how many 6-digit numbers (using 1,2,3 , ... ,9) are there if repetition is not allowed? how many are there which have at least one digit repeated?

The answer is decreases.

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations. For example, 3x² − 2xy + c is an algebraic expression.

The algebraic equation can be written in the many forms. It can be in one variable , two variable or even three or four variable. There are also many ways to put all into the equations.

So, as the question stated As x is increases, the value of the expression decreases.

Therefore, the answer is decreases.

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Step-by-step explanation:

For denominator:

x²-5x -24 = x² -(8-3)x -24

= x² -8x+3x-24 = x(x-8) +3(x-8)

Taking common (x-8): = (x-8)(x+3)

So option d is accurate.

And for numerator, 7x+56 =7(x+8)

So, option a is accurate.

Answer:

B

Step-by-step explanation:

If average size of bass caught in strawberry lake is normally distributed, then the probability that the size of fish we caught is more than 15 inches is 0.3085.

The mean-size of the bass caught is (μ) = 13 inches,

The standard-deviation of the bass caught is (σ) = 4 inches,

we have to find probability that size of fish we caught is more than 15 inches.

We will use the z-score formula:

⇒ z = (x - μ)/σ,

So,

⇒ z = (15 - 13)/4 = 0.5,

Now, we need to find the probability of getting a z-score of 0.5 or higher. We use a standard normal distribution table to find this probability.

⇒ P(Z > 0.5) = 0.3085

Therefore, the required probability is 0.3085 or 30.85%.

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The student can improve the investigation by using balls that are the same mass. This is because the investigation aims to study the effect of gravity on objects on Earth, and the gravitational force acting on an object is directly proportional to its mass. Therefore, in order to compare the effect of gravity on different objects, they should all have the same mass.

Using balls of different masses will make it difficult to draw any valid conclusion about how the gravitational force operates on different materials. For measuring the circumference of the balls, we would not be able to draw any conclusive results on the effect of gravity. The other option of dropping the balls from the same height is already part of the criteria mentioned and is used to ensure a consistent experimental setup.

Answer:

V = 75[tex]\pi[/tex] or 235.619449... cm / 235.62 cm

Hope this helps!

Step-by-step explanation:

The formula for the volume of a cone is  [tex]V=\frac{1}{3} *h*\pi r^{2}[/tex].

[tex]V = \frac{1}{3} *9*\pi 5^{2}[/tex]  ( Simplify 1/3 and 9 )

[tex]V=3*25\pi[/tex]

[tex]V=75\pi[/tex]

V = 235.619449019 or 235.62

The area of the square whose diagonal length is 2√2 is 4 square units.

what is area of square?

In mathematics, the area is a measure of the size or extent of a two-dimensional figure or shape, typically measured in square units. It is the amount of space inside the boundary of a flat object, such as a triangle, rectangle, circle

In the given question,

The diagonal of a square divides it into two congruent right triangles, where the hypotenuse of each triangle is the diagonal of the square and the legs are the sides of the square.

Let the side length of the square be "s". Then, by the Pythagorean theorem, we have:

s² + s² = (2√2)²

Simplifying the right-hand side gives:

2s² = 8

Dividing both sides by 2 gives:

s² = 4

Taking the square root of both sides gives:

s = 2

Therefore, the area of the square is:

A = s² = 2² = 4

So the area of the square whose diagonal length is 2√2 is 4 square units.

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A variant expression is a mathematical expression used to analyze the progress of a recursive function and ensure its termination. To guarantee that a recursive function terminates, a variant expression must have two essential properties which are Boundedness and monotonicity.

1. Boundedness: A variant expression must be bounded, which means that it has an upper or lower limit. This limit is often a non-negative integer value, such as 0. The boundedness property ensures that the variant expression cannot grow indefinitely, which would lead to non-termination of the recursive function.

2. Monotonicity: A variant expression must be monotonically decreasing, meaning that its value strictly decreases with each recursive call. Monotonicity ensures that the variant expression is always moving closer to the bound, eventually reaching the limit and causing the function to terminate.

To guarantee the termination of a recursive function, follow these steps:

Step 1: Identify a suitable variant expression for the function. The expression should be related to the problem size or input parameters of the function and should reflect the progress towards the function's termination.

Step 2: Verify the boundedness property of the variant expression. Ensure that the expression has an upper or lower limit, typically a non-negative integer, which it cannot exceed.

