a tortoise and hare are competing in a 1000 meter race. the function f and g are such that f ( t ) represents the tortoise's distance from the finish line (in meters) t seconds after the start of the race and g ( t ) represents the hare's distance from the finish line (in meters) t seconds after the start of the race. if we want to compute the number of seconds needed for the hare to finish the race, which of the following procedures should be used?
o Solve g(t) = 0 for the value of t o Solve f(t) = g(t) for the value of t o Evaluate (1000) o Solve g(1) = 1000 for the value of t o Evaluate (0)

The numeric values of the function are given as follows:

An appropriate domain for the situation is of:

{x ∈ N | x ≥ 0.}

The function in this problem is defined as follows:

f(x) = 6x - 70.

In which the variables are given as follows:

Hence when x = -2, the numeric value is given as follows:

f(-2) = 6(-2) - 70 = -82.

This point is outside of the domain, as the number of shirts cannot be negative, hence an appropriate domain for the function is of:

{x ∈ N | x ≥ 0.}

As the number of shirts is also a countable amount.

When x = 12, the numeric value is given as follows:

f(12) = 6(12) - 70 = 72 - 70 = 2.

When x = 17.5, the numeric value is given as follows:

f(17.5) = 6(17.5) - 70 = 35.

Learn more about the numeric values of a function at brainly.com/question/28367050

#SPJ1

The formula for the area of a circle is pi times the radius squared (A = π r²)

A circle is a two-dimensional closed figure in which the set of all points in the plane is equidistant from a given point known as the "centre." The line of reflection symmetry is formed by every line that passes through the circle. It also has rotational symmetry around the center for all angles.

It is a curved portion of its circumference. A semicircle is an arc that connects the endpoints of the diameter and has a measure of 180°. The circle is divided into two parts by an arc. The minor arc is the smaller part, and the major arc is the larger part.

To find the area goes thus;

Identify the radius of a circle.

Square the radius.

Multiply by pi. Pi.

In conclusion, the formula is πr².

Learn more about circle on:

https://brainly.com/question/24375372

#SPJ1

Complete question

what is the formula for the area of a circle?

Answer: 10 months

Step-by-step explanation:

432 + 40x >505 + 32x

40x >32x + 73

8x > 73

8x/8 > 73/8

x > 73/8 = 9.125

Round 9.125 to 10

The number of months that will take Lola to have more trading cards is obtained as 8.

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The number of cards with Lola and Joel are 432 and 505 respectively.

Suppose the number of required month be x.

Then, the inequality expression can be written for the given case as,

432 + 40x > 505 + 32x

⇒ 40x - 32x > 505 - 432

⇒ 8x > 63

⇒ x > 63/8

The number of months should be an integer value.

And, the nearest integer value of the greater than 63/8 is 8.

Hence, the number of months required for the given case is 8.

To know more about linear inequality click on,

https://brainly.com/question/11897796

#SPJ2

here you are the answer.

(1 – 3cosx – 4cos^2x) / sin^2x = 

(1+cos x)(1-4cos x) /(1-cos^2 x) =

 (1+cos x)(1-4cos x) /[(1-cos x)(1+cos x)] = 

(1-4cos x) /(1-cos x)
Factor:

1+cos(x))(1 – 4cos(x)) / (1 + cos(x))(1 – cos(x)) =

RHSCancel:(1 – 4cos(x)) / (1 – cos(x)) = RHSQED

The cube root of unity are found to be 1, -1±i√3/2 and -1±i√3/2.

In order to find the cube root of unity let us say,

x³ = 1

Solving further,

x³-1 = 0

Now,

(x-1)(x²+x+1)=0

For, x-1=0

x = 1.

And,

For, (x²+x+1)

Solving by using quadratic formula,

x = -1±√(-3)/2.

x = -1±i√3/2

x = -1+i√3/2 and,

x = -1-i√3/2

also, x = 1.

So that cube root of unity are 1, -1±i√3/2 and -1±i√3/2.

To know more about cube root, visit,

https://brainly.com/question/12846420

#SPJ4

Answer:

=

Step-by-step explanation:

Answer:

y= -2x -1

Step-by-step explanation:

m= (5-7)/(-3- -4) = -2/1 = -2

y-intercept = -1

y= -2x -1

We reject the null hypothesis and come to the conclusion that their argument is adequately supported.

Given that,

z = 2.14 and p value = 0.0162

a) Hypotheses are

H₀ : p≤  0.40

H₀ : p > 0.40  (claim)

This is right tailed test.

b) p value = 0.0162

c) Test statistic Z =2.14

P(Z>2.14) = 1 - P(Z≤2.14)

               = 1 - 0.98382

               = 0.01618

P value ≈  0.01618

d) P value is less than α = 5% = 0.05

So, we reject the null hypothesis and conclude that they have enough evidence in support of their claim

To learn more about hypotheses click here:

brainly.com/question/18064632

#SPJ4

Answer:

The answer is    x=2

Step-by-step explanation:

1. Rearrange terms-

29x + 3 (  5 - 35x) = - 119 - 9x

29x + 3 ( - 35x + 5) = - 119 - 9x

2. Distribute-

29x + 3 ( - 35x + 5) = - 119 - 9x

29x - 105x + 15 = - 119 - 9x

3. Combine like terms-

29x - 105x + 15 = - 119 - 9x

- 76x + 15 = -119 -9x

4. Rearrange terms-

- 76x + 15 = - 119 - 9x

- 76x + 15 = - 9x - 119

5. Subtract 15 from both sides-

- 76x + 15 = - 9x - 119

- 76x +15 -15 = -9x - 119 - 15

6. Simplify-

- 76x = - 9x - 134

7. Add 9x to both sides-

- 76x + 9x = - 9x - 134 + 9x

8. simplify-

- 67x = - 134

9. Divide both sides by the same factor-

[tex]\frac{-67x}{-67} = \frac{-134}{-67}[/tex]

10. Simplify-

x = 2

Answer:

A

Step-by-step explanation:

3 - (-1.5)
when you open the backet it will be 3 - - 1.5
minus and minus makes plus
therefore it will be 3+1.5
so the answer is 4.5

The age of the fossil is 24, 312 years assuming an exponential decay model.

Exponential decay model refers to model in which the amount of something decreases at a rate proportional to the amount left and this rate is given by a constant ratio k. The formula for remaining quantities of a substance is given by:

P = 100 e^(-kt)

Where P is the remaining quantity, k is the constant of decay, and t is time.

As the half life of the carbon 14 is 5700, when 50% of the substance remains,

50 = 100 e^(-5700k)

1/2 = e^(-5700k)

In(1/2) = In(e^(-5700k))

- In (2) = -5700k

k = In(2)/5700 = 0.0001216

Since, 5.2% carbon-14 remains,

5.2 = 100 e^(-0.0001216t)

0.052 = e^(-0.0001216t)

In(0.0052) = - 0.0001216

t = In(0.052) * - 0.0001216

t ≈ 24, 312 years.

Learn more about Exponential decay model:

https://brainly.com/question/29364908

#SPJ4

Answer: 6.25%

Step-by-step explanation:

To find what percent 61 is of 976, we divide 61/976. This comes out to be 0.0625. Multiply by 100 to get your percentage, and it's 6.25%.

The length of OM is 20 if MN=20 and N0=14

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Angle can also refer to a rotation or the measurement of an angle. This measurement is the ratio of the length of a circular arc to its radius.

To find the length of OM

Given,

MN=20

ON=14

∠O≅∠N

Since, ∠O≅∠N

ΔMNO is isosceles triangle with

OM=MN=20

Hence, the length of OM is 20.

Therefore, The length of OM is 20 if MN=20 and N0=14

To know more about angle, visit:

https://brainly.com/question/28451077

#SPJ1

The null hypothesis is

H₀:The defendant is innocent

The alternative hypothesis or research hypothesis is

H₁ : The defendant is guilty

Which of the two hypotheses is correct is unknown to the jury.

Given that,

Think about a case where a jury must choose between the hypotheses that the defendant is guilty and the defendant is innocent.

We have to find which of the hypotheses ought to be the null hypothesis in the context of hypothesis testing and the American legal system.

We know that,

A jury in a trial must choose between two hypotheses. The null hypothesis is

H₀:The defendant is innocent

The alternative hypothesis or research hypothesis is

H₁ : The defendant is guilty

Which of the two hypotheses is correct is unknown to the jury. They must decide based on the information provided.

To learn more about hypothesis visit: https://brainly.com/question/28920252

#SPJ4

Answer:

ITS B

Step-by-step explanation:

Answer: 5.072

Step-by-step explanation: -0.8-2.14=-6.2

                                                     +2.14 |  +2.14

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

                                                              -4.06/-0.8=5.072

A variable which is required to construct a confidence interval for population proportion is qualitative variable with two possible outcomes. So the correct option is D.

In the given question we have to find what type of variable is required to construct a confidence interval for a population proportion.

As we know that;

Population proportion is the percentage of the entire population that possesses the given quality (which is qualitative in nature). The confidence interval for the population proportion must thus be constructed using a qualitative variable with two possible outcomes.

So, the correct option is identified from nature of different type of the variables. A variable which is required to construct a confidence interval for population proportion is qualitative variable with two possible outcomes.

To learn more about confidence interval link is here

brainly.com/question/29657444

#SPJ4

The right question is:

What type of variable is required to construct a confidence interval for a population proportion?

A. Quantitative

B. Qualitative with any number of possible outcomes

C. Continuous

D. Qualitative with 2 possible outcomes

E. Discrete

F. Qualitative with 3 or more possible outcomes

The rank of population size from fastest to slowest growth is N = 1250, N = 1500, N = 1000, N = 750, N = 500, and N = 250.

The population growth rate is the measure that helps to determine how much the population size changes over time. The population growth rate shows either logistic growth or exponential growth. The formula for logistic population growth is given by [tex]\frac{dN}{dt}=r_{\text{max}}N\left(\frac{K-N}{N}\right)[/tex]. Here, N is the population size, t is time, r (max) is the maximum rate of increase, and K is the carrying capacity.

The one that grows fast will have a large population size, and the one that grows slowly will have a small population size. To rank the population size, arrange the given population size from the largest to the smallest. As a result, we get,

Fastest growth rate N=1250, N=1500 , N=1000, N= 750, N= 500, N= 250 Slowest growth rate

The complete question is -

Arrange the following population sizes in the order of decreasing growth rate. Rank the population sizes (N) from fastest to slowest growth. If two population sizes have the same growth, overlap them.

N = 1250, N = 1500, N = 1000, N = 750, N = 500, N = 250

To know more about logistic population growth:

https://brainly.com/question/15631218

#SPJ4

The smallest possible value of c is 1 in this case.

If the integer a, b and c are in arithmetic progression.

Then we can write,

b = (a+c)/2

If the integer a, b and c are in geometric progression,

Then, we can write,

b = √(ac)

Now, we can write,

a+b = 2√(ac)

Squaring both sides,

a²+c²+2ac = 4ac

(a-c)² = 0

So,

a = c.

If a = c.

Then,

b = (a+a)/2

b = a

So, a = b = c.

Smallest possible positive integer is 1.

So, the smallest possible value of c is 1.

To know more about Arithmetic progression, visit,

https://brainly.com/question/6561461

#SPJ4

The probability that the sample mean will be between 1195 and 1205 is 0.445

What is a probability distribution?

In mathematics, a probability distribution is a function that expresses the likelihood of many possible values for a variable. Graphs and probability tables are common ways of displaying probability distributions.

Given, mean = [tex]\mu[/tex] = 1200

standard deviation = [tex]\sigma[/tex] = 60

n = 50

[tex]\mu_{\bar x} = 1200\\\sigma_{\bar x} =\sigma / \sqrt(n) = 60/ \sqrt50=8.485[/tex]

[tex]P(1195 < \bar x < 1205 ) = P[(1195-1200) / 8.485 < (\bar x - \mu\bar x ) / \sigma\bar x < (1205-1200) / 8.485)][/tex]

= P(-0.59 < Z <0.59 )

= P(Z <0.59 ) - P(Z <-0.59 )  

Using the z table, we get

=0.7224-0.2776

=0.4448 = 0.445 ( rounded to 3 decimal places)

Hence, the probability that the sample mean will be between 1195 and 1205 is 0.445

To learn more about a probability distribution

https://brainly.com/question/25023966

#SPJ4

The probability of getting 5 black chips and 6 white chips is [tex]\frac{7}{22}[/tex].

What do you mean by probability?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

According to data in the given question,

We have the given information:

Total number of different colored chips = 35

Number of black chips = 20

Number of white chips = 15

And you draw 11 chips at random.

Now, we will calculate the probability of getting 5 black chips and 6 white chips,

[tex]P(B) = \frac{5}{20} =\frac{1}{4} \\P(W) = \frac{6}{15} =\frac{2}{5} \\P( black and white ) = \frac{\frac{1}{4}*\frac{2}{5}}{\frac{11}{35} } \\=\frac{\frac{1}{2}*\frac{1}{5}}{\frac{11}{35} }\\=\frac{1}{10}*\frac{35}{11}=\frac{7}{22}[/tex]

Therefore, the probability of getting 5 black chips and 6 white chips is 7/22.

To learn more about probability, visit:

brainly.com/question/11234923?referrer=searchResults

#SPJ4

Answer:

52[tex]a^{2}[/tex] + 26

The sum of DE+FG+HI=90 if DE, FG, HI are all parallel to BC and BC=60.

Quadrilaterals with at least one set of parallel sides are referred to as "trapezoid" quadrilaterals. In British and other dialects of English, the word "trapezium" is used.

Euclidean geometry dictates that a trapezoid must be a convex quadrilateral. The base of the trapezoid is referred to by its parallel sides. If the other two sides are parallel, the trapezoid is a parallelogram, and there are two pairs of bases. If not, the other two sides are known as the legs (or lateral sides). Unlike the specific situations below, a scalene trapezoid is a trapezoid where none of the sides have equal lengths.

Given,

ΔABC is a scalene triangle.

And BC=60

DE, FG, HI are all parallel to BC.

From the midpoint-theorem,

DE||BC then,

DE=(1/2)BC

FG||BC

FG=(1/2)BC

HI ||BC

HI=(1/2)BC

DE+FG+HI=(1/2BC+1/2BC+1/2BC)

=(1/2(3BC))

1/2(3(60))

=90

Therefore,

The sum of DE+FG+HI=90

To know more about midpoint-theorem, visit:

https://brainly.com/question/28667736

#SPJ1

Answer:

Step-by-step explanation:

What are you supposed to do

Answer:

Step-by-step explanation:

a^2 +b^2 =c^2

8^2 +14^2=y^2

64+196 =y^2

260=y^2

(260)^1/2 =y

Simplified: 4^1/2  * 65^1/2= 2(65^1/2)

Step-by-step explanation:

v=1/3πr²h

98=1/3×22/7×(5.13)²×h

98=1/3×22/7×(27.2403)×h

98=28.537×h

h=28.537/98

h=0.291m

hope it helps. please mark brainliest

Answer:

Answer to your question is in the attachment

Answer:

Proportional

y is 0.4 times x

or

y is 2/5 times x

Both numbers are the same, I don't know which form the computer expects you to enter

Step-by-step explanation:

x and y are proportional since there is a linear relationship between y and x.

Let's verify this

When x = 5, y = 2. So y/x = 2/5 = 0.4
So y = 0.4x  

When x = 10, y = 4
So y/x = 4/10 = 2/5 = 0.4

Again y = 0.4x

So the answer is 0.4, same as 2/5

Answer:

Step-by-step explanation:

the x and y are proportional because the number increases by the same number each time. so y =2 and x=5 then on the next one, if it's proportional, y will = 4 and x will = 10. another way you can be sure that it is proportional is that every time you add the first number you can divide it and get the first number. for example if you divide 4 by 2 you will get 2. if you divide 10 by 2 you get 10. so in a short answer yes it is proportional

By evaluating the piecewise function we will see that the difference is:

f(1) - f(-7) = 3

Here we have a piecewise function defined on the image, and we want to find the difference:

f(1) - f(-7).

First, let's find these values.

f(1) means that we need to evaluate the function in x = 1.

Notice that the second piece can be used on the domain 4 < x ≤ 1, so we need to use that part.

f(1) = -(1)^2 - 3*1

f(1) =-1 - 3 = -4

To evaluate in x = -7 we need to use the first piece of the function:

f(-7) = |-7 + 5| - 9

f(-7) = |-2| - 9 = -7

Then the difference is:

f(1) - f(-7) = -4 - (-7) = -4 + 7 = 3

Learn more about piecewise functions:

https://brainly.com/question/3628123

#SPJ1