Solve the simultaneous equations
2x + 3y = 6
7x – 2y = 1

The volume of cylindrical tin is 1584 \(cm^3\). The depth of the oil in the tin is 9cm.

\(V_1 =\) VOLUME OF CYLINDRICAL TIN

   \(= \pi r^2 h\)

  \(=\frac{22}{7}\) x 6 x 6 x 14

  = 44 x 36

  = 1584 \(cm^3\)

\(V_2 =\) VOLUME OF RECTANGULAR TIN

    = lbh = 1584

    = (16)(11)(h) = 1584

    = 176h =1584

    = h = 1584 / 176

    = h = 9 cm

A cylinder is a three-dimensional shape that consists of a circular base and a curved surface that extends upward to meet at a point known as the apex. The volume of a cylinder is the amount of space occupied by the shape and is given by the formula V = πr²h, Once we have calculated the area of the circular base, we can multiply it by the height of the cylinder to get the volume.

To calculate the volume of a cylinder, we need to know its dimensions, which are the radius and height. The radius is the distance from the center of the circular base to the edge, while the height is the distance between the two circular bases.

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Answer: x=-10

Step-by-step explanation:

5*(12+x)=10

Distribute

60+5x=10

Subtract(60)

5x=-50

x=-10

Hope it helps <3

Answer:

Heeyyy hope it helps

Step-by-step explanation:

Ok, so the product is the answer to a multiplication problem.

The product of 5 and the sum of a number(X) and 3 is

5(X + 3) = 12

5X + 15 = 12

5X = 12 - 15

5X = -3

X = -3/5

Answer:

The vector that describes their hike from their starting position to their final destination is \(\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi]\).

Step-by-step explanation:

In this problem we assume that orthogonal axes coincide with the north and east. We proceed to translate each sentence from statement into vectorial equations:

(i) A group of hikers walks 3 miles east and then 1 mile north:

\(\vec r_{A} = 3\,\hat{i}+1\,\hat{j}\,\,\,[mi]\)

(ii) After taking a break, they then hike 4 miles east to their final destination:

\(\vec r_{B} = 4\,\hat{i}\,\,\,[mi]\)

The vector that describes their hike from their starting position to their final destination is the sum of the vectors deducted above. That is:

\(\vec r = \vec r_{A}+\vec r_{B}\)  (1)

\(\vec r = (3\,\hat{i}+1\,\hat{j})+4\,\hat{i}\,\,\,[mi]\)

\(\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi]\)

The vector that describes their hike from their starting position to their final destination is \(\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi]\).

If nominal wages and prices are not flexible, then the short-run aggregate supply curve is vertical.

This means that the economy is operating at full employment, and any increase in aggregate demand will not result in an increase in output but rather lead to higher prices.

In other words, the economy is supply-constrained, and there is no excess capacity to produce more output in response to an increase in demand.

In a severe recessionary gap, the economy is operating below its potential output, and there is excess capacity in the economy. However, if nominal wages and prices are not flexible, firms cannot adjust their prices downwards,

and wages cannot be reduced, leading to a situation where the short-run aggregate supply curve is vertical.

This results in a situation where any increase in aggregate demand will not lead to an increase in output, and the economy remains stuck in a recessionary gap with high unemployment and low output.

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The length of the line segment with points (-5, 5) (3, -1) is 10 units

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-5, 5) and (3, -1) is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(-5 - 3)² + (5 - -1)²}

d =√{64 + 36}

d = √100

d = 10 units

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The Composite Trapezoidal rule is used to approximate the given integrals. In part (a), the integral \(\( \int_{1}^{2} x \ln x \, dx \)\) is approximated using \(\( n = 4 \)\)subintervals. In part (b), the integral\(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) is given with incorrect limits, so it cannot be evaluated.

