Solving a word problem involving rates and time conversion
A car travels at an average speed of 68 miles per hour. How long does it take to travel 221 miles?

Answer:

60

Step-by-step explanation:

The discount is the original price times the discount rate

200 * .30

60

Actual time is much longer than the 50-year timeframe suggested by the speaker.

How to verify the statement?

This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.

To verify this claim, we can use the following formula to calculate the expected total pollution after n years:

Total pollution after n years = \(Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n\)

Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.

We can set the expected total pollution after n years equal to the present pollution level and solve for n:

\(Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n\)

Simplifying this equation, we get:

\(1 = 1.03^n \times 0.2^n\)

Taking the logarithm of both sides of the equation, we get,

\(n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56\)

Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.

It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.

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Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"

if 5/8 is given in the question, then YES. If not, then NO

Answer:

Step-by-step explanation:

1) You can show that two pairs of angles of each triangle are equal, ∠SRP = ∠SRT = 90°, and the given ∠QPR and ∠STR

2) This means that ∠PQR and ∠TSR must be identical as well as the internal angles of a triangle must sum to 180°

3) Three angles of triangles identical is sufficient to say that the triangles are similar. (Actually you only need two equal pairs of angles for proof because  step 2 is rather redundant)

Using proportions, it is found that due to the smaller division of the exchange rate by the cost, the souvenir would be less expensive in Egypt.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The souvenir would be less expensive in the country in which the division of the exchange rate by the cost is smaller.

In Britain, the cost is of 17, with an exchange rate of 0.83, hence the cost in US dollars is:

c = 17/0.83 = $20.48.

In Egypt, the cost is of 288, with an exchange rate of 18, hence the cost in US dollars is:

c = 288/18 = $16.

16 < 20.48, hence the souvenir would be less expensive in Egypt.

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Answer:

\(19.9+0.05t<25\)

Less than 102 text messages.

Step-by-step explanation:

Monthly charge of cell phone = $19.90

Cost of one text message = $0.05

Let number of text messages be \(t\)

The monthly bill should be less than $25. So,

\(19.9+0.05t<25\)

The required inequality is \(19.9+0.05t<25\)

\(19.9+0.05t<25\\\Rightarrow 0.05t<25-19.9\\\Rightarrow t<\dfrac{5.1}{0.05}\\\Rightarrow t<102\)

So, the number of text messages that can be sent while keeping the bill under $25 is less than 102.

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

Let's denote the original scholarship amount as "P."

According to the given information, Margaret receives $72,000, which means the remaining scholarship amount for the other three individuals is P - $72,000.

Ron receives 1/3 of the scholarship, which can be represented as (1/3)(P - $72,000). Nick receives 1/4 of the scholarship, which can be represented as (1/4)(P - $72,000). Mary receives the same as Nick, so Mary's share is also (1/4)(P - $72,000).

Now, we can sum up all the shares to equal the original scholarship amount:

Ron's share + Nick's share + Mary's share + Margaret's share = P

(1/3)(P - $72,000) + (1/4)(P - $72,000) + (1/4)(P - $72,000) + $72,000 = P

To simplify the equation, we can combine like terms:

(P/3 - $24,000) + (P/4 - $18,000) + (P/4 - $18,000) + $72,000 = P

Combining the fractions and constants:

(4P + 3P - 3P + 12P)/12 - $24,000 - $18,000 - $18,000 + $72,000 = P

16P/12 - $48,000 = P

Multiplying both sides of the equation by 12 to eliminate the denominator:

16P - $576,000 = 12P

Subtracting 12P from both sides of the equation:

4P = $576,000

Dividing both sides of the equation by 4:

P = $144,000

Therefore, the original scholarship amount is $144,000.

Ron's share: (1/3)($144,000 - $72,000) = $24,000

Nick's share: (1/4)($144,000 - $72,000) = $18,000

Mary's share: (1/4)($144,000 - $72,000) = $18,000

Margaret's share: $72,000

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

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Answer:

300kms

Step-by-step explanation:

900÷300 is 300. so then i think it would be 300kms

Answer:

m=−4/15

Step-by-step explanation:

if my answer right or wrong plz tell me and like and rate plz. THANK YOU

Answer:

The length for the edge should be 6.

Step-by-step explanation:

Hope this helps

Answer:

The numerical limits for a D grade are 58(lower limit) and 61(upper limit).

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Scores on the test are normally distributed with a mean of 67.3 and a standard deviation of 7.3.

This means that \(\mu = 67.3, \sigma = 7.3\)

D: Scores below the top 80% and above the bottom 9%

This means that lower bound is the 9th percentile and the upper bound is the 100 - 80 = 20th percentile.

9th percentile:

This is X when Z has a pvalue of 0.09. So X when Z = -1.34.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.34 = \frac{X - 67.3}{7.3}\)

\(X - 67.3 = -1.34*7.3\)

\(X = 57.52\)

Rounding to the nearest whole number, 58.

20th percentile:

This is X when Z has a pvalue of 0.2. So X when Z = -0.84

\(Z = \frac{X - \mu}{\sigma}\)

\(-0.84 = \frac{X - 67.3}{7.3}\)

\(X - 67.3 = -0.84*7.3\)

\(X = 61.17\)

Rounding to the nearest whole number, 61.

The numerical limits for a D grade are 58(lower limit) and 61(upper limit).

The rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

The mathematical concept of rate of change describes how much one quantity changes in relation to another. It is calculated as the difference between the change in the output (the dependent variable) and the change in the input (independent variable).

The rate of change, in other words, informs us of how quickly or slowly something is changing through time or in relation to another variable. When tracking the distance an automobile travels over time, for instance, the rate of change would be the car's speed, which is calculated as the distance traveled divided by the time required.

Slope, which is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a graph, is a common way to depict the rate of change. The rate of change of the dependent variable with respect to the independent variable is depicted by the slope of a straight-line graph.

The rate of change in the total amount charged with respect to the time spent on the service call represents the slope of the graph. We can find the slope of the graph by taking any two points on the line and calculating the change in y (total amount) divided by the change in x (time spent on the service call).

Looking at the graph, we can choose two points: (2, 130) and (8, 370). The change in y is:

370 - 130 = 240

And the change in x is:

8 - 2 = 6

Therefore, the slope (rate of change) of the graph is:

240/6 = 40

So the rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

Therefore, the correct option is $40 per hour.

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A = 139°

B = 139°

You can see A and B are coefficients of each other, which means they have the same angle because they are opposite each other on the straight line. just like the two 41° angles are.

The angle around a point always add up to 360°, so add the 41° angles.

41 + 41 = 82°

Then minus this by 360°.

360 - 82 = 278°

And to work out one angle, which gives you the angle for both, divide 278 by two.

278 ÷ 2 = 139°

Both A and B have an angle of 139°

Example:

To find the value of two intersecting lines, you need to know the equations of both lines. Then, you can set the equations equal to each other and solve for the variable x. This will give you the x-coordinate of the point where the lines intersect. To find the y-coordinate, you can plug the value of x into either equation and solve for y. For example, if one line is y = 3x - 5 and another line is y = -2x + 7, then you can set 3x - 5 = -2x + 7 and solve for x:

3x - 5 = -2x + 7

5x = 12

x = 12/5

Then, plug x = 12/5 into either equation and solve for y:

y = 3(12/5) - 5

y = 36/5 - 25/5

y = 11/5

Therefore, the point of intersection is (12/5, 11/5).

If one of the lines has a given angle, such as 41 degrees, then you can use trigonometry to find its equation. For example, if one line passes through the origin and has an angle of 41 degrees with the positive x-axis, then you can use the slope formula to find its equation:

slope = tan(41 degrees) ≈ 0.87

y = mx + b

y = 0.87x + 0

Then, you can use the same method as before to find the point of intersection with another line.

_______________________________________________________

The answer is 139 degrees, using the method I gave.

MARK AS BRAINLIEST!!!

Answer:

1296

Step-by-step explanation:

Simple interest is

I = PRT where I is the interest P is the principle, r is the rate and t is the time

I = 1350 * .08 * 12

I = 1296

Since the base is a triangle its area is given as:

In this case the lenght of the base of the triangle is 3 and its height is 4, then the area of the base is:

Therefore the answer is the third option.

The mean of the data set is 82.77

If we want to find the mean, we would have to put it at the back of our minds that the mean is the same as the average. As such, we would have to take the sum of all the values that have been listed in the data set and divide by the total number of the data.

The first step is to arrange the data set orderly from smallest to largest;

70, 71,79, 82,88,85,87,91,92

We have nine values in the data set thus the mean is;

70+71+79+82+88+85+87+91+92/9= 745/9= 82.77

Hence the mean of the data set is 82.77

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Answer:

a 270° rotation about point P

Step-by-step explanation:

Because after transformation MK and M'K 'are at 90°, that implies that MK is rotated as 90 ° clockwise around P or 270 ° counterclockwise around P.

Therefore the transformation composition that maps \(\triangle KLM\) to \(\triangle\)K"L"M",

So, for this composition, the first transformation is 270° is the 270° rotation i.e to be counterclockwise about point P.

While the transformation of the second would be down translation that goes to the right.

hence, the last option is correct

Answer:

D 270 Degree Rotation About Point P

Step-by-step explanation:

E2020

Answer:

you can only afford basic as both other options are over $100

Step-by-step explanation:

standard = 964 - 50 = 914 left

914/8 = 114.25 per month

formula: 8m + 50 = 964

deluxe = 1940-50 = 1890 left

1890/18 = 105 per month

formula: 18m + 50 = 1940

Answer:

Hope this helps ;)

Step-by-step explanation:

To find the time it takes the T-shirt to reach its maximum height, we need to find the value of t when the velocity of the T-shirt is zero, because at this point the T-shirt has reached its maximum height and starts falling back down. We can find the velocity of the T-shirt by taking the derivative of the height equation with respect to time:

v(t) = h'(t) = 72

The velocity of the T-shirt is a constant 72 feet per second, so it will never reach a velocity of zero and will never reach its maximum height. The T-shirt will keep going up indefinitely.

If the problem had specified that the T-shirt was launched with an initial upward velocity of -72 feet per second (meaning it was launched downward), then we could have found the time it takes the T-shirt to reach its maximum height by setting v(t) = 0 and solving for t. In this case, we would find that t = 1, so it would take the T-shirt 1 second to reach its maximum height. The maximum height would be h(1) = -16 + 72(1) + 6 = 62 feet.

In given fractions 8/9 is 1/36 large than 31/36

Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.

We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).    

If the denominators are the same then it is easy to compare the fractions.

Here we have

31/36 and 8/9

To find the largest fraction convert both denominators into the same  

Here LCM(36, 9) = 36  

Now multiply both numerator and denominators of fractions with a number to change the denominators  

=> \(\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}\)  

=> \(\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}\)  

From the above calculations given fractions are 31/36 and 32/36

Difference = \(\frac{32}{36} - \frac{31}{36} = \frac{1}{36}\)  

Therefore,

In given fractions 8/9 is 1/36 large than 31/36

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Answer:

The answer is D

Step-by-step explanation:

Please let me know if I'm wrong i will do the work on my notebook over again.

Have a blessed day

Answer:

Option D

Step-by-step explanation:

If angles of triangles are same then the triangles must be similar .Side length not gonna be instructed.

Here

Option D has 2 same angles

So option D is correct

Answer:

12(1+3)

6(3+1)

12(4)

6(4)

48

24

answer = 2

Answer:

35 students

Step-by-step explanation:

So if every 3 boys there is 4 girls you can solve that there is 5 times the amount of girls to get to 20. So to solve for the boys you do the same.

3 x 5 = 15

That means there are 15 boys and 20 girls but we want to know the total so what you do is just add 15+20=35

So 35 total students.

Hope that helps and have a great day!

The average ticket cost for each concert is given as follows:

The ticket costs are obtained by a system of equations, for which the variables are given as follows:

It cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B, hence:

6a + 6b = 1707

a + b = 284.5.

Three tickets for concert B cost a total of $687, hence the cost for concert B is of:

3b = 687

b = 287/3

b = $95.67.

Replacing into the first equation, the cost for concert A is given as follows;

a = 284.5 - 95.67

a = $188.83.

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Answer:

3

Step-by-step explanation:

6/7 divided by 2/7

=

6/7 divide 7/2 (cancel out 7)

=

6 multiply 1/2 (reduce)

=

3