A rectangular soccer field is 6w yards wide
and 10w yards long. What is an expression for the
distance from one corner to the opposite corner?


Plz help

The response variable is the amount of tax, whereas the explanatory variable is whether the student believes global warming is a serious issue or not.

An explanatory variable is a variable that can influence another variable or cause changes in the response variable. It is the variable that is controlled or manipulated to study its effect on the dependent variable (response variable) and is an independent variable in statistical analysis. The response variable is a dependent variable or an output variable that changes based on the influence of other variables (explanatory variable).The researchers wanted to compare the mean response on gasoline taxes (the first question) for those who answer yes and for those who answer no to the second question. Therefore, the response variable is the amount of tax the student is willing to add to a gallon of gasoline. This response variable is an indication of how much students are willing to pay to mitigate global warming. On the other hand, the explanatory variable is whether the student believes that global warming is a serious issue or not. This variable will help determine if students' perception of global warming has any effect on their willingness to pay for mitigative measures.

In conclusion, the response variable in the given scenario is the amount of tax, while the explanatory variable is students' perception of global warming.

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Answer:

The answer is

Step-by-step explanation:

C. f(x) = 500(2)^x

2020

Answer

\(168in^{2}\)

Step-by-step explanation:

SA=2(wl+hl+hw)

2·(6·2+9·2+9·6)

=168

Answer:

maybe there's a typo, that dot usually represents the multiplication, and I got 5.52

Answer:

\(\huge\boxed{\sf 44\ units}\)

Step-by-step explanation:

Solution:

So,

= 3 + 8 + 3 + 6 + 5 + 6 (again) + 4 + 5 + 4

\(\rule[225]{225}{2}\)

Answer:

8-4=4

therefore 6+4=10

then perimeter =2(5)+10+6+2(3)+8+4=44units

answer: 1/16

If you flip a coin 4 times, the probability of getting all heads is 1/16.

Answer:

77

Step-by-step explanation:

Substitution pretty much involves replacing a value (in this case, the letter x) with another value (from the set).

To make 3x = 231 true, we have to replace x with each element in the set and see if the equation holds.

{77, 78, 79}

77

3(77) = 231 This is correct

78

3(78) = 234 This is incorrect!

79

3(79) = 237 This is incorrect!

Answer:

Step-by-step explanation:

m∠1 = 17° {The diagonal of angle A divides this angle in half}

m∠2 = 90°  {Diagonals of a kite cross at right angles}

m∠3 = 180° - 90° - 17° = 73°  {The sum of the measures of angles in triangle is 180°}

The  dimensions of the rectangle is 1mm x 0.5mm.

The area of a sector of a circle can be calculated using the formula A = (1/2)*r2*θ,  

 where r is the radius of the circle and

θ is the angle of the sector.

Therefore, the area of the sector given in the question is A = (1/2)*r²*1, where r = 1.

Since the rectangle has the same area as the sector,

the area of the rectangle can be calculated as A = l*w,

 where l is the length and

w is the width.

This equation can be rearranged to give l = A/w,

 where A = (1/2) and w is the width.

Substituting the values for A and w into the equation gives l = (1/2) / w.

Since the width of the rectangle is the same as the radius of the circle,

w = 1.

Therefore, the length of the rectangle is l = (1/2), which gives the dimensions of the rectangle as 1mm x 0.5mm, rounded to the nearest millimeter.

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Using a calculator, it can be found that

Rounding to three decimal places,

The probability that the next piece of track Carly picks will be straight is 8/24 or 1/3

From the given information, Carly has picked 8 straight, 7 curved, 4 cross, and 5 switch tracks.

The total number of pieces of the track she has picked is 8 + 7 + 4 + 5 = 24

The probability that the next piece of track Carly picks will be straight is calculated as follows:

Probability = Number of straight tracks/Total number of tracks= 8/24= 1/3T

Therefore, the probability that the next piece of track Carly picks will be straight is 1/3.

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Answer: 1/3

Step-by-step explanation: i did this question and got it right

Answer:

Step-by-step explanation:

The angle measure we need is twice the angle ACB.

Find its measure considering AB = 4/2 = 2 in and BC = 6 in.

Use trigonometry:

The angle between the line segments is:

Step-by-step explanation:

Radius = Diameter/2

Radius = 4/2

Radius = 2 cm

Now,

tan <ACB = AB/BC

tan <ACB = 2/6

tan <ACB = ⅓

<ACB = 18.43

Now,

Angle = 2 × <ACB

Angle = 2 × 18.43

Angle = 36.86⁰

If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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Answer:

The maximum cost per ticket that will be in their budget is 325.

Step-by-step explanation:

\(4(t+25)=1400\\t+25=1400/4\\t+25=350\\t=350-25\\t=325\)

The choices that are equivalent to the given expression are

A. \(\sqrt[4]{x^{9} }\)

B. \((x^{9} )^{\frac{1}{4} }\)

E. \((\sqrt[4]{x })^{9}\)

From the question, we are to determine which of the given choices are equivalent to the given expression

The given expression is

\(x^{\frac{9}{4} }\)

We will simplify each of the given choices to determine which are equivalent to the given expression

By law of indices,

\(\sqrt[n]{x^{m} } = x^{\frac{m}{n}}\)

∴  \(\sqrt[4]{x^{9} }=x^{\frac{9}{4} }\)

Hence, \(\sqrt[4]{x^{9} }\) is equivalent to the given expression

If we clear the bracket and multiply the powers, we get

\(x^{9\times \frac{1}{4} }\)

= \(x^{\frac{9}{4} }\)

Hence,    \((x^{9} )^{\frac{1}{4} }\) is equivalent to the given expression

If we clear the bracket and multiply the powers, we get

\(x^{4\times \frac{1}{9} }\)

= \(x^{\frac{4}{9} }\)

Hence,    \((x^{4} )^{\frac{1}{9} }\) is not equivalent to the given expression

By law of indices,

\(\sqrt[n]{x^{m} } = x^{\frac{m}{n}}\)

∴  \(\sqrt[9]{x^{4} }=x^{\frac{4}{9} }\)

Hence, \(\sqrt[9]{x^{4} }\) is not equivalent to the given expression

By law of indices,

\((\sqrt[n]{x })^{m}= (x^{\frac{1}{n}})^{m}\)

∴  \((\sqrt[4]{x })^{9}= (x^{\frac{1}{4}})^{9}\)

If we clear the bracket and multiply the powers, we get

\(x^{\frac{1}{4}\times 9 }\)

= \(x^{\frac{9}{4} }\)

Hence,  \((\sqrt[4]{x })^{9}\) is equivalent to the given expression

By law of indices,

\((\sqrt[n]{x })^{m}= (x^{\frac{1}{n}})^{m}\)

∴  \((\sqrt[9]{x })^{4}= (x^{\frac{1}{9}})^{4}\)

If we clear the bracket and multiply the powers, we get

\(x^{\frac{1}{9}\times 4 }\)

= \(x^{\frac{4}{9} }\)

Hence, \((\sqrt[9]{x })^{4}\) is not equivalent to the given expression

Thus, the choices that are equivalent to the given expression are

A. \(\sqrt[4]{x^{9} }\)

B. \((x^{9} )^{\frac{1}{4} }\)

E. \((\sqrt[4]{x })^{9}\)

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Answer:

D

Step-by-step explanation:

Area = 1/2 a * p

Multiply both sides by 2

2*A = ap

Divide by p

2A / p = a

D

Answer: D

Step-by-step explanation:

The option that is not characteristic of the t-test is "The Student t distribution has mean of t = 0 and a standard deviation of 5 = 1". The correct answer is option A.

The t-test is a statistical test that uses the Student t-distribution. The Student t-distribution has a mean of 0, but its standard deviation is not equal to 1. The standard deviation of the t-distribution varies depending on the degrees of freedom, which is determined by the sample size. Therefore, the statement in option A is not true. The correct answer is option A.

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Answer:

D

Step-by-step explanation:

Since RS is parallel to PQ, gradient of RS is equal to gradient of PQ.

\(\boxed{gradient = \frac{y1 - y2}{x1 - x2} }\)

Gradient of RS

= gradient of PQ

\( = \frac{18 - 10}{ - 9 - ( - 3)} \)

\( = \frac{8}{ - 9 + 3} \)

\( = \frac{8}{ - 6} \)

\( = - \frac{4}{3} \)

y- intercept occurs at x= 0. Let the coordinates of the y-intercept of RS be (0, y).

\( \frac{y - 6}{0 - 3} = - \frac{4}{3} \)

\( \frac{y - 6}{ - 3} = - \frac{4}{3} \)

Multiply both sides by -3:

y -6= 4

y= 6 +4

y= 10

Thus, the correct option is D.

x = 3

Divide each term by  3  and simplify.

The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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To construct a 4x2 matrix D such that AD=I2, we can use the following matrix: D = [0 0 1 0; 0 0 0 1]. It is not possible for CA to be equal to 4 or 14 for any 4x2 matrix C.

