The base radius and height of a circular cone are measured as 10cm
and 25cm respectively, with a possible error in measurement of as much as 0.1cm in
each. Using linear approximation, estimate the magnitude of maximum error in the
calculated volume of the cone.

Answer:

We dissect each statement from the problem above to fully understand it.

the sum of a number and 7 is (x + 7)

3 times this is 3(x + 7)

is means the equal sign here 3(x + 7) =

Two less then 5 times the number is 5x - 2.

Therefore, the answer is B, 3(x + 7) = 5x - 2

Answer:

The answer to your questionis 3.65

Answer:

3.25, 3.50, 3.50, 3.50, 3.65, 4.00, 4.00, 7.50, 7.99

3.65 is the median.

Step-by-step explanation:

You're welcome.

Answer:

The height of the building is 43.7 feet.

Step-by-step explanation:

Attached is a sketch of the problem.

We can use SOH CAH TOA to find our answer.

In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.

We can calculate the height of the building by using the TAN function.

So we can say the tangent of angle x is the opposite side divided by the adjacent side.

[tex]tan(x)=\frac{O}{A}[/tex]

Lets solve for [tex]O[/tex].

Multiply both sides by [tex]A[/tex].

[tex]tan(x)*A=\frac{O}{A}*A[/tex]

Simplify the right side by cancelling the common factor of [tex]A[/tex].

[tex]tan(x)*A=O\\O=A*tan(x)[/tex]

Now lets evaluate the height of the building.

In this example we are given

[tex]x=17\\A=143[/tex]

[tex]O=143*tan(17)[/tex]

[tex]O=43.7195[/tex]

No, we cannot conclude that pedestrians are safer in San Francisco than in Los Angeles based on the data provided. The number of pedestrian fatalities in a given county is only one factor in determining the safety of pedestrians in that county.

Other factors, such as the number of pedestrians in each county, the number of vehicles in each county, the number of traffic laws in each county, and the number of traffic enforcement officers in each county, all play a role in determining the safety of pedestrians in a given county.

We would also need to consider other factors such as the number of pedestrian-friendly infrastructure in each county, the number of pedestrian-friendly policies in each county, and the number of pedestrian-friendly initiatives in each county. With this additional data, we would be able to make a more informed conclusion about which county is safer for pedestrians.

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a) The ecosystem is in the sea. Option D

b) The ecological level is population. option D

c) The factors in the study are pressure, and temperature

d) The common limiting factor in biomes is lack of water

e) The carrying capacity is the highest population an environment can support over a long period. Option A

We have to note that the ecosystem has to do with the part of the habitat that is composed of the living and the non living parts. The non living parts of the ecosystem are called the abiotic factors while the living parts of the ecosystem are called the biotic factors.

In the ecosystem, we have the producers, the consumers and the decomposers and these are called the trophic or the feeding levels in the system.

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Answer:

10

Step-by-step explanation:

120/a = 12

120=12a

120/12 = a

a = 10

Answer:

1,440

Step-by-step explanation:

120 x 12 = 1,440

120 / 1,440 = 12

The percent change for each year is given as follows:

The percent change is obtained applying the proportions in the context of this problem.

The equation that defines the percent change is the change in the year divided by the initial population during the year.

Hence the percent change for each year during the period is given as follows:

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An equation of a line, in slope-intercept form, for the total fee y for any number of hours x is y = 15x + 60.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Since the total fee that is being charged by this construction company is denoted by y and it charges $15 per hour for debris removal, plus a one time fee, an equation that models this situation is given by;

y = 15x + c

Next, we would determine the y-intercept as follows;

195 = 15(9) + c

y-intercept, c = 195 − 135

y-intercept, c = 60.

Therefore, the required equation is y = 15x + 60.

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The temperature drop between noon and 10 PM is 14.4° F.

Celsius to Fahrenheit is the conversion of temperature from Celsius unit to Fahrenheit unit. Temperature scales provide a way of measuring how hot or cold a body is. Fahrenheit and Celsius are temperature scales.

The formula to convert Celsius to Fahrenheit is given by: °F = °C × (9/5) + 32.

Given that, Maha checked the outside temperature at noon one day and found it was 26° C.

