which step is included in the graph of the function f(x)=[x-1]?

Step-by-step explanation:

When x = 0    y = 20      Plug in:

20 = 20 b^0  

20 = 20      true , but we didn't find 'b'

when x = 1   y = 10        Plug in:  

10 = 20 * b^1

10 = 20 b

b = 1/2

When analyzing a resultant vector, the equation to find the magnitude of the vector is the Pythagorean theorem. This equation states that the magnitude of the resultant vector is equal to the square root of the sum of the squares of its components.

To find the direction of the resultant vector, the trigonometric function of inverse tangent or arctan can be used. This involves taking the inverse tangent of the vertical component divided by the horizontal component, which gives the angle of the vector with respect to the positive x-axis.

Alternatively, the direction can also be found using the trigonometric functions of sine and cosine by dividing the vertical and horizontal components of the vector by its magnitude.

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Step-by-step explanation:

Circumference of a circle is found by:

Circ = pi * d

      = pi * 9.7 cm = 30.5 cm

Answer:

Number of Hours | Money

0 hrs — 22$ (+0$)

1 hrs — 27$ (+5$)

2 hrs — 32$ (+5$)

3 hrs — 37$ (+5$)

(he would gain 15$ after 3 hours of baby sitting)

Step-by-step explanation:

Y = 5x + 22

5x is the amount being added each time, 22 is the y-intercept of the slope; the slope is going at a linear rate of 5 per hour.

The equation about the conic is r = 6/(4|sinθ| - 3cosθ).

We have,

Since the focus is at the pole, the conic is a polar equation with the form

r = e d / (1 - e cosθ), where d is the distance from the pole to the directrix and e is the eccentricity.

In this case,

e = 3/4 and the directrix is r sinθ = -2.

We can rewrite the equation of the directrix in Cartesian coordinates as

y = -2/sinθ.

Now we can use the formula for the distance from a point (x, y) to a line Ax + By + C = 0, which is:

d = |Ax + By + C| / sqrt(A^2 + B^2)

In our case,

The equation of the directrix is y + 2/sinθ = 0, which we can rewrite as

y = -2/sinθ.

The coefficients of x and y are both 0 and the constant term is 2/sinθ, so

A = 0, B = 1, and C = -2/sinθ.

Substituting into the formula.

d = |-2/sinθ| / √(0² + 1²)

d = 2/|sinθ|

Now we can write the equation of the conic as:

r = e d / (1 - e cosθ) = (3/4) (2/|sinθ|) / (1 - (3/4) cosθ)

Simplifying.

r = 6/(4|sinθ| - 3cosθ)

This is the polar equation of the conic with focus at the pole and directrix r sinθ = -2, and eccentricity e = 3/4.

Thus,

The equation about the conic is r = 6/(4|sinθ| - 3cosθ).

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Answer: 2.333  

Step-by-step explanation:

Since 3 feet equal 1 yard, we can divide 7 feet by 3 to get the equivalent distance in yards:

7 feet ÷ 3 feet/yard = 2.333 yards (rounded to 3 decimal places)

Therefore, 7 feet is equivalent to approximately 2.333 yards.

hope this help mark me brainst  

Answer:

The volume of a pyramid can be calculated using the formula:

V = (1/3) * base area * height

where "base area" is the area of the base of the pyramid.

In this case, the base of the pyramid has a length of 9 meters and a width of 7 meters, so its area is:

base area = length * width = 9 m * 7 m = 63 m^2

The height of the pyramid is 13 meters.

Now we can calculate the volume:

V = (1/3) * base area * height

= (1/3) * 63 m^2 * 13 m

= 273 m^3

Therefore, the volume of the pyramid is 273 cubic meters.

