a) The** velocity vector **of the particle is [2, -2t].

b) The equation of the tangent line at[tex](2t, 36 - t^2) is y - (36 - t^2) = -t(x - 2t).[/tex]

c) The** x-coordinate** of the point on the x-axis that the laser light hits is [tex]x = 2t + (36 - t^2)/t.[/tex]

d) The speed of the laser light along the x-axis at time t = 3 is 1, as it is the absolute value of the derivative of x with respect to t at t = 3.

(a) The velocity vector of the particle is the derivative of the position vector with respect to time:

v(t) = [x'(t), y'(t)] = [2, -2t]

(b) The slope of the tangent line is the derivative of y with respect to x:

dy/dx = (dy/dt)/(dx/dt) = (-2t)/(2) = -t

Using the **point-slope** form of the equation of a line, the tangent line at [tex](2t, 36 - t^2)[/tex] is:

[tex]y - (36 - t^2) = -t(x - 2t)[/tex]

(c) To find the x-coordinate of the point on the x-axis that the laser light hits, we need to find the intersection of the tangent line and the x-axis. Setting y = 0, we get:

[tex]-t(x - 2t) + (36 - t^2) = 0[/tex]

Solving for x, we get:

[tex]x = 2t + (36 - t^2)/t[/tex]

(d) The **speed **of the laser light along the x-axis is the absolute value of the derivative of x with respect to t:

[tex]|dx/dt| = |2 - (36 - t^2)/t^2|[/tex]

At time t = 3, we have:

|dx/dt| = |2 - (36 - 9)/9| = |2 - 3| = 1

Therefore, the speed of the laser light along the x-axis at time t = 3 is 1. The justification is that the absolute value of the derivative gives the magnitude of the rate of change of x with respect to time, which represents the speed.

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Select the correct answer.

What is the zero of the function represented by this graph?

x = 5

x= -6

x=-5

x=6

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the explanation ~

Zeros or roots of a function is the value of independent variable (usually x - coordinate or absicca) where the value of dependent variable (y - coordinate or ordinate) is 0.

That is :

The point where it cuts the x - axis, it has an x - coordinate = -6

Therefore, we can conclude that The zero of given function is **-****6**

**Answer:**

**x = -6.**

**Step-by-step explanation:**

It is where the graph cuts the x-axis (where the function is zero).

That is -6.

Given: Circle X with Radius r and circle Y with radius s

Prove: Circle X is similar to Circle Y

It can be proved that Circles X and Y are **similar.**

We were told that circle Y have a radius of s

And X have the Radius r

Going with the theorem that Similar shapes are proportional, we can find the scale factor from circle X to circle Y by making a division on the radii of both circles.

Then the scale factor is [tex]\frac{s}{r}[/tex] which implies that circle Y will gotten by dilation of circle Y.

Therefore, both circles are **similar**

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The number of Minghua's stamps is 1 1/2 times that of John's.

**Step-by-step explanation:**

Let the number of stamps of John be **x**.

Then number of Minghua's stamps:

1 1/2 * x3/2 * x**John's****:**** ****x**

**Minghua's:**** ****(****3****/****2****)****x**

A science test, which is worth 100 points, consist of 24 questions. Each question is worth either 3 points or 5 points. If X is the number of 3 point questions and why is the number of 5 point questions, the system shown represents this situation. X+y=24, 3x+5y=100. What does the solution of this system indicate about the questions on the test?

**Answer:**

x= 10 y=14 : 10 3 point, 14 5 point

**Step-by-step explanation:**

Write your equation down vertically,

3x + 5y = 100

x + y = 24

Next find multiply bottom equation by one number from the tops opposite,

3x + 5y = 100

(-3)x +(-3)y = (-3)24

3x + 5y = 100

-3x - 3y= -72

Add the two functions to isolate y

2y= 28 **y=14**

Plug y back into original and solve

3x +5(14) =100 --> 3x + 70 =100 --> 3x = 30 **x=10**

Find the zeros of: [tex]f(x)=-\frac{1}{1500} (x^3+10x^2-275x-1500)[/tex], and the use them to find all of the linear factors of the polynomial function

The *linear* **factors** of the *polynomial* **function** are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).