Step 3: Verify the monotonicity property of the variant expression. Check that the expression's value strictly decreases with each recursive call, moving closer to the bound.

Step 4: Ensure that the recursive function terminates when the variant expression reaches the bound. This condition is usually implemented as the base case of the function, which prevents further recursive calls and initiates the return process.

In summary, a variant expression must have boundedness and monotonicity properties to guarantee that a recursive function terminates. By verifying these properties and incorporating them into the recursive function, you can ensure that the function will reach its termination condition and not result in infinite recursion.

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The total energy value from these stated amounts is 214 calories.

To calculate the total energy value (in calories) from the stated amounts of protein, carbohydrates, fat, and alcohol, we can follow these steps:
1. Protein: Multiply the amount of protein (8 grams) by the energy value of protein (4 calories/gram).
2. Carbohydrates: Multiply the amount of carbohydrates (25 grams) by the energy value of carbohydrates (4 calories/gram).
3. Fat: Multiply the amount of fat (6 grams) by the energy value of fat (9 calories/gram).
4. Alcohol: Multiply the amount of alcohol (4 grams) by the energy value of alcohol (7 calories/gram).
5. Add the resulting values from steps 1-4 to find the total energy value (in calories).
Applying these steps:
1. Protein: 8 grams * 4 calories/gram = 32 calories
2. Carbohydrates: 25 grams * 4 calories/gram = 100 calories
3. Fat: 6 grams * 9 calories/gram = 54 calories
4. Alcohol: 4 grams * 7 calories/gram = 28 calories
5. Total energy value: 32 + 100 + 54 + 28 = 214 calories.

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Answer:

the gravity is 100

Step-by-step explanation:

machel liconl said it in 1st ammenmens

So the point of intersection is (8, 8), which is the solution to the simultaneous equations. This means that x = 8 and y = 8 satisfy both equations simultaneously. the solution to the simultaneous equations is  [tex]x = 4[/tex] and  [tex]y = -6.5[/tex]  .

f the equations were more complicated or if graphing was not possible, we could use algebraic methods such as substitution or elimination to find the solution.

a)

To plot the lines[tex]y - 1/4 x + 6[/tex]  and  [tex]y = -2x + 3/2[/tex] , we can complete the following table of values:

x [tex]y - 1/4 x + 6[/tex]  [tex]y = -2x + 3/2[/tex]

[tex]0[/tex] [tex]6[/tex]                

1 6.75            -0.5

2 7.5                 -2.5

3 8.25         -4.5

4 9                -6.5

Using these values, we can plot the two lines on the same set of axes:

b)

To find the solution to the simultaneous equations     and [tex]y = -2x +3/2[/tex] , we need to find the point where the two lines intersect on the graph. From the graph, we can see that this point is approximately (4, -6.5).

Therefore, the solution to the simultaneous equations is [tex]x = 4[/tex] and [tex]y = -6.5.[/tex]

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Answer: 1 4/8 or 1 1/2

Step-by-step explanation:

1 5/8

-1/8

5/8 - 1/8 = 4/8  

add 1.....  1 4/8

Step-by-step explanation:

scalene    === all of the sides are different lengths

acute     ==== all of the angles are < than 90 degrees

  that's all

Therefore, the expression that Tesha wrote is most likely option. [tex]C: (5 *6 + 2 *3)/(3*2*3).[/tex]

An equation is a mathematical statement that shows the equality of two expressions or values. It contains an equal's sign (=) which separates the two expressions that are equal to each other. Equations can be simple or complex and can involve one or more variables, which are typically represented by letters. Equations are used extensively in mathematics, science, engineering, and many other fields to model and solve problems. Solving an equation involves finding the values of the variables that make the equation true.

To solve this problem, we need to simplify the expression.[tex](20 + 4) /12[/tex]:

[tex](20 + 4) / 12 = 24 / 12 = 2[/tex]

So, the expression that Tesha wrote must also simplify to 2. Let's check each of the options:

A. [tex]36 / 3 *5 = 12 * 5 = 60[/tex], which is not equivalent to 2. So, option A is not the correct one.

B. [tex](3 * 3 * 3) / 3 * 1 = 27 / 3 *1 = 9 * 1 = 9[/tex], which is not equivalent to 2. So option B is not the correct one.