If the water were redistributed equally among the 4 glasses, the fractional part of each glass that would be filled include the following: K. 31/80.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided above, the division can be calculated as follows;

Fraction = (1/4 + 1/2 + 4/5) ÷ 4

Fraction = 31/20 ÷ 4

Next, we would multiply the fraction 31/20 by the reciprocal of 4 as follows;

Fraction = 31/20 × 1/4

Fraction = 31/80

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Independent events- events that do not affect each other's probability of occurring. Dependent events- events where the occurrence of one event affects the probability of the other event happening. Mutually exclusive events- events that cannot occur at the same time. Exhaustive events- events that cover all possible outcomes.


1. Independent events: Independent events are events in which the occurrence of one event does not affect the probability of the occurrence of another event. In other words, the outcome of one event has no impact on the outcome of the other event.

2. Dependent events: Dependent events are events in which the occurrence of one event does affect the probability of the occurrence of another event. The outcome of one event is influenced by the outcome of the other event.

3. Mutually exclusive events: Mutually exclusive events are events that cannot occur at the same time. The occurrence of one event means the other event cannot occur. For example, flipping a coin and getting both heads and tails at the same time is a mutually exclusive event, as it is impossible for both to happen simultaneously.

4. Exhaustive events: Exhaustive events are a set of events that include all possible outcomes in a given situation. They are complete and cover every possibility, leaving no room for additional outcomes. For example, when flipping a coin, the set of exhaustive events includes both heads and tails, as there are no other possible outcomes.

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If a card is drawn from a pack of playing cards, then the probability that card is "red-king" or "4-of-diamonds" is 3/52.

There are 2 card of "red-kings" and 1 card of "4-of-diamonds" in a deck of cards. There are 52 cards in total.

So, probability of drawing a "red-king" is "2/52", because there are two "red-kings" out of 52 cards, and

The probability of drawing 1-card of "4-of-diamonds" is "1/52", because there is only 1 "4-of-diamonds" out of 52 cards,

To find probability of drawing a "red-king" or "4-of-diamonds", we add the probabilities of these two events and subtract the probability of drawing both of them, because they are not mutually exclusive,

⇒ P(red-king or 4-of-diamonds) = P(red king) + P(4 of diamonds) - P(red king and 4 of diamonds),

⇒ P(red-king or 4-of-diamonds) = 2/52 + 1/52 - 0,

⇒ P(red-king or 4-of-diamonds) = 3/52,

Therefore, the required probability is 3/52.

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After discount the cost is $53.6 and  the processing fee is $5.36

The discount reduces the price of the shoes by 20%, which means Evan only has to pay 80% of the original price.

To find the price after the discount

we multiply the original price by 0.8:

Price after discount = 0.8 × $67 = $53.60

Next, the website applies a 10% processing fee to this discounted price. To find the processing fee, we can multiply the discounted price by 0.1:

Processing fee = 0.1 × $53.60

= $5.36

Hence, the processing fee is $5.36 and after discount the cost is $53.6

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Decision variables are the unknown quantities that need to be determined in a linear programming problem.

The objective function is a mathematical expression that needs to be maximized or minimized. It represents the goal or objective of the problem. Constraints are the restrictions or limitations that need to be satisfied in a linear programming problem. These constraints limit the feasible region of the problem and provide boundaries for the decision variables. Linear programming involves finding the optimal solution by maximizing or minimizing the objective function, subject to the constraints. The solution must satisfy all the constraints and provide the best possible value for the objective function.

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The volume of the box is 72 cubic feet.

We have,

To find the volume of the box, we need to multiply its length, width, and height.

Given:

Length = 4 ft

Breadth = 6 ft

Height = 3 ft

The volume of the box is:

Volume = Length x Breadth x Height

Volume = 4 ft x 6 ft x 3 ft

Volume = 72 cubic feet

Therefore,

The volume of the box is 72 cubic feet.

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The type of error occurs when certain sample elements are excluded is sample frame error. Then the required answer for the given question is Option B.

The type of error that takes place when a particular sample elements are eliminated or when the whole population is not accurately projected in the sampling frame is called sample frame error.

There are 4 types of sampling error

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If each bag of chips costs $1 less than a granola bar, and jack buys 2 more items than jane buys, Jack buys 15 bags of chips

Let's assume that Jack buys x bags of chips and Jane buys y granola bars. We know that they each spend $24 on snacks, so we can set up the following equation:

x*(price of one bag of chips) + y*(price of one granola bar) = $24

We also know that each bag of chips costs $1 less than a granola bar, so we can write:

(price of one bag of chips) = (price of one granola bar) - $1

Substituting this into the first equation, we get:

x*((price of one granola bar) - $1) + y*(price of one granola bar) = $24

Expanding and simplifying, we get:

x*(price of one granola bar) + y*(price of one granola bar) - x = $24

We also know that Jack buys 2 more items than Jane, so we can write:

x = y + 2

Substituting this into the previous equation, we get:

(y + 2)(price of one granola bar) + y(price of one granola bar) - (y + 2) = $24

Simplifying, we get:

2*(price of one granola bar) + y = $26

We can now solve for y:

(price of one granola bar) = ($26 - y)/2

Substituting this back into the equation for x, we get:

x = y + 2

x = (26 - y)/2 + 2

Simplifying, we get:

x = (28 - y)/2

We know that x and y must be whole numbers, so we can test different values of y until we find one that makes x a whole number. Starting with y = 2, we get:

(price of one granola bar) = ($26 - 2)/2 = $12

2*(price of one granola bar) + y = $26

2*($12) + 2 = $26

Therefore, Jack buys 15 bags of chips (x = (28 - y)/2 = (28 - 2)/2 = 15) and Jane buys 13 granola bars (y = 2).

In summary, Jack and Jane each spend $24 on snacks. Jack buys bags of chips and Jane buys granola bars. Each bag of chips costs $1 less than a granola bar, and Jack buys 2 more items than Jane buys. We can solve for the number of bags of chips Jack buys by setting up and solving equations based on these facts. We find that Jack buys 15 bags of chips.

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Step-by-step explanation:

V = 4/3 pi r^3

64 pi = 4/3 pi r^3      divide both sides of the equation by pi :

64  = 4/3 r^3              multiply both sides by 3/4

3/4 * 64  = r^3              simplify a bit

48   = r^3                     take cube root of both sides

r = 3.63     units

Answer:

The formula for ordinary interest is:

I = P * r * t

where:

I = the interest

P = the principal

r = the interest rate per year

t = the time in years

In this case, the principal is $12,500, the interest rate is 4%, and the time is 292/360 years (since there are 360 days in a year according to the problem statement). Therefore, we have:

t = 292/360 = 0.811111111

I = 12500 * 0.04 * 0.811111111 = 405.5555555

To find the maturity value, we add the interest to the principal:

M = P + I = 12500 + 405.5555555 = 12905.56

Therefore, the maturity value of the promissory note is $12,905.56 rounded to the nearest cent.

The measure of variability that the Charity should use is B. The IQR of 13 is the most accurate to use, since the data is skewed.

Adopting the IQR gives a better picture of the standard donations, since it is less responsive to outliers and unbalanced data than the range. The charity must take advantage of the Interquartile Range (IQR) for an exact depiction of the data, as it is less impressionable to outliers and skewed data.

The IQR would be:

= Q3 - Q1

Q1 from the data is:

= (6 + 8) / 2 = 7

Q3 is :

(20 + 20) / 2 = 20

The IQR is:

= 20 - 7

= 13

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Answer: it is only a mind set

Step-by-step explanation: when you are in a good mindset you will do well but when you are in a negative mindset it will be hard.

Answer:

It depends if its like 1st grade then you might have to get that checked out but if its 12th grade probally to make kids question life :)

Step-by-step explanation:

PLS GIVE BRAINLIST

HAVE A GOOOOODY DAY!!!

