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The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

According to the question, the total number of students is; 25.

15 of them have a cat

16 of them have a dog

while, 3 of them have neither

where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

the number of students who own a cat and a dog is 9.

Therefore, probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

Therefore probability that a student chosen at random has a cat or a dog is 22/25.

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Answer:

36 back

Step-by-step explanation:

100 - 64 = 36

Answer:

36¢

Step-by-step explanation:

1.00-0.64=0.36

The shortest distance ladder that will reach from the ground, over the fence (4 ft tall) to the wall of the building (2 ft away) is 8.04 ft long.

The first step is to calculate the total height that needs to be reached by the ladder. The height of the fence (4 ft) is added to the distance between the fence and the wall of the building (2 ft). This gives a total height of 6 ft.Next, the length of the ladder is calculated using the Pythagorean theorem, which states that a2 + b2 = c2. The equation is rearranged to solve for c, the length of the ladder. In this case, a is equal to the height (6 ft) and b is equal to half the height (3 ft). This gives a result of c = 8.24 ft. This result is rounded to the nearest hundredth, giving a final result of 8.04 ft.

a2 + b2 = c2

62 + 32 = c2

36 + 9 = c2

45 = c2

√45 = c

c = 6.708 ft (rounded to 8.04 ft)

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The vertex is the point on the curves with minimum distance from focus and the center is the midpoint between the vertices.

A set of points on a plane such that they have a positive and constant absolute difference from its 2 fixed points is called a hyperbola.

The two separate curves of a hyperbola are called its branches. The point on each branch with a minimum distance from the focus is called the vertices of the hyperbola.

It is the midpoint between the vertice that is called the center.

Here, we can see that the center is marked by (h,k) while the left vertex is (h - a , k)and (h + a , k)

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The probability of choosing an American having Type O blood is  \(0.40\), the probability of choosing an American with Type A or Type B blood is \(0.17\), and the probability of choosing an American with neither Type O nor Type A blood is \(0.48\).

Human blood types are classified into four major types: A, B, AB, and O. A person's blood type is determined by the presence of specific antigens (proteins) on the surface of red blood cells. The percentage of Americans with each blood type is listed in the problem as 40% Type O, 12% Type A, 5% Type B, and 43% Type AB or other types. To find the probability of selecting a person with a certain blood type from the US population, the percentage of people with that blood type is divided by 100.

a. The probability that a randomly chosen American has Type O blood is 0.40 (40%).
b. The probability that a randomly chosen American has Type A or Type B blood is 0.12 + 0.05 = 0.17 (12% + 5%).
c. The probability that a randomly chosen American does not have Type O or Type A blood is \(1 - (0.40 + 0.12) = 0.48\).

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When sampling is finished without replacement, each member of a population could also be chosen just once. during this case, the chances for the second pick are full of the results of the primary pick. The events are considered to be dependent or not independent.

lets understand with the help of an Example

You have a good, well-shuffled deck of 52 cards. It consists of 4 suits. The suits are clubs, diamonds, hearts and spades. There are 13 cards in each suit consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king) of that suit.

Sampling without replacement:

Suppose you decide three cards without replacement. the primary card you choose out of the 52 cards is that the K of hearts. you place this card aside and pick the second card from the 51 cards remaining within the deck. it's the three of diamonds. you place this card aside and pick the third card from the remaining 50 cards within the deck. The third card is that the J of spades. Your picks are . Because you have got picked the cards without replacement, you can not pick the identical card twice.

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Answer:

2x,5x

Step-by-step explanation:

thats right I am not smart

Answer:

(x,y) = ( -6,8)

Step-by-step explanation:

waiting for brainlist

Answer:

2+32×5

If you want the answer:

2+160

162

Step-by-step explanation:

Answer:

2+5^32

Step-by-step explanation:

in the equation ONp/ot = -rpP + OPN describes the rate of change of the concentration of a substance in a chemical reaction, considering both the decrease of reactant concentration and the increase of product concentration.

In the equation ONp/ot = -rpP + OPN, the term -rpP + OPN describes the rate of change of the concentration of a substance in a chemical reaction with respect to time. Here's a step-by-step explanation:
ONp/ot represents the rate of change of the concentration of a substance N with respect to time (t). This is often used to describe the rate at which a chemical reaction proceeds.
-rpP is the rate of decrease of the concentration of a reactant (P) due to the reaction. The negative sign indicates that the concentration of the reactant is decreasing over time.
OPN is the rate of increase of the concentration of a product (N) due to the reaction. The positive sign indicates that the concentration of the product is increasing over time.
The equation ONp/ot = -rpP + OPN connects these two terms, stating that the rate of change of the concentration of substance N with respect to time is equal to the rate of decrease of reactant P plus the rate of increase of product N.
5. The term -rpP + OPN describes the balance between the decrease of reactant concentration and the increase of product concentration in the chemical reaction. This balance is important in understanding the reaction kinetics and determining the rate at which a reaction occurs.
In summary, -rpP + OPN in the equation ONp/ot = -rpP + OPN describes the rate of change of the concentration of a substance in a chemical reaction, considering both the decrease of reactant concentration and the increase of product concentration.