C. [tex](5 * 6 + 2 * 3) / (3 * 2 * 3) = (30 + 6) / 18 = 36 / 18 = 2[/tex], which is equivalent to 2. So, option C is the correct one.

D. [tex](8 * 5 *2) / (10 * 2) = 80 /20 = 4[/tex], which is not equivalent to 2. So option D is not the correct one.

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Answer:

To solve the equation, we need to isolate the square root term and square both sides of the equation. We have:

1 + √n + 11 = n

√n = n - 12

Squaring both sides:

n = (n - 12)^2

n = n^2 - 24n + 144

n^2 - 25n + 144 = 0

Factorizing the quadratic equation:

(n - 16)(n - 9) = 0

Therefore, n = 16 or n = 9. We need to check these solutions in the original equation to see if they are valid.

For n = 16:

1 + √16 + 11 = 16

1 + 4 + 11 = 16

16 = 16

The solution n = 16 satisfies the equation.

For n = 9:

1 + √9 + 11 = 9

1 + 3 + 11 = 9

15 = 9

The solution n = 9 does not satisfy the equation.

Therefore, the only real solution is n = 16, which corresponds to option C: -2 is an extraneous solution and 5 is a real solution.

Hope This Helps!

Answer:

the answer is B) 1/2, 3.

Step-by-step explanation:

To solve the system of linear equations by graphing, we need to graph both lines and find the point where they intersect. This point will be the solution to the system.

The equation y = -1/2x+2 has a y-intercept of 2 and a slope of -1/2. We can plot this on a graph by starting at the y-intercept (0, 2) and then going down 1 unit and to the right 2 units to get another point on the line. We can then draw a straight line through these two points.

The equation y=1/2x-1 has a y-intercept of -1 and a slope of 1/2. We can plot this on the same graph by starting at the y-intercept (0, -1) and then going up 1 unit and to the right 2 units to get another point on the line. We can then draw a straight line through these two points.

The point where these two lines intersect is the solution to the system of equations. From the graph, we can see that this point is approximately (1/2, 3).

the answer is B) 1/2, 3.

To solve the system of linear equations by graphing, we need to plot the lines represented by the equations on the same coordinate plane and find the point of intersection.

|

3 | .

| \

2 | \

| \

1 | . \

| \

0 |_____________

0 1 2 3 4

Hernán Cortés had around 600 men, including soldiers and sailors, under his command during the Spanish conquest of the Aztec Empire.

Hernán Cortés led the Spanish conquest of the Aztec Empire in the early 16th century. The size of his expeditionary force varied over time, but at its peak, it is estimated that he had about 600 men under his command, including soldiers and sailors.

When Cortés first set out from Cuba to explore the mainland of Mexico in 1519, he had a force of about 600 men, including 11 ships with sailors and about 100 soldiers. However, some of his soldiers were left behind to establish a settlement on the coast, reducing his fighting force to around 500 men.

As Cortés made his way inland, he was able to recruit more indigenous allies to his cause, which increased his overall fighting strength. By the time he reached the Aztec capital of Tenochtitlan in 1521, he had an army of around 80,000 men, including native allies, although the core of his fighting force was still made up of Spanish soldiers and sailors.

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Answer:

17 males, 10 females

Step-by-step explanation:

Let f be the number of females and m be the number of males.

f + m = 27

f = m - 7, so m - 7 + m = 27

2m - 7 = 27

2m = 34

m = 17, f = 10

Answer:13,595,327.65

Step-by-step explanation:

Answer:

Step-by-step explanation:

The appropriate type of t-test for this study is a one-sample t-test.

A one-sample t-test is used to determine whether a sample mean is significantly different from a known or hypothesized population mean. In this case, the researcher wants to compare the obesity rate in a small community to the known obesity rate in the United States. As the population variance is unknown, the appropriate test is a one-sample t-test instead of a z-test.

The test involves calculating the t-statistic, which measures the difference between the sample mean and the hypothesized population mean, divided by the standard error of the sample mean. The t-statistic is then compared to the critical t-value from the t-distribution to determine whether the difference is statistically significant.

Therefore, a one-sample t-test is appropriate for this study.

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a. The null hypothesis 2 is correct.

b. 0.1346 is the -value for your hypothesis test in part (a).

c. We lack sufficient data to draw the conclusion that Tulsa's average household water rate differs considerably from the average residential water rate paid by U.S. public utilities.

d.  The critical value is  -1.5277.

a. The hypotheses can be formulated as follows:

Null Hypothesis: The population mean rate per ccf of residential water charged by U.S. public utilities is equal to the rate charged by Tulsa (μ = [tex]\mu_0[/tex]).

