i need equivalent expressions

The distance being proportional to the time Hector walked 2 km in 18 minutes.

Two variables are proportional if they can be written in the form ak=b where k is the proportionality constant.

Here the proportionality constant is speed.

Speed is defined as the distance covered in unit time. The unit of speed can be written as kilometer per hour, miles per hour or meters per second.

The distance is proportional to the time walked therefore:

1.5/2=13.5/T₁

or, T₁=18

Similarly:

1.5/4.5=13.5/T₂

or, T₂=40.5 minutes

again,

1.5/5=13.5/T₃

or, T₃=45 minutes.

Hence the total time taken to complete the distances 2,4.5 and 5 is given by 18,40.5 and 45 minutes.

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Answer:

-1/2

Step-by-step explanation:

You find the change in the y coordinates. 6 -> 5 is -1. Now the same for the x. 2 -> 4 is +2. now place them in a fraction with the y/x -1/2. if both were negative then you would just cancel out the negatives.

Given, Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph.Both Jada and Elena start walking along a walking trail at the same time.

Let us determine the distance covered by both of them.Distance travelled by Jada in 3 hours is:Distance = Speed × Time= 3 mph × 3 hours= 9 miles Distance travelled by Elena in 3 hours is:Distance = Speed × Time= 2.8 mph × 3 hours= 8.4 miles Thus, Jada will walk 0.6 miles farther than Elena after 3 hours.

To determine how far Jada will walk after 3 hours, we need to calculate the distance traveled based on her speed.

Jada walks at a speed of 3 miles per hour (mph), so we can calculate her distance using the formula:

Distance = Speed × Time

Plugging in the values, we have:

Distance = 3 mph × 3 hours

Distance = 9 miles

Therefore, Jada will walk a distance of 9 miles after 3 hours.

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The given information is as follows:

Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph. If they both begin walking along a walking trail at the same time.

Therefore, Jada will walk 9 miles after 3 hours.

The distance covered by Jada after 3 hours can be calculated as follows:

Distance = Speed x Time

Since Jada walks at a speed of 3 mph, the distance covered by her in 3 hours can be calculated as:

Distance covered by Jada = 3 mph x 3 hours

= 9 miles.

Therefore, Jada will walk 9 miles after 3 hours.

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Based on the percentage each spent on new school clothes, Hannah spent $42.90 (difference in spending) more than Katie.

The difference is the result of the subtraction of the total spending by Hannah and Katie on their new school clothes.

However, before this difference is determined, we first apply the percentage spent on their total earnings during the period.

                                                                   Hannah     Katie

Rate per week                                            $78.50    $95.25

Number of weeks worked                              9             8

Total earned during the period               $706.50    $762 ($95.25 x 8)

Percentage spent on new school clothes  60%      50%

Amount spent on new school clothes    $423.90   $381 ($762 x 50%)

The difference in spending by Hannah and Katie = $42.90 ($423.90 - $381)

Thus, we can conclude that Hannah spent $42.90 more than Katie, even though Katie earned more than Hannah.

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The hippopotamus's mass increased by about 164.5% over the two-month period.

Mass plays an important role in determining the behavior of objects under the influence of external forces. For example, Newton's second law of motion states that the acceleration of an object is directly proportional to the force applied to it, and inversely proportional to its mass. This means that objects with greater mass require more force to accelerate them than objects with lower mass.

In the given question,

To find the percentage increase, we need to calculate the difference between the final and initial mass, divide that difference by the initial mass, and then multiply by 100 to get a percentage.

The difference between the final and initial mass is:

89.3 kg - 33.8 kg = 55.5 kg

The percentage increase is:

(55.5 kg / 33.8 kg) x 100% ≈ 164.5%

Therefore, the hippopotamus's mass increased by about 164.5% over the two-month period.

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The probability that a homebuilder takes 200 days or less to complete a house is approximately 0.8238, or 82.38%.

Explanation :

To answer this question, we can use the concept of the z-score. The z-score tells us how many standard deviations a data point is from the mean.

Let's calculate the z-score for a completion time of 200 days:
z = (x - μ) / σ
where x is the completion time, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get:
z = (200 - 176.7) / 24.8 = 0.93

To find the probability associated with this z-score, we can use a z-table or a calculator. In this case, the probability is 0.8238.

This means that there is an 82.38% chance that the completion time of a house will be 200 days or less, given that the completion time follows a normal distribution with a mean of 176.7 days and a standard deviation of 24.8 days.

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Answer:

0 represents ground level.

Step-by-step explanation:

0 on the number line represents ground level. Based on the photo, the 0 is in between the underground and the space above. The answer cannot be one of the negative numbers because those are all shown to be underground in the photo.

Answer:

SAS because they stand for side angle side

Answer:

2 outcomes

Step-by-step explanation

The Roslin has 32 students in her class, of these students, 14 are girlsl number of outcomes are 252.

It is a branch of mathematics that deals with the occurrence of a random event.

The total number of outcomes can be found by multiplying the number of options for choosing a boy by the number of options for choosing a girl:

Number of outcomes = number of options for choosing a boy x number of options for choosing a girl

Since Mrs. Roslin has 32 students in her class, there are 32 - 14 = 18 boys in her class.

So the number of options for choosing a boy is 18, and the number of options for choosing a girl is 14.

Therefore, the total number of outcomes is:

18 x 14 = 252

Hence, the total number of outcomes is 252.

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Answer:

The height of the flagpole is approximately 5.774 meters.

Step-by-step explanation:

Let's call the height of the flagpole h. We can use trigonometry to set up the following equation:

tan(30°) = h/10

Simplifying this equation, we get:

h = 10 tan(30°)

Using a calculator, we find that tan(30°) ≈ 0.5774, so:

h ≈ 5.774 meters

Therefore, the height of the flagpole is approximately 5.774 meters.

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Regression analysis is a statistical method for making predictions by using data on the correlation between independent or predictor variables and dependent variables.

Regression analysis, a collection of statistical methods used in statistical modeling, is used to compare a dependent variable (also known as the "outcome" or "response" variable, or a "label" in machine learning jargon) and one or more independent variables (also known as "predictors," "covariates," "explanatory variables," or "features").

In linear regression, the most popular kind of regression analysis, the line (or more complex linear combination) that most closely matches the data in terms of a given mathematical criterion is found.

Regression analysis is employed to deduce the causal relationships between the variables in a given situation. It should be noted that regressions by themselves only reveal relationships between a dependent variable and a set of independent variables in a particular dataset.

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Answer:

x > 5

Step-by-step explanation:

14-3x< -1

Subtract 14 from each side

14-3x-14< -1-14

-3x < -15

Divide each side by -3, remembering to flip the inequality

-3x/-3 < -15/-3

x > 5

Answer:

x>5

Step-by-step explanation:

14-3x<-1

What we need to do here is to isolate x.

Let's subtract 14 from both sides.

14-14-3x<-1-14

-3x<-15

Divide both sides by 3.

-x<-5

Divide both sides by -1.

Note that when you divide an inequality by a negative number, you have to flip the sign.

x>5

Answer:

6

Step-by-step explanation:

rearrange the numbers from smallest to biggest:

-19, -14, -9, -3, 6, 8, 14, 19, 20

the set of data the question requires is the middle data. there are 9 sets of data. the middle data = (9 + 1) ÷ 2 = 5

find the fifth piece of data from the rearranged order.

ans: 6

Answer:

6

Step-by-step explanation:

gotchu G

No, it is not possible for matrix A and B to be similar when B = A + I, where A is an nxn matrix and I is the identity matrix of the same size.

Two matrices A and B are said to be similar if there exists an invertible matrix P such that \(B = P^{(-1)}AP\). In this case, A and B have the same eigenvalues, and their corresponding eigenvectors can be related through the matrix P.

Let's consider the eigenvalues of B. Since B = A + I, the eigenvalues of B are obtained by adding 1 to each eigenvalue of A. In other words, if λ is an eigenvalue of A, then λ + 1 is an eigenvalue of B.

Now, suppose A and B are similar. This means that they have the same eigenvalues. However, the eigenvalues of B are shifted by 1 compared to the eigenvalues of A. Therefore, it is not possible for A and B to have the same eigenvalues, unless A has eigenvalues that are all equal to -1.

Since the eigenvalues of A and B are different, we can conclude that A and B cannot be similar.

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The surface area and volume of a cube with different edge length are

When a cube with edge length 4inches ,

Surface area = 96 square inches and Volume =64 cubic inches.

Cube dilated by scale factor 0.25 ,  

Surface area = 6 square inches and Volume =1 cubic inches.

The surface area of a cube is = 6 times the area of one face.

Each face of this cube has an area equals to

= (4 inches) x (4 inches)

= 16 square inches,

So the total surface area is,

Surface area

= 6 x 16 square inches

= 96 square inches

The volume of a cube =  length of one edge cubed.

Here, the edge length is 4 inches,

Volume

= (4 inches)^3

= 64 cubic inches

When a cube is dilated by a scale factor of 0.25, all of its edges are multiplied by 0.25.

This implies,

The edge length of the image cube is

0.25 x 4 inches = 1 inch.

Surface area of the image cube =  6 times the area of one face.

Each face of the image cube has an area of

= (1 inch) x (1 inch)

= 1 square inch,

So the total surface area is,

Surface area

= 6 x 1 square inch

= 6 square inches

Volume of the image cube = length of one edge cubed.

Here, the edge length is 1 inch,

Volume

= (1 inch)^3

= 1 cubic inch

Therefore, the surface area and volume for the given dimensions are

For edge length 4inches , Surface area = 96 square inches and Volume =64 cubic inches.

For scale factor 0.25 ,  Surface area = 6 square inches and Volume =1 cubic inches.

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>3. its less than 3 because it is

Answer:

16, 64, 256

Step-by-step explanation:

Answer:

1 full physical and 33 routine visits per day to maximize income for the day.

Maximum income is $2080.

Step-by-step explanation:

The doctor has 9 hours per day which equals to 9 x 60 = 540 minutes

If there are 10 physicals per day, the maximum minutes will be 45 x 10 = 450 minutes.

so the time left for routine office visits will be 540 - 450 = 90 minutes

then the number of routine office visits will be 90 / 15 = 6

Her income will be ($100 x 10) + ($60 x 6) = 1000 + 360 = $1360

If there is 1 physical per day, then the time will be 45 x 1 = 45 minutes

so time left for routine office visits will be 540 - 45 = 495 minutes

then the number of routine office visits will be 495 / 15 = 33

Her income will be ($100 x 1) + ($60 x 33) = 100 + 1980 = $2080

If there are 2 physicals per day, then the time will be 45 x 2 = 90 minutes

so time left for routine office visits will be 540 - 90 = 450 minutes

then the number of routine office visits will be 450 / 15 = 30

Her income will be ($100 x 2) + ($60 x 30) = 200 + 1800 = $2000

Answer:

Step-by-step explanation:

You want to maximize the doctor's income when she makes $60 for a 15-minute routine visit and $100 for a 45-minute physical. She can work 9 hours per day.

For a routine visit, the doctor is charging $60 for 15 minutes, or $4 per minute.

For a physical, the doctor is charging $100 for 45 minutes, or $2.22 per minute.

Clearly, the doctor earns income faster by spending her time doing routine office visits. There appears to be no limit on the number of those she can do.

Working 9 hours at $4 per minute, the doctor earns ...

  (9 h/day)(60 min/h)($4/min) = $2160/day

The number of routine visits in a day will be ...

  (9 h/day)(60 min/h)/(15 min/visit) = (9·60/15) visits/day = 36 visits/day

The doctor's maximum income is $2160 per day, making 36 routine office visits per day.

__

Additional comment

Each physical will reduce the doctor's income by $80. (In that 45 minutes, she could have done 3 routine visits, for a revenue of 3·60 = 180, instead of the physical for a revenue of 100.)

The radius of convergence (r) for the given series is 0.

To determine the radius of convergence for the given series, we need to consider the convergence of the series expansion of the function f(x) = ln(2 - x) around a specific point. The radius of convergence (r) is the distance from this point to the nearest singularity of the function.

In this case, the series expansion is centered around x = 2 since ln(2 - x) is not defined for x = 2. Therefore, the radius of convergence (r) is the distance from x = 2 to the nearest singularity.

