3s

s = 5

t = 3s + 2

when t = 23

23 = 3s + 2

23 – 2 = 3s

21 = 3s

s = 7

t = 3s + 2

when t = 29

29 = 3s + 2

29 – 2 = 3s

27 = 3s

s = 9

I HOPE ALL THIS HELPS

RATE AS BRAINLIEST PLS

find dy/dx

x= t sin(t); (Given in the question)

y= t²+8t; (Given in the question)

then, x= t sin(t)

dx/dt = sin t + t cos t ;

y= t²+8t

dy/dt = 2t + 8;

then, dy/dx = dy/dt x dx/dt

dy/dx = (2t+8)/(sin t + t cos t)

dy/dx = 2(t+4)/(sin t + t cos t)

Learn more about derivative at:

brainly.com/question/23847661

#SPJ4

We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

To learn more about Deficit, visit the link below:

brainly.com/question/2290367

#SPJ4

the location of the g point is 3.

Two ratios are set to be equal in an equation called a proportion. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls.

Point G Partition the directed line segment form d to f into a

5:4 ratio

so,

g - d = (5/9) x (f - d)

We have that d = -2 and f = 7, Therefore

g - d = (5/9) x (f - d)

g + 2 = (5/9) x (7 + 2)

g + 2 = 5

g = 3

Therefore the location of the g point is 3.

To know more about Proportion visit:

https://brainly.com/question/27733852

#SPJ4

Answer: OPTION D

Step-by-step explanation:

First, we need to set up our two equations. For the picture of this scenario, there is one length (L) and two widths (W) because the beach removes one of the lengths. We will have a perimeter equation and an area equation.

P = L + 2W

A = L * W

Now that we have our equations, we need to plug in what we know, which is the 40m of rope.

40 = L + 2W

A = L * W

Then, we need to solve for one of the variables in the perimeter equation. I will solve for L.

L = 40 - 2W

Now, we can substitute the value for L into L in the area equation and get a quadratic equation.

A = W(40 - 2W)

A = -2W^2 - 40W

The maximum area will occur where the derivative equals 0, or at the absolute value of the x-value of the vertex of the parabola.

V = -b/2a

V = 40/2(2) = 40/4 = 10

Derivative:

-4w - 40 = 0

-4w = 40

w = |-10| = 10

To find the other dimension, use the perimeter equation.

40 = L + 2(10)

40 = L + 20

L = 20m

Therefore, the dimensions of the area are 10m by 20m.

Hope this helps!

Answer:

Width: 10 m

Length: 20 m

Step-by-step explanation:

Hi there!

Let w be equal to the width of the enclosure.

Let l be equal to the length of the enclosure.

1) Construct equations

\(A=lw\) ⇒ A represents the area of the enclosure.

\(40=2w+l\) ⇒ This represents the perimeter of the enclosure. Normally, P=2w+2l, but because one side isn't going to use any rope (sandy beach), we remove one side from this equation.

2) Isolate one of the variables in the second equation

\(40=2w+l\)

Let's isolate l. Subtract 2w from both sides.

\(40-2w=2w+l-2w\\40-2w=l\)

3) Plug the second equation into the first

\(A=lw\\A=(40-2w)w\\A=40w-2w^2\\A=-2w^2+40w\)

Great! Now that we have a quadratic equation, we can do the following:

4) Solve for w

\(A=-2w^2+40w\)

Factor out -2w

\(A=-2w(w-20)\)

For A to equal 0, w=0 or w=20.

The average of 0 and 20 is 10, so the width that will max the area is 10 m.

5) Solve for l

\(40=2w+l\)

Plug in 10 as w

\(40=2(10)+l\\40=20+l\\l=20\)

Therefore, the length of 20 m will max the area.

I hope this helps!

Answer:

Step-by-step explanation:

y = k/x

Margin of error is statistical expressing the amount of a random sampling error in survay results not the error term from biased sampling method. So, correct answer is False.

