Select all the side lengths that would create a right triangle:
0
6,8,10
4,10,15
8,15,21
12, 16, 20
15, 17, 25
5,12,13

To use the intermediate value theorem to show that there is a root of the given equation in the specified interval, we first need to find the values of the function at the two endpoints of the interval. Let's say the function is denoted by f(x) and the interval is [a, b].

If f(a) and f(b) have opposite signs (one is positive and the other is negative), then by the intermediate value theorem, there must be at least one root of the equation f(x) = 0 in the interval [a, b]. This is because the intermediate value theorem states that if a function is continuous on a closed interval and the function takes on different values at the endpoints of the interval, then there must be at least one point in the interval where the function takes on the value of the intermediate value between the two endpoints.

For example, suppose we have the equation f(x) = x^2 - 3 and we want to show that there is a root of the equation in the interval [1, 2]. We can evaluate the function at the two endpoints of the interval:

f(1) = 1^2 - 3 = -2

f(2) = 2^2 - 3 = 1

Since f(1) and f(2) have opposite signs, by the intermediate value theorem, there must be at least one root of the equation f(x) = 0 in the interval [1, 2]. To find the root, we can use a root-finding algorithm such as bisection or Newton's method.

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Graph (C) which has points (0, 400) and (16, 0) represent the solution to the given situation of Rashawn.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

Graphs and charts are useful visual aids because they make information accessible and quick to understand.

Therefore, it is not unexpected that print and electronic media frequently use graphs.

When data is displayed as a graph rather than a table, it can often be easier to understand because the graph might show a pattern or comparison.

So, Rashawn consumed 25 pages of his book daily till it was finished. There were 400 pages in his book.

400 / 25 = 16 days is the estimated number of days he needs to finish the book.

He will have 400 pages finished in 0 days and 0 pages in 16 days.

As a result, the situation is represented by a graph with a line segment in the first quadrant.

Days are shown on the x-axis, and Pages left are listed on the y-axis.

The line segment's ends are (0, 400) and (16, 0).

Therefore, graph (C) which has points (0, 400) and (16, 0) represent the solution of the given situation of Rashawn.

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Complete question:
Rashawn read 25 pages of his book each day until he finished the book. His book was 400 pages long.

Which sketch represents this situation?

a) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 400 end ordered pair and begin ordered pair 25 comma 0 end ordered pair.

b) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 16 end ordered pair and begin ordered pair 400 comma 0 end ordered pair.

c) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 commas 400 end ordered pair and begin ordered pair 16 commas 0 ends ordered pair.

d) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y-axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 commas 25 ends ordered pair and begin ordered pair 400 commas 0 ends ordered pair.

Answer: 84 bells

Step-by-step explanation:

12 + 9x8

84

As pre the concept of vector, div F is negative at P1 and divF is positive at P2.

In math the term vector refers the quantity that has both magnitude and direction but not position

Here we have to determine whether div F is positive or negative at P1 and at P2.

Let us consider if  div F(P)>0, the net flow is outward near P and P is called a source and if  div F(P)<0, the net flow is inward near P and P is called a sink.

Here by observing the graph of F, we have identified that the vectors end near the P1 are the larger than the vectors starts near the point P1,

So, the net flow is inward near P1 and div F is negative at P1

Where P1 is called a sink

Whereas, by observing the graph of F we have identified that the vectors end near P2 are shorter than the vectors starts near the point P2,

So, the net flow is outward and div F   is positive at P2 and the P2 is called a source

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The alternative hypothesis is often abbreviated as Ha or H1. When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < o

What is hypothesis?

A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientists typically build their scientific ideas on prior observations that cannot be adequately explained by the current body of knowledge.

In statistics, the null hypothesis is usually denoted by letter H with subscript '0' (zero), such that H0. It is pronounced as H-null or H-zero or H-nought

At the same time, the alternative hypothesis expresses the observations determined by the non-random cause.It is represented by H1 or Ha.

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Answer:

slope: -3

Y- intercept: (0,10)

The volume of the cube with side length 8 inches is 512 inches cube.

The cube with side length s has volume s³. Matt has a cube-shaped wooden box that he uses to store his marble collection. It has 8-inch sides.

The volume of the cube can be calculated as follows:

A cube has all side length equal to each other.

