Tell whether the two ratios are proportional or not proportional 3/7=6/9

Answer:

34

Step-by-step explanation:

We are here given a modulus expression and we need to find out the value when m = -5 and n = 3 .

Modulus :- It always gives positive value . For example ,

\(\rm\implies |-a| = a \)

\(\rm\implies |a| = a \)

The given modulus expression is :-

\(\rm\implies |m^2+ n^2| \)

As the number inside the modulus operator are already squared therefore they will always give positive value for real numbers . Here we can omit the modulus .

\(\rm\implies m^2 + n^2 \)

Plug in the given values ,

\(\rm\implies (-5)^2 + 3^2 \)

Solve 5² and 3² and add them ,

\(\rm\implies 25 + 9 \)

On adding ,

\(\rm\implies 34 \)

Therefore ,

\(\rm\implies \boxed{\blue{\rm |m^2+n^2| = 34 }}\)

Hence the required answer is 34 .

solution of the linear equation is x = (2a - 16)/ 3 and y = - (a+16)/ 9

An algebraic expression that shows a relationship between two variables   that have only first order term. One of the main criteria for linear equation is that we get a straight line when plot this equation in a coordinate system.

.

we are given, two linear equations x - a -3y = 0

and a - 2x -3y - 16 =0

from the first equation, x = a + 3y

we put the value of x in the second equation, a - 2(a +3y) - 3y -16= 0

                                                                     a - 2a - 6y - 3y -16 = 0

                                                          - a - 9y -16 =0

                                                   - (a + 16) = 9y

                                              y = - (a+16) / 9

now we put the value of y in the equation, x = a + 3y

                                    get, x = a+ 3 [ - (a+16)] / 9

                                      x = a + [ - (a+16)] / 3

                                          x = (3a - a -16) / 3

                              x = (2a - 16)/ 3

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Answer: D) -20.99

Step-by-step explanation:

-4.97-2.36+-5.19-8.47 = -20.99

The integral evaluates to 32π/3, which is the volume of the solid sphere with radius 4.

To evaluate the given integral by changing to polar coordinates, we first need to convert the given region of integration from Cartesian coordinates to polar coordinates.

Since R = {(x, y) : x2 + y2 ≤ 16, x ≥ 0} is a disk centered at the origin with radius 4, we can express the region in polar coordinates as 0 ≤ r ≤ 4 and 0 ≤ θ ≤ π/2 (because x ≥ 0).

Next, we need to express the integrand 16 − x2 − y2 in terms of polar coordinates.

Using the relationship x2 + y2 = r2, we have:
16 − x2 − y2 = 16 − r2

Thus, the integral becomes:
∫∫R 16 − x2 − y2 dA = ∫0^(π/2) ∫₀⁴ (16 − r2) r dr dθ

We can now evaluate the integral using polar coordinates.

The inner integral with respect to r is:
∫₀⁴ (16 − r2) r dr = [8r2 − (1/3)r3]₀⁴= 64/3

Substituting this result into the outer integral with respect to θ, we have:
∫0^(π/2) 64/3 dθ = (64/3)(π/2) = 32π/3
Therefore, the value of the given integral by changing to polar coordinates is 32π/3.

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The population density of Philadelphia is approximately 11,761.76 people per square mile, while the population density of Pottstown is approximately 4,672.16 people per square mile.

To compare the densities of Philadelphia and Pottstown, we need to calculate the population density for each city. Population density is typically measured as the number of individuals per unit area.

For Philadelphia:

Population = 1,579,000

Land area = 134.28 sq miles

Population density = Population / Land area

Population density = 1,579,000 / 134.28

Population density \(^\sim_\sim\) 11,761.76 people per square mile

For Pottstown:

Population = 22,670

Land area = 4.85 sq miles

Population density = Population / Land area

Population density = 22,670 / 4.85

Population density \(^\sim_\sim\) 4,672.16 people per square mile

Therefore, the population density of Philadelphia is approximately 11,761.76 people per square mile, while the population density of Pottstown is approximately 4,672.16 people per square mile.