How to find the linear factors of a cubic equation

*Cubic* **equations** are **polynomials** of *third* **grade**, whose *standard* and *factor* **forms** are shown below:

**Standard form**

y = a · x³ + b · x² + c · x + d

**Factor form**

y = (x - r₁) · (x - r₂) · (x - r₃)

Where r₁, r₂, r₃ are the **zeros** of the *cubic* **equation**.

There are several approaches to find the **roots** of the **polynomial**, in this question we decided to use the *graphical* **approach**, which offers sufficiency and quickness for analysis. The **roots** of the **polynomials** are the points that pass through the x-**axis**.

In accordance with the image attached below, the **polynomial** has three *real ***roots**: r₁ = - 20, r₂ = - 5, r₃ = 15. Then, the *linear* **factors** of the *polynomial* **function** are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).

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find the volume of a sphere with a raduis of 3 in.

**Answer:**

V≈113.1in³.

brainlist me

Answer is 113 cubic inches

Step by step

We know the formula is

V = 4/3 pi radius ^3

I am using 3.14 for pi

Substitute (3 in.) into radius

V = 4/3 pi 3^3

V = 4/3 pi 27

V = (4/3) (3.14) (27)

Multiply and you get

V = 113.04 cu.inches

Round to 113 cu.inches

Problem solved!

Step by step

We know the formula is

V = 4/3 pi radius ^3

I am using 3.14 for pi

Substitute (3 in.) into radius

V = 4/3 pi 3^3

V = 4/3 pi 27

V = (4/3) (3.14) (27)

Multiply and you get

V = 113.04 cu.inches

Round to 113 cu.inches

Problem solved!

The function f is defined by f(x)=2-x. If 2f(p)=8, what is f(2p)?

The answer is 6. Details are below

If function 'f' is **defined **by f(x)=2-x and 2f(p)=8 then the value of** f(2p) is 6.**

Given, f(x) = 2-x

Solve this problem by making a series of **substitutions**.

First, find the value of p.

Then use the definition of the **function **f to find the value of f(2p).

We are given

f(x) = 2 - x

**Multiply **both sides by 2, and simplify.

2f(x) = 2(-x +2)

2f(x) = -2x + 4

Let x = p.

2f(p) = -2(p) + 4

We are given that 2f(p) = 8.

**Substitute **20 for 2f(p).

8 = -2p + 4

2p = -4

p = -2

Now we know that p = -2, so we can find f(2p).

f(x) = -x + 2

f(2p) = -2p + 2

**Substitute **-2 for p.

f(2p) = -2(-2) + 2

f(2p) = 4 +2

f(2p) = 6

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For a certain bathtub, the hot water faucet can fill the tub in 12 minutes. The cold water faucet can fill the tub in 8 minutes. If both faucets are used together, how long will it take to fill the tub

If both **faucets **are used together, it time taken by them to fill the** tub** is 4.8 minutes.

Time and work share a fundamental idea in common with other arithmetic topics, namely the idea of** proportionality. **

When the **amount of work **is constant, efficiency is inversely proportional to the length of time required.

Important **Time and Work **Formula:

Calculation for the time taken by both **faucet **to fill the tub.

The unit should be tub per minute.

Then, do the reciprocal of the result to have minute per tub.

The hot water faucet can fill the tub in 12 minutes.

The cold water faucet can fill the tub in 8 minutes.

The** filling rate **for both faucets filling the tub at the same time is the sum of their rates.

Let **'t'** be the time taken by both faucets.

Then,

[tex]\frac{1}{12} +\frac{1}{8} =\frac{1}{t}[/tex]

[tex]\frac{8+12}{8*12} =\frac{1}{t}[/tex]

[tex]\frac{1}{t} =\frac{20}{96}[/tex]

[tex]\frac{t}{1} =\frac{96}{20}[/tex]

t = 4.8

Therefore, the time taken by both** faucets** to fill the tub is** **4.8 minutes.

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In a model of a construction project, 1 yard is represented as 0.25 inch. What would be the actual area of a garden in square yards, if it is represented by 20 square inches in the model?

Actual length: Model Length

1 yard : 0.25 inch

Actual Area: Model Area

(1)^2 : (0.25)^2

1 square yard: 0.0625 square inch

0.0625 square inch — 1 square yard

20 square inches — 1/0.0625 x 20

= 320 square yards

Therefore the actual area of a garden is 320 square yards.

1 yard : 0.25 inch

Actual Area: Model Area

(1)^2 : (0.25)^2

1 square yard: 0.0625 square inch

0.0625 square inch — 1 square yard

20 square inches — 1/0.0625 x 20

= 320 square yards

Therefore the actual area of a garden is 320 square yards.

Decide whether the triangles are similar. if so, determine the appropriate expression to solve for x. triangles abc and edf; triangle abc has angle a measuring 53 degrees, angle c measuring 62 degrees, side ac labeled as y, side ab labeled as w, and side bc labeled as x; triangle edf has angle d measuring 61 degrees, angle f measuring 53 degrees, side de labeled z, side ef labeled u, and side df labeled r.

**Answer:**

**Step-by-step explanation:**

**Similar Triangle:**

**Triangle ABC has angles of 53 and 62 degrees....the sum is 115 degrees. The third angle must be 180 - 115 = 65 degrees.**

**A triangle with one angle = 61 degrees cannot be similar**

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**Answer: The triangles are not similar; no expression for x can be found.**

What is Permutations and Combinations?

**Answer:**

See below

**Step-by-step explanation:**

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

[tex]\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }[/tex]

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

[tex]\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}[/tex]

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

[tex]\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }[/tex]

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

[tex]\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}[/tex]

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

Permutations and combinations have many practical applications in various fields such as statistics, **Probability theory**, and computer science.

Permutations and **combinations **are two concepts in mathematics that deal with counting and arranging elements in a set.

Permutations refer to the number of ways in which a set of objects can be arranged or ordered. In other words, **permutations **involve counting the number of possible ways in which a group of objects can be arranged in a particular order. For example, if we have three objects A, B, and C, the possible permutations would be ABC, ACB, BAC, BCA, CAB, and CBA. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects being arranged.

Combinations, on the other hand, refer to the number of ways in which a subset of objects can be selected from a larger set, without regard to the order in which they are selected. In other words, combinations involve counting the number of possible subsets that can be formed from a larger set. For example, if we have three objects A, B, and C, the possible combinations would be AB, AC, and BC. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects being selected.

The key difference between permutations and combinations is that permutations involve ordering **objects**, while combinations do not. Another important distinction is that in permutations, each arrangement is considered distinct, whereas in combinations, different arrangements that contain the same objects are considered identical.

Permutations and combinations have many practical applications in various fields such as statistics, probability theory, and computer science. For example, they are commonly used in solving problems related to probability, combinations of locks, and permutations of passwords. Understanding these concepts is essential in order to effectively analyze and solve problems in these fields.

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The programmer at a local public radio station is compiling data on listeners who stream podcasts. an executive for the national broadcaster has communicated that the overall population mean is 20,500 with a standard deviation of 2,180. the local programmer has a sample of 30 podcasts for her station. by the central limit theorem, which interval do about 99.7% of the sample means fall within?

The **interval** in which **99.7**% of the sample means fall within **3** standard deviations of the mean is **19,306** to **21,694**.

According to the **central** **limit** **theorem**,

**Sample** **mean** = Population mean = **μ**

**Sample** **standard** **deviation** = (Population standard deviation)/√n = **σ/√n**

where **n** is at least **30**.

It is given that,

The overall **population** **mean** = 20,500

Population standard deviation **σ** = 2180

Sample size **n** = 30

Since **n = 30**, the **central** **limit** **theorem** can be applied.

According to the **Empirical** **rule**(68-95-99), 99.7% of the sample means fall within the **3** **standard** **deviations **of the **mean**.

So, the **interval** is calculated by

**Sample** **mean** = Population mean = μ = 20500

**Standard** **deviation**(**sample**) = σ/√n

⇒ S = 2180/√30 =398.011 ≅ **398**

Thus,

The **lower** bound = 20500 - 3 × 398 = **19,306**

The **upper** bound = 20500 + 3 × 398 = **21,694**

Therefore, the required **interval** is from **19,306** to **21,694**.

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The graph of the piecewise function f(x) is shown.

On a coordinate plane, a piecewise function has 2 connecting lines. The first line has a closed circle at (negative 2, negative 5) and goes up to a closed circle at (2, negative 1). The second line has a closed circle at (2, negative 1) and goes down to an open circle at (4, negative 2).

What is the range of f(x)?

{x | −2 ≤ x < 4}

{x | −2 < x ≤ 4}

{y | −5 < y < −1}

{y | −5 ≤ y ≤ −1}

**Answer:** {y | −5 ≤ y ≤ −1}

**Step-by-step explanation:**

The extreme values are -5 and -1.

There is a closed circle at (-2, -5), so -5 is in the range.There is a closed circle at (2, -1), so -1 is in the range.So, the answer is {y | −5 ≤ y ≤ −1}.

Solve 5x=125 using the one-to-one property of exponents.

A) X=In(125)

B) x = 1

C) x = 3

OD) x = 5

Anyone is here

**Answer:**

**Step-by-step explanation:**

hello :

A) X=In(125)

A survey was conducted in the class about their favorite subjects. 35% of the class voted for Math and Science. 45% of the class voted for Math. Find the percent of the class who voted for Math also voted for Science.

The** percent** of the class who voted for Math also voted for Science is **38.8%**

Therefore,

1 = p(m) + p(s) - p(m ∩ s)

Hence,

p(m) = 45% = 0.45

p(s) = ?

p(m ∩ s) = 35% = 0.35

Therefore,

1 = 0.45 + p(s) - 0.35

1 - 0.45 + 0.35 = p(s)

**p(s) = 0.9**

Therefore,

p(m | s) = 0.35 / 0.9 = 0.38888888888 = **38.8%**

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uppose you want to test the value of the mean in a population. You collect a random sample of 60 which yields a sample mean and sample standard deviation. You only know sampled information to perform the test. What type of procedure is appropriate for your data

To test the value of the mean in a population when only sample mean and sample deviation are known to perform the test then it is appropriate to use **z-test procedure**.

**What is a Z-test?**

A statistical method of testing a hypothesis is the **z-tes**t where either:

Additional prerequisites for using the** z-test** include the following:

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Maria is creating a round stained glass window like the one below. She needs to cut the dark pink glass to the correct size to fit into the frame. At what angle (x) should she cut the glass so that it fits if she knows the arc measure of a is 35º and the arc measure of b is 45º. What does x equal?

Applying the **angle of** **intersecting chords theorem**, the value of x is: 40º.

According to the **angle of** **intersecting chords theorem** the following **equation** is true:

x = 1/2(a + b).

Given the following:

a = 35º

b = 45º

Plug in the values

x = 1/2(35 + 45)

x = 1/2(80)

x = 40º

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Given the series below, find S29.

{13+4+(−5)+(−14)+(−23)+...}

Select one:

a. -2,480

b. -2,752

c. -3,016

d. -3,277

**Answer:**

d

**Step-by-step explanation:**

there is a common difference between consecutive terms in the series, that is

4 - 13 = - 5 - 4 = - 14 - (- 5) = - 23 - (- 14) = - 9

this indicates the series is arithmetic with sum to n terms

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 13 and d = - 9 , then

S₂₉ = [tex]\frac{29}{2}[/tex] [ (2 × 13) + (28 × - 9) ]

= 14.4(26 + (- 252))

= 14.5(26 - 252)

= 14.5 × - 226

= - 3,277

Jay went to an amusement park. the park charges an entrance fee of $10.50 and $4.50 for every ride. jay spent $46.50 on entrance fees and rides. which fuction can be used to find the number of rides he went on? f (x) = 4.5 x + 10.5 f (x) = 4.5 x f (x) = 4.5 x minus 10.5 f (x) = negative 4.5 x

The **function **that can be used to find the number of rides Jay went on is, f(x) = 4.5x + 10 = 46.5. Hence, the first option is the right choice.

Also, on solving the **function **we get that, Jay went on 8 rides.

We assume the number of rides Jay spent to be x.

The cost of each ride is given to be $4.50.

Thus, the total amount Jay spent on rides = $4.50x.

The entrance fee to the park is given to be $10.50.

Thus, the total expenditure of Jay can be shown as $(4.5x + 10.5).

But, in the question we are given that Jay spend $46.50 altogether.

Thus, the **function **to find the number of rides Jay went on can be shown as:

f(x) = 4.5x + 10 = 46.5.

Hence, the first option is the right choice.

To find the number of rides he went, we can solve this **function **as:

4.5x + 10 = 46.5,

or, 4.5x = 46.5 - 10.5 = 36,

or, x = 36/4.5 = 8.

Thus, Jay went on 8 rides.

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twice a certain number is 58. 4 times that number will be

a) 4x58 b) 58 + 4 c) 58x2 d)8x58

**Answer:**

c) 58x2

**Step-by-step explanation:**

Twice the number 29 is 58

So, 29 is related to 58

Therefore 29*4 = 58*2

URGENT WHOEVER ANSWERS CORRECTLY AND FAST GETS BRAINLY

40% of the house plants were watered today. 320 house plants were watered. Which equation can be used to find how many plants there were?

40x = 320

0.40x = 320

x

=

0.40

--------

320

x = 0.40(320)

**Answer:**

0.40x = 320

**Step-by-step explanation:**

If 40% of the total houseplants watered = 320

0.40 times x (total houseplants) = 320

**Answer:**

[tex]\frac{x}{0.40} = 320 Plants[/tex]

**Step-by-step explanation:**

[tex]\frac{x}{0.40} = 320 Plants[/tex]

[tex]X = (0.40)(320)Plants[/tex]

[tex]X = 128Plants[/tex]

Consider the function f(x)=x2 bx c. if the minimum of this function is located at point (2,0), then what are the values of b and c?

The **values **of b and c are -4 and 4 respectively

The **function **is given as:

f(x) = x^2 + bx + c

Differentiate f(x)

f'(x) = 2x + b

Set to 0

2x + b = 0

Solve for b

b = -2x

The **minimum **is (2, 0).

So, we have:

b = -2 * 2

b = -4

Substitute b = -4 in f(x) = x^2 + bx + c

f(x) = x^2 - 4x + c

Substitute (2, 0)

0 = (2)^2 - 4(2) + c

This gives

0 = 4 - 8 + c

Evaluate

c = 4

Hence, the **values **of b and c are -4 and 4 respectively

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can someone please help me

**Answer:**

Cos (3pi/4) =0.999154554

Sin (3pi/4)=0.041111762

**Step-by-step explanation:**

On your calculator there should be **SIN**** **and **COS**** **next to each other

#1 tap **COS**** **

#2 put your given numbers, in this case

**COS****(****3pi****/****4****)**** ****=**** ****0.999****1****5****4****5****5****4**

same goes for **SIN**

**SIN**** ****(****3pi****/****4****)****=****0.041****1****1****1****7****6****2**

give the answer please

Using the **domain **concept, the **only value of x** that is not on the domain of [tex]f(x) = \frac{1}{3x + 5}[/tex] is given as follows:

[tex]x = -\frac{5}{3}[/tex]

What is the domain of a function?The domain of a function is the set that contains all possible **input values** for the function. For a rational function, for example, the zeros of the denominator are excluded from the domain. Another example is an even root, where the inside term has to be positive.

The **rational function **for this problem is given by the function f(x) presented below:

[tex]f(x) = \frac{1}{3x + 5}[/tex]

The denominator is 3x + 5, hence the **restriction **in the domain of f(x) is given as follows:

3x + 5 = 0

3x = -5

[tex]x = -\frac{5}{3}[/tex]

The solution to the equation above is the **only value** of x that is not part of the domain of f(x).

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(FIRST TO ANSWER GETS BRAINLIEST OR 5 STARS) For consecutive weeks, the manager of a local restaurant collected data on the number of cheese pizzas sold each week. The data is shown in the scatterplot below.

(scatterplot is below)

Can the given line be used to make reasonable predictions of the number of cheese pizzas that will be sold in upcoming weeks? Explain your reasoning.

**Yes**, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the **line of best fit**

From the question, we are to determine if the line can be used to make **reasonable predictions **of the number of cheese pizzas that would be sold in the upcoming weeks

In the graph, we have a **scatterplot**.

The line drawn is the line of best fit

Hence,

**Yes**, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the **line of best fit**.

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5. The two rectangles are similar. Which is the correct proportion that can

be used to find the missing side?

12/4=x/20

12/4=x/8

12/8=x/4

4/12=x/8

**Answer:**

The second choice.

**Step-by-step explanation:**

Correspond sides are in the same ratio

12/4 = x/8

.

Helen had $12 but spent $3 of it. What per cent did she spend?

12%

25%

30%

33 1/3%

**Answer:**

25%

**Step-by-step explanation:**

3/12 = 0.25 = 25%

**Answer:**

25%

**Step-by-step explanation:**

$3 pent out of the original $12. We can ask what is the percentage of $12 that is equal to $3? This can be written as:

X($12) = $3, where X is the percentage.

X = (3/12)

X = 0.25 or 25%

the cost of 4 ice cream cones from the snack bar was $10.40. if each ice cream costs the same amount, which model correctly illustrates the relationship? check all that apply

I hope this helps, good luck!

a carpool contains three kindergartners and five first-graders. if two children are ill, find the probability tyhat at lease one of them

The** probability** that at least one of them is a** kindergartner; **0.643.

Calculating or estimating how likely something is to occur is what probability is all about. The **likelihood** of an event occurring can be expressed using words like "certain," "impossible," or "**probable**."

Probabilities are always expressed in mathematics as fractions, decimals, or **percentages** with values ranging from 0 to 1.

Calculation for the probability of the one of them is a kindergarden;

The total number of children is 8.

The total number of kindergarden are 3.

The total number of first graders are 5.

Let 'P' be the probability that at least one of them is** kindergarden.**

P(at least one kindergartner) = 1 - P(no kindergartner) = 1 - P(all first-graders)

The probability that all are first-graders = (5/8)×(4/7)

= 5/14

Therefore, P(at least one kindergartner) = 1 - (5/14)

= 9/14

= 0.643

Therefore, if two children are ill then, the probability that at least one of them is a kindergartner is 0.643.

To know more about **probability**, here

**https://brainly.com/question/13604758**

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The correct question is-

A carpool contains three kindergartners and five first-graders. if two children are ill, find the probability that at least one of them is a kindergartner.

Point W is on line segment \overline{VX} VX . Given VX=4x,VX=4x, VW=3x,VW=3x, and WX=5,WX=5, determine the numerical length of \overline{VX}. VX .

The **numerical length** of VX is undefined

The given parameters are

VX = 4x

VW = 3x

WX = 5x

Point W is on **line segment **VX

So, we have

VX = VW + WX

This gives

4x = 3x + 5x

Evaluate

4x= 8x

The above equation is false

Hence, the **numerical length** of VX is undefined

Read more about **lengths **at:

https://brainly.com/question/24571594

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