Alternative Hypothesis: The population mean rate per ccf of residential water charged by U.S. public utilities differs from the rate charged by Tulsa (μ ≠ [tex]\mu_0[/tex]).

The correct null hypothesis is 2.

b. To test the hypotheses, we can use a two-sided t-test with a significance level of α = 0.05.

Using the data in the "residential water" file, we can calculate the test statistic and p-value as follows:

Sample mean = 2.358

Sample standard deviation = 1.011

Sample size = 50

Hypothesized population mean = 2.44 (the rate charged by Tulsa)

t = (2.358 - 2.44) / (1.011 / [tex]\sqrt{(50)}[/tex]) = -1.5277

Degrees of freedom = 50 - 1 = 49

Using a t-distribution table or calculator, the p-value for a two-sided test with 49 degrees of freedom and a t-statistic of -1.5277 is approximately 0.1346.

The p-value for the hypothesis test is 0.1346.

c. At α = 0.05, the critical value for a two-sided t-test with 49 degrees of freedom is ± 2.0096.

Since the calculated t-statistic (-1.5277) falls within the range of the critical values, we cannot reject the null hypothesis.

Therefore, we do not have enough evidence to conclude that the mean rate per ccf of residential water charged by U.S. public utilities differs significantly from the rate charged by Tulsa.

d. Using the critical value approach, we would compare the calculated t-statistic (-1.5277) with the critical values from the t-distribution table.

At α = 0.05 and 49 degrees of freedom, the critical values are ±2.0096.

Since the calculated t-statistic (-1.5277) falls within the range of the critical values, we cannot reject the null hypothesis.

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When the beginning value or ending value is closing the set, a square bracket is used. A parenthesis is used to show that the beginning value or ending value is open. A parenthesis is always used with open intervals.

When we use an interval notation to describe sets of numbers, parentheses, and brackets have different meanings. Parentheses "(" and ")" describes an open interval, which means that the endpoints are not included in the set. For example, the interval (-3,5) includes all real numbers greater than -3 and less than 5, but it does not include -3 or 5 themselves. On the other hand, brackets "[" and "]" denote a closed interval, which means that the endpoints are included in the set. For example, the interval [-3,5] includes all real numbers greater than or equal to -3 and less than or equal to 5. If the endpoint is included in the set, use a bracket; if it is not, use a parenthesis.

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Answer:

See below for proof.

Step-by-step explanation:

Given expression:

[tex]\implies \dfrac{1+\csc(x)}{\cot(x)+\cos(x)}[/tex]

[tex]\boxed{\begin{minipage}{4.3 cm}\underline{Trigonometric Identities}\\\\$\csc(x)=\dfrac{1}{\sin(x)}$\\\\\\$\cot(x)=\dfrac{\cos(x)}{\sin(x)}$\\\\\\$\sec(x)=\dfrac{1}{\cos(x)}$\\\\\end{minipage}}[/tex]

Use the trigonometric identities to rewrite csc(x) and cot(x) in terms of sin(x) and cos(x):

[tex]\implies \dfrac{1+\dfrac{1}{\sin(x)}}{\dfrac{\cos(x)}{\sin(x)}+\cos(x)}[/tex]

Simplify the numerator and denominator:

[tex]\implies \dfrac{\dfrac{\sin(x)+1}{\sin(x)}}{\dfrac{\cos(x)+\sin(x)\cos(x)}{\sin(x)}}[/tex]

[tex]\textsf{Apply the fraction rule:} \quad \dfrac{\dfrac{a}{b}}{\dfrac{c}{b}}=\dfrac{a}{c}[/tex]

[tex]\implies \dfrac{\sin(x)+1}{\cos(x)+\sin(x)\cos(x)}[/tex]

Factor out cos(x) from the denominator:

[tex]\implies \dfrac{\sin(x)+1}{\cos(x)(1+\sin(x))}[/tex]

Cancel the common factor (1 + sin(x)):

[tex]\implies \dfrac{1}{\cos(x)}[/tex]

Rewrite 1/cos(x) using the identity:

[tex]\implies \sec(x)[/tex]

Therefore, the equation has been verified.