So, the temperature in Fahrenheit is °F =26° ×(9/5)+32

= 46.8+32

= 78.8° F

At 10 PM when she checked, the outside temperature was 18° C.

So, the temperature in Fahrenheit is °F =18° ×(9/5)+32

= 32.4+32

= 64.4° F

Difference in temperature =78.8-64.4

= 14.4° F

Therefore, the temperature drop between noon and 10 PM is 14.4° F.

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The correct answer is, the figure is a line segment.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

from the given figure,

we get,

AB is a line segment.

Hence, The correct answer is, the figure is a line segment.

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Answer:

4

Step-by-step explanation:

because its the factor

The scale factor of the dilation of triangles is k = 4/3

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.

Given data ,

Let the scale factor of the dilation be represented as k

Now , the measure of leg of the first triangle is a = 3 units

The measure of leg of the second triangle is b = 4 units

So , the dilated triangle is given by

3 k = 4

Divide by 3 on both sides , we get

k = 4/3

Hence , the dilation factor is k = 4/3

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Expected values are = 150/7 .Ci-square distribution is Day of the week observed count Expected Chi-square = O E (O -E )2/E

testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Statistical hypothesis: A statement about the nature of a population. It is often stated in terms of a population parameter.

Null hypothesis: A statistical hypothesis that is to be tested. : The alternative to the null hypothesis.

Test statistic: A function of the sample data.

The critical value for the chi-square statistic is determined by the level of significance (typically . 05) and the degrees of freedom. The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.

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Expected values are = 150/7 .Ci-square distribution is Day of the week observed count Expected Chi-square = O E (O -E )2/E

testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Statistical hypothesis: A statement about the nature of a population. It is often stated in terms of a population parameter.

Null hypothesis: A statistical hypothesis that is to be tested. : The alternative to the null hypothesis.

Test statistic: A function of the sample data.

The critical value for the chi-square statistic is determined by the level of significance (typically . 05) and the degrees of freedom. The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.

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Answer:

Step-by-step explanation:

1/2 is your answer

The best grade that can be earned is given as 0.8575

If he is able to get the sum of 100 percent in the final exam, trhis would count as 25 percent of the total grade that he has

100 - 25 = 75%

Then we would have

0.75 * 81 + 25 / 100

= 85.75 / 100

= 0.8575

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Question

A friend has a 81% average before the final exam for a course. That score includes everything but the final, which counts for 15% of the course grade.

What is the best course grade your friend can earn?

x = -2 and x = -3 are the two values of x that are roots of the equation x^2 + 3x - 6 = 0

What is the root of the equation?

A root of an equation is a value of the variable that makes the equation true. An equation is a statement that asserts the equality of two expressions. A root of an equation is also known as a solution or a zero of the equation.

The two values of x that are roots of the equation x^2 + 3x - 6 = 0 are x = -2 and x = -3.

To find the roots of the equation, we can use the factoring method, which consists of factoring the polynomial on the left side of the equation.

x^2 + 3x - 6 = 0

(x-2)(x+3) = 0

So, x - 2 = 0, x = 2 and x + 3 = 0, x = -3

Alternatively, we can use the Quadratic formula, which states that for any quadratic equation in the form ax^2 + bx + c = 0, the roots are given by:

x = (-b ± √(b^2 - 4ac))/ 2a

So, by plugging in the values of a, b and c we have:

x = (-3 ± √(3^2 - 41-6))/ 2*1 = (-3 ± √(9+24))/2 = (-3 ± √33)/2 = (-3 ± √33)/2 = -2, -3

Hence, x = -2 and x = -3 are the two values of x that are roots of the equation x^2 + 3x - 6 = 0

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There are 2100 workers in​ the company

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Since 85​% of the workers are women, we can say:

The percentage of worker that aren't women = 100% - 85​% = 15​%

Let N represent the number of all workers. If 315 people work for the company who​ aren't women. We can say:

15​% of N = 315

15/100 × N = 315

0.15N = 315

N = 315/0.15

N = 2100 workers

Method 2:

We can write:

N - 0.85N = 315

0.15N = 315

N = 315/0.15

N = 2100 workers

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The average rate of change on the interval [2, 2 + h] is r = 2.