Therefore,

volume of the cube = s³

where

Therefore,

s = 8 inches

Hence,

volume of the cube = 8³

volume of the cube = 8 × 8 × 8

volume of the cube = 512 inches cube

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Answer:

y=-5.5x-52

Step-by-step explanation:

Your input: find the equation of a line given two points P = (-10 , 3) and Q = (-8 , -8). The slope of a line passing through the two pointsP=(x1,y1) and Q=(x2,y2) is given byWe have that x1 = -10 , y1 = 3, x2 = -8 , y2 = -8Step 2:Plug the given values into the formula for slope:Step 3:Now, the y-intercept is b=y1−m⋅x1 (or b=y2−m⋅x2, the result is the same).b = 3 - (-5.5) ⋅ (-10) = -52Step 4:Finally, the equation of the line can be written in the form y=mx+b.y = -5.5x -52The equation of the line in the slope-intercept form is:y = -5.5x -52The equation of the line in the point-slope form is:y - (3) = -5.5 ⋅ ( x - (-10))The equation of the line in the point-slope form is:y - (-8) = -5.5 ⋅ ( x - (-8))The general equation of the line is:-5.5x - y -52 = 0

Answer:

the answer would be e because you can't determine the side length

Answer: (B)

Step-by-step explanation:

Step 1: Find minimum values of the third side.

53-17 = 36

Step 2: Find maximum values of the third side.

17+53 = 70

Step 3: Find equation

36 < x < 70

(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.

(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.

(9) We have drawn the graph passing through the point P and parallel to line AB.

(10)We have drawn the graph passing through the point P and perpendicular to line AB.

What is the property of slopes of parallel lines and perpendicular lines?

If two lines are given and they are parallel to each other then the slopes are equal and for perpendicular lines, the product of their slopes is equal to -1.

(7) The line AB is passing through the points (-1, 5/2) and (3/2, -1/2).

   Slope = y2 - y2/x2 - x1

              = (-1/2 - 5/2)/(3/2-(-1))

              = -6/5

   As line AB and line CD are parallel in nature so the slope of line CD is also -6/5.

(8) The line AB is passing through the points (1/2, 1) and (5/2, 5/2).

    Slope = y2 - y2/x2 - x1

              = (5/2 - 1)/(5/2-1/2)

              =3/2/2

             = 3/4

    Line CD is passing through points (1, 1) and (2, 3).

    Slope = y2 - y2/x2 - x1

              = (3 - 1)/(2-1)

              =2/2

             = 1

  As the product of their slopes is not equal to -1.

  So lines are neither parallel nor perpendicular.

(9) Slope of AB can be computed as (-2, 1) and (-5, 5)

     Slope = 5 - 1/-5 + 2

                = 4/-3.

  The slope of line passing through the point P = -4/3 as we have to draw the parallel line.

 Point P = (-1, 3)

Equation of the line :

      y - 3 = -4/3(x + 1)

    3y +9 = -4x - 4

   3y = -4x - 13

Now we can draw the line

(10) Slope of line AB = -4/3

    So the slope of the line passing through point P should be 3/4 in order to be perpendicular to line AB.

     Equation of the line passing through point P:

       y - 3 = 3/4(x - (-1))

       y - 3 = 3/4(x+1)

Hence,

(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.

(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.

(9) We have drawn the graph passing through the point P and parallel to line AB.

(10)We have drawn the graph passing through the point P and perpendicular to line AB.

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The term that encompasses a variety of people and requires an openness and willingness to accept and appreciate that which is different is diversity.

The world by its very nature is diverse. The meaning of this is that there are a lot of people that can be found in the world and all of them do  come from different walks of life and speak different languages and are from different races.

It is expected that we must be able to embrace people that are coming from so many different backgrounds so that we can be able to live a productive life and thereby contribute meaningfully to the society.

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There are two angles for the sine function such that sin θ = - 0.093: (i) 185.3°, (ii) 354.7°.

In this problem we must determine two values of the angle of the sine function such that its result is - 0.093. According to the features of the trigonometric function, sine is negative for angles between 180° and 360°.

Since trigonometric functions are trascendent functions, we can only obtain approximate values of the angle by means of inverse trigonometric functions and numerical methods. There are two possible solutions:

sin⁻¹ - 0.093

θ₁ ≈ 185.336° or θ₂ ≈ 354.664°

θ₁ ≈ 185.3° or θ₂ ≈ 354.7°

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Answer:

$23.85

Step-by-step explanation:

1 3/4 = 1.75 pounds of coffee

8 1/2 = 8.5 pounds of rice

1.75 x 13= 22.75

8.5 x 0.4= 3.4

22.75 + 3.4 = 26.15

50-26.15=23.85

The coefficients of static friction at a and b are T = 3600 lb and N_b = 2882 lb.