Comparing the two, we can see that Philadelphia has a higher population density compared to Pottstown.

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Answer:i belive the answer should be 8800 dollars a year

Step-by-step explanation:

500000/25000

= ans  X  440

Hence r=1.11

What is compound interest?

When interest is calculated by taking compound interest formula  which is \(A = P(1 + r/n)^{nt}\)

where p is principal ,r is rate of interest , t is time , n of time compounded

How to calculate?

\(A = P(1 + r/n)^{nt}\)

given P=25000, A=500000,t=4 years n=1

\(500000 = 25000(1 + r)^{4}\)

2.11=1+r

r=1.11

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Answer:

16

Step-by-step explanation:

9-9:9 +9 - 9 :9 =

9 - 1 +9 - 1 =

8 +9 - 1 =

17 - 1 =

16

Answer:

A.P

Step-by-step explanation:

P is on the 1/8 mark (Hope this helps )

The weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

To determine the percentage of newborn African lions that weigh less than 3 pounds and the percentage that weigh more than 3.8 pounds, we would need statistical data on the weight distribution of newborn African lions. Since we don't have that information, we cannot provide the exact percentages.

However, if we assume that the weights of newborn African lions follow a normal distribution, we can use the properties of the standard normal distribution to make an estimation.

For the percentage of newborn African lions weighing less than 3 pounds:

We would need to know the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3 pounds and then find the corresponding percentage using a standard normal distribution table. Without this information, we cannot provide an accurate estimation.

For the percentage of newborn African lions weighing more than 3.8 pounds:

Similarly, we would need the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3.8 pounds and find the corresponding percentage using a standard normal distribution table. Without the required information, we cannot provide a specific estimation.

Please note that the weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

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Answer:

Step-by-step explanation:

8x^2 - 8x + 2

2(4x^2 - 4x + 1)

2(2x - 1)(2x - 1) or 2(2x - 1)^2

answer is C

The complete factorization of \(8x^2 - 8x + 2\) will be  \(2(2x-1)^2\) .

Factorization is a process consists of writing a number or another mathematical object as a product of several factors solving it into other factors.

We have,

\(8x^2 - 8x + 2\)

Using the mid term splitting method;

\(=8x^2-4x-4x+2\)

\(=4x(2x-1)-2(2x-1)\)

\(=(4x-2)(2x-1)\)

\(=2(2x-1)(2x-1)\)

\(=2(2x-1)^2\)

So, the factorization of the given expression is given in option \((c)\)  i.e.   \(2(2x-1)^2\) .

Hence, we can say that the complete factorization of \(8x^2 - 8x + 2\) will be  \(2(2x-1)^2\) .

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Given :

Han says that we can wrap a 5 foot rope around a wheel with a 2 foot rope.

To Find :

It this true or false.

Solution :

Radius of wheel, r = 1 foot.

Circumference of wheel is given by :

\(C = 2\pi r\\\\C = 2\times 3.14\times 1\\\\C = 6.28 \ foot\)

Since, circumference is greater than 5 foot, therefore, we cannot wrap a  5-foot rope around a wheel with a 2-foot diameter.

Hence, this is the required solution.

agree Step-by-step explanation:

Answer:

0.023

Step-by-step explanation:

Answer:

Step-by-step explanation:

sussy

Answer:

14 is the answer have a nice day

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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The decision-making process involved in Mikaela's decision to attend a Zumba class on Tuesday and Thursday afternoons and make it her regular exercise routine is "escalation."

In the scenario described, Mikaela initially started attending the Zumba class on Tuesday and Thursday afternoons. She found that it gave her a good workout and was satisfied with the results. As a result, she continued attending the class on those days and made it her regular exercise routine. This decision to stick to the same schedule without considering other options or making changes over time is an example of escalation.

Escalation in decision-making refers to the tendency to persist with a chosen course of action even if it may not be the most optimal or efficient choice. It occurs when individuals continue to invest time, effort, and resources into a decision or course of action, even if there may be better alternatives available. In this case, Mikaela has decided to stick with the Zumba class on Tuesday and Thursday afternoons because she found it effective and enjoyable, and she hasn't explored other exercise options since then.

It's important to note that escalation may not always be the best approach in decision-making. It's always a good idea to periodically reassess and evaluate the choices we make to ensure they still align with our goals and needs. Mikaela might benefit from periodically evaluating her exercise routine to see if it still meets her fitness goals and if there are other options she could explore for variety or improved results.

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Answer:

1+10×y

I think this is the answer...hope it helps ☆☆☆

Explanation: Finding 110 of a number is the same as dividing it by 10 . To find a tenth of something simply multiply it by 110 and then simplify.

Answer:

y=4/5+3 and 3/5

Step-by-step explanation:

Answer:

the answer is 56

Step-by-step explanation:

2x+3x+5=90

5x=90-5

5x=85

x=85/5

x=17

YVZ= 3(17)+5

YVZ=51+5

YVZ=56

Answer:

Maybe try 'A'..good luck

Answer:

We have system of equations

James's total cost: Y = 2x + 6 (1)

Sarah's total cost: Y = 3x + 4 (2)

replace y = 2x + 6 and (2) => 2x + 6 = 3x + 4 => x = 2 => y = 10

So the total cost of renting movies by James And Sarah is equal

Step-by-step explanation:

Step-by-step explanation:

Price of a book costing sh.250

reduced to sh.200

percentage decrease on the price = (250-200)/250×100

= 20%

Answer:

768,092,054

Step-by-step explanation:

700,000,000+60,000,000+8,000,000+90,000+2,000+50+4

The easiest way to solve is to put the numbers in every place value they go in. So, the answer would be...

768,092,054

Hope this helps! Have a nice day :D

Answer:

14 students per teacher

Step-by-step explanation:

Answer:

Second answer

Step-by-step explanation:

We are given \(\displaystyle \large{\sec \theta = -3}\) and \(\displaystyle \large{\sin \theta > 0}\). What we have to find are \(\displaystyle \large{\cot \theta}\) and \(\displaystyle \large{\cos \theta}\).

First, convert \(\displaystyle \large{\sec \theta}\) to \(\displaystyle \large{\frac{1}{\cos \theta}}\) via trigonometric identity. That gives us a new equation in form of \(\displaystyle \large{\cos \theta}\):

\(\displaystyle \large{\frac{1}{\cos \theta} = -3}\)

Multiply \(\displaystyle \large{\cos \theta}\) both sides to get rid of the denominator.

\(\displaystyle \large{\frac{1}{\cos \theta} \cdot \cos \theta = -3 \cos \theta}\\\displaystyle \large{1=-3 \cos \theta}\)

Then divide both sides by -3 to get \(\displaystyle \large{\cos \theta}\).

Hence, \(\displaystyle \large{\boxed{\cos \theta = - \frac{1}{3}}}\)

__________________________________________________________

Next, to find \(\displaystyle \large{\cot \theta}\), convert it to \(\displaystyle \large{\frac{1}{\tan \theta}}\) via trigonometric identity. Then we have to convert \(\displaystyle \large{\tan \theta}\) to \(\displaystyle \large{\frac{\sin \theta}{\cos \theta}}\) via another trigonometric identity. That gives us:

\(\displaystyle \large{\frac{1}{\frac{\sin \theta}{\cos \theta}}}\\\displaystyle \large{\frac{\cos \theta}{\sin \theta}\)

It seems that we do not know what \(\displaystyle \large{\sin \theta}\) is but we can find it by using the identity \(\displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta}}\)  for \(\displaystyle \large{\sin \theta > 0}\).

From \(\displaystyle \large{\cos \theta = -\frac{1}{3}}\) then \(\displaystyle \large{\cos ^2 \theta = \frac{1}{9}}\).

