Identify each situation as a permutation or a combination.

1. choosing friends to invite to a party

2. choosing your top 10 favorite actors

The complete representation of the expression is 7/ 10^-1 = 7 x 10^1

Index forms are simply defined as the exponent or power of a number raised to a variable or number.

It is known as the standard form of a number.

It is also known as the exponential representation of an expression or number .

Example;

The index form of 200 is 2 × 10^2

The index form of 40 is 4 × 10 ^1

Given the expression;

7/10-  = 7x10^

We have;

7/ 10^-1 = 7 x 10^1

Thus, the complete representation of the expression is 7/ 10^-1 = 7 x 10^1

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The description refers to the diagnosis of brief psychotic disorder, which consists of abnormal behaviors identical to those in schizophrenia lasting for at least 1 month but fewer than 6 months.

Brief psychotic disorder is a psychiatric diagnosis characterized by the presence of psychotic symptoms, such as hallucinations, delusions, disorganized thinking, or grossly disorganized or catatonic behavior. These symptoms are similar to those seen in schizophrenia, but the key distinction is that brief psychotic disorder lasts for a shorter duration, specifically between 1 month and 6 months.

During this period, individuals with brief psychotic disorder may experience a sudden onset of symptoms that significantly impact their thoughts, emotions, and behavior. However, unlike schizophrenia, the duration of symptoms in brief psychotic disorder is limited, typically resolving within a few weeks to a few months.

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Answer:

(3, 6)

Step-by-step explanation:

I hope this helps you!

Answer: 3/5

Step-by-step explanation:

Answer:

28+2x

Step-by-step explanation:

simplificar la expresión.

The speeds for each of the given distance and times are;

A) 45 miles per hr

B) 22 miles per hr

C) 30 miles per hr

D) 50 miles per hr

E) 65 miles per hr

To convert the given values of distance and time to speed in miles per hour, we will just divide the time by the distance. Speed = distance/time

A) 135 miles in 3 hours. Thus;

Speed = 135/3 miles per hour = 45 miles per hr

B) 22 miles in 1 hour. Thus;

Speed = 22/1 miles per hr = 22 miles per hr

C) 7.5 miles in 1/4 hour. Thus;

Speed = 7.5/(1/4) miles per hour = 30 miles per hr

D) 100/3 in 2/3 hour. Thus;

Speed = (100/3 ÷ 2/3) = 50 mph

E) 97.5 in 1.5 hours. Thus;

Speed = 65 miles per hr

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Answer:

1.) Reflection over y=1

2.) Translation rule: (x-5, y-3)

3.) Reflection over the y axis

4.)Translation rule: (x-4, y+1)

Step-by-step explanation:

Answer: The model of the Cape Hatteras Lighthouse is 7 feet tall, as it follows a scale of 8 inches = 30 feet. The actual lighthouse is 210 feet, so to calculate the height of the model, you would divide the actual lighthouse's height by the scale that is used. 210 feet divided by 30 equals 7 feet, which is the height of the model. This is why models are made to a specific scale, as it allows us to calculate the size of the model accurately, without having to measure every single dimension.

Answer:

It is on sale for $80.

Step-by-step explanation:

20% -> 0.20

0.20*100= 20

100-20=80

$80

Hope this was helpful. Have a nice day/night! :)

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Answer:

5319

Step-by-step explanation:

There are two ways that the answer can be determined

Method 1

0.1 x 5710 = 571

5710 - 571 = 5319

Method 2

If the plants planted this year are 10% fewer, the plants this year are (100% - 10%) 90% of last year's plant

90% x 5710

0.9 x 5710 = 5319

Answer:

Plots that can detect violations in regression assumptions, while response plots help analyse the relationship between the response variable and predictors are Residual plots and scatterplot matrix.

Step-by-step explanation:

There are several graphical plots commonly used to detect violations of regression model assumptions and analyze estimated regression models. Here are a few examples:

Residual plot: A residual plot shows the difference between the observed values of the response variable and the predicted values from the regression model. Patterns in the residuals, such as nonlinearity, heteroscedasticity (unequal variances), or outliers, can indicate violations of assumptions.

Response plot: This plot examines the relationship between the response variable and one of the predictor variables while holding other predictors constant. It helps identify nonlinearity or other issues in the relationship between the response and predictors.

Scatterplot matrix: A scatterplot matrix displays scatterplots between pairs of predictor variables. It can help detect issues like perfect multicollinearity, which occurs when two or more predictors are highly correlated, leading to problems in estimating the regression coefficients.

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The quadrilateral named D, H, and E will be the scaled copies of the unlabeled rectangle.

A quadrilateral may be defined as a closed figure having four sides whereas a rectangle is a type of quadrilateral which has four sides in which any two sides are equal and the other two sides are also equal. The interior angles are 90°. The scale factor may be defined as the ratio of two dimensions such that one figure is large, and another is small. The scale factor is done due to the unpractical measurement of any figure. For example, if a figure is a scale copy of the scale factor of 6/2 it means 2 is converted into 6. Now, from the question If any figure is a scaled copy, then all dimensions must be enlarged with the same factor it means length and width both must be enlarged with the same factor. So, the unlabeled rectangle has 4 grid lengths and 2 grid widths. In H length is 8 grids and width are 4 which is the multiplication of 2 by 4 and 2. Quadrilateral D and E also follow the same.

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The population will grow the fastest at half of the carrying capacity, which is 250 crabs.

In the logistic growth equation, the population growth rate is highest when the population is at half of the carrying capacity. This is because, at this point, there is a balance between birth rates and death rates, maximizing the net population growth.

For the given logistic growth equation with a carrying capacity of 500 crabs, the population will grow the fastest at half of the carrying capacity, which is 250 crabs.

Regarding the second question, to determine the initial population size of widowbirds when tracking started, we can use the equation λ = (births - deaths) / initial population.

Given that 150 individuals were born and 75 birds died during the tracking period, and λ is equal to 2, we can solve the equation for the initial population.

2 = (150 - 75) / initial population

Multiplying both sides by the initial population:

2 * initial population = 150 - 75

2 * initial population = 75

Dividing both sides by 2:

initial population = 75 / 2

initial population = 37.5

Since population size cannot be a decimal, we round down to the nearest whole number.

Therefore, when tracking the population of widowbirds, the initial population size would be approximately 37 birds.

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Answer:

It is a horizontal line at the point (0,-4) and goes on forever.

Step-by-step explanation:

Answer: O-22, C-6, H-76

Step-by-step explanation:

Given

There are 164 atoms available

Suppose there are x oxygen atoms

So, carbon atoms are 3x

Hydrogen atoms are 3x+10

The sum of the three must be equal to 164

\(\Rightarrow x+3x+3x+10=164\\\Rightarrow 7x=154\\\Rightarrow x=22\)

\(\text{Oxygen atoms}=22\\\text{Carbon atoms}=3\times 22\\\quad \quad =66\\\text{Hydrogen atoms}=66+10\\\quad \quad=76\)

Answer:

It is already the farthest that can be

Step-by-step explanation:

5x4 - 7x3 + x + 2

5x^2 - 7x^2 + 1x + 2

Answer:

$1.50

Step-by-step explanation:

first, find the unit rate which is 0.3 (7.2/24)

then multiply that by 5

The Scale factor was used to enlarge the picture is 7/ 31.5.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

A picture is 7 inches wide and 9 inches long.

A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.

So, scale factor is

= Original dimension / Enlarged dimension

= 9/ 40.5

= 90/ 405

= 10/45

= 2/9

Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.

= 7/ 3.15

= 70/31.5

= 2/9

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The mass of the piece of paper is 550 times greater than the mass of the feather.

Herein we have the masses of a piece of paper and a feather, the former is in common notation but the latter is in scientific notation. Due to comfort issues and the desire for clearer and quicker operations, we decided to convert the mass of the piece of paper to scientific notation:

Piece of paper

4.4 × 10⁰ grams

Feather

8.0 × 10⁻³ grams

Then, by definition of ratio, we divide the mass of the piece of paper to the mass of the feather:

r = (4.4 × 10⁰ / 8.0 × 10⁻³)

r = (4.4 / 8.0) × 10³

r = 0.55 × 10³

r = (5.5 × 10⁻¹) × 10³

r = 5.5 × 10²

By converting r into normal notation:

r = 5.5 × 100

r = 550

The mass of the piece of paper is 550 times greater than the mass of the feather.

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The probability that all the numbers rolled are distinct is 0.015.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that suppose six 6-sided dice are rolled. The probability of the numbers rolled are distinct is calculated as,

Probability = 6! / 6⁶

Probability = ( 720 ) / ( 46656)

Probability = 5 / 324

P = 0.015

Therefore, the probability that all the numbers rolled are distinct is 0.015.

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The answer of the given question based on the finding the work done by the force, is  field F on a particle moving along the path C is 1/6.

A force is defined as influence that causes object to undergo change in motion. It is vector quantity, means it has both magnitude and direction.

To find the work done by the force field F on a particle moving along the given path, we need to evaluate the line integral of F along the path C.

The line integral of a vector field F along a curve C parameterized by r(t) is given by:

∫ F(r(t)) ⋅ r'(t) dt

where r'(t) is the derivative of r(t) with respect to t.

In this case, the force field F(x, y) = x²i − xyj, and the path C is given by x = cos³(t), y = sin³(t) from (1, 0) to (0, 1).

First, we need to parameterize the path C in terms of t. Since x = cos³(t) and y = sin³(t), we can express the path C as a vector function r(t) = ⟨cos³(t), sin³(t)⟩, where t goes from 0 to π/2.

we need to find derivative of r(t) with the respect of  t:

r'(t) = ⟨-3cos³(t)sin(t), 3sin²(t)cos(t)⟩

Now, we can evaluate the line integral of F along C:∫ F(r(t)) ⋅ r'(t) dt

= ∫ (cos⁶(t)i - cos³(t)sin⁴(t)j) ⋅ (-3cos²(t)sin(t)i + 3sin²(t)cos(t)j) dt

= ∫ (-3cos⁸(t)sin(t) + 3cos³(t)sin⁵(t)) dt

= [-3/9cos⁹(t) - 3/6cos⁴(t)cos²(t)]_0^(π/2)

= 0 - (-3/9 - 3/12)

= 1/6

Therefore, the work done by the force field F on a particle moving along the path C is 1/6.

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The Extreme Value Theorem states that if a function f(x) is continuous over a closed interval \([a,b]\), then \(f(x)\) attains an absolute maximum and an absolute minimum at least once in the interval.

Therefore, the function that is guaranteed by the Extreme Value Theorem to have an absolute maximum on the interval [0,3] is the one that is continuous on the interval.  

\(y = cos(x) and y = tan(x)\) are not guaranteed to have absolute maximums on [0,3] as they are not continuous over this interval.

\(y = cos^ -1\) is also not guaranteed to have an absolute maximum on [0,3] because its range is [-π/2, π/2] which does not contain the value 3, and it is not defined over the interval [0,3].

Thus, the function that is guaranteed by the Extreme Value Theorem to have an absolute maximum on the interval [0,3] is \(y = cos(x) \).

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Answer:

Step-by-step explanation:

4. A) \(\frac{13}{100}\)×79.50 = 10.335

tax=10.335

total cost=79.50+10.335=89.835

B) \(\frac{13}{100}\)×189.99=24.6987 = tax

189.99+24.6987=214.6887

5) \(\frac{20}{100}\)×544.99=108.998

yes Brittany will have enough money

Answer:

A) X<5

Step-by-step explanation:

The circle is open, and the line is pointing left meaning it is less than five.

X is a connected set but not a path-connected set. X={x,0xe[0,1}U{1/nyneN,ye{0,1]}U{0,1}.

To prove that X is connected, let us assume that X can be divided into two disjoint non-empty open sets A and B. Since X is the union of different points, any point in X will be in either A or B. Let us take an arbitrary point p in A. Since A is open, there is an open ball centered at p that is contained in A. Because B is disjoint from A, it follows that every point in this ball is also in A. By a similar argument, any point in B must have a ball centered at that point that is entirely contained in B. Thus, X must be either in A or B and hence, cannot be divided into two disjoint non-empty open sets. However, X is not path-connected since there is no path between points in [0,1] x {0} and {1} x {1}. Thus, it is connected but not path-connected.

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a. The amount to which $500 will grow when compounded annually at a rate of 16% for 10 years is approximately $1,734.41.

b. The amount to which $500 will grow when compounded semiannually at a rate of 16% for 10 years is approximately $1,786.76.

c. The amount to which $500 will grow when compounded quarterly at a rate of 16% for 10 years is approximately $1,815.51.

d. The amount to which $500 will grow when compounded monthly at a rate of 16% for 10 years is approximately $1,833.89.

e. The amount to which $500 will grow when compounded daily at a rate of 16% for 10 years (365 days in a year) is approximately $1,843.96.

a. The amount to which $500 will grow when compounded annually at a rate of 16% for 10 years is approximately $1,734.41.

To calculate this, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $500, r = 0.16, n = 1, and t = 10.

Plugging these values into the formula, we get:

A = 500(1 + 0.16/1)^(1*10)

 = 500(1 + 0.16)^10

 ≈ 1,734.41

Therefore, $500 will grow to approximately $1,734.41 when compounded annually at a rate of 16% for 10 years.

b. The amount to which $500 will grow when compounded semiannually at a rate of 16% for 10 years is approximately $1,786.76.

To calculate this, we can use the same compound interest formula, but with a different value for n. In this case, n = 2 because the interest is compounded twice a year.

A = 500(1 + 0.16/2)^(2*10)

 ≈ 1,786.76

Therefore, $500 will grow to approximately $1,786.76 when compounded semiannually at a rate of 16% for 10 years.

c. The amount to which $500 will grow when compounded quarterly at a rate of 16% for 10 years is approximately $1,815.51.

Using the compound interest formula with n = 4 (compounded quarterly):

A = 500(1 + 0.16/4)^(4*10)

 ≈ 1,815.51

Therefore, $500 will grow to approximately $1,815.51 when compounded quarterly at a rate of 16% for 10 years.

d. The amount to which $500 will grow when compounded monthly at a rate of 16% for 10 years is approximately $1,833.89.

Using the compound interest formula with n = 12 (compounded monthly):

A = 500(1 + 0.16/12)^(12*10)

 ≈ 1,833.89

Therefore, $500 will grow to approximately $1,833.89 when compounded monthly at a rate of 16% for 10 years.

e. The amount to which $500 will grow when compounded daily at a rate of 16% for 10 years (365 days in a year) is approximately $1,843.96.

Using the compound interest formula with n = 365 (compounded daily):

A = 500(1 + 0.16/365)^(365*10)

 ≈ 1,843.96

Therefore, $500 will grow to approximately $1,843.96 when compounded daily at a rate of 16% for 10 years.

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