Constructing a matrix D such that AD=I2

Let A = -1 be a 1x1 matrix. We want to construct a 4x2 matrix D such that their product AD is equal to the 2x2 identity matrix I2. We can use the following matrix for D:

D = [0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]

To verify that AD=I2, we can compute the matrix product:

AD = [-1 0 0 0; 0 -1 0 0] [0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]

= [0 0 -1 0; 0 0 0 -1]

= -I2

Note that D only uses 1 and 0 as entries.

Now, it is not possible for CA to be equal to 4 or 14 for any 4x2 matrix C. To see why, we can use the definition of matrix multiplication. Let C be a general 4x2 matrix:

C = [c11 c12; c21 c22; c31 c32; c41 c42]

Then, we can compute CA as:

CA = [-1 0; 0 -1] [c11 c12; c21 c22; c31 c32; c41 c42]

= [-c11 -c12; -c21 -c22; -c31 -c32; -c41 -c42]

Since CA is a 4x2 matrix and 4 is a scalar, it is not possible for CA to be equal to 4. Similarly, since the entries of C are only 0 or 1, it is not possible for CA to be equal to 14.

Therefore, there is no matrix C that satisfies the equations CA=4 or CA=14.

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Simplified value of given expression is 2x³√10x.

What is simplification?

In arithmetic,  simplification is reducing the expression / fraction problem during a less complicated type.

Main body:

Factor 40 into its prime factors

          40 = 2³ • 5

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          4 = 2²

Factors which will remain inside the root are :

          10 = 2 • 5

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          2 = 2

At the end of this step the partly simplified SQRT looks like this:

        2 • sqrt (10x7)

Rules for simplifing variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

     (3.1) sqrt(x⁸)=x4

    (3.2) sqrt(x-⁶)=x-3

     (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     (4.1) sqrt(x5)=x²•sqrt(x)

    (4.2) sqrt(x-7)=x³•sqrt(x-1)

Applying these rules to our case we find out that

    SQRT(x7) = x³ • SQRT(x)

 sqrt (40x7) =

       2² x³• sqrt(10x)

Hence the simplification to the value is as 2² x³ • sqrt(10x)

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Answer:

Step-by-step explanation:

5

Using angle sum property of triangle, the measure of angle ∠3 is 87.1°.

The angle sum prοperty οf a triangle states that the sum οf the angles οf a triangle is equal tο 180º. A triangle has three sides and three angles, οne at each vertex. Whether a triangle is an acute, οbtuse, οr a right triangle, the sum οf its interiοr angles is always 180º.

The angle sum prοperty οf a triangle is οne οf the mοst frequently used prοperties in geοmetry. This prοperty is mοstly used tο calculate the unknοwn angles.

Here, we will use angle sum property, i.e.

m∠1 + m∠2 + m∠3 = 180°

Given that:

m∠1 = (5x)°

m∠2 = (4x + 10)°

m∠3 = (10x − 5)°

Apply the data in the formula:

(5x)° + (4x + 10)°  + (10x − 5)° = 180°

(5x + 4x + 10  + 10x − 5) = 180

(19x + 10 − 5) = 180

(19x + 5) = 180

19x = 180 - 5

19x = 175

x = 175/19

x ≈ 9.21

Then, substitute the value of x in (10x − 5)°,

= (10(9.21) − 5)°

= (92.1 − 5)°

= (92.1 − 5)°

= 87.1°

Thus, Using angle sum property of triangle, the measure of angle ∠3 is 87.1°.

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Complete question:

In the figure, m∠1 = (5x)°, m∠2 = (4x + 10)° and, m∠3 = (10x − 5)°.

What is m∠3, in degrees?

The correct option is c) Easier interpretation. One of the main advantages of simple models is their ease of interpretation. Simple models tend to have fewer parameters and less complex mathematical equations, making it easier to understand and interpret how the model is making predictions.

This interpretability can be valuable in various domains, such as medicine, finance, or legal systems, where it is important to have transparent and understandable decision-making processes.

Complex models, on the other hand, often involve intricate relationships and numerous parameters, which can make it challenging to comprehend the underlying reasoning behind their predictions. While complex models can sometimes offer higher accuracy or make more detailed predictions, they often sacrifice interpretability in the process.

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Answer:

x > -2/3

Step-by-step explanation:

\(\frac{x}{2} +\frac{1}{3} > 0\) , subtract 1/3 from both sides

\(\frac{x}{2} > \frac{-1}{3}\) , multiply both sides by 2

\(x > \frac{-2}{3}\)

Answer:

(2,1)

Step-by-step explanation:

The answer is (2,1)

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



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45.5 acres of land can be farmed and 24.5 cannot be farmed.