If x = yand y = z, which statement must be true?

O A. -x=-z

O B. z=x

O c. x=z

O D. -x=z

The exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

from the question:

This is the shape of the exponential function:

f(x) = a *\(b^x\)

where a represents the starting point and b represents the exponential function's base.

We must solve the system of equations to determine the values of a and b that meet the requirements:

a * \(b^(-1)\) = 2/5 (equation 1) 

a *\(b^3\)= 250 (equation 2) 

We can solve for an in equation 1 by multiplying both sides by b:

a = (2/5) * b

Substituting this expression into equation 2, we get:

(2/5) * b *\(b^3\) = 250

Simplifying, we get:

\(b^4 = 3125\)

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

to know more about functions visit:

https://brainly.com/question/12431044

#SPJ1

Answer:

(-12, -18)

Step-by-step explanation:

https://www.omnicalculator.com/math/endpoint

Answer:

See attachment

Step-by-step explanation:

Each high school in Indiana is considered a cluster. Let's say there are 1000 high schools in that state. That would mean there are 1000 clusters.

You would then randomly select say 5 clusters. Once those selections are made, you would then survey every student at those five schools selected. The number of clusters selected will depend on the situation of course.

\( \fbox{(2,5)}\)

Hello, substitute all the given coordinates & see if RHS match with LHS

given equation,

y = 4x-3

First coordinate,

(x,y) = (2,5)

5= 4×2-3

5=5

Hence, first solution satisfies the given equation,

let's solve for rest other cordinates,

second coordinate,

(x,y) = (5,5)

5= 4×5-3

5 ≠ 17

does not satisfy,

third coordinate,

(x,y) = (4,5)

5= 4×4-3

5 ≠ 13

does not satisfy,

fourth coordinate,

(x,y) = (4,5)

5 = 4×3-3

5 ≠ 9

does not satisfy.

Hence the correct answer is (2,5)

\( \sf \small Thanks \: for \: joining \: brainly \: community! \)

The population reaches 50% of the carrying capacity at around t = 0.4 years (or 4.8 months).

(a) The maximum population size is the carrying capacity which can sustain environment derivative dP/dt to zero and solve for P:

\(0.8P - 0.001P^2 = 0\)

\(0.001P(1000 - P) = 0\)

\(P = 0 or P = 1000\)

Since the population can't be zero, the carrying capacity is 1000.

(b) P'(0) is the derivative of P with respect to t evaluated at t = 0. From the given equation, we have:

\(dP/dt = 0.8P - 0.001P^2\)

So, \(0.8P(t) - 0.001P(t)^2=P'(t)\)

Hence, P'(0) can be 32.

(c) To find when the population reaches 50% of the carrying capacity, we need to solve for the time t such that P(t) = 0.5(1000) = 500. Numerical method to be used which is  Euler's method, which involves iteratively approximating the solution using small time steps. We can start with t = 0 and use a time step of h = 0.1 (for example):

P(0) = 40

P(0.1) = 43.2

P(0.2) = ≈ 46.5

P(0.3) ≈ 49.3

P(0.4) ≈ 50.8

P(0.5) ≈ 50.6\(P(0) = 40P(0.1) = 43.2P(0.2) = ≈ 46.5P(0.3) ≈ 49.3P(0.4) ≈ 50.8P(0.5) ≈ 50.6\)

So the population reaches 50% of the carrying capacity at around t = 0.4 years (or 4.8 months).

To know more about carrying capacity

brainly.com/question/30880725

#SPJ4

sin(x) = O(x) and sin(sin(x)) = O(sin(x)) as x → 0, we have sin(sin(x)) = O(x) as x → 0. Therefore, we can write f(x) = O(x) - x = O(x), which means that \(f(x) = O(x^p) if p ≥ 1\). Therefore, f(x) = O(x^p) holds for all p ≥ 1.

lim x→0 |f(x)|/|x^p| = C > 0, then f(x) = O(x^p). For a polynomial f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, we know that f(x) = O(x^p) if p ≥ n. This is because |f(x)|/|x^p| ≤ |a_n| + |a_{n-1}|/|x| + ... + |a_0|/|x^p|, and since all terms except for the last one go to 0 as x → 0, we must have p ≥ n to ensure that |f(x)|/|x^p| → C > 0.For part (a), we have f(x) = x^2, so we know that f(x) = O(x^p) if p ≥ 2.

Therefore, f(x) = O(x^2) as x → 0.For part (b), we have f(x) = 1/x, so we know that f(x) = O(x^p) if p ≤ -1. Therefore, f(x) = O(x^p) does not hold for any p ≥ 0.For part (c), we have f(x) = cos(x) - 1, so we know that f(x) = O(x^p) if p ≥ 0.

To know more about polynomial visit:-

https://brainly.com/question/11536910

#SPJ11

Answer:

X=6

Step-by-step explanation:

Simplify:

(2p^3x)^3 = 8p^54 into:

2p^3x = 2p^18

p^3x = p^18

3x = 18

x=6

Answer:

162cm

Step-by-step explanation: LxWxH which is 3x9x6 which = 162cm

and ur welcome

The probability that the person also buys cereal at least once a month, given that a randomly chosen person eats breakfast almost every day is 53/64

Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.

A survey asked about the number of people who eat breakfast almost every day (B) and the number of people who buy cereal at least once a month (C).

The results of the survey are shown in the Venn diagram as,

Therefore, for circle B, it can be given as,

\(n(B)=11+53=64\)

Similarly, for the circle C,

\(n(C)=53+4=57\)

As the intersection of circle B and C contains 53,

\(n(BC)=53\)

Now the probability that the person also buys cereal at least once a month, given that a randomly chosen person eats breakfast almost every day,

\(P(C|B)=\dfrac{P(BC)}{P(B)}\\P(C|B)=\dfrac{n(BC)}{n(B)}\\P(C|B)=\dfrac{53}{64}\)

Hence, the probability that the person also buys cereal at least once a month, given that a randomly chosen person eats breakfast almost every day is 53/64

Learn more about the random sample here;

https://brainly.com/question/17831271

Answer:

C or 53/64

Step-by-step explanation:

Ed2022

Answer:

2^6 x 3^3 and 12^3

Step-by-step explanation:

First, solve

6^3 x 2^6/2^3

216 x 64/8

13824/8 = 1728

lets solve for the answers

6^3 = 216

Therefore, 6^3 is not an answer

2^6 x 3^3= 64 x 27 = 1728

because both expressions are equal to 1728, this is an answer. this answer can also eliminate 2^3 x 3^3 because it has a lower exponent than the answer that is equal to 1728. therefore, the value of it must be smaller than 1728

12^3 = 1728

This answer is correct, because both values are equal to each other, meaning that 12^6 is larger than 1728  

Therefore, your answers will be 2^6 x 3^3 and 12^3          

The correct option is the second one, the quadratic equation is:

f(x) = 1 - 8x²

A quadratic equation is a polynomial where the degree is 2.

So, we only have integer exponents and the larger exponent is 2.

For example, in the first equation we can see that, but the coefficient of the term with the exponent of 2 is zero, so that term is zero, and thus, that is a linear equation.

The option that is quadratic is the second one:

f(x) = 1 - 8x²

Learn more about quadratic equations at:

https://brainly.com/question/1214333

#SPJ1

1. The variable is qualitative or quantitative is the variable is qualitative because it is an attribute characteristic (option d). 2. The quantitative variable is discrete or continuous is the variable is discrete because it is countable (option d).

The variable "Hair color" is qualitative because it represents an attribute characteristic rather than a numerical measure. It refers to the different categories or qualities of hair color, such as blonde, brown, black, or red. It is not based on a numerical scale or measurement. Therefore, the correct answer is D) The variable is qualitative because it is an attribute characteristic.

The variable "Number of members present at a meeting" is discrete because it is countable and takes on distinct, separate values. It cannot take on any value between the integers, and there are no fractions or decimals involved. The number of members present can only be whole numbers, such as 0, 1, 2, 3, and so on. Therefore, the correct answer is D) The variable is discrete because it is countable.

To know more about variable:

https://brainly.com/question/16906863

#SPJ4

Step-by-step explanation:

You cannot conclude this

 A  can be as short as  1.20  and as long as 1.30

  B can be 1.12  to  1.52 m

          so B COULD be shorter than A  !  

Answer:

152 and 9

Step-by-step explanation:

Answer:

\(n + 24 = 99 \\ \\ n = 99 - 24 \\ \\ n = 75\)

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

For more questions on: combinations

https://brainly.com/question/29595163

#SPJ8                  

Using system of linear equations he will require 20kg of 15% copper and 30kg of 70% copper to produce an alloy of 48% in 50kg

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.

To solve this problem, we need to write a system of linear equations and find the equivalent amount of the metal required to make the desired amount of the alloy.

0.15x + 0.7y = 0.48(50) ..eq(i)

0.15x + 0.7y = 24 ...eq(i)

x + y = 50 ...eq(ii)

solving equation (i) and (ii)

x = 20, y = 30

He needs 20kg of 15% copper and 30kg of 70% copper to get 48% of 50kg of alloy.

Learn more on system of linear equation here;

https://brainly.com/question/13729904

#SPJ1

we have that

the radius is

r=12.1 in

the volume of a sphere is

substitute the given values

Part 2

In this problem we have the diameter of the sphere

D=13.6 mm

so

r=D/2=13.6/2=6.8 in

substitute in the formula

The sine and the cosine of the acute angle are the same for θ = π / 4. (Correct choice: 2)

Acute angles are angles whose measures are greater than 0° and less than 90°. According to the statement, we must find at least a value such that sin θ = cos θ:

sin θ = cos θ                     Given

sin θ / cos θ = 1                 Compatibility with multiplication / Existence of multiplicative inverse / Modulative property

tan θ = 1                            Definition of tangent

θ = π / 4                            Inverse trigonometric function / Result

In a nutshell, the sine and the cosine of the acute angle are the same for θ = π / 4. (Correct choice: 2)

To learn more on trigonometric functions: https://brainly.com/question/14746686

#SPJ1

0.55 is the probability that a vacationer will visit at least one of these magnificent attractions.

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

50% of the vacationers going to toronto visit the CN tower= 0.5

40% visit skydome= 0.4

35% visit both=0.35

P( At lease one) = P(Toronto) + P(Skydome) - P(Both)

P( At lease one) = 0.4 + 0.5 - 0.35

P( At lease one)  = 0.55

learn more about probability here :

brainly.com/question/11234923

#SPJ4

The speed of the truck is higher (or lower) than the speedometer value  

when a larger (or smaller) than standard sized tire.

Responses:

The standard tire size diameter = 25.7 inches

Diameter of the replacement tire = 28.2 inches

Circumference of the standard tire = π·25.7 inches

1 mile = 63,360 inches

65 miles = 65 × 63,360 inches

\(Number \ of \ rotation =\dfrac{63,360 \times 65}{\pi \times 25.7} \approx \mathbf{ 51,008.85}\)

Distance travelled by the replacement tire with the same number of

rotations is therefore;

\(Distance =\dfrac{63,360 \ in. \times 65}{\pi \times 25.7 \ in.} \times \pi \times 28.2 \ in. \approx \mathbf{4519022.6\ in.}\)

Actual distance travelled in one hour = 4519022.6 ÷ 63,360 ≈ 71.32

Second part; Tire diameter = 24 inches

Distance traveled in one hour = 51,008.85 × π × 24 ≈ 3845976.68

Distance traveled in one hour ≈ 3845976.68 inches

3845976.68 inches ≈ 60.7 miles

The actual speed if a 24 inch tire is used is approximately 60.7 mph

Details of the truck speed with different sized wheels

Learn more about rotation and speed here:

https://brainly.com/question/14745232

Transforming the following mathematical statement "A number decreased by 30 is 246" into an equation will be:

Where,

x = unknown number

Answer:

its the second one

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to identify the true statements regarding angles at a transversal crossing parallel lines, and perpendicular bisectors.

The Corresponding Angles theorem tells you that corresponding angles are congruent where a transversal crosses parallel lines. Since vertical angles are congruent, and angles congruent to the same angle are congruent to each other, this also means that alternate interior angles are congruent.

A bisector of a segment passes through its midpoint, a point that is equidistant from the end points. When the bisector is perpendicular to the segment, all points on the perpendicular bisector are equidistant from the segment's endpoints.

The men's pole vault finals' scores for the 2004 Olympic games in Athens are shown, the mean is not a good descriptor of this set because the outliers have too much effect on it. Thus, the correct option is D.

The given set of scores for the men's pole vault finals in the 2004 Olympic games has a wide range of values, including some repeated values. However, there are a few scores that stand out as outliers, such as 5.95 and 5.55.

When outliers have a substantial effect on the mean, it may not be a good descriptor of the set as a whole.

The mode being higher or more reasonable does not directly impact the suitability of the mean as a descriptor of the data set.

Thus, the correct option is D.

For more details regarding mean, visit:

https://brainly.com/question/31101410

#SPJ1

the probability that the next song played is one of the favorite songs is 0.1 or 10%.

Since there are 20 CDs with 10 songs each, there are a total of 20 x 10 = 200 songs in the player.

Since there is one favorite song on each CD, there are a total of 20 favorite songs in the player.

The probability of the next song played being one of the favorite songs is equal to the number of favorite songs divided by the total number of songs in the player:

Probability = Number of favorite songs / Total number of songs

Probability = 20 / 200

Probability = 0.1

Therefore, the probability that the next song played is one of the favorite songs is 0.1 or 10%.

learn more about Probability here:

https://brainly.com/question/30034780

Answer: s>u

Step-by-step explanation:

gl