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Answer:

x = 3 and y = 14

Step-by-step explanation:

opposite angles of a parallelogram are congruent. Hence,

1) 7y + 2 = 6y + 16

I. e. 7y - 6y = 16 - 2

I. e. y = 14

2) 8x + 8 = 6x + 14

I. e. 8x - 6x = 14 - 8

I. e. 2x = 6

I. e. x = 6/2

I. e. x = 3

The 95% confidence interval for the difference in mean parts produced per hour by these two machines is given as 10 ± 4.516.

It is given to us that -

Numbers of items produced per hour by machine a and by machine b are normally distributed

There is a standard deviation of 8.4 items for machine a and a standard deviation of 11.3 items for machine b

The mean hourly amount produced by machine a for a random sample of 40 hours was 130 units

The mean hourly amount produced by machine b for a random sample of 36 hours was 120 units

We have to find out the 95% confidence interval for the difference in mean parts produced per hour by these two machines.

Let us say that -

x = Number of units of machine a

y = Number of units of machine b

According to the given information, we have

Number of units of machine a = x⁻ = 130

Standard deviation of machine a = σx = 8.4

Number of hours of machine a = \(n_{x}\) = 40

Similarly,

Number of units of machine b = y⁻ = 120

Standard deviation of machine b = σy = 11.3

Number of hours of machine a = \(n_{y}\) = 36

We know that mean of the differences can be find out as -

d⁻ = x⁻ - y⁻

=> d⁻ = 130 - 120

=> d⁻ = 10

In order to find out the 95% confidence interval for the difference in mean parts produced per hour by these two machines, we have to make use of the formula mentioned below -

d⁻ - \(z_{a/2}\) √[(σx²/ \(n_{x}\)) + (σy²/ \(n_{y}\))] < μd < d⁻ + \(z_{a/z}\) √[(σx²/ \(n_{x}\)) + (σy²/ \(n_{y}\))]  ---- (1)

From the z-score table, for a 95% confidence interval, we have -

α = 0.05

α/2 = 0.025

=> F(z) = 1 - α/2 = 1 - 0.025 = 0.975

For a z-distribution function of 0.975, we have -

\(z_{a/2}\) = 1.96

Substituting all the values in equation (1), we have

d⁻ - \(z_{a/2}\) √[(σx²/ \(n_{x}\)) + (σy²/ \(n_{y}\))] < μd < d⁻ + \(z_{a/z}\) √[(σx²/ \(n_{x}\)) + (σy²/ \(n_{y}\))]

=> \(10-1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }\) < μd < \(10+1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }\)

=> \(10-1.96\sqrt{1.764+3.54 }\) < μd < \(10+1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }\)

=> \(10-(1.96 * 2.303)\) < μd < \(10+(1.96 * 2.303)\)

=> 10 - 4.516 < μd < 10 + 4.516

=> 5.483 < μd < 14.516

=> μd = 10 ± 4.516

Thus, the 95% confidence interval for the difference in mean parts produced per hour by these two machines is given as 10 ± 4.516.

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Answer:

translations v (1;-3)

Step-by-step explanation:

We have shown that for any ε > 0, we can choose δ = ε/3, and if

0 < |x - 2| < δ, then |f(x) - (-1)| < ε.

This satisfies the definition of lim (x → 2) f(x) = -1.

We have,

To show that lim (x → 2) f(x) = -1 using the definition of a limit, we need to find a value δ > 0 such that if 0 < |x - 2| < δ, then |f(x) - (-1)| < ε, for any ε > 0.

Let's proceed with the calculations:

We have the function f(x) = -3x + 5. Let's find the value of f(x) - (-1):

f(x) - (-1) = -3x + 5 - (-1) = -3x + 5 + 1 = -3x + 6.

Now, we want to find a δ > 0 such that if 0 < |x - 2| < δ, then |f(x) - (-1)| < ε.

We can rewrite the inequality |f(x) - (-1)| < ε as follows:

|-3x + 6| < ε.

We want to isolate x in this inequality, so let's divide all terms by 3 (since it's negative, we need to reverse the inequality sign):

|x - 2| < ε/3.

Now, we can see that if we choose δ = ε/3, then whenever 0 < |x - 2| < δ, we have |f(x) - (-1)| < ε.

Therefore,

We have shown that for any ε > 0, we can choose δ = ε/3, and if

0 < |x - 2| < δ, then |f(x) - (-1)| < ε.

This satisfies the definition of lim (x → 2) f(x) = -1.

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The complete question:

Consider the function f(x) = -3x + 5.

Apply the definition of lim (x → 2) f(x) to show that lim (x → 2) f(x) = -1.  

Given ε > 0, find a value δ > 0 such that if 0 < |x - 2| < δ, then

|f(x) - (-1) | < ε

Answer: it’s geometry

Step-by-step explanation:

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The required scale factor is :

Step-by-step explanation:

from (2)

x-y=2

y=x-2 (3)

subs (3) into (1)

x²-2x+(x-2)=8

x²-2x+X-10=0

x²+x-10=0

quadratic formula

x= (-1±√1²-4×1×(-10))/2(1)

X=( -1±√41)/2

X=(-1+√41)/2

=

x=(-1-√41)/2

=

Answer:

-6/23

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-10-(-4))/(11-(-12))

m=(-10+4)/(11+12)

m=-6/23

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The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Answer:

x = 20

Step-by-step explanation:

(2 + 3x) and 62° are vertically opposite angles and are congruent, so

3x + 2 = 62  ( subtract 2 from both sides )

3x = 60 ( divide both sides by 3 )

x = 20

Step-by-step explanation:

24min= 2miles

? 6miles

it will be 6×24min÷2= 72minutes or 1hr 12min

Answer:

2 that is the answer for this question

Answer:

25%

Step-by-step explanation:

let the Market Price of the Watch (M.P.) be x

CP for Rahim=x-[(20/100)*x]

CP = (1 *x) /5 = 4x/5

SP for Rahim = MP = x

Difference (Profit) = SP-CP = x - (4x/5) = (5x - 4x)/5 = x/5

Profit % = (Profit/CP) * 100

Profit % = (x/5)/(4x/5) * 100

Profit % = 25 %

the original number Juan started with was 6.

Let "x" represent the original number. Juan first adds 2 to the original number, which can be expressed as (x + 2). He then multiplies this by 2, resulting in 2(x + 2). Next, he subtracts 2 from this product: 2(x + 2) - 2. Finally, he divides the resulting number by 2, giving us the equation [(2(x + 2) - 2) / 2] = 7.
Now, let's solve for the original number, x:
1. Simplify the equation by distributing the 2: [2x + 4 - 2] / 2 = 7
2. Combine the constants: (2x + 2) / 2 = 7
3. Multiply both sides by 2 to remove the denominator: 2x + 2 = 14
4. Subtract 2 from both sides: 2x = 12
5. Divide both sides by 2: x = 6

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x = 9-5^(3/2)*i or x = 5^(3/2)*i+9

ok done. Thank to me :>

To determine the sequence of transformation matrices that map the shape on the left to the shape on the right, we need to analyze the changes in the shape's position, size, and orientation.

One possible sequence of transformation matrices is:

1. Translation matrix to move the shape to the right position.
2. Scaling matrix to adjust the size of the shape.
3. Rotation matrix to rotate the shape to the desired orientation.

The specific values of each transformation matrix will depend on the precise changes between the two shapes. For example, the translation matrix will have different values depending on how far the shape needs to be moved and in which direction. Similarly, the scaling matrix will depend on the degree of change in size required, while the rotation matrix will depend on the angle of rotation needed.

By applying these three transformation matrices in the correct order, we can map the shape on the left to the shape on the right.

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Variable and Coefficient of the given algebraic expression 3b + 6 is b and 3 respectively.

A variable is a symbol or letter that represents a value that can change or vary in a given context. Variables are often used to represent unknown or changing quantities in equations,

A coefficient is a numerical factor that is multiplied by a variable or variables in an algebraic expression. In other words, it is the number that appears in front of a variable.

3b + 6 identify the first term of the algebraic expression. Indicate whether the term is a variable term or a constant term. For a variable term, identify the variable and the coefficient of the term:

The first term of the algebraic expression 3b + 6 is 3b.

This is a variable term because it contains the variable "b".

The variable is "b" and the coefficient of the term is 3.

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Answer:

8x+4

Step-by-step explanation:

8x+4=56

56-4=52      52 divided 8 = 6.5

Answer:

Decreasing linear

Step-by-step explanation:

An arithmetic sequence decreases by a set amount every time through subtraction, so that means it's linear