Write the terms a1, a2, a3, and a4 of the following sequence. If the sequence appears to converge, make a conjecture about its limit. If the sequence diverges, explain why an = 4n - 1; n=1,2,3.. . a1 = (Simplify your answer.)
a2 = (Simplify your answer.)
a3 = (Simplify your answer.)
a4 = (Simplify your answer.)

A sample size of 329 would be required to be 99% confident that the estimated proportion of women-owned businesses not providing employee benefits is within 6 percentage points of the true population proportion.

To calculate the required sample size, we can use the formula:

n = (\(z^2\) * p * q) /\(e^2\)

where n is the sample size, z is the z-score corresponding to the desired level of confidence (in this case, 2.576 for 99% confidence), p is the estimated population proportion (0.165, based on the NWBC's finding), q is 1-p, and e is the maximum error we want to tolerate (in this case, 0.06 or 6 percentage points).

Substituting the values, we get:

n = (2.576^2 * 0.165 * 0.835) / \(0.06^2\)

Solving for n, we get:

n ≈ 329

Therefore, a sample size of 329 would be required to be 99% confident that the estimated proportion of women-owned businesses not providing employee benefits is within 6 percentage points of the true population proportion. Note that this assumes a simple random sample and that the population size is much larger than the sample size, so the finite population correction is not needed.

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\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 1~~)^2 + (~~-4 - (-6)~~)^2} \implies d=\sqrt{(-8 -1)^2 + (-4 +6)^2} \\\\\\ d=\sqrt{( -9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }\implies d\approx 9.22\)

The true about the sum of the two polynomials- 6s^2t – 2st^2 and 4s^2t – 3st^2 is The sum is a binomial with a degree of 3.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.

Now the given polynomials are,

6s^2t – 2st^2 and 4s^2t – 3st^2

Now adding these two polynomials we get,

Sum of polynomials = 6s^2t – 2st^2 + 4s^2t – 3st^2

Taking alike terms together,

= 6s^2t + 4s^2t – 2st^2 – 3st^2

Now simplifying we get,

= 10s^2t – 5st^2

Here we see that the highest power of a variable is 2.

Thus this sum of polynomials is a binomial.

Now sum of the powers of variable s and t = 2 + 1 = 3

Thus, Degree of the sum of polynomials is 3.

Thus, the true about the sum of the two polynomials- 6s^2t – 2st^2 and 4s^2t – 3st^2 is The sum is a binomial with a degree of 3.

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Answer: B. 4 × 10⁻⁵

Step-by-step explanation:

0.00003762 = 3.762 × 10⁻⁵ ≈ 4 × 10⁻⁵

Answer:

b

Step-by-step explanation:

\(4 \times {10}^{ - 5} = 4 \times \frac{1}{100000} \)

Answer:

Solution,

or, 2x-4=24

or, 2x=24+4

or, 2x=28

or, 2×x=28

or, x=28÷2

or, x=14 (answer)

The solution of the equation is x = 14.

An equation is two algebraic expressions that have the same value and have the equal sign in between them.

We have the equation:

2x-4=24

Adding 4 to the both of side,

2x=24+4

2x=28

Divide by 2 on both side,

x=28÷2

x=14

Therefore, x = 14 is the solution of the equation.

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The dimensions that will minimize the cost of the metal to manufacture the can are,

Radius = 4.08 cm

Height = 10.84 cm

To minimize the cost of the metal to manufacture the can, we need to minimize the surface area of the can. The surface area of a cylinder is given by

A = 2πrh + 2πr^2

where r is the radius of the cylinder, h is the height of the cylinder, and π is a constant equal to approximately 3.14159.

We are given that the can needs to hold 1.4 liters of oil. We can use this information to find the relationship between the radius and height of the cylinder. The volume of a cylinder is given by

V = πr^2h

Substituting the given volume of 1.4 liters (1400 cubic centimeters) and the constant π, we get

1400 = 3.14159r^2h

Solving for h, we get

h = 1400/(3.14159r^2)

Now we can substitute this expression for h in the formula for the surface area of the cylinder to get

A = 2πr(1400/(3.14159r^2)) + 2πr^2

Simplifying this expression, we get

A = (2800/πr) + 2πr^2

To minimize the surface area, we need to find the value of r that makes the derivative of A with respect to r equal to zero. Taking the derivative, we get

dA/dr = -2800/πr^2 + 4πr

Setting this equal to zero and solving for r, we get:

-2800/πr^2 + 4πr = 0

2800/πr^2 = 4πr

r^3 = 700/π

r ≈ 4.08 cm

Now we can use the formula for h in terms of r to find the corresponding value of h

h = 1400/(3.14159(4.08)^2) ≈ 10.84 cm

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= (7+20+9+35+12+15+7+10+20+25) : 10

with 10 = number of values

average distance = 160 : 10 = 16

The competition took 2 minutes.

Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.

Given that, the Turtle and Achilles compete. They start at the same time from the same place. Achilles runs at a speed of 13 mph while the Turtle moves at a speed of 1 mph. When Achilles reaches the finish line, the Turtle is 2/5 of a mile behind him.

Let t be the time taken in competition and the distance covered by Achilles be x miles.

We have been given that when Achilles reaches the finish line, the Turtle is 2/5 of a mile behind him. This means that the distance covered by turtle will be: x - 2/5

Since we know that, speed = distance / time

So, we can set two equations for time taken by Achilles and turtle as:

t = x / 13

x = 13t......(i)

t = (x-2/5)/1....(ii)

Substituting this value in equation (2) we will get,

t = 13t - 2/5

5t = 65t - 2

60t = 2

t = 2/60

t = 1/30

So, the competition took 1/30 hour, let us convert our given time in minutes.

1/30 × 60 minutes

= 2 minutes

Hence, the competition took 2 minutes.

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Answer:

the answer your looking for is 3

Step-by-step explanation:

Step-by-step explanation:

please mark me as a brainlist...

Answer:

y=2/5x-3

Step-by-step explanation:

So, first, let's find the slope. m=y1-y2/x1-x2. We will use our points and plug them into this equation. -9-(-7)/-5-(-10)=2/5. Our slope is 2/5. Now, let's find the y-intercept. We only need 1 point, I will choose (-10,-7). y=mx+b will help us find the y-intercept. -7=2/5(-10)+b. B is the y-intercept. -7=-4+b. -7-(-4)=-3. Our y-intercept is -3. So, using our y-intercept and slope, the equation is: y=2/5x-3

The response variable in the given linear regression output is seasonal catch, as indicated by the coefficient estimate and standard error of the variable "size."

The response variable in this simple linear regression is the seasonal catch (thousands of bass per square mile of lake area). In a linear regression, the response variable is the variable we are trying to predict or estimate based on the values of other variables. In this case, we are trying to estimate the seasonal catch of bass in the lake based on the size of the lake. So, the correct answer is b. seasonal catch.

                                                The response variable in the given linear regression output is seasonal catch, as indicated by the coefficient estimate and standard error of the variable "size."

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Answer:

<AED

Step-by-step explanation:

Ima be real I cant really explain but i think that's right

Answer:

The decimal is 4.980

Step-by-step explanation:

BRAINLIEST PLS

Answer:

56

Step-by-step explanation:

Answer:

Line 1:  \(y=-x+2\)

Line 2:          \(y=2x-1\)

Step-by-step explanation:

Line 1

Staring with line one, let's find the slope!

Between the two known points, the rise, or change in y, is 2, and the run, or change in x, is -2. The slope is the rise over the run, so:

\(-\frac{2}{2} =-1\)

The slope is negative 1! The line crosses the y-axis at \(y=2\), so 2 is the y-intercept. Using the slope-intercept formula, the equation is:

\(y=-x+2\)

Line 2

To find the slope of line 2, find the rise and the run between the two known points! The rise is 4, and the run is 2. Simplified, this is:

\(\frac{4}{2} =2\)

The slope is 2! The line crosses the y-axis at \(y=-1\), so -1 is the y-intercept. Using the slope-intercept formula, the equation is:

\(y=2x-1\)

Answer:

y=2x-1 , y=x+2 , the solution of the system is (1,1)

Step-by-step explanation:

Lines can be expressed in the form y=mx+b where m is the slope and b is the y-intercept.

m= rise/run

Looking at the blue line:

m =2/1 =2

The slope is 2 since you rise 2 squares and run to the right one square.

We see that the line crosses the y-axis at (0,-1) so the y-intercept is -1.

Putting it all together: y=2x-1

Looking at the red line:

m = -1 / 1 = -1

We see that the line crosses the y-axis at (0,2) so the y-intercept is 2.

Putting it all together: y=1x+2 or simply y=x+2

The solution to the system is the point that satisfies both equations. Rather than solving it algebraically, we can simply look at the graph and find a point that is on both lines, aka the intersection. In this case, the intersection is (1,1).

A

Explanation

Step 1

remember some properties of the logarithms:

then

I hope this helps you

Answer:

1: 55

2: 128

3: 175

Step-by-step explanation:

I believe that this is correct.

(a) The value of Ay can be approximated using the formula Ay = dy * Δx. In part (b) by taking the difference between the exact value of e^(-0.02) and the approximation, and dividing it by the exact value.

(a) To compute dy, we need to find the derivative of g(x) with respect to x. Once we have the derivative, we can substitute the given values x = 0 and Δx = -0.1 to find the corresponding dy. The value of Ay can be approximated using the formula Ay = dy * Δx.

(b) Using differentials, we can approximate e^(-0.02) by considering the linear approximation of the exponential function. The linear approximation states that for small values of Δx, Δy (the change in y) is approximately equal to the derivative of the function evaluated at a specific point, multiplied by Δx. In this case, we have Δx = -0.02. So, we need to find the derivative of e^x, evaluate it at x = 0, and multiply it by Δx to get the approximate change in y. Then, we can compute e^(-0.02) by adding the change in y to the value of e^0. Finally, we can calculate the relative error by taking the difference between the exact value of e^(-0.02) and the approximation, and dividing it by the exact value.

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Answer:

160 packages in 4 minutes

Step-by-step explanation:

If this helped please mark brainliest

Answer:

brainliest?

Step-by-step explanation:

Answer:174339220050

Step-by-step explanation: Raise 3 to the 20th power, then multiply by 50

Answer:

$54,144

Step-by-step explanation:

To answer this question, we must break up the problem into separate parts. First, we know 10 out of 98 empolyees earn $150 per day, and they work 6 days a week. Therefore, we can multiply 150 by the amount they work each week, which is 6:

150 * 6 = 900

Now, we multiply that number by the amount of workers earning this money, which is 10:

900 * 10 = 9,000

Now, we know that 10 employees out of the 98 total earn $9,000 altogether, but we aren't finished.

Next, we look at the remaining 88 workers. They earn $85.50 per day, working 6 days a week as well. We must multiply these numbers:

85.50 * 6 = 513

Now, we multiply that number by the amount of workers earning this money, which is 88:

513 * 88 = 45,144

So, we know that the 88 employees earn $45,144 total during a work week, and the other 10 earn $9,000 total. We must now combine these numbers to get our final answer:

45,144 + 9,000 = 54,144

So, the factory pays out $54,144 each week

Hope this helps :)

Step-by-step explanation:

amt. means amount

explaination in my workings

hope this helps!!

Answer:

b(20) = 60

Step-by-step explanation:

Here, given that ;

b(x) = -2(x-50)

we want to find the value of b(20)

what we need to do is to simply substitute x for 20

That will be:

b(20) = -2(20-50)

b(20) = -2(-30)

b(20) = 60

Answer: 28282

Step-by-step explanation:

I think

If he water in Earth’s oceans has a volume of about 3.2x10⁸ cubic miles, it would take 3.52x10²⁰ gallon jugs to hold all the water in Earth's oceans.

To calculate how many gallon jugs it would take to hold all the ocean water on Earth, we need to multiply the volume of the water by the conversion factor from cubic miles to gallons.

Given that the water in Earth's oceans has a volume of about 3.2x10⁸ cubic miles and there are about 1.1x10¹² gallons in 1 cubic mile, we can calculate the total number of gallons using the following equation:

Total gallons = (Volume in cubic miles) x (Gallons per cubic mile)

Substituting the given values, we get:

Total gallons = (3.2x10⁸) x (1.1x10¹²) = 3.52x10²⁰

This number is very large and is written in scientific notation to make it more manageable. Scientific notation is a compact way of writing very large or very small numbers using a power of ten. In this case, the number is expressed as a coefficient (3.52) multiplied by 10 raised to the power of 20 (10²⁰).

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Answer:

A. y = 1.3x + 10

Step-by-step explanation:

\(f(x) = 1 .3x + 10 \\ f(0) =1.3(0) + 10 = 10 \\ f(5) =1.3(5) + 10 = 16.5 \\ f(10) =1.3(10) + 10 = 23 \\ f(15) =1.3(15) + 10 = 29.5 \\ f(20) =1.3(20) + 10 = 36\)

Answer:

7/3

Step-by-step explanation:

12x - 15 = 6 - 3x

=> 12x + 3x =  6 + 15

=> 15x = 21

=> x = 21/15

=> x = 7/3