how is the general multiplication rule different than the multiplication rule for independent events

i think it's correct so far

Answer:

yes it is correct so far

The total amount of the initial deposit of Natalie account when she opened the account is $225.

Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.

The formula for the simple interest can be given as,

\(I=\dfrac{Prt}{100}\)

Here, (I) is the interest amount earned on the principal amount of (P) with the rate of (r) in the time period of (t).

Natalie opened a bank account that earns 2. 5% simple interest.

Natalie's account earned $180 over the period of 10 years. The interest amount she earned is,

\(I=\dfrac{Prt}{100}\\I=\dfrac{180\times2.5\times10}{100}\\I=45\)

The interest amount she earned is $45 and the initial amount was $180. Thus, the total amount,

\(A=P+I\\A=180+45\\A=225\)

Thus, the total amount of the initial deposit of Natalie account when she opened the account is $225.

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The domain of the function shown in the graph is the one in option A:

6 ≤ k ≤ 11

The domain of a function y = f(x) is the set of the inputs of the function. To identify the domain in a graph, we need to look at the horizontal axis (also called the x-axis).

On the graph we can see that it starts at x = 6 with a closed dot, and it ends at x = 11 also with a closed dot.

That means that these values belong to the domain, so we can write the domain as follows:

Domain = 6 ≤ k ≤ 11

(notice that the variable in the horizontal axis is k).

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Answer:

it would be 7

Step-by-step explanation:

the equation would be ( if you read the problem) -2+9 and that is equal to 7

Answer:

110 paper plates

Step-by-step explanation:

Given values:

1 Pack of paper cups (50) = 1.89

1 pack of paper plates (10) = 0.49

Anton has 15.00 to spend

If Anton were to buy 250 paper cups, that would cost him 5 packs since each pack is 50 cups. 5 packs would cost him 1.89 x 5 or 9.45. He now has 5.55 left to spend on paper plates.

Each pack of paper plates is 0.49. To find how many packs he can buy with the remaining amount of money, divide the money buy the cost.

5.55/0.49 ≈ 11.32

Since you can't buy .32 packs, Anton can buy 11 packs, or 110 paper plates.

Answer:

I think its a (it might be wrong tho )

Step-by-step explanation:

pls double check

The following are the solution to the given inequalities;

-13 < 4x + 7 ; -5 < x

-2x + 7 < 19 ; x > -6

-45 < 5(p - 2) ; -7 < p

21 < -7(x - 2) ; -1 > x

-9x + 10 > -8 ; x < 2

2 - 6 < 3 ; -4 < 3

-13 < 4x + 7

combine like terms

-13 - 7 < 4x

-20 < 4x

divide both sides by 4

-5 < x

-2x + 7 < 19

combine like terms

-2x < 19 - 7

-2x < 12

x < 12/-2

x > -6

When dividing inequality with negative, the inequality sign will flip.

-45 < 5(p - 2)

open parenthesis

-45 < 5p - 10

-45 + 10 < 5p

-35 < 5p

-7 < p

21 < -7(x - 2)

21 < -7x + 14

21 - 14 < -7x

7 < -7x

divide both sides by -7.

-1 > x

-9x + 10 > -8

-9x > -8 - 10

-9x > -18

x > -18/-9

x < 2

2 - 6 < 3

-4 < 3

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A Pearson correlation coefficient of +1.00 between two variables, X and Y, indicates a perfect positive correlation between them. This means that as the values of X increase, so do the values of Y, and vice versa.

In other words, the two variables are perfectly linearly related, and there is no variability in their relationship. A Pearson correlation coefficient of +1.00 is the strongest possible correlation coefficient, and it suggests that there is a direct and strong association between the two variables being measured.

For example, let's say we have data on the height and weight of a group of individuals. If we find a Pearson correlation coefficient of +1.00 between height and weight, it means that as a person's height increases, their weight will also increase perfectly in a linear fashion. This information can be useful in predicting weight based on height, or vice versa, and can help inform decisions related to health and fitness.

Overall, a Pearson correlation coefficient of +1.00 suggests that the two variables being measured have a strong and direct relationship, which can be useful in many different contexts.

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The probability of drawing a head card of diamonds and then a head card of hearts is:

P = 0.003

Here we assume that we have a deck of 52 cards, and we want to find:

P(Head, Diamond AND Head, Heart)

This is the probability of drawing a head of diamonds and then a head of hearts.

Remember that for each suit has 3 head cards, J, Q, and K.

Then for the first card, the probability of getting a head of diamonds is equal to the quotient between the number of cards with these properties (3) and the total number of cards (52).

P = 3/52

Then we need to draw a head of hearts, the probability is computed in the same way, but before we drew a card, so now the total number of cards is 51, so we get:

Q = 3/51

Then the joint probability is:

p = (3/52)*(3/51) = 0.003

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1. ratio of ears to paws to tail, therefore:

ratio is 2: 4: 1

2. sentence:

there 4 paws per very tail

Answer:i think its 115 degres

Step-by-step explanation:

The equation that expresses the combined weight of the tank and algebrol in pounds, w, in terms of the number of gallons of algebrol in the tank, v, is:

w = 8.8v + 126.5

The weight of the algebrol per gallon is given as 8.8 pounds/gallon. Therefore, the weight of the algebrol in the tank is 8.8 times the number of gallons, which is represented by 8.8v.

Additionally, we are given that the combined weight of the tank and algebrol is 126.5 pounds. This weight includes the weight of the tank itself, which is independent of the number of gallons.

Hence, we add the weight of the tank to the weight of the algebrol, resulting in the equation: w = 8.8v + 126.5.

This equation allows us to calculate the combined weight (w) based on the number of gallons (v) of algebrol in the tank.

Therefore, the combined weight, w, of the tank and algebrol in pounds can be calculated by multiplying the number of gallons, v, of algebrol by 8.8 and adding 126.5.

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The smallest possible value of the seventh term of the sequence is 104 .

A sequence is an ordered group of items in mathematics where repetitions are permitted and order is important.

Let the first two terms of the first sequence be a and b and the first two of the second sequence be c and d.

Computing the seventh term,

we see that 5a + 8b = 5c + 8d.

Note that this means that a and c must have the same value of |8|.

To minimize, let one of them be 0;

We assume that a= 0.

Thus, the smallest possible value of c is 8; and since the sequences are non-decreasing we get d > 8.

To minimize, let d = 8. Thus, 5c + 8d = 40 + 64 = 104.

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The answers have been shown below.

Questions regarding the time spent by Jack jogging and bike riding are needed to be answered.

(A) The equations are \(x+y=75, y=15+x\)

Time spent jogging is 30 minutes

The total time would be \(45+60=105\) minutes which is not equal to 75 minutes.

(B) Let \(x\) be the time spent jogging.

\(y\) be the time spent bike riding.

\(x+y=75\\y=15+x\\x+15+x=75\\2x+15=75\\x=\frac{75-15}{2} =30\)

Time spent jogging is 30 minutes.

\(y=60\\x+y=75\)

(C) If he rides his bike 15 minutes longer than he jogs then he would have to jog \(60-15 = 45\) minutes.

Therefore, the total time would be \(45+60=105\) minutes which is not equal to 75 minutes.

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the vector equation for the line segment from (3, -4, 4) to (7, 2, 3) is:

r = <3, -4, 4> + t<4, 6, -1>

We can find a vector equation for the line segment by first finding the direction vector of the line segment, and then using it to write the equation in vector form.

The direction vector of the line segment is the difference between the two endpoints:

d = <7, 2, 3> - <3, -4, 4> = <4, 6, -1>

To write the vector equation in terms of the parameter t, we can use the parametric form of the equation of a line:

r = r_0 + td

where r is the position vector of a point on the line, r_0 is the position vector of a known point on the line (in this case, (3, -4, 4)), t is a scalar parameter, and d is the direction vector we just found.

Substituting the values we know, we get:

r = <3, -4, 4> + t<4, 6, -1>

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The number of zeros which this graphed polynomial function have is: B. 3.

A polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.

Additionally, a polynomial graph simply refers to a type of graph that is commonly used for the representation of only positive (non-negative) integer exponents of a variable in an equation.

This ultimately implies that, a polynomial graph touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

In this context, we can reasonably and logically deduce that the zeros of a polynomial function are all of the values (x-intercepts) on the x-coordinate that makes this polynomial function equal to zero and these include the following:

Zeros = (-2, 0)

Zeros = (-1, 0)

Zeros = (1, 0)

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Answer:

x = a/7

Step-by-step explanation:

Area is length x width, so let's call our unknown, the length, x

So the total area is 7 (the width) times x

If the total area is a, then we can write the equation a = 7(x)

Next, we have to isolate the variable for the length, x

To do this, we divide both sides by 7, leaving a/7 = x, or x = a/7

Answer:

10.63

Step-by-step explanation:

Use pythagorean theorem:

c=√(a^2+b^2)

√(7^2+8^2)

√(49+64)

√(113)

10.63

The common ratio of the geometric sequence is 1/8, and the sum of the first nine terms is 15,998.75.

In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio.

Let's denote the first term as a₁ and the common ratio as r. We are given that a₁ = 8,000.

The formula for the nth term of a geometric sequence is given by aₙ = a₁ * r^(n-1).

Given that the fifth term is 500, we can substitute the values into the formula to get:

500 = 8,000 * r^(5-1)

500 = 8,000 * r^4

Dividing both sides of the equation by 8,000, we have:

r^4 = 500 / 8,000

r^4 = 0.0625

Taking the fourth root of both sides, we get:

r = ∛(0.0625)

r = 1/2

Therefore, the common ratio of the geometric sequence is 1/2.

To find the sum of the first nine terms of the sequence, we can use the formula for the sum of a geometric series:

Sₙ = a₁ * (1 - rⁿ) / (1 - r)

Substituting the values, we have:

S₉ = 8,000 * (1 - (1/2)⁹) / (1 - 1/2)

Simplifying the expression:

S₉ = 8,000 * (1 - 1/512) / (1/2)

S₉ = 8,000 * (511/512) / (1/2)

S₉ = 8,000 * 511 / 256

S₉ ≈ 15,998.75

Therefore, the sum of the first nine terms of the geometric sequence is approximately 15,998.75.

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Answer:

The area of the circle

Step-by-step explanation:

The area of a circle is given by:

A = pi•r^2

☝️That is "Area equals pi times r squared"

Fun fact: you can use r (radius) or d (diameter) to find the circumference (distance all the way around a circle)

C = pi • d

or C = 2pi • r

But for area (all the space inside)

A = pi • r^2

You get:

Work/Explanation:

When multiplying pi by the square of a circle's radius, we get the circle's area.

This is how it looks in a formula:

\(\bf{\pi\times r^2}\)

Which can be simplified to

\(\bf{\pi r^2}\)

Which is the same as

\(\bf{A=\pi r^2}\)

A system of 4 linear equations in 3 variables x, y, z can have at most one solution.

It is because a system with more than three equations and only three variables will not have a unique solution due to the fact that the dimension of the solution space of 3-dimensional equations is three, so adding an extra equation will result in an over-determined system.

In other words, there are not enough variables in the system to meet the requirements of all the equations, which leads to an over-determined system where there is either no solution or a unique solution. If the system has exactly two solutions, it means that the solution space of the system of equations has a dimension greater than 3, which contradicts the fact that the dimension of the solution space of a system of 3-dimensional equations is 3.

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The blue graph is a translation of 2 units to the left and 1 unit up of the parent function, thus, the equation is:

g(x) =  |x + 2| + 1

We know that the red graph is an absolute value function, so we have:

f(x) = |x|

And we want to find the equation of the blue absolute value function, which is a translation of the above one.

Notice that the vertex of the blue one is at (-2, 1), so we have a translation of 2 units to the left and one unit up, it is just written as:

y = |x + 2| + 1

We conclude that the translated function is:

g(x) =  |x + 2| + 1

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Answer: The first

D: [-3,∞)

R: [-1,∞)

The second

D: [-3,2)

R:[-5,4]

Step-by-step explanation:

Answer:

Step-by-step explanation:

A

Answer:

1546

Step-by-step explanation:

just divide 3092 by 2

Answer:

y = -1x - 7

Step-by-step explanation:

y2 - y1 / x2 - x1

-6 - (-3) / -1 - (-4)

-3/3

= -1

y = -1x + b

-6 = -1(-1) + b

-6 = 1 + b

-7 = b