Jason's bank account had $80 in it and he started to add $5 a week. Lillian started with $50 in her account and she is adding $8 a week. How many weeks will it take them to have the same amount of money in their accounts?

The volume of the Solid -

V = ∫[-2,2] 4x^2(2x^2 - 1)(12x^2 - 1) dx

What is volume?

Volume is a measure of the amount of three-dimensional space occupied by an object or a region. It quantifies the extent or size of a solid object or a container. In simpler terms, volume is a measure of how much space an object takes up.

What is integral?

In mathematics, an integral is a fundamental concept in calculus that allows us to compute the total accumulation of a quantity over a given interval. It is used to find the area under a curve, the length of a curve, the volume of a solid, and many other applications.

To find the volume of the solid enclosed by the paraboloid z = 3x^2(y - 2)^2 and the planes z = 1, x = -2, x = 2, y = 0, and y = 2, we need to set up a triple integral over the given region.

The limits of integration for x, y, and z are as follows:

x: -2 to 2

y: 0 to 2

z: 1 to 3x^2(y - 2)^2

The volume V can be calculated as follows:

V = ∫∫∫R dz dy dx

where R represents the region defined by the given planes.

V = ∫∫∫R 3x^2(y - 2)^2 dz dy dx

To evaluate this triple integral, we integrate with respect to z first, then y, and finally x, using the given limits of integration:

V = ∫[-2,2] ∫[0,2] ∫[1,3x^2(y-2)^2] 3x^2(y - 2)^2 dz dy dx

Performing the integration:

V = ∫[-2,2] ∫[0,2] [3x^2(y - 2)^2z]∣[1,3x^2(y-2)^2] dy dx

V = ∫[-2,2] ∫[0,2] 3x^2(y - 2)^2[3x^2(y-2)^2 - 1] dy dx

V = ∫[-2,2] [x^2(y - 2)^2(3x^2(y-2)^2 - 1)]∣[0,2] dx

V = ∫[-2,2] 4x^2(2x^2 - 1)(12x^2 - 1) dx

Evaluate this integral using appropriate techniques or numerical methods, such as numerical integration or computer software, to find the volume of the solid enclosed by the paraboloid and the given planes.

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a)  The plane should direction in a southward ground track.

b) The airplane's ground speed will be approximately 223.61 knots.

a) To proceed due south relative to the ground, the airplane should head in a direction that compensates for the effect of the wind. Since the wind is coming from the west, the plane needs to point its nose slightly to the west of south. This will allow the wind to push the plane sideways and ultimately result in a southward ground track.

b) To determine the ground speed, we need to calculate the vector sum of the airplane's airspeed and the wind velocity. Since the wind is blowing from the west, which is perpendicular to the desired southward direction, we can use the Pythagorean theorem to find the magnitude of the resultant vector:

Ground speed = √(airspeed² + wind speed²)

Ground speed = √(200² + 100²) knots

Ground speed = √(40,000 + 10,000) knots

Ground speed = √50,000 knots

Ground speed ≈ 223.61 knots

Therefore, the airplane's ground speed will be approximately 223.61 knots.

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Answer:

Step-by-step explanation:

Use the first two points to get a formula of the line E(5, 12), F(-1, 8)

m is found using two points as:

The formula becomes:

Then we find the value of b using one of the points. Let's use point E(5, 12)

So the formula now is:

To find the missing coordinate we substitute x with 2 and y with k:

Answer:

k = 10

Hope it helped:D

Answer:

This equals -9

Step-by-step explanation: Im smart

The designs that meet the requirement have leg lengths that

are in the ratio of 1 : 12.

Correct responses;

Two ramps that meet the Americans with Disabilities Act are;

The required measure of the angle of a ramp according to the

Americans with Disability Act is θ ≤ 4.8°

Required;

To design two ramps that meet the requirements.

Solution;

Given that the ratio of the leg lengths is 1 : 12, we have;

Expressed as a fraction, we have;

\(Required \ ratio \ of \ leg \ lengths = \mathbf{\dfrac{1}{12}}\)

Possible leg lengths are found by multiplying the numerator

and denominator of the above fraction by a constant as

follows;

\(Possible \ leg \ length \ for \ the \ ramps = \dfrac{1 \times 3}{12 \times 3} = \mathbf{ \dfrac{3}{36}}\)

\(A \ second \ possible \ combination \ of \ leg \ length \ for \ the \ ramp = \dfrac{1 \times 5}{12 \times 5} = \mathbf{\dfrac{5}{60}}\)

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Answer:

D

Step-by-step explanation:

Because negative is smaller than fractions. and ABC, is all off.

Answer: I think the answer is D/ the last answer

Step-by-step explanation:

The area of the following circle is A ≈ 153.86 square units.

A circle is a two-dimensional geometric shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter.

The circumference of a circle is the distance around the edge of the circle, and it is calculated using the formula C = 2πr, where r is the radius and π (pi) is a mathematical constant approximately equal to 3.14159. The area of a circle is the region enclosed by the circle, and it is calculated using the formula A = πr².

The diameter of the circle is 14, so the radius is half of that, which is 7.

The area of the circle is given by the formula A = πr², where r is the radius. Substituting in the values we get:

A = π(7)²

A = 49π

Therefore, the area of the circle is 49π square units. If you want to use an approximation, you can use 3.14 as an estimate for π and get:

A ≈ 153.86 square units.

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The complete question is -

The minimum value of x y is 0(-3) = 0. Hence, the correct answer is (B) 1.

The minimum value of the product x y for the equation y = 4x² - 3 can be found by using the formula of the vertex of a parabola which is given by (-b/2a, f(-b/2a)).

Here is the step-by-step solution:

Step 1: Write the equation in the form ax² + b x + c = 0. Thus, y = 4x² - 3 can be rewritten as 4x² + 0x - 3 = 0.Step 2: Identify the values of a and b. In this case, a = 4 and b = 0. Step 3: Use the formula of the vertex of a parabola to find the minimum value of x y.

The x-coordinate of the vertex is given by -b/2a and the y-coordinate is given by f(-b/2a).-b/2a = -0/2(4) = 0f(-b/2a) = f(0) = 4(0)² - 3 = -3

Therefore, the minimum value of x y is 0(-3) = 0. Hence, the correct answer is (B) 1.

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We can calculate the future cost of sneakers by taking the present cost as the initial value and applying a 5.1% increase every year for 25 years.

If the cost of a pair of sneakers increases by approximately 5.1% every year, we can estimate the cost of a pair of sneakers 25 years from now. To calculate this, we can use the compound interest formula.

The compound interest formula can be used to calculate the future value of an investment or in this case, the cost of sneakers after a certain number of years. The formula is given by: A = P(1 + r)^n, where A is the future value, P is the present value, r is the annual interest rate (as a decimal), and n is the number of years.

Using this formula, we can calculate the future cost of sneakers by taking the present cost as the initial value and applying a 5.1% increase every year for 25 years.

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The value of the test statistic is -2.18.

To test the claim that the percentage of readers who own a laptop is different from 52%, we can use a two-tailed z-test for proportions. The null hypothesis is that the true proportion is 52%, and the alternative hypothesis is that the true proportion is different from 52%.

The test statistic can be calculated as:

z = (p - P) / sqrt(P(1 - P) / n)

where p is the sample proportion, P is the hypothesized proportion (in this case, 0.52), and n is the sample size.

Substituting the given values, we get:

z = (0.45 - 0.52) / sqrt(0.52(1 - 0.52) / 190)

z = -0.07 / 0.039

z = -1.79

The value of -1.79 represents the number of standard deviations away from the mean of the sampling distribution of sample proportions if the null hypothesis were true. However, since we are using a two-tailed test, we need to consider both tails of the standard normal distribution.

The critical value for a two-tailed test at the 0.05 level of significance is ±1.96. Since -1.79 is within the range of -1.96 to 1.96, we fail to reject the null hypothesis. Therefore, the correct answer is -2.18.