Let's see

LHS

[tex]\\ \sf\longmapsto \dfrac{1+csc(x)}{cot(x)+cos(x)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1+\dfrac{1}{sin(x)}}{\dfrac{cos(x)}{sin(x)}+cos(x)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{1+sin(x)}{\cancel{sin(x)}}}{\dfrac{cos(x)+sin(x)cos(x)}{\cancel{sin(x)}}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1+sinx}{cosx(1+sinx)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{cosx}[/tex]

[tex]\\ \sf\longmapsto sec(x)[/tex]

verified

Given that Steve handed him a black king, the probability of Scott's second card being a red card is 13/25, or around 0.52.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

A conventional deck of playing cards has 52 cards, including two black kings. When Steve deals a black king to Scott, the deck has 51 cards, 26 of which are red.

We only need to analyse the likelihood of obtaining a red card on the second draw because we know Scott's initial card is a black king. There are 50 cards remaining in the deck, 26 of which are red. As a result, the likelihood that Scott's second card will be a red card is:

P(red card drawn on second draw) = 26/50 = 13/25

Given that Steve handed him a black king, the likelihood of Scott's second card being a red card is 13/25, or around 0.52.

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Answer: (12a + b)(12a - b)

Step-by-step explanation:

1. Begin by writing the expression in expanded form: 12a - b

2. Rewrite the expression as 12a + (-b)

3. Factor out 12a from the expression: 12a(1 + (-b))

4. Factor out 1 from the expression: (12a)(1 + (-b))

5. Rewrite (1 + (-b)) as (1 - b): (12a)(1 - b)

6. Rewrite (12a)(1 - b) as (12a + b)(12a - b): (12a + b)(12a - b)

Step-by-step explanation:

A C and H would all also be 120 degrees due to corresponding and vertical angles

Option D. between 6 and 9 is correct.

Since we don't have the specific function, we cannot definitively determine which interval shows the function is increasing.

However, based on the information given, we can say that the function increases within one of these intervals.

It is important to know the specific function to identify the correct interval.

To determine the correct answer, we first need to understand the terms "domain," "function," and "increasing."
- Domain: The set of all possible input values (x-values) for a given function.
- Function: A mathematical relationship between input (x) and output (y) values, often represented as y = f(x).
- Increasing: A function is increasing when the output (y-value) increases as the input (x-value) increases.
Now, let's analyze the given options:
A. between 0 and 6
B. between 3 and 9
C. between 3 and 6
D. between 6 and 9

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Question:

The maximum-volume of open box which could made from a "10-inch" by "20-inch" piece of cardboard by cutting out squares of equal sides from 4 corners is 192.5 inch³.

We know that "Volume" of box is ⇒  V = L × W × H.

The dimensions of a piece of cardboard is 10 inches by 20 inches.

Let x = height of box, x will also be side of square taken out of each corner.

The length of box = 20 - 2x; width of box = 10 - 2x and

So, equation of Volume is ⇒ V = (20-2x) × (10-2x) × (x),

⇒ V = 4x³ - 60x² + 200x

On differentiating both sides, to get "dv/dx" :

We get,

⇒ dv/dx = 12x² - 120x + 200

Using general formula for finding roots of equation,

We get,  x = 7.886 and x = 2.113,

Since 7.886 × 2 = 15.772 inches, this is greater than the 10 inch side,

So,  x = 2.113 inches.

We have cut "2.113 inches" from each-corner to get maximum volume.

The sizes of cubes are :

⇒ Length = 20 - (2 × 2.113) = 15.774,

⇒ width = 10 - (2 × 2.113) = 5.774

⇒ Height = 2.113

So, volume = 15.774 × 5.774 × 2.113 = 192.5 cubic inches.

Therefore, the volume of cube is 192.5 inch³.

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To factor the polynomial 10x³ + 35x² − 4x − 14 by grouping, the greatest common factor is factored out from the first two terms and the last two terms separately. Both terms have a common factor of (2x + 7), which is the missing factor in the parentheses, and the correct answer is (B) 2x + 7.

To factor the polynomial by grouping, we need to factor out the greatest common factor from the first two terms and the last two terms separately:

10x³ + 35x² − 4x − 14

5x2(2x + 7) − 2(2x + 7)

We can see that both terms have a common factor of (2x + 7), so the missing factor in the parentheses is (2x + 7). Therefore, the answer is (B) 2x + 7.

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