Given:

Coefficient of static friction at a u_a = 0.2

Coefficient of static friction at b u_b = 0.3

Weight of the loaded bin W = 8500 lb

Find:

Find the force in the cable needed to begin the lift.

Solution:

Draw the forces on the diagram. see attachment.

Take the sum of moments about point B as zero:

                    (M)_b =   W*12 - N_a * 22 = 0

                     N_a = W*12 / 22 = 8500*12 / 22

                     N_a = 4636.364 lb

Compute friction force F_a at point A:

                     F_a = u_a*N_a = 4636.364*0.2

                     F_a = 927.2727 lb

Take the sum of moments about point A as zero:

                    -W*10 - F_b*sin(30)*22+ 22*N_b*cos(30) + 22*T*sin(30) = 0

Where,           F_b = u_b*N_b = N_b*0.3            

Hence,           -85000 - 3.3*N_b + 11sqrt(3)*N_b + 11 T = 0

                     15.753*N_b + 11*T = 85000    ...... (1)    

Take the sum of forces in the x-direction equal to zero:

                     T*cos(30) - N_b*sin(30) - u_b*N_b*cos(30) - F_a = 0

                     T*cos(30) - 0.75981*N_b = 927.2727   ..... (2)

Solve two equations simultaneously:

T = 3600 lb , N_b = 2882 lb

Refer to this complete question:

The winch on the truck is used to hoist the garbage bin onto the bed of the truck. If the loaded bin has a weight of 8500 lb and a center of gravity at G, determine the force in the cable needed to begin the lift. The coefficients of static friction at A and B are MuA = 0.2 And MuB = 0.3 respectively. Neglect the height of the Support at A.

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The value of p is 0.16. So the option b is correct.

A local entrepreneur takes a random sample of 100 people.

Of the urban participants, 22 buy a real tree.

Of the rural participants, 28 buy a real tree.

Let p1 = the proportion of all people who live in rural communities and buy a real Christmas tree.

Let p2 = the proportion of all people who live in urban communities and buy a real Christmas tree.

We have to find the p-value

p1 = X1/N1

p1 = 28/100

p1 = 0.28

p2 = X2/N2

p2 = 22/100

p2 = 0.22

p = (X1 + X2)/(N1 + N2)

p = (28+22)/(100+100)

p = 0.25

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: p1 = p2

Alternate Hypothesis, Ha: p1 > p2

Test statistic

z = (p1 - p2)/√(p*(1-p)*(1/N1 + 1/N2))

z = (0.28-0.22)/√(0.25*(1-0.25)*(1/100 + 1/100))

z = 0.9798

P-value Approach

P-value = 0.16

Hence, the option A is correct. 0.16 is the p-value.

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Answer:

fragile breakable

Step-by-step explanation:

basically the meaning of frail is anything that can be broken easily for example the glass was frail therefore meaning of dropped of damaged it could break extremely easily and if your describing a person think of someone who's old of sick they can be described as weak or in other words not strong. I hope this helped

The domain and range of such equation in which case the distance travelled d is dependent on the time, t is best described by the answer choice; 2. The domain is time (t) and the range is distance (d).

It follows from the task content that the domain and range of the function as described in the task content is to be determined.

According to the task content; A train travels at 80 miles per hour.

On this note, the equation that compares the time (t) with the distance (d) as required is;

d = 80 t

On this note, the dependent and independent variables are d and t respectively.

Consequently, the domain is time which is the set of all possible inputs while the range is distance which is the set of all possible output values.

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a) The amounts that the team needs to sell is given as follows:

b) The advantage and disadvantage is given as follows:

The amounts needed are found applying the proportion, considering the costs and the number of candles.

A package of 5 candles for $18, hence the number of candles needed to earn $1404, in packages, is given as follows:

5 candles - $18

n candles - $1404

Applying cross multiplication, we have that:

18n = 5 x 1404

n = 5 x 1404/18

n = 390 candles.

With a single candle, the number of candles is calculated as follows:

1404/4 = 351 candles.

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Economies of scale occur when average cost declines with an increase in output. This occurs up to output level Q1.

Diseconomies of scale occur when average cost increases with an increase in output. This begins at output level Q3.

The phenomenon known as economies of scale occurs when the size or magnitude of the production generated by a business increases while the average cost per unit of output decreases.

The Long Run Average Cost Curve demonstrates how a firm's average expenses change over time. The shift from point A to point B illustrates how the cost per unit decreases as the curve slopes down. Because of economies of scale, the average cost grows less proportionally to output over the downward sloping region of the curve.

Minimum efficient scale is the level of output where economies of scale have been fully exploited.

A competitive firm produces at the minimum point of ATC in the long run and thus achieves productive efficiency.

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Answer:

Step-by-step explanation:

12.5663706144

Answer: Answer is 8.47

Step-by-step explanation:

[(6x2.99)-1] ÷2

16.94 / 2

8.47

Answer:

8.47

Step-by-step explanation:

[(6x2.99)-1] ÷2  16.94 /2 =8.47

Answer:

There is 1/32 pound food for each fish

Step-by-step explanation:

24 fish = 3/4 pound food

1 fish = (3/4)/24 pound food = 1/32 pound food

(Problem solved by using unitary method)

The probability of tossing 10 tails in a row is  [tex]\frac{1}{1024}[/tex]

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that,

When a fair coin is tossed 10 times, the sample size (n) is:

n = [tex]2^{10}[/tex]

This is so because a fair coin has 2 sides.

So, we have:

n = 1024

There is only one occurrence of having 10 tails in a row in the 1024 possible outcomes.

So, the probability is:

P = [tex]\frac{1}{1024}[/tex]

Therefore,

The probability of tossing 10 tails in a row is  [tex]\frac{1}{1024}[/tex]

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Answer: the number is -16

Step-by-step explanation: if you add 17 to -49, you will get -32. you do this because it is 17 less than NOT more than. that would be called inverse operations. then, you divide that number by 2 to get -16. again, you use inverse operations because you are going backwards to try and find the number.

Answer: -16

Step-by-step explanation: So, to solve, we should write an equation. It should look like this:

2x - 17 = -49

So, using inverse operations, we would add 17 to - 49, which is -32, then divide that by 2, which would be -16. I hope this helped!

P.S. our new equation would look like 2(16) - 17 = -49

32-17 = 49

32 + -17 = 49

49 = 49

It checks out.

Answer

2x73

Step-by-step explanation:

Answer:

(11.5, 7.5)

Step-by-step explanation:

17 + 6 / 2 = 11.5

2 + 13 / 2 = 7.5

Hello,

I hope you and your family are doing well!

The classmate should bike for 50 minutes at 11 mph and at 150 minutes for 15 mph. (See explanation below)

First, let's find how many calories your classmate burns while biking at 11 mph:

calories burned = time * rate of calorie burn

Since your classmate bikes at 11 mph for 50 minutes, the number of calories he burns at this speed is:

calories burned = 50 minutes * 5 calories/minute = 250 calories

Now, let's find how many calories your classmate burns while biking at 15 mph:

calories burned = 400 calories - 250 calories = 150 calories

Since your classmate burns 1 calorie per minute while biking at 15 mph, he needs to bike at this speed for 150 minutes to burn the remaining calories:

time = calories burned / rate of calorie burn

time = 150 calories / 1 calorie/minute = 150 minutes

Please rate this answer 5 stars and brainliest if you find it helpful.

Happy Holidays!

A true average strain in a way that converys information about precision and reliability (24.33, 27.67)

From given information we have:

the sample size n = 20

the mean failure strain x(bar) = 26.0

the standard deviation s = 3.4

Assuming a normal distribution for failure strain, we need to estimate true average strain in a way that converys information about precision and reliability.

A 95% confidence interval is necessary; other confidence intervals can be calculated in a similar way.

c = 0.95 or 95%

In the table with the critical values for t distributions in the appendix, locate the row beginning with degrees of freedom.

Here, the degree of freedom :

df = 20 - 1

df = 19

and  α = (1-c)/2

          = 0.025

To find the t-value:

t_(α/2) = 2.145

Therefore, the error margin is:

E = t_(α/2) × s/√n​

E = 2.145× 3.4/√19

E ≈ 1.67

And the confidence interval would be,

(x{bar} - E, x{bar} + E) = (24.33, 27.67)

Therefore, the confidence interval is: (24.33, 27.67)

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Answer: You simply subtract 315 from 975

Step-by-step explanation: