can there be a right triangle with sides of lengths 1, 2, and 3? why or why not? can you find a right triangle whose side lengths are consecutive natural numbers?

Step-by-step explanation:

scalene    === all of the sides are different lengths

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

  that's all

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

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:

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

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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Answer:

$33.80

Step-by-step explanation:

If Noah gave away 2/7, that means that he still has 5/7

[tex]\frac{5}{7}[/tex] x [tex]\frac{4732}{1}[/tex] = [tex]\frac{23660}{7}[/tex] = 3380

Helping in the name of Jesus.

The amount that is left using a dollar sign and decimal point is $33.80.

Pennies saved by Noah are 4732 pennies.

He gave 2/7 of the pennies in the missionary offering.

The number of pennies he gave in missionary offerings is:

PENNIES = (2/7) × 4732

PENNIES = 1352

Hence, he gave 1352 pennies.

Therefore, he has left with:

LEFTOVER PENNIES = TOTAL PENNIES - PENNIES GIVEN

LEFTOVER PENNIES = 4732 - 1352

LEFTOVER PENNIES = 3380

Therefore, The amount that is left using a dollar sign and the decimal point is $33.80.

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The faster puppy takes 12 seconds to eat the bowl of kibble, and the slower puppy takes 12 + 24 = 36 seconds to eat the same bowl.

To solve the student question about how long it takes for each puppy to

eat the bowl of kibble individually, we can set up a rate equation.

Let x be the time it takes for the faster puppy to eat the bowl of kibble.

Then, the time it takes for the slower puppy is x + 24 seconds.

Since the two puppies can eat the bowl together in 9 seconds, their

combined rate is 1 bowl per 9 seconds.

The rate of each puppy eating individually is 1/x for the faster puppy and

1/(x+24) for the slower puppy.

Now, we can set up the equation for their combined rate:

1/x + 1/(x+24) = 1/9

To solve this equation, we need to find a common denominator, which is

x(x+24). We can then rewrite the equation as:

(x+24) + x = x(x+24)/9

Now, simplify the equation:

[tex]2x + 24 = x^2 + 24x / 9[/tex]

Next, multiply both sides by 9 to get rid of the denominator:

[tex]18x + 216 = x^2 + 24x[/tex]

Move all terms to one side:

[tex]x^2 + 6x - 216 = 0[/tex]

Now, factor the quadratic equation:

(x+18)(x-12) = 0

There are two solutions: x = -18 and x = 12. However, since time cannot

be negative, we only consider x = 12 seconds.

for the faster puppy.

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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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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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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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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

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: 3x - 2y - 6 = 0

Step-by-step explanation:

The equation would be on the line, so you would have to work it out through using x and y values.

Answer:

B

Step-by-step explanation:

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:

the gravity is 100

Step-by-step explanation:

machel liconl said it in 1st ammenmens

Answer:

Step-by-step explanation:

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.

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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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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Because there are no outliers in the data set, the mean is the best indicator of the centre in this particular situation.

An outlier in statistics is an incident that deviates greatly from the predicted range of values for a given dataset. There are several different reasons why outliers can happen, including measurement errors, data entry issues, or genuinely odd numbers in the population getting measured. If they are not handled properly, outliers can significantly affect statistical analysis and skew results. For instance, outliers have a big impact on measurements of variability like the standard deviation as well as central tendency indicators like the mean. Consequently, before conducting statistical analysis on a dataset, it is crucial to find and assess any outliers.

given

There are no extreme outlier numbers in this instance, and the data seems to be rather symmetrical around the core value. As a result, the mean would be a suitable gauge of the centre.

The mean would be impacted by any values that were significantly out of the ordinary, such as a book that cost $100, and might not accurately reflect the data's mean if there were one or more of these values.

Since it is unaffected by extreme values, the median would be a better indicator of the centre in these situations.

Because there are no outliers in the data set, the mean is the best indicator of the centre in this particular situation.

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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:

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)

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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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 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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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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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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Step-by-step explanation:

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

The similarity between <2 and <B is that both arcs have a 65° measure.

When two angles add up to 180 degrees, they are said to be each other's auxiliary angles.

For instance, since x + y = 180°, x and y are complementary angles to one another.

The triangle's angles are 50° and 65°.

50° and 65° are the angles on the path.

We are aware that a triangle's total number of angles is 180°. Consequently, the B measure is

50° + 65° + ∠B = 180°

∠B = 180° - (50° + 65°)

∠B = 65°

So, 65 degrees is the gauge of the B.

The total number of angles on the specified line will be due to the fact that all angles are extra angles, and will be 180 degrees.

∠2 + 50° + 65° = 180°

∠2 = = 65°

As a result, 65° is the measure of the 2.

As we can see, both arcs have a measure of 65 degrees.

Therefore, the relationship between 2 and B is that both angles have a value of 65°.

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