Wewant to find the average rate of change of p(x) = 2x + 5 on the interval [2, 2 + h]

Remember that the average rate of change on an interval [a, b] is:

r = ( p(b) - p(a))/(b - a)

So on this case, we have:

r = ( p(h + 2) - p(2))/(2 + h - 2)

r = ( 2*(x + h) + 5 - 2*x - 5)/h

r = (2h)/h

r = 2

The average rate of change is 2.

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Answer:

Step-by-step explanation:

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &12 \end{cases} \\\\\\ A = 500[1+(0.04)(12)] \implies A = 740[/tex]

The factorised for. of the given Polynomial expression using the greatest common factor is; 2 (14x - 1).

It follows from the task content that the factorised form of the given Polynomial expression is to be determined using the greatest common factor.

Since the given expression is; 28x - 2.

By careful observation of the two terms (28x and -2) in the polynomial expression; the greatest common factor is; 2.

Hence, the factorised form of the polynomial expression as required is; 2 (14x - 1).

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The exponential model for the population can be written as P(t) = 11,000(1.163)t, where P(t) represents the population size in t years and 1.163 is the growth rate.

We can calculate the population size at any time t by multiplying the initial population size (11,000) by the growth rate (1.163) raised to the power of t. For example, after 10 years the population size would be P(10) = 11,000(1.163)10 = 22,906.7. We can also use the model to predict the population size in future years. For example, the population size in 20 years will be P(20) = 11,000(1.163)20 = 40,803.7. For example, if the population is measured after 10 years, the equation would be P(10) = 11,000(1.163)^10. Solving for P(10) yields a population of 21,945 organisms. Thus, the population has grown by 16.3% per year over the 10-year period and has increased by 10,945 organisms.

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The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.

The base will be calculated as:-

tan(38.6) = P / B

tan(38.6) = 67.7 / B

B = 67.7 / tan(38.6)

B = 54.8 ft

The height will be calculated as:-

Cos(42.4) = B / H

H = 84.8 / Cos(42.4)

H = 114.83 ft

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The value of x is found to be 3 and the arithmetic sequence is found to be 4, -2, -8, ... .

What is arithmetic sequence?

The nth term of an arithmetic progression is determined using the arithmetic sequence formula. The series where the common difference between any two next words stays constant is known as an arithmetic sequence.

The arithmetic sequence is 3x - 5, x - 5, 2x - 14, ....

If the numbers are in an arithmetic sequence, then the difference between the first and second term must be the same as the difference between the second and third term.

(x - 5) - (3x - 5) = (2x - 14) - (x - 5)

x - 5 - 3x + 5 = 2x - 14 - x + 5

-2x = x - 9

-2x - x = -9

-3x = -9

x = 3

The first three terms can be obtained by substituting the value of x in the terms -

The first term - 3(3) - 5 = 4

The second term - 3 - 5 = -2

The third term = 2(3) - 14 = -8

Therefore, the arithmetic sequence is 4, -2, -8, .....

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The value of  PQ / BD of given parallelogram where Diagonal BD intersects line CM and line CN at P and Q, respectively  = 1/3

Let's consider the two triangles BMP and DCP.
Here,
∠DPC = ∠BPM (because they are vertically opposite angles)
∠DCP = ∠BMP (because they are alternate interior angles of transversal CM with DC // BM)
∴△BMP∼△DCP (By AA theorem)
Thus,
ABCD is a parallelogram. Therefore AB = DC and AD = BC.
It is given that M is the midpoint of AB
BD  = DQ  + BQ                BD = BP  + PD

BD = 2BQ  + BQ               BD = 2PD + PD

BD  = 3BQ                        BD = 3PD

therefore

BQ  = PD And

Since DQ  = 2BQ  then  DQ  = 2PD and

PD + PQ = 2PD   subtract PD from each side

PQ  = PD

so BQ = PD  = PQ

BD = PD + PQ + BQ

BD  = PQ  + PQ  + PQ

BD  = 3PQ

Therefore the value of  PQ / BD of given parallelogram is PQ / BD  = 1/3.

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The amount of work that the laborer has done, given the weight of the bricks and the laborer is 4, 577 Joules .