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{1}}} \implies \cfrac{ 3 }{ 4 } \implies \cfrac{3}{4} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{1}}} \implies \cfrac{ -3 }{ 4 } \implies - \cfrac{3}{4} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{5}}} \implies \cfrac{ -4 }{ -3 } \implies \cfrac{4}{3}[/tex]

The Rutherford model of the atom is known to be a term that is also seen as planetary model. It was said to have been proposed by Ernest Rutherford in 1911. It was a vital improvement over previous models, but it had some few limitations.

Below are some advantages and disadvantages of the Rutherford model:

In terms of Advantages:

In terms of Disadvantages:

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See text below

advantages and disadvantages of the rutherford model of the atom

Answer:

6 tins of red paint

Step-by-step explanation:

blue = 1, red = 3 so:

from 1 to 2 tins of blue, you multiply 1 x 2 = 2 tins. Now we have to multiply by 2 on the other side

So: 3 x 2 = 6 tins of red

In ratios, multiplying or dividing has to be applied to both sides

1 : 3 becomes 2: 6

The largest possible number that he could be thinking of is given as follows:

3.

A number a is said to be a factor of another number b when the divisibility of b by a has a remainder of zero, that is, it is an exact division.

The factors of 18 are given as follows:

{1, 2, 3, 6, 9}.

The factors of 30 are given as follows:

{1, 2, 3, 5, 6, 10, 15, 30}

The number is odd, hence the largest possible number is of 3.

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The probability that Tally is on the red team would be 1/4

Probability means a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that Tally's teacher divides her class of 16 students into 4 equally sized teams: red team, yellow team, green team and the blue team.

Therefore, the probability that Tally is on the red team will be;

P(E) = Number of favorable outcomes / total number of outcomes

P(E) = Number of teams / total number of students

P(E) = 4/16

P(E) = 1/4

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Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

To establish that S is a subspace of ℝ^3, we must confirm that S is closed under vector summation and scalar multiplication.

A pertinent theorem from linear algebra that can be applied here is the "Subspace Criterion" theorem. This principle states that a non-empty subset S of a vector space V is a subspace if and only if it fulfills the following conditions:

For any vectors a, b ∈ S, their addition a + b ∈ S.

For any vector a ∈ S and any scalar k, the product ka ∈ S.

Now, let's define a vector m = v - e.

Observe that for any y in S, we have:

m • y = (v - e) • y = (v • y) - (e • y) = 0.

This implies that y is orthogonal to the vector m.

Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

As the plane is closed under vector summation and scalar multiplication, S is indeed a subspace of ℝ^3.

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Suppose v = (2, 4, 5) and e = (6, 7, 3) are a pair of vectors in ℝ^3. Let S be the collection of all y in ℝ^3 such that the inner product of v and y equals the inner product of e and y (i.e., v • y = e • y).

What principle can be utilized to demonstrate that S is a subspace of ℝ^3? Describe S in geometric terms.

Answer:We can estimate that 900 people in attendance would prefer mustard on a hot dog.

Step-by-step explanation:What is proportion?

Proportion is a mathematical concept that refers to the relationship between two quantities, expressed as a ratio or a fraction. It represents the size of one quantity relative to another quantity, typically within a larger population or sample.

To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.

The proportion of people in the sample who prefer mustard is:

27/150 = 0.18

To estimate the number of people who prefer mustard in the entire population of 5,000 attendees, we can multiply this proportion by the total number of attendees:

0.18 x 5,000 = 900

Therefore, we can estimate that 900 people in attendance would prefer mustard on a hot dog.

A table that matches the data in the graph include the following:

Correct answers       Points

0                                   0

5                                   30

12                                  72

18                                  108

20                                 120

In Mathematics, a proportional relationship produces equivalent ratios and it can be represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points contained in the table as follows:

Constant of proportionality, k = y/x = t/d

Constant of proportionality, k = 30/5 = 72/12 = 108/18 = 120/20

Constant of proportionality, k = 6.

Therefore, the required equation is given by;

y = kx

y = 6x

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.