What is the slope of the line

Answer:

2

Step-by-step explanation:

The numerical coefficient is the number that is multiplied to a variable.

Example.

2x^2 + 7y^3

The numerical coefficients would be 2 and 7.

So for your problem it would be 2 since 2 is the number being multiplied to x and y.

Step-by-step explanation:

Rate UP stream =  ( s - w) = 106 km / 2 hr  

                                               (  where s = boat speed       w = current speed )

                              (s-w) = 53  km/hr

Rate DOWNstream = ( s+w) = 142 / 2 = 71 kmhr

( s-w) + ( s+w) = 53  + 71   km/hr

2s = 124  

s = 62 km /hr      then   s+w = 71   shows w = 9 km/hr

The truth set of the inequality is all values of x greater than -9. In interval notation, this can be written as (-9, ∞)

Multiply both sides by -2 (and reversing the direction of the inequality because we are multiplying by a negative number) gives:

x > -2*(5/2 + 2)

x > -5 - 4

x > -9

Therefore, the truth set of the inequality is all values of x greater than -9. In interval notation, this can be written as:

(-9, ∞)

Below is the complete question:

Find the truth set of x*(-1/2) < 5/2 + 2

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Step-by-step explanation:

first of all, remember, the sum of all angles in a triangle is always 180°.

now, we see that both bottom angles are 45°.

that means

180 = 45 + 45 + top-angle

90° = top-angle

aha ! we are dealing with a right-angled triangle, that is also isoceles (both legs are equally long, because the angles with the baseline are equal).

via Pythagoras

c² = a² + b²

where "c" is the Hypotenuse (the side opposite of the 90° angle), "a" and "b" are the legs.

in our case both legs are 7×sqrt(2) units long.

so,

baseline² = (7×sqrt(2))² + (7×sqrt(2))² = 49×2 + 49×2 =

= 98 + 98 = 196

baseline = sqrt(196) = 14 units

x is now the height of this triangle, and because of the isoceles form, it splits the baseline exactly in half.

so, one side of the baseline from x is 14/2 = 7 units.

and now Pythagoras for that sub-triangle :

(7×sqrt(2))² = 7² + x²

98 = 49 + x²

49 = x²

x = sqrt(49) = 7 units

the area of the triangle is

baseline × height / 2

in our case

14 × 7 / 2 = 7×7 = 49 units²

Answer:

7

Step-by-step explanation:

[4x2+(5+1)] ÷ 2

[8+(6)] ÷ 2

14 ÷ 2

7

The dimensions of the strongest beam are 27 inches x 13.5 inches.

In general, dimension refers to a measurable extent of a physical quantity, such as length, width, height, depth, or time. These dimensions provide a framework for describing and measuring objects and events in the physical world. In geometry, dimension are refers to the number of coordinates needed to specify a point in a space. In physics, the concept of dimension is used to describe the properties of space and time.

We know that the strength of the beam is directly proportional to its width multiplied with the square of its height. Let's call the width of the beam "w" and the height "h". Then we can write the strength of the beam as:

S = kwh², where "k" is the constant of proportionality.

We want to find the dimensions of the strongest beam, which means we want to find the values of "w" and "h" that will maximize the strength "S". To do this, we need to find the maximum value of the function S = kwh² subject to the constraint that the diameter of the log is 18 inches.

The diameter of the log is equal to the width of the beam plus twice the height of the beam:

d = w + 2h

Since the diameter of the log is 18 inches, we can write:

w + 2h = 18

or

w = 18 - 2h

Substituting this expression for "w" into the equation for the strength of the beam, we get:

S = k × w(18-2h) × h²

Expanding and simplifying this expression, we get:

S = 36kh³ - 2kh⁴

To find the maximum value of S, we take the derivative of S with respect to h and set it equal to zero:

dS/dh = 108kh² - 8kh³ = 0

Simplifying this expression, we get:

h²(108 - 8h) = 0

This equation has two solutions: h = 0 and h = 13.5.

Since a beam with height equal to zero would have zero strength, we reject the solution h = 0. Therefore, the maximum strength is achieved when h = 13.5 inches.

To find the corresponding width, we can use the equation we derived earlier:

w = 18 - 2h = 18 - 27 = -9

Since the width of the beam cannot be negative, we reject this solution as well.

Therefore, the required dimensions of the strongest beam are:

Width = 2h = 2(13.5) = 27 inches

Height = h = 13.5 inches

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The probability of spinning a number less than 5 is P =70%

To find the probability just take the quotient between the number of numbers that are smaller than 5, and the total amount in the spinner. That is because we assume that all the regions have the same individual probability of being spun.

There are 10 in total, and of these, 7 are smaller than 5, then the probability is:

P= 7/10 = 0.7

And to write as a percent, multiply it by 100%

0.67*100% = 70%

That is the probability.

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Answer:

(a) To calculate how much it would cost to hire the coach to travel a distance of 42 miles, we can substitute m = 42 into the formula and solve for C:

C = (42/3) + 40

C = 14 + 40

C = 54

Therefore, it would cost £54 to hire a coach to travel 42 miles.

(b) To find how many miles the coach travels if the cost of the hire is £75, we can set the formula equal to 75 and solve for m:

75 = (m/3) + 40

35 = m/3

m = 105

Therefore, the coach travels 105 miles if the cost of the hire is £75.

Answer: Jenny's score is no less than 5 points greater than 4/5 of Terrance's score.

Step-by-step explanation:

The inequality that represents the situation described is:

Jenny's score (denoted as "J") is no less than 5 points greater than 4/5 of Terrance's score (denoted as "T"):

J ≥ (4/5)T + 5

In this inequality, we are saying that Jenny's score "J" must be greater than or equal to 4/5 of Terrance's score "T", plus an additional 5 points. This reflects the condition that Jenny's score should be at least 5 points higher than 4/5 of Terrance's score.

For example, if Terrance's score "T" is 80, then 4/5 of Terrance's score is (4/5) * 80 = 64. Adding 5 points to this gives us 69. Therefore, Jenny's score "J" must be greater than or equal to 69 in this case, since it should be no less than 5 points greater than 4/5 of Terrance's score.

This study uses blocking: True. The study randomly assigns each child to one of the four treatment groups, which helps to control for individual differences that could affect the results.

This study uses blinding: It is not mentioned in the scenario whether the study uses blinding or not in individual.

This study uses a control group: True. The first group, with no screen time, serves as the control group. By comparing the results of the other groups to the control group, the scientists can see the effects of different amounts of screen time.

This study uses a repeated measures design: True. Each subject experiences each of the four treatments, so the study design is repeated measures.

This study uses random sampling: True. The study randomly selects group of 100 children for the experiment.

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The inequality that would represent the possible values for the number of hours walking dogs is 9d + 8c ≥ 130

Inequalities in mathematics can be described as one that is been used in the expression of the relationship between two values that are not equal

It should be noted thed that Inequality  implies not equal with the symbol (≠)” symbols ≥ < > ≤. From the question , number of hours walking dogs (d) Let number of hours clearing tables  an be represented by( c) Hence the  appropriate inequality is 9d + 8c ≥ 130.

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The true-relationship between 1 inch and 1 foot is  (b) 1 foot is 12 times as long as 1 inch.

An "inch" is a unit to measure length and is equal to 1/12th of a foot. It is denoted by symbol "in"

A "foot" is a unit which measures the length and is equal to 12 inches. It is denoted as "ft" .

In the imperial system, the unit of length is the foot, and it is divided into 12 smaller units called inches,

So, 1 foot is equal to 12 inches, and we can write this as : 1 foot = 12 inches,

We rearrange this equation to get the relationship between 1 inch and 1 foot,

⇒ 1 inch = 1/12 foot,

This means that 1 inch is equal to one-twelfth of a foot. In other words, it takes 12 inches to make 1 foot.

Therefore, the correct option is (b).

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Answer:

We can use a numerical method such as the Newton-Raphson method or the bisection method to approximate the positive zero of the function f(x) = 2x - 16x³ - 3x² - 8x - 2.

Let's use the Newton-Raphson method to approximate the positive zero of f(x). We start by choosing an initial guess x_0, and then compute successive approximations using the formula:

x_(n+1) = x_n - f(x_n) / f'(x_n)

where f'(x) is the derivative of f(x). We continue this process until we get an approximation that is accurate enough for our needs.

Let's choose an initial guess of x_0 = 1.5. Then we have:

f(x) = 2x - 16x³ - 3x² - 8x - 2

f'(x) = 2 - 48x² - 6x - 8

Using these expressions, we can compute successive approximations as follows:

x_1 = x_0 - f(x_0) / f'(x_0) = 1.5 - (-23.375) / (-73) ≈ 1.320

x_2 = x_1 - f(x_1) / f'(x_1) = 1.320 - (-12.608) / (-50.673) ≈ 1.141

x_3 = x_2 - f(x_2) / f'(x_2) = 1.141 - (-5.364) / (-35.883) ≈ 1.067

x_4 = x_3 - f(x_3) / f'(x_3) = 1.067 - (-1.949) / (-31.120) ≈ 1.042

x_5 = x_4 - f(x_4) / f'(x_4) = 1.042 - (-0.361) / (-30.251) ≈ 1.029

x_6 = x_5 - f(x_5) / f'(x_5) = 1.029 - (-0.012) / (-30.055) ≈ 1.028

So the positive zero of f(x) is approximately 1.028, rounded to two decimal places.

The correct statement is option a) The height of the terrain can measure between 2 meters and 10 meters.

Let the base of the triangular piece of land be x meters. Then, the height of the triangular plot is (x+2) meters.

The area of a triangle is given by the formula: A = (1/2)bh, where b is the base and h is the height.

Substituting the given values:

A = (1/2)x(x+2)

Simplifying:

A = (1/2)(x² + 2x)

Since the area is less than 40 m², write:

(1/2)(x² + 2x) < 40

Multiplying both sides by 2:

x² + 2x < 80

Rearranging and factorizing:

x² + 2x - 80 < 0

(x+10)(x-8) < 0

The roots of the quadratic equation are -10 and 8. Since the coefficient of x² is positive, the parabola opens upwards and is negative in between the roots. Therefore, the inequality is true when -10 < x < 8.

However, x cannot be negative, so the base of the triangular terrain is between 0 and 8 meters.

Substituting the values in the expression for the height, the height is between 2 and 10 meters.

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Answer:

-31

Step-by-step explanation:

The correct option are - A. x²  + (y – 3)²  = 36 and E. x²  + (y + 8)²  = 36 , for the equation of circle.

The standard form equation for just a circle, which is (x - s)² + (y - t)² = r², is used to formulate our equation if we assume a generic centre point like (s,t)and r is the radius of circle.

By simply expanding basic binomial squares in their regular form and merging like words, circles can likewise be presented in expanded form.

Now for the given data:

Put the values in the standard form of the circle:

(x - s)² + (y - t)² = r²,

(x - 0)² + (y - t)² = 6²,

x² + (y - t)² = 36

Where 't' can be any integer.

Thus, the options that satisfy the stated conditions are-

A. x²  + (y – 3)²  = 36 : here t = 3

and E. x²  + (y + 8)²  = 36 ; here t = - 8.

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Correct question:

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis?

Select two options.

A. x²  + (y – 3)²  = 36

B. x²  + (y – 5)²  = 6

C. (x – 4)² + y² = 36

D. (x + 6)² + y² = 144

E. x²  + (y + 8)²  = 36

Answer:

Mean: 9.9

Median: 10.5

Step-by-step explanation:

Step-by-step explanation:

sadly, we have only 14 data points. that is a very small sample to find a more or less reliable standard deviation for the production of softballs.

because to create the desired answer we need to calculate the mean value and the standard deviation. and we need to mix that with the Z- value of the standard normal distribution table representing the 99% confidence (= coverage of 99% of the area under the normal distribution curve, meaning therefore from 99.5% to 0.5%).

the confidence interval limits are

mean ± Z×sd/sqrt(n)

mean = mean value of the sample.

sd = standard deviation (either of - preferred - the entire population or of the sample)

n = number of data points (here 14).

Z = Z value of the standard normal distributing table for 99% (2.576).

here a little table for different confidence intervals :

Confidence Interval Z

80% 1.282

85% 1.440

90% 1.645

95% 1.960

99% 2.576

99.5% 2.807

99.9% 3.291

mean value = sum of all data points divided by the number of data points :

mean = 66.74/14 = 4.767142857...

sd = sqrt(sum((data point difference to mean)²)/n)

let's use some calculation tool like Excel (after all, the mean value is not a simple number, and to write this all up here takes a lot of space).

sd = 0.069941667...

the confidence interval limits are then

4.767142857... ± 2.576×0.069941667.../sqrt(14) =

= 4.767142857... ± 0.048152387...

upper limit = 4.815295244 ... ≈ 4.82

lower limit = 4.71899047 ... ≈ 4.72

that means, we are 99% sure that the true mean value across all produced softballs is between these 2 limits.

in other words, for 99% of such samples we can pick, their mean values will be between these 2 limits. and 1 % of such samples we expect to have a mean value outside of these 2 limits.

Answer:

27 cubes

Step-by-step explanation:

The volume of Cube A is 1 cubic centimeter. The volume of one Cube C is 1/27 of a cubic centimeter. So 27 Cube C's will fit into Cube A.

Answer:

Yes, it is

Step-by-step explanation:

The mean absolute deviation of the entire data set is 4.

To find the mean absolute deviation (MAD) of the given data set, we need to follow these steps:

Calculate the mean (average) of the data set.

Subtract the mean from each data point to find the deviation.

Take the absolute value of each deviation.

Calculate the mean of the absolute deviations.

Let's calculate the MAD for the given data set: 18, 13, 6, 14, 11, 22.

Calculate the mean.

Mean = (18 + 13 + 6 + 14 + 11 + 22) / 6 = 84 / 6 = 14.

Calculate the deviation for each data point.

Deviation = data point - mean.

Deviation for 18 = 18 - 14 = 4.

Deviation for 13 = 13 - 14 = -1.

Deviation for 6 = 6 - 14 = -8.

Deviation for 14 = 14 - 14 = 0.

Deviation for 11 = 11 - 14 = -3.

Deviation for 22 = 22 - 14 = 8.

Take the absolute value of each deviation.

Absolute deviation = |deviation|.

Absolute deviation for 4 = |4| = 4.

Absolute deviation for -1 = |-1| = 1.

Absolute deviation for -8 = |-8| = 8.

Absolute deviation for 0 = |0| = 0.

Absolute deviation for -3 = |-3| = 3.

Absolute deviation for 8 = |8| = 8.

Calculate the mean of the absolute deviations.

Mean absolute deviation = (4 + 1 + 8 + 0 + 3 + 8) / 6 = 24 / 6 = 4.

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Using the tests for symmetry, the following are symmetric with respect to y-axis:

A graph is symmetric with respect to the y-axis if replacing x with -x produces an equivalent equation.

A graph is symmetric with respect to the x-axis if replacing y with -y produces an equivalent equation.

A graph is symmetric with respect to the origin if replacing x with -x and y with -y produces an equivalent equation.

(a) symmetric with respect to the y-axis:

y = 7x - 4 (no)

y = - x + 7 (yes)

y = - 7x² (yes)

y = 6x² - 9 (no)

x = 1/4 × y² (no)

x = - y² + 9 (yes)

y = - 1/6 × x³ (no)

y = x³ - 1 (no)

y = √(x) (no)

y = √(x) - 6 (no)

Therefore, the graphs that are symmetric with respect to the y-axis are:

y = - x + 7

y = - 7x²

x = - y² + 9

None of the graphs are symmetric with respect to the x-axis or the origin.

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The option that interchanges the hypothesis with the conclusion is the Converse.

In logic and mathematics, the Converse of an if-then statement switches the positions of the hypothesis (the "if" part) and the conclusion (the "then" part).

It is formed by flipping the original statement.

For example, let's consider the statement: "If it is raining, then the ground is wet."

The hypothesis is "it is raining," and the conclusion is "the ground is wet."

The Converse of this statement would be: "If the ground is wet, then it is raining."

Here, the positions of the hypothesis and the conclusion are interchanged.

It's important to note that the Converse is not always true.

In some cases, the original statement and its converse may have different truth values.

A statement and its converse can be both true, both false, or one true while the other false.

The Converse is a distinct logical operation from other concepts such as the Biconditional and the Inverse.

The Biconditional establishes a two-way relationship between two statements, while the Inverse negates both the hypothesis and the conclusion of the original statement.

Therefore, the option that interchanges the hypothesis with the conclusion is the Converse.

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Answer: Converse

Step-by-step explanation: Took the exam answer above correct

The direct distance between Thom's house and his school, as the crow flies, is  7.21 miles.

To find the direct distance between Thom's house and his school, we can use the Law of Cosines.

The Law of Cosines is a formula used to find the length of one side of a triangle when the lengths of the other two sides and the angle between them are known. In this case, we have a triangle with sides of length 6 miles, 8 miles, and the angle between them is 60 degrees.

The Law of Cosines formula is:

c² = a² + b² - 2ab * cos(C)

where:

a and b are the lengths of the known sides of the triangle

C is the angle between those two sides

c is the length of the unknown side (the distance we want to find)

In this case:

a = 6 miles

b = 8 miles

C = 60 degrees

First, convert the angle from degrees to radians:

C (radians) = (60 degrees * π) / 180 = 1.047 radians

Now, apply the Law of Cosines:

c² = 6² + 8² - 2 x 6 x 8 x cos(1.047)

c² = 36 + 64 - 96 x cos(1.047)

c² ≈ 36 + 64 - 96 x 0.5

c² ≈ 36 + 64 - 48

c² = 52

Finally, find the square root to get the distance:

c = √52 = 7.21 miles

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Answer:

the required answer is √5-√6

Answer:

Step-by-step explanation:

The total amount of money she spent on books and notebooks is:

2/3x + 1/6x = 5/6*x

Jessica had $30 left, so we can set up an equation:

x - 5/6*x = 30

Simplifying the equation:

1/6*x = 30

x = 180