To calculate the amount of work done by the laborer, we can use the formula:

work = force x distance x

where:

force is the force applied,

distance is the distance moved,

The force applied by the laborer is the combined weight of the laborer and the bricks:

= 895N + 575N

= 1, 470N

Therefore, the work done by the laborer is:

Work = 1, 470N x 3.1m

= 4577 Nm or Joules (J)

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A manufacturer buys a new machine costing $180000 dollars. The value of the machine at the end of 10 years is $6000.

Calculate the annual depreciation of the machine.

Depreciation = (Purchase Price - Salvage Value) / Useful Life

Depreciation = (180000 - 6000) / 10

Depreciation = 174000 / 10

Depreciation = $17400 per year

Calculate the value of the machine at the end of each year.

Year 1: 180000 - 17400 = $162600

Year 2: 162600 - 17400 = $1452000

Year 3: 1452000 - 17400 = $1277600

Year 4: 1277600 - 17400 = $1103200

Year 5: 1103200 - 17400 = $928800

Year 6: 928800 - 17400 = $754400

Year 7: 754400 - 17400 = $580000

Year 8: 580000 - 17400 = $405600

Year 9: 405600 - 17400 = $231200

Year 10: 231200 - 17400 = $6000

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A one-sigma uncertainty criterion means that if a theoretical value falls within one standard deviation of the measured data, it is considered consistent with the data.

Using this criterion, we can rule out theoretical value D. 19.7, since it is outside the range of measured values.

The other theoretical values A. 15.6, B. 15.9, and C. 19.5 fall within one standard deviation of the measured data, so they cannot be ruled out by this criterion.

Therefore, the only theoretical value that can be ruled out by our usual     1-sigma uncertainty criterion is D. 19.7

It's worth noting that this method just gives a rough idea of the consistency of a theoretical value with the data.

Other methods, such as the chi-squared test, or Bayesian analysis could be used to find the best-fit theoretical value and its uncertainty, and confirm or rule out other theoretical values.

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The solution equation gives us y = 5x/2 - 2, so when x = 0, we get y = -2, which matches the initial condition.

The solution to the initial value problem can be obtained by using the substitution method. We first substitute the given function into the differential equation, which gives us the linear differential equation in y:

y' + 2y = 5x

We can then solve this linear differential equation by integrating both sides and applying the initial condition. This gives us the solution in y:

y = 5x/2 + C

where C is an arbitrary constant. To calculate the value of C, we plug in the initial condition y(0) = 2 into the equation. This gives us C = -2, so the solution to the initial value problem is given by:

y = 5x/2 - 2.

To illustrate this, let's consider the initial condition y(0) = 2. Plugging this into the solution equation gives us y = 5x/2 - 2, so when x = 0, we get y = -2, which matches the initial condition.

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If we take a sample of 50 Reece's Pieces candies, we would expect about 20 of them to be orange.

The manufacturer says that exactly 40% of the candies are orange. We can use this information to find the expected value of the number of orange candies in a sample of 50 candies.

Expected value is found by multiplying the number of trials (in this case, 50) by the probability of success (in this case, 40% or 0.40)

x = (50)(0.40) = 20 candies.

So, if we take a sample of 50 Reece's Pieces candies, we would expect about 20 of them to be orange.

It's worth noting that this is an expectation, the actual number of orange candies in the sample of 50 candies may be different from the expected value.

The correct question of the following problem is:

If a sample of 1000 Reese's Pieces contains 40% orange candies, and a random sample of 50 Reese's Pieces is selected, how many orange candies can be expected to be in the sample of 50 Reese's Pieces?  Let x be the number of orange candies in the sample of 50 Reese's Pieces.

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now, the assumption being that your granpa's are depositing the money at the beginning of the month.

[tex]~~~~~~~~~~~~\stackrel{\textit{deposits at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic deposits}\dotfill & 100\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &18 \end{cases}[/tex]

[tex]A=100\left[ \cfrac{\left( 1+\frac{0.03}{12} \right)^{12 \cdot 18}-1}{\frac{0.03}{12}} \right]\left(1+\frac{0.03}{12}\right) \\\\\\ A=100\left[ \cfrac{(1.0025)^{216}-1}{0.0025} \right](1.0025) \implies \boxed{A \approx 28665.52}[/tex]