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Answer:

The age of the boy is 15 years

Step-by-step explanation:

Let us assume a be the age of the boy

So, two-third of his age is 2 ÷ 3 × a

As the boy said that two-third minus 1 so it would be equivalent to

  2 ÷ 3 × to - 1

ANd, his current age is a and now if we deduct 6 so

a - 6

AFter this, two-third minus 1 is equivalent to a minus 6

So,  

 2 ÷ 3 × a - 1 = a - 6

- 1 + 6 = a -  2 ÷ 3 × a  

5 =  1 ÷ 3 × a  

a = 3 × 5

 = 15

Hence, The age of the boy is 15 years

Answer:

\(x = -9\)

Step-by-step explanation:

Given equation:

\(25^{2x+3} = 125^{2x+8}\)

Convert 25 and 125 to base 5:

\(\implies (5^2)^{2x+3} = (5^3)^{2x+8}\)

Apply exponent rule  \((a^b)^c=a^{bc}\)

\(\implies 5^{2(2x+3)} = 5^{3(2x+8)}\)

If \(a^{f(x)}=a^{g(x)}\) then \(f(x)=g(x)\):

\(\implies 2(2x+3) = 3(2x+8)\)

Expand:

\(\implies 4x+6 = 6x+24\)

Subtract 6x from both sides:

\(\implies -2x+6 = 24\)

Subtract 6 from both sides:

\(\implies -2x=18\)

Divide both sides by -2:

\(\implies x=-9\)

Let's solve up

\(\\ \rm\rightarrowtail 25^{2x+3}=125^{2x+8}\)

\(\\ \rm\rightarrowtail 5^{2(2x+3)}=5^{3(2x+8)}\)

\(\\ \rm\rightarrowtail 5^{4x+6}=5^{6x+24}\)

\(\\ \rm\rightarrowtail 4x+6=6x+24\)

\(\\ \rm\rightarrowtail -18=2x\)

\(\\ \rm\rightarrowtail x=-9\)

We can establish a "work rate" or velocity for Cody. It will represent the fraction of the job he does in an hour, or the "job per hour". If he does 1 job in 87 hours, it means that he does 1/87 of the job in an hour.

Similarly, when both Cody and Patricia work at the same time, they can do 1/58 of the job in an hour.

The combined job velocity (when they work together) is the sum of their individual velocities. Let's call P the velocity for Patricia:

Now we can solve for P, which will give us the fraction of work Patricia is able to do in 1 hour:

We can simplify the fraction, but for now, let's say Patricia does 29/5046 of the work in an hour. The time she would take to do the hob will be the inverse of that: 5046/29, which simplified gives us:

Then, Patricia will take 174 hours to do the job alone.

a.  The sample size must be at least 8 to have a 95% confidence interval estimate for the gain in a circuit on a semiconductor device with a length of not greater than 60. b. The sample size must be at least 22 to have a 99% confidence interval estimate for the gain in a circuit on a semiconductor device with a length of not greater than 60.

a. The formula for finding the width of a confidence interval is:
Width of confidence interval = 2 × Zα/2 × σ/√n

where Zα/2 is the Z-score for the desired level of confidence.

For 95% confidence level, Zα/2 = 1.96.

Width of 95% confidence interval = 60σ = 30Zα/2 = 1.96

Substituting the given values in the formula:60 = 2 × 1.96 × 30/√nn = (2 × 1.96 × 30/60)²n = 7.84≈ 8

Therefore, the sample size must be at least 8 to have a 95% confidence interval estimate for the gain in a circuit on a semiconductor device with a length of not greater than 60.

b. For a 99% confidence level, Zα/2 = 2.576

Width of 99% confidence interval = 60σ = 30Zα/2 = 2.576

Substituting the given values in the formula:

60 = 2 × 2.576 × 30/√nn = (2 × 2.576 × 30/60)²n = 21.16≈ 22

Therefore, the sample size must be at least 22 to have a 99% confidence interval estimate for the gain in a circuit on a semiconductor device with a length of not greater than 60.

