Grace drew a triangle with sides of equal length. Its measured with sides of 3 cm. What is the perimeter of the triangle?

Answer:

C. 9 gallons per minute

Step-by-step explanation:

Divide 135 by 15 to see how many gallons he can fill in one minute.

135 ÷ 15 = 9

Hope this helps!

We may infer from the number line that A and B are separated by 8 units (AB).

Let AB stand for the separation between points A and B, and let AC stand for the separation between points A and C. Let B stand for the separation between points B and C. Hence:

Point B being halfway between A and C, we can infer:

AB + BC Equals AC (Postulated segment addition)

As a result, since the distance between points A and B is equal to 1/3 of AC:

AC/3 = AB = 1/3(AC)

But as shown in the accompanying image:

AC equals 16 – (–8) to 24 units.

Therefore:

AB = 1/24 = 8 unit

A and B are separated by 8 units.

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On the number line, Point B is between points A and C. The distance between points A and B is 1/3 of AC. What is AB?​

Answer: \(\dfrac19\text{ miles per minute}\)

Step-by-step explanation:

Given: Length of one lap = \(\dfrac16\) mile.

Jane ran 7 laps, Total distance covered = \(7\times\dfrac16=\dfrac76\text{ miles}\)

Time taken =  10 minutes 30 seconds

\(=\text{ 10 minutes}+\dfrac{30}{60}\text{ minutes}\text{ [1 minute = 60 seconds]}\\\\=(10+\dfrac{1}{2})\text{ minutes}\\\\=\dfrac{21}{2}\text{ minutes}\)

Jane's average speed = \(\dfrac{\text{Total distance covered}}{\text{ Time taken}}\)

\(=\dfrac{\dfrac76}{\dfrac{21}{2}}\\\\=\dfrac{7}{6}\times\dfrac{2}{21}\\\\=\dfrac{1}{9}\text{ miles per minute}\)

Hence, Jane’s average speed = \(\dfrac19\text{ miles per minute}\)

Based on the number of laps that Jane ran and the time she ran it in, her average speed per minute must have been 0.11 miles per minute.

First convert the number of laps ran to miles:

= Number of laps x Conversion factor

= 7 x 1/6

= 7/6 miles

The number of minutes was:

= 10 minutes 30 seconds

= 10.5 minutes

The speed in miles per minute is:

= Number of miles / Number of minutes

= 7/6 ÷ 10.5

= 0.11 miles per minute

In conclusion, find out more at 0.11 miles per minute.

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Answer:

---------------------------

There are total 20 numbers and half of them odd and half of them even.

Without replacement, the probability of an odd and then even number is:

Answer:

assuming that you start at the origin (0,0)

(-4,-1) would be the poiny

x coord = -4

y coord = -1

the point is in the 3 quadrant

Step-by-step explanation:

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer:

Step-by-step explanation:

1) f(-4) --> if x < or equal to 3

2) 1/(-4)-4

3) The answer is - 1/8

Answer:

There are many ways to solve this problem, here let's follow the hints

Probability of having exact 6 boys in 8 children:

8C6 x P(boys)^6 x P(girls)^2 = 8C6 x (1/2)^6 x (1/2)^2 =8C6 x (1/2)^8

Probability of having exact 7 boys in 8 children:

8C7 x P(boys)^7 x P(girls)^1 = 8C7 x (1/2)^7 x (1/2)^1 =8C6 x (1/2)^8

Probability of having exact 8 boys in 8 children:

8C8 x P(boys)^8  = 8C8 x (1/2)^8

Add these three, we have the solution

P = (8C6 + 8C7 + 8C8) x (1/2)^8 = (28 + 8 + 1) x (1/2)^8 = 0.1445

=> Option D is correct.

Note: 8C6, 8C7, 8C8 are combination notation.

Hope this helps!

:)

Answer:

the answer is d

Step-by-step explanation:

Answer:

  499.338 feet

Step-by-step explanation:

You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.

The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...

  \(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)

The distance traveled in 25 seconds is 499.33 feet.

It is required to find the distance traveled in 25 seconds.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

We have to find the distance , we will integrate v(t) from 0 to 25 second.

Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.

Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is

1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.

According to given question we have

Given a velocity function v, the distance s is figured by taking the integral. In this case,

v = 20 + 5 cos(t)

s = 20t + 5 sin(t) from 0 to 25

= s(45)-s(0)

s(0) = 0

so, the distance is

s(25) = 20*25 + 5sin(25)

= 500 -0.661

=499.33 feet.

Therefore, the distance traveled in 25 seconds is 499.33 feet.

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Answer:

4 outcomes

Step-by-step explanation:

Based on the information given, the night crawler worm burrows 15.17 yards. This prompt requires a lot of conversion between Units of Length.

Given that Night Crawler Worms burrow 6.5 feet per day.

Yards burrowed per week = 6.5 x 7 x 0.333333

Where 1 foot = 0.333333

Hence,

6.5 x 7 =45.5

45.5 x 0.333333

\($\approx$\) 15.17 yards

We have been given:

Night Crawler Worms live up to 6 years.

If they burrow 6.5 feet per day

Hence, Total miles burrowed in a life time = 365 x 6 x 6.5 x 0.000189394

Where 1 foot = 0.000189394

Recall that there are 365 days in a year.

Hence,

Total miles burrowed in a life time = 365 x 6 x 6.5 x 0.000189394

= 2.69602359

\($\approx$\) 3 miles

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About 88.49% of cellphone plans have charges that are less than $83.60.

To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.

z = (x – μ) / σ

where x = 83.60, mean, μ =  62 and standard deviation, σ = 18

Thus, the z-score of $83.60 is:

z = (83.60 - 62) / 18 = 1.2

Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).

Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.

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Answer:

\(f = 7s -2\)

\(f + s =53\)

Step-by-step explanation:

Given

Let

f = Father's age

s = Son's age

We'll solve this question, while reading through the instructions

From the first statement;

f is 2 less than 7 times s.

This means

\(f = 7s -2\)

In two years time, the father will be f +2 and the son will be s + 2

So, their sum is:

\((f+2) + (s + 2) = 57\)

\(f + 2 + s + 2 =57\)

Collect like terns

\(f + s =57-2-2\)

\(f + s =53\)

So, the equations are:

\(f = 7s -2\)

\(f + s =53\)

In a case whereby In 1950, a U.S. population model was y = 151. (1.013)^t-1950 million people, where t is the year, the model predict the U.S. population would be 288 million in the year 2000.

Population models are mechanical theories that link alterations in population structure and density to responses at the individual level (life history features in eco-evolutionary theory or vital rates in demographic theory).

The model was given as y=151x(1.013)^t-1950

where the future time t = 2000

Then we can substitute the given year 2000 as the value of 't'

then we will have y=[151x(1.013)^(2000-1950)] = 288 million

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answer:

A' (-3,3) B' (-2,-1) C' (-6, -2)

The value of piecewise function at x = -1 is f(-1) = 11, and the value of piecewise function at x = 9 is f(9) = 1.

what is piecewise function?

A piecewise-defined function in mathematics is one that is composed of several smaller functions, each of which has a specific interval of the domain it applies to. Instead of being a property of the function itself, piecewise definition is a way to express the function.

We have to evaluate the piecewise function for x = -1 and x = 9.

Let, function has value for x = -1 in the domain x ≤ 5 which is 11.

And function has value for x = 9  in the domain 6 < x which is 1.

⇒  f(-1) = 11 and f(9) = 1

Hence, the value of piecewise function at x = -1 is f(-1) = 11, and the value of piecewise function at x = 9 is f(9) = 1.

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It is helpful to write the inverse of the function to allow for a problem to be solved when the original function cannot be used to solve the problem.

The equation that defines the inverse function is x = e^ y - 4.

The inverse of a function is a reflection of the original function across the line y = x. Writing the inverse of a function can be helpful in solving problems where the original function is not solvable in terms of its inputs. In such cases, finding the inverse of the function and solving for the outputs in terms of the inputs can provide a solution.

To find the inverse of the function y = In ( x + 4 ), we need to solve for x in terms of y. We can do this by switching the places of x and y in the original equation and solving for x:

y = In ( x + 4 )

x + 4 = e^y

x = e^y - 4

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The full question is:

A function is given as y = In ( x + 4 )

Explain why it might be helpful to write the inverse of the function you wrote earlier

Then, write an equation that defines the inverse function.

Answer:

$202.5

Step-by-step explanation:

13.5 sqyd area

13.5 x 15= $202.5

Answer:

Step-by-step explanation:

X: -2, -1, 0, 1, 2,...

Y: -2, -1, 0, 1, 2,...

(y=x)

Answer: 3.5 grams

8/8=1, 28/8=3.5

3.5 grams per serving

Step-by-step explanation: Hope this helps shor.ty :)

Answer:

step by step explanation Is given above

A possible hypothesis for this study is: "The organic pesticide Z will reduce the number of grasshoppers in cornfields compared to water treatment alone."

The purpose of conducting this experiment is to determine if the new organic pesticide Z is effective at killing grasshoppers that typically invade cornfields and to study its effect on reducing the number of grasshoppers.

The independent variable in the experiment is the treatment with organic pesticide Z.

The dependent variable in the experiment is the number of grasshoppers in the cornfield.

The west field treated only with water is the control group.

It is important to have a control group in the experimental design because it provides a baseline comparison for evaluating the effect of the treatment.

The most accurate conclusion is: "If a cornfield is sprayed with pesticide Z, it will have fewer grasshoppers 10 weeks later."

Based on the results, my recommendation to the farmer would be to spray the cornfield with pesticide Z to decrease the number of grasshoppers in the cornfield.

The stages of the scientific method in order from first to last are: Make observations about nature, formulate hypothesis, conduct experiments, analyze data, reject or accept hypothesis.

This is an example of making observations about nature.

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The ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) do not correspond to the intervals where the graph of f(x) is decreasing. The pairs (1, -2) and (-3, -18) are the correct ones.

To determine where the graph of f(x) is decreasing, we need to examine the intervals where the function's derivative is negative. The derivative of f(x) is given by f'(x) = -3x^2 - 8x + 3.

Now, let's evaluate f'(x) for each of the given x-values:

f'(-1) = -3(-1)^2 - 8(-1) + 3 = -3 + 8 + 3 = 8

f'(2) = -3(2)^2 - 8(2) + 3 = -12 - 16 + 3 = -25

f'(0) = -3(0)^2 - 8(0) + 3 = 3

f'(1) = -3(1)^2 - 8(1) + 3 = -3 - 8 + 3 = -8

f'(-3) = -3(-3)^2 - 8(-3) + 3 = -27 + 24 + 3 = 0

f'(-4) = -3(-4)^2 - 8(-4) + 3 = -48 + 32 + 3 = -13

From the values above, we can determine the intervals where f(x) is decreasing:

f(x) is decreasing for x in the interval (-∞, -3).

f(x) is decreasing for x in the interval (1, 2).

Now let's check the ordered pairs in the table:

(-1, -6): Not in a decreasing interval.

(2, -18): Not in a decreasing interval.

(0, 0): Not in a decreasing interval.

(1, -2): In a decreasing interval.

(-3, -18): In a decreasing interval.

(-4, -12): Not in a decreasing interval.

Therefore, the ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) are not located in the intervals where the graph of f(x) is decreasing. The correct answer is: (1, -2), (-3, -18).

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Note the complete and the correct question is

Q- Consider the function below, which has a relative minimum located at (-3, -18) and a relative maximum located at 1/3, 14/27).

\(f(x) = -x^3 - 4x^2 + 3x\).

Select all ordered pairs in the table which are located where the graph of f(x) is decreasing: Ordered pairs: (-1, -6), (2, -18), (0, 0),(1 , -2), (-3 , -18), (-4. , -12)

Answer:

64.58

Step-by-step explanation:

1 meter is 3.28084 so 3 meters is 9.84252 because you multiply it by 3 or add them to each other 3 times. 2 meters is 6.56168 because you multiply it by 2 or add them to each other. now that you have 6.56168 and 9.84252 multiply them with each other and you get 64.5834666336 but it was said to round to nearest hundredth so since the 3 in front of the 8 is not a 5 and above the answer is 64.58 and not 64.89

To confirm that the solution is correct, we can use the method of substitution. Substitute the solution back into the original differential equation, and if the equation is satisfied, then the solution is correct.

To confirm that the proposed solution is indeed a valid solution to the original equation, we can use the method of substitution. This involves substituting the proposed solution into the original equation and verifying that it satisfies the equation. If the equation holds, then the solution is correct. This method is useful for verifying the correctness of a proposed solution. It can also be used to determine if a proposed solution is the only solution, or if there are other solutions to the equation.

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Answer:

1. d)

4.a)

2.a)

5.d)

Step-by-step explanation:

The total of the even and odd positions digits yields 82, which does not terminate with 0 and is therefore not a UPC number.

A UPC is examined in the manner described below: Add up the values in the first, third, fifth, seventh, ninth, and eleventh positions. The average of the digits mostly in places of 2, 4, 6, 8, 10, and 12 should be added to this. The code will be recognised by the computer as valid if the outcome is a multi of 10. Every version of your offering will often require its own UPC. Each distinct colour or pattern of your product, if it has either, will require a UPC. Each size of your product will require a UPC if it comes in various sizes. The same is true for various packing and setups.

given

0-52200-48826-5

= 3( 0+ 2+0+4+8+6)+ ( 5+2+0+8+2+5)

= 3(20)+ 22 = 60+22

= 82

hence it is not UPC number as it ends by 2

The total of the even and odd positions digits yields 82, which does not terminate with 0 and is therefore not a UPC number.

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Answer:

The intensity of the 2012 earthquake was about 126 times the intensity of the 1952 earthquake.

Step-by-step explanation:

To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.

Convert the magnitudes to intensities and convert to exponential form.

R=logI

2012 earthquake:

8.6I=logI=108.6

1952 earthquake:

6.5I=logI=106.5

Form a ratio of the intensities.

intensity for 2012intensity for 1952

Substitute in the values and divide by subtracting the exponents to find

108.6106.5102.1≈126.

The intensity of the 2012 earthquake was about 126 times the intensity of the 1952 earthquake.

Your answer:

The intensity of the 1952 earthquake was about 110 times the intensity of the 2012 earthquake.

Answer:

The intensity of the 2012 earthquake was about 126 times the intensity of the 1952 earthquake.

Step-by-step explanation:

To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.

Convert the magnitudes to intensities and convert to exponential form.

R=logI

2012 earthquake:

8.6I=logI=108.6

1952 earthquake:

6.5I=logI=106.5

Form a ratio of the intensities.

intensity for 2012intensity for 1952

Substitute in the values and divide by subtracting the exponents to find

108.6106.5102.1≈126.

The intensity of the 2012 earthquake was about 126 times the intensity of the 1952 earthquake.