To approximate \(\( \int_{1}^{2} x \ln x \, dx \)\) using the Composite Trapezoidal rule, we divide the interval \(\([1, 2]\) into \( n = 4 \)\) subintervals. The step size, \(\( h \)\), is calculated as\(\( h = \frac{b-a}{n} = \frac{2-1}{4} = \frac{1}{4} \)\). Then, we evaluate the function \(\( x \ln x \)\)at the endpoints of each subinterval and sum the areas of the trapezoids formed. The approximation formula for the Composite Trapezoidal rule is: \(\[\int_{a}^{b} f(x) \, dx \approx \frac{h}{2} \left[ f(a) + 2\sum_{i=1}^{n-1} f(x_i) + f(b) \right]\]\)

Using this formula, we can calculate the approximation for the given integral. The limits of the integral \(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) are given as \(\( 2 \)\) to 2 which indicates an interval of zero length. In this case, the integral cannot be evaluated since there is no interval over which to integrate.

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Answer:B

Step-by-step explanation: it's because you're choosing random peoplepeoplepeople

Answer:

I don't exactly know how to answer this, maybe I need more information. But if not, then all he can do is add one gallon of yellow paint and one gallon of blue paint. If that's all the paint he has, that is all he can add. Is there a diagram that's supposed to go with this? If not, hope I answered your quesiton.

Cybil would be financially better off by $ 3000 to have the vehicle restored.

Cybill is either going to sell the car for $ 10000

Or he can have it restored and then sell it for 22000

The restoration will cost him $9000

Incremental revenue = selling price after restoration - selling price without restoration

Incremental revenue = $ 22000 - 10000 = $ 12000

Incremental costs = 9000

Incremental income = 12000 - 9000 = 3000

Therefore, Cybil would be financially better off by $ 3000 to have the vehicle restored.

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The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .

The charge at which anything happens is referred to as the velocity at which it happens.

The required details for mean rate :

(a) H0: µ = 21.62

Ha: µ ≠ 21.62

(b) t = -1.231

p-value = 0.2253

(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.

(d) H0: µ = 21.62

Ha: µ ≠ 21.62

t = -1.231

check statistic ≥ 2.020

Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.

The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.

The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.

The crucial values for t at this level of significance are t=2.019.

Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.

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The number of fishes and chicken are 24 and 72 respectively

From the question, we have the following parameters that can be used in our computation:

Number of guests = 96

Chicken = 3 times as many a fish

Using the following representations

When the statements are interpreted, we have the system of equations to be

y = 3x

x + y = 96

Substitute y = 3x in x + y = 96

This gives

x + 3x = 96

Evaluate the like terms

4x = 96

Divide by 4

x = 24

Recall that

y = 3x

So, we have

y = 3 * 24

y = 72

Hence, the number of chicken is 72

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Answer:

-27

Step-by-step explanation:

Draw a big X over the equal sign, then cross multiply the terms to get:

6(p) = 9(p+9)

Then you want to get p by itself.

Answer:

FALSE.

Step-by-step explanation:

Given:

To Find:

Formula used:

Using the above formula, we have

h'(x) = [2x*f(x) - f'(x)*x^2]/(f(x))^2

So, h'(3) = [2*3*2 - 4*(3)^2]/(2)^2

h'(3) = (12-36)/4

h'(3) = -24/4 = -6

So, h'(3) = -6 and not -12.

So, the given value is FALSE.

The integral ∫[0,3]∫[1,e^3] eyg(x,y) dx dy can be written as:

∫[1,e^3] ∫[0,3] ln(x^3)g(x,y) dy dx

Therefore, the correct answer is:

∫[1,e^3] ∫[0,3] ln(x^3)g(x,y) dy dx

The integral ∫[0,3]∫[1,e^3] eyg(x,y) dx dy represents a double integral over the region where x ranges from 0 to 3 and y ranges from 1 to e^3.

To evaluate this integral, we can first integrate with respect to x and then with respect to y.

∫[0,3]∫[1,e^3] eyg(x,y) dx dy

Integrating with respect to x first:

∫[0,3] ( ∫[1,e^3] eyg(x,y) dx ) dy

Now, integrating the inner integral with respect to x:

∫[0,3] [ y ∫[1,e^3] g(x,y) dx ] dy

Finally, integrating the remaining expression with respect to y:

∫[0,3] [ y * (integral of g(x,y) with respect to x from 1 to e^3) ] dy

The limits of integration for x are fixed as 1 to e^3, and y ranges from 0 to 3.

Therefore, the correct representation of the integral is:

∫[1,e^3] ∫[0,3] g(x,y) dy dx

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The maximum profit is $923.44 which is gotten when 83 T shirts are produced.

Given the function:

Profit = Revenue - Cost

Profit (P) = 100x - (0.6x²+0.52x+3200)

P = -0.6x² + 99.48x - 3200

The maximum profit is at dP/dx = 0, hence:

dP/dx = -1.2x + 99.48

0 = -1.2x + 99.48

1.2x = 99.48

x = 82.9

x ≅ 83

The maximum profit is at x = 83, hence:

P = -0.6(83)² + 99.48(83) - 3200

P = 923.44

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Answer:

Step-by-step explanation:

if the number of votes is 25, 12 is not majority

but if the number is 23 then 12 is majority

Answer: 26 minutes

Step-by-step explanation:

Assume that the total time spent in the morning which includes getting dressed, eating breakfast, making her bed, and driving to work is x.

Time getting dressed = ¹/₃x

Eating breakfast = 10 mins

Making bed = 5 mins

¹/₃x + 10 + 5 = 35 ½

¹/₃x + 15 = 35 ½

¹/₃x = 35 ½ - 15

¹/₃x = 20 ½

x = 20 ½ / ¹/₃

= 61.5 minutes

Total morning routine is is 61.5 mins

Time taken to drive to work is;

= 61.5 - 35 ½

= 26 minutes

Answer: 11 times

Step-by-step explanation:

Have a wonderful day!

Answer:

the answer is 140

........

Answer:

Hi... Your answer is

-22d+f

The equation of the line of best fit is y = 1.7x  - 58

We start by drawing the line of best fit (see attachment)

From the attached graph, we have the following points

(x, y) = (70, 75) and (61, 60)

The slope (m) is:

m = (y2 - y1)/(x2 - x1)

This gives

m = (60 - 75)/(61 - 70)

Evaluate

m = 1.7

The line of best fit is then calculated as:

y = m(x - x1) + y1

This gives

y = 1.7(x - 70) + 61

This gives

y = 1.7x - 119 + 61

Evaluate

y = 1.7x  - 58

Hence, the equation of the line of best fit is y = 1.7x  - 58

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Answer:

1/2

Step-by-step explanation:

It's a reduction; the scale factor is 1/3. It's a reduction; the scale factor is 1/2.

Answer:

13 ocicats

Step-by-step explanation:

Here, we are told that an Ocicat eats 3/5 pounds of food per day.

Now, we have a bag of 19 1/2 pound of food and we want to know the number of ocicats this will feed

What we just need to do is to divide the weight of the bag by the amount in pounds that can feed a single ocicat

Thus, we have;

19 1/2 divided by 3/5

= 39/5 divided by 3/5

= 39/5 * 5/3

= 13 Ocicats

Answer:

\(Depth = 100m\)

Step-by-step explanation:

Given

Initial Level = 340 m

Number of stages = 4

Difference in each stage = 60 m

Required

Determine the depth of the submarine after 4 stages

First, we have to calculate the total distance moved towards the surface of the sea;

This is calculated as

\(Total\ Distance = Number\ of\ Stages * Difference\ in\ each\ stage\)

\(Total\ Distance = 4 * 60m\)

\(Total\ Distance = 240m\)

This implies that the submarine moved a total distance of 240 metres;

It;'s new depth is calculated as follows;

\(Depth = Initial\ Depth - Total\ Distance\)

\(Depth = 340m - 240m\)

\(Depth = 100m\)

Hence, its new depth after 4 stages of rising is 100m

Answer:

14 feet

Step-by-step explanation:

Area= base x height

Height=area/base

182/13=14

Answer:

135 meters

Step-by-step explanation:

Answer:

C hope it helppppssssss

y= 3/2x

Step-by-step explanation:

BTW the right angle triangle has the measurements of 17,8 & 15 - can't post the answer to that question.

Hope this helps!

Answer:

6? If its a squared machine than it is 6 bc 6 squared is 36.  sorry if it is wrong.

Step-by-step explanation:

Answer: F

Step-by-step explanation: I think....