Since the function ln(2 - x) is not defined for x = 2, we can say that the nearest singularity is located at x = 2. Hence, the distance from x = 2 to the nearest singularity is 0.

Therefore, the radius of convergence (r) for the given series is 0.

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As per the unitary method, there are 64.29 weeks does it take to empty the lake.

The term unitary method is known as a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here we have given that officials begin to release water from a full man-made lake at a rate that would empty the lake in 12 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time.

And we need to find the number of weeks does it take to empty the lake

While we looking into the given question, we have identified the following values,

=> Empty rate = 1/18 job/week

=> Fill rate = 1/25 job/week

Then together rate is written as 1/x

Then the equation of the given situation is written as,

=> rate - rate = together rate

When we apply the values, then we get,

=> 1/18 - 1/25 = 1/x

Now we have to multiply thru by 18*25x, then we get,

=> 25x - 18x = 18*25

=> 7x = 18*25

Therefore, x = 64.29 weeks.

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Answer:

y=-1/10x+50 I beleive.

Step-by-step explanation:

y=mx+b

y2-y2/x2-x1

(10,4); (20,3)

3-4/20-10

-1/10

y=-1/10x+50

Answer:

A. i think

Step-by-step explanation:

Answer:

4, -16, 64, -256

the common ratio is -4

Step-by-step explanation:

The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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Answer:

b. line j or MT

Step-by-step explanation:

as the plane contains the points Q, N, P, R, T also the lines connecting only these points are in the plane, and are not intersecting the plane.

only M is outside of the plane, and so (only) the connecting line MT intersects the plane (at point T).

by the way, the question means the line RQ and not RO, as there is no point O in the graphic.

The celestial sphere and Earth is the example of a beach ball with a ping pong ball inside of it can be used to imagine the relationship between what two entities.

The heavenly sphere is what Why is this old idea still relevant today?

Which phrase most accurately sums up the celestial sphere?

The entire sky as seen from Earth is portrayed by the celestial sphere. Keep in mind that the celestial sphere is intended to depict the sky as it appears from our planet rather than physical reality.

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If a=4, b=6, and sina=3/5 in triangle abc, then sin b equals: 9/10

To find sin(b) in triangle ABC, we can use the sine function in a right angle and the given information.

Given:

a = 4

b = 6

sin(a) = 3/5

We know that the sine of an angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In triangle ABC, let's label the side opposite angle a as side c and the hypotenuse as side h.

sin(a) = c / h

Substituting the given values:

3/5 = 4 / h

To solve for h, we can cross-multiply:

3h = 5 * 4

3h = 20

h = 20 / 3

Now, we can use the sine function to find sin(b):

sin(b) = side opposite angle b / hypotenuse

sin(b) = 6 / (20 / 3)

sin(b) = 6 * (3 / 20)

sin(b) = 18 / 20

sin(b) = 9 / 10

Therefore, sin(b) equals 9/10.

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a) The software output provides a 95% confidence interval of 29.202 to 31.844 weeks for the average age at which babies begin to crawl.

b) The margin of error for this interval is 2.642 weeks.

c) If the researcher had calculated a 90% confidence interval, the margin of error would likely be smaller as a narrower interval is required to capture a smaller confidence level.

a) The software output presents a 95% confidence interval , which means that if we were to take repeated samples from the population and construct confidence intervals in the same way, approximately 95% of those intervals would contain the true population mean age at which babies begin to crawl. The interval 29.202 < μ(age) < 31.844 suggests that the true population mean age lies somewhere within this range.

b) The margin of error for this interval can be calculated by subtracting the lower bound from the upper bound. In this case, the margin of error is 31.844 - 29.202 = 2.642 weeks. This represents the range within which the estimated population mean is likely to vary.

c) If the researcher had calculated a 90% confidence interval instead of a 95% confidence interval, the margin of error would likely be smaller. This is because a narrower interval is needed to capture a smaller confidence level. A 90% confidence interval allows for a higher degree of precision but sacrifices some level of certainty compared to a 95% confidence interval. As a result, the margin of error would be smaller for a 90% confidence interval.

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it is going to be true