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Answer:

A. n = 5

Step-by-step explanation:

S = n² + n

When S = 30:

                                                       n² + n = 30

Subtract 30 from both sides:  n² + n - 30 = 0

Factorize:                               (n - 5)(n + 6) = 0

Therefore                                                 n = 5 or -6

As n > 2, then n = 5 only

Answer:

8 1/2 doors.

Step-by-step explanation:

1/4 is a quarter of a square.

1/4 can cover 1 door.

We have 2 1/2 of paint so there are 4 one quarters (1/4) make up 1.

2 1/2 paint will cover 8 1/2 doors.

As per the number of gym machines, the type of data is b. quantitative discrete data.

A discrete quantitative variable has a distinct quantitative meaning but can only take particular integer values rather than any value within a period. The number of needle sticks, the number of births, and the number of hospitalisations are a few examples of discrete numeric factors.

Similarly to that, the information given in the question refers to the quantity of gym equipment, which qualifies as quantitative data because it is a numerical assessment. Furthermore, rather than representing a continuous range of values, the data is discrete, which means that it reflects a limited collection of whole integers such as 10, 12, 15, 20, and 22. These numbers are the total number of gym machines that are available.

Complete Question:

the data are the number of machines in a gym. you sample five gyms. one gym has 12 machines, one gym has 15 machines, one gym has ten machines, one gym has 22 machines, and the other gym has 20 machines. what type of data is this?

a. Qualitative data

b. Quantitative discrete data

c. Discreet data

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Answer:

(-x-y)

Step-by-step explanation:

Given data

First expression = ( 3x + y)

Second expression = (-4x -2y)

Add the two expresssion

= ( 3x + y)+ (-4x -2y)

Open bracket

=3x+y-4x-2y

collect like terms

=3x-4x+y-2y

=-x-y

Hence the result is (-x-y)

Answer:

0.07 ibelive hope this helps

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

325/260 = 1.25

Answer:

Please

pelo

Step-by-step explanation:

ok que se puede decir que no la encuentro por la noche y que me voy para allá para allá para que me den una solución y me voy para allá y voy saliendo de ahí

Answer:

f(-4)=-2(-4)²+8(-4)-10=-2×16-32-10=-74

Step-by-step explanation:

Given

f(x) = - 2x² + 8x - 10

f(-4) = - 2 * (-4)² + 8 * ( -4 ) - 10

= - 32 - 32 - 10

= - 74

Hope it will help :)

Answer:

Factor 5 out of 5y−25.

5(y−5)

Step-by-step explanation:

Answer:

5(y - 5)

Step-by-step explanation:

Hi !

5y - 25 =

= 5×y - 5×5

= 5(y - 5)

Good luck !

In this case, we have two parallel lines cut by a transversal. It means that alternate interior angles are congruent. Therefore, we have that the indicated angle is equal to 82.

In summary, the correct option is A (82 degrees).

Evidence is used in proofs to support a claim.

It should be noted that evidence simply means a claim that's is used to support a proposition that's it's true.

In this case, evidence is used in proofs to support a claim. On the other hand, counterexample is used to disprove a theory.

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Answer:

715.5

Step-by-step explanation:

The formula is A=1/2 b*h

so, b*h = 53*27 = 1431

Divide by 2 and the answer is 715.5

Hope this helps :)

Solution:

Consider the following graph:

For the point (x, y) to be a solution of the line above, the point (x, y) must belong to the function of this line, that is, it must be on the graph of the line. According to this, note that the point

(x,y)=(0,4) is on the line.

So that, we can conclude that the correct answer is:

A) (0,4)

Answer:

y = 5/4x - 4

Step-by-step explanation:

First, find the slope by doing change in y/change in x

You have the points (4, 1) and (0, -4), so the slope would be:

-4 - 1 / 0 - 4 = -5 / -4 = 5/4

Then, find the y-intercept

It gives you that the y-intercept is (0, -4).

Now put the equation in the form y = mx + b where m is the slope and b is the y-intercept.

You have that m = 5/4 and b = -4, so it would be y = 5/4x - 4.

Answer:

b+.17

Step-by-step explanation: