a man ran 640m of a 2km track what percentage did he run?

Solution

- The shirt shrank a little. This implies that when you take the ratio of the dimensions of the shrunk shirt, and that of the original shirt.

- This would mean that the scale factor (the result from the above ratio), would be less than 1. But it would not be that much less than 1.

- Thus, the possible scale factor is 0.9

Answer:

A. \(f(x)=451(0.68)^x\)

Step-by-step explanation:

Function \(f(x)=451(0.68)^x\) best models the given data.

The quadratic equation that describe the speed of Raj's car is c) x² + 5x - 500 = 0

speed of raj car = x km/h .

speed of ajay car = 5 km faster than speed of raj car = (x + 5) km/h .

Distance cover by ajay in 2 hours = 2(x + 5) km

time taken by raj to cover 400 km = D/S = (400/x) hours .

time taken by ajay to cover 400km = D/S = 400/(x + 5) hours .

A/q,

400/x - 400/(x + 5) = 4

400{1/x - 1/(x + 5)} = 4(x + 5 - x)/x(x + 5) = 1/100

x² + 5x = 5 * 100

x² + 5x - 500 = 0

In this case, it should be noted that the concept that was Illustrated here is the concept of quadratic equations.

Therefore, based on the calculation above, the correct option is C.

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Complete question

Which of the following quadratic equation describe the speed of Raj's car?

a) x² - 5 X - 500 = 0

b) x² + 4x - 400 = 0

c) x² + 5x - 500 = 0

d) x² - 4x + 400 = 0

Answer:

it would be: A.

Step-by-step explanation:

Answer:

Area of the base is 10.5 cm².

Step-by-step explanation:

Formula for the volume of the given oblique prism = Area of the triangular base × Vertical height between two triangular bases

Vertical height = 6 cm

Volume = 63 cm³

From the formula,

63 = Area of the triangular base × 6

Area of the base = \(\frac{63}{6}\)

                            = 10.5 cm²

Therefore, area of the base is 10.5 cm².

So, approximately 7.71 grams of radium will be present after 100 years.

To calculate the remaining amount of radium after 100 years, we will use the half-life formula:
Remaining Amount = Initial Amount * (1/2)^(time passed / half-life)
Here, the initial amount is 8 grams, the half-life is 1690 years, and the time passed is 100 years.
Step 1: Plug in the values
Remaining Amount = 8 * (1/2)^(100 / 1690)
Step 2: Calculate the exponent
Exponent = 100 / 1690 ≈ 0.05917
Step 3: Calculate the base raised to the exponent
(1/2)^0.05917 ≈ 0.9634
Step 4: Multiply the initial amount by the base raised to the exponent
Remaining Amount = 8 * 0.9634 ≈ 7.7072
So, approximately 7.71 grams of radium will be present after 100 years.
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The estimate of the number of students with a height greater than 155 cm is 24.

A cumulative frequency graph is a curve that shows the total number of values in a grouped data that is below the upper boundary of each variable.

Number of students with heights greater than 155cm = total cummulative frequency - cumulative frequency of students with heights of 155

60 - 36 = 24

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Answer:

       Age                               Frequency                   Cumulative Frequency

 Less than 30                             27                                       27

 Less than 40                             37                                27 + 37  =  64

 Less than 50                              1 1                                 64 + 11   =  75

 Less than 60                               3                                  75 + 2   =  77

 Less than 70                               5                                   77 + 5   =  82

 Less than 80                               1                                     82 + 1  =  83

 Less than 90                              2                                    83 +2  =  85

Step-by-step explanation:

Given:

The Frequency Distribution table of ages of best actresses when award was won

To find:

Construct the cumulative frequency distribution

Solution:

In order to construct cumulative frequency distribution for the given data, each frequency from above table is added to the sum of the previous frequencies. For example, frequency for Less than 40  is 37 and the previous frequency (less than 30) is 27 so in order to calculate cumulative frequency 27 i.e. previous frequency is added to 37 (frequency of less than 30). The complete table is given above.

Based on the information provided, a) if X has a binomial distribution, n = 5 and p = 0.256. b) X can take values in the range of 0 to 5. c) The values of P(x) for x = 0, 1, 2, 3, 4 , 5 are 0.228, 0.392, 0.269, 0.093, 0.016, and  0.011 respectively. d) mean = 1.28 and standard deviation = 0.995.

a) If X has a binomial distribution n represents the number of tickets bought which is 5 and p represents the probability of winning a prize after taking a single ticket which is 0.256.

b) X can take values in the range of 0 to 5, which indicates the possible number of won tickets. Hence, x = 0, 1, 2, 3, 4, 5. c)

Using the binomial distribution formula, P (x) = nCx*p^x*(1 – p)^(n-x). Hence,

P(0) = 5C0*(0.256)^0*(1 – 0.256)^)(5-0) = 0.228

P(1) = 5C1*(0.256)^1*(1 – 0.256)^)(5-1) = 0.392

P(2) = 5C2*(0.256)^2*(1 – 0.256)^)(5-2) = 0.269

P(3) = 5C3*(0.256)^3*(1 – 0.256)^)(5-3) = 0.093

P(4) = 5C4*(0.256)^4*(1 – 0.256)^)(5-4) = 0.016

P(5) = 5C5*(0.256)^5*(1 – 0.256)^)(5-5) = 0.011

d) The mean and standard deviation of the distribution is given by:

mean = n*p = 5*0.256 = 1.28

standard deviation = √np(1 – p) = √5(0.256)(1 – 0.256) = 0.995

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Answer:

5 * w = 15

w= 3

Hope this helps!

Answer:

5•15=w

(Is this subtracting from the total?)

was there more to this question that you didn’t include?

The another equivalent expression of total liquid is (x+2)/4.

Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value for the variable is entered, two algebraic expressions that are equivalent will have the same result.

x quarts liquid in the container 3/4 part of liquid is removed

Then remaining liquid in container = X - \(\frac{3}{4}X\)

Then remaining liquid in container = x/4quarts

Another 1/2 quart is poured into container

Then total liquid = \(X-\frac{3}{4}X+\frac{1}{2}\) quarts

total liquid = \(\frac{X+2}{4}\) quarts

So, then the another equivalent expression of total liquid is (x+2)/4.

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Answer:

kdwnoioinfeoawfbcaeiuhvaeoihvaeoidvajae

Answer:

120

Step-by-step explanation:

Answer:

I think C

Step-by-step explanation:

{x|x≠-3, 2, 4}  is the domain of the given graph.

A relation is a function if it has only One y-value for each x-value.

The domain of a function is the set of input values the function can take.

What can go into a function is called the Domain.

What may possibly come out of a function is called the Codomain.

What actually comes out of a function is called the Range.

From the graph, we have the following highlights

{x|x≠-3, 2, 4} is the domain of the function.

Hence, {x|x≠-3, 2, 4}  is the domain of the given graph.

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Answer:

y = 2.5x + 5

Step-by-step explanation:

Slope intercept form is y = mx + b, where m is the gradient or slope and b is the y-intercept.

To find the gradient/slope (m), we need to do change in y ÷ change in x.

Now we have y = 2.5x + b. The y-intercept is simply where the line crosses the y axis (it crosses at 0,5). This means the equation of the line is y = 2.5x + 5.

Hope this helps!

Answer:

y = \(\frac{5}{2}\) x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line

m = \(\frac{5-0}{0-(-2)}\) = \(\frac{5}{0+2}\) = \(\frac{5}{2}\)

The line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = \(\frac{5}{2}\) x + 5 ← equation of line

to factor we must recognize the elements in common

the r exist on both terms, so we can divide by r on each term to factor

The probability of it raining 5 days out of the week, given an average chance of rain of 36% each day, is approximately 0.036 or 3.6%.

To find the probability of it raining 5 days out of the week when the chance of rain each day is 36%, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = (nCk) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of getting exactly k successes

n is the number of trials

k is the number of desired successes

p is the probability of success in a single trial

(1-p) is the probability of failure in a single trial

In this case, we have:

n = 5 (number of days in the week)

k = 5 (desired number of rainy days)

p = 0.36 (probability of rain each day)

Using the formula, we can calculate the probability:

P(X = 5) = (5C5) * (0.36)^5 * (1-0.36)^(5-5)

Simplifying the equation:

P(X = 5) = 1 * 0.36^5 * 0.64^0

P(X = 5) ≈ 0.036

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The solution to the differential equation dy/dx = x/y^x, which passes through the point (1,0) is (1/(x+1))y^(x+1) = (1/2)x^2 - 1/2.

To find the solution to the differential equation dy/dx = x/y^x, which passes through the point (1,0), we can use the method of separation of variables. This involves separating the variables x and y on opposite sides of the equation and then integrating both sides.

First, we can rewrite the differential equation as:
y^x dy = x dx

Next, we can integrate both sides of the equation:
∫y^x dy = ∫x dx
(1/(x+1))y^(x+1) = (1/2)x^2 + C

Now, we can use the initial condition (1,0) to solve for the constant C:
(1/(1+1))0^(1+1) = (1/2)(1)^2 + C
0 = 1/2 + C
C = -1/2

Therefore, the solution to the differential equation is:
(1/(x+1))y^(x+1) = (1/2)x^2 - 1/2

This is the solution to the differential equation dy/dx = x/y^x, which passes through the point (1,0).

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Answer:

4th option

Step-by-step explanation:

let the number be n , then

the product of 4 and n = 4n

The equation is

4n - 16 = 22

The area of the trapezoid in simplest radical form is 78 feet².

Given a trapezoid.

Length of the bases are 10 feet and 16 feet.

We have to find the height.

Consider the smaller right triangle formed by the height of the trapezoid.

Triangle base length or one leg = 16 - 10 = 6 feet

Since one of the angle is 45°, the other angle in the right triangle is also 45°.

Since it is isosceles, opposite sides for 45° angles are same.

Other leg = 6 feet, which is the height.

Area of the trapezoid = 1/2 (a + b)h, where a and b are bases and h is the height.

A = 1/2 (10 + 16) 6

   = 78 feet²

Hence the correct option is b.

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Answer: 2x2+70x+68 Not sure if this was what you meant.

The 2 after 2x is an exponent.

Step-by-step explanation:

(2x+2)(x+34)

=(2x+2)(x+34)

=(2x)(x)+(2x)(34)+(2)(x)+(2)(34)

=2x2+68x+2x+68

=2x2+70x+68

Answer:

f(15) = 49

Step-by-step explanation:

f(x) = 4x - 11

f(15) = 4(15) - 11 (substitute 15 instead of x)

f(15) = 60 -11

f(15) = 49

Answer:

f(5)=9

Step-by-step explanation:

f(x)=4x-11

f(5)=4(5)-11

= 20-11

=9

The required volume of Famotidine is 4 mL.

To calculate the required volume in milliliters (mL) for the provided dosage of Famotidine, we can use the following formula:

Volume (mL) = (Dosage ordered / Available dosage) * Volume per dose

We have:

Dosage ordered = 40 mg

Available dosage = 20 mg/2 mL (This means there are 20 mg of Famotidine in 2 mL)

Volume per dose = 2 mL

Let's substitute these values into the formula:

Volume (mL) = (40 mg / 20 mg) * 2 mL

Simplifying the expression:

Volume (mL) = 2 * 2 mL

Volume (mL) = 4 mL

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Answer:

\( \frac{142}{25} \)

Step-by-step explanation:

\( \frac{568}{100} = \frac{142}{25} \)

hope it helps

To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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Answer:

x ≈ 27.7 cm

Step-by-step explanation:

Using the sine ratio in the right triangle, that is

sin60° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{12}\) ( multiply both sides by 12 )

12 × sin60° = x , thus

x ≈ 27.7 cm ( to 3 significant figures )

Answer:

Yes-

Step-by-step explanation:

It repeats .121212 infinitely... I assume. You didn't say if it repeated or not.

Answer:

Yes

Step-by-step explanation:

Every repeating decimal satisfies a linear equation with integer coefficients, and those equations have solutions that are always rational numbers.

Therefore, every repeating decimal is a rational number.