Margin of error in statistics represents the amount of random sampling error in the survey results. The larger the margin of error, the less confident that the survey results reflect the results of the census of the entire population. It is denoted by E or MOE. It is calculated by dividing the square root of the sample size by the standard deviation of the population. 99% level is the most conservative, 90% level is the least conservative. The sampling error is a statistical error that occurs when the analyst does not select a sample that is representative of the entire data population.

False - Margin of error only account for sample variability (the fact that my sample differs from many others' samples and therefore provides different statistics.

To learn more about margin of error , refer:

https://brainly.com/question/10218601

#SPJ4

Answer:

You are Correct!!!

Step-by-step explanation:

The are the Laplace transforms for the given functions.

a. 2/s - 4/s * \(e^{(-2s)\) + 4/s * \(e^{(-4s)\)

b. 2/(s + 2) + 2/(s + 4)

c. 10/(s + 2) + 8 * \(e^{(-4s)\) / s

To find the one-sided Laplace transform of the given functions, we'll use the properties and formulas of the Laplace transform. Let's calculate the Laplace transform for each function:

a. f(t) = 2u(t) - 4u(t - 2) + 4u(t - 4)

The unit step function u(t) has a Laplace transform of 1/s. Using this property and linearity of the Laplace transform, we have:

L{2u(t)} = 2/s

L{4u(t - 2)} = 4/s * \(e^{(-2s)\)

L{4u(t - 4)} = 4/s * \(e^{(-4s)\)

Taking into account the shifting property of the Laplace transform, we obtain:

L{f(t)} = L{2u(t) - 4u(t - 2) + 4u(t - 4)}

       = 2/s - 4/s * \(e^{(-2s)\) + 4/s * \(e^{(-4s)\)

b. f(t) = 2\(e^{(-2t)\)u(t) + 2\(e^{(-4t)\)u(t)

Using the property of the Laplace transform for exponential functions, we have:

L{2\(e^{(-2t)\)u(t)} = 2/(s + 2)

L{2\(e^{(-4t)\)u(t)} = 2/(s + 4)

Therefore, the Laplace transform of f(t) is:

L{f(t)} = L{2\(e^{(-2t)\)u(t) + 2\(e^{(-4t)\)u(t)}

       = 2/(s + 2) + 2/(s + 4)

c. f(t) = 10\(e^{(-2t)\) + 8u(t - 4)

Using the properties of the Laplace transform, we have:

L{10\(e^{(-2t)\)} = 10/(s + 2)

L{8u(t - 4)} = 8 * \(e^{(-4s)\)/ s

Therefore, the Laplace transform of f(t) is:

L{f(t)} = L{10\(e^{(-2t)\) + 8u(t - 4)}

       = 10/(s + 2) + 8 * \(e^{(-4s)\) / s

These are the Laplace transforms for the given functions.

Learn more about Laplace transforms here

https://brainly.com/question/32942177

#SPJ4

Answer:

the rotational symmetry is

I just think so

We must find the length of one side of the new square.

Step one

The area of the square is 64. We know that the is of a rectangle is given by n x n, so:

The value of n is a number that multiplied by itself gives us 64, that number is 8, so we have:

Step two

The length of one side of the new square is obtained by multiplying the original length 8 by the scale factor 3/2, which gives us:

Answer

Answer:

1.32 * 10^2

Step-by-step explanation:

Given the expression;

(5×10−3)+(6×10−3)2.2×10^4

First we need to do the multiplication first;

= (5×10−3)+(13.2×10−3+4)

= (5×10−3)+(13.2×10^1)

= 0.005 + 132

= 132.005

= 1.32 * 10^2

Hence the equivalent expression is 1.32.0 * 10^2

The results obtained by central limit theorem are given below-

μ = 170 customers per day

σ = 45 customers per day

n = 31

\(\begin{aligned}&\mu_{x}=170 \\&\sigma_{x}=8\end{aligned}\)

The Central Limit Theorem proves that the distribution of a sample means of size n can be estimated to the normal distribution with mean  (μ) and standard deviation (σ) for one random normally distributed variable X, with mean (μ) and standard deviation (σ);

\(s=\frac{\sigma}{\sqrt{n}}\)

This Central Limit Theorem may also be applied to skewed variables if n is at least 30.

She observes that the rival business averages 170 clients per day, with a standard deviation of 45 clients.

Thus, \(\mu=170, \sigma=45\)

Let's say she selects a random sampling of 31 days.

So, n = 31

Now, the mean is according to the Central Limit Theorem is

\(\mu_{x}=170\), and

standard deviation = \(\sigma_{x}=\frac{45}{\sqrt{31}}=8\)

Therefore, by using central limit theorem the data is obtained as,

μ = 170 customers per day

σ = 45 customers per day

n = 31

\(\begin{aligned}&\mu_{x}=170 \\&\sigma_{x}=8\end{aligned}\)

To know more about central limit theorem, here

https://brainly.com/question/18403552

#SPJ4

The complete question is-

A business woman wants to open a coffee stand across the street from a competing coffee company. She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers. Suppose she takes a random sample of 31 days. Identify the following to help her decide whether to open her coffee stand, rounding to the nearest whole number when necessary:

μ = _____customers per day

σ = _____customers per day

n = ____

\(\mu_{x}\) =____

\(\sigma_{x}\) = ____

a) The margin of error for an 80% confidence interval in Arkansas is 0.1041

b) if we want to get an 80% confidence interval with a small margin of error, say only 7%. then the sample size must be 53,599,359

The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.

n = 3600

standard deviation = 399.876

Confidence Interval = 80%

a) α = 0.20

The margin of error = Zα/2 (σ / √n)

Zα/2 = 1.4395 --- (From the tabular value)

The margin of Error = 1.4395 + 399.876 / √3600

Therefore, the Margin of Error = 8.1041

b) Margin of Error = 0.07 = 7%

α = 0.20

Critical Value = 1.2816

Sample Size = (Zc²σ² / ME²) = (Zcσ / ME)²

n = [(1.2816 * 399.876) / 0.07]²

n = 53599358.98

Therefore, Sample size, n = 53599359

To know more about the Margin of Error, refer to this link:

https://brainly.com/question/11832344

#SPJ4

Answer:

The exponent will be 4*10^11

Step-by-step explanation:

^11 This means 11 is an exponent on top.

Hope it helps. Let me know.

The measure of the arc KL and MJ in the given attached figure is equal to = 20° and 80°.

Measure of angle MEJ = 30 degrees

Measure of angle MFJ = 50 degrees

In the attached figure apply angle intersecting secant theorem we get,

m∠MEJ = 1/2(MJ - KL)

Substitute the value of m∠MEJ = 30 degrees we get,

⇒30° = 1/2(MJ - KL)

Multiply both the side by 2 we get,

⇒60° = MJ - KL

⇒ KL = MJ - 60°

Now , we have from the attached figure,

m∠MFJ = 1/2(MJ + KL)

⇒50° = 1/2(MJ + MJ - 60°)

⇒100° = 2MJ - 60°

⇒2MJ = 100° + 60°

⇒2MJ = 160°

⇒MJ = 160°/2

⇒MJ = 80°

⇒KL = MJ - 60°

       = 80° - 60°

This implies that,

KL = 20°

Therefore, the measures of the arcs are equal to measure of arc KL = 20° and MJ = 80°.

Learn more about measures here

brainly.com/question/27302544

#SPJ4

The above question is incomplete, the complete question is:

Given: m∠MEJ=30, m∠MFJ=50

Find the measure of the arc KL, MJ.

Attached figure.

The expression that calculates the length of the hypotenuse is  c = √a² + b²

where

c = hypotenuse

a and b are the other legs

Therefore, the expression that calculates the length of the hypotenuse is as follows:

square root both sides to get the length of the hypotenuse c.

√c² = √a² + b²

Therefore,

c = √a² + b²

learn more on right triangle here: https://brainly.com/question/9214495?referrer=searchResults

Answer: B.x = 52

we have;

2x + 76 = 180

⇔ 2x = 104

⇔ x = 52

Step-by-step explanation:

Answer:

I think C but im not 100% sure so don't take my word

Answer:

The answer is C beacause it is 20 times greater than the other numbers