Therefore:

\(\displaystyle \large{\sin \theta=\sqrt{1-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{9}{9}-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{8}{9}}}\)

Then use the surd property to evaluate the square root.

Hence, \(\displaystyle \large{\boxed{\sin \theta=\frac{2\sqrt{2}}{3}}}\)

Now that we know what \(\displaystyle \large{\sin \theta}\) is. We can evaluate \(\displaystyle \large{\frac{\cos \theta}{\sin \theta}}\) which is another form or identity of \(\displaystyle \large{\cot \theta}\).

From the boxed values of \(\displaystyle \large{\cos \theta}\) and \(\displaystyle \large{\sin \theta}\):-

\(\displaystyle \large{\cot \theta = \frac{\cos \theta}{\sin \theta}}\\\displaystyle \large{\cot \theta = \frac{-\frac{1}{3}}{\frac{2\sqrt{2}}{3}}}\\\displaystyle \large{\cot \theta=-\frac{1}{3} \cdot \frac{3}{2\sqrt{2}}}\\\displaystyle \large{\cot \theta=-\frac{1}{2\sqrt{2}}\)

Then rationalize the value by multiplying both numerator and denominator with the denominator.

\(\displaystyle \large{\cot \theta = -\frac{1 \cdot 2\sqrt{2}}{2\sqrt{2} \cdot 2\sqrt{2}}}\\\displaystyle \large{\cot \theta = -\frac{2\sqrt{2}}{8}}\\\displaystyle \large{\cot \theta = -\frac{\sqrt{2}}{4}}\)

Hence, \(\displaystyle \large{\boxed{\cot \theta = -\frac{\sqrt{2}}{4}}}\)

Therefore, the second choice is the answer.

__________________________________________________________

Summary

\(\displaystyle \large{\sec \theta = \frac{1}{\cos \theta}}\\ \displaystyle \large{\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}}\\ \displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta} \ \ \ (\sin \theta > 0)}\\ \displaystyle \large{\tan \theta = \frac{\sin \theta}{\cos \theta}}\)

\(\displaystyle \large{\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}}\)

Let me know in the comment if you have any questions regarding this question or for clarification! Hope this helps as well.

Answer:

Exact volume = 30,000 + 5,000pi cubic mm

Approximate volume = 45,700 cubic mm

========================================================

Explanation:

Break the figure into two pieces.

The top part is a half-cylinder with radius r = 20/2 = 10 mm and height h = 100 mm.

The volume of this half-cylinder is

V = 0.5*(full cylinder volume)

V = 0.5*pi*r^2*h

V = 0.5*pi*10^2*100

V = 5000pi

This is exact in terms of pi.

The lower part is a 20 mm by 100 mm by 15 mm rectangular block. It has volume of length*width*height = 20*100*15 = 30,000 cubic mm.

---------

We'll add the two volumes found earlier to get the overall volume.

The total exact volume is 30,000+5,000pi cubic mm.

To get an approximation, you can use something like pi = 3.14

30000+5000pi = 30000+5000*3.14 = 45,700 cubic mm is the approximate volume when using pi = 3.14

Answer:

68x

Step-by-step explanation:

you first of all find the area

1/2b×h=

1/2x×34

1/2×1/34x

68x

The 98% confidence interval for the mean of the repeated measurements of the weight, with the sample size of 5, is approximately (5.3503, 14.6515).

To get the confidence interval, first let's see what we know:

To calculate the standard deviation, we'll use the sample mean as an estimate for the population standard deviation:

Standard Deviation = SD = x / √n

SD = 10.0009 / √5 ≈ 4.4721

Now we can calculate the margin of error:

Margin of Error = 2.326 * (SD/ √n) = 2.326 * (4.4721 / √5) ≈ 4.6506

Finally, we can calculate the 98% confidence interval:

Confidence Interval = (x - Margin of Error, x + Margin of Error) = (10.0009 - 4.6506, 10.0009 + 4.6506) ≈ (5.3503, 14.6515)

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